How many different committees can be formed from 7 teachers and 30 students if the committee consists of three teachers and four students

Answer:

Step-by-step explanation:

Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and  

            6,which is 12.

            3*3/4*3=9/12

             5*2/6*2=10/12

Step 2:Subtract 9/12 from 10/12,which is 1/12.

Answer:

x < - 3 i guess I'm not sure

Answer:

x=13.6

Step-by-step explanation:

-2(5x-12)>54

5x-12>54+2

5x-12>56

5x>56+12

5x>68

x>68/5

x>13.6

The Residual is -8.4 hours and the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.

A residual plot is a type of scatter plot where the horizontal axis represents the independent variable, or input variable of the data, and the vertical axis represents the residual values.

Now, looking at the given residual plot and using a calculator online, we can say that the equation of the least squares regression line is;

y^ = 180.8 + 15.2x

Now, for 2 tablespoons of sugar , we have x = 2. Thus;

y^ = 180.8 + 15.2(2)

y^ = 212.4 hours

Residual for 204 hours is;

Residual = 204 - 212.4 = -8.4 hours

Thus, the interpretation of the given residual is that the carnation stayed fresh for 8.4 hours less than expected based on how much sugar it received.

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Complete question is;

Does adding sugar to the water in a vase help flowers stay fresh? To find out, two statistics students went to a flower shop and randomly selected 12 carnations. When they got home, the students prepared 12 identical vases with exactly the same amount of water in each vase. They put one tablespoon of sugarin 3 vases, two tablespoons of sugar in 3 vases, and three tablespoons of sugar in 3 vases.In the remaining 3 vases, they put no sugar. After the vases were prepared, the students randomly assigned 1 carnation to each vase and observed how many hours each flower continued to look fresh.

Calculate and interpret the residual for the flower that had 2 tablespoons of sugar and looked fresh for 204 hours.

Answer:

The answer is 24.22

Step-by-step explanation:

17.82 + 6.4 = 24.22

Step-by-step explanation:

the answer is going to be 24.22

Answer:

Each child will get 1/4 of a pie

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The recipe serves 36 people. You need to serve 108 people.

In the example,

original serving (8) * multiplier (4) = new serving (32)

Here,

original serving = 36 and new serving = 108

36 * multiplier = 108

divide both sides by 36 to isolate the multiplier

108/36 = multiplier = 3

Answer:

AL

Step-by-step explanation:

AL would be the angle bisector because it divides the triangle into equal halfs.

Answer:

2\(\sqrt{2}\)

Step-by-step explanation:

A 45-90-45 triangle will have two equivalent side lengths and the hypotenuse. The hypotenuse is 4 and one of the side lengths is x. Since one of the side lengths is x, the other side length is x as well. Using the Pythagorean theorem, you can create this equation:

x^2 + x^2 = 4^2

or

2x^2 = 16

Now do the algebra:

2x^2 = 16

x^2 = 8

x = \sqrt{8\\}

which can be simplified as 2\(\sqrt{2}\)

Answer:

Population mean= mu = μ= $102,342

Step-by-step explanation:

Here

Sample size= n= 15

Population mean= mu = μ= $102,342

Population standard deviation = sigma = σ =$21,756

The population mean is given by mu = μ

Both the means , the sample mean and the population mean give the same measure but there is difference in their calculations and usage.

The population mean mu is calculated by using the population size N but the sample mean x bar is calculated using sample size.

In the given question the sample size is given of the students whereas the mean salaries for attorneys in New York City  gives the population mean because the attorneys in New York City contains all the attorneys given in the city. It is not a sample.

The population gives all the members of the group. So here none is missing.

Answer:

The answer for Question #1 is 3x + 40
The answer for Question #2 is X + 2
The answer for Question #3 is 2x + 4x +8x

Step-by-step explanation:

Answer:

1. 3x + 40

2. x + 2

3. A: 2x + 4x + 8x, D: x (2 + 4 + 8)

Step-by-step explanation:

1. 5 (x + 8) - 2x

= 5x + 40 - 2x

= 3x + 40

2. 2 (3x + 1) - 5x

= 6x + 2 - 5x

= x + 2

3. Imagine if x = 2.

A. 2x + 4x + 8x

2 (2) + 4 (2) + 8 (2)

= 4 + 8 + 16

= 28

D. x (2 + 4 + 8)

= 2 (2 + 4 + 8)

= 2 (14)

= 28

Therefore, answer choices A and D are the correct answer.

Answer:

B and 7

Step-by-step explanation:

because 9 minus 2 is 7

Answer:

-10

Step-by-step explanation:

The equation in slope-intercept form to model this situation is g = (1/13) * d - 35.

We can start by using the given information to find the slope of the equation, which represents the rate at which gas is consumed:

1 gallon of gas is used for every 13 miles driven

So the slope of the equation will be:

slope = 1 gallon / 13 miles = 1/13

Now we can use the point-slope form of a linear equation to find the equation that models this situation. We know that when the tank is full, we can travel 455 miles, which means that we have not used any gas yet:

Starting point: (0, 455)

Using the slope we found earlier, we can write the equation in point-slope form:

g - 0 = (1/13) * (d - 455)

Simplifying this equation by distributing the 1/13 on the right side, we get:

g = (1/13) * d - (1/13) * 455

Simplifying further, we get:

g = (1/13) * d - 35

So the equation in slope-intercept form to model this situation is:

g = (1/13) * d - 35

where g is the gallons of gas used and d is the miles you can still travel.

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The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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1) Whenever we have problems that deal with the real distance and distance on the map, we can write out the following formula:

So, let's call the Real distance "R". Note that in this question, 1 centimeter represents 20 kilometers

2) So, in order to plug that as the scale we need to convert kilometers to centimeters:

3) Finally, we can plug that into the formula and cross multiply the ratios this way:

Converting it back to kilometers we can write:

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:40.25

Step-by-step explanation:

23% of 175

23/100 x 175

(23 x 175)/100

4025/100=40.25

Answer:

500

Step-by-step explanation:

65 is 13% of 500

500 x .13= 65

Answer:

See I don't know the answer but I did another one like this if it doesn't help you can report it no problem

Step-by-step explanation:

There are 2 different ways you can solve this problem and you'll get the same answer.

To help you visualize what you have to do, it might be easiest to translate your problem to a unit that easier to use.

Since you only have a ribbon 5 feet long, but you must cut it into 6 pieces, you know it won't even be 1 foot long.

One way to solve the problem would be to translate your 5-foot ribbon into a ribbon divided into inches.

1 foot = 12 inches

To find out how many inches long your ribbon is, you'll need to multiply the number of feet by 12.

Once you know that, then you can more easily divide it by 6. This will tell you how many inches each ribbon is.

Careful! the answer is to be put into feet so once you know how many inches long the ribbon is, you must then divide by 12 to get the correct answer in feet. Don't forget to round to the nearest tenth.

Another way to solve the problem is to simply divide the 5 feet by the number 6 and then round your number to the nearest tenth. It may be harder to visualize the answer this way, but you will get the same answer as if you translated your ribbon into inches and then divided by 12.

Good luck! I hope this helps!

Yes, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row. This is because each flip of a fair coin is an independent event and has an equal chance of landing on either heads or tails.

The probability of getting heads on a single coin flip is 0.5 (or 1/2), and the same is true for getting tails on a single coin flip. The probability of getting three heads in a row is calculated by multiplying the probability of getting heads on each of the three flips together, which is"

(1/2) x (1/2) x (1/2) = 1/8.

Similarly, the probability of getting three tails in a row is also:

(1/2) x (1/2) x (1/2) = 1/8.

Therefore, the theoretical probability of getting three heads in a row is the same as the theoretical probability of getting three tails in a row, both of which are 1/8.

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Answer:

\(\huge\boxed{\bf\:r > -4 }\)

Step-by-step explanation:

\(3(r+1)+2 > -7\)

Use the distributive property to solve 3 (r + 1).

\(3r+3+2 > -7 \\3r + 5 > -7\)

Now, bring 5 to the right hand side of the inequality .

\(3r > -7-5 \\3r > -12\)

Divide both sides of the inequality by 3.

\(r > \frac{-12}{3} \\\boxed{\bf\:r > -4 }\)

\(\rule{150pt}{2pt}\)

Answer:

495

Step-by-step explanation:

using the definition

n\(C_{r}\) = \(\frac{n!}{r!(n-r)!}\)

where n! = n(n - 1)(n - 2) ... × 3 × 2 × 1

then

12\(C_{4}\)

= \(\frac{12!}{4!(12-4)!}\)

= \(\frac{12!}{4!(8!)}\)

cancel 8! on numerator/ denominator

= \(\frac{12(11)(10)(9)}{4!}\)

= \(\frac{11880}{4(3)(2)(1)}\)

= \(\frac{11880}{24}\)

= 495

Answer:

The percent decrease is approximately 21%.

Step-by-step explanation:

Answer:

To find ratio mph (miles PER hour), we can write the information given as a fraction. (The miles will go on top and the number of hours will go on the bottom).

1/2=.5 miles

1/4-.25 miles

So we have .5miles/.25 hours

From here, we can do 2 things: divide to get 2miles/hour or you can see that you can reduce the fraction (.5/2=.25 and .25/.25=1). So again we get 2/1 miles per hour OR 2 mph

Hope that helps,

Gracie

Answer:

It could be 0, is the question multiple choice?

a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}\)

Answer:

2; 28.5 ; 34 ; 36 ; 38

Step-by-step explanation:

Given the data:

X = 25, 28, 29, 30, 34, 35, 35, 37, 38

n = 9

Values have been arranged in ascending order ;

The 5 number summary :

Maximum value : highest data value in the list = 38

Minimum value : Lowest data value in the list = 25

The lower quartile ; Q1 = 1/4(n+1)th term

Q1 = 1/4(10) th term = 2.5th term

Q1 = (2nd + 3rd) / 2 = (28+29)/2 = 28.5

Q2 = 1/2(n+1)th term

Q2 = 1/2(10) th term = 5th term

Q2 = 34

Q3 = 3/4(n+1)th term

Q3 = 3/4(10) th term = 7.5th term

Q3 = (7th + 8th) / 2 = (35+37)/2 = 36

Maximum value = 38 (highest data value in the list)

The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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The required probability of getting at least one red card is \(\frac{3}{4}\).

A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The probability of getting at least one red card can be found by calculating the probability of getting two black cards and then subtracting that from 1 (since the sum of the probabilities of all possible outcomes must be 1).

The probability of getting a black card on the first draw is 26/52 = 1/2, and the probability of getting a black card on the second draw (assuming the first card was replaced) is also 1/2. Therefore, the probability of getting two black cards is:

\($\frac{26}{52} \cdot \frac{26}{52} = \frac{1}{4}$$\)

So the probability of getting at least one red card is:

\($1 - \frac{1}{4} = \frac{3}{4}$$\)

Therefore, the probability of getting at least one red card is \(\frac{3}{4}\).

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Answer:

3/4 i took the test

Step-by-step explanation: