Evaluate the expression when x=-3<br><br> x ^2 + 8x-7

A submarine is running at a depth of 235 ft underwater. It changes course and rises 101 ft. What is the change in elevation?

Bumek [7]

Answer:

The change in elevation is -134 ft

Step-by-step explanation:

Given;

initial depth of the submarine, d₁ = 235 ft

final depth of the submarine, d₂ = 101 ft

The change in the elevation of the submarine is given by;

Δd = d₂ - d₁

Δd = 101 ft - 235 ft

Δd = -134 ft

The change in elevation is negative because the submarine is moving closer to the surface.

Therefore, the change in elevation is -134 ft

8 0

3 years ago

A local marketing company wants to estimate the proportion of consumers in the Oconee County area who would react favorably to a

Burka [1]

Answer:

C. n=423

Step-by-step explanation:

1) Notation and important concepts

Margin of error for a proportion is defined as "percentage points your results will differ from the real population value"

Confidence=90%=0.9

$\alpha=1-0.9=0.1$ represent the significance level defined as "a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant".

$\hat p=0.5$ represent the sample proportion of consumers in the Oconee County area who would react favorably to a marketing campaig. For this case since we don't have enough info we use the value of 0.5 since is equiprobable the event analyzed.

$z_{\alpha/2}$ represent a quantile of the normal standard distribution that accumulates ${\alpha/2}$ on each tail of the distribution.

2) Formulas and solution for the problem

For this case the margin of error for a proportion is given by this formula

$ME=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$ (1)

For this case the confidence level is 90% or 0.9 so then the significance would be

$\alpha=1-0.9=0.1$ and $\alpha/2=0.05$

With $\alpha/2=0.05$ , we can find the value for $z_{\alpha/2}$ using the normal standard distribution table or excel.

The calculated value is $z_{\alpha/2}=1.644854$

Now from equation (1) we need to solve for n in order to answer the question.

$\frac{ME}{z_{\alpha/2}}=\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Squaring both sides:

$(\frac{ME}{z_{\alpha/2}})^2=\frac{\hat p(1-\hat p)}{n}$

And solving for n we got:

$n=\frac{\hat p(1-\hat p)}{(\frac{ME}{z_{\alpha/2}})^2}$

Now we can replpace the values

$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.644854})^2}=422.739$

And rounded up to the nearest integer we got:

n=423

3 0

3 years ago

Explain how showing fractions with models and a number line are alike and different

Leni [432]

You use a number line to see what is greater and less than.
And use a model to visualize it more.
And they are alike because they can both help in the same way but for different people.

7 0

3 years ago

How do i find the area of a circle to the nearest tenth

Dmitry_Shevchenko [17]

A=pi multiplied by the radius squared

7 0

3 years ago

Read 2 more answers

The question is in the picture:

rosijanka [135]

Answer:

b) The measure of angle B is 117°.

Step-by-step explanation:

Angles A and C are vertical angles, so are congruent. Angles C and 27° total 90°, so ...

∠C = 90° -27° = 63° . . . . . not 53°

The measure of angle B is the supplement of angle A or C, so is ...

∠B = 180° -∠C = 180° -63°

∠B = 117°

Only choice B is correct.

8 0

4 years ago

Evaluate the expression when x=-3 x ^2 + 8x-7