The flow rate in a device used for air quality measurement depends on the pressure drop x (inches of water) across the device's filter. Suppose that for x values between 5 and 20, these two variables are related according to the simple linear regression model with true regression line y = -0.17 + 0.095x.
A) What is the true average flow rate for a pressure drop of 10 in. and drop of 15 in.?
B) What is the true average change in flow rate associated with a 1 inch increase in pressure drop?
C) What is the average change in flow rate when pressure drop decreases by 5 in.?

Answers

Answer 1

Answer:

A. 0.78 and 1.255.

B.  0.095

C. -0.475

Step-by-step explanation:

The given regression line is

y=-0.17+0.095x

A.

The true average flow rate for a pressure drop of 10 inch can be computed by putting x=10 in above equation.

y=-0.17+0.095*10

y=-0.17+0.95

y=0.78

The true average flow rate for a pressure drop of 10 inch is 0.78.

The true average flow rate for a pressure drop of 15 inch can be computed by putting x=15 in above equation.

y=-0.17+0.095*15

y=-0.17+1.425

y=1.255

The true average flow rate for a pressure drop of 15 inch is 1.255.

B.

The slope represents average change in y due to unit change in x.

So, the true average change in flow rate associated with a 1 inch increase in pressure drop is 0.095(1)= 0.095.

C.

When pressure drops decreases by 5 in. then the average change in flow rate is 0.095(-5)=-0.475.

Answer 2

The flow rate in the device is an illustration of average rates.

The true average flow rates when pressure drops 10 and 15 in are 0.78 and 1.255 respectivelyThe true average flow rates associated to a 1 in pressure increment is 0.095A decrement of -5 in is out of the domain of the function

The function is given as:

[tex]\mathbf{y = -0.17 + 0.095x}[/tex]

(a) The true average flow rate when pressure drops 10 and 15 in

When x = 10, we have:

[tex]\mathbf{y = -0.17 + 0.095 \times 10}[/tex]

[tex]\mathbf{y = 0.78}[/tex]

When x = 15, we have:

[tex]\mathbf{y = -0.17 + 0.095 \times 15}[/tex]

[tex]\mathbf{y = 1.255}[/tex]

Hence, the true average flow rates when pressure drops 10 and 15 in are 0.78 and 1.255 respectively

(b) The true average flow rate when pressure increases by 1 in

This simply represents the slope of the function.

The function is given as:

[tex]\mathbf{y = -0.17 + 0.095x}[/tex]

A linear regression equation is represented as:

[tex]\mathbf{y = b + mx}[/tex]

Where m represents the slope

By comparison:

[tex]\mathbf{m = 0.095}[/tex]

Hence, the true average flow rates associated to a 1 in pressure increment is 0.095

(c) The average change in flow rate when pressure drops decreases by 5 in

The domain of the function is given as:

[tex]\mathbf{x = 5\ to\ 20}[/tex]

A decrement of -5 in means: x = -5

This is out of the domain of the function

Hence, the average change at a decrement of 5 in cannot be calculated

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Related Questions

The number of customers that visit a local small business is 51,200 and has been continuously declining at a rate of 3.8% each year. What is the approximate number of
customers that visit the business in 14 years?

Answers

Answer:

Final amount of customers =30141.44

Step-by-step explanation:

Amount of customer remaining

A= p(1-r/n)^(nt)

P= initial amount of customers

R= rate but it's a negative rate

N= number of times

T= number of years

A= final amount of customers

A= p(1-r/n)^(nt)

A= 51200(1-0.038/14)^(14*14)

A= 51200(1-0.0027)^196

A= 51200(0.9973)^196

A= 51200(0.5887)

A= 30141.44

What is the distance between point (6, -1) and point (5, 3) rounded to the nearest tenth?

Answers

Answer:

The answer is

4.1 units

Step-by-step explanation:

The distance between two points can be found using the formula

[tex] \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } [/tex]

where

( x1 , y1) and ( x2 , y2) are the points

From the question

The points are (6, -1) and (5, 3)

The distance between the points is

[tex] \sqrt{( {6 - 5})^{2} + ({ - 3 - 1})^{2} } [/tex][tex] = \sqrt{ {1}^{2} + ( { - 4})^{2} } [/tex][tex] = \sqrt{1 + 16} [/tex][tex] = \sqrt{17} [/tex]

= 4.123105

We have the final answer as

4.1 units

Hope this helps you

part 6: please assist me with these problems​

Answers

Answer:  12) 34°     13) 90°

Step-by-step explanation:

[tex]\text{Law of Sines:}\quad \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

12) Given: a = 10.2,  b = 6.8, A = 122°

[tex]\dfrac{\sin 122^o}{10.2}=\dfrac{\sin B}{6.8}\\\\\\\dfrac{6.8\sin 122^o}{10.2}=\sin B\\\\\\\sin^{-1}\bigg(\dfrac{6.8\sin 122^o}{10.2}\bigg)=B\\\\\\34.4^o=B[/tex]

*****************************************************************************

Law of Cosines: a² = b² + c² - 2bc · cos A

Note: The letters can be swapped

13) Given: a = 3,  b = 4,  c = 5, C = ???

3² = 4² + 5² - 2(4)(5) · cos C

9  = 16 + 25 - 40 cos C

9 = 41 - 40 cos C

-32 = -40 cos C

0.8 = cos C

90° = C

a kayak travels in a lake at an average speed of 35m/min. if the perimeter of a lake was 8400 m how many hours does it take for the kayak to travel around the whole lake

Answers

Answer:

I think Its 4hrs

Step-by-step explanation:

8400m÷ 35m = 240mins

240mins= 4hrs

rw/6+y=f And I have to solve for y so I’m confused on how to isolate it.

Answers

Answer:

The answer is

[tex]y = \frac{rw - 6f}{f} [/tex]

Step-by-step explanation:

[tex] \frac{rw}{6 + y} = f[/tex]

Cross multiply

We have

f(6 + y) = rw

6f + fy = rw

Move 6f to the right side of the equation to make fy stand alone

That's

fy = rw - 6f

Divide both sides by f to isolate y

That's

[tex] \frac{fy}{f} = \frac{rw - 6f}{f} [/tex]

We have the final answer as

[tex]y = \frac{rw - 6f}{f} [/tex]

Hope this helps you

Find the recursive formula for this general term formula. [tex]t_{n} = n!/9^{-(n-1)}, n\geq 3[/tex]

Answers

Please give me a couple of minutes, I’ll answer in the comment section

Simply the answer and write it as a mixed number.

Answers

Answer:

The answer is 1 4/7

Step-by-step explanation:

First you will want to take the mixed number and make it unmixed which will make it 11/3 divided by 7/3. Then you do the keep change flip method to divide fraction which makes it 11/3 times 3/7 then you multiply across and get 33/21 which as a mixed number is 1 12/21 but you can simplify it to be 1 4/7.

The answer is the first one which is 1 4:7

A right triangle has vertices (−7,9),(3,9),(−7,−15). Find the perimeter of the triangle.

Answers

The perimeter of a triangle is 60 units if the right triangle has the vertices (-7, 9), (3, 9), (-7, -15).

What is meant by perimeter?

The perimeter calculation has various practical uses. A calculated perimeter is the length of fencing required to encircle a yard or garden. The circumference (perimeter) of a wheel/circle specifies how far it will roll in one revolution.

If the lengths of the triangle's sides are a, b, and c, the perimeter is the sum of their lengths:

P = a + b + c

The distance formula can be used to calculate any of the side lengths. However, because two of the sides are parallel to the axes, their lengths may be simply calculated by subtracting coordinates.

If the points are designated A, B, and C in that sequence, the two right-angle sides are as follows:

c = AB

= 3 -(-7)

= 10

b = AC

= 9 -(-15)

= 24

The Pythagorean theorem states that the third side of the relation can be found:

a² = b² +c²

a² = 10² +24² = 676

a=√676

a= 26

Now we can plug these numbers into the perimeter formula:

P = a + b + c = 26 + 24 + 10

P = 60

As a result, the perimeter of a triangle is 60 units.

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100 megatons+234 help please

Answers

Answer:

we know,

1 megaton=1000kg

100 megaton=100000

now,

total weight=100000+234

=100234.

g In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that: (a) the first question she gets right is the 5th question

Answers

Answer:

81 / 1024

Step-by-step explanation:

First, let's find the total number of ways that Nancy can choose random choices for the questions. This would be 4 * 4 * 4 * 4 * 4 = 4⁵ = 1024 because there are 4 choices and 5 questions. In order for first question she gets right to be the 5th question, she has to get the first 4 questions wrong. Therefore, since there are 4 choices for each question and only 1 of them is right, she has 4 - 1 = 3 options for the first 4 questions and only 1 option for the 5th one, so the total number of "successful" ways Nancy can do this would be 3 * 3 * 3 * 3 * 1 = 81. Therefore, the probability is 81 / 1024.

determine whether y = 4x+5 and y= 1/4x-2 are perpendicular

Answers

Answer:

No, they are not perpendicular

Step-by-step explanation:

Perpendicular lines will have opposite reciprocal slopes, meaning that the slopes will have opposite signs and be the reciprocals of each other.

We can see that the slopes of the lines are not opposite reciprocals.

4 and 1/4 are not opposite reciprocals because they do not have opposite signs.

add or subtract as indicated and write the result in standard form 3i+(-6-i)

A:6-4i
B:-6+2i
C:6-2i
D:-6+4i

Answers

Answer:

B: -6+2i

Step-by-step explanation:

3i + (-6 - i) =                ⇒ open parenthesis3i - 6 - i =                ⇒ simplify-6 + 2i                     ⇒ answer in standard form of a+bi

Luke is 5 years younger than 3 times Sydney's age, s. In this situation, what does 3s represent?
0 Luke's age
O Sydney's age
o three times Luke's age
O three times Sydney's age

Answers

Answer:

Step-by-step explanation:

'3s' represents 'three times Sydney's age.'

Answer:

three times Sydney's age

Step-by-step explanation:

i took a test on this

pt 2 6-7 Pleaseee Helpp

Answers

Answer:

w = 15

Step-by-step explanation:

5      

        x   ___w___  =      3 x  5

                   5

w = 15

Hi there! Hopefully this helps!

----------------------------------------------------------------------------------------------------

Answer: w = 15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\frac{w}{5} = 3[/tex]

Multiply both sides by 5.

[tex]w = 3 \times 5[/tex]

Multiply 3 and 5 to get, you guessed it, 15!

What is value of
X+8
Enter your answer in the box
2x-5
B
10
14
Plz help

Answers

Answer:

not 100% but i think x may be 23.5

Step-by-step explanation:

The values of (x+8) and (2x-5) are 35 and 49 respectively.

What is a triangle?

A triangle is defined as a two-dimensional shape with three sides, three interior angles, and three vertices.

Given a triangle, ABC

We have,

(x+8)/10 = (2x-5)/14

7x+56 = 10x-25

3x = 81

x = 27

X+8 = 35

2x-5 = 49

Hence, The values of (x+8) and (2x-5) are 35 and 49 respectively.

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what is 1.13 times 0.001​

Answers

the answer is 0.001113

A line slope of 2 passes through the point (4,8). What is the equation in slope-intercept form?

Answers

The equation would be Y=2x

2. What is the sum of the three solutions (find the values for x, y, and z, then add the answers)?
2x + 3y − z = 5 x
− 3y + 2z = −6
3x + y − 4z = −8
please show steps

Answers

Answer:

x = 30/7 , y = 46/7 , z = 48/7

Step-by-step explanation:

Solve the following system:

{2 x + 3 y - z = 5 x | (equation 1)

2 z - 3 y = -6 | (equation 2)

3 x + y - 4 z = -8 | (equation 3)

Express the system in standard form:

{-(3 x) + 3 y - z = 0 | (equation 1)

0 x - 3 y + 2 z = -6 | (equation 2)

3 x + y - 4 z = -8 | (equation 3)

Add equation 1 to equation 3:

{-(3 x) + 3 y - z = 0 | (equation 1)

0 x - 3 y + 2 z = -6 | (equation 2)

0 x+4 y - 5 z = -8 | (equation 3)

Swap equation 2 with equation 3:

{-(3 x) + 3 y - z = 0 | (equation 1)

0 x+4 y - 5 z = -8 | (equation 2)

0 x - 3 y + 2 z = -6 | (equation 3)

Add 3/4 × (equation 2) to equation 3:

{-(3 x) + 3 y - z = 0 | (equation 1)

0 x+4 y - 5 z = -8 | (equation 2)

0 x+0 y - (7 z)/4 = -12 | (equation 3)

Multiply equation 3 by -4:

{-(3 x) + 3 y - z = 0 | (equation 1)

0 x+4 y - 5 z = -8 | (equation 2)

0 x+0 y+7 z = 48 | (equation 3)

Divide equation 3 by 7:

{-(3 x) + 3 y - z = 0 | (equation 1)

0 x+4 y - 5 z = -8 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Add 5 × (equation 3) to equation 2:

{-(3 x) + 3 y - z = 0 | (equation 1)

0 x+4 y+0 z = 184/7 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Divide equation 2 by 4:

{-(3 x) + 3 y - z = 0 | (equation 1)

0 x+y+0 z = 46/7 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Subtract 3 × (equation 2) from equation 1:

{-(3 x) + 0 y - z = -138/7 | (equation 1)

0 x+y+0 z = 46/7 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Add equation 3 to equation 1:

{-(3 x)+0 y+0 z = -90/7 | (equation 1)

0 x+y+0 z = 46/7 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Divide equation 1 by -3:

{x+0 y+0 z = 30/7 | (equation 1)

0 x+y+0 z = 46/7 | (equation 2)

0 x+0 y+z = 48/7 | (equation 3)

Collect results:

Answer: {x = 30/7 , y = 46/7 , z = 48/7

Solve 14n2+32n=−34 by using the quadratic formula. Simplify any fractions. If there are multiple answers, list them separated by a comma, e.g. 1,2. If there is no solution, enter ∅.

Answers

Answer:

Step-by-step explanation:

Hello, first of all we can divide by 2.

[tex]7n^2+16n+17=0\\\\\Delta=b^2-4ac= 16^2-4*7*17=-220 < 0 \ \ !![/tex]

The discriminant is negative so there is no real solutions.

Thank you.

Find the a. MEAN and b. STANDARD DEVIATION for the data set. Round to two decimal places.
10) Country Number of Television Sets per 100 people
A 124
B 94
C 129
D 109
E 114
A) a. 115
b. 13.69
B)
a. 114
b. 13.69
C)
a. 114
b. 169
D) a. 113
b. 13.69
Provide an appropriate response.
11) If an adult male is told that his height is within 2 standard deviations of the mean of the normal distribution of heights of adult males, what can he assume?
A) His height measurement is in the same range as about 99.7% of the other adult males whose heights were measured.
B) His height measurement is in the same range as about 95% of the other adult males whose heights were measured.
C) He is taller than about 99.7% of the other men whose heights were measured.
D) He is taller than about 95% of the other men whose heights were measured. The scores on a driver's test are normally distributed with a mean of 100. Find the score that is:_____
12) Find the score that is 2 standard deviations below the mean, if the standard deviation is 26.
A) 126
B) 48
C) 152
D) 74
Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid:____
13) between $147,700 and $152,300 if the standard deviation is $2300.
A) 34%
B) 95%
C) 99.7%
D) 68%
14) more than $154,800 if the standard deviation is $2400.
A) 95%
B) 2.5%
C) 47.5%
D) 97.5%
A set of data items is normally distributed with a mean of 60. Convert the data item to a z-score, if the standard deviation is as given. 15) data item: 100; standard deviation:_____
a) 10
b) 40
c) 10
d) 4/3

Answers

Answer:

Explained below.

Step-by-step explanation:

(10)

The data set is:

S = {124, 94, 129, 109, 114}

The mean and standard deviation are:

[tex]\bar x=\frac{1}{n}\sum x=\frac{1}{5}\times [124+94+...+114]=114\\\\s=\sqrt{\frac{1}{n-1}\sum ( x-\bar x)^{2}}[/tex]

  [tex]=\sqrt{\frac{1}{5-1}\times [(124-114)^{2}+(94-114)^{2}+...+(114-114)^{2}]}\\=\sqrt{\frac{750}{4}}\\=13.6931\\\approx 13.69[/tex]

The correct option is B.

(11)

According to the Empirical 95% of the data for a Normal distribution are within 2 standard deviations of the mean.

So, the adult male's height is in the same range as about 95% of the other adult males whose heights were measured.

The correct option is B.

(12)

Let the score be X.

Given:

μ = 100

σ = 26

[tex]X=\mu-2\sigma[/tex]

    [tex]=100-(2\times 26)\\=100-52\\=48[/tex]

The correct option is B.

(13)

Let X be the prices of a certain model of new homes.

Given: [tex]X\sim N(150000, 2300^{2})[/tex]

Compute the percentage of buyers who paid between $147,700 and $152,300 as follows:

[tex]P(147700<X<152300)=P(\frac{147700-150000}{2300}<\frac{X-\mu}{\sigma}<\frac{152300-150000}{2300})[/tex]

                                         [tex]=P(-1<Z<1)\\=0.68\\[/tex]                                        

According to the 68-95-99.7, 68% of the data for a Normal distribution are within 1 standard deviations of the mean.

The correct option is D.

(14)

Compute the percentage of buyers who paid more than $154,800 as follows:

[tex]P(X>154800)=P(\frac{X-\mu}{\sigma}>\frac{154800-150000}{2400})[/tex]

                                         [tex]=P(Z>2)\\=0.975\\[/tex]

According to the 68-95-99.7, 95% of the data for a Normal distribution are within 2 standard deviations of the mean. Then the percentage of data above 2 standard deviations of the mean will be 97.5% and below 2 standard deviations of the mean will be 2.5%.

The correct option is D.

(15)

The z-score is given as follows:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Pre Calc Introduction to Derivatives-Using Limits Help!

Answers

Answer:

Attachment 1 : Option A,

Attachment 2 : Option D,

Attachment 3 : Option B,

Attachment 4 : Instantaneous rate of change will be 24

Step-by-step explanation:

"Remember that we can solve such questions by finding the derivative first"

1 : Let's consider this approach a bit differently. If we were to graph this function, we would see that the point (-2,26) would lie on the curve having a negative slope.

The rate of change would thus be negative, eliminating choices b and d. And, the slope of this function would be much greater than 4 due to the coefficient of " 5 " in f(x) = 5x² + 6. Hence our answer will be option a.

2 : f'(5) = - 2 * 5 + 4,

f'(5) = - 10 + 4 = - 6

Your solution is option d.

3 : f'(2) = 12 / 2 + 1 / - 3,

f'(2) = 12 / 3 / - 3 = 4 / - 3,

f'(2) = - 4 / 3

Your solution is option b.

4 : Here again we can apply the power rule, where using constant multiple rule and derivative of a constant, you can quickly find the derivative of  g .

g'(t) = 3(2x¹) + 0 = 6t,

And now we can evaluate the derivative at that value of  t.

g'(4) = 6(4) = 24 - hence the instantaneous rate of change at t = 4, will be 24

A 4% error is made in measuring
the radius of a sphere. Find the
Percentage error in the surface
area.

Answers

Answer:

8.51%

Step-by-step explanation:

Let us assume the radius of the sphere is r. The surface area of a sphere is:

Surface area = 4πr².

There is a 4% error in the measurement of the radius, therefore the radius being measured = (100% - 4%)r = (96%)r = 0.96r

The surface area as a result of error is:

Surface area after measurement = 4π(0.96r)² = 3.6864πr²

The percentage error is the ratio of the difference between the actual and measured value to the measured value. It is given as:

[tex]Percent\ error =\frac{Actual\ area-Measured\ area}{Measured \ area}*100\%\\ \\Percent\ error =\frac{4\pi r^2-3.6864\pi r^2}{3.6864\pi r^2}*100\%\\ \\Percent\ error =\frac{0.3136\pi r^2}{3.6864\pi r^2}*100\%\\ \\Percent\ error =0.0851*100\%\\\\Percent\ error =8.51\%[/tex]

5. Evaluate
a) (-3)²/(-9/4)²​

Answers

Answer:

16/9

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Exponents

(-3)² = 9

(-9/4)² = 81/16

9/81/16

Step 2: KCF (Keep Change Flip)

9(16/81)

144/81

Step 3: Simplify

144/9 = 16

81/9 = 9

16/9

A researcher wishes to estimate the proportion of college students who cheat on exams. A poll of 560 college students showed that 15% of them had, or intended to, cheat on examinations. Find the 95% confidence interval.

Answers

Answer:

0.1198 < p < 0.1802

Step-by-step explanation:

Percentage who had, or intended to cheat (p) = 15% = 0.15.

1 - p = 1 - 0.15 = 0.85

Confidence interval = 95%, z = 1.96 = 2

number of observation= 560

p ± z * √(p * (1 -p)/n)

Lower limit:

0.15 - 2 * √0.15 * 0.85/560

0.15 - 0.0301780 = 0.119822

= 0.1198

Upper limit:

0.15 + 2 * √0.15 * 0.85/560

0.15 + 0.0301780 = 0.180178

= 0.1802

0.1198 < p < 0.1802

Which number best represents the slope of the graphed line?

Answers

Answer: A

Explanation:

-5

Because the slope rise 5 and run to the left once.

If a slope run to right it means positive
If a slope run to left it means negative

Answer:

the answer is A.

Step-by-step explanation:

for every time you move over one in the x axis you move down 5 on the y axis

Which of the following inequalities matches the graph?

Answers

Answer:

The last option y<4. Y is less than 4 since the shaded region is below 4 on the y Axis.

Answer: D  y <4

Step-by-step explanation:

The line is horizontally passing through the 4 which is the y intercept and all the solutions are less than 4.

Given that Cos60=sin30=1/2 and cos30=sin60=root3/2.Evaluate tan60-1/1-tan30​

Answers

Answer:

1/2

Step-by-step explanation:

The value of the given expression is 1 / √3.

What is trigonometry?

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

The given values are  cos60=sin30=1/2 and cos30=sin60=√3/2.

Divide sin30 and cos30,

[tex]\dfrac{sin30}{cos30}=tan30 = \dfrac{\dfrac{1}{2}}{\dfrac{2}{\sqrt{3}}}=\dfrac{1}{\sqrt{3}}[/tex]

Divide sin60 and cos60.

[tex]\dfrac{sin60}{cos60}=tan60 = \dfrac{\dfrac{2}{\sqrt{3}}}{\dfrac{1}{2}}= \sqrt3[/tex]

The value of the expression is.

[tex]\dfrac{ tan60-1}{1-tan30}=\dfrac{\sqrt{3}-1}{\sqrt{3}-1}}\times \dfrac{1}{\sqrt{3}}=\dfrac{1}{\sqrt{3}}[/tex]

Therefore, the value of the given expression is 1 / √3.

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Please Help With This Problem
Show Work​

Answers

Answer:

$64,800

Step-by-step explanation:

First, we calculate the total she pays all three employees in 1 month.

$2300 + $1700 + $1400 = $5400

Since there are 12 months in 1 year, we multiply the total monthly wages by 12 to find the total yearly wages.

12 * $5400 = $64,800

Answer: $64,800

Please help. Will select brainliest.

Answers

Answer:

Heptagon: D

Spetagon: D

Nonagon: B

At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?

Answers

Answer:

The cost of a chicken shawarma wrap is $10.99 and the cost of one order of spiced potatoes is $4.99.

Step-by-step explanation:

X denotes the cost of a chicken shawarma wrap and Y denotes the cost of an order of spiced potatoes.

From the provided information we can form two equations for the total price paid by Ms. Ironperson and Mr. Thoro.

[tex]3x+2y=42.95...(i)\\5x+4y=74.91...(ii)[/tex]

Multiply (i) by 4 and (ii) by 2 and subtract the two resulting equations:

[tex]3x+2y=42.95\ \ \ ]\times 4\\5x+4y=74.91\ \ \ ]\times2\\\\\Rightarrow\\\\12x+8y=171.80\\10x+8y=149.82\\\\\text{subtract}\\\\2x=21.98\\\\x=10.99[/tex]

Substitute x = 10.99 in (i) and solve for y as follows:

[tex]3x+2y=42.95\\\\(3\times 10.99)+2y=42.95\\\\2y=9.98\\\\y=4.99[/tex]

Thus, the cost of a chicken shawarma wrap is $10.99 and the cost of one order of spiced potatoes is $4.99.

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