What is the equation in point-slope form of the line that passes through (-9, 12) with a slope of 5/6?
A. y-12=6/5(x+9)
B. y-12=5/6(x+9)
C. y-9=5/6(x-12)
D. y-12=6/5(x-9)​

Step-by-step explanation:

Equation at the end of step 1

(3x2 - 38x) + 24 = 0

STEP2:Trying to factor by splitting the middle term

 2.1     Factoring  3x2-38x+24 

The first term is,  3x2  its coefficient is  3 .

The middle term is,  -38x  its coefficient is  -38 .

The last term, "the constant", is  +24 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 24 = 72 

Step-2 : Find two factors of  72  whose sum equals the coefficient of the middle term, which is   -38 .

     -72   +   -1   =   -73     -36   +   -2   =   -38   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -36  and  -2 

                     3x2 - 36x - 2x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                    3x • (x-12)

              Add up the last 2 terms, pulling out common factors :

                    2 • (x-12)

Step-5 : Add up the four terms of step 4 :

                    (3x-2)  •  (x-12)

             Which is the desired factorization

Equation at the end of step2:

(x - 12) • (3x - 2) = 0

STEP3:Theory - Roots of a product

 3.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

 3.2      Solve  :    x-12 = 0 

 Add  12  to both sides of the equation : 

                      x = 12

Solving a Single Variable Equation:

Step-by-step explanation:

\(if \: (x + 12) = (3x + 2) \\ 12 - 2 = 3x - x \\ 2x = 10 \\ x = 5 \\ \\ \\ if(x + 12)(3x + 2) = 0 \\ x + 12 = 0 \: \: \: or \: \: \: 3x + 2 = 0 \\ x = - 12 \: \: \: or \: \: \: x = - \frac{2}{3} \)

False. The value of the sample mean is not static and can change with different data sets.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

False.

The value of the sample mean is calculated based on the data in the sample, and it can change if the data set from which the sample is drawn changes.

For example, suppose we have a population with a certain mean and take a random sample from that population to calculate the sample mean. If we take a different sample from the same population, we may get a different sample mean. Similarly, if we take a sample from a different population with a different mean, we will get a different sample mean.

Therefore, the value of the sample mean is not static and can change with different data sets.

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Answer:

o/-5/-9/8/11

Step-by-step explanation:

Hopefully this helps :)

Answer:

6.557

Step-by-step explanation:

Answer:

6.557

Step-by-step explanation:

Hope this helps and have a great day!!!

Answer:

Vertex: (-2, 3) Axis of symmetry: x = -2 The parabola opens downward.

Step-by-step explanation:

The given double integral is ∫ ∫ (x² + y²)dx dy, and we need to evaluate it over the region in the positive quadrant where x+y≤1.

To evaluate this double integral, we can first determine the limits of integration for both x and y based on the given region. In the positive quadrant, x and y both range from 0 to 1.

Now, integrating the inner integral with respect to x, we get:

∫ (x² + y²)dx = (1/3)x³ + y²x + C1,

where C1 is the constant of integration.

Next, we integrate the resulting expression with respect to y:

∫ [(1/3)x³ + y²x + C1] dy = (1/3)x³y + (1/3)y³x + C1y + C2,

where C2 is another constant of integration.

Finally, we evaluate this double integral over the given region by substituting the limits of integration:

∫∫ (x² + y²)dx dy = ∫[0 to 1] ∫[0 to 1-x] (x² + y²)dy dx.

Performing the integration, we can find the numerical value of the double integral within the given region.

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Answer:

2x+2x+2x= 180

6x=180

x= 30

Step-by-step explanation:

Answer: x=30

Step-by-step explanation:

Answer:

1/4x^2 + 7x + 49

Step-by-step explanation:

Use binomial theorem (a + b)^2 = a^2 + 2ab + b^2 to expand (1/2x + 7)^2

Answer:

To determine if Daniel should have filled out his W-4 form differently to receive a refund, we need to compare his tax liability with the total amount withheld from his paychecks for the year.

If Daniel's tax liability for the year is less than $3,900, he will receive a refund when he files his taxes. If his tax liability is more than $3,900, he will owe additional taxes when he files his taxes.

