Question 2(Multiple Choice Worth 2 points)
(Factoring Algebraic Expressions MC)
Rewrite 1/6x³y + 5/6xy² using a common factor.
xy(x² +5y)
xy(3x² +15y)
xy(x² +5y)
x³y²(y+5x)

The description that represents a sample is A. The first 5,000 people who downloaded its No. 1 hit song.

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

It should be noted that all people who downloaded its No. 1 hit song represents the entire population. The sample is a subset of the population.

In conclusion, the correct option is A.

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The missing partial products are:

10 x 2 = 20

6 x 50 = 300

6 x 2 = 12

The sum of the  partial products is,

16 x 52 = 500 + 300 + 20 + 12 = 832

Here the partial products method is used to find the product of two two digit numbers 16 and 52.

For this a table of the form given in the figure is constructed in which the partial products are found.

For this first split 16 and 52 into 10 + 6 = 16 and 50 + 2 = 52.

Then take the partial products between 10 and 50, 10 and 2, 6 and 50, 6 and 2. Then take the sum of all these four values to get the final answer. This is the method of partial products.

So finding the partial products,

10 x 50 = 500

10 x 2 = 20

6 x 50 = 300

6 x 2 = 12

To find the final answer, take the sum of these products.

500 + 300 + 20 + 12 = 832

⇒ 16 x 52 = 832

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Let Bailey drive x miles.

So, Kacie drove 2x miles.

Kaiden drove 2x + 10 miles.

According to the question,

x + 2x + 2x + 10 = 50

x = 8

Therefore, Bailey drove 8 miles and Kacie drove 16 miles, while Kaiden 36 miles.

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Answer:

A, 9100 210 C 1520 99144 NO ES PERO BUENO MIRA AVER SI

The solution set to the inequality, -1/2m ≥ 7/11, is: m ≤ -14/11.

See attachment for the graph.

If the possible set of values to an inequality is "greater than or equal to" (≥), or "less than or equal to" (≤), then a closed circle is used to indicate the point on the graph.

On the other hand, an open circle is used for "< or >".

If it is "> or ≥" the shaded arrow is drawn to the right, if "< or ≤", it is drawn to the left of the inequality graph.

Given the inequality, -1/2m ≥ 7/11, solve for m:

-1/2m(-2) ≥ 7/11(-2)

m ≤ -14/11 [the sign changes because we are multiplying both sides by negative number]

The solution to the inequality is: m ≤ -14/11.

The graph is given below for m ≤ -14/11.

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Answer:

D

Step-by-step explanation: the answer is D with the arrow pointing to the left.

Hope this helps!

Answer:

[tex]g(x)=\dfrac{x^2+1}{3}[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=3x-1\\(f \circ g)(x)=x^2\end{cases}[/tex]

Composite functions are when the output of one function is used as the input of another.

Therefore, the given composite function (f o g)(x) means to substitute function g(x) in place of the x in function f(x).

[tex]\begin{aligned}(f \circ g)(x) & = x^2\\f(g(x)) & = x^2\\\implies 3(g(x))-1 & = x^2\\3(g(x))-1+1 & = x^2+1\\3(g(x))&=x^2+1\\\dfrac{3(g(x))}{3}&=\dfrac{x^2+1}{3}\\\implies g(x)&=\dfrac{x^2+1}{3}\end{aligned}[/tex]

Therefore:

[tex]\boxed{g(x)=\dfrac{x^2+1}{3}}[/tex]

Answer: y=x2+3x−1

Hope this helps! :)

Each person gets 1/12 fraction of the original cake.

What is a fraction?

A fraction, which derives from the Latin word fractus, which means "broken," is a portion of a whole or, more broadly, any number of equal pieces. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. A common, vulgar, or simple fraction is one that has a non-zero denominator shown below (or after) the line that separates the numerator from the denominator. Composite fractions, complicated fractions, and combined numeral fractions are examples of uncommon fractions that use numerators and denominators.

Each person gets = 1/2 x 1/6 = 1/12

Hence, each person gets 1/12 fraction of the original cake.

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Answer:

the formula for the vertex is f(x)=a(x-h)²+k

so if you replace -4= a(0-5)²+-2

so a=-0.08

The formula would end up like this f(x)=-0.08(x-5)²+-2

Step-by-step explanation:

The original price of the motorcycle is approximately $7,987.

Here, we are given that p represent the motorcycle’s original price.

The sale price of Dealer A will be-

7.5% less that the original price

= 92.5% of p

= 0.925p

Similarly, the sale price of dealer B will be-

$599 less than original price

= (p - 599)

Now, these two prices are equal, so we can equate the two-

0.925p = (p - 599)

0.925p = p - 599

0.925p - p = -599

-0.075p = -599

p = -599/-0.075

p = 599/0.075

p = 599000/75

p = 7,986.67

Thus, the original price of the motorcycle comes out to be approximately $7,987.

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The best plot for these results is given by:

C. Plot C.

The mean result for each group is given as follows:

Then we have to look at the vertical bars of each plot, and see the scores given.

For plot A, the scores are given as follows:

For plot B, the scores are given as follows:

For plot C, the scores are given as follows:

For plot D, the scores are given as follows:

Plot C has the closest value readings to the actual values of 36.8 and 52.4, hence it is the best option to plot the scores for each group.

The problem is missing and is given by the image at the end of the answer.

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The interval where the product will at least break even is [tex]$\left[\begin{array}{cc}\text { Solution: } & x \leq-5 \\ \text { Interval Notation: } & (-\infty,-5]\end{array}\right]$[/tex]

Given C= 305 x+1350C

R=60 x

To find the interval where the product will at least break even we must have [tex]$R(x) \geq c(x)$[/tex]

[tex]$\Rightarrow \quad 35 x \geq 305 x+1350$[/tex]

[tex]$$35 x \geq 305 x+1350$$[/tex]

Subtract 305 x from both sides

[tex]$$35 x-305 x \geq 305 x+1350-305 x$$[/tex]

Simplify

[tex]$$-270 x \geq 1350$$[/tex]

Multiply both sides by - 1 (reverse the inequality)

[tex]$$(-270 x)(-1) \leq 1350(-1)$$[/tex]

Simplify

[tex]$$270 x \leq-1350$$[/tex]

Divide both sides by 270

[tex]\frac{270 x}{270} \leq \frac{-1350}{270}$$[/tex]

Simplify

[tex]$$x \leq-5$$[/tex]

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

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Answer:

the first opinion is  the right answer

Step-by-step explanation:

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The Zero Product Property simply notes that if ab = 0, then either a = 0 or b = 0. The solutions exists x = -4, x = -2, x = 1.

The zero-product property in algebra asserts that two nonzero items cannot be multiplied together to produce zero.

The Zero Product Property simply notes that if ab = 0, then either a = 0 or b = 0 (or both). A product of factors exists zero if and only if one or more of the factors exists zero.

Let the given equation be (x+4)(x+2)(x-1)=0

By using the Zero Factor Principle, we get

If ab = 0 then a = 0 or b = 0

then x + 4 = 0 or x + 2 = 0 or x - 1 = 0

Solve x + 4 = 0

⇒ x = -4

Solve x + 2 = 0

⇒ x = -2

Solve x - 1 = 0

⇒ x = 1

The solutions are x = -4, x = -2, x = 1

Therefore, the correct options exists:

b) 1

c) -4

e) -2

The complete question is:

An equation is shown below.

(x + 4)(x + 2)(x - 1) = 0

Select all of the following values that make the equation true.

a) 4

b) 1

c) -4

d) 0

e) -2

f) 2

g) -1

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Suppose a life insurance company sells a $280,000 one year term life insurance policy to a 24 year old female for $290.Then The expected value of this policy to the insurance company is $168.76

Probability that Person doesn't die = 0.999567. Profit = Revenue - Cost; Profit = $290 - 0 = $290

Probability that Person dies = 1 - 0.999567 = 0.000433. Profit = Revenue - Cost; Profit = $290 - $280000 = -$279710

Expected Value E(X) = ∑xp(x)

E(X) = $290*(0.999567) + (-$279,710* 0.000433)

E(X) = $289.87443 - $121.11443

E(X) = $168.76

Thus, the expected value of this policy to the insurance company is $168.76

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Diameter = 13.93771776 cm

a.) In Line 1 Kylie made her error.

b.) Kylie's error is that she opened the bracket -2(x - 5) in the first line and did not change the negative sign to a positive sign as she multiplied -2 and -5 as a negative number multiplied by a negative number is a positive number.

c.) The correct solution to the problem is given by,

Given: 6x - 2(x - 5) = 22

6x - 2x + 10 = 22

4x = 22 - 10

4x = 12

x = 12/4

x = 3

Hence, the value of x is 3 and not 8.

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Step-by-step explanation:

the set of prime numbers that, when multiplied together, give

13824:

2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3

Answer:

24

Step-by-step explanation:

In a case whereby triangle ABC is congruent to triangle DEC, angle B = 2x + 31 and angle E = 7x - 24, the X is 11.

It should be noted that when a Triangles are exactly the same in term of size and shape then it is congruent.

Since the angle E and angle B is the same, then we can equate it so that we can find the value of X , then this can be calculated as

(2x + 31) = (7x - 24)

The we have

(7x - 2x) = (31 +24)

The we will have

(5x) =( 55)

Then

x = 11

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In a square, if the side is 8 cm and the square is having all its sides equal. Therefore, the area will be 8×8 = 64 cm²

Square: A plane-closed figure with four sides, having all four sides equal and connected with one another at 90° which creates four right angles.

unlike a rectangle that has both length and breadth and all sides are not equal, rather rectangle has two opposite sides equal.

if, length = breadth, this will result in the formation of a square.

Therefore, Breadth in the square doesn't exist as all sides are equal in the square. Area of a square = side× side

⇒ 8×8 = 64 cm².

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The expression that represents the distance is |-1/4 - 3/4|

From the question, the endpoints are given as

-1/4 and 3/4

Rewrite the endpoints properly

This is done as follows

Endpoint 1 =  -1/4

Endpoint 2 =  3/4

The distance expression between the endpoints is then calculated as

Distance = |Endpoint 1 - Endpoint 2 |

Substitute the known values in the above equation

So, we have the following equation

Distance = |-1/4 - 3/4|

Hence, the disance expression is |-1/4 - 3/4|

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0.020 is a probability for student selects at least 6 .

What is a probability simple definition?

There are two ways to do it. You can either interpret this as

One minus the probability that the student will guess 5 or fewer

correct answers with a probability of a correct answer being = 1/4  ⇒      

0.0197277069

The probability that the student will guess 4 or fewer wrong answers

with a probability of a wrong answer being = 3/4

  binomcdf (10,3/4,4)

     = 0.0197277069

Either way it rounds to 0.020

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We have to find the side of a square with a diagonal with length 12√10 ft.

We can sketch this as:

We can apply the Pythagorean theorem as:

Answer: the square side length is 12√5

Due to the fact that the line does not pass through the origin, the equation does not represent a proportionate relationship.

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.

Given Data

The remaining length (L) of 120-inch rope after x inches have been cut off: 120- x = L.

The fact that

If a relationship between two variables, x and y, can be written as or, then it represents a proportionate variation.

y = kx

The line passes through the origin, and the constant of proportionality, k, is equal to the slope of the line, m.

There are

The length (L) of a 120-inch rope that is left after x inches have been removed.

There are

The dependent variable is L —->. (output variable)

The independent variable is x. (input variable)

The linear formula is

L = 120-x

Due to the fact that the line does not pass through the origin, the equation does not represent a proportionate relationship.

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Answer:

This is the most optimal way to resolve the problem:

Step-by-step explanation:

15/n+2 = 3n/n

15/n+2 = 3

3 (n+2) = 15

n = 5 - 2

n = 3

The mathematical sentence can be written as:

3 = x/6

And the solution is x = 18.

Here we have the following mathematical sentence:

"three is a number divided by 6"

If we define x as the "number", then we can write this as:

3 = x/6

So we have a simple linear equation, to solve this, we just need to multiply both sides of the equation by 6, we will get:

3*6 = (x/6)*6

18 = x

We conclude that the solution is 6.

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Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

2([tex]\frac{2}{5}[/tex] ) + 2(- [tex]\frac{1}{5}[/tex] )

= [tex]\frac{4}{5}[/tex] + (- [tex]\frac{2}{5}[/tex] )

= [tex]\frac{4}{5}[/tex] - [tex]\frac{2}{5}[/tex]

= [tex]\frac{2}{5}[/tex]

Answer: C

Step-by-step explanation:

Starting off we need to understand what the circles are in inequalities.

A closed circle means that the number on the inequality is included in the solution. An open circle means that the number in the inequality is not included in the solution. A closed circle would use [tex]\leq or \geq[/tex]. An open circle would use < or >.

So, using these processes, -2<x[tex]\leq[/tex]7 would be the answer.

Answer:

y + 2 = -2(x - 2) (point-slope form)

y = -2x + 2 (slope-intercept form)

2x + y = 2 (standard form)

Step-by-step explanation:

[tex]m = \frac{ - 4 - ( - 2)}{3 - 2} = - \frac{2}{1} = - 2[/tex]

[tex]y + 2 = - 2(x - 2)[/tex]

[tex]y + 2 = - 2x + 4[/tex]

[tex]y = - 2x + 2[/tex]

[tex]2x + y = 2[/tex]