Daniel has 3/4 of a glass of water. He wants to share the water equally with his brother. How much water will each brother get?

Mathematics

1 answer:

andrew11 [14]3 years ago

7 0

Answer:

0.375

Step-by-step explanation:

You have to just divide 3/4 divided by 2 = 0.375

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A retired couple has up to $50,000 to invest. As their financial adviser, you recommend that they place at least $35,000 in Trea

patriot [66]

Answer:

See Explanation

Step-by-step explanation:

According to the Question,

Given that, A retired couple has up to $50,000 to invest. As their financial adviser, you recommend that they place at least $35,000 in Treasury bills yielding 1% and at most $10,000 in corporate bonds yielding 3%.

Therefore,

Let, x be the amount of money invested in Treasury bills

y be the amount invested in corporate bonds

Thus, the system of equations of linear inequalities is

x + y ≤ 50000

x ≥ 35000

0 ≤ y ≤ 10000

For, the graph of the system of equations of linear inequalities describes the possible amounts of each investment.

(Please find in the attachment)

3 0

2 years ago

In a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a quarter-system

Contact [7]

Answer:

n=206

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$t_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.09$ , we can use as prior estimate of p 0.5, since we don't have any other info provided, and we are interested in order to find the value of n, if we solve n from equation (a) we got: