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spin [16.1K]
3 years ago
14

Vanessa kicked a soccer ball laying on the ground. It was in the air for 4 seconds before it hit the ground. While the soccer ba

ll was in the air it reached a height of approximately 20 feet. Assuming that the soccer ball’s height (in feet) is a function of time (in seconds), what is the domain in the context of this problem?
Mathematics
1 answer:
Galina-37 [17]3 years ago
6 0

Answer:

The domain would be 0 to 4 seconds

Step-by-step explanation:

According to the given conditions a ball was lying on the ground but when it was hit by Vanessa it was in the air for 4 seconds. We have to find the domain.

We know that the domain is the input values. According to the given statement it would start at time 0 and end when it hit the ground at 4 seconds.

Therefore the domain would be 0 to 4 seconds.

[0,4] ....

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4 0
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Talia works 6 hours per day on Fridays and Saturdays each week. She earns $8.20 per hour
Simora [160]

<u>Question 1 </u>

Talia works 6 hours on Friday and 6 hours on Saturday. Total Work = 6+6 = 12 hours.

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Hence, option D is correct i.e. 98.40 dollars.

<u>Question 2 </u>

Mikey worked 8 hours on Wednesday, 6 hours on Thursday and 7 hours on Friday.

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Hence, option A is correct i.e. 8.95 dollars per hour.

<u>Question 3 </u>

Nina's Hourly Rate for first 40 hours = 12.25 dollars per hour.

Overtime rate for after first 40 hours = 1.5 x 12.25 = 18.375 dollars per hour.

Total work = 46 hours.

Gross Pay = (Hourly rate)x(first 40 hours) + (Overtime rate)x(Excess time after first 40 hours)

Gross pay = (12.25 x 40) + (18.375 x 6)

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Hence, option A is correct i.e. 600.25 dollars.

<u>Question 4 </u>

Tip amount = 15 dollars.

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Hence, option B is correct i.e. 20%

<u>Question 5 </u>

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Hence, option C is correct i.e. 974.00 dollars.

5 0
3 years ago
The weights of 1250 pumpkins are normally distributed with mean of 28 pounds and a standard deviation of 6 pounds. About how man
Mekhanik [1.2K]
Kropot72
kropot72 3 years ago
This can be solved by using a standard normal distribution table. The z-score for 34 pounds is 1, the reason being that 34 is one standard deviation above the mean of 28 pounds.
Can use the table to find the cumulative probability for z = 1.00 and post the result? If you do this we can do the next simple steps.
5 0
3 years ago
If a² + b² = z and ab = y, which of the following is equivalent to 4z + 8y? Show all the steps.
Ivenika [448]

Answer:

The answer to your question is:       (2a + 2b)²

Step-by-step explanation:

a² + b² = z

ab = y

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Substitution

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Simplify                        4a² + 4b² + 8ab

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Factorize                     (2a + 2b)²

7 0
3 years ago
Read 2 more answers
2. A marketing firm is trying to estimate the proportion of potential car buyers that would consider
Maurinko [17]

Answer:

a. The number of people that should be in the pilot study are 600 people

b. The point estimate is 0.62\overline 6

c. At 95% confidence level the true population proportion of potential car buyers of hybrid vehicle is between the confidence interval (0.588, 0.6654)

d. Two ways to reduce the margin of error are;

1) Reduce the confidence interval

2) Use a larger sample size

Step-by-step explanation:

a. The given parameters for the estimation of sample size is given as follows;

The margin of error for the confidence interval, E = 4% = 0.04

The confidence level = 95%

The sample size formula for a proportion as obtained from an online source is given as follows;

n = \dfrac{Z^2 \times P \times (1 - P)}{E^2}

Where, P is the estimated proportions of the desired statistic, therefore, we have for a new study, P = 0.5;

Z = The level of confidence at 95% = 1.96

n + The sample size

Therefore, we have;

n = \dfrac{1.96^2 \times 0.5 \times (1 - 0.5)}{0.04^2} = 600.25

Therefore, the number of people that should be in the pilot study in order to meet this goal at 95% confidence level is n = 600 people

b. The point estimate for the population proportion is the sample proportion  given as follows;

\hat p = \dfrac{x}{n}

Where;

x = The number of the statistic in the sample

n = The sample size

From the question, we have;

The number of potential car buyers, n = 600

The number of respondent in the sample that indicated that they would consider purchasing a hybrid, x = 376

Therefore, the point estimate, for the proportion of potential car buyers that would consider buying a hybrid vehicle, \hat p = 376/600 = 0.62\overline 6

c. The confidence interval for a proportion is given as follows

CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

Therefore, we get;

CI=0.62 \overline 6\pm 1.96\times \sqrt{\dfrac{\hat{0.62 \overline 6}\cdot (1-\hat{0.62 \overline 6})}{600}}

C.I. ≈ 0.6267 ± 0.0387

The 95% confidence interval for the true population proportion of potential buyers of hybrid vehicle, C.I. =  (0.588, 0.6654)

d. The margin of error is given by the following formula;

MOE_\gamma = z_\gamma  \times \sqrt{\dfrac{\sigma ^2}{n} }

Where;

MOE_\gamma = Margin of error at a given level of confidence

z_\gamma = z-score

σ = The standard deviation

n = The sample size

Therefore, the margin error can be reduced by the following two ways;

1) Reducing the confidence interval and therefore, the z-score

2) Increasing the sample size

6 0
2 years ago
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