Samuel is buying a pair of boots with an original price of $80 ...

Answer:

a) x = -4

b) x = 4

c) y = 4

d) y = -2

y = -3/4x + 1

Step-by-step explanation:

Your horizontal lines are going to be written

y =

Your vertical lines are going to be written

x =

y = mx + b is the slope intercept form of a line.

The b is there the line crosses the x axis.  It is crossing at 1,  The slope is m.  In this case, if you select a point on the line and go down 3 units and 4 units to the right, you will end up right back on the line again.

In picking the smoothing constant for an exponential smoothing model, we should look for a value that produces values which compare well with actual values based on a standard measure of error.

What is exponential smoothing model?

Using the exponential window function, exponential smoothing is a general method for blending time series data. Exponential functions are used to assign exponentially decreasing weights over time, as opposed to the simple moving average, which weights previous observations equally.

The correct answer is, produces values which compare well with actual values based on a standard measure of error.

Quantitative forecasting utilizes a compilation of past performance data of the organization to arrive at an accurate forecast for any given process.

The smoothing constant selected requires to optimize accuracy the unknown parameters and the initial values need to be considered with the implementation of the sum of squared errors providing the required accuracy.

Hence, in picking the smoothing constant for an exponential smoothing model, we should look for a value that produces values which compare well with actual values based on a standard measure of error.

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Complete question:

Complete question is attached below.

The value of an investment with a $1500 principal and a nominal interest rate of 2.5% compounded monthly after 5 years is $1,699.11. So, option 1 is correct.

Compound interest is the term used to describe interest on savings that is calculated using both the initial principal and interest that has accrued over time. You can earn interest on interest, which is known as compound interest. Mathematically, if you have $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will have $110.25 by the conclusion of the second year.

Amount =[tex]P(1+r/n)^{nt}[/tex]

= 1500(1+0.25/12)5*12

= $1699.50 for an investment with a principal of $1500 and a nominal interest rate of 2.5% compounded monthly after five years.

Therefore, after five years, $1,699.50 reflects the value of an investment with a $1500 principal and a nominal interest rate of 2.5% compounded monthly.

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Answer:

100 pounds

Step-by-Step Explanation:

20+100=120

cat weighs 20

dog weighs 100

dog weighs 80 pounds more than the cat (20) = 100

Single transformation maps ABC onto A'B'C' is reflection.

Given :

Reflection the single  transformation maps ABC onto A'B'C' is reflection .

The rigid transformations can map triangle Δ ABC onto triangle Δ FED is reflection then translation .

The rigid transformations that will map Δ ABC to Δ DEF is rotation then translation .

pair of triangles can be proven congruent by the HL theorem is rotation then translation .

rigid transformation S can map Triangle abc onto Triangle dec is reflection then rotation .

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Answer:

a²/(b²ce^7)

Step-by-step explanation:

a^2b^-2c^-1 / e^7 =

= a²/(b²ce^7)

When she did all three activities on Tuesday, the number of days that Gina will do all three activities again on the same day is in 48 days.

The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, denoted by lcm in arithmetic and number theory, is the smallest positive integer that is divisible by both a and b.

LCM is an abbreviation for "Least Common Multiple." The smallest multiple that two or more numbers have in common is defined as the least common multiple.

Since Gina runs every 8 days, cycles every 16 days, and jogs every 24 days. This will be:

Multiples of 8 = 8, 16, 24, 32, 40, 48

Multiples of 16 = 16, 32, 48

Multiples of 24 = 24, 48

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Burton Bush has to invest $93,199 to get $400,000 at the end. Hence, option D is correct.

Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.

As per the given information in the question,

Rate, r = 6%

Number of years, n = 25

Present value, PV = ?

Final value, FV = $400,000

Use the equation of compound interest:

[tex]PV = FV (1 + r)^-^n[/tex]

Put values from above in the given equation,

PV = 400,000 (1 + 0.06)⁻²⁵

PV = 400,000 × 0.23

PV = $93,199.

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As per the given confidence interval, the population mean remodeling costs for the two types of projects is -1.6

Confidence interval

The  range of values that's likely to include a population value with a certain degree of confidence is known as confidence interval.

Given,

A certain association provided data on the cost of the most popular home remodeling projects.

Here we need to find the the population mean remodeling costs for the two types of projects.

Here we will find the point estimate of the difference between the population mean remodeling costs for the two types of projects using an equation,

=> X1​ − X2​

In order to calculate the sample mean we will use equation,

=> X = ∑x/n

Now, we have to substitute values we get,

=> X1 ​= 21.2

=> X2 ​= 22.8

Here X1 refers the sample mean remodeling costs for the kitchen and X2​refers the sample mean remodeling cost for the master bedroom.

Therefore, the point estimate of the difference between the population mean remodeling costs for the two types of projects are,

=> X1 ​− X2​ ​= −1.6

Therefore, we estimate that the remodeling master bedroom has the mean costs of 1.6 greater than mean remodeling costs for the kitchen.

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If a sample of 40 teams is selected at random from the population, the expected mean is $750 and the standard deviation is $29.25

The mean of the cost of joining a team = $750

Standard deviation = $185

A sample of 40 teams is selected at random from the population

The expected standard deviation = [tex]\sqrt{\frac{185^2}{40} }[/tex]

= $29.25

Here the cost of joining a team is normally distributed with a mean of $750

Here the distribution of the cost of joining is normal the mean of the sample distribution, so it will be equal to the mean of the population

The mean = $750

Therefore, the standard deviation is $29.25 and the mean is $750

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The variable is m so it is being divided by 5

What is the arithmetic operations?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

We have,

-5m = -40

It's being multiplied by -5.

-5m = -40

-5m * (-5) = -40(-5)

25m = 200

m = 8

It's being multiplied by -40.

-5m * (-40)= -40 * (-40)

200m = 1600

m = 8

it's being divided by -5

-5m= -40

m = 8

It's being divided by -40.

-5m / (-40)= -40 / (-40)

m = 8

Hence, The variable is m so it is being divided by 5

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Dimensions of the rectangle of maximum area will be [3, 12]

Area of Rectangular?

The formula for the area of a rectangle is multiply length x width.

The given equation represents an ellipse centered at the origin with semi-major axis 12 and semi-minor axis 3. The semi-major axis is the longer axis of the ellipse, and the semi-minor axis is the shorter axis.

unitsize(1.5 cm);

draw((-12,0)--(12,0));

draw((0,-3)--(0,3));

draw(shift((0,0))*xscale(12)*yscale(3)*unitcircle);

To find the dimensions of the rectangle with maximum area that can be inscribed in the ellipse, we should look for a rectangle with sides parallel to the coordinate axes and with one side coinciding with a semi-axis of the ellipse. This is because the semi-axes are the longest lines that can be drawn within the ellipse, and the rectangle will have the maximum area if it coincides with one of these lines.

In this case, we can see that the semi-minor axis of the ellipse is 3, so we can inscribe a rectangle with sides parallel to the coordinate axes and with one side of length 3 within the ellipse. The other side of the rectangle will be the semi-major axis of the ellipse, which is 12. Therefore, the dimensions of the rectangle with maximum area that can be inscribed in the ellipse are 3 and 12, and the maximum area of the rectangle is 3 * 12 = 36.

Answer: [3, 12]

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After simplifying the given equation the answer will be -2tanx.

What is identity?

An equation is referred to as an identity if it has one or more variables and is true for all alternate values of the variables for which both sides of the equation are defined.

Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.

Given: [tex]\frac{cosx}{1+sinx}-\frac{cosx}{1-sinx}[/tex]

We have to solve this.

Take cross multiplication.

[tex]= \frac{cosx - cosxsinx-cosx-cosxsinx}{(1-sin^2x)}\\= \frac{-2cosxsinx}{(1-sin^2x)}[/tex]

Since,

[tex]1-sin^2x=cos^2x[/tex]

[tex]= \frac{-2sinx}{cosx}[/tex]

Since, [tex]\frac{sinx}{cosx} = tanx[/tex]

[tex]= -2tanx[/tex]

Hence, after simplifying the given equation the answer will be -2tanx.

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Answer:

the interval is positive

Answer:6/3 or 1/2

Step-by-step explanation:

If A is a 3x3 matrix with real entries that has complex eigenvalue -5-8i then the other eigen value is -5+8i and the other eigen vector is [tex]\left[\begin{array}{ccc}-6+5i\\-1\\-5i\end{array}\right][/tex]  .

In the question ,

it is given that ,

the eigen value of the matrix is = -5+8i .

we know that ,

if A is a matrix with real entries , then both the eigen values and eigen vectors occurs in conjugate pairs ,

the other complex eigen value is conjugate ,

that is the other eigen value is = -5+8i .

and the other eigen vector corresponding to eigen value of -5+8i is conjugate at eigen vector [tex]\left[\begin{array}{ccc}-6-5i\\-1\\5i\end{array}\right][/tex]  is [tex]\left[\begin{array}{ccc}-6+5i\\-1\\-5i\end{array}\right][/tex]  .

Therefore , the eigen value is -5+8i and the other eigen vector is [tex]\left[\begin{array}{ccc}-6+5i\\-1\\-5i\end{array}\right][/tex]  .

The given question is incomplete , the complete question is

Suppose A is a 3x3 matrix with real entries that has complex eigenvalue -5-8i with corresponding eigenvector [tex]\left[\begin{array}{ccc}-6-5i\\-1\\5i\end{array}\right][/tex] . Find another eigenvalue and eigenvector for A .

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No, least-squares fitting of a regression line doesn't only applies when there is one dependent variable and one independent variable.

A least-squares regression line, which minimizes the vertical distance between the data points and the regression line, is the line that best fits a linear relationship between two variables when the data indicates such a relationship.

The most used modeling technique is without a doubt linear least squares regression. It is what most people mean when they claim they fitted a model to their data using "regression," "linear regression," or "least squares."

The independent variable in a cause-and-effect relationship is the cause, while the dependent variable is the effect. A technique for predicting the value of a dependent variable Y based on the value of an independent variable X is known as least squares linear regression. That's why least-squares fitting of a regression line doesn't only applies when there is one dependent variable and one independent variable.

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The volume of the solid obtained by rotating the specified region about the x-axis is 12.

Here we have to find the volume of the solid.

Data given:

f(x) = x² + 3

Limit of x is -1≤x≤2

Volume = [tex]\int\limits^2_-1 {(x^{2} + 3}) \, dx[/tex]

             = ( x³/3 + 3x[tex])^{2} _{-1}[/tex]

             = [( 8/3 + 6) - ( -1/3 - 3)]

             = 26/3 +10/3

             = 36/3

             = 12

Therefore the volume is 12.

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Answer:

Step-by-step explanation:

1. Inequality will switch

2. Inequality will stay the same

3. Inequality will stay the same

4. Inequality will switch

Here, on solving the provide question to us, we got to know that - 210 feet represents  = 825/4

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

Here,

15 feet represents = 1/8 of an inch

1 feet represents = 1/8 X 15

210 feet represents = 1/8 X 15 X 210 = 825/4

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Answer:  -2

Step-by-step explanation:

Draw that point of intersection. Similarly construct a horizontal line which goes through the point of intersection. The value of the function here at x = 2 is -2.

The statistical method used to predict the values of one numerical variable based on the values of another is regression analysis.

Regression analysis:

Regression analysis is a statistical method that shows the relationship between two or more variables. Usually expressed in a graph, the method tests the relationship between a dependent variable against independent variables.

Regression analysis is used to estimate the relationship between a dependent variable and one or more independent variables.

The common form of regression analysis is linear regression. Regression analysis allows us to infer that there is a relationship between two or more variables.

Therefore regression method is used to predict values of one numerical on another.

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Answer:

D) 1

Step-by-step explanation:

(1/8) x 8= 1

Hope this helps!

Answer:

Step-by-step explanation:

3/4x + 5 = 5 -2( x + 7 )

First, use Distributive Property.

-2 ( x + 7 ) --> -2x - 14

3/4x + 5 = 5 -2x - 14

Next, you can get rid of the fraction by multiplying EVERYTHING by 4...

3x + 20 = 20 - 8x - 56

Then, move x by subtracting 3x on BOTH sides...

20 = 20 - 11x - 56

Combine like terms...

20 = - 11x - 36

Add 36 on BOTH sides...

56 = - 11x

Divide -11 on BOTH sides...

56/11 = 5.09 repeating

x = 5.0909090909090909...

Correct me if I'm wrong, but there you go!

Activities in which students participated in sports benefit in a variety of ways, including greater grades and test scores, higher academic achievements, more regularity in class attendance, and an increase in self.

There had been a link between extracurricular involvement and grades, but there was not definitely a causal relationship, thus they cannot make any conclusions from this research.

This was an observational study since students were not randomly assigned to treatment groups—so we can say that there is an association or a relationship extracurricular participation and grades. Since this wasn't an experiment, we don't necessarily know that extracurricular participation caused higher grades.

Hence we get the required answer.

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The radius of convergence is a-R a+R = 6+12 =18 and 6-12 = -6 for the |6x 12/<78 and diverges if |6x 12| 78.

The set of actual numbers x wherein the collection converges is the c program language period of convergence. If there exists a actual wide variety R such that the collection converges for |x−a|R, then R is the radius of convergence.

The radius of convergence is 1/2 of of the duration of the c program language period of convergence. If the radius of convergence is R then the c program languageperiod of convergence will consist of the open c program languageperiod: (a − R, a + R). To discover the radius of convergence, R, you operate the Ratio Test.

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Answer:

The two sides of the triangle are the same as marked.

118+Y=180

Y=180-118=62

Y=62

X+Y+Y=180

X+2Y=180

X=180-2Y

X=180-2x62

X=56

Step-by-step explanation:

The sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class.

At the null hypothesis, it is tested if the scores are not different from the regular class, that is, if the mean is of 81.7, hence:

[tex]H_0: \mu = 81.7[/tex]

At the alternative hypothesis, it is tested if the scores are different from the regular class, that is, if the mean is different of 81.7, hence:

[tex]H_1: \mu \neq 81.7[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 9 - 1 = 8 df, hence the critical value is given as follows:

|t| = 2.306.

Thus the decision rule is given as follows:

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are of:

[tex]\overline{x} = 77.2, \mu = 81.7, s = 5.7, n = 9[/tex]

Hence the test statistic is calculated as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{77.2 - 81.7}{\frac{5.7}{\sqrt{9}}}[/tex]

t = -2.37.

|t| > 2.306, hence the sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class.

The problem asks if the sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class? Use a two-tailed test with α = .05.

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Answer: 5 i think

because if x^3 = 1/125 then 625 times 1/125 is 5

The fraction that will be equivalent to 5/8 with a denominator of 16 is 10/16

From the question, we have the following parameters that can be used in our computation:

Fraction = 5/8

This fraction is to be converted to a fraction  with a denominator of 16

This is so because the scale only measures in 16ths

So, we have the following representation

Fraction = 5/8

When 8 is multiplied by 2, the result is 16

So, we multiply 5 and 8 by 16

This gives

Fraction = 10/16

Hence. the solution is 10/16

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