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lara [203]
3 years ago
12

The path of a projectile launched from a 16-ft-tall tower is modeled by the equation y = −16t2 + 64t +16. What is the maximum he

ight, in feet, reached by the projectile?
Mathematics
1 answer:
Aleks04 [339]3 years ago
5 0

Answer:

<h3>80 feet</h3>

Step-by-step explanation:

Given the path of a projectile launched from a 16-ft-tall tower modeled by the equation y = −16t^2 + 64t +16

h is the maximum height reached

t is in seconds

The velocity of the projectile at its maximum height is zero;

velocity v = dy/dt

v = -32t + 64

Since v = 0 at maximum height

0 = -32t + 64

32t = 64

t = 2secs

Substitute t = 2secs into the equation of the height to get the maximum height.

y = −16t^2 + 64t +16

at t = 2secs

y = −16(2)^2 + 64(2) +16

y = -64 + 128 + 16

y = 64+16

y = 80 feet

Hence the maximum height, in feet, reached by the projectile is 80 feet

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Is n+4 equal to 8(n - 4)
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Which expression is equivalent to 10a + 6?
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There are a number of expressions that are equivalent to 10a+6.
To find them, you simply have to list the multiples of both 10 and 6.
10- 10 20 30 40 50 60 70 80 90 100
6- 6 12 18 24 30 36 42 48 54 60.
Then, when you multiply the fraction by anything, whether this is 2, 3 or 10, you just have to do this to both parts. 
All of the following expressions are equivalent to 10a+6
20a+12, 30a+18, 40a+24, 50a+30, 60a+36, 70a+42, 80a+48, 90a+54, 100a+60

Or, if you're looking to simplfy, then you have to find a common multiple, which is 2. Therefore, 2 goes outside of the bracket, and you then have to divide 10 by 2 to find out what goes inside the brack. 10a/2= 5a. 6/2=3, therefore, in a bracket, it becomes 2(5a+3)

Hope this helps :) 

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Timothy has $1111 and Mary has $777. How much money does Timothy need to give Mary, so that they would have the same amount of m
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LUV YA!!

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3 years ago
A ski lift is designed with a total load limit of 20,000 pounds. It claims a capacity of 100 persons. An expert in ski lifts thi
Yanka [14]

Answer:

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n values of a distribution, the mean is \mu \times n and the standard deviation is \sigma\sqrt{n}

An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. 100 individuals.

This means that \mu = 200*100 = 20000, \sigma = 30\sqrt{100} = 300

If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload

Total load of more than 20,000 pounds, which is 1 subtracted by the pvalue of Z when X = 20000. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{20000 - 20000}{300}

Z = 0

Z = 0 has a pvalue of 0.5

1 - 0.5 = 0.5

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

5 0
3 years ago
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