What is 3.00 in a fraction?

What is the discriminant of the quadratic equation 0 = –x2 + 4x – 2?

kvv77 [185]

0=-x2+4x-2
+x2-4x+2=+x2-4x+2
___________________
x2-4x+2=0

(-4)^2-4(1)(2)

16-8

Final Answer: 8

3 0

3 years ago

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6x^2-5x+3 - (3x^2+8x-4)

amid [387]

The answer should be 3x^2 -13x+7.

5 0

3 years ago

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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

Can you plzz do 426 div by 30 thanks you and tell me how u got it

olasank [31]

Answer:

14.2

Step-by-step explanation:

4 0

3 years ago

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The sum of the roots of 8x^2- 2x

Andrews [41]

Answer:

1/4

Step-by-step explanation:

To find the roots of the expression, factor the expression by GCF.

$8x^2 - 2x\\2x(4x-1)$

The roots are the factors set equal to 0 and solved for x.

2x = 0

x=0

4x-1 = 0

x = 1/4

The sum is the addition of the two roots 0 + 1/4 = 1/4

8 0

3 years ago