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QUIZ:
Foundations - Systems of Equations
Which expression is equivalent
Please help

Answer:

[tex]V=6x^3+3x^2[/tex]

Step-by-step explanation:

The given figure shows a cuboid whose length is (2x+1) breadth is x and height is 3x.

We need to find the volume of the three dimensional figure.

The volume of a cuboid is given by :

V = lbh

Substitute all the values,

[tex]V=(2x+1)\times x\times 3x\\\\V=(2x+1)\times 3x^2\\\\= 3x^2(2x)+3x^2\\\\V=6x^3+3x^2[/tex]

So, the volume of the figure is equal to [tex]6x^3+3x^2[/tex].

Answer:

0.47

Step-by-step explanation:

f(x) = (x - 2)^(1/3)

average rate of change from x = -2 to x = 4 is [f(4) - f(-2)]/[4 - (-2)]

f(-2) = (-4)^(1/3) = -1.587401

f(4) = 2^(1/3) = 1.25992

[f(4) - f(-2)]/[4 - (-2)] = [1.25992 - (-1.587401)]/[4 - (-2)] = 0.47

Answer:18.2

Step-by-step explanation: you add them up and and divide them

Answer:

The integer that represents the situation is 5.

Step-by-step explanation:

When you gain 5 yards, that is considered a positive increase in value.

You can either put 5 or +5 because they indicate the same positive value.

there are four lateral faces

Answer:

1

2

4

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

so it is 20 c because like why not

Answer:

[tex]Z = 2[/tex]

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 21 and a standard deviation of 5.

This means that [tex]\mu = 21, \sigma = 5[/tex]

Find the Z score for a student that gets a 31

This is Z when X = 31. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{31 - 21}{5}[/tex]

[tex]Z = 2[/tex]

Solution :

95% confidence interval for the difference between the means of ACT scores between two schools, is given by :

[tex]$[(\overline X_1 - \overline X_2)-ME, (\overline X_1 - \overline X_2)+ME]$[/tex]

[tex]$\overline X_1 = 25.90 , \ \ \ \overline X_2 = 27.70$[/tex]

[tex]$S_1=3.49, \ \ \ S_2 = 2.47$[/tex]

[tex]$n_1=39, \ \ n_2=37$[/tex]

M.E. , Margin of error,

[tex]$=t_{n_1+n_2-2,0.025} \times \left( s \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}$[/tex]

[tex]$s^2 = \frac{(n_1-1)S_1^2+(n_2-1)S^2_2}{n_1+n_2-2}$[/tex]

  [tex]$=\frac{38(3.49)^2+36(2.47)^2}{39+37-2}$[/tex]

 = 9.222

s = 3.03

[tex]$t_{74,0.05} = 1.99$[/tex]

[tex]$M.E. = 1.99 \times 3.03 \times \sqrt{\frac{1}{39}+\frac{1}{37}}$[/tex]

        = 1.4

Therefore, 95% CI = [(25.90-27.70) - 1.4 , (25.90-27.70) + 1.4]

                              = [-3.2, -0.4]

Therefore, the lower bound is -3.2

9514 1404 393

Answer:

  A)  15

Step-by-step explanation:

The angle where the tangent meets the radius is 90°, so the Pythagorean theorem applies to this right triangle.

  ?² +8² = 17²

  ?² = 289 -64 = 225

  ? = √225 = 15

The unknown side length is 15.

Answer:

lenght indicated appear to be tangent

Answer: 32%

Step-by-step explanation:

The percentage increase will be gotten by using the formula:

= Increase in score / Former score × 100

= (33 - 25) / 25 × 100

= 8/25 × 100

= 8 × 4

= 32%

The percentage increase is 32%.

Answer:

40

Step-by-step explanation:

Angle 1 and 2 are alternate angles

Then they are equal

2x+20=3x+10

Solve for x

X=10

Then 2 (10)+20 =40

Answer:

test statistic = 12.115

Step-by-step explanation:

Given data :

std = 2.1 years

n = 10

( std )^2 = 4.41

determine the test statistic

apply a two-tailed test ( chi squared test for one population variance )

test statistic

λ^2 = [tex]\frac{(n-1)s^2}{3.2761}[/tex]   ( Referring to Exhibit 11-1 )

      = ( 10 - 1 )*(2.1)^2 / 3.2761

      = 12.115

Answer:

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Step-by-step explanation:

3:

h(x)=(-3x-15)/5

let y=(-3x-15)/5

interchanging role of x &y

x=(-3y-15)/5

5x+15=-3y

y=-(5x+15)/3

h-1(x)=-(5x+15)/3

not

equal to f(x)=(-3x-6)/4

Given function are not function of each other .

