An item is regularly priced at $81. Shen bought it on sale for 45% off the regular price
Use the ALEKS calculator to find how much Shen paid.

We can not write the polynomial g(x) as a product of linear factors.

What is polynomial?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents (No division operation by a variable).

Given:

g(x)=x³ + 3x² - 7x − 3 and x = -1 is a zero of g(x).

Since, if x = a is a zero of the polynomial then (x - a) is a factor of polynomial.

Here (x - (-1)) = (x + 1) is a factor of g(x).

First to check x = -1 is a zero of polynomial or not.

Plug x = -1 in g(x).

g(-1) = (-1)^3 + 3(-1)^2 - 7(-1) - 3

g(-1) = -1 + 3+ 7 - 3

g(-1) = 6

g(-1) ≠ 0

Hence, we can not write the polynomial g(x) as a product of linear factors.

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Answer: (x+5)(2x+10)

Step-by-step explanation: Hope you find it helpful, I am in the rush so can't give you a full explanation on paper yet!

Answer:

y = -x - 4

Step-by-step explanation:

y = mx + b is slope intercept form,

where m is the slope, and b is the y-intercept.

As we can see from the picture, the line has a negative slope of 1 (we can also just say -1). We know this is the slope because it has a rise of -1 and a run of -1. (I hope that made sense lol :/)

[Side note, we use x instead of 1.]

The y-intercept is -4 since we can see the line passes through the y-axis at -4.

Therefore, the equation can be written as y = -x - 4

When we reject the null and the null is true, we have a made a TYPE 1 ERROR

A null hypothesis is either true or false. Unfortunately, we do not know which is the case, and we almost never will. It is important to realize that there is no probability that the null hypothesis is true or that it is false, because there is no element of chance. For example, if you are testing whether a potential mine has a greater gold concentration than that of a break-even mine, the null hypothesis that your potential mine has a gold concentration no greater than a break-even mine is either true or it is false; you just don’t know which. There is no probability associated with these two cases (in a frequentist sense) because the gold is already in the ground, and as a result there is no possibility for chance because everything is already set.

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You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The relationship between the two variables in a bivariate data set is graphically represented by a scatter plot. Consider them to be the graphic depiction of two data sets that have been combined by allocating each axis in the plot to a distinct variable.

Due to the presence of two variables, this type of data is known as bivariate data. Only 1 variable may be displayed on a line plot. You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The standard deviation of each variable and the covariance between them must first be determined in order to calculate the Pearson correlation. Covariance is subtracted from the product of the standard deviations of the two variables to get the correlation coefficient.

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We can make 19 oatmeal cookies from the bag.

1 pound = 16 ounces

for making a single unit of oatmeal cookie it uses 21 ounces of oats.

We have 25 pound of oats in the bag which means we have 25 X 16 which is equal to 400 ounces of oats in the bag .

To find how much of oatmeal cookies can be made we have to divide the total amount of oats available in the bag divided by the number of ounces required in making of the single unit of oatmeal .

Therefore,

= 400 / 21

= 19.047

Which means 19 overall pieces of oatmeal can be prepared in the 25 pound of oats bag

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The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b)

This is incomplete question

Complete question is this:

With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?

Choose the correct option:

Now, According to the question:

Hence, The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b).

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Step-by-step explanation:

Using log properties

[tex] log_{7}(rz {}^{12} ) [/tex]

[tex] log_{7}(r) + log_{7}(z {}^{12} ) [/tex]

Then

[tex] log_{7}(r) + 12 log_{7}(z) [/tex]

Plug in the knowns

[tex] - 7.87 + 12( - 12.59)[/tex]

[tex] - 158.95[/tex]

(4,3): 2x-5y = -7 is  the ordered pair on the graph lies.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it can be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers. The coordinates of one point in the coordinate system are included in an ordered pair. An ordered pair of the form of a point's name is (x, y). The x-coordinate is represented by the first integer, and the y-coordinate by the second. You must place a dot at the coordinates of the ordered pair in order to graph a point.

Given

We enter the values of the variables into each equation to see if an ordered pair is a solution to the system of two equations. The ordered pair is the system's solution if it makes both equations true.

For this,

(4,3): 2x-5y = -7

Equating values,

2(4) - 5(3)

8 -15

-7

(4,3): 2x-5y = -7 is  the ordered pair on the graph lies.

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Answer:

A.   y = -1/2 x + 3/2

Step-by-step explanation:

An x-intercept of 3 means point (3, 0).

The line passes through points (3, 0) and (-5, 4).

y = mx + b

m = (4 - 0)/(-5 - 3) = 4/(-8) = -1/2

y = -1/2 x + b

0 = -1/2 × 3 + b

b = 3/2

y = -1/2 x + 3/2

The student did better in the test of Geography.

The standard deviation is a measure of the amount of variation or dispersion of a set of values.

To solve this question, we will use the z-score formula to find the w test in which the student scored better. The z-score formula is;

z = (x - μ)/σ

Now, for Geography we have given :

              Test score (x) = 68

                      Mean (μ) = 80

Standard deviation (σ) = 10

Thus, the z-score here will be :

z = (68 - 80)/10

z = -1.2

Similarly, for Mathematics we have given :

              Test score (x) = 249

                      Mean (μ) = 300

Standard deviation (σ) = 34

Thus, the z-score here will be :

z = (249 - 300)/34

z = -1.5

Since the z-score for Geography is less than that of Mathematics, thus, we can conclude that the Geography test is the one in which the student scored better.

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For instance, if the multiplication error is 8 x 7 = 56, then the matching division error  56/8 = 7, demonstrating that the result of the division is the other component that was used in the multiplication.

Finding the product of two or more corresponding integers is done mathematically through the action of multiplication. It is frequently represented by the letters "x" or "*." In order to discover the result of multiplication, a multiplicand, also known as the multiplicand, is multiplied by a multiplier, also known as the multiplier. The result of the two integers, for instance, is 56 if the multiplicand and multiplier are both 8. A multiplication process always yields a greater number as the outcome than either of the initial factors. Multiply is also used to describe the process of adding a number to itself a certain number of times, as in "7 multiplied by 3 equals 21."

How to solve?

 For instance, if the multiplication error is 8 x 7 = 56, then the matching division error  56/8 = 7, demonstrating that the result of the division is the other component that was used in the multiplication.

This connection is true for every multiplication and division problem as long as the numbers are utilised consistently in both operations.

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Answer:

B. x = 3

Step-by-step explanation:

3³ = 27

3 · 3 · 3 = 27

9 · 3 = 27

Answer:

Step-by-step explanation:

P+N+2Q=?

P= Pennies

N= Nickels

Q= Quarters

Answer:

the first company would be cheaper because it has a lower total cost.

Step-by-step explanation:

To determine which company is more cost-effective, you will need to compare the total costs for each company based on the amount of sugar being transported.

If the first company is used, the total cost for transporting x tons of sugar will be 3204 + 75.25x dollars.

If the second company is used, the total cost for transporting x tons of sugar will be 275.50x dollars.

To determine which company is cheaper for a given amount of sugar, you can compare these two equations by setting them equal to each other and solving for x.

For example, if you want to transport 100 tons of sugar, you can set the two equations equal to each other and solve for x:

3204 + 75.25x = 275.50x

Solving for x, we get: x = 3204 / (75.25 - 275.50) = 107.8 tons

This means that if you want to transport 100 tons of sugar, the first company would be cheaper, because it costs less than the second company for any amount of sugar greater than 107.8 tons.

If you want to transport a different amount of sugar, you can repeat this process to determine which company is cheaper.

Answer:

[tex]\textsf{A)} \quad -1\dfrac{3}{20}y+4[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(11-9 \dfrac{3}{5}y\right)+\left(8 \dfrac{9}{20}y-7 \right)[/tex]

Remove the parentheses:

[tex]11-9 \dfrac{3}{5}y+8 \dfrac{9}{20}y-7[/tex]

Collect like terms:

[tex]8 \dfrac{9}{20}y-9 \dfrac{3}{5}y+11-7[/tex]

Subtract the numbers 11 - 7:

[tex]8 \dfrac{9}{20}y-9 \dfrac{3}{5}y+4[/tex]

Factor out y:

[tex]\left(8 \dfrac{9}{20}-9 \dfrac{3}{5}\right)y+4[/tex]

Partition the mixed numbers into fractions and whole numbers, and then subtract them separately.

