a committee of 4 is being formed randomly from the employees at a school: 6 administrators, 38 teachers and 4 staff. what is the probability that all 4 members are administrators? express your answer as a fraction

Answer:

The area of this triangle is (1/2)(9)(8) = 36.

she could have scored the 10 points in 302400 ways.

The given parameters are

n= total points =10

r1 =one-point free throw = 1

r2 = two-point field goals = 2

r3 =  three-point field goals = 3

The number of ways (k) she could have scored the points is:

k=(n!)/(r1!×r2!×r3!)

The factorial function is a mathematical formula represented by an exclamation mark "!".

k= 10!/(1!×2!×3!)

k= 3628800/(1×2×6)

k= 302400

so.. she could have scored the 10 points in 302400 ways.

To learn more about Combinations

visit : brainly.com/question/15301090

#SPJ9

The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

Learn more about standard deviation here: https://brainly.com/question/24298037

#SPJ1

Answer:

0.872

Step-by-step explanation:

Given that :

P(cloudy) = P(C) = 0.94

P(cloudy and rainy) = P(C n R) = 0.82

Probability that a given day will be rainy if it is cloudy ; this is a conditional probability problem:

Recall ; P(A|B) = P(AnB) / P(B)

P(R|C) = P(C n R) / P(C) = 0.82 / 0.94 = 0.872

The car that drove off had a year of manufacture of 2013. However, this answer does not make sense, as all of the given cars were manufactured before 2010 and was solved by using mean.

In mathematics, the mean is a measure of central tendency of a set of numbers. It is commonly referred to as the average and is calculated by adding up all the numbers in a set and dividing by the total number of numbers in the set.

In the given question,

Let's start by finding the mean of the five cars:

Mean = (1971 + 1986 + 1993 + 2003 + 2010) / 5 = 1992.6

Now, let's assume that one of the cars drove off and we need to find out which one. Let's call the year of manufacture of the car that drove off "x".

If the mean of the remaining four cars is 1990, we can use the formula for the mean of a set of numbers to set up an equation:

(1971 + 1986 + 1993 + 2003 + 2010 - x) / 4 = 1990

Simplifying this equation, we get: (9973 - x) / 4 = 1990

Multiplying both sides by 4, we get: 9973 - x = 7960

Subtracting 9973 from both sides, we get: -x = -2013

Dividing both sides by -1, we get: x = 2013

Therefore, the car that drove off had a year of manufacture of 2013. However, this answer does not make sense, as all of the given cars were manufactured before 2010. Therefore, we can conclude that there was a mistake in the problem, or that the problem was poorly worded. Without additional information, we cannot determine which car drove off.

To Know more about mean, visit:

https://brainly.com/question/31098693

#SPJ1

The guests in the birthday party ate 33 cookies.

We know that Mrs. Smith made 6 1/4 dozen cookies and there were 3 1/2 dozen cookies left.

Let's first convert these fractions to a common denominator of 4, so we can easily subtract them.

6 1/4 dozen = 25/4 dozen

3 1/2 dozen = 14/4 dozen

Now we can subtract the number of cookies that were left from the number of cookies that were made:

25/4 - 14/4 = 11/4 dozen

To find out how many cookies this represents, we need to multiply by the number of cookies in one dozen.

There are 12 cookies in one dozen, so:

11/4 x 12 = 33

Therefore, the guests ate 33 cookies.

Read more about fractions at

https://brainly.com/question/1330447

#SPJ1

The expression which shows how many grams of raisins are in the bowl will be

(0.01x) * 150 + (0.01y) * 250

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The expression which shows how many grams of raisins are in the bowl will be:

= (x% × 150) + (y% × 250)

= (0.01x) * 150 + (0.01y) * 250

This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.

Learn more about expressions on:

https://brainly.com/question/723406

#SPJ1

The perimeter of the trapezoid is given as follows:

44 cm.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The missing side is a side of a right triangle, in which the other side is of 18 - 10 = 8 cm, while the hypotenuse is of 10 cm, hence:

8² + h² = 10²

64 + h² = 100

h² = 36

h = 6.

Hence the perimeter is given as follows:

P = 18 + 10 + 10 + 6 = 44 cm.

The trapezoid is given by the image presented at the end of the answer.

More can be learned about the perimeter of a polygon at https://brainly.com/question/3310006

#SPJ1

This is an incomplete question, I think the question will be

A sandwich shop employee named Lucy takes 2.5 minutes to make a sandwich. If she continues at the same rate, how long will it take her to make 10 sandwiches? Write the answer in minutes.

it will take Lucy 25 minutes to make 10 sandwiches if she continues at the same rate.

If Lucy takes 2.5 minutes to make a sandwich, then to find out how much time it would take for her to make 10 sandwiches, we simply multiply the time taken for one sandwich (2.5 minutes) by the number of sandwiches required (10).

10 x 2.5 = 25 minutes

Therefore, if she continues to work at the same rate of making one sandwich in 2.5 minutes, she will be able to make 10 sandwiches in 25 minutes.

To learn more about the Conversion of hours to minutes click:

https://brainly.com/question/30775919

#SPJ1

Answer:

2.98

Step-by-step explanation:

First find 3% of 16.05 which is 0.48.

Then add 0.48 to 16.05 which is 16.53.

Then multiply .18 by 16.53 which gets you 2.98

Hope it helps

Answer:

To find the amount of the sales tax, we need to multiply the bill amount by the tax rate of 3% or 0.03:

Sales tax = 0.03 x $16.05 = $0.48

To find the total amount of the bill after the sales tax was added, we need to add the bill amount to the sales tax:

Total bill = $16.05 + $0.48 = $16.53

To find the amount of the tip, we need to calculate 18% of the total bill after the sales tax was added:

Tip = 0.18 x $16.53 = $2.98

Rounding to the nearest cent, Penelope left a tip of $2.98.

Step-by-step explanation:

Answer:

1 is to 4

Step-by-step explanation:

the factor is 1-4 meaning 32÷8 is 4 so having 1 would mean the other factor is 4

a) The difference between​ carrier's highest data speed and the mean of all 50 data​ speeds is of: 54.62 Mbps.

b) This difference represents 1.54 standard deviations.

c) The z-score is of z = 1.54.

d) The carrier's highest data speed​ is not significant, as it is less than 2 standard deviations from the mean.

The parameters to this problem are given as follows:

Hence the difference between​ carrier's highest data speed and the mean of all 50 data​ speeds is obtained as follows:

72.6 - 17.98 = 54.62 Mbps.

Then we calculate the z-score, which is the division of this difference by the standard deviation, giving how many standard deviations the data is from the mean.

z = 54.62/35.53

z = 1.54

Hence the measure is 1.54 standard deviations from the mean, which is not unusual, as it is less than 2 standard deviations from the mean.

More can be learned about z-scores at https://brainly.com/question/25800303

#SPJ1

Answer:

a) P(x > 43) = 0.9599

b) P(x < 42) = 0.0228

c) P(x > 57.5) = 0.03

d) P(x = 42) = 0.

e) P(x<40 or x>55) = 0.1118

f) 43.42

g) Between 46.64 and 53.36.

h) Above 45.852.

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:

\(Z = \frac{X - \mu}{\sigma}\)

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, we have that:

\(\mu = 50, \sigma = 4\)

a) x>43

This is 1 subtracted by the pvalue of Z when X = 43. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{43 - 50}{4}\)

\(Z = -1.75\)

\(Z = -1.75\) has a pvalue of 0.0401

1 - 0.0401 = 0.9599

P(x > 43) = 0.9599

b) x<42

This is the pvalue of Z when X = 42.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{42 - 50}{4}\)

\(Z = -2\)

\(Z = -2\) has a pvalue of 0.0228

P(x < 42) = 0.0228

c) x>57.5

This is 1 subtracted by the pvalue of Z when X = 57.5. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{57.5 - 50}{4}\)

\(Z = 1.88\)

\(Z = 1.88\) has a pvalue of 0.97

1 - 0.97 = 0.03

P(x > 57.5) = 0.03

d) P(x = 42)

In the normal distribution, the probability of an exact value is 0. So

P(x = 42) = 0.

e) x<40 or x>55

x < 40 is the pvalue of Z when X = 40. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{40 - 50}{4}\)

\(Z = -2.5\)

\(Z = -2.5\) has a pvalue of 0.0062

x > 55 is 1 subtracted by the pvalue of Z when X = 55. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{55 - 50}{4}\)

\(Z = 1.25\)

\(Z = 1.25\) has a pvalue of 0.8944

1 - 0.8944 = 0.1056

0.0062 + 0.1056 = 0.1118

P(x<40 or x>55) = 0.1118

f) 5% of the values are less than what X value?

X is the 5th percentile, which is X when Z has a pvalue of 0.05, so X when Z = -1.645.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.645 = \frac{X - 50}{4}\)

\(X - 50 = -1.645*4\)

\(X = 43.42\)

43.42 is the answer.

g) 60% of the values are between what two X values (symmetrically distributed around the mean)?

Between the 50 - (60/2) = 20th percentile and the 50 + (60/2) = 80th percentile.

20th percentile:

X when Z has a pvalue of 0.2. So X when Z = -0.84.

\(Z = \frac{X - \mu}{\sigma}\)

\(-0.84 = \frac{X - 50}{4}\)

\(X - 50 = -0.84*4\)

\(X = 46.64\)

80th percentile:

X when Z has a pvalue of 0.8. So X when Z = 0.84.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.84 = \frac{X - 50}{4}\)

\(X - 50 = 0.84*4\)

\(X = 53.36\)

Between 46.64 and 53.36.

h) 85% of the values will be above what X value?

Above the 100 - 85 = 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.037 = \frac{X - 50}{4}\)

\(X - 50 = -1.037*4\)

\(X = 45.852\)

Above 45.852.

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

For more such questions on investment

https://brainly.com/question/29227456

#SPJ8

The rate at which the depth of the liquid is increasing when it reaches one-third of the height of the bowl is (7/3)π cm³/s.

To ascertain the rate at which the liquid's depth rises, let's find the derivative of the depth function with respect to time.

Let;

The rate of change of the volume of the liquid with respect to time is constant and equal to 7π cm³/s.

To determine the height of the bowl, we can evaluate the curve y = [-4 / (8 - x)] - 1 when x = 4 and y = 7.6 and then find the absolute difference between the values.

h = |[-4 / (8 - 4)] - 1 - [-4 / (8 - 7.6)] - 1|

Let's calculate the rate at which the depth rises when it reaches one-third of the bowl's height.

D = depth of bowl

Using this relationship from the question given;

D = (1/3) * h

In order to determine the rate at which D will change with respect to time, let's differentiate both sides of the equation.

dD/dt = (1/3) * dh/dt

Since dh/dt is the rate at which the depth of the liquid is changing, which is constant and equal to 7π cm³/s, we can substitute it into the equation:

dD/dt = (1/3) * (7π)

Simplifying, we have:

dD/dt = (7/3)π cm³/s

Learn more on rate of change of volume here;

https://brainly.com/question/22716418

#SPJ1

Answer:

.2

Step-by-step explanation:

Simplify the fraction: how many times does 3 go into 15? 5 times.

1/5

divide 100 by 5 then divide the quotient by 100 and you get .2

Each piece Measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

When a particular angle is cut into nine equal parts, the measure of each piece needs to be calculated.

Therefore, it is essential to first calculate the total angle measure and then divide it by the number of parts into which it is being cut.

What is an Angle?

An angle is a geometrical shape that consists of two rays sharing a common endpoint. The common endpoint is known as the vertex, and the two rays are known as the arms of the angle. An angle can be measured in degrees, radians, or gradians. Degrees are the most commonly used unit of measuring angles.How to Calculate Each Piece Measurement of an Angle if Cut into 9 Equal Lengths

To determine each piece measurement of an angle if cut into nine equal lengths, we will need to carry out the following steps:

Step 1: Calculate the total angle measure Suppose the angle being cut into nine equal lengths is an obtuse angle measuring 120 degrees. In that case, the total angle measure will be 120 degrees.

Step 2: Divide the total angle measure by the number of parts into which it is being cut.120 degrees ÷ 9 = 13.3333 degrees

Step 3: Add the kerf width to the piece measurements.0.125 x 9 = 1.125 degrees13.3333 + 1.125 = 14.4583 degrees

Therefore, each piece measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

For more questions on Measurement .

https://brainly.com/question/27233632

#SPJ8

Answer:

6

Step-by-step explanation:

318 / 53  = 6

the remainder is 0

Answer:

B) -2

Step-by-step explanation:

The slope of the line can be solved by using the following equation:

slope \((m) = \frac{y_2 - y_1}{x_2 - x_1}\)

Let: \((x_1, y_1) = (0 , 4)\\(x_2 , y_2) = (-1 , 6)\)

Plug in the corresponding numbers to the corresponding variables:

\(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (4)}{-1 - (0)}\)

\(m = \frac{6-4}{-1 - 0} = \frac{2}{-1}\)

m = -2 is your answer.

~

Learn more about solving for the slope of the line, here:

https://brainly.com/question/14511992

Answer:

The answer is B

-2

Step-by-step explanation:

slope =rise/run

\(m = \frac{y(2) - y(1)}{x(2) - x(1)} \)

\(m = \frac{6 - 4}{ - 1 - 0} \)

\(m = \frac{2}{ - 1} \)

\(m = - 2\)

Answer:

14

Step-by-step explanation:

f(-1) = 10-4(-1)

=10-(-4)

=10+4

=14

Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

\(24+32p=8(3+4p)\)

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

As per the 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year is (0.1859,0.2133).

Confidence interval:

In statistics, confidence interval is an estimate of an interval in statistics that may contain a population parameter.

Given,

According to a recent pew research center report, many American adults have made money by selling something online. in a random sample of 4579 American adults, 914 reported that they earned money by selling something online in the previous year. assume the conditions for inference are met.

Here we need to construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year.

As per the given question, the value of

Confidence interval = 98%

Number of samples = 4579

Reported numbers = 914

Therefore, the number of failure is calculated as,

=> 4579 - 914

=> 3665

Here the sample proportion is the number of successes divided by the sample size:

=> 941/4579

=> 0.1996

Here for confidence level 1 − α = 0.98,

We have to determine zα / 2 ​= z0.01​ using the normal probability table in the appendix, we get

zα/2 ​= 2.33

Then the margin of error is calculated as,

E = 2.33 x √[0.1996 x (1 - 0.1996)]/4579

E = 0.0137

Then the boundaries of the confidence interval are then:

p⁻ˣ = 0.1996−0.0137 = 0.1859

p⁺ˣ = 0.1996+0.0137 = 0.2133

To know more about confidence interval here.

https://brainly.com/question/24131141

#SPJ4

Answer:

1) 4T+T=125

2) Rhonda drove 25 miles

and Jamie drove 100 miles

Step-by-step explanation:

1) Rhonda drove = T

Jamie drove = 4T

4T+T=125

2) 5T=125

T=125/5

T=25

So Rhonda drove T = 25

And Jamie drove 4T = 100

The artist should buy the canvas with dimensions 26" x 16" as it most closely matches the Golden Rectangle.

To determine which canvas size most closely matches the Golden Rectangle, we need to calculate the aspect ratios of the available options and compare them to the Golden Ratio.

The Golden Ratio is approximately 1.618. A rectangle is considered to be a Golden Rectangle if its aspect ratio (width divided by height) is equal to the Golden Ratio.

Let's calculate the aspect ratios for each canvas size:

Canvas 1: 24" x 36"

Aspect ratio = 24 / 36 = 0.67

Canvas 2: 24" x 40"

Aspect ratio = 24 / 40 = 0.6

Canvas 3: 10" x 16"

Aspect ratio = 10 / 16 = 0.625

Canvas 4: 26" x 16"

Aspect ratio = 26 / 16 = 1.625

Canvas 5: 20" x 12"

Aspect ratio = 20 / 12 = 1.667

Now, let's compare the aspect ratios of the available options with the Golden Ratio (1.618) to see which one is closest:

Canvas 1: |0.67 - 1.618| = 0.948

Canvas 2: |0.6 - 1.618| = 1.018

Canvas 3: |0.625 - 1.618| = 0.993

Canvas 4: |1.625 - 1.618| = 0.007

Canvas 5: |1.667 - 1.618| = 0.049

The canvas with the aspect ratio closest to the Golden Ratio is Canvas 4: 26" x 16". Its aspect ratio of 1.625 is only 0.007 away from the Golden Ratio.

To learn more about the ratio;

https://brainly.com/question/13419413

#SPJ1

Answer:

76

Step-by-step explanation:

36+40=76

Hope this helps!!

Answer:

76 games in total

Step-by-step explanation:

The diameter of the circle is 8, because the diameter is twice the radius. The circumference of the circle is 25.1327, because the circumference is calculated using the formula C = 2πr, where r is the radius and π is approximately equal to 3.14.

In general, an inverse variation relation has the form shown below

It is given that x=16, then y=5/4; thus,

Therefore, the equation is y=20/x

2) Set x=4 in the equation above; then

When x=4, y=5.

Answer:

1. yes

2. yes

3. no

4. no

5. yes

Step-by-step explanation:

Answer:

the first one

Step-by-step explanation: