Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Factor completely and then place the factors in the proper location on the grid.
4n^2 +28n +49

Answer:

[tex]-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y + \pi - \frac{1}{2}[/tex]

Step-by-step explanation:

Given the initial value problem [tex]\frac{1}{\theta}(\frac{dy}{d\theta} ) =\frac{ ysin\theta}{y^{2}+1 } \\[/tex] subject to y(π) = 1. To solve this we will use the variable separable method.

Step 1: Separate the variables;

[tex]\frac{1}{\theta}(\frac{dy}{d\theta} ) =\frac{ ysin\theta}{y^{2}+1 } \\\frac{1}{\theta}(\frac{dy}{sin\theta d\theta} ) =\frac{ y}{y^{2}+1 } \\\frac{1}{\theta}(\frac{1}{sin\theta d\theta} ) = \frac{ y}{dy(y^{2}+1 )} \\\\\theta sin\theta d\theta = \frac{ (y^{2}+1)dy}{y} \\integrating\ both \ sides\\\int\limits \theta sin\theta d\theta =\int\limits \frac{ (y^{2}+1)dy}{y} \\-\theta cos\theta - \int\limits (-cos\theta)d\theta = \int\limits ydy + \int\limits \frac{dy}{y}[/tex]

[tex]-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y +C\\Given \ the\ condition\ y(\pi ) = 1\\-\pi cos\pi +sin\pi = \frac{1^{2} }{2} + ln 1 +C\\\\\pi + 0 = \frac{1}{2}+ C \\C = \pi - \frac{1}{2}[/tex]

The solution to the initial value problem will be;

[tex]-\theta cos\thsta+sin\theta = \frac{y^{2} }{2} + ln y + \pi - \frac{1}{2}[/tex]

Using separation of variables, it is found that the solution of the initial value problem is:

The differential equation is given by:

[tex]\frac{1}{\theta}\left(\frac{dy}{d\theta}\right) = \frac{y\sin{\theta}}{y^2 + 1}[/tex]

Applying separation of variables, we have that:

[tex]\frac{y^2 + 1}{y}dy = \theta\sin{\theta}d\theta[/tex]

[tex]\int \frac{y^2 + 1}{y}dy = \int \theta\sin{\theta}d\theta[/tex]

The first integral is solved applying the properties, as follows:

[tex]\int \frac{y^2 + 1}{y}dy = \int y dy + \int \frac{1}{y} dy = \frac{y^2}{2} + \ln{y} + K[/tex]

The second integral is solved using integration by parts, as follows:

[tex]u = \theta, du = d\theta[/tex]

[tex]v = \int \sin{\theta}d\theta = -\cos{\theta}[/tex]

Then:

[tex]\int \theta\sin{\theta}d\theta = uv - \int v du[/tex]

[tex]\int \theta\sin{\theta}d\theta = -\theta\cos{\theta} + \int \cos{\theta}d\theta[/tex]

[tex]\int \theta\sin{\theta}d\theta = -\theta\cos{\theta} + \sin{\theta}[/tex]

Then:

[tex]\frac{y^2}{2} + \ln{y} + K = -\theta\cos{\theta} + \sin{\theta}[/tex]

[tex]y(\pi) = 1[/tex] means that when [tex]\theta = \pi, y = 1[/tex], which is used to find K.

[tex]\frac{1}{2} + \ln{1} + K = -\pi\cos{\pi} + \sin{\pi}[/tex]

[tex]\frac{1}{2} + K = \pi[/tex]

[tex]K = \pi - \frac{1}{2}[/tex]

Then, the solution is:

[tex]\frac{y^2}{2} + \ln{y} + \pi - \frac{1}{2} = -\theta\cos{\theta} + \sin{\theta}[/tex]

[tex]\frac{y^2}{2} + \ln{y} + \pi - \frac{1}{2} + \theta\cos{\theta} - \sin{\theta} = 0[/tex]

To learn more about separation of variables, you can take a look at https://brainly.com/question/14318343

Answer:

Yes, the function satisfies the hypothesis of the Mean Value Theorem on the interval [1,5]

Step-by-step explanation:

We are given that a function

[tex]f(x)=ln(x)[/tex]

Interval [1,5]

The given function is defined on this interval.

