MATHEMATICS HIGH SCHOOL

The points (-5, -14) and (4, r) lie in a line with slope 4. Find the missing coordinate r.

Answers

Answer 1

Answer:

Answer: r = 22

Step-by-step explanation:

To answer this question, we can create a point-slope form equation.

y - y1 = m(x - x1)

y - r = 4(x - 4)

y - r = 4x - 16

y = 4x - 16 + r

Then, we will substitute the given point to solve for r.

y = 4x - 16 + r

(-14) = 4(-5) - 16 + r

(-14) = -20 - 16 + r

-14 = -36 + r

22 = r

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You would divide the two numbers and get 25

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Answers

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Answers

I hope this helps you

The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F. If 25 adults are randomly selected, find the probability that their mean body temperature is less than 99° F?

Answers

Answer: 0.9996

Step-by-step explanation:

Given : The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F.

Sample size : n=25

Let x be the random variable that represents the body temperatures of adults.

z-score : $z=(x-\mu)/((\sigma)/(√(n)))$

For x= 99° F

$z=(99-98.6)/((0.60)/(√(25)))\approx3.33$

Now, the probability that their mean body temperature is less than 99° F will be :-

$P(X<99)=P(z<3.33)=0.9995658\approx0.9996$

Hence, the probability that their mean body temperature is less than 99° F = 0.9996

Final answer:

To find the probability that the mean body temperature of 25 randomly selected adults is less than 99°F, we can use the Central Limit Theorem and calculate the Z-score. The mean body temperature of adults is 98.6°F with a standard deviation of 0.60°F. The sample size is 25.

Explanation:

To find the probability that the mean body temperature of 25 randomly selected adults is less than 99°F, we can use the Central Limit Theorem. According to the Central Limit Theorem, the sampling distribution of the sample mean follows a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the mean body temperature of adults is 98.6°F with a standard deviation of 0.60°F. The sample size is 25. So, the mean of the sampling distribution would still be 98.6°F, but the standard deviation would be 0.60°F divided by the square root of 25, which is 0.12°F.

Now, we can use the Z-score formula to find the probability that the mean body temperature is less than 99°F. The Z-score is calculated by subtracting the population mean from the desired value (99) and dividing it by the standard deviation of the sampling distribution (0.12). We can then use a Z-table or calculator to find the probability associated with the Z-score.

Learn more about Probability here:

brainly.com/question/32117953

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For a standard normal distribution, which of the following expressions must always be equal to 1?A) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
B) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
C) P(z≤-a)+P(-a≤z≤a)-P(z≥a)
D) P(z≤-a)+P(-a≤z≤a)+P(Z≥a)

Answers

P(z ≤ -a) + P(-a ≤ z ≤ a) + P(z ≥ a) = 1 - P(z ≤ a) + [P(z ≤ a) - P(z ≤ -a)] + 1 - P(z ≤ a) = 2 - 2P(z ≤ a) + P(z ≤ a) - [1 - P(z ≤ a)] = 2 - P(z ≤ a) - 1 + P(z ≤ a) = 1

Therefore, option D is the correct answer.

Answer:

D. $P(z\le -a)+P(-a\le z\le a)+P(z\ge a)$

Step-by-step explanation:

Properties of normal distribution-

The normal curve is symmetrical about the mean (μ).
The mean is at the middle of the graph and it divides the area into two equal halves.
The total area under the curve is equal to 1.

The total area under the curve can be divided into parts like,

area below $-a$ , i.e $z\le -a$ ,
area between $-a$ to $a$ , i.e $-a\le z\le a$
area above $a$ , i.e $z\ge a$

Therefore, $P(z\le -a)+P(-a\le z\le a)+P(z\ge a)=1$

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The scale drawing of a swimming pool measures 2 inches by 3 inches on the drawing 25 inches = 3 feet. What are the actual
dimensions of the pool?
18 feet x 24 feet
24 feet x 36 fees
30 feet x 40 feet
Submit

Answers

Answer:

The answer is 24 feet x 36 feet

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