Making an inference is the second part of the process of investigating a

Consider an angle with a measure of θ=225∘.

wel

Answer:

cos 225° = $-\frac{\sqrt{2} }{2}$

sin 225° = $-\frac{\sqrt{2} }{2}$

tan 225° = 1

Step-by-step explanation:

I cannot sketch a diagram, but a 225° angle is a 3rd quadrant angle and the reference angle is 45° (225 - 180 = 45)

cos and sin are negative in the 3rd quadrant and the tan is positive

cos 225° = - cos 45° = $-\frac{\sqrt{2} }{2}$

sin 225° = -sin 45° = $-\frac{\sqrt{2} }{2}$

tan 225° = tan 45° = 1

8 0

3 years ago

How to solve this equation?

Novay_Z [31]

Answer:

x = √(28), or x = 5.292

Step-by-step explanation:

First you distribute the square to the values inside of the parentheses. so it ends up looking like this

5(x^2 - 25) - 9 = 6

add 9 to both sides

so its 5(x^2 - 25) = 15

Then distribute the multiplication of 5 to the contents within the parentheses

so it would be 5x^2 - 125 = 15

add 125 to both sides

you get 5x^2 = 140

divide by 5 on both sides

you get x^2=28

then, take the square root of both sides to reverse the square

√(x^2)=√(28)

and in the end you get x=5.292

but √(28) will probably be fine if your teacher doesn't want u to solve for that kind of stuff.

6 0

3 years ago

An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining.

strojnjashka [21]

Answer:

1. The 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-2411.84, -1332.16).

2. The point estimate for the true difference between the population means is of -1872.

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of Normal Variables:

When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

A sample of 212 brakes using Compound 1 yields an average brake life of 47,895 miles. The population standard deviation for Compound 1 is 1590 miles.

This means that $\mu_1 = 47895, \sigma_1 = 1590, n = 212, s_1 = \frac{1590}{\sqrt{212}} = 109.2$

A sample of 180 brakes using Compound 2 yields an average brake life of 49,767 miles. The population standard deviation for Compound 2 is 4152 miles.

This means that $\mu_2 = 49767, \sigma_2 = 4152, n = 180, s_2 = \frac{4152}{\sqrt{180}} = 309.47$

True difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.

This is the distribution 1 - 2. So

$\mu = \mu_1 - \mu_2 = 47895 - 49767 = -1872$

This is also the point estimate for the true difference between the population means, which is question 2.

$s = \sqrt{s_1^2+s_2^2} = \sqrt{109.2^2+309.47^2} = 328.17$

90% confidence interval

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.645.

Now, find the margin of error M as such

$M = zs = 1.645*328.17 = 539.84$

The lower end of the interval is the sample mean subtracted by M. So it is -1872 - 539.84 = -2411.84

The upper end of the interval is the sample mean added to M. So it is -1872 + 539.84 = -1332.16.

The 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-2411.84, -1332.16).

5 0

4 years ago

Rewrite in simplest terms: (-4x + 8y) - (-3x - 8y)

Gre4nikov [31]

Answer:

im pretty sure its − x + 16 y

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

4) Suppose the points shown on the coordinate plane are vertices of a rectangle. Which statements are correct? A) The perimeter

Assoli18 [71]

Answer:

B) The perimeter of the rectangle is 28 units.

E) The coordinates for the fourth vertex of the rectangle are (−5, −3).

Step-by-step explanation:

The length of the rectangle is 9 and width is 5.

The perimeter is 2( 9 + 5 ) = 28 units

as the upper one is right. Option A eliminated.

The coordinates for the fourth vertex of the rectangle are (−5, −3).

as the upper one is right. option C and D will be eliminated.

7 0

2 years ago

Read 2 more answers