If AC is 11 inches and BC is 4 inches, then AB

Given that P = (2, 9) and Q = (4, 14), find the component form and magnitude of vector PQ.

vredina [299]

The magnitude of the vector is
$\sqrt{2 {}^{2} + 5 {}^{2} } = \sqrt{29}$
the component form is
<2,5>

8 0

3 years ago

What is the area of the sector? Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter

n200080 [17]

Question:

What is the area of the sector? Either enter an exact answer in terms of π or use 3.14 and enter your answer as a decimal rounded to the nearest hundredth.

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as the values of radius and central angle are not given.

However, I'll answer the question using the attached figure.

From the attached figure, the radius is 3 unit and the central angle is 120 degrees

The area of a sector is calculated as thus;

$Area = \frac{\alpha }{360} * \pi r^2$

Where $\alpha$ represents the central angle and r represents the radius

By substituting $\alpha = 120$ and r = 3

$Area = \frac{\alpha }{360} * \pi r^2$ becomes

$Area = \frac{120}{360} * \pi * 3^2$

$Area = \frac{1}{3} * \pi * 9$

$Area = \pi * 3$

$Area = 3\pi$ square units

Solving further to leave answer as a decimal; we have to substitute 3.14 for $\pi$

So, $Area = 3\pi$ becomes

$Area = 3 * 3.14$

$Area = 9.42$ square units

Hence, the area of the sector in the attached figure is $3\pi$ or 9.42 square units

8 0

3 years ago

A recipe calls for 2 3/4 cups of sugar and 4 1/3 cups of flour. How many cups of sugar are used for every 1 cup of flour?

worty [1.4K]

4 1/3 cup of flour = 2 3/4 cup of sugar

1 cup of flour = 2 3/4 ÷ 4 1/3 = 33/52 cup of sugar <=== answer

6 0

3 years ago

According to the University of Nevada Center for Logistics Management, 6% of all merchandise sold in the United States gets retu

jeka57 [31]

Answer:

$p_v =P(z>3.390)=0.000349$

If we compare the p value and the significance level given $\alpha=0.1$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 10% of significance the proportion of returns at the Houston store is significantly higher than 0.06 or 6%.

Step-by-step explanation:

1) Data given and notation n

n=80 represent the random sample taken

X=12 represent number of items returned

$\hat p=\frac{12}{80}=0.15$ estimated proportion of items returned

$p_o=0.06$ is the value that we want to test

$\alpha=0.1$ represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

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

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that proportion of returns at the Houston store was more than the national expectation (0.06):

Null hypothesis: $p\leq 0.06$

Alternative hypothesis: $p >0.06$

When we conduct a proportion test we need to use the z statistic, and the is given by:

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

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.15 -0.06}{\sqrt{\frac{0.06(1-0.06)}{80}}}=3.390$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.1$ . The next step would be calculate the p value for this test.

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

$p_v =P(z>3.390)=0.000349$

If we compare the p value and the significance level given $\alpha=0.1$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 10% of significance the proportion of returns at the Houston store is significantly higher than 0.06 or 6%.

4 0

3 years ago

Raul is a saver. He sets aside $100 per month during his career of 40 years to prepare for retirement. He does not like the idea

Svet_ta [14]

The total balance in Raul's account after 40 years when he retires is $65,714.90.

<h3>What is the total balance?</h3>

The formula that can be used to determine the balance of the accout is: monthly amount saved x annuity factor.

Annuity factor = {[(1+r)^n] - 1} / r

Where:

r = interest rate = 1.5/12
n = number of periods = 12 x 40 = 480

$100 x [(1.00125^480) - 1 ] / 0.00125 = $65,714.90

Here is the complete question:

Raul is a saver. He sets aside $100 per month during his career of 40 years to prepare for retirement. He does not like the idea of investing because he prefers to minimize his risk as much as possible, so he puts his money in a savings account which earns 1.5% interest per year. What is the balance in the account after 40 years?

To learn more about annuites, please check: brainly.com/question/24108530

6 0

2 years ago