What does it mean when a set is closed under addition?

To calculate the probability of selecting a boy or a red-haired person as a homeroom representative to student council, we need to find the probability of each event and then use the formula P(A or B) = P(A) + P(B) - P(A and B).

There are 31 students in total (16 girls + 15 boys). The probability of selecting a boy is 15/31.

There are 5 red-haired students (3 girls + 2 boys). The probability of selecting a red-haired person is 5/31.

However, we need to account for the overlap between boys and red-haired students. There are 2 red-haired boys, so the probability of selecting a red-haired boy is 2/31.

Now we can use the formula: P(boy or red-haired) = P(boy) + P(red-haired) - P(boy and red-haired) = (15/31) + (5/31) - (2/31) = 18/31.

So, the probability of selecting a boy or a red-haired person as a homeroom representative to student council is 18/31.

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Answer:

Answer option 2

Step-by-step explanation:

When a shape is rotated counterclockwise by 90°, each point of the shape is moved in a circular motion in the counterclockwise direction by 90° around the fixed point of rotation.

As the triangle is rotated about point O, the position of point O does not change (i.e. it is "fixed").

Line segment OA is horizontal in the original figure. When it is rotated 90° counterclockwise, it becomes vertical, where A is above O.

Line segment BA is vertical in the original figure. When it is rotated 90° counterclockwise, it becomes horizontal, where B is to the left of A.

Therefore, the figure that represents the image after the given rotation is the second answer option.

Answer:

Answer option number two.

Answer:

12*3 is 36 and (2^2 + 2^3 ) is 12 so you have to get 12 to 36

Step-by-step explanation:

which is 12 *3 so 3

Answer:

3.25x + 4 = 30

3.25x = 30-4

3.25x = 26

x= 26/3.25

x = 8 Games

She played 8 games

Using the together rate, it is found that it takes 144.5 hours to fill the empty pool when only the input pipe is open.

It is the sum of each separate rate.

In this problem:

Hence:

\(\frac{1}{x} + \frac{1}{x - 1} = \frac{1}{72}\)

\(\frac{x - 1 + x}{x(x - 1)} = \frac{1}{72}\)

\(x^2 - x = 144x - 72\)

\(x^2 - 145x + 72 = 0\)

Which is a quadratic equation with coefficients a = 1, b = -145, c = 72, hence:

\(\Delta = b^2 - 4ac = (-145)^2 - 4(1)(72) = 20737\)

\(x_1 = \frac{145 + \sqrt{20737}}{2} = 144.5\)

\(x_2 = \frac{145 - \sqrt{20737}}{2} = -0.5\)

Time is a positive measure, hence, it takes 144.5 hours to fill the empty pool when only the input pipe is open.

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The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:

1441.08 in^3

Step-by-step explanation:

Volume of rectangular prism = 15 * 9 * 9 = 1215 in^3

radius = 3 in

Volume of the cylinder = 3^2 * 3,14 * 8 = 226.08 in^3

Total volume = 1215 + 226.08 = 1441.08 in^3

Answer:

HJHJGHJHG

Step-by-step explanation:

JGHU45565677689789

Answer:

this is a very difficult question.....

Step-by-step explanation:

u should google the answer and see if it helps or ask a teacher at brampton manor academy

Answer:The answer is C. y=1/4x +7

Step-by-step explanation:A perpendicular line has a slope of -1/m

Apply point-slope formula, y-y1 = m(x - x1)

y-4= 1/4(x-(-12))

y-4 = 1/4x +3

y= 1/4x + 7

Answer:

You need to be more specific of this question.

Answer:

To find the value of a4, we need to use the recursive formula for the sequence. The formula gives us the nth term in the sequence in terms of the (n-1)th term.

We are given that a1 = -7, so we can use the recursive formula to find a2, a3, and a4:

a2 = a1 - 4 = -7 - 4 = -11

a3 = a2 - 4 = -11 - 4 = -15

a4 = a3 - 4 = -15 - 4 = -19

Therefore, the value of a4 is -19.

Answer:

b

Step-by-step explanation:

Answer:

-39

Step-by-step explanation:

just plug -3 into x

-4(-3)^2-3=-4*9-3=-36-3=-39

so, g(-3)=-39

hope this helped

At a significance level of 0.010, there is not enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average based on the given sample data.

To determine the evidence regarding the income of Delaware, which is more than the national average income of the residents of Wilmington.

State the hypotheses:

Null hypothesis (H₀): Residents of Wilmington, Delaware, have the same income as the national average.

Alternative hypothesis (H₁): Residents of Wilmington, Delaware, have more income than the national average.

Set the significance level:

The significance level (α) is given as 0.010.

Calculate the test statistic

We'll use a one-sample t-test to compare the sample mean to the population mean. To find test statistic use the formula given below

The value of t represents the standardized difference between the sample mean and the population mean. It is obtained by dividing the difference between the sample mean and the population mean by the standard error of the sample mean."

Here "t" is often used in statistics to represent the t-statistic, which is a measure used in hypothesis testing and confidence intervals.

In this case, the sample mean is $45,500, the population mean is $39,500, the sample standard deviation is $9,800, and the sample size is 16.

t = (45,500 - 39,500) / (9,800 / sqrt(16))

t = 6,000 / (9,800 / 4)

t ≈ 2.449

Since the alternative hypothesis is that the residents of Wilmington, Delaware, have more income, we'll perform a one-tailed test. With a significance level of 0.010 and 15 degrees of freedom (sample size - 1), the critical value is approximately 2.624.

If the calculated test statistic (2.449) is larger than the critical value (2.624), we can conclude that there is sufficient evidence to reject the null hypothesis.

In this case, the test statistic (2.449) is smaller than the critical value (2.624), so we fail to reject the null hypothesis.

Based on the available data and the conducted hypothesis test, we do not have sufficient evidence to support the conclusion that the residents of Wilmington, Delaware, have a higher income than the national average at a significance level of 0.010.

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\(r(1) = (2 \: .1 \: . \frac{2}{3} )\)

\(r(0) = (0 \: .0 \: .0)\)

\( \gamma r =( 2 \: .1 \: . \frac{2}{3} )\)

\(l = \sqrt{2 {}^{2} + 1 {}^{2} + \frac{4}{9} } \)

\(l = \sqrt{4 + 1 + \frac{4}{9} } \)

\(l = \sqrt{ \frac{36 + 9 + 4}{9} } \)

\(l = \sqrt{ \frac{49}{9} } = \frac{7}{9} \)

(I'm not sure of my answer tho)

Normally I'd see a plus sign between the x,y and z values of the r(t) equation, so im assuming these represent the x,y,z coordinates in terms of t.

So i calculated ∆r(t) and found the length of the equation using the formula for length

Answer:

10.3

Step-by-step explanation:

a^2 + b^2 = c^2

3.9^2 + b^2 = 11^2

b^2 = 121 - 15.21

b = 10.3

Answer:

10.3

Step-by-step explanation:

We use the pythagorean theorem. (a^2+b^2=c^2)

3.9^2 + b^2 = 11^2

3.9^2 = 15.21

11^2 = 121

15.21 + b^2 = 121

Subtract 15.21 from both sides

b^2=105.79

Take the square root of both sides

b = 10.28

10.28 is closest to 10.3 and it is also rounded to 10.3, therefore 10.3 is the answer.

Step-by-step explanation:

Volume of a sphere is given by

\(V = \frac{4}{3} \pi {r}^{3} \)

Where r is the radius of the sphere

From the question

radius = 41 in

Substitute the value into the above formula

We have

\(V = \frac{4}{3} \times {41}^{3} \pi\)

\( = \frac{275684}{3} \pi\)

= 288695.6097

We have the final answer as

Hope this helps you

The answer on deltamath is

288695.6 in³

Answer:

they could've walked 4 miles east to make the trip quicker. Would look alot nicer if i had grid paper

Step-by-step explanation:

_ _ _ _

| |

_ _ _ | |

The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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Hello!

10 - 1 × (2 + 1)2 =

= 10 - 1 × 3 × 2 =

= 10 - 3 × 2 =

= 10 - 6 =

= 4

Good luck! :)

Answer:

4

Step-by-step explanation:

10-1*2(3)

10-1*6

10-6

4

The manufacturer set up a two-sided alternative but should have set up a one-sided alternative hypothesis.

A Type I error would mean that the manufacturer concludes the mean life of the tires is 50000 miles, even though the mean actually is not 50000 miles.

This means that the null hypothesis, which states that the mean life of the tires is 50000 miles, is rejected even though it is actually true.

This error occurs when the manufacturer sets up a one-sided alternative hypothesis when a two-sided alternative hypothesis should have been set up.

In this case, the two-sided alternative hypothesis should be used because the manufacturer is testing to see if the mean life of the tires is equal to 50000 miles, and the two-sided alternative hypothesis would allow for the possibility that the mean life may be either higher or lower than 50000 miles.

Therefore, the manufacturer set up a two-sided alternative but should have set up a one-sided alternative hypothesis.

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Answer:

The value of x=35 and the co-ordinates at the top of the chair lift are (35,20).

What are co-ordinates?

Step-by-step explanation:

Given:

    20 = 1/2x + 5/2

20 * 2 = x + 5

     40 = x + 5

        x = 35

Therefore, the co-ordinates of the chair at the top of the chair lift are (35,20)

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The major methods of recording unstructured observational data are Narrative Description, Field Notes, Audio or Video Recording, Photography, Diagrams or Maps.

