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4 years ago

If y = x2 + 2x , find the value of y when x = 5

Mathematics

1 answer:

Arturiano [62]4 years ago

8 0

Answer:

Step-by-step explanation:

Okay so you are gonna substitute x for 5 so the equations will look like y= (5)2+(5)2

So 10+10 = 20

So y=20

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WILL MARK BRAINLIEST IF CORRECT ANSWER! HOW MANY SOLUTIONS???

elena-14-01-66 [18.8K]

The answer is 1 solution which is x=1

6 0

3 years ago

How can you match up the disk and the given information?

olga nikolaevna [1]

Answer: The first diagram you selected is the correct visual representation.

Check out the diagram I posted below. The red vertical line is x = 0, aka the y axis. The blue parabola is 3x = y^2. The green horizontal line is y = 6. The region bounded by these curves is the gray shaded region.

Spinning that gray region around the y axis results in the first diagram in your answer choices. The disk in pink is a cross section to help find the volume (through the use of integral calculus).

7 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

3 years ago

What's 75 as a product of prime factors

Grace [21]

The primes factors of 75 are 3 and 5

3 0

3 years ago

To which set(s) of numbers does the number sqrt -16 belong? Select all that apply.

Mice21 [21]

<span>The square root of -16 is an imaginary number and a complex number. Sqrt(-16)=4i. We use the i to indicate that the number is imaginary since there is no number that can be multiplied by itself to get a negative number (a negative times a negative is a positive, and a positive times a positive is also a positive). So the use of i tells you immediately that it's an imaginary number. You can tell the number is complex because it has both a real and an imaginary part and could be written in the form a+bi, where a is a real number and bi is an imaginary number. In this specific case, the real part (a) is 0 and the imaginary part (bi) is 4i.</span>

6 0

4 years ago