MATHEMATICS COLLEGE

The average starting salary of this year's vocational school graduates is $35,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and the maximum starting salaries of the middle 95% of the graduates

Answers

Answer 1

Answer:

Answer:

Minimum: $25,200

Maximum: $44,800

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

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.

In this question:

$\mu = 35000, \sigma = 5000$

What are the minimum and the maximum starting salaries of the middle 95% of the graduates

Minimum: 50 - (95/2) = 2.5th percentile.

Maximum: 50 + (95/2) = 97.5th percentile

2.5th percentile:

X when Z has a pvalue of 0.025. So X when Z = -1.96.

$Z = (X - \mu)/(\sigma)$

$-1.96 = (X - 35000)/(5000)$

$X - 35000 = -1.96*5000$

$X = 25200$

The minimum is $25,200

97.5th percentile:

X when Z has a pvalue of 0.975. So X when Z = 1.96.

$Z = (X - \mu)/(\sigma)$

$1.96 = (X - 35000)/(5000)$

$X - 35000 = 1.96*5000$

$X = 44800$

The maximum is $44,800

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Choose the missing number. 36 x ____ = 7,200

Answers

Answer:

200

Step-by-step explanation:

What is the greatest common factor of 8x and 40y?

8
8xy
320
320xy

Answers

The greatest common factor of 8x and 40y is 8.

What are Factors?

Factors of a number or an algebraic expression are the numbers or expressions which divides the given number evenly.

For example, 10 = 2 × 5

So we can say that 2 and 5 are factors of 10.

Greatest common factor of two or more numbers is the factor which is the greatest among all the common factors of both the numbers.

8x can be prime factorized as,

8x = 2 × 2 × 2 × x

Similarly, 40y can be prime factorized as,

40y = 2 × 2 × 2 × 5 × y

Greatest common factor of both the numbers is the product of the common prime factors of both.

Greatest common factor = 2 × 2 × 2 = 8, which is common to both.

Hence 8 is the greatest common factor of 8x and 40y.

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Answer:

Hope this helps!

Angle of the Sun A 96-ft tree casts a shadow that is 120 ft long. What is the angle of elevation of the sun

Answers

Answer:

The angle of elevation of the sun is 39⁰

Step-by-step explanation:

Given;

height of the tree, h = 96 ft

length of the shadow, L = 120 ft

| 96ft

θ------------------------------------

120ft

Completing this triangle to cut across the top of the tree gives you a right angled triangle with θ as the angle of elevation of the sun.

Apply trig-ratio to determine the angle of elevation of the sun;

tanθ = opposite side / adjacent side

tanθ = 96 / 120

tanθ = 0.8

θ = tan⁻¹(0.8)

θ = 38.7⁰

θ = 39⁰

Therefore, the angle of elevation of the sun is 39⁰

Write a problem in which $180 would be a reasonable answer

Answers

Answer: Word problem: Mya goes to a carnival and buys food for her and her friends. She buys 5 funnel cakes that were $20 each. She buys 10 buckets of popcorn that were 8 dollars each.

Regular problem: $20+$15+$20+$100+$25=180

Step-by-step explanation: I didn't know what you needed. I'm sorry if that's not it, but hope it helps.

Consider the initial value problem:y' + 5/3y =1 - 1/5t, y(0)= yo

What equation expresses the requirement that the solution touches the t-axis?
a. y(t)= 0
b. y'(t)= 0
c. y''(t)= 0

Answers

Answer:

a. y(t) = 0

Step-by-step explanation:

There are two axis on the graph. One is x-axis which is horizontal line on the graph and the other is y-axis which is vertical side of the graph. The point where x-axis and y-axis meet is origin which has value 0. The equation to write the points of the graph is represented by y(x) = 0. In the given equation there is t variable used in the values.

Final answer:

The requirement that the solution of the given initial value problem 'touches' the t-axis is represented by the equation y(t) = 0. This is because the output of the function is zero at that specific value of t. Contrastingly, y'(t) = 0 and y''(t) = 0 indicate conditions of slope and rate of slope change.

Explanation:

In the given initial value problem, the requirement that the solution 'touches' the t-axis is represented by the equation y(t) = 0. This is because when the function Touches the t-axis, the y-value (output of the function) is zero for that specific value of t.

It's worth noting that y'(t) = 0 and y''(t) = 0 represent the conditions where the slope of a function is zero (which corresponds to a localminimum or maximum), and where the rate of change of the slope is zero (which can indicate a point of inflection), respectively.

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A doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 90% confident that her estimate is within 4 ounces of the true mean

Answers

Answer:

The minimum sample size needed is $n = ((1.96√(\sigma))/(4))^2$ . If n is a decimal number, it is rounded up to the next integer. $\sigma$ is the standard deviation of the population.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = (1 - 0.9)/(2) = 0.05$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.645.

Now, find the margin of error M as such

$M = z(\sigma)/(√(n))$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

How large a sample must she select if she desires to be 90% confident that her estimate is within 4 ounces of the true mean?

A sample of n is needed, and n is found when M = 4. So

$M = z(\sigma)/(√(n))$

$4 = 1.96(\sigma)/(√(n))$

$4√(n) = 1.96√(\sigma)$

$√(n) = (1.96√(\sigma))/(4)$

$(√(n))^2 = ((1.96√(\sigma))/(4))^2$

$n = ((1.96√(\sigma))/(4))^2$

The minimum sample size needed is $n = ((1.96√(\sigma))/(4))^2$ . If n is a decimal number, it is rounded up to the next integer. $\sigma$ is the standard deviation of the population.

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