the answer for the question that you are asking will possibly be 17
Answer:
-3[tex]x^{6}[/tex] + 5
Step-by-step explanation:
3 - 3[tex]x^{6}[/tex] + 2 = ?
-3[tex]x^{6}[/tex] + 5
So, the answer is -3[tex]x^{6}[/tex] + 5
Two cyclists, 54 miles apart, start riding toward each other at the same time. One cycles 2 times as fast as the other. If they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
Answer:
In summary, the faster cyclist cycles at a speed of 18 mi/h since they travel 36 of the 54 miles in 2 hours while cycling twice as fast as the slower cyclist.
Explanationn:
The two cyclists are 54 miles apart and heading toward each other.
One cyclist cycles 2 times as fast as the other. We will call the faster cyclist A and the slower cyclist B.
They meet 2 hours after starting. This means they travel a total distance of 54 miles in 2 hours.
Since cyclist, A cycles 2 times as fast as cyclist B, cyclist A travels 2/3 of the total distance, and cyclist B travels 1/3 of the total distance.
In two hours, cyclist A travels (2/3) * 54 miles = 36 miles.
We need to find the speed of cyclist A in miles per hour.
Speed = Distance / Time
So the speed of cyclist A is:
36 miles / 2 hours = 18 miles per hour
Therefore, the speed of the faster cyclist is 18 mi/h.
A round pencil is sharpened to a cone shape at both ends.calculate the volume of the pencil if the two radius is 1.2 and heights are 8cm
Answer:
A round pencil is sharpened at both ends the hight of the pencil is 16cm the length of the pencil is 1cm the radius of the two sharpened ends is 16cm 1.2cm
Calculate the volume using the value 22/7.
Step-by-step explanation:
The axis of symmetry for the function f(x) = -x² - 10x + 16 is x = -5. What are the coordinates of the vertex of the
graph?
A. (-5,41)
B. (-5,56)
C. (-5,76)
D. (-5,91)
Answer:
A
Step-by-step explanation:
the axis of symmetry passes through the vertex
its equation x = - 5 is the x- coordinate of the vertex
substitute x = - 5 into f(x) for corresponding y- coordinate
f(- 5) = - (- 5)² - 10(- 5) + 16
= - 25 + 50 + 16
= - 25 + 66
= 41
coordinates of vertex = (- 5, 41 )
7. At age 20, Heather began investing $3000 annually
into an account earning 7.5% interest compounded
annually. Lesley invested $6000 annually into a similar
account but began at age 40. They both stopped
contributing at age 65.
a) How much money did Heather and Lesley contribute
to their account?
b) What is the value of each of their investments when
they are 65 years old?
c) At age 65, when the investments mature, who has
more money and by how
much?
a) Heather contributed $135,000 and Lesley contributed $150,000 to their accounts.
b) Heather's investment is approximately $273,714.17, while Lesley's investment is approximately $191,048.18 when they are 65 years old.
c) Heather has more money by approximately $82,665.99 at age 65.
a) To find out how much money Heather and Lesley contributed to their accounts, we need to calculate the total contributions made by each of them.
Heather:
Heather started investing at age 20 and stopped at age 65, contributing $3000 annually. The number of years she contributed is (65 - 20) = 45 years.
Total contributions by Heather = $3000 × 45 = $135,000.
Lesley:
Lesley started investing at age 40 and stopped at age 65, contributing $6000 annually. The number of years she contributed is (65 - 40) = 25 years.
Total contributions by Lesley = $6000 × 25 = $150,000.
Therefore, Heather contributed $135,000 and Lesley contributed $150,000 to their respective accounts.
b) To calculate the value of their investments at age 65, we can use the formula for compound interest:
Future Value = Principal × (1 + interest rate)^number of years
Heather:
Principal (initial investment) = $3000
Interest rate = 7.5% = 0.075 (converted to decimal)
Number of years = 65 - 20 = 45
Future Value of Heather's investment = $3000 × (1 + 0.075)^45
Lesley:
Principal (initial investment) = $6000
Interest rate = 7.5% = 0.075 (converted to decimal)
Number of years = 65 - 40 = 25
Future Value of Lesley's investment = $6000 × (1 + 0.075)^25
Calculating these values:
Future Value of Heather's investment = $3000 × (1.075)^45 ≈ $273,714.17
Future Value of Lesley's investment = $6000 × (1.075)^25 ≈ $191,048.18
c) To determine who has more money at age 65 and by how much, we compare the future values of their investments.
Heather's investment value at age 65 = $273,714.17
Lesley's investment value at age 65 = $191,048.18
Therefore, Heather has more money at age 65, and the difference in their investments is approximately $273,714.17 - $191,048.18 = $82,665.99.
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Please look at photo. I’ll give good rating!
An output value for (fog)(x) is 55/(x² + 2x).
Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.
How to determine the corresponding composite function?In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;
(fog)(x) = 5/(x + 2) × 11/x
(fog)(x) = 55/x(x + 2)
(fog)(x) = 55/(x² + 2x)
For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;
x² + 2x ≠ 0
x² ≠ -2x
x ≠ -2
Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.
In conclusion, we can reasonably infer and logically deduce that x must not be equal to 0 and -2.
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Assume that Canes customer would buy. A maximum of 82000. Units of Alpha and62000 of beta assume that the raw material availability for production is limited to 162000 pounds how many units of each product should Cane produce to maximize profits
The units of each product that Cane should produce to maximize profits will be 62000 units of Beta and 7600 units of
Alpha.
Contribution margin per poundAlpha Beta
Selling price 130 90
Variable cost 78 48
Contribution margin 52 42
Pound per unit 5 2
Contribution margin per pound 10.4 21
Pound Unit
Beta 62000*2 = 124000 62000
Alpha 38000 38000/5 = 7600
Total 162000
Maximum contribution margin = (38000*10.4+124000*21) = 2999200
Highest price = 10.4+5 = 15.40 per pound
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quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 62
minutes with a mean life of 606
minutes.
If the claim is true, in a sample of 99
batteries, what is the probability that the mean battery life would be greater than 619
minutes? Round your answer to four decimal places.
Answer:
Step-by-step explanation:
Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over x = −1.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−5, 5), M′(−2, 3), O′(−3, 7)
N′(3, 2), M′(0, 1), O′(1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
To determine the vertices of the image N'M'O' after reflecting triangle NMO over the line x = -1, we need to apply the reflection transformation to each vertex.
For a reflection over the line x = -1, we can find the image of a point (x, y) by finding its reflection as (2(-1) - x, y).
Applying this transformation to each vertex of triangle NMO, we get:
N' = (2(-1) - (-5), 2) = (5, 2)
M' = (2(-1) - (-2), 1) = (2, 1)
O' = (2(-1) - (-3), 3) = (3, 3)
The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).
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7. The Taylor Rule states that the central bank should set the short-term nominal interest rate (i)
based on the inflation gap [the difference between inflation (3.14) and desired inflation (3.14*)] and the
output gap (the percentage difference between real GDP (Y) and potential GDP (Y*) An
example of a Taylor Rule would be the formula
i - 3.14 = 1.5 +0.5(3.14-3.14*) +0.5 (Y-Y*/Y*)
The term on the left-hand side is the real interest rate. Consider the following table
Inflation rate (3.14), %
Target inflation rate (3.14*), %
Output gap, %
Real interest rate
Nominal interest rate
Base Scenario Scenario B Scenario C
4.0
20
2.0
20
0.0
20
20
20
00
a. Fill in the real and nominal interest rates chosen by the policy maker in the base scenano
b. How does scenario B differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move the inflation rate toward its target?
c. How does scenario C differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move output toward the potential level?
d. Suppose a new chair of the central bank is appointed and she switches to a new policy rule of
the form given in the next equation. Recalculate the real and nominal interest rates for the
three scenarios. What has been the effect of the change in weights?
i-3.14=1.5 +0.75(3.14-3.14*) +0.25(Y-Y*/Y*)
The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%
a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.
b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).
Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).
Now, let's calculate the real interest rate.
Real interest rate in base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)
= 19.22%.
The real interest rate has moved in the direction to move inflation rate towards its target.
c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.
