Which situation represents a combination?
a. Seven people running for chair and vice-chair
b. first and second place in a race
c. choosing a committee of three people from a group of 10
d. Five people in line to buy tickets

Answer:

16x = -40

Explanation:

Multiply 2 by 8, which gives you 16, and -5 by 8, which gives you -40.

Answer: The new equation would be: 16x = -40

Explanation: 2x (8)= 16x

-5 (8) = -40

The variables in the equations are aligned as follows:   2x - 3y = 9 and

2x - 3y = 8/3

When we talk about aligning a system of linear equations, we mean rearranging the equations so that the variables are in the same order and have the same coefficients. This is done to make it easier to apply methods for solving systems of equations, such as substitution or elimination.

In a system of linear equations, each equation typically involves two or more variables. The variables may have different coefficients in each equation, and they may appear in a different order. Aligning the system involves rearranging the equations in a way that puts the variables in the same order, with the same coefficients.

Align the variables in given the system of linear equations :

To align the variables in the given equations, we need to rearrange the second equation so that the coefficients of  and  are the same as in the first equation.

To align the variables in the equations, we need to rearrange the terms so that the x, y, and constant terms are all grouped together.

Starting with the first equation:

2x - 3y = 9

We can rearrange this as:

2x = 3y + 9

Now we can divide both sides by 2 to get x by itself:

x = (3/2)y + 4.5

Now let's move on to the second equation:

1-6x +9y = -7

We can rearrange this as:

-6x + 9y = -8

Next, we'll divide both sides by -3 to get x by itself:

2x - 3y = 8/3

Now both equations are in the form of:

ax + by = c

where a, b, and c are constants. The aligned equations are:

2x - 3y = 9

2x - 3y = 8/3

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If the Cylinder's height equals to the diameter of its base , then the fraction of the total surface area of the cylinder to the total surface area of the two bases is 1/3 .

The curved surface area of the cylinder with height "h" and radius "r" is written as ⇒ \(2\pi rh\) ;

the area of the top and bottom of the cylinder is ⇒ \(\pi r^{2} + \pi r^{2}\) = \(2\pi r^{2}\) ;

the total surface area of the cylinder will be ⇒ \(2\pi rh\) \(+2\pi r^{2}\)  ....equation(1)

it is given that the height of cylinder is equal to the diameter of the base ,

that means ; \(h = 2r\)

Substituting the value \(h = 2r\) in the equation(1) ,

we get ,

total surface area of cylinder = \(4\pi r^{2} +2\pi r^{2}\) = \(6\pi r^{2}\)

So , the required fraction is = \(\frac{2\pi r^{2} }{6\pi r^{2} }\) ,

On simplifying ,

we get ,

= \(\frac{1}{3}\)  .

Therefore , the fraction of two bases to the total surface area is \(\frac{1}{3}\) .

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We then divide the difference in y-coordinates by the difference in x-coordinates to find the slope of the line. This can be expressed mathematically as follows: slope = (y₂ - y₁) / (x₂ - x₁).

This procedure calculates the slope of a line using the coordinates of two points. It takes four numeric parameters as input: the x coordinate of the first point, the y coordinate of the first point, the x coordinate of the second point, and the y coordinate of the second point. The slope of a line is a measure of its steepness and is defined as the change in y divided by the change in x between two points on the line.

To calculate the slope of a line using the coordinates of two points, we need to first find the difference between the y-coordinates of the two points and the difference between the x-coordinates of the two points.

We then divide the difference in y-coordinates by the difference in x-coordinates to find the slope of the line. This can be expressed mathematically as follows: slope = (y₂ - y₁) / (x₂ - x₁). The resulting slope value can be positive, negative, or zero depending on the direction and steepness of the line. A positive slope indicates that the line is increasing from left to right, while a negative slope indicates that the line is decreasing from left to right. A slope of zero indicates a horizontal line.

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a. To estimate the percentage of homes selling for more than $500,000 and analyze the normality of the price distribution, we use the mean and standard deviation provided. Additionally, we compare the expected number of homes with prices greater than the mean to the actual number. A frequency distribution of prices can also provide insights.

b. For estimating the number of homes on the market for more than 24 days and assessing the normality of the days on the market distribution, we utilize the mean and standard deviation given. We compare the expected number of homes with more than the mean days on the market to the actual number. A frequency distribution of days on the market can help in understanding the distribution pattern.
a. To estimate the percentage of homes selling for more than $500,000, we need to calculate the area under the normal distribution curve beyond $500,000 using the mean ($357,000) and standard deviation ($160,700). We can then compare this estimate to the actual results to assess the normality of the price distribution. Additionally, by comparing the expected number of homes with prices greater than the mean to the actual number, we can evaluate the distribution's fit. Constructing a frequency distribution of prices can reveal patterns or skewness.
b. To estimate the number of homes on the market for more than 24 days, we can use the mean (30 days) and standard deviation (10 days) with the normal distribution. Comparing this estimate to the actual results helps assess the normality of the days on the market distribution. Furthermore, by comparing the expected number of homes with more than the mean days on the market to the actual number, we can evaluate the approximation. Constructing a frequency distribution of days on the market can provide insights into the distribution's shape and characteristics.
Note: The actual results and observations from the frequency distributions will depend on the specific data and its distribution pattern.

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The true statement is (b): there exists a positive real number x such that for all positive real numbers y, xy < y^2.

To see why (a) is false, consider the case where x=0. Then for any y>0, xy = 0 and y^2 > 0, so xy < y^2 is not satisfied.

To prove (b), we can choose x=1. Then for any positive real number y, we have 1y = y, and y^2 > y, so xy < y^2 is satisfied. Therefore, there exists a positive real number x (namely, x=1) such that for all positive real numbers y, xy < y^2.

what is numbers?

Numbers are mathematical objects used to represent quantities or values. There are several types of numbers, including natural numbers (1, 2, 3...), integers (..., -2, -1, 0, 1, 2, ...), rational numbers (fractions), real numbers (numbers that can be expressed as a decimal, including both rational and irrational numbers), and complex numbers (numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1). Numbers are used in a wide variety of fields, including mathematics, science, engineering, economics, and finance, to name a few.

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Answer:

30/7

Step-by-step explanation:

So we have the equation:

\(2x-30+5x+2=2\)

Combine like terms:

\((2x+5x)+(-30+2)=2\)

Add:

\(7x-28=2\)

Add 28 to both sides:

\(7x=30\)

Divide both sides by 7:

\(x=30/7\)

So, our answer is 30/7

Or approximately 4.2857 :)

Answer:

7.994×10^3

3.99780×10^5

1.0051×10^4

3.5×10^1

3.5094013×10^7

Step-by-step explanation:

7994:Seven thousand nine hundred ninety four .

399,780 :Three hundred thousand ninety nine , seven hundred eighty.

10,051 :Ten thousand fifty one .

35 :thirty five .

35,094,013 :thirty five million ninety four thousand and thirteen.

The time is needed between injections is 3.6 hours, i.e., the drug is to be injected again when the number of milligrams reaches 6 mg.

We have the exponential function of number of milligrams D (ht) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is

\(D(h)=25 {e}^{ - 0.4 h}\)

We have to solve for h (the numbers of hours) that would have passed when the D(h) (the amount of medication in the patient's bloodstream) equals 6 mg in order to know when the patient needs to be injected again.

\(6 = 25 {e}^{ - 0.4h} \)

\( \frac{6}{25} = \frac{25}{25} {e}^{ - 0.4h} \)

\(0.24= {e}^{ - 0.4h} \)

Taking logarithm both sides of above equation , we get,

\( \ln(0.24) = \ln( {e}^{ - 0.4h)} \)

Using the properties of natural logarithm,

\( \ln(0.24) = - 0.4h\)

\( - 1.427116356 = - 0.4h\)

\(h = \frac{1.42711635}{0.4} = 3.56779089\)

=> h = 3. 6

So, after 3.6 hours, the patient needs to be injected again.

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Answer:

-4(y-2)=12

-4y+8=12

-4y=4

y = -1

Step-by-step explanation:

Have a wonder rest of your day!!! I hope this helps you!!! :)

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The table mentioned in the question is not provided. However, we can use the following formula to find the probability of two independent events occurring together:

P(A and B) = P(A) x P(B)

Here, A represents the event of the coin landing heads up, and B represents the event of the pointer landing on either 1, 2, or 4.

Assuming that the spinner has equal sections, the probability of the pointer landing on either 1, 2, or 4 is 3/8 (since there are three out of eight possible sections on the spinner).

The probability of flipping a fair coin and getting heads is 1/2.

Therefore, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is:

P(A and B) = P(A) x P(B) = (1/2) x (3/8) = 3/16

So, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.

The probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.

Probability denotes the possibility of the outcome of any random event. The meaning of this term is to check the extent to which any event is likely to happen.

Given that, a spinner is spined and coin is flipped,

P(A and B) = P(A) x P(B)

Here, A represents the event of the coin landing heads up, and B represents the event of the pointer landing on either 1, 2, or 4.

Assuming that the spinner has equal sections, the probability of the pointer landing on either 1, 2, or 4 is 3/8 (since there are three out of eight possible sections on the spinner).

The probability of flipping a fair coin and getting heads is 1/2.

Therefore, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is:

P(A and B) = P(A) x P(B) = (1/2) x (3/8) = 3/16

So, the probability of the coin landing heads up and the pointer landing on either 1, 2, or 4 is 3/16.

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The margin of error for a 95% confidence interval estimate for the proportion of all students with cell phones is approximately 0.0932.

To find the margin of error for a 95% confidence interval estimate for the proportion of all students with cell phones, we can use the formula:

Margin of Error = Z* * sqrt(p*(1-p)/n)

where:
Z* is the z-score corresponding to the desired level of confidence (in this case, 1.96 for 95% confidence)
p is the sample proportion (55/75 = 0.7333)
n is the sample size (75)

Plugging in the values, we get:

Margin of Error = 1.96 * sqrt(0.7333*(1-0.7333)/75)
Margin of Error ≈ 0.0932

Therefore, the margin of error for a 95% confidence interval estimate for the proportion of all students with cell phones is approximately 0.0932.

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Answer:

The average rate of change of the function \(g(x)=x^2+10x+18\) over the interval \(-11 \leq x\leq -1\) is -1

Step-by-step explanation:

We are given the function \(g(x)=x^2+10x+18\) over the interval \(-11 \leq x\leq -1\)

We need to find average rate of change.

The formula used to find average rate of change is : \(Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}\)

We have b=-1 and a=-11

Finding g(b) = g(-1)

\(g(x)=x^2+10x+18\\Putting \ x=-1\\g(-1)=(-1)^2+10(-1)+18\\g(-1)=1-10+18\\g(-1)=9\)

Finding g(a) = g(-11)

\(g(x)=x^2+10x+18\\Putting \ x=-11\\g(-11)=(-11)^2+10(-11)+18\\g(-1)=121-110+18\\g(-1)=29\)

Finding average rate of change

\(Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}\\Average \ rate \ of \ change=\frac{9-29}{-1-(-11)}\\Average \ rate \ of \ change=\frac{-10}{-1+11}\\Average \ rate \ of \ change=\frac{-10}{10}\\Average \ rate \ of \ change=-1\)

So, the average rate of change of the function \(g(x)=x^2+10x+18\) over the interval \(-11 \leq x\leq -1\) is -1

The complete table is.

Number of T-shirts                 Cost

10                                          $636

20                                          $752

30                                          $868

40                                           $984

50                                           $1100

60                                           $1216

70                                           $1332

80                                           $1448

90                                           $1564

100                                           $1680

To calculate the total cost Elena will spend to make a specific number of T-shirts,

Multiply the cost per shirt ($7.60) by the number of shirts.

For example, to make 20 shirts, you would do,

⇒ 20 x $7.60 = $152

So Elena would spend $152 on 20 blank shirts, ink, and other supplies.

Add the cost of the printing machine ($560) to the cost from

For example, to find the total cost for 20 shirts, you would do,

⇒ $152 + $560 = $712

So the total cost for 20 shirts would be $712.

Repeat steps 1 and 2 for each number of shirts in the table.

We get,

Number of T-shirts                 Cost

10                                          $636

20                                          $752

30                                          $868

40                                           $984

50                                           $1100

60                                           $1216

70                                           $1332

80                                           $1448

90                                           $1564

100                                           $1680

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Answer:

The lines y = x + 7 and y = 5x - 13 intersect at (3.5,10.5)

The intrinsic value of Todd Mountain Development Corporation's stock is $50. (option c)

To calculate the intrinsic value of the stock using the constant-growth DDM, we need to consider several factors: the expected dividend, the dividend growth rate, and the required rate of return. Let's break down the process step by step.

In this case, the risk-free rate of return is given as 4%, and the expected return on the market portfolio is 19%. The stock of Todd Mountain Development Corporation has a beta of 0.60.

The formula to calculate the required rate of return (RRR) using the Capital Asset Pricing Model (CAPM) is as follows:

RRR = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)

RRR = 4% + 0.60 * (19% - 4%)

RRR = 4% + 0.60 * 15%

RRR = 4% + 9%

RRR = 13%

Calculate the intrinsic value using the constant-growth DDM formula:

The constant-growth DDM formula is as follows:

Intrinsic Value = Dividend / (RRR - Dividend Growth Rate)

Given that the expected dividend is $2 and the dividend growth rate is 9%, we can substitute these values into the formula:

Intrinsic Value = $2 / (13% - 9%)

Intrinsic Value = $2 / 4%

Intrinsic Value = $50

Hence the correct option is (c).

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Complete Question:

Todd Mountain Development Corporation is expected to pay a dividend of $2 in the upcoming year. Dividends are expected to grow at the rate of  9% per year. The risk-free rate of return is 4%, and the expected return on the market portfolio is 19%. The stock of Todd Mountain Development Corporation has a beta of 0.60. Using the constant-growth DDM, the intrinsic value of the stock is _____.

a. 22.22.

b. 9.09.

c. 50.00.

d. 3.60.

k = 1/3 when two parabolas open up with f of x passing through negative 3 negative 3 and g of x passing through negative 1 negative 3.

Here,,

We must consider how the graph of f(x) gets transformed into the graph of g in order to determine the k value for the transformation of f(x) in the format g(x) = f(kx).(x). The vertex of a parabola is its lowest or highest point, depending on whether it is opening up or down, thus we can use the vertex coordinates of f(x) and g(x) to get the k value.

We know the vertices of both parabolas will be the lowest points on each graph because they both open up. Given that g(x) goes through and f(x) passes through (-3, -3), (-1, -3). We stretch or compress f(x) horizontally by a factor of k to convert it to g(x).

The x-coordinates of the parabolas' vertices can be used to determine k because it is where the horizontal compression takes place. The vertex of the quadratic function, f(x), has an x-coordinate of -b/2a, where b and an are its coefficients. Because f(x) is a parabola that is widening up in this instance, an is positive and the vertex's x-coordinate is -(-6)/(2*1) = 3. We can utilize this information to solve for k because the vertex of g(x) has an x-coordinate that is also 3k:

-1 = 3*k*(-3)

-1 = -9k

k = 1/9

Therefore, k = 1/3 is the right response.

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are you trying to find the answer or..? because it's -4

Answer:

138

Step-by-step explanation:

The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2. 3(10 + 2) = ? According to this property, you can add the numbers and then multiply by 3.

Answer:

4(6x+3) in distributive property.

Step-by-step explanation:

Answer:

1) x = 12.2

3) x = 21.7

5) x = 17.9

7) x = 31.8

Step-by-step explanation:

Use Pythagorean Theorem (a^2 + b^2 = c^2 where a and b are bases and c is hypotenuse)

1) 10^2 + 7^2 = x^2

100 + 49 = x^2

149 = x^2

x = sqrt 149 which is about 12.2

3) 16^2 + x^2 = 27^2

256 + x^2 = 729

x^2 = 473

x = sqrt 473 which is about 21.7

5) 9^2 + x^2 = 20^2

(we know the other base is 9 because in an isosceles triangle, the altitude (the height) is the same as the median (which divides the base into half)

81 + x^2 = 400

x = sqrt 319 which is about 17.9

7) 16^2 + y^2 = 22^2 (y is the height of the triangle)

256 + y^2 = 484

x = sqrt 228

(sqrt 228)^2 + (44-16)^2 = x^2

228 + 784 = x^2

x^2 = sqrt 1012 which is about 31.8

Answer: A random variable.

Step-by-step explanation:

a numerical description of the outcome of an experiment is called a random variable.

The probability of the interval -1.62 < z < 2.01 in a standard normal distribution is approximately 0.9262 or 92.62%.

In a standard normal distribution, the mean is 0 and the standard deviation is 1. The z-score represents the number of standard deviations a data point is from the mean. To find the probability of a specific interval, we calculate the area under the curve between the corresponding z-values.

Given the interval -1.62 < z < 2.01, we need to find the area under the standard normal curve between these two z-values. This can be done using a standard normal distribution table or by using a statistical software or calculator.

By looking up the z-values in the table or using software, we find the corresponding probabilities: P(z < -1.62) = 0.0526 and P(z < 2.01) = 0.9788.

To find the probability of the interval -1.62 < z < 2.01, we subtract the probability of the lower bound from the probability of the upper bound: P(-1.62 < z < 2.01) = P(z < 2.01) - P(z < -1.62 = 0.9788 - 0.0526 = 0.9262.

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Answer:

it's correct good job :)

Answer:

Step-by-step explanation:

Answer:  Fortunately, you don’t have to prove that x or y must be 1 or -1 in order for x*y to not be an element of G.

You only need to prove that x*y is an element of G for any x,y in G.  (That’s what it means for * to be an operation on G.)

I haven’t thought yet about how to prove that, but let me give you some thoughts off the top of my head.

We know -1 < x, y < 1.  We must show -1 < (x + y) / (xy + 1) and (x + y) / (xy + 1) < 1.

First, let’s show that -1 < (x + y) / (xy + 1).

I want to multiply xy + 1 to both sides, but we need to know whether it’s positive or not, so we know whether to reverse the inequality.

Well, -1 < x, y < 1 implies that xy > -1, which implies that xy +1 > 0.

So we must show that -(xy + 1) < x + y.

That is, let’s show that 0 < x + y + xy + 1.  (I don’t know if this is going anywhere useful; I’m just playing around with algebra.)

Answer:

20k

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

9k + 3k + 8k

Step 2: Simplify

Final Answer: \(20k\)

Steps/Reasons/Explanation:

Because they are all one variable, you can just add them up.

Question: Simplify the expression: \(9k+3k+8k\).

Step 1: Addition.

\(20k\)

~I hope I helped you :)~

Answer:

hey! id love to help but its not loading. do you have a link by any chance?

Step-by-step explanation:

Based on the given information, we can create a differential equation to represent the situation. Let S denote the number of students who have seen the program at time t and let N be the total number of students.

The number of students who have not seen the program is (N - S). The rate of change of students who have seen the program is proportional to the product of these two quantities, and we represent this proportionality with a positive constant k.

The differential equation to model this situation would be:

dS/dt = kS(N - S)

This equation represents the rate of change of the number of students who have seen the program (dS/dt) as proportional to the product of the number of students who have seen the program (S) and the number of students who have not seen the program (N - S), with k being the positive constant of proportionality.

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Answer:  Choice B

MN, NO, OM

Refer to the diagram below

=====================================================

Explanation:

M = 57 and N = 75 are the two given angles.

Angle O is the missing angle of the triangle.

Recall that for any triangle, the three inside angles always add to 180

M+N+O = 180

57+75+O = 180

132+O = 180

O = 180-132

O = 48

Angle O is 48 degrees.

Note: be sure not to mix up the letter 'oh' with the number zero. Unfortunately, they look very similar.

-------------------------

We know the following three angles of this triangle

As a rule, the smallest side is always opposite the smallest angle. The smallest angle is O = 48, and the side opposite that is MN.

Also, the largest side is always opposite the largest angle. The largest angle is N = 75, and the side opposite that is OM

-------------------------

In short, we found that MN is the smallest side and OM is the longest side.

That must mean side NO is placed in the middle of MN and OM

So that's how we get get the answer of MN, NO, OM which is choice B.

Refer to the diagram below.

Answer:

There are no Like Terms.

Answer: 54=x

Step-by-step explanation: