8

An animal shelter spends $2.00 per day to care for each cat and $7.00 per day to care for each dog. Brooklyn noticed that the sh

Oxana [17]

Answer:

The number of cats at the shelter on Friday was 20.

Step-by-step explanation:

Hi there!

Let "x" be the number of cats and "y" the number of dogs.

The shelter spends $2 per cat and $7 per dog. If the total expenses on Friday was $82, then, two times the number of cats plus seven times the number of dogs is equal to 82:

2x + 7y = 82

We also know that the total number of cats and dogs was 26. Then, the number of cats plus the number of dogs is equal to 26:

x + y = 26

Let´s solve this equation for y and replace it in the first equation

y = 26 - x

Then:

2x + 7(26 - x) = 82

Apply distributive property:

2x + 182 - 7x = 82

Subtract 182 to both sides of the equation:

-5x = -100

divide both sides of the equation by -5

x = 20

The number of cats at the shelter on Friday was 20.

Have a nice day!

3 0

4 years ago

What is the rate of change please help asap

pav-90 [236]

The rate of change is 5

3 0

3 years ago

Calibrating a scale:

lana66690 [7]

Answer:

We conclude that the calibration point is set too high.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 1000 grams

Sample mean, $\bar{x}$ = 1001.1 grams

Sample size, n = 50

Alpha, α = 0.05

Population standard deviation, σ = 2.8 grams

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 1000\text{ grams}\\H_A: \mu > 1000\text{ grams}$

We use One-tailed(right) z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{ 1001.1 - 1000}{\frac{2.8}{\sqrt{50}} } = 2.778$

Now, $z_{critical} \text{ at 0.01 level of significance } = 2.326$

Since,

$z_{stat} > z_{critical}$

We reject the null hypothesis and accept the alternate hypothesis. We accept the alternate hypothesis. We conclude that the calibration point is set too high.

6 0

3 years ago

Marlene rides her bike at a rate of 16 miles per hour. The time in hours that she rides is represented by the variable t, and th

Vesna [10]

Question is Incomplete; Complete question is given below;

Marlene rides her bike at a rate of 16 miles per hour. The time in hours that she rides is represented by the variable t, and the distance she rides is represented by the variable d. Which statements are true of the scenario? Check all that apply.

a. The independent variable, the input, is the variable d, representing distance.

b. The distance traveled depends on the amount of time Marlene rides her bike.

c. The initial value of the scenario is 16 miles per hour.

d. The equation t = d + 16 represents the scenario.

e. The function f(t) = 16t represents the scenario.

Answer:

OPTION (b) and (e) are the true statements.

Step-by-step explanation:

Given:

$t=>$ time in hours that she rides

$d=>$ distance she rides

We have to find the statements that are true of the scenario.

Solution:

$d=16t$

The equation itself is a linear equation which presents an equation's scenario and time (t) is a independent variable and distance (d) is a dependent variable.

Equation for distance according to function is $f(t)=16t$