Inflation gap is 0% in both the scenarios
Inflation rate is 3.14% and in scenario C, inflation rate is 2%.
Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)
= 20.15%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.
The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.
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Select the correct answer.
Omar has a gift card for $40.00 at a gift shop. Omar wants to buy a hat for himself for $13.50. For his friends, he would like to buy souvenir bracelets, which are $3.25 each. All prices include taxes.
Which inequality can be used to solve for how many bracelets Omar can buy?
A.
3.25x + 13.50 ≤ 40
B.
3.25x + 13.50 ≥ 40
C.
13.50x + 3.25 ≤ 40
D.
13.50x + 3.25 ≥ 40
Answer:
A.
3.25x + 13.50 ≤ 40
Step-by-step explanation:
A shop sells phone covers in 3 colours: red, blue and green. There are 4 more green covers than blue covers. There are twice as many blue covers as red covers. There are 104 covers altogether. how many green covers are there
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
14Y - 7y = 35. solve for y
Answer:
y = 5
Step-by-step explanation:
[tex]14y-7y=35\\7y=35\\y=5[/tex]
14 minus 7 is 7
7Y is equal to 35
divide both sides by 7 is equal to 5
I need help asap please!!!
The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and
What is sine of angles?he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle. It is defined as the length of the opposite side divided by the length of the hypotenuse
The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360
2∅ 2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720
sin 2∅ = sin0 = 0; Sin90=1; sin180=0; sin240= -0.8660; sin270 = -1;
Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397
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Five clubs at Johnson School raised $2000. The incomplete circle graph shows what percent of the money was raised by each club. How much money did the Math Club raise?
$500
$600
$200
$400
$300
The Math Club raised $400.
To find out how much money the Math Club raised, we need to determine the percentage of the total amount raised that corresponds to the Math Club's portion.
Let's assume the Math Club raised "x" amount of money. The total amount raised by all five clubs is $2000.
According to the incomplete circle graph, the Math Club's percentage is missing, but we know the percentages for the other clubs: Computer Club raised 15%, Gardening Club raised 18%, Art Club raised 30%, and Spanish Club raised 17%.
To find the missing percentage for the Math Club, we subtract the percentages of the other clubs from 100%:
Missing percentage = 100% - (15% + 18% + 30% + 17%) = 100% - 80% = 20%
Now we can set up a proportion to determine the amount raised by the Math Club:
(x / $2000) = 20% / 100%
Cross-multiplying:
x = ($2000 * 20%) / 100%
Simplifying:
x = $400
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Find the numbers with the following property three times the sum of four and a number is less than seven times the same number
Let's represent the number with the variable "x". According to the given property, we can write the following equation:
3(x + 4) < 7x
Now, let's solve this inequality to find the range of numbers that satisfy the property.
3x + 12 < 7x
Subtract 3x from both sides:
12 < 4x
Divide both sides by 4 (since the coefficient of x is 4):
3 < x
So, the range of numbers that satisfy the given property is x > 3.
Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:
Which of the following steps indicates the addition property of equality while solving the equation –1 – 6x = x – 15?
A) x = 14∕2
B) –1 – 6x = x – 15
C) 23 – 6x – 24 = x – 15
D) –1 – 6x + 15 = x – 15 + 15
Answer:
-1 - 6x = x - 15
Add 15 to both sides using the addition property of equality.
14 - 6x = x
14 = 7x
2 = x
D) -1 - 6x + 15 = x - 15 + 15
Answer and Step-by-step explanation:
Please refer to the photo for the solution!
Aright cylinder with a lateral area of 75 units squared and a height of 6 units has a surface area of 100 units squared (if the SA is rounded to the nearest whole).
False
True
True, the surface area of the cylinder is 100units²
What is surface area of cylinder?The surface area of a three-dimensional object is the sum of the area of all the outer surfaces, it is also measured in square units.
The surface area of a cylinder is expressed as;
SA = 2πrh + 2πr²
where 2πr² is the area of the bases
2πrh = lateral area
75 = 2 × 3.14 × 6 × r
r = 75/37.68
r = 1.99 unit
base area = 2 × 3.14 × 1.99²
= 25 units ( nearest whole number)
The surface area = 75+25
= 100units²
Therefore the surface area of the cylinder to nearest whole number is 100units².
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Identify which year’s population will hit zero
The year when the population becomes zero is 2020.2
Which year the population will reach zero?We know that the population decreases at a constant rate, so it is modeled by a line:
y = ax + b
Where a is the slope and b is the y-intercept.
Here we have two points (2010, 5100) and (2012, 4100)
The slope is the quotient between the differences of the y-values and the x-values, then:
a = (4100 - 5100)/(2012 - 2010) = -1000/2 = -500
We can write.
y = -500*x + b
We know that when x = 2010, y = 5100, replacing that we get:
5100 = -500*2010 + b
b = 5100 + 500*2010 = 1,010,100
Then:
y = -500*x + 1,010,100
And it is zero when:
0 = -500*x + 1,010,100
x = 1,010,100/500
x = 2020.2.
That is the year when the pópulation becomes zero.
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Enter the number that belongs in the green box
The angle C in the triangle is 34.05 degrees.
How to use cosine law to find angles in a triangle?
The sum of angles in a triangle is 180 degrees. The angle in a triangle can be found using cosine law as follows:
Therefore, let's find the unknown angle in the triangle as follows;
c² = a² + b² - 2ab cos C
Hence,
4² = 5² + 7² - 2 × 7 × 5 cos X
16 = 25 + 49 - 70 cos X
16 = 74 - 70 cos X
16 - 74 = -70 cos X
-58 = -70 cos X
cos X = 58 / 70
X = cos⁻¹ 0.82857142857
X = 34.0478785629
X = 34.05 degrees
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Students at a major university in Southern California are complaining about a serious housing crunch. They say that many of the university's students have to commute too far to school because there is not enough housing near campus. University officials perform a study, which is reported in the school newspaper. The report contains the following histogram summarizing the commute distances for a sample of 24 students at the university.
The histogram in the school newspaper report provides a visual summary of the commute distances for a sample of 24 students at the major university in Southern California, supporting the students' claims of a housing crunch and long commutes.
According to the study reported in the school newspaper, a histogram was used to summarize the commute distances for a sample of 24 students at the major university in Southern California.
A histogram is a graphical representation that displays the distribution of a dataset by organizing it into intervals or bins along the horizontal axis and showing the frequency or count of observations in each bin on the vertical axis.
The histogram provides valuable insights into the commute distances of the university's students and helps assess the housing crunch issue.
By analyzing the histogram, university officials can gain a better understanding of the distribution of commute distances and identify any patterns or concentrations that may indicate the severity of the problem.
The histogram should provide information about the range of commute distances and the frequency of students within each interval.
It allows university officials to visualize the distribution and assess whether there is a significant portion of students facing long commutes due to the lack of housing near campus.
The officials can use the histogram to determine the central tendency measures such as the mean or median commute distance, which can provide a representative value of the typical commute for the student population.
Additionally, they can examine the spread or variability of the data to understand if there are extreme cases or if most students face similar distances.
By studying the histogram, university officials can gather quantitative evidence to support the students' claims of a housing crunch.
This information can guide their decision-making process in addressing the issue, such as implementing policies to increase affordable on-campus housing options or exploring partnerships with nearby housing providers.
In summary, the histogram in the school newspaper report provides a visual representation of the commute distances of a sample of 24 students at the university.
It serves as a valuable tool for university officials to analyze the housing crunch problem and make informed decisions to alleviate the commuting burden on the students.
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Find the slope and the y-intercept of the following linear equation. 5. 3x + 2y = 14
Answer:
slope = - [tex]\frac{3}{2}[/tex] , y- intercept = 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3x + 2y = 14 ( subtract 3x from both sides )
2y = - 3x + 14 ( divide through by 2 )
y = - [tex]\frac{3}{2}[/tex] x + 7 ← in slope- intercept form
with slope m = - [tex]\frac{3}{2}[/tex] and y- intercept c = 7
See picture dfown below for refgerecnce
The value of the quadratic function y = x² - 4x + 3 is determined by substituting the given value of x into the equation and performing the necessary calculations.
1. Start with the quadratic function: y = x² - 4x + 3.
2. Determine the value of x for which you want to find the value of y.
3. Substitute the given value of x into the equation.
4. Perform the necessary calculations to simplify the expression.
5. Evaluate the expression to find the value of y.
For example, let's find the value of y when x = 2:
1. Start with the quadratic function: y = x² - 4x + 3.
2. We want to find the value of y when x = 2.
3. Substitute x = 2 into the equation: y = (2)² - 4(2) + 3.
4. Simplify the expression: y = 4 - 8 + 3.
5. Perform the necessary calculations: y = -1.
6. Therefore, when x = 2, the value of the quadratic function y = x² - 4x + 3 is -1.
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what is the result of converting 2.3 miles into yards ? remenber that 1 mile=1760 yards.
4048 yards is the answer
Step-by-step explanation:
2.3 × 1760
PLEASE HELP AS SOON AS POSSIBLE
Answer:
B
Step-by-step explanation:
Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.
Natalie is selling fruit at the Saturday market. She has a
otal of 48 pears that she wants to sell. She makes bags of
pears and sells them for $5 per bag. In which equation
oes b represent the number of bags of pears?
If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.
To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:
b = total_number_of_pears / pears_per_bag
In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.
Given that Natalie has a total of 48 pears, we can substitute the value into the equation:
b = 48 / pears_per_bag
Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.
Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:
b = 48 / 4
Simplifying the equation gives:
b = 12
So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.
It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.
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Shireen had a nap for 2 h. After her nap, she played badminton for 1/2h and swam for 1/5h.
(a) How long did Shireen exercise?
(b) How much more time did Shireen spend on her nap than on
her exercise?
Select the expression that is equivalent to (n²-25)
A. n² +10n - 25
B. n²-10-25
C. (n+5)(n-5)
D. (n-5) ²
Answer:
C. (n+5)(n-5)
Step-by-step explanation:
Select the expression that is equivalent to (n²-25)
Let's check each option. A and B are wrong, so we only check C & D.
C. (n + 5) (n - 5)
n² - 5n + 5n - 25
n² - 25
D. (n - 5)²
(n - 5) (n - 5)
n² - 5n - 5n + 25
n² - 10n + 25
So, the correct answer is C. (n+5)(n-5)
Factorise the formula y = 4x² + 16x +15 in the form y = (2x +...)(2x + ...). help
Answer:
y = (2x + 5)(2x + 3)
Step-by-step explanation:
y = 4x² + 16x + 15
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × 15 = 60 and sum = + 16
the factors are + 10 and + 6
use these factors to split the x- term
y = 4x² + 10x + 6x + 15 ( factor the first/second and third/fourth terms )
y = 2x(2x + 5) + 3(2x + 5) ← factor out (2x + 5) from each term
y = (2x + 5)(2x + 3)
since multiplication is commutative , then could be
y = (2x + 3)(2x + 5)
Toula owns the Pita Pan restaurant. She needs to order supplies for the upcoming weekend rush. She needs 150 bags of pita bread. The bread come in crates of 50, and each crate costs $15.00. She also needs 65 containers of hummus dip. There are 5 containers in a box, and each box costs $20.00 What expressions can Toula use to determine how much the pita bread and hummus dips will cost? What will the total be?
The total cost of the pita bread and hummus dips will be $305.00.
To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:
Cost of pita bread:
Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates
Cost of each crate = $15.00
Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00
Cost of hummus dips:
Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes
Cost of each box = $20.00
Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00
Therefore, the expressions Toula can use to determine the costs are:
Cost of pita bread = 3 crates × $15.00/crate
Cost of hummus dips = 13 boxes × $20.00/box
The total cost will be the sum of the costs of pita bread and hummus dips:
Total cost = Cost of pita bread + Cost of hummus dips
Total cost = $45.00 + $260.00
Total cost = $305.00
Therefore, the total cost of the pita bread and hummus dips will be $305.00.
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What is the volume of the triangular prism?
3 in.
15 in.
13 in.