4:

g(x)=2/3x-2/3

let

y=2/3(x-1)

interchanging role of x &y

x=2/3(y-1)

3/2x+1=y

g-1(x)=3/2x+1

not equal to f(x)=½x+1

Given function are not function of each other .

Problem 1

--------------------

Explanation:

One way to see if we have an inverse pair or not is to compute these two composite functions

If both result in x, and just that, then we have shown that they are inverses of one another.

f(x) = (2x)/3

f(x) = (2/3)x

f(g(x)) = (2/3)*g(x)

f(g(x)) = (2/3)*(3/2)x

f(g(x)) = x

The steps to show that g(f(x)) = x are very similar

g(x) = (3/2)x

g(f(x)) = (3/2)*f(x)

g(f(x)) = (3/2)*(2/3)*x

g(f(x)) = x

So this verifies that you have the correct answer.

======================================================

Problem 2

--------------------

Explanation:

We'll use the same idea as problem 1

f(x) = 2 - (3/4)*x

f(g(x)) = 2 - (3/4)*( g(x) )

f(g(x)) = 2 - (3/4)*( (-4/3)x + 8/3 )

f(g(x)) = 2 - (3/4)*(-4/3)x  - (3/4)*(8/3)

f(g(x)) = 2 + x - 2

f(g(x)) = x

So far so good, but we need to check the other way around as well

g(x) = (-4/3)x + 8/3

g(f(x)) = (-4/3)*( f(x) ) + 8/3

g(f(x)) = (-4/3)*( 2 - (3/4)*x ) + 8/3

g(f(x)) = (-4/3)*(2) + (-4/3)*(-3/4)*x + 8/3

g(f(x)) = -8/3 + x + 8/3

g(f(x)) = x

This verifies that f(x) and g(x) are inverses of each other.

Problems 3 and 4 will have similar steps.

Answer:

2.67 hours

Step-by-step explanation:

Diana: 15 cookies per hour

Jamie: 7.5 cookies per hour

15 + 7.5 = 22.5

22.5 cookies per hour

[tex]\frac{60}{22.5} =\frac{y}{1}[/tex]

22.5 · y = 60 · 1

22.5y = 60

22.5y ÷ 22.5 = 60 ÷ 22.5

[tex]y=2\frac{2}{3}[/tex]

[tex]2\frac{2}{3}[/tex]  rounded to the nearest hundredth is 2.67

Answer: 12

Step-by-step explanation:

You can find the area of a rectangle that forms around it, and then subtract the little extra triangles. You can form a 5 by 5 square around the points. There are 4 extra little triangles. Two of them have a base and height of 2 and 2. Two of them have a base and height of 3 and 3. So you get the total area of those 4 triangles to be: 2+2+4.5+4.5=13. So 25-13=12.

Answer:

Hello! question 1: area for question is 547.1136 round if your teacher wants you to. circumference for this question: 82.896 round if teacher wants you to.

Answer:

i rath  r buy...

the twin-pack

sunscreen

Step-by-step explanation:

Step-by-step explanation:

540 espero que que ayude UWU

Answer:

What are the answer choices?

Answer:

3/4

Step-by-step explanation:

2/3a=1/3+1/6

2/3a=3/6

a=1/2x3/2

a=3/4

Answer:

Step-by-step explanation:

Answer:

Is that all to the problem?

Step-by-step explanation:

Answer:

Is there supposed to be more information?

Step-by-step explanation:

Answer:

The weight of a tomato depends on the variety of tomato. There are cherry, plum, grape, roma, and beef tomatoes of various sizes. The following tables shows different types of tomatoes, along with the average weight (in grams and ounces), the number of tomatoes per kilogram, and the number of tomatoes per pound.

Step-by-step explanation:

Answer:

60

Step-by-step explanation

20*3 becasuse it equlatrial

Answer:

x ≈ 5

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

Given

[tex]log_{10}[/tex] x ≈ 0.701 , then

x = [tex]10^{0.701}[/tex] ≈ 5

Answer:

1. C

3. D

5. B

Don't know the others sorry!

Step-by-step explanation:

Answer:

4. [tex]g(x)=-x^{2}-10x-15[/tex]

6.[tex](2, -11)[/tex]