Solve this equation using the "Distributive Property".

[tex] \sf 3(x - 2) = 21[/tex]
​

The equation for the relation is [tex]p=k \frac{qr^2}{s}[/tex].

The value of k when q = 5, r = 4 and s = 6 is 3.

The value of p when q = 8, r= 6 and s= 9 is 96.

The value of s when p= 10, q=5 and r = 2 is 6.

A connection between two different items is called variation. There are two categories of difference. Direct Variation is the name of the first one. When two variables move in the same direction, direct variation occurs. Additionally, as one variable rises, the other variable rises as well. Inverse Variation is the second kind. When the two variables move in the opposite direction, inverse variation occurs. Additionally, this occurs when one variable rises while the other falls.

Since p varies directly as q and the square of r and inversely as s. So the equation will be [tex]p=k \frac{qr^2}{s}[/tex].

Now, finding the value of k, for p = 40 when q = 5, r = 4 and s = 6,

[tex]p=k \frac{qr^2}{s}\\40=k \frac{5\times4^2}{6}\\k = 3[/tex]

Now, finding the value of p when q = 8, r= 6 and s= 9,

[tex]p=3 \frac{8\times 6^2}{9}\\=96[/tex]

Now, finding the value of s when p= 10, q=5 and r = 2,

[tex]10=3 \frac{5\times 2^2}{s}\\\\10=3\times \frac{20}{s}\\s=6[/tex]

Therefore, the equation for the relation is [tex]p=k \frac{qr^2}{s}[/tex] , the value of k when p = 40 when q = 5, r = 4 and s = 6 is 3, the value of p when q = 8, r= 6 and s= 9 is 96 and the value of s when p= 10, q=5 and r = 2 is 6.

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The probability that the first drawing gives green ball and second drawing a red ball is 2/7

Number of green balls = 4 green balls

Number of red balls = 4 red balls

Total number of balls in the bag = 4 + 4

= 8 balls

The probability = Number of favorable outcomes / Total number of outcomes

The probability of getting green balls in first draw = 4 / 8

= 1/2

First ball drawn was not replaced before drawing the second one

The probability of getting red ball in second draw = 4 / 7

The probability that the first drawing gives green ball and second drawing a red ball = (4/8) × (4/7)

= 2/7

Hence, the  probability that the first drawing gives green ball and second drawing a red ball is 2/7

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The lower limit of the 95% confidence interval for the average miles per gallon is 23.32 mpg.

How to calculate the lower limit of the confidence interval?

Given,

n = 30

mean = μ = 24.1

standard deviation = σ = 2.1

confidence interval = 95%

Since the sample is 30, use t-table. If sample is greater than 30 use z-table.

Level of significance, α = 1 - 0.95 = 0.05

degree of freedom, df = n - 1 = 30 - 1 = 29

t value = 2.045

Lower limit = [tex]\mu-t\frac{s}{\sqrt{n}}[/tex]

= [tex]24.1 - 2.045\frac{2.1}{\sqrt{30}}[/tex]

= 24.1 - 0.784

= 23.316

= 23.32 mpg

Thus, the lower limit of the 95% confidence interval for the average miles per gallon is 23.32 mpg.

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Answer:

11

Step-by-step explanation:

Three times an unknown number

= 3(n)

Added to

Two less than four times the same unknown number

= 4 - 2(n)

Total

= 3(n) + 4 - 2(n) = 15

= 3n + 4 - 2n = 15

Collect like terms

= 3n - 2n = 15 - 4

n = 11

The equation of the line that passes through (-1, -1) and is parallel to x + y = 8 is x + y = -2

The equation of the line that passes through (-5, -2) and is parallel to y + 3x = 10 is 3x + y = -17

From the question, we are to determine the equation of the line passing through the given points and parallel to the given line.

NOTE: If two lines are parallel, then their slopes are equal

First, we will determine the slopes of the given line

x + y = 8

Write the equation in the slope-intercept form, y = mx + b

Where m is the slope

and b is the y-intercept

x + y = 8 becomes

y = -x + 8

Therefore, m = -1

Now, we will determine the equation of a line that has a slope of -1 and that passes through (-1, -1)

Using the point-slope form of the equation of a straight line,

y - y₁ = m(x - x₁)

y - (-1) = -1(x - (-1))

y + 1 = -1(x + 1)

y + 1 = -x -1

x + y = -1 -1

x + y = -2

Hence, the equation is x + y = -2

Now, we will determine the slope of y + 3x = 10

Express the equation in slope-intercept form

y + 3x = 10

y = -3x + 10

Therefore, m = -3

Now, we will determine the equation of a line that has a slope of -3 and that passes through (-5, -2)

Using the point-slope form of the equation of a straight line,

y - y₁ = m(x - x₁)

y - (-2) = -3(x - (-5))

y + 2 = -3(x + 5)

y + 2 = -3x - 15

3x + y = -15 -2

3x + y = -17

Hence, the equation is 3x + y = -17

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The surface area of box A is 240in².

the surface area of box B is 246in².

