A bill totalled 37.50 for the use of 125 minutes, what would the bill be if I used 175 minutes

Answers

Answer 1

Answer: 125/37.50= 3.33R so if we take 3.33R and multiply it by 175 we would get 58.27. so i would assume that that would be the closest i can get to the answer. hope this helps!

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Round 3,721 to the nearest hundred.

Answers

Answer: The answer is 3700

Answer:3.72

Step-by-step explanation:

A psychologist designed a new aptitude exam to measure logical and analytical thinking abilities. The time allowed for the exam is 60 minutes, and the exam is made up of 35 multiple choice questions. The psychologist expects that an examinee will spend an average of 1.66 minutes answering each question, with a standard deviation of 0.73 minutes. What proportion of examinees will complete the exam on time? Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places

Answers

Answer:

52.79% of examinees will complete the exam on time.

Step-by-step explanation:

Problems of normally distributed samples can be solved using 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 problem, we have that:

There are 35 questions. The psychologist expects that an examinee will spend an average of 1.66 minutes answering each question, with a standard deviation of 0.73 minutes. This means that the mean and the standard deviation for the time to complete the test is $\mu = 35*1.66 = 58.1, \sigma = 35*0.73 = 25.55$ .

What proportion of examinees will complete the exam on time?

The time allowed for the exam is 60 minutes. So this proportion is the pvalue of Z when $X = 60$ . So:

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

$Z = (60 - 58.1)/(25.55)$

$Z = 0.07$

$Z = 0.07$ has a pvalue of 0.5279.

This means that 52.79% of examinees will complete the exam on time.

Which ordered pairs are solutions to the inequality −2x+y≥−4 ?Select each correct answer.

(0, −5)

(3, −1)

(1, −2)

(0, 1)

(−1, 1)

Answers

Answer:

(0,-5) , (1,-2) , (0,1) and (-1,1)

Step-by-step explanation:

-2x + y ≥ -4

y ≥ 2x - 4

Taking a point (0,-5):

-5 ≥ 0 - 4 , 5 ≥ -4

This situation is true.

Taking a point (3,-1):

-1 ≥ 2(3) - 4 , -1 ≥ 2

This situation is not true.

Taking a situation (1,-2):

-2 ≥ 2(1) - 4 , -2 ≥ -2

This situation is true.

Taking a point (0,1):

1 ≥ 0 - 4 , 1 ≥ -4

This situation is true.

Taking a point (-1,1):

1 ≥ 2(-1) - 4 , 1 ≥ -6

This situation is true.

The correct answers are

(−1, −1)

(5, −12)

(0, 1)

Have a nice day!

1. Suppose f(x) = x^4-2x^3+ax^2+x+3. If f(3) = 2, then what is a? 2. Let f, g, and h be polynomials such that h(x) = f(x) * g(x). If the constant term of f(x) is -4 and the constant term of h(x) is 3, what is g(0)? 3. Suppose the polynomials f and g are both monic polynomials. If the sum f(x) + g(x) is also monic, what can we deduce about the degrees of f and g? 4. If f(x) is a polynomial, is f(x^2) also a polynomial 5. Consider the polynomial function g(x) = x^4-3x^2+9 a. What must be true of a polynomial function f(x) if f(x) and f(-x) are the same polynomial b.What must be true of a polynomial function f(x) if f(x) and -f(-x) are the same polynomial

Answers

Answer:

1. a = -31/9

2. -3/4

3. Different degree polynomials

4. Yes, of a degree 2n

5. a. Even-degree variables

b. Odd- degree variables

Step-by-step explanation:

1. Suppose f(x) = x^4-2x^3+ax^2+x+3. If f(3) = 2, then what is a?

Plugging in 3 for x:

f(3)= 3^4 - 2*3^3 + a*3^2 + 3 + 3= 81 - 54 + 6 + 9a = 33 + 9a and f(3)= 2

9a+33= 2
9a= -31
a = -31/9

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2. Let f, g, and h be polynomials such that h(x) = f(x) * g(x). If the constant term of f(x) is -4 and the constant term of h(x) is 3, what is g(0)?

f(0)= -4, h(0)= 3, g(0) = ?
h(x)= f(x)*g(x)
g(x)= h(x)/f(x)
g(0) = h(0)/f(0) = 3/-4= -3/4
g(0)= -3/4

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3. Suppose the polynomials f and g are both monic polynomials. If the sum f(x) + g(x) is also monic, what can we deduce about the degrees of f and g?

A monic polynomial is a single-variable polynomial in which the leading coefficient is equal to 1.

If the sum of monic polynomials f(x) + g(x) is also monic, then f(x) and g(x) are of different degree and their sum only change the one with the lower degree, leaving the higher degree variable unchanged.

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4. If f(x) is a polynomial, is f(x^2) also a polynomial?

If f(x) is a polynomial of degree n, then f(x^2) is a polynomial of degree 2n

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5. Consider the polynomial function g(x) = x^4-3x^2+9

a. What must be true of a polynomial function f(x) if f(x) and f(-x) are the same polynomial?

If f(x) and f(-x) are same polynomials, then they have even-degree variables.

b.What must be true of a polynomial function f(x) if f(x) and -f(-x) are the same polynomial?

If f(x) and -f(-x) are the same polynomials, then they have odd-degree variables.

Suppose you are an elementary school teacher. You want to order a rectangular bulletin board to mount on a classroom wall that has an area of 90 square feet. Suppose fire code requirements allow for no more than 30% of a classroom wall to be covered by a bulletin board. If the length of the board is three times as long as the width, what are the dimensions of the largest bulletin board that meets fire code?

Answers

Answer:

3 feet wide and 9 feet long.

Step-by-step explanation:

The classroom wall has an area of $90ft^2$ .

The fire code requirements allow a bulletin board with an area of at most 30% of $90ft^2$ . This means that the maximum area of the bulletin board is $27ft^2$