Mathematics College

## Answers

**Answer 1**

**Answer:**

€ 270

**Step-by-step explanation:**

Since the production cost C(x,y) = 2x² + 5y² + 120 is less than or equal to 250, we have 2x² + 5y² + 120 ≤ 250

The selling price S(x,y) = 40x + 80y

The profit P(x,y) = S(x,y) - C(x,y) = 40x + 80y - 2x² - 5y² - 120

Using the principle of lagrange multipliers, we want to maximize the profit P(x,y) under the condition that C(x.y) ≤ 250.

So, dP/dx = 40 - 4x , dC/dx = 4x, dP/dy = 80 - 10y , dC/dy = 10y

dP/dx + λdC/dx = 0

40 - 4x + 4λx = 0 (1)

4λx = 4x - 40

λ = (x - 10)/x

dP/dy + λdC/dy = 0

80 - 10y + 10λy = 0 (2)

substituting λ into (2), we have

80 - 10y + 10(x - 10)y/x = 0

multiplying through by x, we have

80x - 10xy + 10xy - 100y = 0

80x - 100y = 0

80x = 100y

x = 100y/80

x = 5y/4

substituting x into C(x,y) ≤ 250, we have

2(5y/4)² + 5y² + 120 ≤ 250

25y²/8 + 5y² + 120 ≤ 250

25y² + 40y² + 960 ≤ 2000

65y² ≤ 2000 - 960

65y² ≤ 1040

y² ≤ 1040/65

y² ≤ 16

y ≤ ±√16

y ≤ ± 4 since its quantity, we take the positive value.

So x = 5y/4 = 5(± 4)/4 = ± 5

So, x ≤ ± 5

For the maximum value for the profit, P(x,y), we take the maximum values of x and y which are x = 5 and y = 4. Substituting these values into P(x,y), we have

P(5,4) = 40(5) + 80(4) - 2(5)² - 5(4)² - 120

= 200 + 320 - 50 - 80 - 120

= 520 - 250

= 270

So, the maximum profit obtained is € 270

## Related Questions

An extremely simple (and surely unreliable) weather prediction model would be one where days are of two types: sunny or rainy. A sunny day is 90% likely to be followed by another sunny day, and a rainy day is 50% likely to be followed by another rainy day. Model this as a Markov chain. If Sunday is sunny, what is the probability that Tuesday (two days later) is also sunny

### Answers

**Answer:**

The probability that if Sunday is sunny, then Tuesday is also sunny is **0.86**.

**Step-by-step explanation:**

Let us denote the events as follows:

Event 1: a sunny day

Event 2: a rainy day

From the provided data we know that the transition probability matrix is:

[tex]\left\begin{array}{ccc}1&\ \ \ \ 2\end{array}\right[/tex]

[tex]\text{P}=\left\begin{array}{c}1&2\end{array}\right[/tex] [tex]\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right][/tex]

In this case we need to compute that if Sunday is sunny, what is the probability that Tuesday is also sunny.

This implies that we need to compute the value of P₁₁².

Compute the value of P² as follows:

[tex]P^{2}=P\cdot P[/tex]

[tex]=\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\cdot \left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\\\\=\left[\begin{array}{cc}0.86&0.14\\0.70&0.30\end{array}\right][/tex]

The value of P₁₁² is 0.86.

Thus, the probability that if Sunday is sunny, then Tuesday is also sunny is **0.86**.

It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, minutes of activity varied according to the N(373, 61) distribution. Minutes of activity for lean people had the N(525, 104) distribution. Within what limits do the active minutes for 95% of the people in each group fall

### Answers

**Answer:**

Among mildly obese people, 95% of the people have between 251 and 495 minutes of activity per day.

Among lean people, 95% of the people have between 317 and 733 minutes of activity per day.

**Step-by-step explanation:**

**The Empirical Rule states that, for a normally distributed random variable:**

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

**Within what limits do the active minutes for 95% of the people in each group fall**

By the Empirical Rule, within 2 standard deviations of the mean.

**Mildly obese:**

Mean = 373, standard deviation = 61.

373 - 2*61 = 251 minutes

373 + 2*61 = 495 minutes

Among mildly obese people, 95% of the people have between 251 and 495 minutes of activity per day.

**Lean people:**

Mean = 525, standard deviation = 104

525 - 2*104 = 317 minutes

525 + 2*104 = 733 minutes

Among lean people, 95% of the people have between 317 and 733 minutes of activity per day.

Please help. I’ll mark you as brainliest if correct!

### Answers

**Answer:**

a = 13

b = 0

**Step-by-step explanation:**

Conjugate of -3 + 2i is -3 - 2i

(-3 + 2i) (-3 - 2i)

We need to expand:

9 + 6i + -6i + -4i^2

-4i^2 =(-4)(-1) = 4

9 + 4 = 13

a = 13

b = 0

find x.

8

2radius3

8

8radius3

(hurry plz, will give brainliest) -15pts-

### Answers

**Answer:**

Answere is X= 8

**Step-by-step explanation:**

Use sine law

Sin(angle) = Opposite/ Hypotenuse

Sin (30) = 4 /X

X = 4 / sin (30)

X = 8

Amit found and labeled the areas of each of the faces of the triangle prism as shown which area calculation did Amit calculate incorrectly

### Answers

Complete Question:

Amit found and labeled the areas of each of the faces of the triangular prism as shown.

Which area calculation did Amit calculate incorrectly?

Rectangular face with area 30 cm2

Rectangular face with area 40 cm2

Rectangular face with area 50 cm2

Triangular faces with areas 48 cm2

Answer:

Triangular faces with areas 48 cm2

Step-by-step Explanation:

To find out which area calculation Amit got wrong, let's calculate each faces of the given triangular prism attached below:

There area of theb5 faces should be as follows:

Area of rectangular face with L = 10 and B = 5 would be ==> 10*5= 50cm²

Area of rectangular face with L = 8 and B = 5 would be 8*5 = 40cm²

Area of rectangular face with L = 6 and B = 5 would 6*5 = 30cm²

Area of each of the triangular faces will be ½*8*6 = 48/2 = 24cm²

From our calculations, we'd observe that Amit didn't calculate the area of the triangular faces correctly. Amit got 48cm² instead of 24cm²

**Answer:**

Triangular faces with areas 48 cm2

**Step-by-step explanation:**

Which of the following is most likely the next step in the series?

### Answers

**Answer:**

B

**Step-by-step explanation:**

They are increasing by 1 vertically. Hope this helps!! :)

The correct option or answer is .C

Express the following ratio in its simplest form.

4:12

### Answers

**Answer:**

1:3

**Step-by-step explanation:**

divide 4 ...............

.............

ps: idk the explanation

HELP!!! PLEASE!!!

The U.S. Federal Income Tax is a progressive tax, which means that higher incomes are taxed at higher percent rates.

The table shows the 2018 Federal Income Tax rates that are applied to the incomes of unmarried individuals.

Tuan is an unmarried man who earned a taxable income of $48$48,000000 during 2018.

Use the table to complete the statements below.

### Answers

**Answer:**

10%$29,175$2,046$6,499.50

**Step-by-step explanation:**

**a)** The %tax comes from the "Rate" column on the line "up to $9525". It is **10%**.

__

**b)** Simply compute the difference shown:

$38,700 -$9,525 = **$29,175**

__

**c)** 22% of $9,300 is ...

0.22 × $9,300 =** $2,046**

__

**d)** The total from the three previous calculations is ...

$952.50 +3,501.00 +2,046.00 = **$6,499.50**

**Answer:**

10%

$29,175

$2,046

$6,499.50

got it right on ttm.

**Step-by-step explanation:**

just believe me it works

Andrei wants to fill a glass tank with marbles, and then fill the remaining space with water. WWW represents the volume of water Andrei uses (in liters) if he uses nnn marbles. W=32-0.05nW=32−0.05nW, equals, 32, minus, 0, point, 05, n What is the glass tank's volume?

### Answers

Before **Andrei **adds **the marbles **to the **glass tank**, the **glass tank **was empty. This means that **the volume **of the **empty tank **is when **n = 0** and the **volume **is **32 liters.**

Given that:

[tex]W = 32 - 0.05n[/tex]

A **linear function **is represented as:

[tex]y = b + mx[/tex]

Where

[tex]b \to[/tex] **y intercept**

Literally, the **y intercept **is the **initial value **of the **function.**

In this **function**, the **y intercept **means the **initial volume **of the **glass tank **before **filling **it with **marbles.**

Compare [tex]y = b + mx[/tex] and [tex]W = 32 - 0.05n[/tex]

[tex]b = 32[/tex]

This means that the **volume **of the **glass tank **is **32 liters**.