What is Surface area?

This is referred to as the space/ area occupied by a three- dimensional  object by its outer, flat surface of an object.

Formular for calculating surface area is:

Surface area, SA=( 2*L*W)+( 2*L*H) +=( 2*W*H)

where

Length, L

Height,H

Width,W

from the Question box A

L= 6in

W= 6in

H= 7in

Hence

Surface area, SA=( 2*L*W)+( 2*L*H) +=( 2*W*H)

             =( 2*6*6)+( 2*6*7) +=( 2*6*7)

          =72+84+84

          = 240in².

from the Question box B

L= 3in

W= 8in

H= 9in

Hence

Surface area, SA=( 2*L*W)+( 2*L*H) +=( 2*W*H)

                           =( 2*3*8)+( 2*3*9) +=( 2*8*9)

                              =48+54+144

                               = 246in².

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Answer:127.5

Step-by-step explanation:

15% of 150 = 22.5

150-22.5=127.5

Answer:

Step-by-step explanation:

The trigonometric function that can be used when given 2 sides that are not the hypotenuse is tangent.

When two sides are given that is not the hypotenuse, the trigonometric function that can be employed is the tangent.

A right-angle triangle has the following sides:

Hypotenuse

Adjacent side

the opposite side

The following trigonometric ratios can be used to determine the angles in a right-angle triangle:

sin = opposite/hypotenuse

cos = neighboring / hypotenuse

tan = opposite /adjacent

Tangent is the trigonometric function that can be used to determine the angle of a right-angle triangle given two sides other than the hypotenuse.

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The value of the number is 35

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values.These letters are called variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

If the number is represented by x then,

1x/5+3x= 2x+42

making the left hand side a single fraction, then,

(x+15x)/5= 2x+42

16x/5= 2x+42

multiply both sides by 5

16x= 10x+210

collect like terms

16x-10x= 210

6x= 210

x=35

therefore the value of the number is 35

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Step-by-step explanation:

b^3 x b^8 / b^5

b^11/b^5

b^(11-5)

b^6

Answer:

Area = 8 sq cm

Step-by-step explanation:

This shape is a parallelogram. Its like a rectangle that got tipped over. Area is:

base × height.

We don't know the base that is on the bottom of the image as it is shown. But if you turn it sideways, the 4 can be the base and the 2 is the height.

Area = b × h

= 4 × 2

= 8

The area is 8 sq cm.

a. The system of inequalities that models the situation is:

The equation for the cost is: C(x,y) = 0.2x + 0.4y.

b. The graph is given by the image at the end of the answer, and the vertices are (4,4), (10,4) and (10,7).

c. The number of clay beads and glass beads in a necklace that costs the least to make is: 4 clay beads and 4 glass beads.

The variables for the system are presented as follows:

Each necklace has no more than 10 clay beads and at least 4 glass beads, hence the constraints are listed as follows:

The numbers of each beads are countable amounts, meaning that they cannot assume negative values.

Four times the number of glass beads is less than or equal to 8 more than twice the number of clay beads, hence the final constraint is of:

4y ≤ 8 + 2x.

Each clay bead costs $0.20 and each glass bead costs $0.40, hence the cost function is given as follows:

C(x,y) = 0.2x + 0.4y.

Using the three constraints, the graph is given by the image at the end of the answer, and the vertices are as follows:

The minimum cost is at the vertex with the smallest numeric value of the cost function, hence the numeric values are listed as follows:

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The values of x= 10;  y= 5;  z= 20.

Given that

40 applied to the daily times only,

20 applied to the daily graphic only while

45 applied to the punch only.

To find out, if 15 applied to all the three newspaper establishment

I. the number that applied to both the daily times and daily graphic

II. the number that applied to the daily times and the punch.

III. the number that applied to both the daily graphic and the punch.

iv. the number that applied to at least one newspaper establishment.​

Given that:  DT (marked "T"),  70 & 40 (red circle).

       DG (marked "G"),  65 & 20 (green circle).

