The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). If q(t) = 4t³

The square shown has a perimeter of 32 units. The square is rotated about line k.

Bad White [126]

A cylinder with a circumference of about 50 units is formed.

Step-by-step explanation:

Step 1:

The perimeter of the square is 32 units. The perimeter of a square is given by 4 times its side length.

$(4) sidelength = 32, sidelength = \frac{32}{4} = 8.$

So the side length of the square is 8 units.

If a square is rotated a cylinder will be formed. So the options with a cone are wrong as a cone is formed when a triangle is rotated.

Step 2:

To calculate the circumference of the cylinder, we multiply 2π with the radius. The radius is the same as the side length of the square. So r is 8 units.

The circumference of the cylinder $= 2\pi r = (2) (3.1415)(8) = 50.264.$

So the circumference of the cylinder is approximately equal to 50 units so the answer is the fourth option, a cylinder with a circumference of about 50 units.

4 0

2 years ago

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Tootsie rolls cost $0.02 each and Peppermint Patties cost $0.05 each. If you have $1.00, how many of each

Julli [10]

Answer:

With $1 you can buy 50 Tootsie rolls, and 20 Peppermint Patties.

Step-by-step explanation:

100 divided by 2 = 50

100 divided by 5 = 20

4 0

1 year ago

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To plan the budget for next year a college must update its estimate of the proportion of next year's freshmen class that will ne

Naily [24]

Answer:

Null hypothesis: $p\leq 0.35$

Alternative hypothesis: $p > 0.35$

$z=\frac{0.447 -0.35}{\sqrt{\frac{0.35(1-0.35)}{150}}}=2.491$

$p_v =P(z>2.491)=0.0064$

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of applicants who request financial aid is significantly higher than 0.35

Step-by-step explanation:

Data given and notation

n=150 represent the random sample taken

X=67 represent the applicants who request financial aid

$\hat p=\frac{67}{150}=0.447$ estimated proportion of applicants who request financial aid

$p_o=0.35$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

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

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of applicants who request financial aid is higher than 0.35.:

Null hypothesis: $p\leq 0.35$

Alternative hypothesis: $p > 0.35$

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 $p_o$ .

Calculate the statistic

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

$z=\frac{0.447 -0.35}{\sqrt{\frac{0.35(1-0.35)}{150}}}=2.491$

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 next step would be calculate the p value for this test.

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

$p_v =P(z>2.491)=0.0064$

So the p value obtained was a very low value and using the significance level assumed $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of applicants who request financial aid is significantly higher than 0.35

5 0

2 years ago

How does the range of g (x) = StartFraction 6 Over x EndFraction compare with the range of the parent function f (x) = StartFrac

Lerok [7]

Answer: Option: (B) The range of both f(x) and g(x) is all nonzero real numbers is correct.

Step-by-step explanation: ..................Because I said so............................

3 0

2 years ago

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Nadiya determines that there are no fractions equivalent to 2/10 with a denominator greater than 10, but less than 20, that have

frosja888 [35]

Answer:

Yes, Nadiya is correct. By multiplying the numerator and denominator by 2, the first fraction equivalent to 2/10 is 4/20.

Step-by-step explanation:

To find a fraction equivalent to 2/10, we need to multiply (or divide) the numerator and denominator by the same nonzero whole number.

As we need an equivalent fraction with a denominator greater than 10, we will need to multiply and not divide.

The first nonzero whole number we have is 1. If we multiply the numerator and denominator by 1, we get 2/10. Obviously, 2/10 is equivalent to 2/10 but the denominator is not greater than 10, so it doesn't help us.

The next whole number is 2. When we multiply the numerator and denominator by 2, we get 4/20. The denominator is not less than 20.

If we keep going, we will get 6/30, 8/40 and so on.

Therefore, Nadiya is correct.

The correct answer is the first one.

8 0

2 years ago

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The function s(t) = 4t – 21 is a result of the composition (q ∘ p)(t). If q(t) = 4t³ – 1, what is p(t)?