How high is the end of the ladder against the building?

Write an equation of the perpendicular bisector of the segment with endpoints M(1,5) and N(7,−1).

solong [7]

Answer:

Step-by-step explanation:

find the perpendicular bisector of a line segment with endpoints

(ii) Find a point on the perpendicular bisector (the midpoint of the given line segment) using the midpoint formula:

( x 3 , y 3 ) = ( x 1 + x 2 2 , y 1 + y 2 2 )

6 0

3 years ago

A spa employs 54 people. Management wants to gather data about current and future services for clients. A random sample of 22 em

Igoryamba

Answer:

c

Step-by-step explanation:

i choose (c) because that the answer

5 0

3 years ago

What is the quotient StartFraction 15 p Superscript negative 4 Baseline q Superscript negative 6 Baseline Over negative 20 p Sup

zhannawk [14.2K]

Answer:

$- \frac{3}{4} \times \frac{p^{8} }{q^{3} }$

Step-by-step explanation:

We have to find the quotient of the following division, $\frac{15p^{-4}q^{-6} }{- 20p^{-12} q^{-3}}$ .

Now, $\frac{15p^{-4}q^{-6} }{- 20p^{-12} q^{-3}}$

= $- \frac{3}{4} p^{[- 4 - (- 12)]} q^{[-6 - (- 3)]}$ {Since all the terms in the expression are in product form, so we can treat them separately}

{Since we know the property of exponent as $\frac{a^{b} }{a^{c} } = a^{(b - c)}$ }

= $- \frac{3}{4} p^{8} q^{-3}$

= $- \frac{3}{4} \times \frac{p^{8} }{q^{3} }$ (Answer)

{Since we know, $a^{-b} = \frac{1}{a^{b} }$ }

3 0

2 years ago

Read 2 more answers

Suppose the standard deviation of a normal population is known to be 3, and H0 asserts that the mean is equal to 12. A random sa

blagie [28]

Answer:

$z=\frac{12.95-12}{\frac{3}{\sqrt{36}}}=1.9$

$p_v =P(z>1.9)=0.0287$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 5% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=12.95$ represent the sample mean

$\sigma=3$ represent the population standard deviation for the sample

$n=36$ sample size

$\mu_o =12$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 12, the system of hypothesis would be:

Null hypothesis: $\mu \leq 12$

Alternative hypothesis: $\mu > 12$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{12.95-12}{\frac{3}{\sqrt{36}}}=1.9$

P-value

Since is a right tailed test the p value would be:

$p_v =P(z>1.9)=0.0287$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 5% of signficance.

4 0

3 years ago

Read 2 more answers

2) Lisa is ordering sand from the Internet, On one site she found sand on sale for

Anastasy [175]

For this case we must find the unit cost (dollars per pound) of each site and then compare.

We take into account that:

1kg equals 2.205 pounds

So, we have:

Site 1:

$C = 2.25 \frac {dollars} {pound}$