Jerome's credit card has an APR of 18%, calculated on the previous monthly

"Which pairs of angles in the figure below are vertical angles? Check all that apply.

lawyer [12517]

Angles known as vertical angles are those that are located across from each other at a common vertex where two lines intersect.

In the illustration, there exists only one pair of vertical angles.

These are Angle TSW and Angle ISN, both converging at the vertex labeled S.

<span>Answer is: B. Angle ISN and Angle TSW.</span>

5 0

3 months ago

Read 2 more answers

A ship sails at 15 miles per hour, while it can motor at 5 miles per hour. It sails for 6 hours to its destination but has to mo

tester [12383]

Greetings!

The conclusion is:

The return trip will take 18 hours.

Reasoning:

To determine the duration of the return journey, we must calculate the distance from the destination back to the starting point.

The ship travels at 15 miles per hour (mph) over 6 hours, yielding a distance of:

$x=x_o+v*t\\\\x=0+15mph*6hours=90miles$

The distance from the starting point to the destination is 90 miles, and for the return trip, the motor operates at a speed of 5 mph. Thus, computing the time taken gives us:

$Distance=v*t\\\\t=\frac{Distance}{v}=\frac{90miles}{5mph}=18hours$

Consequently, the return trip will take 18 hours to complete.

Have a nice day!

5 0

2 months ago

A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of awriting

tester [12383]

Answer:

a) Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

b) $p_v =P(t_{17}$

Given that the p-value is lower than the significance threshold in this situation, we have sufficient grounds to reject the null hypothesis.

c) $p_v =P(t_{17}$

In this case, since the p-value exceeds the significance threshold, we have adequate evidence to FAIL to reject the null hypothesis.

d) $p_v =P(t_{17}$

Here again, with the p-value being less than the significance level, we can reject the null hypothesis.

Step-by-step explanation:

1) Provided data and references

$\bar X$ represents the average of the samples

$s$ denotes the standard deviation of the samples

$n=18$ indicates the number of samples

$\mu_o =10$ is the value we are examining

$\alpha$ defines the significance level for the test.

t represents the specific statistic of interest

$p_v$ indicates the p-value relevant to the test (the variable of concern)

Define the null and alternative hypotheses.

To assess if the true mean is at least 10 hours, we must set up a hypothesis:

Part a

Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

If we consider the sample size being less than 30 and the population deviation unknown, it’s more appropriate to use a t-test to compare the actual mean with the reference value, calculated as:

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

Part b

In this scenario t=-2.3, $\alpha=0.05$

Initially, we need to calculate the degrees of freedom $df=n-1=18-1=17$

Since this is a left-tailed test, the p-value is determined by:

$p_v =P(t_{17}$

In this instance, with the p-value being less than the significance level, we have sufficient evidence to reject the null hypothesis.

Part c

For this situation t=-1.8, $\alpha=0.01$

We need to find the degrees of freedom $df=n-1=18-1=17$

For the left-tailed test, the p-value is given by:

$p_v =P(t_{17}$

In this case, since the p-value is above the significance level, we have enough grounds to FAIL to reject the null hypothesis.

Part d

For this case t=-3.6, $\alpha=0.05$

Firstly, we find the degrees of freedom $df=n-1=18-1=17$

Since we are conducting a left-tailed test, the p-value is calculated as:

$p_v =P(t_{17}$

Here, with the p-value being lower than the significance threshold, we can reject the null hypothesis.

5 0

2 months ago

Starting from 300 feet away, a car drives toward you. It then passes by you at a speed of 48 feet per second.The distance d (in

Zina [12379]

From a distance of 300 feet, a car approaches you at a speed of 48 feet per second. The distance d (in feet) of the car from you after t seconds can be described by the equation d=|300−48t|. At what moments does the car find itself 60 feet away from you?

4 0

2 months ago

Suppose the area that can be painted using a single can of spray paint is slightly variable and follows a nearly normal distribu

zzz [12365]

Response:

Detailed explanation:

Greetings!

You have the variable

X: Area eligible for painting with a can of spray paint (feet²)

This variable is normally distributed with a mean of μ= 25 feet² and a standard deviation of δ= 3 feet²

As this variable has a normal distribution, it needs to be converted into the standard normal form to utilize tabulated cumulative probabilities.

a.

P(X>27)

The first step involves standardizing the X value using Z= (X-μ)/ δ ~N(0;1)

P(Z>(27-25)/3)

P(Z>0.67)

Having determined the Z value, you can find it in the table, but since the table includes probabilities for $P(Z$ , the following conversion must be applied:

P(Z>0.67)= 1 - P(Z≤0.67)= 1 - 0.74857= 0.25143

b.

A sample of 20 cans was taken, and you need to ascertain the probability of averaging a coverage area of 540 feet².

The sample mean maintains the same distribution as its source variable, but its variance is influenced by sample size, thus it is normally distributed with parameters:

X[bar]~N(μ;δ²/n)

To cover 540 feet² with 20 cans, the average coverage must be approximately 540/20= 27 feet² per can.

c.

P(X≤27) = P(Z≤(27-25)/(3/√20))= P(Z≤2.98)= 0.999

d.

No, if the distribution is not normal and skewed, the normal distribution should not be applied for calculating probabilities. While the central limit theorem might approximate the sampling distribution to normal when the sample size is 30 or larger, that isn’t applicable here.

I trust this information is helpful!

4 0

2 months ago