If it is known that a+b/a-b=c, find the following: 2a-2b/5a+5b

The table shows the number of grapes eaten over several minutes. What is the rate of change for the function on the table? 15 gr

Mkey [24]

Answer:

1. 15 grapes eaten per minute.

Step-by-step explanation:

We have been given a table that shows the number of grapes eaten over several minutes. We are asked to find the rate of change of our given function.

Since we know that rate of change of a function can be found by vertical change of the function divided by horizontal change of the function.

$\text{Rate of change of a function}=\frac{\text{Vertical change}}{\text{Horizontal change}}$

$\text{Rate of change of a function}=\frac{y_2-y_1}{x_2-x_1}$

$y_2-y_1$ =Difference between two y-coordinates.

$x_2-x_1$ =Difference between corresponding x-coordinates of y-coordinates.

Upon substituting coordinates of any two points in above formula we will get,

$\text{Rate of change of the function}=\frac{60-15}{4-1}$

$\text{Rate of change of the function}=\frac{45}{3}$

$\text{Rate of change of the function}=15$

We can see that rate of change of our given function is 15 grapes eaten per minute and 1st option is the correct choice.

7 0

2 years ago

Read 2 more answers

A supervisor records the repair cost for 17 randomly selected stereos. A sample mean of $66.34 and standard deviation of $15.22

expeople1 [14]

Answer:

Critical value: T = 1.337

The 80% confidence interval for the mean repair cost for the stereos is between $45.991 and $86.689

Step-by-step explanation:

We have the standard deviation for the sample. So we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 17 - 1 = 16

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 16 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.8}{2} = 0.9$ . So we have T = 1.337, which is the critical value

The margin of error is:

M = T*s = 1.337*15.22 = 20.349

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 66.34 - 20.349 = $45.991

The upper end of the interval is the sample mean added to M. So it is 66.34 + 20.349 = $86.689

The 80% confidence interval for the mean repair cost for the stereos is between $45.991 and $86.689

3 0

2 years ago

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times

rusak2 [61]

Answer:

$x=30\\y=68\\z=82$

Step-by-step explanation:

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)

$y+z=5x$

The third angle is 14 more than the second

$z=y+14$

And remember that the sum of these three angles must be equal to 180.

$x+y+z=180$

Let's take these equations

$y+z=5x\\z=y+14\\x+y+z=180$

If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....

$x+y+z=180\\x+(y+z)=180\\x+(5x)=180$

Distribute the + sign

$x+5x=180$

Combine like terms;

$6x=180$

Divide by 6.

$x=\frac{180}{6}\\ x=30$

We have now defined that the measure of the first angle is 30º.

Let's take another equation... for example $z=y+14$

I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.

$x+y+z=180\\30+y+(y+14)=180$

Distribute the + sign and Combine like terms;

$30+y+y+14=180\\44+2y=180\\$

Subtract 44 to isolate 2y.

$2y=180-44\\2y=136$

Now divide by 2.

$y=\frac{136}{2}\\ y=68$

We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.

$x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82$

5 0

2 years ago

The distance between New York and Philadelphia by railroad is 90 miles; the distance between them by river and ocean is 240 mile

VladimirAG [237]

Start with 90/240, then reduce the fraction
you can reduce by dividing each by 10 to get 9/24
reduce more from there, seeing that each number can be divided by 3
9/3 = 3
24/3 = 8
answer 3/8

3 0

2 years ago

Julia went into a movie theater and bought 2 bags of popcorn and 5 pretzels, costing

andreyandreev [35.5K]

Answer:

A bag of pop corn costs $8, and each Pretzel costs $4.25.

Step-by-step explanation:

Let $b$ be the price of popcorn, and $p$ the price of Pretzels. If the girl bought 2 bags of popcorn and 5 Pretzels and it cost her $37.25, we have the equation