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Hitman42
5 days ago
10

Geraldine has 200 feet of fencing. She wants to fence in a rectangular area. Which function A(w) represents the area of land tha

t can be fenced in if the width of the rectangular area is w?
Mathematics
1 answer:
Zina [9.1K]5 days ago
5 0
A(w) = -w² + 100w Step-by-step explanation: Initially, we need to express the length (l) of the rectangular area in terms of the width (w). Given that the total perimeter of the rectangle is 200 feet implies that 2(w + l) = 200, leading to l = 100 - w. Hence, the area A can be given as width multiplied by length: A = w * l = w * (100 - w) = -w² + 100w. Consequently, A(w) = -w² + 100w.
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Four friends each ordered individual pizzas at a restaurant. Suzy ate 3/8 of her pizza. Ethan ate 3/5 of his pizza. Tenaya ate 4
PIT_PIT [9117]

Answer:

Ethan and Tenaya consumed more than half of their pizzas.

On the other hand, Sam and Suzy ate less than half of theirs.

Step-by-step explanation:

The four friends ordered individual pizzas and we must determine who consumed more than half and who ate less.

Suzy had 3/8 of her pizza, which is equivalent to 0.375, indicating she ate less than half.Ethan ate 3/5 of his pizza, which is 0.6, hence he had more than half.

Tenaya had 4/6 of her pizza, equating to 0.67, indicating she also ate more than half. Sam consumed 1/3 of his pizza which is 0.3, showing he ate less than half.

Therefore, we conclude that

Ethan and Tenaya ate more than half of their pizzas, while

Sam and Suzy had less than half.

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10 hours ago
Which expression is equivalent to StartFraction 3 x Over x + 1 EndFractiondivided by x + 1?
AnnZ [9099]

Response:

Detailed Breakdown:

Forget all the words! Just apply the math.

\frac{3x/(x+1)}{x+1} = \frac{3x}{(x+1)^2}

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17 days ago
Brenda went to the store with her dad to buy snacks. They bought a box of 16 snack-size bags of chips for $7.84 and a box of 24
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14 days ago
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Let X represent the amount of gasoline (gallons) purchased by a randomly selected customer at a gas station. Suppose that the me
babunello [8412]

Answer:

a) There is an 18.94% chance that the sample mean of the amount purchased will be at least 12 gallons.

b) There is an 81.06% chance that the total gasoline purchased will not exceed 600 gallons.

c) The estimated value for the 95th percentile of the total consumption by 50 randomly chosen customers is 621.5 gallons.

Step-by-step explanation:

The solution to this query involves applying the normal probability distribution and the central limit theorem.

Normal probability distribution

Issues involving normally distributed samples can be addressed using the z-score formula.

In a dataset characterized by mean \mu and standard deviation \sigma, the z-score for a value X is expressed as:

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

The z-score indicates how many standard deviations a particular value is from the mean. After calculating the z-score, we reference the z-score table to find its corresponding p-value, which represents the probability that a measure is less than X, essentially giving us X's percentile. By subtracting the p-value from 1, we find the chance that the measure exceeds X.

Central Limit Theorem

The Central Limit Theorem posits that for a normally distributed variable X, with mean \mu and standard deviation \sigma, the distribution of sample means with size n approximates a normal distribution characterized by mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

Even when dealing with a skewed variable, the Central Limit Theorem remains applicable as long as n is no less than 30.

For sums, this theorem can likewise be employed, accompanied by mean \mu and standard deviation s = \sqrt{n}*\sigma.

In this scenario, we are given that:

\mu = 11.5, \sigma = 4

a. For a group of 50 randomly selected customers, what is the estimated probability that the sample mean amount purchased is at least 12 gallons?

Here we have n = 50, s = \frac{4}{\sqrt{50}} = 0.5657

This probability is derived from 1 minus the p-value of Z corresponding to X = 12.

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

According to the Central Limit Theorem

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

Z = \frac{12 - 11.5}{0.5657}

Z = 0.88

Z = 0.88 yields a p-value of 0.8106.

1 - 0.8106 = 0.1894

Therefore, there is an 18.94% chance that the sample mean amount purchased is at least 12 gallons.

b. For a group of 50 randomly selected customers, what is the estimated probability that the total amount of gasoline purchased does not exceed 600 gallons?

Regarding sums, we have mu = 50*11.5 = 575, s = \sqrt{50}*4 = 28.28

This probability equals the p-value of Z when X = 600. Hence,

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

Z = \frac{600 - 575}{28.28}

Z = 0.88

Z = 0.88 displays a p-value of 0.8106.

Thus, there is an 81.06% chance that the total gasoline purchased will be 600 gallons or less.

c. What is the approximate figure for the 95th percentile regarding the total purchases by 50 randomly chosen customers?

This value corresponds to X when Z indicates a p-value of 0.95, which occurs at Z = 1.645.

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

1.645 = \frac{X- 575}{28.28}

X - 575 = 28.28*1.645

X = 621.5

The 95th percentile estimate for the total amount purchased by 50 randomly selected customers stands at 621.5 gallons.

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17 days ago
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Answer:

Grumpy's age is 20 while Happy's age is 80.

Step-by-step explanation:

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14 days ago
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