Answer:
The volume of the cone is 22 cubic inches.
Step-by-step explanation:
To find the volume of the cone, we need to use the formula for the volume of a cone:
Volume of a cone = (1/3) * π * r^2 * h
Given that the height and base area of the cylinder and cone are the same, we can assume that the radius of the cylinder's base is equal to the radius of the cone's base.
We know that the volume of the cylinder is 66 cubic inches, so we can set up the equation:
66 = π * r^2 * h
To find the volume of the cone, we need to express its height in terms of the radius of the cylinder's base. The height of the cone will be equal to the height of the cylinder.
Now, let's solve for h in terms of r using the given information:
66 = π * r^2 * h
h = 66 / (π * r^2)
Substituting this value of h into the volume formula of the cone:
Volume of the cone = (1/3) * π * r^2 * (66 / (π * r^2))
Volume of the cone = (1/3) * 66
Volume of the cone = 22
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A shop sells two brands of eggs. Brand A and Brand B , Their prices are given in the ratio 4:7, if a baker buys 8 trays of brand A and 6 trays of Brand B at a total cost of R279,45
How much did the baker pay for the 8 trays of brand
The baker paid approximately R15.08 for each tray of Brand A.
Understanding Word ProblemLet:
x = price of each tray of Brand A
y = price of each tray of Brand B
Given that the prices are in the ratio 4:7, we can write the equation:
x/y = 4/7
To find the individual prices of Brand A and Brand B, we can introduce a constant k:
x = 4k
y = 7k
The total cost of 8 trays of Brand A (8x) and 6 trays of Brand B (6y) is R279.45:
8x + 6y = 279.45
Substituting the expressions for x and y:
8(4k) + 6(7k) = 279.45
32k + 42k = 279.45
74k = 279.45
Dividing both sides by 74:
k = 279.45 / 74
k ≈ 3.77
Now we can find the price of each tray of Brand A:
x = 4k ≈ 4 * 3.77 ≈ R15.08
Therefore, the baker paid approximately R15.08 for each tray of Brand A.
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If 15. 0 g of CaCl2 are present in 250 mL of aqueous solution, what is the concentration of CaCl2 in % (w/v)?
The concentration of CaCl2 in % (w/v) can be calculated by dividing the mass of CaCl2 by the volume of the solution and multiplying by 100. In this case, if 15.0 g of CaCl2 is present in 250 mL of solution, the concentration of CaCl2 can be determined.
The concentration of a solution is commonly expressed as a percentage by weight/volume (% w/v), which represents the mass of solute (in this case, CaCl2) in a given volume of solution. To calculate the concentration, divide the mass of CaCl2 (15.0 g) by the volume of the solution (250 mL) and multiply by 100.
Concentration of CaCl2 in % (w/v) = (Mass of CaCl2 / Volume of Solution) x 100
Substituting the given values:
Concentration of CaCl2 in % (w/v) = (15.0 g / 250 mL) x 100
Simplifying the expression:
Concentration of CaCl2 in % (w/v) = 6.0% (rounded to one decimal place)
Therefore, the concentration of CaCl2 in the given solution is 6.0% (w/v).
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What is the surface area of the prism in square inches?A rectangular prism has a height of 2 inches, width of 8 inches, and depth of 11 inches. 90 square inches126 square inches176 square inches252 square inches
The surface area of the prism is 252in²
Given,
Dimensions of rectangular prism:
Height = 2 in
width = 8 in
depth = 11 in
Now,
The surface area of a rectangular prism is given by:
A = 2 * (x * y) + 2 * (x * z) + 2 * (y * z)
where,
x, y, z: are the sides of the rectangular prism
Substituting values we have:
A = 2 * (2 * 8) + 2 * (2 * 11) + 2 * (8 * 11)
A = 252 in²
Hence the surface area of the prism in square inches will be 252 .
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Which expressions are equivalent to 8. 9 x 6. 2 8. 7? Check all that apply. 9 x 6 9 8. 9 6. 2 8. 7 x 8. 9 x 8. 7 6. 2 8. 7 8. 9 x 6. 2 6. 2 8. 7 8. 9 6. 2 8. 7 8. 9 x 8. 9 6. 2 x 8. 7.
The following expressions are equivalent to 8.9 x 6.28.7: 9 x 6; 6.28.7; 8.9 x 6.2. The product of two numbers, in general, is the outcome when we multiply the numbers together.
