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2 years ago

| 2. On rectangle ABCD below, if A is located at

Mathematics

1 answer:

vovangra [49]2 years ago

6 0

Answer:

-2

Step-by-step explanation:

Given that:

A = (3, 4) ; B = (7, 6)

In triangle ABCD, AB and BC are Perpendicular lines :

Slope AB = Rise / Run = (y2 - y1) / (x2 - x1)

y2 = 6 ; y1 = 4 ; x2 = 7 ; x1 = 3

Slope AB = (6 - 4) / (7 - 3) = 2 / 4 = 1 / 2

To obtain the slope of BC:

RECALL:

product of the slope of 2 Perpendicular lines = - 1

Slope AB * Slope BC = - 1

1 / 2 * slope BC = - 1

Slope BC = - 1 ÷ 1/2

Slope BC = - 1 * 2/1

Slope BC = - 2

HENCE, slope of BC = - 2

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34 packages are randomly selected from packages received by a parcel service. The sample has a mean weight of 25.9 pounds and a

Vlad1618 [11]

Answer:

24.6 < μ < 27.2

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{3.8}{\sqrt{34}} = 1.3$

The lower end of the interval is the sample mean subtracted by M. So it is 25.9 - 1.3 = 24.6 pounds.

The upper end of the interval is the sample mean added to M. So it is 25.9 + 1.3 = 27.2 pounds.

So the correct answer is:

24.6 < μ < 27.2

4 0

2 years ago

Find the volume of a sphere and radius is 3. please answer in terms of pi

Ghella [55]

Answer:

12 pi

Step-by-step explanation:

volume of sphere = 4/3 pi r2

4/3 pi 3 x 3

12 pi unit square

6 0

3 years ago

Read 2 more answers

A phycologist is interested in determining the proportion of algae samples from a local rivulet that belong to a particular phyl

LuckyWell [14K]

Answer:

A sample of 16577 is required.

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 z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

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

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a p-value of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

She wants to estimate the proportion using a 99% confidence interval with a margin of error of at most 0.01. How large a sample size would be required?

We have no estimation for the proportion, and thus we use $\pi = 0.5$ , which is when the largest sample size will be needed.