Work hours for College Faculty The average full-time faculty member in a post-secondary degree granting institution works an average of 57 hours per week. Round intermediate calculations and final answers to two decimal places as needed. If we assume the standard deviation is 2.5 hours, then no more than % of faculty members work more than 62 hours a week.

Answer:

x is -34/3 and -26/3

Step-by-step explanation:

Given the expression

3|1/2x+5| + 7 = 5

Removing the modulus sign

3(1/2x+5) + 7 = 5

Subtract 7 from both sides

3(1/2x+5) + 7 - 7= 5 - 7

3(1/2x+5) = -2

Open the bracket

3/2 x + 15 = -2

Subtract 15 from both sides

3/2 x + 15-15 = -2 - 15

3/2 x = -17

3x = -2*17

3x  = -34

x = -34/3

Hence the value of x is -34/3

For the negative function:

3(1/2x+5) + 7 = 5

Subtract 7 from both sides

3(-(1/2x+5)) + 7 - 7= 5 - 7

3(-1/2x-5) = -2

Open the bracket

-3/2 x - 15 = -2

Add 15 from both sides

3/2 x + 15-15 = -2 + 15

-3/2 x = 13

-3x = 2 * 13

-3x  =26

x = -26/3

Hence the value of x is -26/3

The representation which is most appropriate for showing the change in the average hourly wage is: A. scatter plot with the title average hourly wage and the x axis labeled years since 2016 and the y axis labeled hourly wage in dollars, with points at 0 comma 9, 1 comma 9 and a half, 2 comma 10, 3 comma 11, 4 comma 12, 5 comma 13, and 6 comma 14.

In this scenario, the years would be plotted on the x-axis (x-coordinate) of the scatter plot while the hourly wage would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the years and hourly wage, an equation for the line of best fit is given by:

y = 0.8571x + 8.6429

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To calculate the probability that at least two people in a class of 30 share the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to one minus the probability of the event not happening.

If we assume that birthdays are uniformly distributed throughout the year (i.e., each day is equally likely to be someone's birthday), then the probability that no two people in the class share the same birthday is:

365/365 * 364/365 * 363/365 * ... * 336/365

This is because the first person can have any birthday (probability of 365/365), the second person must have a different birthday (probability of 364/365), the third person must have a different birthday than the first two (probability of 363/365), and so on, up to the 30th person, who must have a different birthday than the first 29 (probability of 336/365).

Calculating this probability gives us:

(365/365) * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

So the probability that no two people in the class share the same birthday is approximately 0.2937.

Using the complement rule, the probability that at least two people in the class share the same birthday is:

1 - 0.2937 = 0.7063

Therefore, the probability that at least two people in a class of 30 share the same birthday is approximately 0.7063, or 70.63%.

Answer:

Step-by-step explanation:

Good morning,

You just do it in the pathway, and there is the answer for you :D.

Step-by-step explanation:

A whole number that is not able to be divided by two into two equal whole numbers. Example: 1, 3, 5, and 7 are odd numbers

Answer:

The answer would be 4

Step-by-step explanation:

you can’t have repeating numbers in a function.

The student answered 27 out of 30 questions correctly on the history test, achieving a 90% accuracy rate.

To calculate the number of questions the student answered correctly, we can multiply the total number of questions (30) by the percentage of questions answered correctly (90%). The calculation is as follows:

Number of questions answered correctly = Total number of questions × Percentage of questions answered correctly

= 30 × 0.90

= 27

Therefore, the student answered 27 questions correctly on the history test.

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Answer:

Liner function

x = 5 + n

Step-by-step explanation:

Given:

Height of tree = 5 ft

Grow per month = 1 ft

Find:

Equation:

Computation:

Assume;

New height of tree x

Number of month = n

x = 5 + 1(n)

x = 5 + n

Answer:

Y = 2x+8

Step-by-step explanation:

Y=mx=b equations

The number of cups of rice the restaurant would need for 20 cups of veggies is 5.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

The recipe calls for 1/4 cup of rice for every 1 cup of veggies.

Now,

1cup veggie = 1/4 cup rice

20cup veggies= 1/4 * 20 cup rice

=5

Therefore, by algebra the count of cups of rice will be 5.

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The student's overall final score is 82.55, he has earned a B letter grade. A student's overall final score and letter grade is calculated using the following formula: Overall final score = 0.05 x midterm score + 0.20 x project score + 0.45 x homework score + 0.30 x final exam score .

To calculate the final grade of the student, we need to substitute the values provided in the given question into the above formula. Given, The midterm score is 71.The project score is 89. The homework score is 88.The final exam score is 72. According to the formula given above, the final score will be:

Overall final score = 0.05 x midterm score + 0.20 x project score + 0.45 x homework score + 0.30 x final exam score

= (0.05 x 71) + (0.20 x 89) + (0.45 x 88) + (0.30 x 72)

= 3.55 + 17.8 + 39.6 + 21.6= 82.55

Therefore, the student's overall final score is 82.55. To calculate his letter grade, we use the following grading system: A mean of 90 or above is an A. A mean of at least 80 but less than 90 is a B.A mean of at least 70 but less than 80 is a C.A mean of at least 60 but less than 70 is a D. A mean of less than 60 is an F. Since the student's overall final score is 82.55, he has earned a B letter grade.

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Answer:

45

Step-by-step explanation: Find what 80% of 25 is, you can do this by dividing 25 by 100. Then multiply the output by 80. Add that output to 25 and you should get an answer of 45.

Answer:

11

Step-by-step explanation:

The range of the data set is 11.

A 2-column table with 9 rows titled December Temperatures. Column 1 is labeled Day with entries 1, 2, 3, 4, 5, 6, 7, 8, 9. Column 2 is labeled Temperature (degrees Fahrenheit) with entries 33, 34, 42, 36, 39, 36, 39, 40, 44.

Here,

A 2 - column table with 9 rows titled December temperature.

Column 1 is labeled day with entries 1, 2, 3, 4, 5, 6, 7, 8, 9.

Column 2 is labeled temperature with entries 33, 34, 42, 36, 39, 40, 44.

What is range of data set?

The range is the difference between the highest and lowest values within a set of numbers.

Now,

For find the value of range set,

The highest value in given table = 44

The lowest value in given table = 33

Range of the data set = highest value - lowest value

                                 = 44 - 33

                                 = 11

Hence, The range of the data set is 11.

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The correct choice that describes the shape of the sampling distribution is:

OB. Approximately normal because n ≤ 0.05N and np(1-p) ≥ 10.

To determine the shape of the sampling distribution of the proportion, we need to check if the conditions for the normal approximation are satisfied. The conditions are:

n ≤ 0.05N: The sample size (n) is 150, and the population size (N) is 30,000. Checking this condition: 150 ≤ 0.05 * 30,000, which is true.

np(1-p) ≥ 10: Here, we need to calculate np(1-p) and check if it is greater than or equal to 10.

np(1-p) = 150 * 0.6 * (1-0.6) = 150 * 0.6 * 0.4 = 36

Since np(1-p) is greater than or equal to 10, this condition is also satisfied.

Based on the conditions, we can conclude that the sampling distribution of the proportion is approximately normal because both conditions n ≤ 0.05N and np(1-p) ≥ 10 are met. Therefore, the correct choice is OB.

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Answer:

see below

Step-by-step explanation:

First we need to find the radius

r =d/2 = 15.8/2 = 7.9 cm

The area of a circle is given by

A = pi r^2

   = pi ( 7.9) ^2

   =62.41 pi

Using 3.14 for pi

195.9674  

To the nearest hundredth

195.97

Using the pi button

196.0667975

To the nearest hundredth

196.07

Answer:

fg . 3

Step-by-step explanation:

f(g(3)) = 3fg

steps:

Remove parentheses: (a) = a

= fg . 3

Answ

Step-by-step explanation:

There is 2.625 pounds of food will be in each container.

The division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operationsin maths.

Mr, Thompson has 10 1/2 pounds. Of plant food. He put Equal amounts of the food into 4 containers.

Mr, Thompson has 10 1/2 pounds.

\(=10\dfrac{1}{2}\\\\= \dfrac{10 \times 2+1}{2}\\\\=\dfrac{20+1}{2}\\\\=\dfrac{21}{2}\\\\= 10.5\\\\\)

The amount of food in each container is;

\(\rm = \dfrac{10.2}{4}\\\\= 2.625 \ pounds\)

Hence, there is 2.625 grams of food will be in each container.

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To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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Answer:

C: in terms of the number of books, m, she orders.

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

You would start by subtracting $30 from $151 which is $121.

Then you would divide this by 11 which 121÷11=11

So 11 test were bought.

Answer:

I am assuming that you are talking about problem 2. so I will answer that.

Step-by-step explanation:

-2x + 6 ≥ 3x - 34

+2x        +2x

        6 ≥ 5x - 34

      +34       + 34

       40 ≥ 5x

       ÷5    ÷5

        8 ≥ x

So, x can be anything equal to or less than 8.

Answer:

x≤8

For the graph closed circle on 8 with the shading going to to left

Step-by-step explanation:

-2x+6≥3x-34 (given)

Subtract 6 on both sides

-2x≥3x-40

Subtract 3x on both sides

-5x≥-40

Divide by -5 on both sides

x≤8

*The sign flips because you divided by a negative (-5x)

Answer:

56 degrees

Step-by-step explanation:

The angles are all supplementary, so they add up to 180 degrees. Subtract 90 and 34 from 180 to get your answer.

Answer:

68%.

Step-by-step explanation:

Dalvin's finishing time is normally distributed with a mean of 65 seconds and a standard deviation of 1 second.

Under the empirical rule, 68% of the results will be within 1 standard deviation.

Since the standard deviation is 1 second, 68% of Dalvin's finishing time will be between 64 and 66 seconds.

Answer: x=2

Step-by-step explanation:

The solution of the given logarithmic equation is x = 28.1

Here we have the logarithmic equation:

4*ln(x - 8) = 12

And we want to solve this for x.

Remember the relations:

\(ln(e^x) = x\\e^{ln(x)} = x\)

First, we divide both sides by 4:

\(ln(x - 8) = 12/4 = 3\)

Then, if we apply the exponential equation to both sides of our equation, we get:

\(e^{ln(x - 8)} = e^{3}\\\\x - 8 = e^3\\\\x = e^3 + 8 = 28.1\)

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Answer: a = 5

Step-by-step explanation:

a/6-1/2=1/3

a/6 = 1/3 + 1/2

a/6 = 2/6 + 3/6

a/6 = 5/6

a = 5

Check:

5/6-1/2 = 1/3 ?

5/6 - 3/6 = 1/3?

2/6 = 1/3  ?

1/3 = 1/3   YES

Answer:

a = 5

Step-by-step explanation:

a/6 - 1/2 = 1/3

=> a/6 = 5/6

=> a = 5

Hoped this helped.

scale factor is 4

the blue square is 4 times bigger

Answer:

the scale factor would be 4

Step-by-step explanation:

because the blue square is about 4 times bigger then the other one