Answer: 124.67 cm3
Step-by-step explanation:
To find out how much more the new cans will hold, we first need to calculate the volume of the current cans and the volume of the new cans.
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, π is a constant (approximately 3.14), r is the radius of the base, and h is the height.
Given that the current cans have a height of 12 cm and a diameter of 6 cm, we can calculate the radius by dividing the diameter by 2. So the radius of the current cans is 6 cm / 2 = 3 cm.
Using the formula for the volume of a cylinder, we can calculate the volume of the current cans:
V_current = π(3^2)(12)
= 3.14 * 9 * 12
≈ 339.12 cm^3
Now, let's calculate the dimensions of the new cans. Since the dimensions are being increased by a multiple of 1.11, we can find the new height and new radius by multiplying the current height and radius by 1.11.
The new height = 12 cm * 1.11 ≈ 13.32 cm
The new radius = 3 cm * 1.11 ≈ 3.33 cm
Using the same formula for the volume of a cylinder, we can calculate the volume of the new cans:
V_new = π(3.33^2)(13.32)
= 3.14 * 11.0889 * 13.32
≈ 463.79 cm^3
To find out how much more the new cans will hold, we can subtract the volume of the current cans from the volume of the new cans:
Difference = V_new - V_current
= 463.79 cm^3 - 339.12 cm^3
≈ 124.67 cm^3
Therefore, the new cans will hold approximately 124.67 cm^3 more than the current cans. Hence, the correct answer is 124.67 cm3.
The new cans will hold approximately 141.07 cm³ more than the current cans.
We have,
Volume of the current cans:
Diameter (d) = 6 cm (radius, r, is half of the diameter, so r = 3 cm)
Height (h) = 12 cm
Volume of a cylinder = πr²h
Using π ≈ 3.14, we can calculate the volume:
Volume = 3.14 * (3 cm)² * 12 cm
Volume = 3.14 * 9 cm² * 12 cm
Volume = 339.12 cm³
Now, let's calculate the volume of the new cans:
Since the dimensions are increased by a multiple of 1.12:
New height (h') = 1.12 * 12 cm = 13.44 cm (rounded to two decimal places)
New diameter (d') = 1.12 * 6 cm = 6.72 cm (rounded to two decimal places)
New radius (r') = 6.72 cm / 2 = 3.36 cm (rounded to two decimal places)
Volume of the new cans:
Volume = π(r')²h'
Volume = 3.14 * (3.36 cm)² * 13.44 cm
Volume ≈ 3.14 * 11.2896 cm² * 13.44 cm
Volume ≈ 480.19 cm³ (rounded to two decimal places)
Now, to find out how much more the new cans will hold, subtract the volume of the current cans from the volume of the new cans:
Difference = Volume of new cans - Volume of current cans
Difference ≈ 480.19 cm³ - 339.12 cm³ ≈ 141.07 cm³
Rounded to the nearest hundredth, the new cans will hold approximately 141.07 cm³ more than the current cans.
Thus,
The new cans will hold approximately 141.07 cm³ more than the current cans.
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A plumber charges a $75 flat fee for jobs lasting up to an hour and $30 for each hour of labor after the first hour. Which expression models the cost of a job lasting h hours, when h is greater than 1? 75 30 h 75 30 (h minus 1) 75 h 30 75 (h minus 1) 30.
The expression that models the cost of a job lasting h hours, when h is greater than 1 is:75 + 30(h - 1) Answer: 75 + 30(h - 1).
Given:
A plumber charges a $75 flat fee for jobs lasting up to an hour and $30 for each hour of labor after the first hour.
Expression that models the cost of a job lasting h hours, when h is greater than 1 is:75 + 30(h - 1),
The cost is $75 for the first hour and $30 per hour for every additional hour, so the cost for h hours of work would be:$75 (for the first hour) + $30 x (h - 1)
(for every additional hour beyond the first hour):
75 + 30(h - 1) : 75 + 30(h - 1).
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Find the distance between the car and the building using the angle of ddeprassion given 30° 7m
Answer:11.91 m
Step-by-step explanation:ngle of Depression is the measurement of angle between the horizontal and your line of sight (when looking down).
In this case, to get the distance between the car and the building, the height and other unknown given, just apply the SOHCAHTOA.
SOHCAHTOA, is use on how to compute the sine, cosine, and tangent of an angle. SOH stands for Sine equals Opposite over Hypotenuse. CAH stands for Cosine equals Adjacent over Hypotenuse. TOA stands for Tangent equals Opposite over Adjacent.
In the given problem, let X is the distance between the car and building. The angle of depression is 36°. Use SOH (in sohcahtoa), to solve the problem.
sin(36°) = 7/x
x = 7/sin(36°)
x = 11.91
Therefore, the distance between the car and building is 11.91 m.
Select at least two digital communication strategies you can control to protect yourself. Explain why you chose them and how they can safeguard you if you feel like someone is trying to cause you harm.
Two digital communication strategies you can control to protect yourself are:
1. **Strong Passwords**: One of the most effective ways to safeguard your digital communication is by using strong, unique passwords for your online accounts. A strong password should be a combination of upper and lowercase letters, numbers, and special characters. By using strong passwords and regularly updating them, you can prevent unauthorized access to your accounts. This can safeguard you if someone is trying to cause harm by attempting to gain unauthorized access to your personal information or accounts.
2. **Two-Factor Authentication (2FA)**: Enabling two-factor authentication adds an extra layer of security to your digital communication. With 2FA, you need to provide a second form of verification, such as a unique code sent to your mobile device, in addition to your password, to access your accounts. This can protect you if someone manages to obtain your password, as they would still need the second factor to gain access. 2FA makes it significantly harder for malicious individuals to compromise your accounts, providing an added safeguard against potential harm.
By implementing strong passwords and enabling two-factor authentication, you enhance the security of your digital communication and reduce the risk of unauthorized access and potential harm. These strategies provide an additional barrier against malicious activities and help ensure the confidentiality and integrity of your personal information and online accounts.
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Select a value to tell how each pair of angles is related.
The value to determine the relationship between each pair of angles is their sum. we can determine whether they are complementary (90 degrees), supplementary (180 degrees), or explementary (360 degrees), which helps us understand their relationship and properties.
To determine the relationship between two angles, we can consider their sum. If the sum of two angles is equal to 90 degrees, they are complementary angles. Complementary angles are pairs of angles that, when added together, result in a right angle. For example, if Angle A measures 40 degrees and Angle B measures 50 degrees, their sum is 90 degrees, so they are complementary angles.
If the sum of two angles is equal to 180 degrees, they are supplementary angles. Supplementary angles are pairs of angles that, when added together, result in a straight angle. For instance, if Angle C measures 120 degrees and Angle D measures 60 degrees, their sum is 180 degrees, so they are supplementary angles.
On the other hand, if the sum of two angles is equal to 360 degrees, they are explementary angles. Explementary angles are pairs of angles that, when added together, result in a complete revolution or a full circle. For example, if Angle E measures 120 degrees and Angle F measures 240 degrees, their sum is 360 degrees, so they are explementary angles.
By considering the sum of the angles, we can determine whether they are complementary (90 degrees), supplementary (180 degrees), or explementary (360 degrees), which helps us understand their relationship and properties.
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Calculate the average change in the inflation rate the past five years including 2021 rounded to two decimal places
We calculate the sum of these changes: 0.7% + (current year's change) + (current year's change) + (current year's change).= 0.25%. ( fictional )
To calculate the average change in the inflation rate, we require the inflation rates for each of the five years, including 2021. Let's assume the inflation rates for the five years are: 2.5%, 3.2%, 2.8%, 4.1%, and 3.9%.
To find the change in inflation rate for each consecutive year, we subtract the inflation rate of the previous year from the inflation rate of the current year. For example, the change in inflation rate from 2020 to 2021 would be 3.2% - 2.5% = 0.7%.
Next, we calculate the sum of these changes: 0.7% + (current year's change) + (current year's change) + (current year's change).
Finally, we divide the sum by the number of years (five in this case) to find the average change in the inflation rate over the five-year period. After rounding the result to two decimal places, we will have the desired average change in the inflation rate.
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El precio de una camisa está marcado $28 si se aplica un descuento de 20%¿cual seria el precio?
After applying a 20% discount to the marked price of $28, the final price of the shirt would be $22.40.
To calculate the price after a discount, we need to subtract the discount amount from the original price. In this case, the original price of the shirt is $28, and a 20% discount is applied. To find the discount amount, we calculate 20% of $28, which is $5.60. Subtracting $5.60 from the original price gives us the final price of $22.40. Discount = 20% of $28 = (20/100) * $28 = $5.60. Discounted Price = $28 - $5.60 = $22.40. Therefore, the price of the shirt after applying a 20% discount would be $22.40.
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#Complete/Translate Question:- The price of a shirt is marked $28 if a 20% discount is applied, what would the price be?
Points X(4, 1), Y(7, 1) and Z(4, 6) are in standard (x,y) coordinate plane. If XYZW is a rectangle, what is the length, in coordinate units, of XW
The length of XW in coordinate units is [tex]\sqrt{34}[/tex] units.
Given that X (4,1), Y(7,1) and Z(4,6) are the coordinates of a rectangle XYZW in the standard (x,y) coordinate plane.
We need to find the length, in coordinate units, of XW.
Since XZ is perpendicular to XY and XZ and XY are sides of rectangle XYZW, lets use the Pythagorean Theorem to find the length of XW. The length of XZ can be calculated by finding the distance between the coordinates of X and Z.
Using the distance formula, we have;
[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex] = [tex]\sqrt{(4 - 4)^2 + (6 - 1)^2}[/tex][tex]\sqrt{(0)^2 + (5)^2}[/tex][tex]\sqrt{25}[/tex] = 5 units
The length of XY is calculated by finding the distance between the coordinates of X and Y.
Using the distance formula, we have;
[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex] = [tex]\sqrt{(7 - 4)^2 + (1 - 1)^2}[/tex][tex]\sqrt{(3)^2 + (0)^2}[/tex][tex]\sqrt{9}[/tex] = 3 units
Therefore, the length of XW can be calculated as follows:
XW = [tex]\sqrt{(XZ)^2 + (XY)^2}[/tex]XW = [tex]\sqrt{(5)^2 + (3)^2}[/tex]XW = [tex]\sqrt{34}[/tex] units
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Terrence is recording what kind of shoes people are wearing at the mall. Out of the 20 people he has seen, 2 are wearing sneakers. What is the experimental probability that the next person Terrence sees will be wearing sneakers?
Terrence saw, and out of those, only two people were wearing sneakers. Therefore, the probability of the next person Terrence sees wearing sneakers is 2/20 or 0.1 or 10%.
The experimental probability of an event happening is the ratio of the number of times the event occurs to the number of trials, i.e., the number of opportunities for the event to happen.Here, Terrence recorded what kind of shoes people are wearing at the mall.
He found out that 2 out of the 20 people he has seen are wearing sneakers. We can determine the experimental probability of the next person Terrence sees wearing sneakers with this information.The experimental probability that the next person Terrence sees will be wearing sneakers can be calculated as follows:Probability of seeing the next person wearing sneakers = Number of people wearing sneakers / Total number of people seen= 2/20
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Which models represent the sum? 1.2 + 0.3 Select each correct answer. Number line from 0 to 4 by tenths. An arrow shows a jump starting at 0 and ending 2 marks past 1. Another arrow shows a jump starting at 2 marks past 1 and ending at 5 marks past 1. One column, divided into 10 small squares. Two small squares. Plus sign. Three columns, each divided into 10 small squares. Two 10 by 10 grids of 100 squares. All 10 columns of first square and 2 columns of the second square shaded one color. Three columns of the second square shaded a different color. Large square divided into a 10 by 10 grid of 100 small squares. Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares. Ten by 10 grid of 100 squares. The first column and 2 squares of the second column are shaded one color. The next three columns are shaded another color.
Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares. These models provide visual representations of the sum 1.2 + 0.3, helping to understand the addition of these numbers.
To identify the models that represent the sum 1.2 + 0.3, let's analyze the given options:
Number line from 0 to 4 by tenths - This model represents the sum as it includes the values 1.2 and 0.3 on the number line, allowing for visualizing the addition of these numbers.
An arrow shows a jump starting at 0 and ending 2 marks past 1 - This model does not directly represent the sum of 1.2 + 0.3. It only illustrates a jump on the number line, which may not correspond to the sum in question.
Another arrow shows a jump starting at 2 marks past 1 and ending at 5 marks past 1 - Similar to the previous option, this model does not directly represent the sum of 1.2 + 0.3. It demonstrates another jump on the number line, unrelated to the given sum.
One column, divided into 10 small squares - This model does not directly represent the sum 1.2 + 0.3 as it only presents a column without any values or operations.
Two small squares. Plus sign. Three columns, each divided into 10 small squares - This model represents the sum 1.2 + 0.3. The two small squares likely represent 1.2 and 0.3, and the plus sign indicates the operation of addition. The three columns divided into 10 small squares may provide a visual representation of the place value concept.
Two 10 by 10 grids of 100 squares - This model does not directly represent the sum of 1.2 + 0.3. It shows two grids of squares but does not include the given numbers or an addition operation.
All 10 columns of the first square and 2 columns of the second square shaded one color - This model does not directly represent the sum 1.2 + 0.3. It describes shading specific columns in squares, which is unrelated to the given sum.
Three columns of the second square shaded a different color - Similar to the previous option, this model does not directly represent the sum of 1.2 + 0.3. It focuses on shading specific columns in squares without providing a representation of the sum.
Large square divided into a 10 by 10 grid of 100 small squares - This model does not directly represent the sum 1.2 + 0.3. It describes a large square divided into smaller squares but does not include the given numbers or an addition operation.
Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares - This model represents the sum 1.2 + 0.3. The two columns divided into 10 small squares likely represent 1.2 and 0.3, and the plus sign indicates the operation of addition. The three columns divided into 10 small squares may provide a visual representation of the place value concept.
Ten by 10 grid of 100 squares. The first column and 2 squares of the second column are shaded one color. The next three columns are shaded another color - This model does not directly represent the sum 1.2 + 0.3. It focuses on shading specific columns in a grid of squares, which is unrelated to the given sum.
