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2 years ago

6

A person who had $1,000,000 gave $100 to charity. How much must a student who has $100 give to charity to give proportionally th

e same as the millionaire?

1 answer:

Oksi-84 [34.3K]2 years ago

5 0

(100 / 1,000,000) × 100% = 0.01%

x = amount of money the student has to give.

(x / 100) × 100% = 0.01%

We can cancel out the 100's

x = $0.01

The student would have to give $0.01 or 1 cent

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A poll stated that 32% of those polled think the economy is getting worse. An economist wanted to check this claim so she survey

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Answer:

$z=\frac{0.30 -0.32}{\sqrt{\frac{0.32(1-0.32)}{750}}}=-1.174$

The p value for this case would be given by:

$p_v =2*P(z$

For this case since the p value is higher than the significance level given we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.32 or 32 %

Step-by-step explanation:

Information given

n=750 represent the random sample taken

$\hat p=0.30$ estimated proportion of people who thought the economy is getting worse

$p_o=0.32$ is the value that we want to verify

$\alpha=0.05$ represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to check if the true proportion of interest is equal to 0.32 or not.:

Null hypothesis: $p=0.32$

Alternative hypothesis: $p \neq 0.32$

The statistic would be given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing we got:

$z=\frac{0.30 -0.32}{\sqrt{\frac{0.32(1-0.32)}{750}}}=-1.174$

The p value for this case would be given by:

$p_v =2*P(z$

For this case since the p value is higher than the significance level given we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.32 or 32 %

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2 years ago

A scientist mixes x liters of water into a container that has 10 liters of a mixture that is 12% salt and 88% water. The functio

dsp73

Answer:

110 liters of water

Step-by-step explanation:

Let

x ----> liters of water

f(x) ----> the percent of the sat in the new mixture

we have

$f(x)=\frac{1.2}{x+10}$

For $f(x)=1\%=1/100=0.01$

substitute in the equation

$0.01=\frac{1.2}{x+10}$

solve for x

$x+10=\frac{1.2}{0.01}$

$x+10=120\\x=120-10\\x=110\ L$

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2 years ago

Suppose that in one region of the country the mean amount of credit card debt perhousehold in households having credit card debt

kvv77 [185]

Answer:

The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 15250, \sigma = 7125, n = 1600, s = \frac{7125}{\sqrt{1600}} = 178.125$

The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly

This probability is the pvalue of Z when X = 1600 + 300 = 1900 subtracted by the pvalue of Z when X = 1600 - 300 = 1300. So

X = 1900

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{1900 - 1600}{178.125}$

$Z = 1.68$

$Z = 1.68$ has a pvalue of 0.9535.

X = 1300

$Z = \frac{X - \mu}{s}$

$Z = \frac{1300 - 1600}{178.125}$

$Z = -1.68$

$Z = -1.68$ has a pvalue of 0.0465.

0.9535 - 0.0465 = 0.907.

The probability that the mean amount of credit card debt in a sample of 1600 such households will be within $300 of the population mean is roughly 0.907 = 90.7%.

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Answer:

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Step-by-step explanation:

The Randomized Complete Block Design (RCBD) is a standard experimental design where experimental units or subjects are grouped as blocks (also known as replicates). In RCBD, subjects within each block are randomly assigned to the experimental units within a block. RCBD is a type of design that reduces variability by controlling variation within each treatment, thereby enhancing the estimation of the treatment effects (combinations of the factor levels of the different factors).

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2 years ago

Step 1: Subtract 3 from both sides of the inequality. Step 2: __________ Step 3: Divide both sides of the inequality by the coef

kipiarov [429]

Answer:

Subtract 8x from both sides of the inequality.

Step-by-step explanation:

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2 years ago

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