1. Jacob wants to buy chocolate spread. There are 8-oz container of
chocolate spread for $0.56 or a 32-oz container of chocolate
spread for $2.56. Which one is a better buy? (Which one has a lower
unit rate?) (5 points).
The
container has a lower unit rate.

Answer:

Contract

Step-by-step explanation:

The number of boxes containing both pens and pencils is 2.

What is set?

A set is defined as a well-defined collection of distinct objects. It is denoted by the capital letters of the English alphabet. Its value remains the same for every individual.

Calculation for the number of boxes containing both pens and pencils

Total number of boxes is given by the union of two sets A and B; i.e. A∪B= 20

Boxes having pencils is given by the set A = 13

Boxes having pens is given by the set B = 9

Boxes having neither pens nor pencils, A'∩B' = 3

Boxes containing both pens and pencils are given by the intersection of the sets, A∩B

A∩B = A + B - A∪B

= 13 + 9 - 20

= 2

Hence, the number of boxes containing both pens and pencils is 2.

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[tex]f( - 4) = - 122[/tex]

And

[tex]g(5) = - 21[/tex]

Step-by-step explanation:

Greetings !

For the first expression

[tex]f(x) = 2x {}^{3} + 6[/tex]

plug in -4 at the variable x and solve the expression.

[tex]f( - 4) = 2( - 4) {}^{3} + 6[/tex]

Follow the PEMDAS order of operations

calculate the exponents

[tex]( - 4) {}^{3} = - 64[/tex]

Apply exponent rule

[tex]( - a) {}^{n} = - a {}^{n} . \: if \: n \: is \: odd[/tex]

Thus,

[tex]( - 4) {}^{3} = - 4 {}^{3} = - 64[/tex]

Multiply and divide (left to right )

[tex]2( - 64) = - 128[/tex]

[tex] = - 128 + 6 \\ = - 122[/tex]

Fairly follow the same. process for the second function

Hope it helps !!

Answer:

360 - 6r

Step-by-step explanation:

just simplify the expression

x ≤ 7 days is the maximum number of days Faith can afford to rent while staying within her budget.

When you take a single number and multiply it by several, you are multiplying. There are a number distinct indications of amplification that people utilize. The "x" sign represents the most typical, however, other symbols like the "*" sign are also occasionally used.

Information that is given

Renting a car from a rental car agency costs $62.12 per day plus $0.05 for every mile traveled.

Considering that she will be traveling 500 miles,

She can only spend up to $440.

Assume that the number of days will be x

cost per day will be 62.16 × x

Miles per day will be 0.05 × 500

The inequality used will be

62.16x + 0.05 × 500 ≤ 500

62.16x ≤ 500 - 25

62.16x ≤ 475

x ≤ 475 ÷ 62.16

x ≤ 7.64 days

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Answer:

scale factor = 3

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, copy to original , so

scale factor = [tex]\frac{12}{4}[/tex] = [tex]\frac{9}{3}[/tex] = 3

Answer:

See below

Step-by-step explanation:

The most important info is the rate ft^2 / min and how many minutes it took to mow.

From this, we need to know how much total area there is. We do this by multiplying the rate by the time.

[tex] \frac{ 4{ft}^{2} }{minute} \times 29minutes = 116 {ft}^{2} [/tex]

Then we need to write out the sum of the whole area in terms of length times width

[tex]6ft \times 14 ft + x \times 4ft = 116 {ft}^{2} [/tex]

Notice how we put x for the unknown variable, this turns it into an easy peasy algebra problem. I leave that to you, solve for x

If a researcher wishes to conclude something about a population from a sample, it is best that the sample be taken randomly.

Sampling is the process by which a representative number is taken from a population for the purpose of study. The sample must be taken in such a way that it reflects the properties of the whole.

Thus, if a researcher wishes to conclude something about a population from a sample, it is best that the sample be taken randomly.

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The value of k  such that a is singular is ±√(5/2).

If a singular matrix's determinant is 0, it is a square matrix. Specifically, if and only if det A = 0, a square matrix A is unique. We are aware that the formula A-1 = (adj A) / can be used to get the inverse of a matrix A. Here, the denominator contains det A, which is the determinant of A. We are aware that a fraction with a denominator of 0 is not defined. Since det A = 0, A-1 is not defined. In other words, a single matrix's inverse is not defined. That is to say, there isn't a matrix B such that AB = BA = I.

A singular matrix means that the detA should be 0.

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Answer:

find the value of x file attached x9

Answer:

Step-by-step explanation:

The number of days took by Rita to travel the distance of 1,875 miles is 4.5 days.

We will learn how to calculate the value of such a unit from value of a multiple and thus the value of a multiple from value of a unit using the unitary method.

Now, as per the given question;

The total day taken by Rita to cover 1,250 miles is 3.

Thus,  1250 miles ----> 3 days

Let number of days taken by Rita to cover 1875 miles is 'x'.

So, 1875 miles ----> x

Then, the total distance will be

1875×(3) = 1250x

x = (1875×3)/1250

x = 4.5 days

Therefore, the total time taken by Rita to finish the distance of 1,875 miles is 4.5 days.

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The variable that would be the best choice when Pearce needs to choose a variable to represent the number of wallabies in an exhibit will be D. let w= the number of wallabies on the exhibit.

It should be noted that a variable simply means a symbol that's used to represent a situation in mathematics.

In this case, the variable that would be the best choice when Pearce needs to choose a variable to represent the number of wallabies in an exhibit so be let w= the number of wallabies on the exhibit.

This is because of the first alphabet used which is w.

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In some base [tex]B[/tex], we have

[tex]abab_B \equiv 555_{10}[/tex]

so that

[tex]aB^3 + bB^2 + aB + b = 555[/tex]

Factorize the left side.

[tex]aB (B^2 + 1) + b (B^2 + 1) = 555[/tex]

[tex](aB + b) (B^2 + 1) = 555[/tex]

Now, [tex]B[/tex] is a positive integer greater than 1, and [tex]a,b[/tex] are positive integers taken from [tex]\{0,1,2,\ldots,B-1\}[/tex]. So consider the prime factorization of 555 on the right side.

[tex](aB + b) (B^2 + 1) = 3\times5\times37[/tex]

which we can write as

[tex](aB + b) (B^2 + 1) = 15\times(6^2 + 1) = (2\times6 + 3) \times (6^2+1)[/tex]

and so the base is 6, and the number in question is 2323₆.

Answer:

21

Step-by-step explanation:

.75 x 28 = 21

Sash's elevation is -8/3 miles with respect to the sea level, by basic algebra.

Now,

Given:

To find: Sasha's elevation in miles?

Finding:

=> She will be down by 4 (2/3) = 8/3

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Answer: A=30 degrees, B=60 degrees, C=90 degrees

Step-by-step explanation:

B=2A

C=3A

A+B+C=180

A+2A+3A=180

6A=180

A=30 degrees

B=2A

B=2(30)

B=60 degrees

C=3(30)

C=90 degrees

Answer:

Angle A = 30°

Angle B = 60°

Angle C = 90°

Step-by-step explanation:

Let x represent the measure of A. Using this information, we can figure out the measure of B and C in terms of x.

Since B is twice the measure of A, then it would be 2x. Similarly, C is three times the measure of A, thus it would b 3x.

We also know that the sum of the angles is 180 degrees. We can use this information to set up an equation.

We know that:

Angle A + Angle B + Angle C = 180

Substituting the values we gave for A, B, and C, we find:

x + 2x + 3x = 180

Now, we solve the equation for x.

Start by combining like terms:

6x = 180

Now, divide both sides by 6:

x = 30

Since we know the value of x, we can find the values of the angles.

A = x = 30°

B = 2x = 60°

C = 3x = 90°

The parametric equation of the line that passes through the points (5,2,7) and (8,–6,1) is [tex]\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]

Also, the point (17,–30,31) does not lie on the line.

for given question,

We need to find the parametric equation of the line that passes through the points (5,2,7) and (8,–6,1)

Let [tex]\vec r_0= < 5,2,7 >[/tex]

and

[tex]\vec v= < 8-5,-6-2,1-7 > \\\\\vec v= < 3,-8,-6 >[/tex]

where vector v is the direction vector.

So, the equation of the line would be,

[tex]\vec r=\vec r_0+\lambda \vec v\\\\\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]

Now we need to determine whether the point (17, -30, 31) is on the line.

Let [tex]< 17,-30,31 > = < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]

For first component,

⇒ 17 = 5 + 3λ

⇒ 3λ = 12

⇒ λ = 4

For the second component,

⇒ -30 = 2 - 8λ

⇒ -8λ = -32

⇒ λ = 4

For third component,

⇒ 31 = 7 - 6λ

⇒ -6λ = 24

⇒ λ = -4

since the values of the λ are not consistent, the point (17,–30,31) does not lie on the line.

Therefore, the parametric equation of the line that passes through the points (5,2,7) and (8,–6,1) is [tex]\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]

Also, the point (17,–30,31) does not lie on the line.