Hypothesis of Mean Value Theorem:

(1) Function is continuous on interval [a,b]

(2)Function is defined on interval (a,b)

From the graph we can see that

The function is continuous on [1,5] and differentiable at(1,5).

Hence, the function satisfies the hypothesis of the Mean Value Theorem.

Answer:

Step-by-step explanation:

Given the equation, 2x- y = 5, if x = 3, to get y we will simply substitute the value of x into the expression given as shown;

[tex]2x - y = 5\\\\Substituting \ x = 3\ into \ the \ equation\\\\2(3) - y = 5\\\\6 - y = 5\\\\subtracting\ 6\ from\ both\ sides\\\\6-6-y = 5- 6\\\\-y = -1\\\\multiplying\ both\ sides\ by \ -1\\-(-y) = -(-1)\\\\y = 1[/tex]

Hence, the value of y is 1

Answer:

B. zero

Step-by-step explanation:

If the temperature is supposed to remain constant over time (the same) when working properly, then this means that there is no increase or decrease over time.

If there were a line to represent this, then it would be a straight line with a slope of 0 because the temperature would remain the same.

Answer:

x=9

Step-by-step explanation:

3x subtracted by 2y

is 1 then 1 multiplied by 2 is 2 then 7 + 2 is 9

PEMDAS

Answer:

19cm

Step-by-step explanation:

The area  of a trapezoid [tex]=\dfrac12(a+b)h[/tex] (where a and b are the parallel sides).

Given:

Area = 189 Square cm

Height, h=14cm

a=8cm

We want to find the value of the other parallel side, b.

Substitution of the given values gives:

[tex]189=\dfrac12(8+b)14\\189=7(8+b)\\$Divide both sides by 7\\8+b=27\\Subtract 8 from both sides\\b+8-8=27-8\\b=19cm[/tex]

The length of the second parallel side is 19cm.

Answer: 6x^2

Step-by-step explanation:

The area of a triangle is 1/2bh

Thus, simply multiply 2x*3x = 6x^2

Hope it helps <3

Answer:

Solution,

Base(b)= 3x

Height(h) = 2x

Now,

Finding the area of triangle:

[tex] \frac{1}{2} \times b \times h[/tex]

[tex] \frac{1}{2} \times 3x \times 2x[/tex]

[tex] \frac{1}{2} \times 6 {x}^{2} [/tex]

[tex]3 {x}^{2} [/tex]

Hope this helps....

Good luck on your assignment....

Answer:

The sample mean used for this interval is 1750.

The sample standard deviation used for this interval was of 175.34

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the subtraction of these two bounds divided by two.

In this question:

Lower bound: 1690

Upper bound: 1810

Sample mean

[tex]\frac{1690 + 1810}{2} = 1750[/tex]

The sample mean used for this interval is 1750.

Sample standard deviation:

The first step is finding the margin of error:

[tex]M = \frac{1810 - 1690}{2} = 60[/tex]

Now we have to develop the problem a bit.

We want the sample standard deviation, so we use the T-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.711

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

We have that: [tex]M = 60, T = 1.711, n = 25[/tex]

We have to find s

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

[tex]60 = 1.711\frac{s}{\sqrt{25}}[/tex]

[tex]1.711s = 60*5[/tex]

[tex]s = \frac{60*5}{1.711}[/tex]

[tex]s = 175.34[/tex]

The sample standard deviation used for this interval was of 175.34

Answer:  Sheila today = [tex]46\dfrac{1}{3}[/tex]  yrs old

Step-by-step explanation:

   J + S = 115 v⇒  J = 115 - S

Current Ages                        Ages 14 years ago

 Joe (J) = 115 - S                      J - 14 = 2(S - 14)

 Sheila (S) = S

Substitute J = 115 - S into the "14 years ago" equation

      J    - 14 = 2(S - 14)

(115 - S) - 14 = 2(S - 14)

111 -S = 2S - 28

111 = 3S  - 28

139 = 3S

46 [tex]\frac{1}{3}[/tex] = S

It is odd that the result was not an integer.  I wonder if you meant to type "Joe was twice as old as Sheila is today.  That would change the equation to:

J - 14 = 2S

111 - S = 2S

111 = 3S

37 = S

Answer:

k= 4/33

Step-by-step explanation:

Answer:Yes indeed!

Step-by-step explanation:

Your right!

Answer:

[tex]f(x)=\frac{4x+1}{x^2-5}[/tex]

Step-by-step explanation:

What (f/g)(x) is asking us to do is divided function f(x) by function g(x).

Answer:

GCF - 4

Step-by-step explanation:

36 - 1, 2, 3, 4, 6, 9, 12, 18, 36

44 - 1, 2, 4, 11, 44

Hope this helps! :)

Answer:

Step-by-step explanation:

The factors of the given expression are ...

  6ir +15i +8r +20 = (3i +4)(2r +5)

Which factor is current and which is resistance is not clear. Usually, resistance is referred to using the variable r, so we suppose the expressions are supposed to be ...

  resistance: (2r +5)

  current: (3i +4)

Answer:

A 98% confidence interval for the population mean of  printouts per ink cartridge is [430.5, 489.5].

Step-by-step explanation:

We are given that a consumer advocate group selects a random sample of 20 ink cartridges and finds  that the average number of printouts per ink cartridge is 460 with a standard  deviation of 52.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                              P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average number of printouts per ink cartridge = 460

            s = sample standard deviation = 52

            n = sample of ink cartridges = 20

            [tex]\mu[/tex] = population mean printouts per ink cartridge

Here for constructing a 98% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 98% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.54 < [tex]t_1_9[/tex] < 2.54) = 0.98  {As the critical value of t at 19 degrees of

                                              freedom are -2.54 & 2.54 with P = 1%}  

P(-2.54 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.54) = 0.98

P( [tex]-2.54 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\bar X-\mu}[/tex] < [tex]2.54 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.98

P( [tex]\bar X-2.54 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.54 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.98

98% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.54 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.54 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                       = [ [tex]460-2.54 \times {\frac{52}{\sqrt{20} } }[/tex] , [tex]460+2.54 \times {\frac{52}{\sqrt{20} } }[/tex] ]

                                       = [430.5, 489.5]

Therefore, a 98% confidence interval for the population mean of  printouts per ink cartridge is [430.5, 489.5].

Answer:

3

Step-by-step explanation:

Triangle ABC is an isosceles triangle, so

[tex]x^2+x^2=(6\sqrt{2} )^2\\2x^2=6^2*2\\x^2=6^2\\x=6.[/tex]

Triangle BCD is a notable triangle and the sides are

BD=x, CD=[tex]x\sqrt{3}[/tex],BC=2x=6

2x=6

x=3

Answer:

Volume = 24 ft³

Step-by-step explanation:

Given a rectangular aquarium whose dimensions are

2ft x 4 ft x 3 ft

Total volume = 3 x 4 x 3 = 24 ft³

Answer:

You will have $29,000 in 30 years, and you need to start with about $2,772.28 to make $14,000 in 9 years

Step-by-step explanation:

To find the total investment use the equation [tex]A = P(1 + rt)[/tex]

Where A equals total investment, P is your start investment, r is your rate, and t is time.

[tex]A=2,000(1+(0.45 * 30))[/tex]

[tex]A=2,000(1+13.5)[/tex]

[tex]A=2,000*14.5[/tex]

[tex]A=29,000[/tex]

To find the start investment use the equation [tex]P = A / (1 + rt)[/tex]

[tex]P=14,000/(1+(0.45*9))[/tex]

[tex]P=14,000/(1+4.05)[/tex]

[tex]P=14,000/5.05[/tex]

[tex]P=2,772.28[/tex]

━━━━━━━☆☆━━━━━━━

▹ Answer

(-1, 1) (-2, 2) (-3, 3)

▹ Step-by-Step Explanation

You can use a graphing calculator to find the points. Attached is an image.

Hope this helps!

- CloutAnswers ❁

!

━━━━━━━☆☆━━━━━━━

Answer:

The answer is 60cm^2.

hope it helps..

Answer:

The correct option is (A)

A. Replace row 4 by its sum with - 4 times row 3.

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]

w = 8

x = 17/2

y = 6

z = -5

Step-by-step explanation:

The given matrix is

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&4&5&-1\end{array}\right][/tex]

To solve this matrix we need to create a zero at the 4th row and 3rd column which is 4 at the moment.

Multiply 3rd row by -4 and add it to the 4th row.

Mathematically,

[tex]R_4 = R_4 - 4R_3[/tex]

So the correct option is (A)

A. Replace row 4 by its sum with - 4 times row 3.

So the matrix becomes,

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]

Now the matrix may be solved by back substitution method.

Bonus:

The solution is given by

Eq. 1

-3z = 15

z = -15/3

z = -5

Eq. 2

y + 2z = -4

y + 2(-5) = -4

y - 10 = -4

y = -4 + 10

y = 6

Eq. 3

2x - 6y + 0z = 5

2x - 6(6) = 5

2x - 12 = 5

2x = 12 + 5

2x = 17

x = 17/2

Eq. 4

w - 4x + 4y + 0z = -2

w - 4(17/2) + 4(6) = -2

w - 34 + 24 = -2

w - 10 = -2

w = -2 + 10

w = 8

Answer:

Millennium Dairy Product

a) Share of the company that SBI Caps should require today to get a required rate of return of 50%.

= 50%

b) If the company had 1,000,000 (100,000 x10) shares outstanding before the private placement, SBI Caps should purchase

1,000,000 shares = 50% of (1,000,000 + 1,000,000) shares

Assuming the founding promoters are not giving up their shares, instead, new equity shares are being issued.

c) The price per share SBI Caps should agree to pay, if her required return was 50% is

Rs.50 per share, which will provide the required additional equity financing of (Rs.50 million) since Rs.50 x 1,000,000 equals Rs.50 million.

d) Pre money and post money valuations:

These are based on the calculated Market Price of Rs.1,000 per share from the Price/Earnings Ratio.

Pre money valuation will be Rs.1,000 x 1,000,000 shares = Rs.1 billion

Post money valuation will be Rs.1,000 x 2,000,000 shares = Rs.2 billion

e) Carried interests of the VC and the promoters

VC's carried interest = share of profits = 50% xRs.50 million = Rs.25 million

Promoters' carried interest = Rs.25 million

Step-by-step explanation:

a) Calculation of share in the company:

SBI Cap's required rate of return is 50%

If she invests Rs.50 million today, her expected return will be equal to Rs.50 million x 50% = Rs.25 million

Since rate of return = Net Income/Initial Investment or (Current value of investment - Initial Investment)/Initial Investment.

This return will be equal to 50% of the total net income of Rs.50 million

b) Price/Earnings P/E ratio = Market price per share/Earnings per share (EPS)

Since P/E ratio of similar companies = 20 times,

The company's P/E = 20 times x EPS

With calculated EPS = Rs.50 million /1,000,000 = Rs.50

Therefore, price per share = 20 x Rs.50 = Rs.1,000

Pre money valuation = Rs.1,000 x 1 million shares = Rs.1 billion

Post money valuation = Rs.1,000 x 2 million shares = Rs.2 billion

c) The carried interest is the share of profits to which the promoters and the Venture Capitalists are entitled.  Their respective shares are 50% of the net income = Rs.25 million each.

d) The pre money and post money valuations:  The pre money valuation is the valuation of the company before the additional equity financing.  The post money valuation is the valuation of the company after the additional equity financing.  There are many ways to value a company.  In this case, we have used the P/E ratio as a basis for the valuation.  However, we did not dilute the earnings per share post money, for simplicity.

To prove that △DFE ~ △GFH by SAS similartiy theorem, then option C. ∠DFE is congruent to ∠GFH is appropriate. So that: [tex]\frac{DF}{GF}[/tex] = [tex]\frac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.

Given ΔDEF as shown in the diagram attached to this answer, the following can be observed:

By comparing ΔDEF and ΔGFH

DF = DG + GF

     = 12 + 4

DF = 16

Also,

EF = EH + HF

    = 9 + 3

EF = 12

Comparing the sides of ΔDEF and ΔGFH, we have;

[tex]\frac{DF}{GF}[/tex] = [tex]\frac{EF}{HF}[/tex]

[tex]\frac{16}{4}[/tex] = [tex]\frac{12}{3}[/tex]

4 = 4

Thus, the two triangles have similar sides.

Comparing the included angle <DFE and <GFH, then;

∠DFE is congruent to ∠GFH

So that the appropriate answer to the given question is option C. ∠DFE is congruent to ∠GFH

Therefore, to prove that △DFE ~ △GFH by the SAS similarity theorem;

[tex]\frac{DF}{GF}[/tex] = [tex]\frac{EF}{HF}[/tex] and ∠DFE is congruent to ∠GFH.

