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expeople1 [14]
3 years ago
13

A waterfall has a height of 1900 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 12 feet p

er second. The height, h, of the pebble after t seconds is given by the equation h=-16t^2+12t+1900. How long after the pebble is thrown will it hit the ground?
Mathematics
1 answer:
saw5 [17]3 years ago
7 0

Answer:

Step-by-step explanation:

h is the height of the pebble after a certain amount of time has gone by. Since we are told to find that time when the pebble is on the ground, we say that h = 0 since the height of something on the ground has no height at all. Then factor the quadratic.

-16t^2+12t+1900=0

Throw that into the quadratic formula or however you were taught to factor irrational quadratics (maybe completing the square?) to get that

t = 11.27869 sec and t = -10.52869 sec

Since we all know that time will never carry a negative value, we will disregard it and go with 11.27869 seconds. Not sure to where you are told to round.

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The table shows a golfers score for four rounds of a recent U.S. Women’s Open. Her total score was even with par. What was her s
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The answer for the third round is S = +2
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4 years ago
To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine foun
QveST [7]

Answer:

We conclude that  the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 31.7 milligrams

Sample mean, \bar{x} = 28.5 milligrams

Sample size, n = 9

Alpha, α = 0.05

Sample standard deviation, s =  2.8 milligrams

First, we design the null and the alternate hypothesis

H_{0}: \mu = 31.7\text{ milligrams}\\H_A: \mu < 31.7\text{ milligrams}

We use One-tailed t test to perform this hypothesis.

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

Putting all the values, we have

t_{stat} = \displaystyle\frac{28.5 - 31.7}{\frac{2.8}{\sqrt{9}} } = -3.429

Now, t_{critical} \text{ at 0.05 level of significance, 8 degree of freedom } = -1.860

Since,                  

t_{stat} < t_{critical}

We fail to accept the null hypothesis and accept the alternate hypothesis. We conclude that  the mean nicotine content is less than 31.7 milligrams for this brand of cigarette.

3 0
3 years ago
On a trip mrs. ahmed drove 188 miles in 4 hours. On the return trip, she took a different route and traveled 197 miles in 4.5 ho
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Answer:

45.29 miles per hour

Step-by-step explanation:

Speed is the distance over time.  To find the average rate of speed for a trip, we simply need to take the total distance divided by the total time.

Avg. Speed = (188 miles + 197 miles) / (4 hours + 4.5 hours)

Avg. Speed = 45.29 miles per hour

Hence the average rate of speed for the trip was 45.29 miles per hour.

Cheers.

--------------------------------------------------------

Edit:  Thanks to Chegsnut36 for calculation correction

6 0
3 years ago
Read 2 more answers
Question: Antonio is working with a new geometric series generated by the equation A(n)=20(1.1)^n-1.His sister challenged him to
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Answer:

sum of 22nd = 1,428.05

sum of 23 to 40 is 932.53

Step-by-step explanation:

A(n)=20(1.1)^n-1

20 is the first term or a1

1.1 is the common ratio or r

A(22) = 20(1.1)^22-1

22nd term = 20(1.1)^21

22nd term = 148.00

sum of geometric sequence

formula

Sn = a1(1-r^n)/1-r

Sn = sum

a1 = first term

n = number of term

r = constant ratio

sum of 22nd = 1,428.05.

23 to 40 is 17 terms

Sequence: 23, 25.3, 27.83, 30.613, 33.6743, 37.04173, 40.745903 ...

The 17th term: 105.684378686

Sum of the first 17 terms: 932.528165548

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miniwebtoolcomgeometricsequencecalculator

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3 years ago
A spotlight can be adjusted to effectively light a circular area of up to 6 meters in diameter. To the nearest tenth, what is th
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You would find the radius by halving the diameter. Then you use the equation
\pi \: r { }^{2}  =
and you get about 28.2 meters.
3 0
3 years ago
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