Really need help on this , thanks so much! (:

The components of vector are ax and ay (both positive), and the angle that it makes with respect to the positive x axis is θ. Fi

Andru [333]

we can use formula

$\theta=tan^{-1}(\frac{a_y}{a_x})$

(a)

we are given

$a_x=12,a_y=12$

now, we can plug values

$\theta=tan^{-1}(\frac{12}{12})$

$\theta=tan^{-1}(1)$

$\theta=\frac{\pi}{4}rad$

(b)

we are given

$a_x=20,a_y=12$

now, we can plug values

$\theta=tan^{-1}(\frac{12}{20})$

$\theta=tan^{-1}(\frac{3}{5})$

$\theta=30.96^{\circ \:}$

(c)

we are given

$a_x=12,a_y=20$

now, we can plug values

$\theta=tan^{-1}(\frac{20}{12})$

$\theta=tan^{-1}(\frac{5}{3})$

$\theta=59.03^{\circ \:}$

6 0

3 years ago

What is the area of a triangle whose vertices are P(−1, 4), Q(3, 2), and R(3, −4)?

sp2606 [1]

What kind of triangle is it?

7 0

3 years ago

The mean consumption of bottled water by a person in the United States is 28.5 gallons per year. You believe that a person consu

Over [174]

Answer:

$t=\frac{27.8-28.5}{\frac{4.1}{\sqrt{100}}}=-1.707$

$p_v =P(t_{99}$

If we compare the p value with a significance level for example $\alpha=0.1$ we see that $p_v$ so we can conclude that we reject the null hypothesis, so there is not enough evidence to conclude that the mean for the consumption is less than 28.5 gallons at 0.1 of significance, so we can reject the claim that person consume more than 28.5 gallons.

Step-by-step explanation:

Data given and notation

$\bar X=27.8$ represent the mean for the account balances of a credit company

$s=4.1$ represent the population standard deviation for the sample

$n=1000$ sample size

$\mu_o =28.5$ represent the value that we want to test

$\alpha=0.1$ represent the significance level for the hypothesis test.

t 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 determine if the mean for the person consume is more than 28.5 gallons, the system of hypothesis would be:

Null hypothesis: $\mu \geq 28.5$

Alternative hypothesis: $\mu < 28.5$

We don't know the population deviation, so for this case we can use the t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-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:

$t=\frac{27.8-28.5}{\frac{4.1}{\sqrt{100}}}=-1.707$

Calculate the P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=100-1=99$

Since is a one-side lower test the p value would be:

$p_v =P(t_{99}$

In Excel we can use the following formula to find the p value "=T.DIST(-1.707,99)"

Conclusion

If we compare the p value with a significance level for example $\alpha=0.1$ we see that $p_v$ so we can conclude that we reject the null hypothesis, so there is not enough evidence to conclude that the mean for the consumption is less than 28.5 gallons at 0.1 of significance, so we can reject the claim that person consume more than 28.5 gallons.

5 0

3 years ago

Plz help..............

IrinaVladis [17]

The correct answer is -15 because the absolute value is 15 but there is a negative outside the absolute value lines making it negative :)

7 0

3 years ago

Read 2 more answers

Jeremy used 11 gallons and 3 quarts of water to water his garden. How many quarts of water did Jeremy use?

Anon25 [30]

Answer:

47

Step-by-step explanation:

since each gallon is 4 quarts you would multiply by 11. 44 quarts then add 3 extra quarts to get 47

6 0

3 years ago