It means, when we take two quantities and multiply them, we get the result as a product. Let us understand how the multiplication of numbers works with an example. When we multiply 3 and 4, we get:3 × 4 = 12Here, 3 and 4 are called factors, and the result, 12, is called the product. Equivalent expressions are the expressions that have the same value, but their structures may differ. The expressions can be equivalent if they have the same value, but their format is different .Let's list the expressions that are equivalent to 8.9 x 6.28.7:The product of 9 and 6 is equal to 54. The product of 8.9 and 6.2 is equal to 55.18.The expression 6.28.7 is the same as 55.18. The product of 8.9 and 6.2 is the same as 6.28.7.Therefore, the following expressions are equivalent to 8.9 x 6.28.7:9 x 66.28.78.9 x 6.2.
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£360 is shared between Abby, Ben, Chloe and Denesh. The ratio of the amount Abby gets to the amount Ben gets is 2 : 7 Chloe and Denesh each get 1. 5 times the amount Abby gets. Work out the amount of money that Ben gets. (4)
The amount of money that Ben gets is £140.
Let's denote the amount Abby gets as 2x. Since the ratio of Abby's amount to Ben's amount is 2:7, the amount Ben gets can be represented as 7x.
Chloe and Denesh each get 1.5 times the amount Abby gets, which means they each get 1.5 * 2x = 3x.
The total amount shared between Abby, Ben, Chloe, and Denesh is £360. So we can write the equation: 2x + 7x + 3x + 3x = £360.
Simplifying the equation, we have: 15x = £360.
Dividing both sides by 15, we find that x = £24.
Substituting x back into the equation for Ben's amount, we get: Ben's amount = 7x = 7 * £24 = £168.
Therefore, Ben gets £140.
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What is the value of n when 3/5 of n is 27? Enter answer in the box
n = 45 satisfies the equation, and it is the value that makes 3/5 of n equal to 27. The value of n can be determined by setting up an equation based on the given information that 3/5 of n is equal to 27.
By solving the equation, we can find the value of n. Let's set up the equation based on the given information:
(3/5) * n = 27
To solve for n, we need to isolate n on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of 3/5, which is 5/3:
n = 27 * (5/3)
Simplifying the right side of the equation:
n = (27 * 5) / 3
n = 135 / 3
n = 45
Therefore, the value of n is 45. We can confirm this by substituting n = 45 back into the equation:
(3/5) * 45 = 27
(3/5) * 45 = 135/5 = 27
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Milo wants to make a mixture that is 50% lemon juice and 50% lime juice. How much 100% lemon juice should he add to a juice mixture that is 20% lemon juice and 80% lime juice to make 4 gallons of the 50% lemon/50% lime juice mixture? 0. 5 gallon 1. 5 gallons 2 gallons 2. 5 gallons.
To solve this problem, we can set up an equation based on the volume of lemon juice in the mixture:
Let's assume Milo needs to add x gallons of 100% lemon juice.
The total volume of the final mixture is given as 4 gallons, and it should be a 50% lemon juice and 50% lime juice mixture.
The initial mixture contains 20% lemon juice, which means it contains 20% of 4 gallons = 0.2 * 4 = 0.8 gallons of lemon juice.
So, the equation becomes:
0.8 gallons (initial lemon juice) + x gallons (additional 100% lemon juice) = 0.5 * 4 gallons (final lemon juice)
Simplifying the equation:
0.8 + x = 2
Subtracting 0.8 from both sides:
x = 2 - 0.8
x = 1.2
Therefore, Milo needs to add 1.2 gallons of 100% lemon juice to make 4 gallons of the 50% lemon/50% lime juice mixture.
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If the frequency of a FM wave is 8. 85 × 107 hertz, what is the period of the FM wave? A. 2. 58 × 10–8 seconds B. 1. 13 × 10–8 seconds C. 1. 25 × 10–7 seconds D. 5. 82 × 10–7 seconds.
The period of the FM wave is 1.13 × 10–8 seconds.
The correct option is B. 1. 13 × 10–8 seconds.
How to find the period of an FM wave.
The period of a wave can be defined as the time required to complete one cycle.
The period is represented by the symbol T.
It is measured in seconds (s).
Frequency is the number of cycles per second. It is measured in Hertz (Hz).
It is represented by the symbol f.
The formula for finding the period of a wave is given by:
T = 1/f
Given that the frequency of a FM wave is 8.85 x 10⁷ Hertz.
We have to find the period of the FM wave.
The period of the FM wave can be found using the formula:
T = 1/f
Where frequency
= 8.85 × 107 Hz
T = 1/fT
= 1/8.85 x 10⁷T
= 1.13 × 10–8 seconds
Therefore, the period of the FM wave is 1.13 × 10–8 seconds.
Thus, option B is the correct answer.
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Walter had new carpeting installed in his 13-foot by 18-foot family room. He paid $7 per square foot for the carpet and $2 per square foot for the pad under the carpet. What was the total cost for the carpet and pad
Walter had new carpeting installed in his 13-foot by 18-foot family room. He paid $7 per square foot for the carpet and $2 per square foot for the pad under the carpet.
The total area of the room will be A
= l × w= 13 × 18= 234 sq. feet The cost of carpet per square feet is $7. The cost of carpeting the family room is:Total cost of carpeting
= Cost of carpet per sq. ft. × Area of the room
= $7 × 234
= $1638The cost of the pad per square feet is $2.Therefore, the cost of padding the family room is: Total cost of padding
= Cost of pad per sq. ft. × Area of the room
= $2 × 234
= $468The total cost of the carpet and pad will be the sum of the cost of the carpeting and the cost of the padding. Total cost of carpet and pad
= Total cost of carpeting + Total cost of padding
= $1638 + $468
= $2106Hence, the total cost of the carpet and pad is $2106.
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Karen drew a plan for a rectangular piece of material that she will use for a blanket. Three of the vertices are (−1.3,−3.1), (−1.3,1.2), and (1.1,1.2). What are the coordinates of the fourth vertex?
The coordinates of the fourth vertex are (1.1, -3.1).
We know that a rectangular piece of material has two pairs of parallel sides and four right angles. Therefore, we can calculate the distance between two opposite sides by using the distance formula. The two sides that are parallel to the x-axis have the same y-coordinate, and the two sides parallel to the y-axis have the same x-coordinate.
Thus, the distance between opposite sides is given by the difference between the x-coordinates or the difference between the y-coordinates. The x-coordinates of the vertices are −1.3, −1.3, and 1.1. So the difference between them is 1.1 − (−1.3) = 2.4. The y-coordinates of the vertices are −3.1, 1.2, and 1.2. So the difference between them is 1.2 − (−3.1) = 4.3. The fourth vertex is located at the point with an x-coordinate of 1.1 and a y-coordinate of −3.1. Therefore, the coordinates of the fourth vertex are (1.1, -3.1).
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ken can work at most 12 hours next week He needs too earn at least $80 to cover his gas and food expenses. He earns $10 per hour in a supermarket and $5 per hour in a farm. Let x be the number of hours he works in the supermarket and y be the number of hours he works in the farm, write a system of linear inequlaties to model the situaition then solve
Given that Ken can work at most 12 hours next week, he needs to earn at least $80 to cover his gas and food expenses. He earns $10 per hour in a supermarket and $5 per hour in a farm.
Let x be the number of hours he works in the supermarket and y be the number of hours he works in the farm. We need to write a system of linear inequalities to model the situation.Linear inequality to model the situation will be:x + y ≤ 12 ---(1) [Ken can work at most 12 hours next week]10x + 5y ≥ 80 ---(2) [Ken needs to earn at least $80 to cover his gas and food expenses]Thus, the required system of linear inequalities is[tex]:x + y ≤ 12 (1)10x + 5y ≥ 80[/tex] (2)Now, we need to solve the system of linear inequalities to find the feasible solutions. We will solve the inequalities using the method of graphing.Linear Inequality (1)[tex]:x + y ≤ 12x + y = 12y = -x + 12[/tex]The graph of the inequality y = -x + 12 is shown below:Graph of inequality y = -x + 12:Let's test the point (0, 12) in the inequality x + y ≤ 12:0 + 12 ≤ 12⇒ 12 ≤ 12This is true. So, the solution to this inequality is below or on the line y = -x + 12.
Linear Inequality (2):10x + 5y ≥ 8010x + 5y/5 ≥ 80/5⇒ 2x + y ≥ 16y ≥ -2x + 16The graph of the inequality y ≥ -2x + 16 is shown below:Graph of inequality y ≥ -2x + 16:Let's test the point (0, 16) in the inequality 2x + y ≥ 16:2(0) + 16 ≥ 16⇒ 16 ≥ 16This is true. So, the solution to this inequality is above or on the line y = -2x + 16.Thus, the feasible solutions are the region in the graph where both the inequalities overlap and hence, are satisfied. The shaded region in the graph below represents the feasible region. The points on the line are also included.Feasible region:Let's solve for the points of intersection of the lines y = -x + 12 and
y = -2x + 16:y
= -x + 12y
= -2x + 16
⇒ -x + 12 = -2x + 16
⇒ x = 4y = -x + 12
⇒ y = 8
Thus, the point of intersection of the two lines is (4, 8).So, the solution is (x, y) = (4, 8). Therefore, Ken should work for 4 hours in the supermarket and 8 hours in the farm to earn at least $80 to cover his gas and food expenses.
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A system of linear inequalities to model the situation is given by:
x + y ≤ 12
10x + 5y ≥ 80
A possible solution for this system of linear inequalities is (4, 8).
How to write a system of inequalities to model this situation?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of hours Ken works in the supermarket and the number of hours Ken works in the farm respectively, and then translate the word problem into a linear inequality as follows:
Let the variable x represent the number of hours Ken works in the supermarket.Let the variable y represent the number of hours Ken works in the farm.Since Ken would work at most 12 hours while earning $10 per hour in a supermarket and $5 per hour in a farm, and he needs too earn at least $80, a system of linear inequalities that models the situation and constraints is given by;
x + y ≤ 12
10x + 5y ≥ 80
By solving the system of linear inequalities, we have:
10(12 - y) + 5y ≥ 80
120 - 10y + 5y ≥ 80
120 - 5y ≥ 80
5y ≥ 120 - 80
5y ≥ 40
y ≥ 40/5
y ≥ 8
For the value of x, we have:
x ≤ 12 - y
x ≤ 12 - 8
x ≤ 4
In conclusion, a possible solution (x, y) is (4, 8).
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Brenda found a store online where he can buy a package of 8-tshirts .these t-shirts sell at the time rate as the t-shirts jacob bought .how much does brendan pay for the package of 8t-shirts?
The amount that Brenda would pay for the 8 t- shirts at the same rate would be $ 37. 60.
How to find the amount paid ?To determine how much Brenda pays for the package of 8 T-shirts, we need to calculate the price per T-shirt based on Jacob's purchase and then multiply it by 8.
Jacob bought 7 T-shirts for $32.90, so the price per T-shirt can be calculated as:
Price per T-shirt = Total cost / Number of T-shirts
Price per T-shirt = $32.90 / 7
Price per T-shirt = $4.70
The cost of 8 shirts is therefore:
Total cost = Price per T-shirt * Number of T-shirts
Total cost = $4.70 x 8
Total cost = $37.60
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Missing detail is:
Jacob bought 7 T shirts for $32.90 Kyle bought 12 T shirts for $60.00
16 oz = 1 lb
it says to write it in two unit multipliers.
The two-unit multipliers for the conversion of 16 oz to 1 lb are as follows are 16 oz / 1 lb and 1 lb / 16 oz
Unit multiplier refers to a way to convert one unit of measurement to another unit of measurement by multiplying it by a ratio of two equivalent units. This ratio is known as the conversion factor. A unit multiplier can be used to convert from one unit to another because it represents the relationship between the two units of measure.
There are different methods to convert between units of measure. One of these methods is the use of unit multipliers. The use of unit multipliers is an effective way of converting between units because it is straightforward and consistent with the basic principles of mathematics.
The two-unit multipliers for the conversion of 16 oz to 1 lb are 16 oz / 1 lb and 1 lb / 16 oz. The first ratio represents the number of ounces in one pound, while the second ratio represents the number of pounds in one ounce. To convert 16 oz to pounds, we multiply by the ratio of 1 lb / 16 oz. To convert 1 lb to ounces, we multiply by the ratio of 16 oz / 1 lb.
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Janet cut 9 pieces of ribbon that were each 0.4 meter. She then cut 5 pieces of ribbon that were each 0.6 meter. How many meters of ribbon did Janet cut
Janet cut a total of 6.6 meters of ribbon by combining 9 pieces measuring 0.4 meters each and 5 pieces measuring 0.6 meters each.
Janet cut a total of 9 pieces of ribbon, each measuring 0.4 meters, and 5 pieces of ribbon, each measuring 0.6 meters.
To find the total length of ribbon Janet cut, we need to calculate the sum of the lengths of all the individual pieces.
For the 9 pieces of ribbon measuring 0.4 meters each, we can multiply the length of each piece by the number of pieces: 9 * 0.4 = 3.6 meters.
Similarly, for the 5 pieces of ribbon measuring 0.6 meters each, we can calculate the total length: 5 * 0.6 = 3 meters.
To find the total length of ribbon Janet cut, we add the lengths of the two sets of ribbons together: 3.6 + 3 = 6.6 meters.
Therefore, Janet cut a total of 6.6 meters of ribbon by combining the 9 pieces of 0.4-meter ribbon and the 5 pieces of 0.6-meter ribbon.
In summary, Janet cut a total of 6.6 meters of ribbon by combining 9 pieces measuring 0.4 meters each and 5 pieces measuring 0.6 meters each.
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A Mad Professor has created a new kind of creature called a Blorg. For each Blorg, one hour after it is born, it gives birth to a new Blorg. Two hours after it is born, it gives birth to two more new Blorgs and then it immediately dies. If the Professor starts with one newborn Blorg at noon, how many live Blorgs does he have at 4:05 PM that afternoon after the new Blorgs have been born and the 2-hour-olds have died?
Blorgs have a lifespan of two hours, and after that, they die. The newborn Blorgs continue the reproductive cycle, but all Blorgs born before 3 PM would have reached their lifespan and died by 4:05 PM.
To determine the number of live Blorgs the Mad Professor has at 4:05 PM, we need to understand the pattern of Blorg reproduction and lifespan.
From the given information, we know that one hour after a Blorg is born, it gives birth to a new Blorg. Two hours after birth, it gives birth to two more new Blorgs and then immediately dies.
Let's break down the timeline:
At noon, the Professor has one newborn Blorg.
One hour later, at 1 PM, the initial Blorg gives birth to a new Blorg. So, there are two Blorgs now.
Two hours after birth, at 2 PM, the initial Blorg dies, but the newborn Blorg from 1 PM gives birth to two more Blorgs. So, there are four Blorgs now.
At 3 PM, the two newborn Blorgs from 1 PM give birth to two more Blorgs each, resulting in a total of eight Blorgs.
At 4 PM, the four Blorgs that were born at 2 PM die, while the four Blorgs born at 3 PM are still alive. The four living Blorgs are from the second generation.
Now, let's calculate the number of live Blorgs at 4:05 PM:
At 4 PM, there are four living Blorgs.
Since each Blorg lives for two hours, at 4:05 PM, it has been 5 minutes past their lifespan, and all the living Blorgs from the 3 PM generation would have died.
Therefore, at 4:05 PM, the Mad Professor would have zero live Blorgs.
It is important to note that Blorgs have a lifespan of two hours, and after that, they die. The newborn Blorgs continue the reproductive cycle, but all Blorgs born before 3 PM would have reached their lifespan and died by 4:05 PM.
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Use the Pythagorean Theorem to determine the lengths of QT and RS Show your work
(HURRY I WILL GIVE BRAINLEST)
To determine the lengths of QT and RS using the Pythagorean Theorem, we need additional information such as the lengths of the other sides or the measurements of angles in the triangle. Without this information, we cannot accurately calculate the lengths of QT and RS.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. However, in the given question, we are not provided with any measurements or information about angles in the triangle or the lengths of the other sides.
Therefore, without additional information, we cannot determine the lengths of QT and RS using the Pythagorean Theorem.
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a baseball league has a rule that when one team is winning by atleast 10 runs the game is over after the fith inning. the home team has 7 more runs than the visiting team. determine how many more runs the home team must score for the game to end after the fith inning if the visiting team does not score. then interpret the solution.
Given a baseball league has a rule that when one team is winning by at least 10 runs the game is over after the fifth inning, and the home team has 7 more runs than the visiting team. We are to determine how many more runs the home team must score for the game to end after the fifth inning if the visiting team does not score.
In the game of baseball, the number of runs scored by each team is known as the scoreline. The home team has a scoreline of X while the visiting team has a scoreline of X - 7, where X is a positive integer and X - 7 is the scoreline of the visiting team.
Since the game is to be over after the fifth inning, we need to determine the number of runs the home team will need to score to have a 10 run difference or more after the fifth inning. Let's analyze two different scenarios, the first being if the home team were to score one run, and the second scenario being if the home team were to score two runs.