Subtract the whole numbers:

[tex]\implies 8-9=-1[/tex]

Subtract the fractions by changing both fractions into equivalent fractions so both fractions have the same denominator:

[tex]\implies \dfrac{9}{20}-\dfrac{3}{5}[/tex]

[tex]\implies \dfrac{9}{20}-\dfrac{3 \cdot 4}{5 \cdot 4}[/tex]

[tex]\implies \dfrac{9}{20}-\dfrac{12}{20}[/tex]

[tex]\implies -\dfrac{3}{20}[/tex]

Put the two answers from the whole numbers and fractions back together:

[tex]\implies -1-\dfrac{3}{20}=- \left(1+\dfrac{3}{20}\right)=-1\dfrac{3}{20}[/tex]

Therefore:

[tex]\left(8 \dfrac{9}{20}-9 \dfrac{3}{5}\right)y+4=\left(-1\dfrac{3}{20}\right)y+4=-1\dfrac{3}{20}y+4[/tex]

The  graph that represents the solution to the inequality −0.96 is greater than or equal to the product of a number and 0.3 number line with a closed circle on point negative 3.2 and arrow shaded to the left

Generally, To solve this inequality, we can start by multiplying both sides by the reciprocal of 0.3, which is 3. Doing so gives us the inequality:

−0.96 * 3 >= x * 0.3 * 3

Simplifying the right side gives us:

−0.96 * 3 >= x * 0.9

Then we can simplify both sides further:

−2.88 >= x * 0.9

Dividing both sides by 0.9 gives us:

−3.2 >= x

The solution to this inequality is all values of x that are less than or equal to -3.2.

The graph of this inequality would be a number line with a solid dot at -3.2, and a solid line extending to the left of -3.2, as shown below:

(graph with number line and solid dot at -3.2, and solid line extending to the left)

This graph represents the solution to inequality.

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Answer:

here

Step-by-step explanation:

1. How tall was the tree when Vlad moved into the house?

292-26*4.5=175 cm

2. How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?

175+26*x=357

357-175=182=26*x

x=7  


hope this helped

The greatest amount that a person can receive is 19$. Option D

A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved.

Total amount = $30

Total number of people = 8

According to the problem, each person gets at least 1$ and also exact amount.Let's consider only one person gets more than 5$ because, we have to find the greatest value.

4 people get more than 1$,that includes the person who gets the maximum amount.

Let the person who gets maximum amount =x

x + 2+2+2+1+1+1+1

Maximum amount = 30- (2+2+2+1+1+1+1+1)= 11$

Hence, the maximum amount will be 19$.

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The number of associates assigned in the case is 7.

The number of partners assigned in the case is 9.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

Number of associates = m

Cost of each associates = $400

Number of partners = n

Cost of each partner = $1000

Now,

Total number of lawyers = 16

Total amount charged = $11800

Now,

m + n = 16

m = 16 - n

400m + 1000n = 11800

Putting m = 16 - n.

400(16 - n) + 1000n = 11800

6400 - 400n + 1000n = 11800

6400 + 600n = 11800

600n = 11800 - 6400

600n = 5400

n = 5400/600

n = 9

Now,

m = 16 - n

m = 16 - 9

m = 7

Thus,

The number of associates assigned in the case is 7.

The number of partners assigned in the case is 9.

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The number of cubic feet of concrete that would be needed is 586491840 cubic feet

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

These parameters can be represented using the following notations

The number of cubic feet of concrete that would be needed is the volume of the dam

So, the number of cubic feet of concrete that would be needed can be calculated using the following volume equation

The number of cubic feet of concrete that would be needed = Length x Width x Height

Substitute the known values in the above equation, so, we have the following representation

The number of cubic feet of concrete that would be needed = 1224 * 660 * 726

Evaluate

The number of cubic feet of concrete that would be needed = 586491840

Hence, the cubic feet is 586491840

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The value of the expression 24 + x ÷ 12 as required to be evaluated when the variable, x = -180 as required in the task content is; 9.

It follows from the task content that given expression is required to be evaluated for its value when the variable, x = -180.

Since the given expression is; 24 + x ÷ 12.

It follows that when the variable, x is given as; x = -180; we have that;

24 + ( -180 ) ÷ 12

Following from PEMDAS guidelines in which case;

Therefore, we have that;

24 + ( -180 / 12 )

= 24 + ( -15 )

= 24 - 15

= 9.

Upon evaluation, by means of the PEMDAS guidelines in which case; Parentheses, Exponents, Multiplication, Division , Addition and Subtraction are solved in order; the value of the expression is; 9.

Therefore, the required value of the expression; 24 + x ÷ 12; as required to be evaluated according to the given parameter; x = -180 is; 9.

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When Sam buys 10 tickets for $135 at fundraiser, the amount for each ticket will be $13.50.

It should be noted that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, Sam buys 10 tickets for $135 at fundraiser, the amount for each ticket will be:

= $135 / 10

=$13.50

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Complete question

Sam buys 10 tickets for $135 at fundraiser. Calculate the amount for each ticket.

The profit, y, can be written in terms of x, the number of computers sold.  as ​y = 150x

The table that completes the question is added at the end of this solution as an attachment

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

Amount of items sold = x

Profit made by the company = y

The equation of a proportional relationship is represented as

k = Y/X * h

Where

(X, Y) is the coordinate of any ordered pair from the function or table

Using the above as a guide, we have the following:

(X, Y) = (3, 450)

Substitute the known values in the above equation, so, we have the following representation

y = 450/3 * x

Evaluate the quotients in the equation

y = 150 * x

Evaluate the products in the equation

y = 150x

Hence, the equation of the proportional relationship is y = 150x

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The possible values of x in the figure are given as follows:

x > 3/2.

The possible values of x are obtained verifying if the given dimensions form a triangle, and the condition is that the sum of the lengths of the two smaller sides has to be greater than the length of the greatest side.

For the triangle given in the image, the dimensions are given as follows:

Hence, applying the condition, the inequality to obtain the values of x is given as follows:

2x + 4x - 3 > 4x.

Then, solving the inequality, the possible values of x in the triangle are given as follows:

2x + 4x - 3 > 4x

2x > 3

x > 3/2.

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162.5  is the simple interest for one year.

What does the term "simple interest" mean?

The principal of a loan or the initial deposit into a savings account serves as the foundation for simple interest.

                   Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

P = $812.50

T = 1 Year

S.I. = ?

R = 20

According to question,

                 S.I. = P * R* T/100

                     = 812.50 * 20 * 1/100

                     = 16250/100

                    = 162.5

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The measure of angle A and angle B is equal to 70° as per the given relation of both the angles.

As given in the question,

Given measure of angle A is equal to ( 8x + 6 )°

Given measure of angle B is equal to ( 4x + 38 )°

Given condition :

Measure of both the angles are equal to each other

Measure of ∠A = Measure of ∠B

⇒ ( 8x + 6 )° =  ( 4x + 38 )°

Now simplify the above equation to get the value of x

⇒(8x - 4x)° = (38 -6)°

⇒4x°= 32°

⇒x = 32°/4

⇒x = 8°

Measure of ∠A = 8(8) + 6

                         = 70°

Measure of ∠B = 4(8) +38°

                          = 70°

Therefore, the measure of both the angles A and B is equal to 70°.

The complete question is:

The measure of ∠A = (8x + 6)° , measure of ∠B = ( 4x+ 38)° and  both are equal to each other. Find the measure of each angle?

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The rules of logarithms, which are derived from the exponent rules, are what make up the attributes of log. The solution is 36.

The rules of logarithms, which are derived from the exponent rules, are what make up the attributes of log.

These logarithm features are used to simplify logarithmic expressions and solve logarithmic problems.

solution to log4(y – 9) + log43 = log481.

log4 (y − 9) + log4 3 = log4 81

We know that log a(b) + loga ( c) = loga ( b*c)

log4 (y − 9) * 3 = log4 81

We know have log a( BC ) = loga ( d)

This means BC = d

(y − 9) * 3  = 81

Divide each side by 3

y - 9 = 81/3

y - 9 = 27

Add 9 to each side

y-9+9 = 27+9

y = 36

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Answer:

y = 36

Step-by-step explanation:

STEP 1:

The given equation is 

log4(y – 9) + log4(3) = log4(81)

STEP 2:

log4(y – 9)(3) = log4(81)

STEP 3:

log4(3y - 27) = log4(81)

STEP 4:

3y - 27 = 81

     +27.   +27

STEP 5:

3y = 108

__   ____

 3.      3

STEP 6:

y = 36