The major methods of recording unstructured observational data are:

1. Narrative Description: This method involves writing a detailed, chronological account of the observed events or behaviors, capturing the context and interactions as they occur naturally.

2. Field Notes: In this method, the observer takes brief, concise notes during the observation, focusing on key events, behaviors, or interactions. These notes can be expanded and organized later for further analysis.

3. Audio or Video Recording: Using audio or video equipment, the observer captures the events and interactions in their entirety. This allows for a more accurate record and the ability to review and analyze the data multiple times.

4. Photography: Taking photographs during the observation can provide a visual record of the events and behaviors. These images can supplement other data collection methods and help to illustrate specific aspects of the observation.

5. Diagrams or Maps: Drawing diagrams or maps of the observation setting can help capture the spatial relationships between individuals and objects, as well as the overall layout of the environment.

These methods can be used individually or in combination, depending on the research question and the specific needs of the study. Remember to always respect participants' privacy and obtain informed consent when necessary.

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Answer:

6 minutes

Step-by-step explanation:

20 miles jogs at 1 hour, so for 2 miles,

2/20

= 1/10 hours

= 1/10×60

= 6 minutes

Answered by GAUTHMATH

The number of hot Cheetos with cheese sold is 50, while the number of chilli cheese sold is 30.

A set of simultaneous equations, often known as a system of equations or an equation system, is a finite collection of equations for which common solutions are sought.

Let the number of hot Cheetos with cheese sold be represented by x, while the number of chilli cheese is represented by y.

It is given that the total number of items sold by Evelyn during the event is 80. Therefore,

x + y = 80

x = 80 - y

Given that the cost of hot Cheetos with cheese is $1.50, while the cost of chilli cheese is $2.50, also the total amount that was collected in the event is $150. Therefore, we can write,

1.50x + 2.50y = 150

1.50(80 - y) + 2.50y = 150

120 - 1.50y + 2.50y = 150

1y = 150 - 120

y = 30

Substitute the value of y in the first equation,

x + y = 80

x + 30 = 80

x = 80 - 30

x = 50

Hence, the number of hot Cheetos with cheese sold is 50, while the number of chilli cheese sold is 30.

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The number of hot Cheetos with cheese sold is 50, while the number of chili cheese sold is 30.

What is a System of equations?

"A system of equations is a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. The equations in the system can be linear or non-linear."

Let the number of hot Cheetos with cheese sold be represented by P, while the number of chili cheese is represented by Q.

It is given that the total number of items sold by Evelyn during the event is 80. Therefore,

P + Q = 80

P = 80 - Q --------- (1)

Given that the cost of hot Cheetos with cheese and chili cheese

So the equation

1.50P + 2.50Q = 150 --------- (2)

Put the equation (1) in equation (2)

1.50(80 - y) + 2.50y = 150

120 - 1.50Q + 2.50Q = 150

1Q = 150 - 120

Q = 30

Substitute the value of Q in the first equation,

P+Q = 80

P + 30 = 80

P = 80 - 30

P = 50

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Answer:28

Step-by-step explanation: the whole angle has to sum to 90 ( 62 + x =90) so take away 90 from 62 to get x

Answer:

90

Step-by-step explanation:

just look at it with a ruler

Answer:

A The inverse of a linear function is a function. - this is not always true.

Answer:

10

Step-by-step explanation:

7 + (-3) = -10

But it's |7| + |-3| which means it is the absolute value

So 10

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Answer:

a = 7.5

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin30° = \(\frac{1}{2}\) , then

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{a}{15}\) = \(\frac{1}{2}\) ( cross- multiply )

2a = 15 ( divide both sides by 2 )

a = 7.5

Answer:

See below

Step-by-step explanation:

The LHS and RHS are exactly the same, so the equality is true.

The associate property of addition says that

\(\boxed{a+(b+c)=(a+b)+c}\)

In order to make the addition of fractions, the denominators should be same. So we can write three fractions as one.

\(\dfrac{1}{2} +\left(\dfrac{2}{3}+\dfrac{3}{4} \right )\)

\(\dfrac{1}{2} +\dfrac{2}{3}+\dfrac{3}{4}\)

\(\dfrac{1\cdot 6 }{2\cdot 6} +\dfrac{2 \cdot 4}{3 \cdot 4}+\dfrac{3 \cdot 3 }{4 \cdot 3}\)

\(\dfrac{ 6 }{12} +\dfrac{8}{12}+\dfrac{9 }{12}\)

\(\dfrac{ 23 }{12}\)

Answer:

You gotta give me (us) more to work with homie.

Step-by-step explanation:

If I have more of a picture with it I could possibly help but all there is a barely readable and legible nonsense equation. Sorry :(

Answer:

A

Step-by-step explanation: