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3 years ago

For the question "Which binomial is a factor of 9x² – 64?

Mathematics

1 answer:

SashulF [63]3 years ago

6 0

Answer:

3x-8

Step-by-step explanation:

9x²-64 is the same as

(3x)² - 8²

now we have the difference of 2 squares, a²-b² =(a -b)(a +b), where a=3x, b=8

9x²-64 = (3x-8)(3x+8)

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A researcher wants to estimate the percentage of all adults that have used the Internet to seek pre-purchase information in the

Lubov Fominskaja [6]

Answer:

The required sample size for the new study is 801.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

25% of all adults had used the Internet for such a purpose

This means that $\pi = 0.25$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

What is the required sample size for the new study?

This is n for which M = 0.03. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.96\sqrt{\frac{0.25*0.75)}{n}}$

$0.03\sqrt{n} = 1.96\sqrt{0.25*0.75}$

$\sqrt{n} = \frac{1.96\sqrt{0.25*0.75}}{0.03}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.25*0.75}}{0.03})^2$

$n = 800.3$

Rounding up:

The required sample size for the new study is 801.

4 0

3 years ago

In which of the following sampling designs do all members of a population have an equal chance of being selected?

jolli1 [7]

Answer: d. Random

Step-by-step explanation:

In statistics, a simple random sampling is a sampling technique in which a subset of the population named as sample is drawn by the researcher in such a way that all the individuals have equal probability of getting selected.

If the Total population size is N , then the probability for any individual of getting selected is $\dfrac{1}{N}$ .

Therefore , the sampling designs do all members of a population have an equal chance of being selected is random sampling.

Rest of other sampling methods does not give equal chance to the members of the population of getting selected.

7 0

3 years ago

At a sale this week, a digital camera is on sale for $547.40. This is a 57% discount off of the original price. What is the orig

zhuklara [117]

Answer:

725.623

Step-by-step explanation:

547.40:?

43 :57

?=547.40×57÷43

7 0

3 years ago

A movie-theater employee notes an inverse relationship between the theater's popcorn sales and its nacho sales. On a given night

zubka84 [21]

the employee earned $1813 from Nachos

Explanation:

The theater's popcorn sales is inversely proportional to nacho sales

Let theater's popcorn = P

nacho sales = N

$P\text{ }\alpha\text{ }\frac{1}{N}$

Equating the relationship:

$\begin{gathered} P\text{ = k(}\frac{1}{N}) \\ P\text{ = }\frac{k}{N} \\ \text{where k = constant of proportionality} \end{gathered}$

when theater sales = $2,254

Nacho sales = $1,628

$\begin{gathered} 2254\text{ =}\frac{k}{1628} \\ k\text{ = 2254(1628)} \\ k\text{ = 3}669512 \end{gathered}$

The relationship becomes:

$P\text{ = }\frac{3669512}{N}$

When cost of the theater popcorn = $2,024

The cost from nachos = ?

We would use the relationship to get the above:

$\begin{gathered} 2024\text{ = }\frac{3669512}{N} \\ 2024N\text{ = 3669512}18 \\ N\text{ = }\frac{\text{3669512}}{2024} \\ N\text{ = }1813 \end{gathered}$

Hence, the employee earned $1813 from Nachos

6 0

1 year ago

Line p and q are perpendicular if the slope of line p is 2 what is the slope of line q

Fudgin [204]

The slope is negative one half because perpendicular lines always have slopes that are opposite reciprocals

meaning not only are they reciprocals meaning 1 over the number (or flipping the numerator and the denominator of a fraction) you also change the sign

6 0

4 years ago