Simplify<br> -3/4(5p-12)+2(8-1/4p)

Darlene wrote this proof of the identity (x + y)2 - (x - y)2 = 4xy. Which of the following is a justification for Step 3 of her

vodka [1.7K]

Solution:

we are given that

Darlene wrote this proof of the identity (x + y)2 - (x - y)2 = 4xy.

we have been asked to find

Which of the following is a justification for Step 3 of her proof?

Step 3 of her proof is

$Step 3: (x^2 + xy + xy + y^2) - (x^2 - xy - xy + y^2) = (x^2 + 2xy + y2) - (x^2 - 2xy + y^2)$

As we can observe inside each of the paranthesis only like terms have been added. It mean the required justification is

C. Combining like terms

7 0

2 years ago

A sample of 900 college freshmen were randomly selected for a national survey. Among the survey participants, 372 students were

Rufina [12.5K]

Answer:

a) $ME=2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.0423$

b) $0.413 - 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.371$

Step-by-step explanation:

1) Data given and notation

n=900 represent the random sample taken

X=372 represent the students were pursuing liberal arts degrees

$\hat p=\frac{372}{900}=0.413$ estimated proportion of students were pursuing liberal arts degrees

$\alpha=0.01$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

p= population proportion of students were pursuing liberal arts degrees

2) Solution to the problem

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

The margin of error is given by:

$ME=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

If we replace we have:

$ME=2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.0423$

And replacing into the confidence interval formula we got:

$0.413 - 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.371$

$0.413 + 2.58 \sqrt{\frac{0.413(1-0.413)}{900}}=0.455$

And the 99% confidence interval would be given (0.371;0.455).

We are confident (99%) that about 37.1% to 45.5% of students were pursuing liberal arts degrees.

7 0

2 years ago

2. Every month, Jenny and Gopal ________ the orphanages in China. They have been to five orphanages so far.

aleksandr82 [10.1K]

Answer:

2. A

3. B

4. B

5. B

6. C

7. C

8. B

9. D

10. C

6 0

2 years ago

Read 2 more answers

When a problem involves more than one unit for a characteristic ( such as length) how can you tell which unit use is more approp

Art [367]

In the absence of clues, it is a judgment call.

Often, the problem statement or answer choices will tell you the desired units.

In general, units are available so that you can express dimensions in 4 or fewer digits with appropriate units. There are a few gaps, but the reason units are what they are is to make expressing everyday values easy to do.

SI units are easy to work with on this score, as the various available prefixes ensure that you can always express a quantity using a number between 1 and 1000. This is generally what you want to do (in the absence of direction otherwise).

For some things, there are customary units that are expected. Vehicle speed is unusally miles (or kilometers) per hour, for example. Land area is usually square feet, acres, or square miles in US units, or square meters, hectares, or square kilometers in SI units.

Generally, too, it is appreciated by your reader if the units you choose are ones they are familiar with. In most applications, you'd choose feet or yards or miles instead of furlongs, for example (unless your audience is familiar with racetrack distances).

7 0

2 years ago

Read 2 more answers

Roger went shoe shopping with his cousins Derek and Kamal. Roger bought a pair of basketball shoes that cost $74.95. Derek spent

bezimeni [28]

Answer:

I'm pretty sure its $19.65

8 0

2 years ago

Simplify -3/4(5p-12)+2(8-1/4p)