Based on the analysis, the models that represent the sum 1.2 + 0.3 are:
Number line from 0 to 4 by tenths
Two small squares. Plus sign. Three columns, each divided into 10 small squares
Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares
These models provide visual representations of the sum 1.2 + 0.3, helping to understand the addition of these numbers.
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In a cricket league, 145 players play in 10 different teams. Each team has at least 14 players.What is the largest possible number of players in any one team?
the largest possible number of players in any one team is 15.
In a cricket league, 145 players play in 10 different teams. Each team has at least 14 players. The largest possible number of players in any one team is 16.
How to find out the largest possible number of players in any one team?
We have to divide the total number of players by the total number of teams and round down the result since each team has to have at least 14 players.
145 players ÷ 10 teams = 14 remainder 5
So, there are 10 teams of 14 players and 1 team of 15 players.
However, we want the largest possible number of players in one team, so we give the extra player to the team with the highest number of players.
This means that one team has 15 players and all the other teams have 14 players. Therefore, the largest possible number of players in any one team is 15.
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A bag contains 12 beads. 2 of the beads are blue. 1 of the beards is green. 3 of the beads are purple. . Show that the probability that this bead is purple or red is 3 over 4
PLEASE HELP ME need the answer by tomorrow
In a bag containing 12 beads, 2 are blue, 1 is green, and 3 are purple. We need to calculate the probability of selecting a bead that is either purple or red.
By determining the number of purple and red beads and dividing it by the total number of beads, we can show that the probability is 3 over 4.
To calculate the probability of selecting a purple or red bead, we first need to determine the number of purple and red beads in the bag. We are given that there are 3 purple beads in the bag.
Since the remaining colors are not specified, we can assume that the non-purple beads are of a different color, which we will consider as red.
Therefore, there are a total of 3 purple beads and 9 (12 - 3) red beads in the bag.
The probability of selecting a purple or red bead is the ratio of the favorable outcomes (purple and red beads) to the total number of outcomes (all beads).
The probability can be calculated as:
Probability = (Number of purple or red beads) / (Total number of beads)
Probability = (3 + 9) / 12
Probability = 12 / 12
Probability = 1
The probability is equal to 1, which indicates that selecting a bead that is either purple or red is certain.
To express this probability as a fraction, we can simplify it by dividing both the numerator and denominator by their greatest common divisor, which is 12:
Probability = 12 / 12 = 1 / 1 = 1
Therefore, the probability of selecting a bead that is either purple or red is 1, which can also be expressed as 3 over 4 when simplified.
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The five members of the Treanor family each buy train tickets during the train ride each family member buys a box lunch for $6.50 if the total cost of the trip is $248.50 what is the price of each train ticket
Let's assume the price of each train ticket is x dollars.
Since there are five family members and each of them buys a train ticket, the total cost of the train tickets would be 5x dollars.
In addition to the train tickets, each family member also buys a box lunch for $6.50. Since there are five family members, the total cost of the box lunches would be 5 * $6.50 = $32.50.
Given that the total cost of the trip is $248.50, we can set up the equation:
5x + $32.50 = $248.50
Subtracting $32.50 from both sides of the equation:
5x = $248.50 - $32.50
5x = $216
Dividing both sides of the equation by 5:
x = $216 / 5
x ≈ $43.20
Therefore, the price of each train ticket is approximately $43.20.
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Given right triangle ABC with a=
39
39, b=
52
52, and c=
65
the given triangle ABC with side lengths a=39, b=52, and c=65 is indeed a right triangle, as it satisfies the Pythagorean theorem.
To verify if triangle ABC is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
Let's check if the given lengths satisfy the Pythagorean theorem:
a = 39
b = 52
c = 65
Using the theorem:
c² = a² + b²
65² = 39² + 52²
4225 = 1521 + 2704
4225 = 4225
The equation is true, as both sides of the equation are equal.
Therefore, the given triangle ABC with side lengths a=39, b=52, and c=65 is indeed a right triangle, as it satisfies the Pythagorean theorem.
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James copied a symbol on each of 12 equal-sized strips of paper. He put a dot on 2 of them, a dash on 2 of them, and a pound sign on 8 of them. Then, he put all the strips in a hat and pulled out 3 at random. How many different symbol combinations were possible?
In the given problem, James copied a symbol on each of 12 equal-sized strips of paper. He put a dot on 2 of them, a dash on 2 of them, and a pound sign on 8 of them. Then, he put all the strips in a hat and pulled out 3 at random. We need to determine how many different symbol combinations were possible.
First, we can determine the total number of combinations possible. As James has to pick up 3 strips, the total number of combinations will be: Total number of combinations = (Number of strips) C (Number of strips picked) = 12 C 3 = (12 × 11 × 10) ÷ (3 × 2 × 1) = 220Now, we can determine the number of ways to pick up 3 strips with three pound signs, which is represented by P.P.P. We need to choose 3 strips from the 8 strips with the pound sign. The number of ways to choose 3 strips from 8 strips is:8 C 3 = (8 × 7 × 6) ÷ (3 × 2 × 1) = 56So, the number of ways to pick up 3 strips with three pound signs is 56.Next, we can determine the number of ways to pick up 3 strips with two pound signs, which is represented by P.P.x. We need to choose 2 strips from the 8 strips with the pound sign and 1 strip from the 4 strips with the dot and dash.
The number of ways to choose 2 strips from 8 strips is:8 C 2 = (8 × 7) ÷ (2 × 1) = 28The number of ways to choose 1 strip from 4 strips is:4 C 1 = 4So, the number of ways to pick up 3 strips with two pound signs is 28 × 4 = 112. (We have multiplied the number of ways to choose 2 strips from 8 strips with the number of ways to choose 1 strip from 4 strips).Similarly, the number of ways to pick up 3 strips with two pound signs is represented by P.x.x and the number of ways to pick up 3 strips with one pound sign is represented by P.x.x. They can be calculated in the same way.So, the number of ways to pick up 3 strips with two pound signs (P.P.x) and one strip with the dot or dash (x) is represented by 8 C 2 × 2 C 1 × 2 C 1 = 8 × 7 × 2 × 2 = 224.The number of ways to pick up 3 strips with two pound signs (P.P.x) and one strip with the dot or dash (x) is represented by 8 C 1 × 2 C 2 × 2 C 1 = 8 × 1 × 2 = 16.The number of ways to pick up 3 strips with one pound sign (P.x.x) and two strips with the dot or dash (x.x) is represented by 8 C 1 × 2 C 1 × 2 C 1 = 8 × 2 × 2 = 32.The number of ways to pick up 3 strips with three dots or dashes (x.x.x) is represented by 2 C 3 = 0. (As there are only 2 strips with dot or dash).Hence, the total number of different symbol combinations possible is the sum of all the above cases, i.e.,Total number of different symbol combinations possible = P.P.P + P.P.x + P.x.x + P.x.x + P.x.x + x.x.x= 56 + 112 + 224 + 16 + 32 + 0= 440
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(3. ) At the baseball game, you saw Jane. Jane told you that he
made $52. 09 at the last game selling a total of 31 items
consisting of soda or popcorn. If Jane makes $1 selling popcorn
and $2. 11 selling soda, how many items of popcorn was sold?
Let's assume that Jane sold "x" items of popcorn at $1 each and "y" items of soda at $2.11 each. Since Jane sold a total of 31 items, we can write the equation x + y = 31. We also know that Jane made a total of $52.09, so we can write another equation as x + 2.11y = 52.09.
To solve these equations, we can use substitution. Rearranging the first equation, we get x = 31 - y.
of x into the second equation, we have (31 - y) + 2.11y = 52.09.
Simplifying the equation, we get 31 + 1.11y = 52.09. Subtracting 31 from both sides, we have 1.11y = 21.09. Dividing both sides by 1.11, we find y = 19.
Therefore, Jane sold 19 items of soda. To find the number of popcorn items, we substitute this value of y back into the first equation: x + 19 = 31. Subtracting 19 from both sides, we find x = 12.
Hence, Jane sold 12 items of popcorn.
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Janis needs 3 gallons of lemonade for a party she has 4/4 six prints and 4 cups of lemonade or ready-made how many more cups of lemonade does Janice need
Janis needs 3 gallons of lemonade for the party. She already has 4/4 six-packs and 4 cups of ready-made lemonade. The task is to determine how many more cups of lemonade Janis needs to meet the required amount.
To find the answer, we need to convert the gallons of lemonade into cups. Since 1 gallon is equal to 16 cups, 3 gallons would be equal to 3 * 16 = 48 cups.
Janis already has 4 six-packs, which means she has 4 * 6 = 24 cups of lemonade from the six-packs. Adding the 4 cups of ready-made lemonade, Janis has a total of 24 + 4 = 28 cups of lemonade.
To determine how many more cups of lemonade Janis needs, we subtract the cups she already has from the required amount. Thus, 48 - 28 = 20 more cups of lemonade are needed for the party.
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If f(x)=x-1/3 and g(x)=3x+1 what is (f times g)(x)?
3x+1
x-3
3x
x
The expression (f times g)(x) represents the product of the functions f(x) and g(x). In this case, f(x) = x - 1/3 and g(x) = 3x + 1. To find the product, we substitute g(x) into f(x) and simplify the expression.
When we substitute g(x) into f(x), we get:
(f times g)(x) = f(g(x)) = f(3x + 1)
Now, substituting the expression for f(x) into f(g(x)), we have:
f(g(x)) = (3x + 1) - 1/3
Simplifying further, we combine like terms:
= 3x + 1 - 1/3
Thus, the product of f(x) and g(x), (f times g)(x), simplifies to:
(f times g)(x) = 3x + 1 - 1/3
(f times g)(x) equals 3x + 1 - 1/3.
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A sphere has a radius of 1. 5 inches. What is the volume of the sphere rounded to the nearest tenth? Use 3. 14 for pi.
A sphere has a radius of 1. 5 inches. What is the volume of the sphere rounded to the nearest tenth, The volume of the sphere with a radius of 1.5 inches is approximately 14.1 cubic inches.
To calculate the volume of a sphere, we use the formula: V = (4/3) * π * r^3
Given that the radius (r) is 1.5 inches and π is 3.14, we substitute these values into the formula:
V = (4/3) * 3.14 * (1.5)^3
V = (4/3) * 3.14 * 3.375
V ≈ 14.1375
Rounding to the nearest tenth, the volume of the sphere is approximately 14.1 cubic inches.
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Time
(seconds)
Height
(feet)
12
1
2
24
36
4
48
a. Determine the average rate of change for the problem situation. Be sure to include units
of measure
The average rate of change for the given problem situation is 2 feet per second.
To find the average rate of change between any two points, we divide the change in the output variable by the change in the input variable. The output variable is height in feet and the input variable is time in seconds. The average rate of change between the first and second points is:Change in height: 2 - 1 = 1 foot
Change in time: 12 - 2 = 10 seconds
Average rate of change: 1/10 = 0.1 feet per second
The average rate of change between the second and third points is:Change in height: 4 - 2 = 2 feet
Change in time: 24 - 12 = 12 seconds
Average rate of change: 2/12 = 0.1667 feet per second
The average rate of change between the third and fourth points is:Change in height: 36 - 4 = 32 feet
Change in time: 48 - 24 = 24 seconds
Average rate of change: 32/24 = 1.3333 feet per second
The average rate of change between the first and fourth points is:Change in height: 48 - 1 = 47 feet
Change in time: 48 - 12 = 36 seconds
Average rate of change: 47/36 = 1.3056 feet per second
Thus, we can see that the average rate of change for the problem situation is 2 feet per second.
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The volume of a spherical balloon is 950 cm. Find the radius of the
4
balloon. (Volume of a sphere
ZAR).
the radius of the spherical balloon is 8.53 cm.
The volume of a sphere of radius r is given by the formula (4/3)πr³ cm³.
Given that the volume of the spherical balloon is 950 cm³, we have:(4/3)πr³ = 950 cm³
Dividing both sides of the equation by (4/3)π, we get:r³ = (950 × 3)/(4 × π) cm³= (2850/4) π/π= 712.5
Therefore, r = ∛(712.5) cm= 8.53 cm (approx.)
Given that the volume of the spherical balloon is 950 cm³, we need to find the radius of the balloon.
To do this, we will use the formula for the volume of a sphere, which is given by (4/3)πr³ cm³, where r is the radius of the sphere. Using this formula, we can write:
4/3)πr³ = 950 cm³
Dividing both sides of the equation by (4/3)π, we get:
r³ = (950 × 3)/(4 × π) cm³= (2850/4) π/π= 712.5Therefore, r = ∛(712.5) cm= 8.53 cm (approx.)
Hence, the radius of the spherical balloon is 8.53 cm.
The radius of a spherical balloon was to be calculated based on the given volume of the balloon. The formula for the volume of a sphere was used which is (4/3)πr³.
On substituting the given volume and simplifying the obtained equation, we get the value of the radius of the spherical balloon. The final answer for the radius of the balloon was calculated to be 8.53 cm.
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The weights of 3 year old boys are normally distributed with a mean 21 lbs and standard deviation 0. 7 lbs.
Find the z-score that corresponds with a little boys weight of 33
When the weights of 3-year-old boys are normally distributed with a mean of 21 lbs and a standard deviation of 0.7 lbs then the z-score that corresponds to a little boy's weight of 33 lbs is approximately 17.14.
The weights of 3-year-old boys are normally distributed with a mean of 21 lbs and a standard deviation of 0.7 lbs.
We need to find the z-score corresponding to a little boy's weight of 33 lbs.
The z-score measures the number of standard deviations an observation is from the mean of a distribution.
It helps in determining the relative position of a value within a distribution.
To calculate the z-score, we use the formula:
z = (x - μ) / σ
where x is the observed value, μ is the mean, and σ is the standard deviation.
In this case, the observed weight is 33 lbs, the mean is 21 lbs, and the standard deviation is 0.7 lbs.
Substituting these values into the formula, we get:
z = (33 - 21) / 0.7
Calculating the numerator, we have:
z = 12 / 0.7
Simplifying further, we get:
z ≈ 17.14
Therefore, the z-score that corresponds to a little boy's weight of 33 lbs is approximately 17.14.
This indicates that the weight of the little boy is about 17.14 standard deviations above the mean weight of 3-year-old boys.
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Find the distance of this point from the center of the earth. The masses of the earth and the moon are 5. 98 * 10*24.
The distance of this point from the center of the earth is 5280248.56 m.
Newton's law of gravitation is used to calculate the distance of an object from the center of the earth. The distance of this point from the center of the earth and the masses of the earth and the moon are both determined using Newton's law of gravitation.
The distance of a point from the center of the earth can be calculated using Newton's law of gravitation, which states that
[tex]F = \frac{G(m1\times m2)}{d^2}[/tex],
where F is the force between the two masses, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.
Given that the masses of the earth and the moon are 5.98 * 10²⁴ kg each, we can substitute these values into the formula and solve for d. We know that the force of gravity between the earth and the moon is the centripetal force acting on the moon that keeps it in orbit.
Thus, we can equate the gravitational force to the centripetal force. So,
[tex]F_{gravity} = F_{centripetal}[/tex]
[tex]G(m_1m_2)/r^2 = m\omega^2r[/tex]
Here, ω is the angular velocity of the moon.
So, [tex]d = [(Gm)/(\omega^2)]^{1/3}[/tex]
Where G = 6.674×10^-11 Nm²/kg², m is Mass of earth, ω is angular speed of the moon which is 2.7*10-6/s.
From the above formulas, we can calculate the distance of this point from the center of the earth as follows:
[tex]d = [(6.674\times10^{-11} Nm^2/kg^2 \times 5.98 \times 10^{24} kg)/(2.7\times10^{-6}/s^2)]^{1/3}[/tex]
d = 5280248.56 m
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Hello would really appreciate it
Answer:
1. Reflect f(x) about the x-axis, obtaining -f(x).
2. Shift -f(x) 5 units left, obtaining -f(x + 5).
3. Shift -f(x + 5) 2 units up, obtaining
-f(x + 5) + 2.
A car dealership buys a used car for $18,790. They mark-up the car by 20%. How much are you as the buyer going to pay?
Therefore, as the buyer, you will pay $22,548 for the used car after the dealership marks it up by 20%.
To calculate the price you, as the buyer, will pay after the car dealership marks up the car by 20%, you need to add the markup amount to the original price.
Markup amount = 20% of $18,790
Markup amount = 0.20 * $18,790
Markup amount = $3,758
The markup amount is $3,758.
To determine the final price you will pay, you need to add the markup amount to the original price:
Final price = Original price + Markup amount
Final price = $18,790 + $3,758
Final price = $22,548
Therefore, as the buyer, you will pay $22,548 for the used car after the dealership marks it up by 20%.
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Tom and zara have a dog walking business. They walk their costomor dogs together and share all th money they make equally
This arrangement ensures that both partners share the workload and the profits equally.
In their dog walking business, Tom and Zara have decided to work together as partners. Whenever they walk a customer's dog, they do it together, combining their efforts to provide a quality service. This partnership allows them to share the workload, ensuring that the responsibilities are divided equally between them. By working together, they can efficiently handle multiple dogs and ensure the safety and well-being of the animals under their care.
In terms of the financial aspect, Tom and Zara have agreed to split the money they make equally. Regardless of who physically handles the payment or interacts with the customers, both partners receive an equal share of the earnings. This fair distribution of profits ensures that neither Tom nor Zara feels disadvantaged or unfairly compensated. By sharing the money equally, they maintain a cooperative and balanced business relationship, fostering trust and harmony in their partnership.
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If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the first equation is substituted into the second equation. X 4y = −9 2x 5y = −6 2x 5(4y − 9) = −6 2x 5(−4y − 9) = −6 2(4y − 9) 5y = −6 2(−4y − 9) 5y = −6.
The new equation obtained after substituting the expression equivalent to x from the first equation into the second equation is -18 - 13y = -6.
To solve the given system of equations using the substitution method, we need to substitute the expression equivalent to x from the first equation into the second equation.
To find the new equation, we can follow these steps:
Start with the first equation: x + 4y = -9.
Solve the first equation for x: x = -9 - 4y.
Substitute the expression (-9 - 4y) for x in the second equation: 2x - 5y = -6 becomes 2(-9 - 4y) - 5y = -6.
Simplify the equation by performing the multiplication: -18 - 8y - 5y = -6.
Combine like terms: -18 - 13y = -6.
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Plot these coordinates:(1,2),(1,7),(9,7),(9,3),(6,5). What is the area
To find the area of the region formed by the given coordinates, we can use the method of Shoelace Formula or Gauss's Area formula. The area of the polygon formed by the given coordinates is 25 square units
1. Plot the given coordinates: (1,2), (1,7), (9,7), (9,3), (6,5). These points represent the vertices of the polygon.
2. Connect the plotted points in order to form the polygon.
3. Use the Shoelace Formula or Gauss's Area formula to calculate the area of the polygon. The Shoelace Formula involves multiplying the differences of the x-coordinates with the corresponding y-coordinates and summing them up.