       P,                85 & 45 (blue circle).

x + y + 15 + 40 = 70

y + z + 15 + 45 = 85

x + z + 15 + 20 = 65

==========>

x + y = 15,       (1)

y + z = 25,       (2)

x + z = 30.       (3)

------------------------Add 3 equations  ====>

2x + 2y + 2z = 15 + 25 + 30 = 70  ====>

x + y + z = 35.   (4)

Subtract  (1)  from (4):  z= 20;

Subtract  (2)  from (4):  x= 10;

Subtract  (3)  from (4):  y=  5.

Hence the answer is the values of x= 10;  y= 5;  z= 20.

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Yes, the triangle with the given side lengths exists because the triangle inequality holds true.

At first, students might think that the lengths of the sides of a triangle can be any three lengths, but that is not so. The triangle inequality says that the length of any side must be less than the sum of the lengths of the other two sides.

We are given a set of three side lengths. The side lengths are 3, 4, and 5. We need to check whether a triangle can be formed using the given three side lengths. We will use the triangle inequality.

The first inequality is 3 + 4 > 5. This inequality holds true because 7 is greater than 5. The second inequality is 4 + 5 > 3. This inequality holds true because 9 is greater than 3. The first inequality is 5 + 3 > 4. This inequality holds true because 8 is greater than 4. The triangle inequality holds true, so a triangle with the given side lengths exists.

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The weight of the pig now is 54.9562 kg.

Given that the farm veterinarian, checked, a particular pig weighed 59.8 kilograms. Dr. Mason just weighed the pig again and found out that it weighs 8.1% less now.

The reduction will be:

= Percentage × Original weight

= 8.1% × 59.8

= 4.8438 kg

Therefore the weight of the pig will be:

= Original weight - Reduction

= 59.8 - 4.8438

= 54.9562 kg

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Answer:

below

Step-by-step explanation:

12 + 84/100   = 12.84

Total amount that Subway collect in franchise fees  = $2,189,250,000

Total number of subway franchisees = 42,000

Average annual store revenue           = $417,000

Total paying percentage of franchisees               = 12.5%

12.5% of average revenue = (417000×12.5)÷100

                                              = $52,125

Total subway collection in franchise fee= total number of franchisees×amount of fees per franchisees

                                         = 42,000×52,125

                                         = $2,189,250,000

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Since subways has about 42000 franchisees and about $417000 average revenue is earned. Therefore, the total amount that Subway collect in franchise fees is $2,189,250,000.

Subways Franchise operate 16 submarine sandwich shop and they expanded quickly with its long time slogan "East Fresh".

Franchisor gives a franchisee the authority to do business in the franchisor's trade name using its business system it is called franchising.

Subways franchises pay 12.5% every week (gross sales minus the sales tax), 8% goes toward the franchise royalties and 45% gores towards advertising.

The company has the lowest start-up costs compared to many other fast food franchises but does take more royalty and advertising money.

The franchise fee:

Now, according to the question:

Total number of subway franchisees = 42,000

Average annual store revenue = $417,000

Total paying percentage of franchisees = 12.5%

∴ At 12.5% of average revenue = (417000 × 12.5) ÷ 100

                                                    = $52,125

Total subway collection in franchise fee

= total number of franchisees × amount of fees per franchises

= 42,000×52,125

= $2,189,250,000

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The height of the tree was 56 inches.

We can calculate the percentage of a certain amount by :

Subtracting  New - Original / New multiplied by 100

this implies it will be

75 - x / 75 × 100 = 25 %

7500 - 100 x = 1875

this implies 7500 - 1875 = 100 x

5625 = 100 x

Thus , On dividing both sides by 100 we get

56.25 = x

Now on rounding off this number we will get

56 = x

Thus the original height of the corn plant was 56 inches

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Answer:

P(D) = 0.7

Step-by-step explanation:

There are two routes to D:

We then add these two probabilities:

AD + BD = (0.5*0.6) + (0.5*0.7) = 0.3 + 0.35 = 0.7

Therefore, P(D) should be 0.7, or 70%

From the given graph we get, the coordinates of original P are (-6,-6).

So initial x=-6 and y=-6

Also from the graph we can see that the coordinates of transformed point P' are (-1,3)

So now, (-1,3) = (-6+5,-6+9) = (x+5,y+9)

Hence the first and second box are 5 and 9 respectively.

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A farmer has 180 bushels of wheat to sell at her roadside stand. She sells an average of 14 5/8 bushels each day.

The total change in the number of bushels she has for sale after 5 days can be represented as [tex]\frac{117}{8} X 5[/tex].

Define average.