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Answer: C

Step-by-step explanation:

Answer: The equations are

w + s = 4500

2.25s = 4500

Step-by-step explanation:

Let w represent the number of bottles of water that the football manager bought.

Let s represent the number of bottles of soda that the football manager bought.

The manager needs to buy a total of 4,500 drinks. This means that

w + s = 4500

He also needs to have 25% more water than soda.

25% of soda = 25/100 × s = 0.25s

25% more of water than soda = s + 0.25s = 1.25s

The equation would be

1.25s + s = 4500

2.25s = 4500

Answer:

Yes. At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.

The random variable is the sample mean amount of mercury in the bass fish from the lakes of Florida.

The population parameter is the mean amount of mercury in the bass fish of Florida lakes.

The alternative hypothesis (Ha) states that the amount of mercury significantly differs from 1 mg/kg.

The null hypothesis (H0) states that the amount of mercury is not significantly different from 1 mg/kg.

[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]

Step-by-step explanation:

The question is incomplete.

There is no data provided.

We will work with a sample mean of 0.95 mg/kg and sample standard deviation of 0.15 mg/kg to show the procedure.

This is a hypothesis test for the population mean.

The claim is that the fish in all Florida lakes have different mercury than the allowable amount (1 mg of mercury per kg of fish).

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]

The significance level is assumed to be 0.05.

The sample has a size n=53.

The sample mean is M=0.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.15.

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

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.15}{\sqrt{53}}=0.0206[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.95-1}{0.0206}=\dfrac{-0.05}{0.0206}=-2.427[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=53-1=52[/tex]

This test is a two-tailed test, with 52 degrees of freedom and t=-2.427, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t<-2.427)=0.019[/tex]

As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.

Answer:

1 woman Teacher

Step-by-step explanation:

We proceed as follows;

Let W and M represent the set of women and men respectively , and T represent teachers

from the information given in the question we have

n(W)=29

n(M)=23

n(T)=4

n(M U T)=24

Mathematically;

n(MUT)=n(M)+n(T)-n(MnT)

24=23+4-n(Mn T)

n(MnT)=3

that is number of men teachers is 3,

so out of 4 teachers there are 3 men ,

and remaining 1 is the women teacher .

so the number of women teachers attending the lecture is 1

Answer:

Type I error would be that we conculde to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually equal to 65%.

Type II error would be that we fail to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually different from 65%.

Step-by-step explanation:

We are given that the percentage of households with more than 1 pet is 65%.

Let p = population % of households with more than 1 pet

So, Null Hypothesis, [tex]H_0[/tex] : p = 65%     {means that the percentage of households with more than 1 pet is equal to 65 %}

Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 65%      {means that the percentage of households with more than 1 pet is different from 65 %}

Type I error states that the null hypothesis is rejected given the fact that null hypothesis was true. Or in other words, it is the probability of rejecting a true hypothesis.

So, in our case, type I error would be that we conculde to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually equal to 65%.

Type II error states that the null hypothesis is accepted given the fact that null hypothesis was false. Or in other words, it is the probability of accepting a false hypothesis.

So, in our case, type II error would be that we fail to reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65 % when that percentage is actually different from 65%.

Answer:

The lines will intersect infinitely many times, because they are identical.

Step-by-step explanation:

Let's change the equations of the lines into (y=mx+b) form.

6x-4y=2 Divide by 2.

3x-2y=1 Move x and divide by -2.

-2y=1-3x ---> y= -1/2+3/2x

The equation of the first line is y=3/2x- 1/2

-2y+3x=1

-2y=1-3x

y = 3/2x -1/2

The equation of the second line is y = 3/2x- 1/2.

The lines are identical- infinitely many intersections.

Step-by-step explanation:

I think the answer is third because it doesn't has a solution.

Answer:

4.428 hours

Step-by-step explanation:

If the learning rate is 0.81, the slope of the learning curve is:

[tex]b=\frac{ln(0.81)}{ln(2)} \\b=-0.304[/tex]

The time it takes to produce the n-th unit is:

[tex]T_n=T_1*n^b[/tex]

If T1 = 8 hours, the time required to produce the seventh unit will be:

[tex]T_n=8*7^{-0.304}\\T_n=4.428\ hours[/tex]

It will take roughly 4.428 hours.