Alex can ski 960 meters in 5 minutes. If his skiing speed is increased by 20 m/min, how many meters can he cover in 10 minutes?

<span>Let A = a3b + 9a2b2 - 4ab5, and B = a3b - 3a2b2 + ab5. The difference can be expressed as A - B = a3b + 9a2b2 - 4ab5 - (a3b - 3a2b2 + ab5). When the negative sign is in front of the parentheses, all the internal signs change: this leads to: A - B = a3b + 9a2b2 - 4ab5 - a3b + 3a2b2 - ab5 = a3b - a3b + 9a2b2 + 3a2b2 - 4ab5 - ab5 = 12a2b2 - 5ab5. The first term’s degree is 2 + 2 = 4, while the second term’s degree is 1 + 5 = 6. Thus, the correct response is that the difference is a binomial of degree 6.</span>

Answer:

Step-by-step explanation:

Given data and notation

indicates the sample mean

refers to the sample standard deviation

is the sample size

represents the value we are testing.

indicates the significance level for the hypothesis test.

t refers to the statistic of interest.

is the p-value for the test (the variable we are interested in).

Formulate the null and alternative hypotheses.

I will set up the hypotheses to verify if the mean weight falls below 4 ounces, formalizing:

Null hypothesis:

Alternative hypothesis:

Since our sample size is < 30 and the population standard deviation is unknown, it’s advisable to utilize a t test to compare the actual mean against the reference value, with the statistic calculated as follows:

(1)

t-test: "This test compares group means and is commonly utilized to determine if the mean is (greater than, less than, or not equal to) a specific value."

Calculate the statistic

We can substitute the provided information into formula (1):

 

Given:

It is stated that

PQ ⊥ PS and

∠QPR = 7x-9

∠RPS = 4x+22

To find the measure of ∠QPR.

Formula

According to the problem PR sits between PQ and PS,

Consequently,

∠QPR+∠RPS = 90°

Now,

Inserting the values for ∠RPS and ∠QPR yields

or,

or,

or,

or,

Substituting the value of into ∠QPR gives us

∠QPR =

or, ∠QPR =

So,

The measure of ∠QPR is 40°.

To find the value of z in triangle XYZ, we can utilize the law of sines. We know the following:

1. The measure of angle XYZ is 51 degrees.

2. The measure of angle YZX is 76 degrees.

3. The length of side XZ is 2.6 units.

From these angles, angle XZY can be calculated, and then we can apply the law of sines to determine z.

Thus, we proceed to solve for z using the sine relationship in the triangle.

We will round the result to one decimal place.

Utilizing the normal distribution and the central limit theorem, there's a 0.0284 or 2.84% chance of observing a sample mean mass of 695g or less.