The home team scoreline would be X + 1 in the first scenario and X + 2 in the second scenario. In both cases, the visiting team does not score any additional runs. Thus, the scoreline of the visiting team remains X - 7 in both scenarios.
The difference in the scoreline after the fifth inning would be as follows in the two cases, respectively: (X + 1) - (X - 7) = 8(X + 2) - (X - 7) = 9. From the above calculations, we can see that the home team must score at least nine more runs for the game to end after the fifth inning if the visiting team does not score.
This solution means that if the home team scores nine more runs, then the visiting team will not be given an opportunity to bat in the sixth inning and beyond, because the difference in the scoreline will be at least 10 runs after the fifth inning.
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The music for Savannah’s dance routine lasts for exactly 4 minutes. When Savannah dances
her routine, she starts with her music and finishes 12 seconds before the music ends.
What percent of the time the music is playing is Savannah dancing?
The answer is that Savannah is dancing 95% of the time the music is playing. Duration of music = 4 minutes Duration of Savannah's dance routine = 4 - (12/60) = 3.8 minutes. Now, we need to find the percentage of time the music is playing is Savannah dancing.
To find the percentage of time, we need to divide the time for Savannah's dance routine by the duration of the music and then multiply the quotient by 100.Percentage of time Savannah is dancing = (time for Savannah's dance routine / duration of music) × 100= (3.8 / 4) × 100= 95%.
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For her phone service, Linda pays a monthly fee of $27 and she pays an additional $0.07 per minute of use The least she has been charged in a month is $129.13What are the possible numbers of minutes she has used her phone in a month?
Therefore, the possible numbers of minutes Linda has used her phone in a month are 1459 minutes or more.
To determine the possible number of minutes Linda has used her phone in a month, we can set up an equation based on the given information.
Let's assume the number of minutes Linda has used her phone in a month is represented by 'm'.
The total charge for the phone service consists of the monthly fee of $27 plus the additional charge of $0.07 per minute:
Total charge = $27 + $0.07 * m
According to the given information, the least amount Linda has been charged in a month is $129.13. So we can set up the following equation:
$27 + $0.07 * m ≥ $129.13
Now we can solve this equation to find the possible range of values for 'm'.
$0.07 * m ≥ $129.13 - $27
$0.07 * m ≥ $102.13
m ≥ $102.13 / $0.07
m ≥ 1459
Therefore, the possible numbers of minutes Linda has used her phone in a month are 1459 minutes or more.
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Let b cannot equal 1 and consider the integral 1 to b (6x-9) dx a) what value of b will make this integral equal to 0? b) sketch a graph of y=6x-9 on the interval from x=1 to x=b to verify your answer in (a)
a) To find the value of b that makes the integral equal to 0, we need to solve the integral:
∫(1 to b) (6x - 9) dx = 0
Applying the fundamental theorem of calculus, we can find the antiderivative of the integrand and evaluate it at the limits of integration:
[3x² - 9x] (from 1 to b) = 0
Substituting the limits, we have:
(3b² - 9b) - (3(1)² - 9(1)) = 0
Simplifying further:
3b² - 9b - 6 = 0
Now we can solve this quadratic equation for b using the quadratic formula or factoring:
b² - 3b - 2 = 0
Factoring the quadratic equation, we get:
(b - 2)(b + 1) = 0
Setting each factor to zero, we find two possible values for b:
b = 2 or b = -1.
However, since b cannot equal 1 (as stated in the problem), the only valid solution is b = 2.
b) To verify our answer, we can sketch a graph of y = 6x - 9 on the interval from x = 1 to x = b = 2. The graph will be a straight line with a slope of 6 and y-intercept at -9.
On the interval [1, 2], the line starts at the point (1, -3) and ends at the point (2, 3). By calculating the area under this line, we find that the integral from 1 to 2 of (6x - 9) equals 0, confirming our previous result.
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Write it as a fact family
12. 4-3. 2=9. 2
The fact family 12, 4, 3, 2, and 9 demonstrates the relationship between addition and subtraction. In this fact family, when we subtract 3 from 4, the result is 1. If we then add 2 to 1, we get 3. Furthermore, when we subtract 2 from 9, the result is 7. If we add 7 and 2 together, the sum is 9.
In the given fact family, the numbers 4 and 3 are related through subtraction. When we subtract 3 from 4, we get 1. This is represented by the equation 4 - 3 = 1.
On the other hand, the numbers 2 and 1 are related through addition. If we add 2 to 1, the sum is 3. This is represented by the equation 1 + 2 = 3.
Similarly, the numbers 9 and 2 are related through subtraction and addition. When we subtract 2 from 9, we get 7, represented by the equation 9 - 2 = 7. By adding 7 and 2 together, the sum is 9, represented by the equation 7 + 2 = 9.
Therefore, the fact family 12, 4, 3, 2, and 9 demonstrates the relationship between addition and subtraction within the given numbers.
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The shape shown is made up of three similar right-angled triangles.
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The smallest triangle has two sides of side-length 2, as shown.
What is the area of the shape?
To calculate the area of the shape made up of three similar right-angled triangles, we need additional information about the scale factor or proportions of the triangles. Without that information, we cannot determine the exact area of the shape.
The given information states that the shape is composed of three similar right-angled triangles, and the smallest triangle has two sides of side-length 2. While we know the dimensions of the smallest triangle, we do not have any information about the scale factor or proportions of the other two triangles. Since the shape is formed by three similar triangles, the areas of the triangles would be proportional, but we cannot determine the exact proportions without additional information. Consequently, we cannot calculate the area of the shape accurately based solely on the given information.
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CERAMICS Josh has 8 days to make pots and plates to sell at a local fair. Each potweighs 2 pounds and each plate weighs 1 pound. Josh cannot carry more than 50 poundsto the fair. Each day, he can make at most 5 plates and at most 3 pots. He will make $12profit for every plate and $25 profit for every pot that he sells.a. Write linear inequalities to represent the number of pots p and plates a Josh maybring to the fair.b. List the coordinates of the vertices of the feasible region.c. How many pots and how many plates should Josh make to maximize his potentialprofit?
The given restrictions can be written as follows:Maximum weight carried by Josh: 2p + 1a ≤ 50Maximum number of plates per day: p ≤ 3his objective function would be:Profit = 12a + 25pWe need to find the values of a and p which can maximize his profit.
Thus, the linear inequalities to represent the number of pots p and plates a that Josh may bring to the fair is:2p + 1a ≤ 50, a ≤ 5 and p ≤ 3.b) The feasible region can be found by plotting the given constraints on the coordinate plane. Here is the graph for the same:From the graph, we can see that the vertices of the feasible region are (0,0), (3,5), (8,0), and (16,0).c) Josh wants to maximize his profit.
Therefore, To do so, we can substitute the vertices of the feasible region and calculate the profit to identify the combination of pots and plates that gives the maximum profit.
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Three vertices of parallelogram WXYZ are W(-5,2), X(2,4), and Z(-7, -3). Find the coordinates of vertex Y
The coordinates of Y are (-1,0). Answer: The coordinates of vertex Y are (-1,0).
To find the coordinates of vertex Y of parallelogram WXYZ whose coordinates are given, we need to use the properties of a parallelogram.
A parallelogram is a quadrilateral in which opposite sides are parallel and congruent.
It means the distance between points W and X is equal to the distance between points Y and Z.
W(-5,2), X(2,4), Y(a,b), and Z(-7,-3).
Therefore, the length of side WX is given as,
WX = √ [(2 - (-5))²+ (4 - 2)²]
= √(49 + 4) = √53. ..(1)
As opposite sides of parallelogram are parallel, XY will have the same slope as WZ. The slope of line WZ is given as
(2 - (-3))/(-5 - (-7)) = 5/2.
Therefore, the slope of XY is also 5/2.
(a, b) is on line XY. The equation of line XY can be written as
y - b = 5/2(x - a) ...(2)
It is given that the length of side WZ is equal to the length of side WX. Therefore,
WZ = WX = √53.
Distance WY can be found using the distance formula as follows:
WY² = WZ² - ZY²WY² = 53 - (b + 3)² ...(3)
Similarly, distance XY can be found as,
XY²= WX²- WY²XY²
= 53 - (a - 2)² - (b - 4)² ...(4)
By solving equations (2), (3), and (4) for a and b, we can get the coordinates of Y.a = -1, b = 0
Therefore, the coordinates of Y are (-1,0). Answer: The coordinates of vertex Y are (-1,0).
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Given circle B.If measure of arc AD = 118 degrees, find the measure of angle DBC.
The measure of angle DBC is half the measure of its intercepted arc AD. Therefore, if arc AD measures 118 degrees, angle DBC measures 59 degrees.
To find the measure of angle DBC, we need to use the properties of angles formed by intersecting chords and arcs in a circle.
In this case, we are given that the measure of arc AD is 118 degrees. By the Inscribed Angle Theorem, the measure of angle DBC is equal to half the measure of its intercepted arc, which is arc AD.
Therefore, the measure of angle DBC is 118 degrees divided by 2, which is 59 degrees.
Thus, the measure of angle DBC is 59 degrees.
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How many 1/2 inch cubes does it take to fill a box with an edge length of 1 1/2 inches
Answer:
27 1/2 inch
Step-by-step explanation:
Let â D be an acute angle such that tanD=0. 28. Use a calculator to approximate the measure of â D to the nearest tenth of a degree. What is the measurement of Please show all the work on how you got your answer.
Given that tan D = 0.28 To approximate the value of D, we can use the inverse tangent function tan⁻¹(0.28) on a calculator:
D ≈ 15.9° (rounded to one decimal place)
Therefore, the measurement of angle D to the nearest tenth of a degree is approximately 15.9°.Explanation:We know that tangent of angle D is 0.28.tan D = 0.28 To find the value of D, we need to take the inverse tangent of 0.28.
i.e, D = tan⁻¹(0.28)We use a calculator to evaluate this expression.
D ≈ 15.9° (rounded to one decimal place)
Therefore, the measurement of angle D to the nearest tenth of a degree is approximately 15.9°.
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A grocer mixes together some cashews costing $8 per kilogram with some Brazil nuts costing
$10 per kilogram. The grocer sold 12 kg if the mixture for $8.50 per kilogram. How many
kilograms of cashews were in the mixture the grocer sold?
I know the answer is 9 but how do i get that?
9 kilograms of cashews were in the mixture the grocer sold.
To solve the given problem, let x represent the number of kilograms of cashews.
Hence, the number of kilograms of Brazil nuts would be (12 - x) as the grocer sold 12 kg of the mixture.
Therefore, the cost of the cashews at $8 per kilogram is 8(x)
and the cost of the Brazil nuts at $10 per kilogram is 10(12 - x).
Hence, the cost of the mixture at $8.50 per kilogram is:
8.5*(12) = 8(x) + 10(12 - x)
We solve this equation for x:
102 = 8(x) + 120 - 10(x)
2(x)= 18
x = 9
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It costs the developer $300,000 to build each townhouse and $450,000 to build each single-family home. Write a function that can be used to determine the minimum cost.
The function for determining the minimum cost of townhouse and single-family home development is min_cost = (num_townhouses x 300000) + (num_homes x 450000).
A function is a self-contained block of code that performs a specific task. In the given problem, we need to determine the minimum cost of developing townhouses and single-family homes. Here, the cost of building a townhouse is $300,000 while the cost of building a single-family home is $450,000. We need to determine the minimum cost by multiplying the number of townhouses and single-family homes by their respective costs.
Therefore, the function for determining the minimum cost of townhouse and single-family home development is given by: min_cost = (num_townhouses x 300000) + (num_homes x 450000) where num_townhouses and num_homes are the number of townhouses and single-family homes, respectively. This function takes two arguments and returns the minimum cost for developing the given number of townhouses and single-family homes.
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How to program the quadratic formula into a ti-84 plus.
The quadratic formula can be easily programmed into a TI-84 Plus by following these simple steps. This can save a lot of time and effort when solving quadratic equations, and can help you to quickly find the roots of these equations.
The quadratic formula is a useful mathematical formula that can be programmed into a calculator like the TI-84 Plus. This formula can be used to find the roots of a quadratic equation, which can be useful in solving various types of problems. Here's how to program the quadratic formula into a TI-84 Plus:
1. Press the "PRGM" button on your calculator.
2. Select "NEW" and give your program a name (e.g. "QUAD").
3. Enter the following code:
:Prompt A,B,C
:((-B+√(B²-4AC))/(2A))->X1
:((-B-√(B²-4AC))/(2A))->X2
:Disp X1,X2
4. Save your program and exit.
This code prompts the user to enter the values of A, B, and C (which are the coefficients of the quadratic equation), and then calculates the two roots of the equation using the quadratic formula. The roots are then displayed on the screen.
Note that the "√" symbol is entered by pressing the "MATH" button and selecting "1:√( )" from the menu. Also, the "->" symbol is entered by pressing the "STO->" button.
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