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3 years ago

Simplify. Write answers with positive exponents only.

Mathematics

1 answer:

allochka39001 [22]3 years ago

7 0

Answer:

The answer to your question is 2⁸x²⁰ y²⁴ or 256x²⁰y²⁴

Step-by-step explanation:

Data

(2x³y³)⁴ (2x²y³)⁴

To solve this problem, use the law of exponents.

1.- Use the law of Power of a power rule

(2x³y³)⁴ (2x²y³)⁴ = (2⁴x¹²y¹²) (2⁴x⁸y¹²)

2.- Use the multiplication rule

(2⁴x¹²y¹²) (2⁴x⁸y¹²) = 2⁸x²⁰ y²⁴

3.- The answer is 2⁸x²⁰y²⁴ or we can simplify more like

256x²⁰y²⁴

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Judy is pulling on a trunk with a 12-N force. Ike pulls at right angles to Judy. With how much force must Ike pull to make the r

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To understand the problem, let's first draw a free body diagram of the forces exerted by Judy and Ike on the truck. (Refer to the left side of the attachment).

To solve for the resultant, we just use the tip-to-tail method. This is illustrated on the right side of the attachment.

We can see that the tip-to-tail method forms a right triangle thus we can just apply the Pythagorean theorem in solving for Ike's force.

$20^{2} = 12^{2} + F^{2}$
$400 = 144 + F^{2}$
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ANSWER: Ike must pull the truck with a force of 16.0 N.

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3 years ago

(x + 2) is raised to the fifth power. The third term of the expansion is:

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Answer:

Step-by-step explanation:

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3 years ago

3x-1=5x+10. and the X= -5 1/2

irga5000 [103]

Answer:

The answer is 1 or infinite solutions

Step-by-step explanation:

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2 years ago

What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean

Elena-2011 [213]

Answer:

0.658 is the probability that a sample 90 test takers will provide a sample mean test score within 10 points of the population mean of 502.

Step-by-step explanation:

The following information is missing:

The standard deviation of population is 100.

We are given the following information in the question:

Population mean, μ = 502

Standard Deviation, σ = 100

Sample size, n = 90

Standard error =

$\dfrac{\sigma}{\sqrt{n}} = \dfrac{100}{\sqrt{90}} = 10.54$

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(test score within 10 points)

$P(492 \leq x \leq 512) \\\\= P(\displaystyle\frac{492 - 502}{10.54} \leq z \leq \displaystyle\frac{512-502}{10.54}) \\\\= P(-0.9487 \leq z \leq 0.9487)\\= P(z \leq 0.9487) - P(z < -0.9487)\\= 0.829 -0.171 = 0.658 = 65.8\%$

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0.658 is the probability that a sample 90 test takers will provide a sample mean test score within 10 points of the population mean of 502.

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3 years ago

A jug has a maximum capacity of 14 liters. is filled to 60% of its capacity, and then poured out at a rate of 60 mL/s. Which of

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Answer:

W(x) = 3.4 L - (25/1000)(L/s)*x

Step-by-step explanation:

it a tip

W(x) = 3.4 L - (25/1000)(L/s)*x

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(85%/100%)*4L = 0.85*4L = 3.4L

Now, we pour 25 mL each second, so we could write a linear equation as:

W(x) = 3.4L - (25ml/s)*x

where x is the number of seconds that passed since the beginning,

But we want to write this in Liters, we have that:

1L = 1000mL.

Then 1mL = (1/1000) L

then we can write 25 mL as:

25m L = 25*(1/1000) L = (25/1000) L

Then we can write the equation as

W(x) = 3.4 L - (25/1000)(L/s)*x

which is the amount of water remaining in the jug after x seconds.

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3 years ago