Ask question

Ask question

All categories

mihalych1998 [28]

3 years ago

15

sal makes a 10% commission on the first $5000 of sales and 15% on any sales over $5000. find his total graduated commission on $

15000 in sales

1 answer:

Helga [31]3 years ago

5 0

0.10(5000) = 500
0.15(10,000) = 1500

total commission on 15,000 = (150 + 500) = 2,000

You might be interested in

The average zinc concentration recovered from a sample of measurements taken in 36 different locations in a river is found to be

vazorg [7]

Answer:

The 95% confidence interval for the mean zinc concentration in the river is between 1.75 and 3.45 grams per milliliter.

The 99% confidence interval for the mean zinc concentration in the river is between 1.48 and 3.72 grams per milliliter.

Step-by-step explanation:

95% confidence interval:

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

$\alpha = \frac{1 - 0.95}{2} = 0.025$

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 $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = z\frac{\sigma}{\sqrt{n}}$

$M = 1.96\frac{2.6}{\sqrt{36}}$

$M = 0.85$

The lower end of the interval is the sample mean subtracted by M. So it is 2.6 - 0.85 = 1.75 grams per milliliter.

The upper end of the interval is the sample mean added to M. So it is 2.6 + 0.85 = 3.45 grams per milliliter.

The 95% confidence interval for the mean zinc concentration in the river is between 1.75 and 3.45 grams per milliliter.

99% confidence level:

By the same logic as for the 95% confidence interval, we have that $Z = 2.575$ . So

$M = z\frac{\sigma}{\sqrt{n}}$

$M = 2.575\frac{2.6}{\sqrt{36}}$

$M = 1.12$

The lower end of the interval is the sample mean subtracted by M. So it is 2.6 - 1.12 = 1.48 grams per milliliter.

The upper end of the interval is the sample mean added to M. So it is 2.6 + 1.12 = 3.72 grams per milliliter.

The 99% confidence interval for the mean zinc concentration in the river is between 1.48 and 3.72 grams per milliliter.

5 0

2 years ago

Suppose that v is an eigenvector of matrix A with eigenvalue λA, and it is also an eigenvector of matrix B with eigenvalue λB. (

galben [10]

Answer:

(a) Yes, $λ_{A}+λ_{B}$

(b) Yes, $λ_{A}λ_{B}$

Step-by-step explanation:

First, lets understand what are eigenvectors and eigenvalues?

Note: I am using the notation $λ_{A}$ to denote Lambda(A) sign.

$v$ is an eigenvector of matrix A with eigenvalue $λ_{A}$

$v$ is also eigenvector of matrix B with eigenvalue $λ_{B}$

So we can write this in equation form as

$Av=λ_{A}v$

So what does this equation say?

When you multiply any vector by A they do change their direction. any vector that is in the same direction as of $Av$ , then this $v$ is called the eigenvector of $A$ . $Av$ is $λ_{A}$ times the original $v$ . The number $λ_{A}$ is the eigenvalue of A.

$λ_{A}$ this number is very important and tells us what is happening when we multiply $Av$ . Is it shrinking or expanding or reversed or something else?

It tells us everything we need to know!

Bonus:

By the way you can find out the eigenvalue of $Av$ by using the following equation:

$det(A-λI)=0$

where I is identity matrix of the size of same as A.

Now lets come to the solution!

(a) Show that $v$ is an eigenvector of $A + B$ and find its associated eigenvalue.

The eigenvalues of $A$ and $B$ are $λ_{A}$ and $λ_{B}$ , then

$(A+B)(v)=Av+Bv=(λ_{A})v + (λ_{B})v=(λ_{A}+λ_{B})(v)$

so, $(A+B)(v)=(λ_{A}+λ_{B})(v)$

which means that $v$ is also an eigenvector of $A+B$ and the associated eigenvalues are $λ_{A}+λ_{B}$

(b) Show that $v$ is an eigenvector of $AB$ and find its associated eigenvalue.

The eigenvalues of $A$ and $B$ are $λ_{A}$ and $λ_{B}$ , then

$(AB)(v)=A(Bv)=A(λ_{B})=λ_{B}(Av)=λ_{B}λ_{A}(v)=λ_{A}λ_{B}(v)$

so,

$(AB)(v)=λ_{A}λ_{B}(v)$

which means that $v$ is also an eigenvector of $AB$ and the associated eigenvalues are $λ_{A}λ_{B}$

5 0

2 years ago

Which of the relations given by the following sets of ordered pairs is a function?

solniwko [45]

Answer:

B

Step-by-step explanation:

You can solve this by using the vertical line test. When you do the vertical line test, the vertical line should only pass through one point on the function. That means that there can to be only one value of x for every y. Set B is the only set where the x value doesn't repeat.

8 0

3 years ago

4/12 divided by 4/12

Ad libitum [116K]

When dividing a number by itself the outcome will always be 1

6 0

2 years ago

Need help with these dont really understand geometrey teacher teaching algebra 2 badly

jeyben [28]

Answer:

Which answer do u need help on?>

Step-by-step explanation:

6 0

2 years ago