Read more about linear functions at:

https://brainly.com/question/21107621

**Answer:**

0.05

**Step-by-step explanation:**

The escape time (sec) for oil workers in a simulated exercise, gave the sample mean 370.69, sample standard deviation 24.36, and number of observations as n =26. Suppose the investigators had believed a priori that true average escape time would be at most 6 minutes. Does the data contradict this prior belief? Assuming normality, test the appropriate hypothesis using a significance level of .05.

### Answers

**Answer:**

Null hypothesis:[tex]\mu \leq 6[/tex]

Alternative hypothesis:[tex]\mu > 6[/tex]

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)

Replacing the info we got:

[tex]t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335[/tex]

[tex]p_v =P(t_{25}>1.335)=0.097[/tex]

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes

**Step-by-step explanation:**

**Information given **

[tex]\bar X=370.69/60 =6.178[/tex] represent the sample mean

[tex]s=24.36/36=0.68[/tex] represent the standard deviation for the sample

[tex]n=26[/tex] sample size

[tex]\mu_o =6[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

**System of hypothesis**

We want to test if the true mean is at least 6 minutes, the system of hypothesis would be:

Null hypothesis:[tex]\mu \leq 6[/tex]

Alternative hypothesis:[tex]\mu > 6[/tex]

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)

Replacing the info we got:

[tex]t=\frac{6.178-6}{\frac{0.68}{\sqrt{26}}}=1.335[/tex]

The degrees of freedom are:

[tex]df=n-1=26-1=25[/tex]

The p value would be given by:

[tex]p_v =P(t_{25}>1.335)=0.097[/tex]

And for this case the p value is higher than the significance level so then we FAIL to reject the null hypothesis and we can conclude that the true mean is at most 6 minutes.

Devon wants to build a ramp with the dimensions shown. How much wood does he need?

### Answers

The image of the ramp with dimensions is missing, so i have attached it.

Answer:

680 in² of wood is needed.

Step-by-step explanation:

The way to find how much wood would be needed by devon would be to find the total surface area of the ramp.

From the attached image,

Let's find the area of the 2 triangles first;

A1 = 2(½bh) = bh = 15 x 8 = 120 in²

Area of the slant rectangular portion;

A2 = 17 x 14 = 238 in²

Area of the base;

A3 = 15 × 14 = 210 in²

Area of vertical rectangle;

A4 = 8 × 14 = 112 in²

Total Surface Area = A1 + A2 + A3 + A4 = 120 + 238 + 210 + 112 = 680 in²

What is the perimeter of the shape below?

### Answers

**Answer:**

I think it is 288.6 ft. Lol hope this helps

**Step-by-step explanation:**

5.44 Teaching descriptive statistics: A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam. (a) What are the hypotheses for evaluating if the average test scores are different for the different teaching methods?

### Answers

Answer:

The null hypothesis is that all the different teaching methods have the same average test scores.

H0: μ1 = μ2 = μ3 = μ4 = μ5

The alternative hypothesis is that at least one of the teaching methods have a different mean.

Ha: at least one mean is different. (μ1 ≠ μi)

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above, let μ represent the average test scores for the teaching methods:

The null hypothesis is that all the different teaching methods have the same average test scores.

H0: μ1 = μ2 = μ3 = μ4 = μ5

The alternative hypothesis is that at least one of the teaching methods have a different mean.

Ha: at least one mean is different. (μ1 ≠ μi)

please very soon I offer the crown !!! + 10 points urgently !!!

### Answers

The first one is 10 the second one is 26

**Answer:**

d. 10th e. 26th

**Step-by-step explanation:**

22-12=10

12+14=26

The sum of two numbers is odd. Can the quotient of the two numbers be an odd number?

### Answers

**Answer: **No.

**Step-by-step explanation:**

I guess that here we have the statement:

If the sum of two numbers is odd----> can their quotient be an odd number?

first, for n an integer number, we have that:

an odd number can be written as 2n + 1

an even number can be written as 2n.

The sum of two numbers is only odd if one of them is odd and the other even.

Then we have a number that is 2n and other that is 2k + 1, for n and k integer numbers.

Now, let's see if the quotient can also be an odd number.

One way to think this is:

There is an odd number such that when we multiply it by another odd number, the result is an even number?

no, and i can prove it as:

let 2k + 1 be an odd number, and 2j + 1 other.

the product is:

(2k + 1)*(2j + 1) = 2*(2*k*j + k + j) + 1

and as k and j are integers, also does 2*k*j + k + j, so:

2*(2*k*j + k + j) + 1 is an odd number.

This says that the product of two odd numbers is always odd, then we never can have that the quotient between an even number and an odd number is odd.

Please answer this correctly

### Answers

**Answer:**

4

**Step-by-step explanation:**

Set the height of the missing bar to 4 as there are 4 quantities between 21-25.

The commute would be 4, because in the number bank there’s 2 #21’s and 2 #23’s and 2+2=4

the length of a ruler is 170cm,if the ruler broke into four equal parts.what will be the sum of the length of three parts

### Answers

Answer:

Step-by-step explanation:Srry it's bit rough...

average of a data set was 40, and that standard deviation was 10, what else could you derive from that information.

### Answers

**Answer:**

[tex] \bar x = 40, s =10[/tex]

And from these values we can estimate the sample variance like this:

[tex] s^2 = 10^2 =100[/tex]

And we can also estimate the coeffcient of variation given by:

[tex] \hat{CV} =\frac{s}{\bar x}[/tex]

And replacing we got:

[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]

And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.

**Step-by-step explanation:**

For this case we have the following info given:

[tex] \bar x = 40, s =10[/tex]

And from these values we can estimate the sample variance like this:

[tex] s^2 = 10^2 =100[/tex]

And we can also estimate the coeffcient of variation given by:

[tex] \hat{CV} =\frac{s}{\bar x}[/tex]

And replacing we got:

[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]

And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.

01

The list below shows the prices of T-shirts at a clothing store.

{8, 10, 10, 12, 15, 15, 18)

Which statement best describes the mean of this ser?

the difference between the least and greatest prices

the sum of the prices

the quotient of the difference between the least and greatest prices divided by 7

the sum of the prices divided by 7

dem

### Answers

**Answer:**

the sum of the prices divided by 7

**Step-by-step explanation:**

The mean is the sum of the elements of a set, divided by the number of elements in the set. This set has 7 members, so its mean is ...

** the sum of the prices divided by 7**

The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 15 days. A distribution of values is normal with a mean of 267 and a standard deviation of 15. What percentage of pregnancies last beyond 246 days? P(X > 246 days) =

### Answers

**Answer:**

91.92% of pregnancies last beyond 246 days

**Step-by-step explanation:**

**When the distribution is normal, we use the z-score formula.**

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

**In this question, we have that:**

[tex]\mu = 267, \sigma = 15[/tex]

**What percentage of pregnancies last beyond 246 days?**

We have to find 1 subtracted by the pvalue of Z when X = 246. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{246 - 267}{15}[/tex]

[tex]Z = -1.4[/tex]

[tex]Z = -1.4[/tex] has a pvalue of 0.0808

1 - 0.0808 = 0.9192

91.92% of pregnancies last beyond 246 days

The lifespan of a car battery averages six years. Suppose the batterylifespan follows an exponential distribution.(a) Find the probability that a randomly selected car battery will lastmore than four years.(b) Find the variance and the 95th percentile of the battery lifespan.(c) Suppose a three-year-old battery is still going strong. (i) Find theprobability the battery will last an additional five years. (ii) Howmuch longer is this battery expected to last

### Answers

**Answer:**

**Step-by-step explanation:**

Let X denote the life span of a car battery and it follows and exponential distribution with average of 6 years.

Thus , the parameter of the exponential distribution is calculated as,

μ = 6

[tex]\frac{1}{\lambda} =6[/tex]

[tex]\lambda = \frac{1}{6}[/tex]

a) The required probability is

[tex]P(X>4)=1-P(X\leq 4)\\\\=1-F(4)\\\\1-(1-e^{- \lambda x})\\\\=e^{-\frac{4}{6}[/tex]

= 0.513

Hence, the probability that a randomly selected car battery will last more than four years is 0.513

b) The variance of the battery span is calculated as

[tex]\sigma ^2=\frac{1}{(\frac{1}{\lambda})^2 }\\\\\sigma ^2=\frac{1}{(\frac{1}{6})^2 } \\\\=6^2=36[/tex]

The 95% percentile [tex]x_{a=0.05}[/tex] (α = 5%) of the battery span is calculated

[tex]x_{0.05}=-\frac{log(\alpha) }{\lambda} \\\\=-\frac{log(0.05)}{1/6} \\\\=-6log(0.05)\\\\=17.97 \ years[/tex]

c)

Let [tex]X_r[/tex] denote the remaining life time of a car battery

i)the probability the battery will last an additional five years is calculated below

[tex]P(X_r>5)=e^{-5\lambda}\\\\=e^{-\frac{5}{6} }\\\\=0.4346[/tex]

ii) The average time that the battery is expected to last is calculated

[tex]E(X_r)=\frac{1}{\lambda} \\\\=6[/tex]

What’s the degree of the rotation?

### Answers

**Answer: The answer is C 90**

**Step-by-step explanation: Rotations is ¼ and the Radians is π/2**

The answer is c (90) hope that helped

Question: A box contains 160 Iphone XR's.

60% of the IPhones are Forest Green.

How many IPhones are Forest Green?

### Answers

**Answer:**

96

**Step-by-step explanation:**

60% * 160 = 0.6 * 160 = 96.

**Answer:**

None

**Step-by-step explanation:**

There is no Forest Green iPhone XR's only the 11 Pros have that color.

Joshua ate 2/6 of his sandwich in the afternoon and 2/6 more for a snack later that day. How much of Joshua’s sandwich is left?

### Answers

**Answer:**

1/3 left

**Step-by-step explanation:**

The total sandwich is 1 or in fraction form 6/6

He ate 2/6

6/6 -2/6 = 4/6

Then he ate 2/6 more

4/6 -2/6 = 2/6

He has 2/6 left

Simplifying

2/6 =1/3

The city manager of Shinbone has received a complaint from the local union of firefighters to the effect that they are underpaid. Not having much time, the city manager gathers the records of a random sample of 27 firefighters and finds that their average salary is $38,073 with a standard deviation of $575. If she knows that the average salary nationally is $38,202, how can she respond to the complaint

### Answers

**Answer:**

She can answer, after performing the hypothesis test, that there is not enough evidence to support the claim that the city firefighters salary is significantly lower than the national average.

**Step-by-step explanation:**

She can statistically test the claim of the firefighters to see if it has statistical evidence.

This is a hypothesis test for the population mean.

The claim is that the city firefighters salary is significantly lower than the national average.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=38202\\\\H_a:\mu< 38202[/tex]

The significance level is 0.1. Is less conservative than 0.05, for example, so if there is little evidence, the null hypothesis with be rejected.

The sample has a size n=27.

The sample mean is M=38073.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=575.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{575}{\sqrt{27}}=110.659[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{38073-38202}{110.659}=\dfrac{-129}{110.659}=-1.17[/tex]

The degrees of freedom for this sample size are:

df=n-1=27-1=26

This test is a left-tailed test, with 26 degrees of freedom and t=-1.17, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.17)=0.127[/tex]

As the P-value (0.127) is bigger than the significance level (0.1), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the city firefighters salary is significantly lower than the national average.

simplify (6^7)^3

will give brainlist

### Answers

**Answer:**

The answer is D.

**Step-by-step explanation:**

**You have to apply Indices Law,**

[tex] { ({a}^{m}) }^{n} \: ⇒ \: {a}^{mn} [/tex]

**So for this question :**

[tex] { ({6}^{7}) }^{3} [/tex]

[tex] = {6}^{7 \times 3} [/tex]

[tex] = {6}^{21} [/tex]

What is the next number in the sequence: 3, 8, 12, 48, 29, __

### Answers

**Answer:**

144

**Step-by-step explanation:**

**Answer:**

116

**Step-by-step explanation:**

3x4=12

12x4=48

8x4=32

32-3=29

29x4=116

Hope it's clear

Question 1 of 20 :

Select the best answer for the question.

1. Divide7/15 by 3/5

OA%

O B./25

O c. 75/21

O D.21/75

### Answers

**Answer:**

7/9

**Step-by-step explanation:**

7/15 ÷ 3/5

Copy dot flip

7/15 * 5/3

7/3 * 5/15

7/3 * 1/3

7/9

Please answer this correctly

### Answers

**Answer:**

Set the height up to 4

**Step-by-step explanation:**

Since there are 4 numbers between 1-5, set the height up to 4

**Answer:**

4 temperature recordings.

**Step-by-step explanation:**

2, 2, 4, 5

There are 4 recordings in the range of 1-5°C.

What’s the Midpoint of (2,-1) and (1,-2)

### Answers

**Answer:**

(3/2,-3/2)

**Step-by-step explanation:**

The midpoint of (2,-1)(1,-2) is (3/2,-3/2)

*Answer:*

*(**1**.**5**,**-**1**.**5**)*

*You **have **to **remember **the **formula **to **find **mid-point **and **that **is:*

*[tex]midpoint = ( \frac{x1 + x2}{2} **,**\frac{y1 + y2}{2} )[/tex]*

*please **see** the** attached** picture** for** full** solution*

*Hope **it** helps*

*Good **luck** on** your** assignment*