The average is defined as the mean value, which is equal to the ratio of the sum of the number of values in a given set to the total number of values present in the set.

In plain English, an average is a single number taken as representative of a list of numbers, typically the sum of the numbers divided by how many numbers are in the list. For instance, the average of the digits 2, 3, 4, 7, and 9 is 5.

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Answer:

e and c

Step-by-step explanation:

both are the exact same size, which would allow them to be placed on top of each other without any overlap

Answer:

A, B and E are the correct answers

Step-by-step explanation:

I had that same question on the test too.

Rewrite [tex]x^4y^2-3x^3y^3[/tex] using a common factor.

A) [tex]3xy(x^3y-x^2y)[/tex]

B) [tex]3xy^2(x2-x^2y)[/tex]

C) [tex]x^2y(xy-3xy^2)[/tex]

D) [tex]x^2y^2(x^2-3xy)[/tex]

option d

The equation of the line parallel to 2x + 2y = -12 that passes through the point (2,-7) is y+7= -(x - 2)  , the correct option is (b)  .

In the question ,

it is given that ,

the equation of the line is parallel to 2x + 2y = -12 ,

2x + 2y = 12

2y = -2x + 12

Dividing both sides by 2  , we get

y = -x + 6

So , the slope of the line is -1 ,

since the required line is parallel , so the slope of the required line is -1 .

So , the equation of the line passing through the points (2,-7) with slope -1 is

(y - y₁) = m(x - x₁)

(y -(-7)) = -1(x - 2)

y + 7 = -1(x - 2)

y + 7 = -(x - 2)

Therefore , The equation of the line parallel to 2x + 2y = -12 that passes through the point (2,-7) is y+7= -(x - 2)    .

The given question is incomplete , the complete question is

Find the equation of a line parallel to 2x + 2y = -12 that passes through the point (2, -7) ?

(a) y+7=x-2

(b) y+7= -(x - 2)

(c) y-7=x+2

(d) y-7= -(x + 2)

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Answer:

Step-by-step explanation:

Exact Form: 6/5

Decimal Form : 1.2
Mixed Number Form : 1 (whole number) 1/5

The measure of missing angles in the diagram is angle 1 = 88°, angle 2 = 42° and angle 3 = 113°  .

In the question ,

a figure is given ,

the labelled diagram is show below .

we can see that the angle ACB and angle ECD are vertically opposite angles ,

we know that, the vertically opposite angles are equal ,

So, angle ACB = m∠2 = 42°

In triangle ABC

By Angle Sum Property Of Triangle ,

angle A + angle B [tex]+[/tex] angle C [tex]=[/tex] 180°

50° + m∠1 + 42° [tex]=[/tex] 180°

92° + m∠1 = 180°

m∠1 = 180° - 92°

m∠1 = 88°

In triangle CDE ,

By Angle Sum Property Of Triangle

angle C + angle D [tex]+[/tex] angle E [tex]=[/tex] 180°

42° + m∠3 + 25° [tex]=[/tex] 180°

m∠3 + 67° = 180°

m∠3 = 180° - 67°

m∠3 = 113°

Therefore , The measure of angle 1 = 88°, angle 2 = 42° and angle 3 = 113°  .

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Answer:

[tex]y = 2x - 5[/tex]

Step-by-step explanation:

The first step in finding the equation of a line from a given set of points is to find its slope. The slope of a line is defined by the formula:

[tex]m = \dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

In this problem, we are given two points in the form [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].

So, we can define the x's and y's as:

[tex]x_1 = 3[/tex], [tex]y_1 = 1[/tex], [tex]x_2 = 1[/tex], [tex]y_2 = -3[/tex].

Hence, the slope of the line can be solved for.

[tex]m = \dfrac{-3 - 1}{1 - 3}[/tex]

[tex]m=\dfrac{-4}{-2}[/tex]

[tex]m = 2[/tex]

So, the slope of the line is 2.

Now, we can plug this into the point-slope equation for a line where (a, b) is a point on the line and m is its slope.

[tex]y - b = m(x - a)[/tex]

I will use the point (3, 1):

[tex]y - 1 = 2(x - 3)[/tex]

and isolate y to put it into slope-intercept form.

[tex]y - 1 = 2x - 6[/tex]

[tex]y = 2x - 6 + 1[/tex]

[tex]y = 2x - 5[/tex]

So, the equation in slope-intercept form for the line that goes through the points (3, 1) and (1, -3) is [tex]y = 2x - 5[/tex].

Answer:

36a^10

Step-by-step explanation: