Use conversion factors to find the answer, distance tracked in feet after 12 seconds at 87 miles per hour.

-4 square divided by 8

arlik [135]

Answer:

2

Step-by-step explanation:

If you square -4 it equals 16 and if you take that number and divibe it by 8 you get 2.

3 0

4 years ago

Describe three different methods to solve x²- x - 56 =0

Vika [28.1K]

Methods: 1) Factoring 2) Complete the square 3) Quadratic form

5 0

3 years ago

popcorn kernels are sold in one-pound bags.If four ounces of kernels make two quarts if popped popcorn,how many bags of kernels

Anon25 [30]

Popcorn kernels in 1 lb bags.
4 ounces of kernels make two quartz of popped popcorn

Number of bag of kernels to fill ten gallons of popped popcorn.

1 pound = 16 ounces
16 ounces / 4 ounces = 4
4 * 2 quarts = 8 quarts
8 quarts / 4 quarts per gallon = 2 gallons

1 pound bag of popcorn kernel produces 2 gallons worth of popped popcorn.

To make 10 gallons worth of popped popcorn, you need 5 1-pound bags of popcorn kernels.

4 0

3 years ago

For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel is 400 feet high. You

Mariana [72]

9514 1404 393

Answer:

a. h(t) = -20t +400

b. θ(t) = arctan(2 -2/15t); dθ/dt = -30/(1125 -120t +4t^2)

c. 15 seconds; 100 ft

Step-by-step explanation:

a. The initial height of the elevator is 400 ft. The rate of change of height is -20 ft/s, so the height equation can be ...

h(t) = -20t +400

__

b. The tangent of the angle above the line of sight is "opposite"/"adjacent":

tan(θ) = (h(t) -100)/(150) = -2/15t +2

θ(t) = arctan(2 -2/15t) . . . . radians

The derivative of the angle function is ...

dθ/dt = 1/(1+(2 -2/15t)^2)(-2/15)

dθ/dt = -30/(1125 -120t +4t^2)

__

c. The value of dθ/dt will have a peak where the denominator has a minimum, at t = -(-120)/2(4)) = 15. (The quadratic vertex coordinate is t=-b/(2a).)

The elevator appears to be moving fastest at t=15 seconds.

The height at that time is ...

h(15) = 400 -20(15) = 100

The elevator appears to be moving fastest when it is at eye level, 100 ft above the ground.

5 0

3 years ago

A presidential candidate's aide estimates that, among all college students, the proportion who intend to vote in the upcoming el

inessss [21]

Answer:

$z=\frac{0.529 -0.6}{\sqrt{\frac{0.6(1-0.6)}{240}}}=-2.24$

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 1% of significance the proportion college students expressed an intent to vote is not higher than 0.6

Step-by-step explanation:

Assuming the following question: A presidential candidate's aide estimates that, among all college students, the proportion p who intend to vote in the upcoming election is at least 60% . If 127 out of a random sample of 240 college students expressed an intent to vote, can we reject the aide's estimate at the 0.1 level of significance?

Data given and notation

n=240 represent the random sample taken

X=127 represent the college students expressed an intent to vote

$\hat p=\frac{127}{240}=0.529$ estimated proportion of college students expressed an intent to vote

$p_o=0.6$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

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 at least 60% of students are intented to vote .:

Null hypothesis: $p \geq 0.6$

Alternative hypothesis: $p < 0.6$

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:

$z=\frac{0.529 -0.6}{\sqrt{\frac{0.6(1-0.6)}{240}}}=-2.24$

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 $\alpha=0.01$ . The next step would be calculate the p value for this test.

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

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 1% of significance the proportion college students expressed an intent to vote is not higher than 0.6

7 0

3 years ago