Kareem bought a table on sale for $217. This was 38% less that the original price. What was the original price?

Last year, 50% of MNM. Inc. employees were female. It is believed that there has been a reduction in the percentage of females i

Serhud [2]

Answer:

We conclude that there has been a significant reduction in the proportion of females.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 400

p = 50% = 0.5

Alpha, α = 0.05

Number of women, x = 118

First, we design the null and the alternate hypothesis

$H_{0}: p = 0.50\\H_A: p < 0.50$

This is a one-tailed test.

Formula:

$\hat{p} = \dfrac{x}{n} = \dfrac{118}{400} = 0.45$

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

Putting the values, we get,

$z = \displaystyle\frac{0.45-0.50}{\sqrt{\frac{0.50(1-0.50)}{400}}} = -2$

Now, we calculate the critical value.

Now, $z_{critical} \text{ at 0.05 level of significance } = -1.645$

Since the calculated z-statistic is less than the critical value, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

Thus, there has been a significant reduction in the proportion of females.

3 0

2 years ago

Can someone please help with this trig question?

atroni [7]

First we must understand how to write a logarithmic function:

$log_{b}a=x$

In the equation above, b is the base, x is the exponent, and a is the answer. These same variables can be rearranged to be expressed as an exponential equation as followed:

$b^x=a$

Next, we need to understand basic logarithm rules.

1. When a value is raised to a power, we can move the exponent to the front of the logarithm. Example:

log(a^2) = 2log(a)

2. When two variables are multiplied together, we can add the logarithms of the individual variables together. Example:

log(ab) = log(a) + log(b)

3. When a variable is divided by another variable, we can subtract the logarithms of the individual variables. Example:

log(a/b) = log(a) - log(b)

Now we can use these rules to solve the problem.

$log(r)=log( \sqrt[3]{ \frac{A^2B}{C} } )$

We can rewrite the cube root as:

$log(r) = log( (\frac{A^2B}{C})^ \frac{1}{3} )$

Now we can move the one-third to the front:

$log(r) = \frac{1}{3} log( \frac{A^2B}{C} )$

Now we can split up the logarithm:

$log(r) = \frac{1}{3} (log(A^2)+log(B)-log(C))$

Finally, we can move the exponent to the front of the log of A:

$log(r) = \frac{1}{3} (2log(A)+log(B)-log(C))$

Distribute the one-third to get the answer:

$log(r) = \frac{2}{3} log(A) + \frac{1}{3} log(B) - \frac{1}{3} log(C)$

The answer is (4).

3 0

3 years ago

Can someone please help me solve these two quadratic equations by factoring!

snow_tiger [21]

Answer:

1st one: (x-2)(x+10)

2nd one: (x-7)(x-3)

Step-by-step explanation:

6 0

2 years ago

A boat travels from a port and moves 12 miles north and then moves 5 miles east. what is the present distance of the boat from t

Sedaia [141]

What helped me find the answer if I am correct would be that I drew a number line to represent the distance the boat is moving from the port. The first thing I did was I drew an arrow pointing to the right all the was to the number 12 and then I drew another arrow pointing to the left to show that the boat moved 5 miles to the east and the the question asked now how many miles is the boat from the port so the answer would be 7 miles. P.s. Sorry this is soooo long.

5 0

2 years ago

Just need help with the last question please, which is the one about the confidence interval and the terms of the situation?? AS

telo118 [61]

Well, since the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 6% of 80%, that means there is a 90% confidence interval. 9 / 10 = .90 = 90% 90% = 1.645 1.645 * .9 = 1.4805 Margin of Error - 1.4805and The margin of error is the distance from x-bar, the center of the confidence interval ,to the end of the interval. This distance is 6% of 80% which is given by: 80×6100=4.8 Therefore the margin of error is 4.8% and the confidence interval is: ({80 - 4.8}%, {80 + 4.8}%)

8 0

3 years ago