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aivan3 [116]
3 years ago
12

A model rocket is launched with an initial upward velocity of 60 m/s. The rocket's height h (in meters) after t seconds is given

by the following.
h=60t-512
Find all values of t for which the rocket's height is 27 meters.
Round your answer(s) to the nearest hundredth.
Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
3 0

Answer:

0.47 and 11.53

Step-by-step explanation:

h = 60t − 5t²

27 = 60t − 5t²

5t² − 60t + 27 = 0

Quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

t = [ -(-60) ± √((-60)² − 4(5)(27)) ] / 2(5)

t = (60 ± √3060) / 10

t = 0.47 or 11.53

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A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained i
Scorpion4ik [409]

Answer:

a) We need a sample size of at least 3109.

b) We need a sample size of at least 4145.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

99% confidence level

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

(a) he uses a previous estimate of 25​%?

we need a sample of size at least n.

n is found when M = 0.02, \pi = 0.25. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.02 = 2.575\sqrt{\frac{0.25*0.75}{n}}

0.02\sqrt{n} = 2.575\sqrt{0.25*0.75}

\sqrt{n} = \frac{2.575\sqrt{0.25*0.75}}{0.02}

(\sqrt{n})^{2} = (\frac{2.575\sqrt{0.25*0.75}}{0.02})^{2}

n = 3108.1

We need a sample size of at least 3109.

(b) he does not use any prior​ estimates?

When we do not use any prior estimate, we use \pi = 0.5

So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.02 = 2.575\sqrt{\frac{0.5*0.5}{n}}

0.02\sqrt{n} = 2.575\sqrt{0.5*0.5}

\sqrt{n} = \frac{2.575\sqrt{0.5*0.5}}{0.02}

(\sqrt{n})^{2} = (\frac{2.575\sqrt{0.5*0.5}}{0.02})^{2}

n = 4144.1

Rounding up

We need a sample size of at least 4145.

8 0
3 years ago
I need help on the question in the picture.
Zigmanuir [339]

Answer:

A. There is no solution

Step-by-step explanation:

\frac{1}{3}(12x - 6) = 4x - 9

Evaluate.

4x - 2 = 4x - 9

Deduct 4x from both sides of the equation.

-2 = -9

Multiply both sides by (-1).

2 ≠ 9

Since 2 does not equal to 9, this equation does not make sense and thus does not have a solution.

4 0
3 years ago
A recipe for beef stew calls for 1 pound of beef and 3 potatoes. The recipe is doubled to include 2 pounds of beef and 6 potatoe
ZanzabumX [31]

Answer:

can you please give us the statements?

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A salesman make both a base salary and also a commission which is a percentage of what he sells . Each month if his sales total
MissTica
Commission / Base Salary
8 0
3 years ago
The number of cats increased from 1650650 to 2250015. What is the percentage change to the nearest tenth?
Luden [163]
First you have to subtract 2250015 by 1650650 and the answer is 599365

The you add 2250015 to 1650650 and the answer is 3900665 so you divide

599365 by 3900665 and multiply by 100 and the final result is 517.325002

And to the nearest ten is 517.3 because 2 is below five to round up

Final answer— 517.3

Hope this helps
7 0
3 years ago
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