How many ways can you pick five students for the student council when there are twelve people running ?

Combinations and probability.

Answer:

It is important to analyze the relationships between a sample and full population for several reasons:

To help make more informed statements about a population: Analyzing the relationships between a sample and full population helps us to make more accurate and informed statements about the population. By examining a sample, we can draw conclusions about the characteristics of the larger population.

To bring diverging data into analysis: Sometimes, a sample may not accurately reflect the larger population, particularly if the sample is small or biased. Analyzing the relationship between the sample and population can help to identify any diverging data and adjust the analysis accordingly.

To limit variance: Variance is a measure of how much the data varies from the mean. By analyzing the relationship between the sample and population, we can better understand the variance and take steps to limit it.

To find out how many data points are necessary to be statistically valid: Analyzing the relationship between the sample and population can help us to determine the sample size needed to be statistically valid. This can help us to avoid drawing inaccurate conclusions based on a sample that is too small.

Overall, analyzing the relationship between a sample and full population is important for ensuring that our analysis is accurate, representative, and informative.

It is important to analyze the relationships between a sample and the full population to limit variance and to help make more informed statements about a population.

Analyzing the relationships between a sample and the full population is important because it helps limit variance in the data and brings diverging data into the analysis. It also helps to determine how many data points are necessary to be statistically valid and make more informed statements about the population.

By examining a sample and comparing it to the full population, we can identify any biases or errors in our data and ensure that our conclusions are accurate and representative of the entire population. Additionally, understanding the relationship between the sample and the population can help us make predictions and draw conclusions with greater confidence and precision.
By understanding the relationship, you can ensure that the sample accurately represents the population, leading to better inferences and decision-making.

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Answer:  3 Possibly.

Step-by-step explanation:

I just know:)

PLEASE give THANKS!

Answer:

0.7 radians

Step-by-step explanation:

The equation for converting radians to degrees is:

X radians * 180/pi = degrees

Plugging in 0.7 radians,

we have 0.7 * 180/pi

= approx 40.1070457 degrees.

40.1070457 > 40 degrees,

so 0.7 radians is greater than 40 degrees

The number of solutions that the quadratic equation, 5x² + 3x + 8 can have without solving the equation using discriminant is 0.

Given equation is,

5x² + 3x + 8

This is a quadratic equation.

It can have atmost 2 solutions.

So there can't be any solutions, there can be one solution or 2 solutions.

We can find the discriminant to know this.

Discriminant = √(b² - 4ac)

Here,

discriminant = √(3² - (4 × 5 × 8)) = √(9 - 160) = √(-154)

Discriminant is less than 0.

So there are no solutions.

Hence the number of solutions is 0.

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Answer: 546

Step-by-step explanation:

If you're looking for random paragraphs, you've come to the right place. When a random word or a random sentence isn't quite enough, the next logical step is to find a random paragraph. We created the Random Paragraph Generator with you in mind. The process is quite simple. Choose the number of random paragraphs you'd like to see and click the button. Your chosen number of paragraphs will instantly appear.

While it may not be obvious to everyone, there are a number of reasons creating random paragraphs can be useful. A few examples of how some people use this generator are listed in the following paragraphs.

A graph of each of the function is shown below.

The domain is x = -2, x = 0, x = 1, x = 2.

The range is [-1, -1] U [3, 3].

In Mathematics, a piecewise-defined function is a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is constant over the interval x < -2 and x ≥ -2.

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The coordinates of point Q that partitions line segment AB into the ratio 1:3 is (-0.75, 4.5).

In this scenario, line ratio would be used to determine the coordinates of the point Q on the directed line segment AB that partitions the segment into a ratio of 1 to 3.

In Mathematics, line ratio can be used to determine the coordinates of Q and this is modeled by the following mathematical expression:

Q(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given points into the formula for line ratio, we have;

Q(x, y) = [(1(6) + 3(-3))/(1 + 3)],  [(1(0) + 3(6))/(1 + 3)]

Q(x, y) = [(6 - 9)/(4)],  [(0 + 18)/4]

Q(x, y) = [-3/4],  [18/(4)]

Q(x, y) = [-0.75, 4.5]

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Answer:

Step-by-step explanation:

the standard equation for the circle is:

(x-a)²+(y-b)² = r²

the center is : A(a,b)    and ridus r

you have : a= -10 and b=0    r²= (-12+10)²+(3/2-0)²= 4+ 9/4

r² = 25/4     so : r = 5/2

the standard equation for the circle is:

(x+10)²+y² =25/4

Answer: D

Step-by-step explanation:

typically if something is added on the outside it affects they y, which means it goes up or down

if something is added to the x its left or right

since -5 is on outside shift down.

The surface area of the figure formed by the composite boxes is given as follows:

1840 in².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

For this problem, we have four boxes, with the dimensions given as follows:

12 in, 10 in and 5 in.

Hence the surface area is given as follows:

S = 4 x 2 x (12 x 10 + 12 x 5 + 10 x 5)

S = 1840 in².

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There isn't significant evidence to conclude that the overall average Math SAT score in the state differs from the national average of 514 points based on this sample.

To determine if the average Math SAT score of the 36 randomly selected students significantly differs from the national average of 514 points, we can use a t-test with the given information.
1. Null hypothesis (H₀): The overall average Math SAT score in the state is equal to the national average (μ = 514).
2. Alternative hypothesis (Hₐ): The overall average Math SAT score in the state differs from the national average (μ ≠ 514).
3. Calculate the test statistic (t-value) using the formula: t = (sample mean - population mean) / (standard deviation / √sample size)
t = (525.6 - 514) / (69.5 / √36) = 11.6 / 11.583 = 1
4. Determine the degrees of freedom (df): df = sample size - 1 = 36 - 1 = 35
5. Choose a significance level (α), commonly 0.05.
6. Compare the t-value with the critical t-value from a t-distribution table using the chosen α level and degrees of freedom. For a two-tailed test with α = 0.05 and df = 35, the critical t-values are approximately ±2.03.
Since the calculated t-value (1) is not greater than the critical t-value (±2.03), we fail to reject the null hypothesis.

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the answer is produced by chatgpt, it is a good study tool, you can take it as reference

(a) The coordinates of the midpoint AC can be found by taking the average of the x-coordinates and the average of the y-coordinates of points A and C. Therefore, the midpoint AC is at:

((2+11)/2, (-1-2)/2) = (6.5,-1.5)

(b) Since ABCD is a parallelogram, the midpoint of BD is also at (6.5,-1.5). Let D have coordinates (x,y). Then the midpoint of BD is:

((6+x)/2, (2+y)/2) = (6.5,-1.5)

Solving for x and y, we get:

x = 7 and y = -5

Therefore, the coordinates of D are (7,-5).

(c) The two diagonals of a parallelogram bisect each other. Since AC is one diagonal and it passes through the midpoint of BD, the equation of AC can be found using the two given points A and C:

Slope of AC = (y2 - y1)/(x2 - x1) = (-2 - (-1))/(11 - 2) = -1/9

Using point-slope form of a line, the equation of AC is:

y - (-1) = (-1/9)*(x - 2)

y = (-1/9)*x + (17/9)

Similarly, the other diagonal BD can be found using the two points B and D:

Slope of BD = (y2 - y1)/(x2 - x1) = (-5 - 2)/(7 - 6) = -7

Using point-slope form of a line, the equation of BD is:

y - 2 = (-7)*(x - 6)

y = -7x + 44

Therefore, the equations of the diagonals of the parallelogram are:

AC: y = (-1/9)*x + (17/9)

BD: y = -7x + 44

to solve an expression with a positive number and a variable raised to a positive power, simplify the expression inside the parentheses and then combine any like terms outside the parentheses.

To solve an expression with a positive number and a variable raised to a positive power, you can use the following steps:

Step 1: Simplify the expression inside the parentheses, if possible.

In this case, (3/x) to the 2nd can be simplified to (3^2)/(x^2) = 9/x^2.

Step 2: Combine any like terms outside the parentheses, if applicable.

If there are no like terms outside the parentheses, then you're done. Otherwise, combine them.

For example, if you had the expression (3/x)^2 + 2(x^2), you could combine the like terms to get:

(9/x^2) + 2x^2

Note that in this step, we can also simplify the expression further by finding a common denominator between the two terms, but that depends on the specific problem.

So, in summary, to solve an expression with a positive number and a variable raised to a positive power, simplify the expression inside the parentheses and then combine any like terms outside the parentheses.

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The type of function that models the data in the table is an exponential function

From the question, we have the following table of values that can be used in our computation:

X. Y

-1. 2.5

0. 5

1. 10

2. 20

3. 40

The above definitions imply that we simply multiply 2 to the previous term to get the current term

This means that the function is an exponential function

Hence, the type of function that models the data in the table is an exponential function

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the   perfect square is : (x+3y)² the term is 6xy

The estimated proportion of people who would allow the pressure to reach its maximum level is approximately 0.284 or 28.4%.

Based on the given information, we know that out of the 264 people in the study, 75 allowed the pressure to reach its maximum level of 300 mmHg (MaxPressure=yes). Therefore, the proportion of people who would allow the pressure to reach its maximum level can be estimated by dividing the number of people who allowed the pressure to reach its maximum level (75) by the total number of people in the study (264):

Proportion = 75/264

Using a calculator, we can simplify this to:

Proportion ≈ 0.284

Therefore, approximately 28.4% of people in the study allowed the pressure to reach its maximum level of 300 mmHg without indicating that the pain was too much.

To estimate the proportion of people who allowed the pressure to reach its maximum level, follow these steps:

1. Determine the total number of people in the study: 264 people
2. Find the number of people who allowed the pressure to reach its maximum level (300 mmHg) without ever saying the pain was too much: 75 people
3. Calculate the proportion by dividing the number of people who reached maximum pressure by the total number of people in the study.

Proportion = (Number of people who reached maximum pressure) / (Total number of people in the study)

Proportion = 75 / 264 ≈ 0.284 (rounded to three decimal places)

The estimated proportion of people who would allow the pressure to reach its maximum level is approximately 0.284 or 28.4%.

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To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0), we can use the formula:

dy/dx = (dy/dtheta) / (dx/dtheta) = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))

where r' = dr/dtheta.

First, we need to find r' by taking the derivative of r with respect to theta:

r' = dr/dtheta = -7 sin(theta)

Then, we can plug in the given values to find the slope at (16, 0):

dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]

= [(-7 sin(0) sin(0) + (9 + 7 cos(0)) cos(0))] / [(-7 sin(0) cos(0)) - (9 + 7 cos(0)) sin(0))]

= (9 + 7) / (-9) = -2

Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (16, 0) is -2.

To find the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi), we can use the same formula as above:

dy/dx = (r' sin(theta) + r cos(theta)) / (r' cos(theta) - r sin(theta))

First, we need to find r' by taking the derivative of r with respect to theta:

r' = dr/dtheta = -7 sin(theta)

Then, we can plug in the given values to find the slope at (2, pi):

dy/dx = [(r' sin(theta) + r cos(theta)] / [r' cos(theta) - r sin(theta)]

= [(-7 sin(pi) sin(2) + (9 + 7 cos(pi)) cos(2))] / [(-7 sin(pi) cos(2)) - (9 + 7 cos(pi)) sin(2))]

= (-2) / (7)

Therefore, the slope of the line tangent to the polar curve r = 9 + 7 cos(theta) at the point (2, pi) is -2/7.

The polar curve r = 9 + 7 cos(theta) intersects the origin when r = 0, which occurs when cos(theta) = -9/7, which is not possible since the range of cosine function is [-1, 1]. Therefore, the curve does not intersect the origin.

Since the curve does not intersect the origin, the answer is "The curve does not intersect the origin" for the equation of the tangent line in polar coordinates.

Answer:

The answer for the Area is 847in²

Step-by-step explanation:

Area of shape=Area of square + Area of trapezoid

A=L²+1/2(a+b)h

A=22²+1/2(11+22)22

A=484+33×11

A=484+363

A=847in²

Answer:

The answer to your problem is, C. Car C has the best rate at 25 miles per gallon.

Step-by-step explanation:

Well given,

Car C = 450 / 18 = 25

Car B = 361 / 19 = 19

Car A = 340 / 17 = 20

We can see that Car C has the best MPG.

Thus the answer to your problem is, C. Car C has the best rate at 25 miles per gallon.

Answer:

[tex]49xy + 56x = 7x(7y + 8)[/tex]

The personal expenditure was less than the amount budgeted by $126.48.

First, you have to sum up the figures that represent the budget for the month. Now, these will be compared to the actual spending this month. When this calculation is done, the total amount budgeted stands at $2169.83, and the total amount spent stands at $2043.35.

Now, we subtract the amount spent from the amount budgeted and the figure we arrive at is  $126.48. This remnant shows that the person who drew the budget was well within his limit.

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The arc length equals 18.85 yd

An arc length is given by L = Ф/360 × 2πr where

To find the arc length of the given circle, given that

So, substituting the values of the variables into the equation, we have that

L = Ф/360 × 2πr

L = 135°/360° × 2π × 8 yd

L = 135°/360° × 16π yd

L = 2160π/360° yd

L = 6785.84 yd/360

L = 18.85 yd

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Answer:

u still on here Delilah?

Step-by-step explanation:

The required Isabella would have $6,574.92 in the savings account after 2 years.

After 1 year, Isabella's account would have grown to:

[tex]A = P(1 + r)^n[/tex]

[tex]A = $6,300(1 + 0.02)^1[/tex]

A = $6,426

After 2 years, the account would have grown to:

A = $6,300(1 + 0.02)

A = $6,574.92

Therefore, Isabella would have $6,574.92 in the savings account after 2 years.

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A method to show differences among earth’s layers is "Oscar determines the pressure at different depths of earth’s crust." Option D.

We have,

Generally, the four earth layers are the

The outer crust.

The mantle.

The liquid outer core.

The solid inner core.

In conclusion,  the mineral content of rock core samples at different depths in Earth's crust are the differences among earth’s layers.

D) Oscar determines the pressure at different depths of earths crust.

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The evaluated complex number in rectangular form is (6cos(300) - 3) + (6sin(300) + j5).

To evaluate the complex number 6 e/300 + j5 - 3 + 450 in rectangular form, we need to convert it from polar form to rectangular form.

The polar form of a complex number is given by r e^(jθ), where r is the magnitude and θ is the angle in radians. In this case, we have:

r = 6
θ = 300 degrees = (5π/6) radians

Using Euler's formula e^(jθ) = cos(θ) + j sin(θ), we can write:

6 e^(j300) = 6 (cos(5π/6) + j sin(5π/6))

= 6 (-1/2 + j √3/2)

= -3 + j3√3

Now we can add this to the real number -3 + 450, to get:

-3 + j3√3 + (-3 + 450)

= 444 + j3√3

Therefore, the rectangular form of the complex number 6 e/300 + j5 - 3 + 450 is 444 + j3√3.

To evaluate the complex number in rectangular form, given the expression 6e^(300) + j5 - 3 + 450, follow these steps:

1. Convert the exponential form (6e^(300)) to rectangular form.
2. Combine the real parts and imaginary parts.

Step 1: Converting exponential form to rectangular form:
6e^(300) = 6(cos(300) + jsin(300))

Step 2: Combining real and imaginary parts:
Real part: 6cos(300) - 3
Imaginary part: 6sin(300) + j5

So, the evaluated complex number in rectangular form is (6cos(300) - 3) + (6sin(300) + j5).

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The correct answer is a. the inclusion-exclusion principle must be used to find the number of bit strings of length seven that either begin with two Os or end with three 1s.

This is because we need to subtract the number of bit strings that both begin with two Os and end with three 1s (which are counted twice if we simply add the number of bit strings that begin with two Os and the number that end with three 1s). The inclusion-exclusion principle allows us to do this by first adding the number of bit strings that begin with two Os and the number that end with three 1s, and then subtracting the number of bit strings that both begin with two Os and end with three 1s.

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According to the given information, the noise level in a restaurant is normally distributed with an average of 30 decibels. To find the value below which 99% of the time the noise level is, we need to use the Z-table.

We know that 99% of the area under the normal curve is below a Z-score of 2.33 (found from the Z-table).

To find the corresponding noise level value, we use the formula:

Z-score = (X - μ) / σ

where X is the noise level value we want to find, μ is the average (30 decibels), and σ is the standard deviation (which is not given in this question).

However, we can use the empirical rule (68-95-99.7 rule) to estimate the standard deviation. According to the rule, 99.7% of the data falls within 3 standard deviations of the mean. So, if 99% of the time the noise level is below a Z-score of 2.33, then we can estimate that the standard deviation is approximately:

(2.33 x σ) = 3

Solving for σ, we get:

σ = 3 / 2.33 = 1.29 (approx.)

Now we can use the formula above to find the noise level value below which 99% of the time the noise level is:

2.33 = (X - 30) / 1.29

X - 30 = 2.33 x 1.29

X = 33.01

So, 99% of the time, the noise level in the restaurant is below 33.01 decibels (rounded to two decimal places).

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The answer for the value of the expression 2x² + 5xy - 3y², which is a quadratic equation, for x = 2 and y=-1, is 1.

The values of the unknown variable x that satisfy the equation are known as the roots or zeros of a quadratic equation. A quadratic equation of the type:

ax² + bx + c = 0 with a 0 can have solutions found using the quadratic formula. Given in the question, solutions are given as x= 2 and y=-1.

To evaluate the expression 2x² + 5xy - 3y² for x = 2 and y = -1, we substitute these values into the expression and simplify:

2x² + 5xy - 3y²

= 2(2)² + 5(2)⁻¹ - 3(-1)²

= 8 - 10 + 3

= 1

Therefore, the value of the expression 2x² + 5xy - 3y² for x = 2 and y = -1 is 1.

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The correct answer would be

B) half of her classmates have a sibling and half do not

Add totals for classmates who have chores and those who do not have chores for each group.

7 + 8 = 15

9 + 6 = 15

Therefore, the correct answer would be

B) half of her classmates have a sibling and half do not

Based on the fact that the total for the classmates that have chores and those that don't have are equal which is 15, we can conclude that option B is correct.

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