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According to the question, the line is through the points [tex](0,5)[/tex] and [tex](-2,11)[/tex]

To calculate the slope using standard formula that is :

[tex]m = \frac{(y(2)-y(1))}{(x(2)-x(1))} = \frac{(11-5)}{(-2-0)} =\frac{6}{-2} = -3[/tex]

Now the slope equation will be: [tex]m(x(2)-x(1)) = (y(2)-y(1))[/tex]

[tex]y-5 =(-3)(x-0) = y = -3(x)+5[/tex]

The slope-intercept form is:[tex]y = -3x+5[/tex]

What is the equation of the line?

To represent the set of points in an algebraic form is known as the equation of line. The set of points represent lines in the coordinate system. The parameters can be calculated and those parameters are slope and y-intercept.

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The proportional relationships for these problems are given as follows:

18. y = 0.5x, with constant k = 0.5.

22. y = -0.4x, with constant k = -0.4.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In item 18, we have that when x = 2, y = 1, hence the constant is:

k = y/x = 1/2 = 0.5.

Hence the equation is:

y = 0.5x.

In item 22, we have that when x = -5, y = 2, hence the constant is:

k = y/x = -2/5 = -0.4.

Hence the equation is:

y = -0.4x.

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If Point B [tex](3,1)[/tex] has translated 2 units to the right and 1 unit up, new coordinates of point B' are [tex](5,2)[/tex]

As per the question statement, Point B [tex](3,1)[/tex] is there on a cartesian plane. Point B is translated 2 units to the right and 1 unit up.

Before solving this question, we need to know about cartesian plane system in which, there are four quadrants which are made using positive and negative axes known as positive X and negative X (same for Y axis).

Now point B[tex](3,1)[/tex] lies in the first quadrant and value "3" describes the location of point on X axis and value "1" describes the location of point on Y axis.

If point B [tex](3,1)[/tex] is translated 2 units to the right and 1 unit up, the locations of X and Y axes will change to value "5" on X axis and value "2" on Y axis.

Hence the coordinates of point B' are [tex](5,2)[/tex]

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The value of the given quadratic equation are = x = -(6/5) , x = 2

Quadratics are polynomial equations of the second degree, which means they have at least one squared term. It is also known as quadratic equations. The quadratic equation has the general form: ax2 + bx + c = 0.

Quadratic functions occupy a distinctive place in the school curriculum. They are functions whose values are easily estimated from input values, therefore they are a modest improvement over linear functions and provide a major shift away from attachment to straight lines.

Given (5x + 6)(3x - 6) = 0

Using the zero factor principle: if ab = 0 then a = 0 and b = 0

So,

(5x + 6) = 0 or (3x - 6) = 0

for the (5x + 6):

(5x + 6) = 0 (subtracting both side by 6)

5x + 6 - 6 = 0- 6

so, x = -(6/5)

Same calculation for (3x - 6) = 0 we get x = 2

The value of the given quadratic equation are = x = -(6/5) , x = 2

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The Option A best explains the dual experiments: "In the experimental group, a chosen variable is altered in a known way. In the control group, that chosen variable is not altered so a comparison can be made."

Now,

Hence, amongst all the given options, The Option A best explains the dual experiments: "In the experimental group, a chosen variable is altered in a known way. In the control group, that chosen variable is not altered so a comparison can be made."

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The missing step in the rational number proof is; Reason 2; Multiply to get a common denominator

Let  a/b and c/d be two rational numbers, where b and d are not zero and a, b, c and d are integers.

Step 1; a/b + c/d

Reason 1; Given

Step 2; a/b + c/d = ad/bd + cb/bd

Reason 2; Multiply to get a common denominator

Step 3; a/b + c/d = ad/bd + cb/bd = (ad + cb)/bd

Reason 3; Simplify

Since b and d cannot be zero, then bd cannot be zero. Also, since a, b, c, and d are integers, then bd, ad, bc and ad + bc are integers too. Thus, the fraction(ad + cb)/bd is a rational number.

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Answer:

v= 0

6(2-0)+2(4)=20 is the simplified version of the equation.

After estimating 48 ÷ 7, we get the result as 7.

We are given an expression

48 ÷ 7

We need to estimate the result.

First, we will divide 48 by 7

So, we get that:

48 ÷ 7 = 6.857

Now we will estimate it.

We will round of the result.

as 6 > 5, we will get it as:

48 ÷ 7 ≈ 7

Therefore, after estimating 48 ÷ 7, we get the result as 7.

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Answer:

the answer is -2, substitution took place tht is why w turned to -w

Step-by-step explanation:

-W=9 - 7

-W= 2.

W=-2

Answer: let's see... the coefficient of a number is Placed in front of a variable like 2y. so it's 2y

Step-by-step explanation: your welcome