What are the roots of the following function?

A key board tht cost $400 is marked down 10%for a sale.what is the reducd price for the key board

allochka39001 [22]

$350 at least i think anyways

4 0

3 years ago

Step by step explanation need it

nasty-shy [4]

Answer:

8/17

Step-by-step explanation:

The sine of an angle is defined as the opposite side to the reference angle divided by the hypotenuse.

The side opposite the angle is always the side not connected to the reference angle. In this case the opposite side = ZY

The hypotenuse = XZ

Sin(X) = ZY/XZ

Sin(X) = 1634 = 8 / 17

4 0

3 years ago

At the ice cream shoppe,

motikmotik

Answer:

$2.59

Step-by-step explanation:

Let b and m represent the costs of a banana split and a milkshake, respectively. Then the two purchases are ...

b +5m = 16.24

3b +2m = 15.05

Subtracting the second equation from 3 times the first, we have ...

3(b +5m) -(3b +2m) = 3(16.24) -(15.05)

13m = 33.67 . . . . . . simplify

m = 2.59 . . . . . . . . . divide by 13

The cost of a milkshake is $2.59.

5 0

4 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

Two points are selected randomly on a line of length 32 so as to be on opposite sides of the midpoint of the line. In other word

Paladinen [302]

Solution :

Let us consider the squares be $[1, 16] \times [16, 32]$

If x ranges from the 0 to 16 and the y ranges from 16 to 32, we see that the boundary of the region $y-x \geq 9 \text{\ is}\ y - x = 9$ which goes from the $(7, 16 ) \text{ to}\ (16, 25)$ .

And so it is easier to find the area of region where $y-x \leq 9$ . This is the triangle with points $(7,16),(16,25) \text{ and}\ (16,16)$ as its vertices.