If Daniel's tax liability is exactly $3,900, he will neither owe additional taxes nor receive a refund when he files his taxes.

Therefore, to determine if Daniel should have filled out his W-4 form differently, we need to compare his tax liability with $3,900.

If Daniel's tax liability from part B, question 3, is less than $3,900, he will receive a refund when he files his taxes, as the total amount withheld from his paychecks is more than his tax liability. In this case, Daniel may want to consider filling out his W-4 form differently to reduce the amount withheld from his paychecks and increase his take-home pay.

On the other hand, if Daniel's tax liability from part B, question 3, is more than $3,900, he will owe additional taxes when he files his taxes, as the total amount withheld from his paychecks is less than his tax liability. In this case, Daniel may want to consider filling out his W-4 form differently to increase the amount withheld from his paychecks and reduce the amount he will owe when he files his taxes.

If Daniel's tax liability from part B, question 3, is exactly $3,900, he will neither owe additional taxes nor receive a refund when he files his taxes, and his W-4 form is correctly filled out for his tax situation.

In summary, whether or not Daniel should have filled out his W-4 form differently to receive a refund depends on his tax liability compared to the total amount withheld from his paychecks. If his tax liability is less than the total amount withheld, he may want to reduce the amount withheld to increase his take-home pay. If his tax liability is more than the total amount withheld, he may want to increase the amount withheld to reduce the amount he will owe when he files his taxes. If his tax liability is exactly equal to the total amount withheld, his W-4 form is correctly filled out for his tax situation.

Answer:

1/13 or 4/32

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Answer: The answer is C

To find the value of z when given specific values for r, s, and t, we substitute those values into the equations for x and y, and then substitute the resulting values of x and y into the equation for z. In this case,  z is 4.

Given the equations z = 2xy + x + y, x = r + s + t, and y = rst, we are asked to find the value of z when r = 1, s = -1, and t = 2.

First, we substitute the values of r, s, and t into the equation for x:

x = 1 + (-1) + 2

x = 2

Next, we substitute the values of r, s, and t into the equation for y:

y = 1*(-1)*2

y = -2

Now, we have the values of x and y, so we can substitute them into the equation for z:

z = 2(2)(-2) + 2 + (-2)

z = 8 - 4

z = 4

Therefore, when r = 1, s = -1, and t = 2, the value of z is 4.

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Answer:

A person with $-40 is in more debt

Step-by-step explanation:

The person with $-40 has borrowed or spent money from their credit card more than the person who is in debt for $-30.

Answer:$-40

Step-by-step explanation:

A person with negative 40 dollars has 40 dollars missing, a person with -30 dollars only has 30 dollars missing. So the person with -$40 is missing more money and therefore, is in more debt.

rise/run 1/4 so it can be

Answer:1/4

Step-by-step explanation:

The number of subs in the order is 8 or 9

Let's call the number of subs in the order "x".

Since the cost of 3 subs is $20, the cost per sub is $20 / 3 = $6.67.

And since the cost of 4 subs is $26, the cost per sub is $26 / 4 = $6.50.

So the cost per sub is between $6.50 and $6.67.

If the total cost is $56, then the cost per sub must be $56 / x.

So:

x = 56/6.5 or x = 56/6.67

Evalutate

x = 8.6 or x = 8.4

Approximate

x = 9 or 8

Hence, the subs is 8 to 9

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Answer:

YEAAAAAAAAAAAAAAAAAAAA

Step-by-step explanation:

Answer:

yeeeeeeeeeeeeeeeeee

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

throat bababy

Answer:

72 miles.

Step-by-step explanation:

If he uses 6 gallons of gas, you would do 6 (gallons he used) x 12 (miles per gallon) equaling 72.

There are 432 different portfolios that are possible.

To calculate the number of different portfolios, we have to multiply the number of choices for each type of investment.

Mutual funds: 4 options ,Municipal bond funds: 6 options ,Stocks: 6 options ,Precious metals: 3 options

The number of different portfolios possible is: 4 × 6 × 6 × 3 = 432

Different portfolios are possible. This is because there are four mutual funds, six municipal bond funds, six stocks, and three precious metals.

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Answer:

2

Step-by-step explanation:

slope=rise/run

create a triangle

I chose (2,4)

it goes up 4 and the run is 2

4/2

The mean and the variance of X for the moment generating function ϕX(s)  is equal to  70/3 and 7636/9 respectively.

The moment generating function (MGF) of a random variable Y is defined as ϕY(s) = E[\(e^{(sY)\)],

where E[ ] denotes the expected value.

X has the MGF ϕX(s) = (1/3) × (2\(e^{(3s)\) + 1) × ϕY(s),

Express it as,

ϕX(s) = (1/3) × (2\(e^{3s\)) + 1) × ϕY(s)

To find the mean and variance of X, manipulate the MGF and use the properties of MGFs.

The mean of a random variable can be obtained by evaluating the first derivative of its MGF at s=0,

E[X] = ϕX'(0)

Let us start by finding the derivative of ϕX(s) with respect to s,

ϕX'(s) = (1/3) × [2 × 3\(e^{3s\) × ϕY(s) + (2\(e^{3s\) + 1) × ϕY'(s)]

Now, substituting s = 0 into the derivative,

ϕX'(0)

= (1/3) × [2 × 3 × ϕY(0) + (2 + 1) × ϕY'(0)]

= 2 × ϕY(0) + (1/3) × ϕY'(0)

Since ϕY(0) is the MGF of Y evaluated at s = 0,

it represents the moment of Y, which is the mean of Y.

Mean of Y is 10, we have ϕY(0) = 10.

Similarly, ϕY'(0) represents the first raw moment of Y, which is the mean of Y itself. Therefore, ϕY'(0) is also equal to 10.

Substituting the values, we have,

E[X] = 2 × ϕY(0) + (1/3) × ϕY'(0)

= 2×10 + (1/3) × 10

= 20 + 10/3

= 70/3

So, the mean of X is 70/3.

Now, let us find the variance of X.

The variance of a random variable can be obtained by evaluating the second derivative of its MGF at s=0,

Var[X] = ϕX''(0) + [ϕX'(0)]²

Let us start by finding the second derivative of ϕX(s) with respect to s,

ϕX''(s) = (1/3) × [2 × 3²\(e^{3s\)× ϕY(s) + 2 × 3\(e^{3s\) × ϕY'(s) + 2 × 3\(e^{3s\) × ϕY'(s) + (2\(e^{3s\) + 1) × ϕY''(s)]

Now, substituting s = 0 into the second derivative,

ϕX''(0)

= (1/3) × [2 × 3² × ϕY(0) + 2 × 3× ϕY'(0) + 2 × 3 × ϕY'(0) + (2 + 1) × ϕY''(0)]

= 2 × 3² × ϕY(0) + 4 × 3 × ϕY'(0) + (1/3) × ϕY''(0)

Since ϕY(0) is the MGF of Y evaluated at s = 0,

it represents the moment of Y, which is the mean of Y.

The mean of Y is 10, we have ϕY(0) = 10.

Similarly, ϕY'(0) represents the first raw moment of Y, which is the mean of Y itself. Therefore, ϕY'(0) is also equal to 10.

Finally, ϕY''(0) represents the second raw moment of Y, which is the variance of Y.

The variance of Y is 12, we have ϕY''(0) = 12.

Substituting the values, we have,

ϕX''(0)

= 2 × 3² × ϕY(0) + 4 × 3 × ϕY'(0) + (1/3) × ϕY''(0)

= 2 × 3² × 10 + 4 × 3 × 10 + (1/3) × 12

= 180 + 120 + 4

= 304

Now, let us substitute the values into the formula for the variance,

Var[X] = ϕX''(0) + [ϕX'(0)]²

= 304 + (70/3)²

= 304 + 4900/9

= (2736 + 4900)/9

= 7636/9

Therefore, for moment generating function the mean is  70/3 and the variance of X is 7636/9.

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The given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.

This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.

These points satisfy x = 0 because of this.

The errors of a slope and an intercept will be connected if you fit them simultaneously.

By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept.

Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.

Therefore, the given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.

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The volume of the given solid is πa³/4 cubic units.

Given that the base of a solid is a quadrant of a circle of radius a and each cross-section perpendicular to one edge of the base is a semicircle whose diameter lies in the base.

To find the volume of the solid, we'll integrate the area of the cross-section over the height of the solid.

Let us consider a cross-section with thickness dx at a distance x from the vertex of the quadrant, as shown in the figure below.

Here, the diameter of the semicircle forming the cross-section is 2(x + a).

Therefore, the radius of the semicircle is (x + a).

Area of the cross-section = Area of the semicircle= π[(x + a)²]/2

Volume of the solid = ∫Area dx from 0 to a= ∫π[(x + a)²]/2 dx from 0 to a= π/2 ∫(x² + 2ax + a²) dx from 0 to a= π/2 [(a³/3 + 2a²/2 + a³/2) - (0)] = πa³/4 cubic units

Therefore, the volume of the given solid is πa³/4 cubic units.

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The scale of the diagram as described in the task content is; 1: 8 where k= 8.

It follows from the task content that the original length of the room in discuss is 8cm. It therefore follows that the length of the room in the scale diagram is 1cm. On this note, the scale of the diagram in discuss is; 1 : 8 as 1cm on the diagram corresponds to 8cm actual length.

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Answer:

Even if you achieve practical significance, it is possible to construct some tests that will not result in statistical significance (for instance if you, on purpose or by accident, use a sample in which you know there is no relationship), so practical significance does not imply statistical significance in every study

The sum of the given geometric series is 4165.5

The given series 1331+ 911+ 121+ 9+ 81 can be expressed as Σ arn-1, where a=1331 and r=911/1331=0.682. To see the remaining terms as a geometric series, we can express them as -81(0.75)n-1. The ratio of any two successive terms in this series is -0.75, which is the value of r in the algebraic expression. Therefore, the entire series can be expressed as Σ arn-1, where a=1331 and r=0.682 for the first term and a=-81 and r=-0.75 for the remaining terms.

To determine if this series is convergent or divergent, we need to check if the absolute value of r is less than 1. |r|=0.75<1, so the series is convergent.

To find its sum, we can use the formula S=a/(1-r), where S is the sum of the series. Plugging in the values for a and r, we get:

S = 1331/(1-0.682) + (-81/(1-(-0.75)))
S = 4165.5

The sum of the given geometric series is 4165.5.

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The smaller number is -17, and the quadratic equation that can be used to find it is\(x^2 + x - 272 = 0.\)

The correct answer would be \(x^2 + x - 272 = 0.\)

To find the quadratic equation that can be used to find the smaller number, we can set up the equation using the given information. Let's assume that the smaller number is x.

Since the product of two consecutive integers is 272, we can express this as an equation: x(x + 1) = 272.

Expanding the equation, we have:

\(x^2 + x = 272.\)

To find the quadratic equation, we need to rearrange the equation in the standard form, which is\(ax^2 + bx + c = 0\). In this case, we have:

\(x^2 + x - 272 = 0.\)

Therefore, the correct quadratic equation that can be used to find the smaller number is\(x^2 + x - 272 = 0.\)

This equation can be solved by factoring, completing the square, or using the quadratic formula. Factoring may not be straightforward in this case since 272 does not have obvious factors, so let's use the quadratic formula to find the solutions.

The quadratic formula states that for an equation of the form \(ax^2 + bx + c = 0\), the solutions for x can be found using the formula:

x = (-b ± √\(\sqrt{(b^2 - 4ac)}\)) / (2a).

For the equation\(x^2 + x - 272 = 0,\)we have a = 1, b = 1, and c = -272. Substituting these values into the quadratic formula, we get:

x = (-(1) ± \(\sqrt{((1)^2 - 4(1)(-272))) / (2(1)).}\)

Simplifying further, we have:

x = (-1 ±\(\sqrt{ (1 + 1088)) / 2.}\)

x = (-1 ± \(\sqrt{1089)}\) / 2.

Since we are looking for the smaller number, we take the negative square root:

x = (-1 -\(\sqrt{ 1089}\)) / 2

Calculating the value, we have:

x = (-1 - 33) / 2.

x = -34 / 2.

x = -17.

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Answer:

it so easy that correct

Step-by-step explanation:

$500.00×$8.5