Student scores on Professor Combs' Stats final exam are normally distributed with a mean of 76 and a standard deviation of 7.2Find the probability of the following:**(use 4 decimal places)**a.) The probability that one student chosen at random scores above an 81. b.) The probability that 20 students chosen at random have a mean score above an 81. c.) The probability that one student chosen at random scores between a 71 and an 81. d.) The probability that 20 students chosen at random have a mean score between a 71 and an 81.

Answer:

D is d because when You have to do they graph You have multiplicar

Answer:

102

Step-by-step explanation:

hope this helps

Answer:

2+24+40+39-(33-30)

105-33+30

135-33

132

Answer:

Step-by-step explanation:

d = 6 would not be a solution to the inequality below because it would make the inequality untrue! Plugging in, we get:

13 < d + 3

13 < 6 + 3
13 < 9
We know that 9 is not a solution to the inequality!

To solve, we isolate the d, and from there we can find all values that are a solution to the inequality to the solution!

\(13 < d + 3\\\\13 - 3 < d\\\\10 < d\)

Thus, one can say that the solutions to the inequality are: [R, d > 10]!

Answer:

\(\huge\boxed{\sf x = 17}\)

Step-by-step explanation:

Since m is a straight line, its measure is 180 degrees.

So,

2x + 5 + 8x + 5 = 180

2x + 8x + 5 + 5 = 180

10x + 10 = 180

10x = 180 - 10

10x = 170

Divide both sides by 10

x = 17

\(\rule[225]{225}{2}\)

Hope this helped!

Answer: 624

Step-by-step explanation:

The area of a rhombus is the product of the diagonals divided by 2 so the area of the rhombus in this case is 12 * 16 / 2 or 96 multiply with 6.5 we get 624 so that's the answer

Mean ≈ 0.874

Median ≈ 0.877

Maximum = 0.933

Minimum = 0.83

Mode = None

To find the mean, median, maximum, minimum, and mode of the given numbers:

Mean: The mean is the average of a set of numbers.

To calculate the mean, add up all the numbers and divide the sum by the total count.

Mean = (0.834 + 0.861 + 0.927 + 0.877 + 0.831 + 0.925 + 0.912 + 0.83 + 0.849 + 0.933 + 0.884) / 11

Mean ≈ 0.874

Median: The median is the middle value when the numbers are arranged in ascending or descending order.

Since there are 11 numbers, the median would be the 6th number when arranged in order.

Arranging the numbers in ascending order:

0.83, 0.831, 0.834, 0.849, 0.861, 0.877, 0.884, 0.912, 0.925, 0.927, 0.933

Median ≈ 0.877

Maximum: The maximum is the largest value among the given numbers.

Maximum = 0.933

Minimum: The minimum is the smallest value among the given numbers.

Minimum = 0.83

Mode: The mode is the value(s) that appear most frequently in the given numbers.

If there is no value that appears more than once, there is no mode.

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Based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

To determine whose purple paint will be redder based on the percent of red paint, we need to compare the ratios of red paint to the total paint used by Isaiah and Casho.

Isaiah's Ratio:

Isaiah mixes 3 cups of blue paint and 7 cups of red paint, making a total of 3 + 7 = 10 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (7 cups) by the total amount of paint (10 cups) and multiply by 100 to get the percentage:

Red paint percentage for Isaiah = (7 cups / 10 cups) * 100 = 70%

Casho's Ratio:

Casho mixes 4 cups of blue paint and 13 cups of red paint, making a total of 4 + 13 = 17 cups of paint.

To calculate the percent of red paint, we divide the amount of red paint (13 cups) by the total amount of paint (17 cups) and multiply by 100 to get the percentage:

Red paint percentage for Casho = (13 cups / 17 cups) * 100 = 76.47% (rounded to two decimal places)

Comparing the percentages, we can see that Casho's purple paint will be redder because Casho's paint has a higher percentage of red paint (76.47%) compared to Isaiah's paint (70%).

Therefore, based on the percent of red paint, Casho's purple paint will be redder than Isaiah's.

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Given that the current model of the car cost;

We are informed that the next model of a sports car will cost 14.4% more than the current model.

The price increase in dollars will then be given as;

Answer 1: Price increase in dollars is $5904

The cost of the next model will then be the sum of the current model and the price increase in dollars.

This would give;

Answer 2: The cost of the next price model is $46904

Answer:

−3−99

because if

+0−1−2−3−96

x+0−1−2−3−96

−99−3

The required exponential function will be \(f(x) =9(\frac{2}{3} )^x\) with a and b values 9 and 2/3 respectively.

The given exponential function is:

\(f(x) = ab^x\)

A function is a rule that relates two variables.

Point (0,9) lies on the graph of the given function.

So, \(9=ab^0\)

\(a=9\)

So, f(x) becomes \(f(x)=9b^x\)

Point (1,6) also lies on the graph of the given function.

So, \(6=9b\)

\(b=\frac{2}{3}\)

So, the required function will be \(f(x) =9(\frac{2}{3} )^x\)

Therefore, The required exponential function will be \(f(x) =9(\frac{2}{3} )^x\) with a and b values 9 and 2/3 respectively.

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Answer:

108 inches²

Step-by-step explanation:

Rectangular prism = cuboid

To find how much paper is required to cover the box, we need to find the TSA of the cuboid.

TSA of cuboid = 2 [LB + LH + HB] = 2 [ (3×4) + (3×6) + (4×6) ] = 2 [ 12+18+24 ] = 2 × 54 = 108 inches²

The graph of f(x) relate to its parent function by B. The parent function has been translated up.

Given that

f(x) = 3x +2 +4

When evaluated, we have

f(x) = 3x + 6

The parent function of the above is

f(x) = 3x

When f(x) = 3x is compared to f(x) = 3x + 6, we have

Difference = 6

This means that the parant function is translated up by 6 units

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Answer: 4/33

Step-by-step explanation:

just divide

Answer:

The answer is 4/33.

Step-by-step explanation:

to get this you just have to divide.

you're welcome.

Answer:

25%

Step-by-step explanation:

Answer:

Negative times a negative equals a positive

25x + 30x

55x

When t = 0, the value of n is approximately 3.93 million. The estimated number of people who moved to another state in 2005 is approximately 1.68 million. The predicted number of people who moved to another state in 2014 is approximately 6.81 million.

we need to substitute the given values of t (years since 1990) into the equation n = 0.03t² - 0.6t + 3.93. Let's calculate the values accordingly:

a. When t = 0 (which corresponds to the year 1990), we substitute this value into the equation:

n = 0.03(0)² - 0.6(0) + 3.93

n = 0 + 0 + 3.93

n ≈ 3.93

So, when t = 0, the value of n is approximately 3.93 million. In this context, it means that in the year 1990, around 3.93 million people moved to another state.

b. To estimate the number of people who moved to another state in 2005 (t = 2005 - 1990 = 15), we substitute this value into the equation:

n = 0.03(15)² - 0.6(15) + 3.93

n = 0.03(225) - 9 + 3.93

n = 6.75 - 9 + 3.93

n ≈ 1.68

Therefore, the estimated number of people who moved to another state in 2005 is approximately 1.68 million.

c. To predict the number of people who moved to another state in 2014 (t = 2014 - 1990 = 24), we substitute this value into the equation:

n = 0.03(24)² - 0.6(24) + 3.93

n = 0.03(576) - 14.4 + 3.93

n = 17.28 - 14.4 + 3.93

n ≈ 6.81

Hence, the predicted number of people who moved to another state in 2014 is approximately 6.81 million.

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Answer:

B

Step-by-step explanation:

Answer:

3357

Step-by-step explanation:

Answer: A

Step-by-step explanation: I just did it.

The person who gets to say the last number, 1000, will be Person 6.

Here, we have,

In this scenario, we have seven people sitting in a circle and counting clockwise. The goal is to determine which person will say the last number when they reach 1000. To solve this problem, we can use the concept of modular arithmetic.

When dividing 1000 by the total number of people (7), we get a quotient of 142 and a remainder of 6 (1000 = 142*7 + 6). This means that after completing 142 full rounds of counting, the group will have reached the number 994 (142*7). In the next round, they will continue counting from 995 to 1000.

Since the remainder is 6, it indicates that the last number (1000) will be spoken by the person sitting 6 positions after the first person in the circle (clockwise). In other words, Person 1 says numbers 1, 8, 15, and so on, while Person 6 will say 6, 13, 20, and so on.

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complete question:

10) Seven people sit in a circle and begin counting clockwise starting from 1.Each person in the group is keeping track of the numbers she is saying (e.g. 1,8, 15...) If they continue in this way, counting on and on, until they reach 1000, which person will get to say the last number

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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Im pretty sure it’s B

Answer:

Common ratio r = \(\dfrac{2}{3}\)

Sequence  is described by
\(a_n = \dfrac{3}{2}\cdot \left(\dfrac{2}{3}\right)^{n-1}\\\)

Step-by-step explanation:

\(S_n = \dfrac{a_1(1-r^n)}{1-r}\)

where
r = common ratio
a₁ = first term

Sum of first two terms

\(S_2 = \dfrac{a_1(1-r^2)}{1-r}\)

Sum of first four terms:
\(S_4 = \dfrac{a_1(1-r^4)}{1-r}\)

\(\dfrac{S_4}{S_2} = a_1 \cdot \dfrac{1-r^4}{1-r} \div a_1 \cdot \dfrac{1-r^2}{1-r}\\\)

To divide, flip the divisor and multiply

\(\dfrac{S_4}{S_2} =\dfrac{a_1(1-r^4)}{1-r} \times \dfrac{1-r}{a_1(1-r^2)}\)

The a₁ and (1-r) terms cancel out from numerator and denominator leaving

\(\dfrac{S_4}{S_2} =\dfrac{1-r^4}{1-r^2} \cdots [1]\)  

Using the identity
\(a^2 - b^2 = (a- b)(a+b)\)

\(1- r^4 = 1^4 - r^4 = (1^2 - r^2)(1^2+r^2) = (1-r^2)(1+r^2)\)

Plugging this into equation 1 we get
\(\dfrac{S_4}{S_2} =\dfrac{(1-r^{2})(1+r^{2})}{1-r^{2}}\)

The \(1- r^2\) terms cancel out leaving:
\(\dfrac{S_4}{S_2} =1 + r^2\)

We are given

\(S_4 =\dfrac{65}{18}\\\\S_2 = \dfrac{5}{2}\)

\(\dfrac{S_4}{S_2} = \dfrac{65}{18} \div \dfrac{5}{2}\)

To divide, flip the denominator \(\dfrac{5}{2}\) and multiply
\(\dfrac{S_4}{S_2} = \dfrac{65}{18} \times \dfrac{2}{5}\\\\= \dfrac{13}{9}\)

Therefore
\(1 + r^2 = \dfrac{13}{9}\\\\r^2 = \dfrac{13}{9} - 1\\\\= \dfrac{13}{9} - \dfrac{9}{9}\\\\= \dfrac{4}{9}\)

\(r = \sqrt{\dfrac{4}{9}}\\\\= \dfrac{\sqrt{4}}{\sqrt{9}}\\\\= \dfrac{2}{3}\)

So the common ratio
\(r = \dfrac{2}{3}\)

To find the first term  we have sum of first two terms = 5/2

\(S_2 = \dfrac{a_1(1-r^2)}{(1-r)} = a_1 (1+ r)\)

Plugging in knowns
\(\dfrac{5}{2} = a_1(1+\dfrac{2}{3})\\\\= a_1 \cdot \dfrac{5}{3}\)

Multiply both sides by 3/5 to get
\(a_1 = \dfrac{5}{2} \times \dfrac{3}{5}\\\\a_1 = \dfrac{3}{2}\)

The nth term of a GP is
\(a_n = a_1 \cdot r^{n-1}\\\)

Plugging in the values obtained
\(a_n = \dfrac{3}{2}\cdot \left(\dfrac{2}{3}\right)^{n-1}\\\)

The correct pairings are:

a) Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3

b) Five times the difference of a number squared and six: 5(n² - 6)

c) Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4

d) O twice the difference of nine and a number squared: 2(9 - n²)

The correct pairings of descriptions and expressions are as follows:

Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3

This expression represents taking a number, cubing it, dividing the result by seven, subtracting four, and then adding three.

Five times the difference of a number squared and six: 5(n² - 6)

This expression represents taking a number, squaring it, subtracting six, and then multiplying the result by five.

Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4

This expression represents taking the cube of a number, dividing six by the cube, adding nine, and then subtracting four.

O twice the difference of nine and a number squared: 2(9 - n²)

This expression represents taking a number, squaring it, subtracting it from nine, and then multiplying the result by two.

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Answer:

0.9595724

Step-by-step explanation:

Time taken to wash a car (μ) = 5 minutes

Hence, Number of cars washed per hour = 60/5 = 12 cars

If 5 cars arrive, 30 minutes to closing ; it takes 25 minutes to finish up ;

If 1 more car arrives, then it takes exactly 30 minutes

Hence, there will be no one in line at closing ;

IF 0 or 1 car arrives, if more than 1 car arrives, then there will be people in line at closing.

Hence, probability of waiting in line at closing :

1 - [p(0) + p(1)]

Using poisson :

P(x) = [(e^-μ) * (μ^x)] / x!

If x = 0

P(0) = [(e^-5) * (5^0)] / 0!

P(0) = (0.0067379 * 1) / 1

P(0) = 0.0067379

X = 1

P(1) = [(e^-5) * (5^1)] / 1!

P(0) = (0.0067379 * 5) / 1

P(0) = 0.0336897

Hence,

1 - (0.0067379 + 0.0336897)

1 - 0.0404276

= 0.9595724

Hence, the probability that anyone would be in the car washing line after closing is 0.9595724

The number of pennies weighing as much s earth is  193 × 10²⁴

Index forms are described as described as those forms that are used to represent numbers that are too large or small in more proper ways.

Other names for index forms are scientific notation and standard forms.

Ratio is described as the comparison of numbers or variables on the basis of their size.

It shows how many times one number contains another.

From the information given, we have that;

The earth weighs = 5. 972 × 10 ²⁴ kilograms

The penny weighs = 3.1 × 10 ⁻³ kilograms

Divide the values

= 5. 972 × 10 ²⁴/3.1 × 10 ⁻³

= 1.93 × 10 ²⁶

= 193 × 10²⁴

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Answer:

Option 2

Step-by-step explanation:

Because the slope is -0.09 the answer is the second option. A negative slope means a decrease.

The value of x for the equation is 0.35.

Simply put, to simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.

Given equation,

89 (54x − 36)  + 2 =  -34( −40 + 16x) + 90x

using PEMDAS

solving Parentheses first,

89(54x) - 36(89) + 2 = -34(-40) + 16x(-34) +90x

4806x - 3204 +2 = -1360 - 544x + 90x

4806x + 544x - 90x = -1360 + 3204 -2

5260x = 1842

x = 0.35

Hence the value of x is 0.35.

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Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

There are two types of errors that could be made:

a Type I error and a Type II error.

We have,

In step 5 of the hypothesis test, we make a decision to either reject or fail to reject the null hypothesis.

If we reject the null hypothesis, there are two types of errors that could be made:

a Type I error and a Type II error.

A Type I error occurs when we reject a true null hypothesis.

In this context, it means that we conclude that the percentage of packages delivered late is greater than 13% when in reality it is not.

This error is also known as a false positive.

A Type II error occurs when we fail to reject a false null hypothesis.

In this context, it means that we conclude that the percentage of packages delivered late is less than or equal to 13% when in reality it is greater than 13%. This error is also known as a false negative.

The probability of making a Type I error is denoted by α, which is given in the problem statement as α = 0.01.

Therefore, if we reject the null hypothesis, there is a 1% chance that we are making a Type I error.

Thus,

The probability of making a Type II error depends on the effect size, sample size, and significance level of the test.

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Answer:

A. positive

Step-by-step explanation:

A line that goes up from down has a positive slope.