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Aleks [24]
2 years ago
14

Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. when sharon jumps, megan throws a beac

h ball up to sharon with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. to the nearest hundredth of a second, how long after she jumps does the ball reach sharon? 0.65 seconds 0.92 seconds 1.08 seconds 1.15 seconds
Mathematics
1 answer:
Alinara [238K]2 years ago
6 0

It will take 1.08 seconds for the ball to reach Sharon after she jumps if the upward velocity of the ball is 16 ft/s from a height of 5 feet option third is correct.

<h3>What is the equation of motion?</h3>

It is defined as the equation by which we can find the motion of a physical particle with respect to time. It is the representation of physical entity movement in a mathematical function.

We have:

The height of the Sharon from the diving board = 18 feet

The initial upward velocity of the Sharon = 4 ft/s

The height of the Megan from the ground = 5 feet

The initial upward velocity of the beach ball = 16 ft/s

We know the equation of motion is given by:

\rm h(t) = x + ut+\frac{1}{2} gt^2

Put x = 18 feet and u = 4 ft/s in the above equation, we get:

\rm h(t) = 18 + 4t+\frac{1}{2} \times9.8t^2 ....(1)     [g = 9.8 m/s²]

Put x = 5 feet and u = 16 ft/s in the equation of motion, we get:

\rm h(t) = 5 + 16t+\frac{1}{2} \times9.8t^2  ....(2)

Equate the equation (1) and equation (2), we get

\rm  18 + 4t+\frac{1}{2} \times9.8t^2= 5 + 16t+\frac{1}{2} \times9.8t^2\\

18 + 4t = 5 + 16t

12t = 13

t = 1.08 seconds

Thus, it will take 1.08 seconds for the ball to reach Sharon after she jumps if the upward velocity of the ball is 16 ft/s from a height of 5 feet.

Learn more about the equation of the motion here:

brainly.com/question/13514745

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               f) subtract 2 from previous term then add 5 to the next term

<u>Step-by-step explanation:</u>

a) 1, 3, 6, 10

    ∨  ∨  ∨

  +2 +3 +4           The next term is 10 +5 = 15

b) 1, 2, 3, 5

    ∨  ∨  ∨

  =3 =5 =8        The next term is 5 + 8 = 13

d)  8, 7, 5, 2

      ∨  ∨  ∨

     -1  -2  -3             zThe next term is 2 - 4 = -2

e) 1, 3, 9, 27

     ∨  ∨  ∨

    ×3 ×3 ×3         The next term is 27 × 3 = 81

f) 49, 47, 52, 50, 55

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     -2   +5   -2   +5      The next term is 55 - 2 = 53

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3 years ago
In a certain section of Southern California, the distribution of monthly rent for a one-bedroom apartment has a mean of $2,275 a
KATRIN_1 [288]

Answer:

100% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,095 per month

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 z-score 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 p-value, 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.

Mean of $2,275 and a standard deviation of $290.

This means that \mu = 2275, \sigma = 290

Sample of 65:

This means that n = 65, s = \frac{290}{\sqrt{65}}

Finding the mean to be at least $2,095 per month

This is 1 subtracted by the p-value of Z when X = 2095. So

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

By the Central Limit Theorem

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

Z = \frac{2095 - 2275}{\frac{290}{\sqrt{65}}}

Z = -5

Z = -5 has a p-value of 0.

1 - 0 = 1

100% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,095 per month

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3 years ago
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Step-by-step explanation:

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However, there are 10 cases are repeated when two digits are the same. so you have  to subtract it by 10

So answer will be 26 * (100-10) = 23400

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