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3 years ago

Geometry math question no Guessing and Please show work

Mathematics

1 answer:

saveliy_v [14]3 years ago

6 0

Here we have to use the theorem tht exterior angle is the sum of non adjacent interior angles. That is ,

z = x+y

And the values of x,y and z are given in terms of n. On substituting these values for x,y and z, we will get

151-5n = 4n-18+n+9

Combining like terms of the right side

151-5n = 5n -9

Moving 5n to the right side and 9 to the left side,

151+9 = 5n+5n

160=10n

Dividing both sides by 10

n = 16

Now we need to find the value of z when n =16. SO we substitute the value of n in z, that is

z =151-5(16) =151-80 = 71 degree .

So the correct option is A

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2. A marketing firm is trying to estimate the proportion of potential car buyers that would consider

Maurinko [17]

Answer:

a. The number of people that should be in the pilot study are 600 people

b. The point estimate is 0.62 $\overline 6$

c. At 95% confidence level the true population proportion of potential car buyers of hybrid vehicle is between the confidence interval (0.588, 0.6654)

d. Two ways to reduce the margin of error are;

1) Reduce the confidence interval

2) Use a larger sample size

Step-by-step explanation:

a. The given parameters for the estimation of sample size is given as follows;

The margin of error for the confidence interval, E = 4% = 0.04

The confidence level = 95%

The sample size formula for a proportion as obtained from an online source is given as follows;

$n = \dfrac{Z^2 \times P \times (1 - P)}{E^2}$

Where, P is the estimated proportions of the desired statistic, therefore, we have for a new study, P = 0.5;

Z = The level of confidence at 95% = 1.96

n + The sample size

Therefore, we have;

$n = \dfrac{1.96^2 \times 0.5 \times (1 - 0.5)}{0.04^2} = 600.25$

Therefore, the number of people that should be in the pilot study in order to meet this goal at 95% confidence level is n = 600 people

b. The point estimate for the population proportion is the sample proportion given as follows;

$\hat p = \dfrac{x}{n}$

Where;

x = The number of the statistic in the sample

n = The sample size

From the question, we have;

The number of potential car buyers, n = 600

The number of respondent in the sample that indicated that they would consider purchasing a hybrid, x = 376

Therefore, the point estimate, for the proportion of potential car buyers that would consider buying a hybrid vehicle, $\hat p$ = 376/600 = 0.62 $\overline 6$

c. The confidence interval for a proportion is given as follows

$CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

Therefore, we get;

$CI=0.62 \overline 6\pm 1.96\times \sqrt{\dfrac{\hat{0.62 \overline 6}\cdot (1-\hat{0.62 \overline 6})}{600}}$

C.I. ≈ 0.6267 ± 0.0387

The 95% confidence interval for the true population proportion of potential buyers of hybrid vehicle, C.I. = (0.588, 0.6654)

d. The margin of error is given by the following formula;

$MOE_\gamma = z_\gamma \times \sqrt{\dfrac{\sigma ^2}{n} }$

Where;

$MOE_\gamma$ = Margin of error at a given level of confidence

$z_\gamma$ = z-score

σ = The standard deviation

n = The sample size

Therefore, the margin error can be reduced by the following two ways;

1) Reducing the confidence interval and therefore, the z-score

2) Increasing the sample size

6 0

3 years ago

Ice thickness decreases at a rate of 0.2 meters per week. After 7 weeks,the ice is only 2.4 meters thick. What is the equation f

sergiy2304 [10]

Answer:

The equation for relationship between the thickness and the number of weeks is f(x)=3.8 -0.2*x

Step-by-step explanation:

Ice thickness decreases at a rate of 0.2 meters per week. This can then be represented by the expression

f(x) = k - 0.2*x

where k is the thickness of the ice before the melting starts and x is the number of weeks.

After 7 weeks, the ice is only 2.4 meters thick. This means that x has a value of 7, while f (7) = 2.4. Replacing in the previous expression:

2.4=k -0.2*7

and solving you get:

2.4=k- 1.4

2.4 + 1.4= k

3.8= k

Then, <u><em>the equation for relationship between the thickness and the number of weeks is f(x)=3.8 -0.2*x</em></u>

7 0

3 years ago

what is the distance from the origin to the midpoint of the line segment defined by the endpoints (-4, 0) and (2, -2)?

Zielflug [23.3K]

Answer. I hope it helps you !!

5 0

3 years ago

Find the product of 5.21 and 3.4

SIZIF [17.4K]

Step-by-step explanation:

5.21× 3.4 = 17.714

thank u

6 0

2 years ago

Can someone help me with 13,14,15 and 16 please

xeze [42]

Answer: -3/5, 18/32, -10/11, and horizontal.

Step-by-step explanation: Remember the equation for slope? Δy (the change in y), over Δx (the change in x). In other words, rise over run. To solve for Δ, you'd have to subtract the second output (y²) from the first (y¹). There are really no rules as to which has to be minuend and the subtrahend, so I chose to subtract (-1,6) from (4,3) for the first problem.

y¹-y² Δy 3-6 -3

------ or ---- so ------- = ----- The slope is represented by -3/5x

x¹-x² Δx 4-(-1) 5

__________________________________________________________

For the second, substitute the values again (make sure you keep the xs and ys together and in the right order, otherwise your answer will be incorrect). Remember that subtracting a negative number is basically just adding a positive number. That's why the slope is 18/32 and not 4/26.

11-(-7) 18

--------- = -------

29-(-3) 32

___________________________________________________________

For number three, they give you a point, then tell you the y-intercept. With that in mind, also know the second point is (0,17), because the x value at the y-intercept is always 0.

7-17 -10

------ = ------- The slope is -10/11x

11-0 11

___________________________________________________________

4-4 0

------ = --------

6-(-9) 15

Because there is no Δy, but there is Δx, we know that the line for y will be straight and shows no change- it will always be at 4. That said, the line will be horizontal.

I hope this helps. I know this is very confusing at first, but with practice, you'll eventually get the hang of it. I've tried to explain the rules to the best of my ability- let me know if there's anything you don't understand or need more help with.

Sincerely,

Lacia :))

5 0

3 years ago