What statement regarding the diagram is true?

A zoo is building a new large-cat exhibit. Part of the space will be used for lions and part for leopards. The exhibit will have

Fittoniya [83]

The equations for the expenses for maintaining 4 lions and 4 leopards in the new large-cat exhibit are as follows:

Lions Leopard

Equations 4x = 32,000 4y = 24,000

<h3>What is an equation?</h3>

An equation is a mathematical statement that shows the values of two mathematical expressions are equal.

An equation is made up of two mathematical expressions connected by an equal sign.

<h3>Data and Calculations:</h3>

Annual expenses for lion per unit, x = $8,000

Annual expenses for leopard per unit, y = $6,000

Total number of larget-cats required = 8

Let the cost of maintaining 4 lions = 4x

Let the cost of maintaining 4 leopards = 4y

Total cost for 4 lions = $32,000 (8,000 x 4)

Total cost for 4 leopards = $24,000 (6,000 x 4)

Total cost for eight large cats per year = $56,000 ($32,000 + $24,000)

Equation for lions, 4x = 32,000

Equation for leopards, 4y = 24,000

The total costs for maintaining eight large cats in all will be <u>$56,000</u> per year.

Thus, the equations for the expenses for maintaining 4 lions and 4 leopards in the new large-cat exhibit are <u>4x = 32,000</u> and <u>4y = 24,000</u>, respectively.

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5 0

2 years ago

Simplify -2xy + 3x -2xy + 3x

Savatey [412]

Answer:

-4xy +6x

Step-by-step explanation:

combine like terms

-2xy + 3x - 2xy + 3x

3x + 3x = 6x

-2xy - 2xy = -4xy

-4xy +6x

3 0

4 years ago

Read 2 more answers

From Statistics and Data Analysis from Elementary to Intermediate by Tamhane and Dunlop, pg 265. A thermostat used in an electri

Leviafan [203]

Answer:

$t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =2*P(t_{(9)}>2.32)=0.0455$

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

Step-by-step explanation:

Information given

data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0

We can calculate the sample mean and deviation with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=201.77$ represent the sample mean

$s=2.41$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =200$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic

$p_v$ represent the p value for the test

Hypothesis to test

We want to determine if the true mean is equal to 200, the system of hypothesis are :

Null hypothesis: $\mu = 200$

Alternative hypothesis: $\mu = 200$

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

The statistic is given by:

$t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =2*P(t_{(9)}>2.32)=0.0455$

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

4 0

3 years ago

The area of a square is represented by the expression 16x4y8. Which expression could represent the length of one side of the squ

RSB [31]

Answer:

4 sq 8

Step-by-step explanation:

7 0

3 years ago

The quadrilateral shown is a rectangle. What is the measure of PR? (round to the nearest hundredth)

sladkih [1.3K]

Option B) 37.12 is the right answer

Step-by-step explanation:

It is given that the qudrilateral is a rectangle which means that opposite sides wil be equal and all interior angles will be 90 degrees

So

PS = 17

PQ = SR = 33

The diagonal PR will form a right-angles triangle with PR being the hypotenuse

So,

Base = SR = 33

Perpendicular = PS = 17

Hypotenuse = PR = ?

The Pythagoras theorem will be used to find the length of PR

So,

$H^2 = B^2+P^2\\(PR)^2 = (SR)^2 + (PS)^2\\PR^2 = (33)^2+(17)^2\\PR^2 = 1089+289\\PR^2 = 1378\\$

Taking square root on both sides

$\sqrt{PR^2} = \sqrt{1378}\\PR = 37.1214$

Rounding off to nearest 100th

PR = 37.12

Hence,

Option B) 37.12 is the right answer

Keywords: Triangle, Pythagoras theorem

Learn more about triangles at:

#LearnwithBrainly

6 0

4 years ago