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Juliette [100K]
3 years ago
8

A baseball is thrown upwards from a height of 5 feet with an initial speed of 64 feet per second, and its height h (in feet) fro

m the ground is given by h(t) = 5 + 64t – 16t2 where t is time in seconds. Using a graphing calculator, determine at what time the ball reaches its maximum height.

Mathematics
2 answers:
Juli2301 [7.4K]3 years ago
8 0

Answer:

2 seconds

Step-by-step explanation:

Given : A baseball is thrown upwards from a height of 5 feet with an initial speed of 64 feet per second, and its height h (in feet) from the ground is given by h(t) = 5 + 64t -16t^2 where t is time in seconds.

To Find: Using a graphing calculator, determine at what time the ball reaches its maximum height.

Solution:

Plot the graph of the given equation

Refer the attached graph

So, the given equation is a downward parabola

So, the y coordinate of vertex of the parabola will give its maximum height and x coordinate will given the time at which the ball is at maximum height

So, Vertex = (2,69)

Maximum height = 69 feet

Time to reach maximum height = 2 seconds

Hence it will take 2 seconds to reach its maximum height.

alexira [117]3 years ago
6 0
A graphing calculator shows the ball reaches its maximum height of 69 feet at t = 2 seconds.

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The option that represents the answers for 6, 8, 10, and 14 is the second option-   31, 41, 51, 71

<h3>Sequence and Series </h3>

From the question, we are to determine the option that represents the answer for pictures 6, 8, 10, and 14

In the given diagram,

The first picture requires 6 matches

The 2nd picture requires additional 5 matches

the 3rd  picture requires additional 5 matches

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That is

1 → 6

2 → 6 + 5 = 11

3 → 11 + 5 = 16

4 → 16 + 5 = 21

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6 → 26 + 5 = 31

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12 → 56 + 5 = 61

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Learn more on Sequence and Series here: brainly.com/question/10321751

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If a=b then b=a unit 2
Svetradugi [14.3K]

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Step-by-step explanation:

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2 years ago
Centerpieces are normally distributed with mean of 30 ounces and standard deviation of 2 ounces. The weights of the shipping box
astraxan [27]

Answer:

0.0901 = 9.01% of packages will incur such a charge

Step-by-step explanation:

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.

Sum of normal variables:

When we add normal variables, the mean will be the sum of the means, while the standard deviation is the square root of the sum of the variances.

Centerpieces are normally distributed with mean of 30 ounces and standard deviation of 2 ounces.

This means that \mu_C = 30, \sigma_C = 2

The weights of the shipping boxes are normally distributed with mean of 12 ounces and standard deviation of 1 ounce.

This means that \mu_S = 12, \sigma_S = 1

Suppose that centerpieces are chosen at random and packed into randomly chosen shipping boxes.

The shipment is given by the centerpice plus the shipping box. So the mean and the standard deviation of the weight are given by:

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\sigma = \sqrt{\sigma_C^2 + \sigma_S^2} = \sqrt{2^2 + 1^2} = \sqrt{5} = 2.236

If a package exceeds 45 ounces, an additional charge is incurred. What is the proportion of packages will incur such a charge

This proportion is 1 subtracted by the pvalue of Z when X = 45. So

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

Z = \frac{45 - 42}{2.236}

Z = 1.34

Z = 1.34 has a pvalue of 0.9099

1 - 0.9099 = 0.0901

0.0901 = 9.01% of packages will incur such a charge

7 0
2 years ago
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