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2 years ago

6

The piney creek swim club is preparing for opening day. the pool holds 22,410 gallons of water and the water is being pumped in

at 540 gallons per hour. The club has it's first practice in 42 hours. Will the pool be full in time?

1 answer:

andrew-mc [135]2 years ago

8 0

Answer:

Yes,

Step-by-step explanation:

all you do is 540x42 which gives you 22680 and the pool only needs to be filled up with 22410, so yes

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(x+12) (3x+2)<br> Find the value of X

KatRina [158]

Step-by-step explanation:

Equation at the end of step 1

(3x2 - 38x) + 24 = 0

STEP2:Trying to factor by splitting the middle term

2.1 Factoring 3x2-38x+24

The first term is, 3x2 its coefficient is 3 .

The middle term is, -38x its coefficient is -38 .

The last term, "the constant", is +24

Step-1 : Multiply the coefficient of the first term by the constant 3 • 24 = 72

Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is -38 .

-72 + -1 = -73 -36 + -2 = -38 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -36 and -2

3x2 - 36x - 2x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

3x • (x-12)

Add up the last 2 terms, pulling out common factors :

2 • (x-12)

Step-5 : Add up the four terms of step 4 :

(3x-2) • (x-12)

Which is the desired factorization

Equation at the end of step2:

(x - 12) • (3x - 2) = 0

STEP3:Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2 Solve : x-12 = 0

Add 12 to both sides of the equation :

x = 12

Solving a Single Variable Equation:

3 0

2 years ago

Read 2 more answers

Write two and forty-two thousandths in decimal notation.<br> please please

dem82 [27]

It’s 2.042

Have a great day! :D

8 0

2 years ago

Read 2 more answers

Taylor climbed a tree and is sitting on one of the branches deciding if she wants to jump. She weighs 45 kilogram and is sitting

olchik [2.2K]

Answer:

Her potential energy is approximately 4481 J.

Step-by-step explanation:

Because the formula for potential energy is PEg = 9.81 * mass * height, just plug in the knowns. After you plug those in, you will get the potential energy as 9.81 * 450, which is approximately 4481 J.

6 0

2 years ago

Kobotan [32]

Answer:

well first 312 in radical form is √312 and that simplified is 2√78 or 17.66352173

Step-by-step explanation:

3 0

2 years ago

A recent study from the University of Virginia looked at the effectiveness of an online sleep therapy program in treating insomn

Ludmilka [50]

Answer:

1. The 99% confidence interval for the difference in average is -6.47377 < μ₁ - μ₂ < -11.34623

2. The possible issues in the calculations includes;

a. The confidence level used in the confidence interval can influence the result of the confidence interval observed

b. The sample size is small

Step-by-step explanation:

1. The number of adults with insomnia in the sample = 45

The number of adults that participated in the therapy, n₁ = 22

The number of candidates that served as control group, n₂ = 23

The average score for the for the 22 participants of the program, $\overline x_1$ = 6.59

The standard deviation for the 22 participants of the program, s₁ = 4.10

The average score for the for the 23 subjects in the control group, $\overline x_2$ = 15.50

The standard deviation for the 23 subjects in the control group, s₂ = 5.34

The confidence interval for unknown standard deviation, σ, is given by the following expression;

$\left (\bar{x}_{1}- \bar{x}_{2} \right )\pm t_{\alpha /2}\sqrt{\dfrac{s_{1}^{2}}{n_{1}}+\dfrac{s_{2}^{2}}{n_{2}}}$

α = 1 - 0.99 = 0.01

α/2 = 0.005

The degrees of freedom, df = 22 - 1 = 21

$t_{\alpha /2}$ = $t_{0.005, \, 21}$ = 1.721

Therefore, we have;

$\left (6.59- 15.5 \right )\pm1.721 \cdot \sqrt{\dfrac{4.10^{2}}{22}+\dfrac{5.34^{2}}{23}}$

The 99% confidence interval for the difference in average is therefore given as follows;

-6.47377 < μ₁ - μ₂ < -11.34623

Therefore, there is considerable evidence that the participants in the survey had lower average score than the subjects in the control group

2. The possible issues in the calculations are;

a. The confidence level used in the confidence interval can influence the result of the confidence interval observed

b. The sample size is small

5 0

1 year ago