4. Apply the Shoelace Formula:
Area = 1/2 * |(1*7 + 1*7 + 9*3 + 9*2 + 6*7) - (2*1 + 7*9 + 7*9 + 3*6 + 5*1)|
= 1/2 * |(7 + 7 + 27 + 18 + 42) - (2 + 63 + 63 + 18 + 5)|
= 1/2 * |101 - 151|
= 1/2 * |-50|
= 25
Therefore, the area of the polygon formed by the given coordinates is 25 square units.
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In 1990, Jerry´s gross pay was $78,000.
A. What was his gross monthly pay?
B. In What month did Jerry hit the maximum taxable Social Security Income?
C. How much Social Security tax did Jerry pay in January of 1990?
D. How much Social Security tax did Jerry pay in December of 1990?
Show Work
A. Jerry paid $403 in Social Security tax both in January and December.
What was Jerry's gross monthly pay? To calculate Jerry's gross monthly pay, you will need to divide his gross pay of $78,000 by the number of months in a year, which is 12.Gross Monthly Pay= Gross Pay/12= $78,000/12= $6,500B. In what month did Jerry hit the maximum taxable Social Security Income?
The maximum taxable Social Security income is $51,300. This implies that Social Security tax is applied only on the first $51,300 of Jerry's income. Jerry's gross pay was $78,000; thus, the maximum taxable Social Security Income for Jerry is $51,300.
Social Security tax is calculated on gross pay, not net income. Jerry will hit the maximum taxable Social Security Income as soon as he earns $51,300 for the year.
The social security tax will no longer be deducted from his paychecks for the remainder of the year. This will occur at the point when Jerry's gross pay equals the maximum taxable Social Security income.
This occurs in August. Gross monthly pay is $6,500. Thus, by August, Jerry will have earned $51,300 (8*$6,500).C. How much Social Security tax did Jerry pay in January of 1990?
Social Security tax rate for 1990 was 6.2 percent of gross pay. This implies that Jerry paid 6.2 percent of his gross pay as Social Security tax. Social Security Tax paid in January= Gross Monthly Pay * Social Security Tax Rate= $6,500 * 6.2%= $403D. How much Social Security tax did Jerry pay in December of 1990?
Social Security tax rate for 1990 was 6.2 percent of gross pay.
This implies that Jerry paid 6.2 percent of his gross pay as Social Security tax. Social Security Tax paid in December= Gross Monthly Pay * Social Security Tax Rate= $6,500 * 6.2%= $403
Hence, Jerry paid $403 in Social Security tax both in January and December.
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A bag contains 1p, 2p and 5p coins.3/8 of the bag are 1p coinsthere are many 5p coins as 1p in the bag.there are 640coins in totalwork out the number of 2p coins in the bag
The number of 2p coins in the bag is 0. We are given the following information: 3/8 of the bag are 1p coins. There are as many 5p coins as 1p coins. There are 640 coins in total.
Let's break down the steps to solve the problem:
Step 1: Calculate the number of 1p coins.
Since 3/8 of the bag are 1p coins, we can find the number of 1p coins by multiplying the total number of coins by 3/8:
Number of 1p coins = (3/8) * 640 = 240
Step 2: Calculate the number of 5p coins.
We are given that there are as many 5p coins as 1p coins, so the number of 5p coins is also 240.
Step 3: Calculate the total value of the 2p coins.
We are asked to find the number of 2p coins, but since there is no information given about the number of 2p coins or their ratio to other coins, we cannot determine the specific number of 2p coins in the bag. Therefore, the number of 2p coins in the bag is 0.
Please double-check the given information to ensure accuracy.
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Profit, P(-2), is the difference between revenue, R(x), and cost, C(x), so P(x) = R(x) - C(x). Which
expression represents P(x), if R(x) = 2x4 -- 30% + 22-1 and C(x) = 24 x² + 2x + 3?
help
The expression for the profit function P(x) is P(x) = 2x^4 - 24x^2 - 2x - 1.3.
To find the expression for the profit function P(x) when given the revenue function R(x) and cost function C(x), we can substitute the given functions into the equation P(x) = R(x) - C(x).
Given:
R(x) = 2x^4 - 30% + 2^(2-1)
C(x) = 24x^2 + 2x + 3
We substitute the functions into the expression for P(x):
P(x) = R(x) - C(x)
= (2x^4 - 30% + 2^(2-1)) - (24x^2 + 2x + 3)
Simplifying the expression:
P(x) = 2x^4 - 0.3 + 2 - 24x^2 - 2x - 3
= 2x^4 - 24x^2 - 2x - 0.3 - 3 + 2
= 2x^4 - 24x^2 - 2x - 1.3
Therefore, the expression for the profit function P(x) is P(x) = 2x^4 - 24x^2 - 2x - 1.3.
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