The solution to the given equations is n = -8, obtained by simplifying and manipulating the equations to isolate the variable n through a series of steps.
The given equations are:
Equation 1: m = 8 + 2n
Equation 2: 4m = 4 + 4n
To solve the equations, we follow the steps provided:
Step 1: Multiply both sides of Equation 2 by -4 to eliminate the coefficient of m:
-4m = -4(8 + 2n)
Step 2: Simplify Equation 2:
-4m = -32 - 8n
Step 3: Combine like terms on the right side of Equation 2:
-4m = 4 + 4n
Step 4: Add 4m to both sides of Equation 3 to eliminate the variable m:
-4m + 4m = -32 - 8n + 4n
0 = -32 - 4n
Step 5: Add 32 to both sides and divide by -4 to isolate n:
32 = -4n
n = -8
Therefore, the solution to the equations is n = -8.
Learn more about Variables here: brainly.com/question/29583350
#SPJ11
Complete Question:
Equation 1: m = 8 + 2n Equation 2: 4m = 4 + 4n Step 1: −4(m) = −4(8 + 2n) 4m = 4 + 4n Step 2: −4m = −32 − 8n 4m = 4 + 4n Step 3: −4m + 4m = −32 − 8n + 4n Step 4: 0 = −32 − 4n Step 5: n = − 8 In which step did the student first make an error?
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.
To learn more about fraction click here:
brainly.com/question/10354322
#SPJ11
A side of the triangle below has been extended to form an exterior angle of
67º. Find the value of x.
52
xº
67°
The value of x in the given triangle is 61 degrees.
In the given triangle, we have an exterior angle of 67 degrees formed by extending one side of the triangle. Let's label the interior angles of the triangle as A, B, and C, with angle A being the exterior angle of 67 degrees.
According to the property of exterior angles of a triangle, the exterior angle is equal to the sum of the two interior opposite angles. Therefore, we have the equation:
A = B + C
Substituting the given values, we have:
67° = B + C
Now, we can observe that angle C is the interior angle labeled as x degrees. So we rewrite the equation as:
67° = B + x
Since the sum of the interior angles in a triangle is always 180 degrees, we have the equation:
A + B + C = 180°
Substituting the given values and rearranging the equation, we get:
67° + B + x = 180°
Simplifying further:
B + x = 180° - 67°
B + x = 113°
Now, we can equate the two expressions for B + x:
B + x = 113°
Since B is given as 52 degrees, we can substitute this value:
52° + x = 113°
Subtracting 52 from both sides, we find:
x = 113° - 52°
x = 61°
Therefore, the value of x in the given triangle is 61 degrees.
Learn more about exterior angle here:
https://brainly.com/question/28835566
#SPJ11
What number represents the same amount as 777 hundreds ~+~0 + 0space, plus, space, 0 tens +~100+ 100plus, space, 100 ones?
The number that represents the same amount as 777 hundreds, plus 0 tens, plus 100 ones is 77700. Adding 100 to 77700 gives us the result of 77800.
First, we have 777 hundreds. Since one hundred is equal to 100, we multiply 777 by 100 to get 77700. This represents the value of 77700 in terms of hundreds.
Next, we have 0 tens. Tens represent the digit in the tens place, and in this case, it is 0. So, we don't need to add anything for the tens place.
Finally, we have 100 ones. This means we simply add 100 to the previous result, which is 77700. Adding 100 to 77700 gives us the final result of 77800.
To learn more about digit click here:
brainly.com/question/30142622
#SPJ11
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.
To know more about number, visit
https://brainly.com/question/3589540
#SPJ11
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.
To learn more about lemonade: -brainly.com/question/24155405
#SPJ11
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.
Learn more about columns here
https://brainly.com/question/30482584
#SPJ11
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%.
To learn more about markup amount visit:
brainly.com/question/20356719
#SPJ11
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.
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.
Learn more about radius here: brainly.com/question/30087126
#SPJ11
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.
To learn more about average click here, brainly.com/question/2426692
#SPJ11
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.
To know more about discount amount here: brainly.com/question/29181625
#SPJ11
#Complete/Translate Question:- The price of a shirt is marked $28 if a 20% discount is applied, what would the price be?
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.
To know more about volume visit:
brainly.com/question/28058531
#SPJ11
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.
To learn more about substitution method click here:
brainly.com/question/22340165
#SPJ11
30-60-90 triangle find the side length if hypotenuse 16
In a 30-60-90 triangle, the ratio of the side lengths is as follows:
The length of the shorter leg is x.
The length of the longer leg (opposite the 60-degree angle) is x√3.
The length of the hypotenuse is 2x.
Given that the hypotenuse is 16, we can set up the equation:
2x = 16
Dividing both sides of the equation by 2:
x = 8
Therefore, the length of the shorter leg is 8.
To find the length of the longer leg (opposite the 60-degree angle), we can multiply the length of the shorter leg by √3:
Longer leg = x√3 = 8√3
So, the length of the longer leg is 8√3.
In summary, in a 30-60-90 triangle with a hypotenuse of 16, the shorter leg is 8 and the longer leg (opposite the 60-degree angle) is 8√3.
To know more about the ratio:- https://brainly.com/question/13419413
#SPJ11
Which of these data sets could best be displayed on a dot plot? 16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97 0.012, 0.078, 0.093, 0.147, 0.187 721, 722, 722, 723, 724, 724, 724, 725, 727, 728, 730 1.3, 1.9, 2.5, 2.7, 2.7, 3.5, 4.8, 5.3, 7.9, 9.0 Done
A dot plot is a type of graph that can be used to represent numerical data. It displays data using a series of dots, with each dot representing a single data point.
The dots are placed on a horizontal number line, with the value of each dot corresponding to the numerical value of the data point it represents.
A dot plot is most useful when displaying small sets of data.
And
In the given options, the set of numbers 16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, and 97 can best be displayed on a dot plot.
To know more about graph, visit
https://brainly.com/question/17267403
#SPJ11
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.
Learn more about solving coin problems here: brainly.com/question/28030993
#SPJ11
Use rhombus DEFG with GE = 42, DH = 16 - find GH THEN with, EF = 13,
DF = 18 to find EH
In rhombus DEFG, we are given that GE is 42 and DH is 16. We need to find GH. Additionally, we are given EF as 13 and DF as 18, and we need to find EH.
Finding GH:
In a rhombus, opposite sides are equal in length. Since GE is given as 42, GH is also equal to 42.
Finding EH:
In a rhombus, the diagonals bisect each other at right angles, forming four right triangles. We can use the Pythagorean theorem to find EH. Using the given information, we have EF as 13 and DF as 18. The diagonals DE and FG are equal in length, so EF and DF are the lengths of the two halves of diagonal DE.
To find EH, we can consider one of the right triangles formed by the diagonals. Let's take triangle DEF.
In triangle DEF, we have:
DE = 2 * EF = 2 * 13 = 26 (because EF is half of DE)
DF = 18
We can use the Pythagorean theorem to find EH:
EH^2 = DE^2 - DF^2
EH^2 = 26^2 - 18^2
EH^2 = 676 - 324
EH^2 = 352
To find EH, we take the square root of both sides:
EH = √352
EH ≈ 18.77
Therefore, EH is approximately 18.77 units.
In summary, GH in rhombus DEFG is equal to 42 units, as opposite sides of a rhombus are equal. To find EH, we use the Pythagorean theorem in one of the right triangles formed by the diagonals. Given EF as 13 and DF as 18, we calculate EH to be approximately 18.77 units. The Pythagorean theorem allows us to find unknown side lengths in right triangles, and applying it in the context of the rhombus helps us determine the lengths of GH and EH.
Learn more about triangles here:- brainly.com/question/2773823
#SPJ11
To give their animals essential minerals and nutrients, farmers and ranchers often have a block of salt—called "salt lick"—available for their animals to lick. A rancher is ordering a box of cube-shaped salt licks. The edge lengths of each salt lick are 3/5 foot. What is the volume of each salt lick? Volume = length x width x height
The volume of each cube-shaped salt lick is 0.216 cubic feet.
1. The given information states that the edge lengths of each salt lick are 3/5 foot.
2. To calculate the volume of a cube, we need to multiply the length, width, and height of the cube. However, in the case of a cube, all three dimensions are the same because each side of a cube has equal length.
3. In this case, the edge length of each salt lick is 3/5 foot. Since all edges of the cube have the same length, we can consider this length as the length, width, and height of the cube.
4. To find the volume, we need to raise the edge length to the power of 3 (cubed). Mathematically, it can be represented as follows:
Volume = (Edge length)³
Substituting the given edge length of 3/5 foot:
Volume = (3/5)³
Volume = (3/5) * (3/5) * (3/5)
Volume = 27/125
5. The result of the calculation is 27/125. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 1 in this case.
Dividing both 27 and 125 by 1:
Volume = 27/125
Volume = 0.216
6. Therefore, the volume of each cube-shaped salt lick is 0.216 cubic feet.
Learn more about volume : https://brainly.com/question/28058531
#SPJ11
Find the circumference and area of the circle. Use 3. 14 for. Round to the nearest hundredth if necessary. 3 m
The circumference of the circle is 18.84 meters and the area is 28.26 square meters, where C is the circumference, π is a mathematical constant approximately equal to 3.14,
The circumference of a circle is the distance around it. It is calculated by using the formula C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. The radius is the distance from the center of the circle to any point on the edge.
In this case, the radius is 3 meters, so the circumference is C = 2πr = 2 × 3.14 × 3 = 18.84 meters.
The area of a circle is the amount of space it takes up. It is calculated by using the formula A = πr², where A is the area, π is the same mathematical constant as before, and r is the radius again.
In this case, the radius is 3 meters, so the area is A = πr² = 3.14 × 3² = 28.26 square meters.
To round to the nearest hundredth, we can simply add two zeros to the end of the decimal places. This gives us a circumference of 18.840 meters and an area of 28.260 square meters.
To know more about decimal click here
brainly.com/question/29775125
#SPJ11
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.
To know more about train tickets:- https://brainly.com/question/1048736
#SPJ11
(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.
Learn more about Dividing both sides here:
https://brainly.com/question/17436880
#SPJ11
What simple interest rate is required for $4790 to grow to $6500 in 9 years? Round to the nearest whole percent.
Therefore, the required simple interest rate is approximately 3.8%.
To find the required simple interest rate, we can use the formula:
Simple Interest = Principal * Interest Rate * Time
We know the principal (P) is $4790, the final amount (A) is $6500, and the time (T) is 9 years. We need to find the interest rate (R).
First, let's calculate the interest (I):
I = A - P = $6500 - $4790 = $1710
Now we can substitute the values into the formula and solve for the interest rate:
I = P * R * T
$1710 = $4790 * R * 9
Dividing both sides by ($4790 * 9):
R = $1710 / ($4790 * 9) ≈ 0.038 (rounded to three decimal places)
To convert this to a percentage, we multiply by 100:
R ≈ 0.038 * 100 ≈ 3.8
Therefore, the required simple interest rate is approximately 3.8%.
To learn more about simple interest rate visit:
brainly.com/question/14599912
#SPJ11
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
To know more about Newton's law , visit ;
https://brainly.com/question/28171613
#SPJ11
Igor, whose eye height is 4.5 ft., wishes to find the height of an oak tree out in front of his castle. He places a mirror on the ground between himself and the tree. He is now 5 ft. from the crosshairs of the mirror and the mirror is 70 ft from the tree. How tall is the oak tree? Show ALL work and include a diagram as part of the answer
The height of the oak tree is approximately 4.846 ft.
To find the height of the oak tree, we can use similar triangles and the concept of vertical angles. Let's set up the problem and include a diagram to illustrate the situation.
Let's assume the height of the oak tree is represented by h.
We have the following information:
Igor's eye height: 4.5 ft
Distance between Igor and the mirror: 5 ft
Distance between the mirror and the oak tree: 70 ft
We can create a right triangle with Igor's eye height, the distance between Igor and the mirror, and the height of the tree. Let's label the points in the diagram as follows:
|\
| \
h | \ <-- Height of the oak tree
| \
| \
|-----\
5 ft 70 ft
Now, using the concept of similar triangles, we can set up the following proportion:
(h + 4.5 ft) / 5 ft = h / 70 ft
Cross-multiplying, we get:
70(h + 4.5 ft) = 5h
70h + 315 ft = 5h
70h - 5h = -315 ft
65h = -315 ft
Dividing both sides by 65, we find:
h = -315 ft / 65
h ≈ -4.846 ft
Since height cannot be negative, we can disregard the negative value. Therefore, the height of the oak tree is approximately 4.846 ft.
Please note that negative values in this context indicate an error in the calculation or a discrepancy in the given measurements.
Learn more about height here:
https://brainly.com/question/29131380
#SPJ11
John buys 20 bunches of bananas for N5. He sells them for N6.50. What is the percentage profit
John's percentage profit can be calculated by determining the difference between his selling price and the cost price, dividing that by the cost price, and then multiplying by 100. In this case, John's percentage profit is 30%.
To calculate the percentage profit, we need to find the difference between the selling price and the cost price. John buys 20 bunches of bananas for N5 each, so his total cost price is N5 multiplied by 20, which equals N100. He sells each bunch for N6.50, so his total selling price is N6.50 multiplied by 20, which equals N130.
To calculate the profit, we subtract the cost price from the selling price: N130 - N100 = N30. The profit is N30.
To find the percentage profit, we divide the profit by the cost price and multiply by 100: (N30 / N100) * 100 = 30%. Therefore, John's percentage profit on the sale of 20 bunches of bananas is 30%.
This means that John made a 30% profit on his investment. For every N100 he spent on purchasing the bananas, he earned an additional N30 when selling them.
Learn more about percentage profit here:
https://brainly.com/question/30938251
#SPJ11
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.
Learn more about Pythagorean theorem here
https://brainly.com/question/14930619
#SPJ4
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
To know more about plane please visit :
https://brainly.com/question/29765572
#SPJ11
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.
Learn more about Standard Deviation here:
https://brainly.com/question/475676
#SPJ11
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).
To know more about Expression , visit ;
https://brainly.com/question/1859113
#SPJ11
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
To know more about combinations visit :-
https://brainly.com/question/31586670
#SPJ11
