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The quotient of a-3/7 / 3-1/21 is 3/2(a - 3)

The quotient of a-3/7 / 3-a/21 is -3

From the question, we are to determine the quotient of the given division operation.

The given division operation is

a - 3/ 7 / 3 -1 / 21

That is,

a - 3/ 7 ÷ 3 -1 / 21

This becomes

a - 3 / 7 × 21 / 3 -1

a - 3 / 7 × 21 / 2

3(a - 3) / 2

= 3/2(a - 3)

If we are to find the quotient of

a - 3/ 7 / 3 -a / 21

This becomes

a - 3/ 7 ÷ 3 - a / 21

a - 3/ 7 × 21 / 3 - a

21(a -3) / 7(3 - a)

3( a - 3) / (3 -a )

Multiply the numerator and the denominator by -1

-1 × 3( a - 3) / -1 × (3 -a )

-3( a - 3) / (-3 + a)

-3( a - 3) / (a - 3)

= -3

Hence, the quotient is -3

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Using percentage we can calculate that the team is expected to lose 4 matches.

A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. Although the abbreviations "pct," and occasionally "pc" is also used, the percent symbol "%" is most frequently used to denote it. A percentage is a number without any dimensions or established units of measurement.

By dividing the value by the entire value and multiplying the result by 100, the percentage may be computed. Calculating percentages using the formula (Value/Total Value)×100%.

Given in percentages the team will win 65% , team will draw =15%

Therefore in percentage the team will lose = 100 - ( 65 + 1 5 )% = 20 %

Now calculating the total number of matches the team will lose :

20% of 20 matches = 4 matches

Hence the team is expected to lose 4 matches out of 20.

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The equation for  the number of athletes who do not play basketball is x = 107 - 81

Athletes surveyed = 107 athletes

Athletes who play basketball

Athletes who play baseball = 48 athletes

Athletes who don't play baseball = 33 athletes

Athletes who play basketball will be:

= athletes who play baseball + athletes who don't play baseball

= 48 + 33.

= 81

Total athletes = Athletes who play basketball + Athletes who don't play basketball

107 = 81 + x

x = 107 - 81

x = 26

The value is 26.

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The most appropriate choice for unitary method will be given by

Total cost of 200g raspberries and 200 g strawberries is £4.14

What is unitary method?

It is the method by which we find the value of single unit form the value of multiple unit and value of multiple unit from the value of single unit.

Here,

500 g of strawberries cost £4.10

1 g of strawberries cost £[tex]\frac{4.10}{500}[/tex]

300 g of strawberries cost £[tex]\frac{4.10}{500} \times 300[/tex]

                                           = £2.46

400 g of raspberries 300g of strawberries cost a total of £7.46

Let the cost of 400 g of raspberries be  £x

so,

x + 2.46 = 7.46

x = 7.46 - 2.46

x =  £5

cost of 400 g of raspberries =  £5

cost of 1 g of raspberries =  £[tex]\frac{5}{400}[/tex]

cost of 200 g of raspberries =  £[tex]\frac{5}{400} \times 200[/tex]

                                                = £2.5

cost of 300 g strawberries = £2.46

cost of 1 g strawberries = £[tex]\frac{2.46}{300}[/tex]

cost of 200 g of strawberries = £[tex]\frac{2.46}{300} \times 200[/tex]

                                                 = £1.64

Total cost of 200g raspberries and 200 g strawberries = £(2.5 + 1.64)

                                                                                            = £4.14

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Complete question

400 g of raspberries and 300 g of strawberries cost a total of £7.46.

500 g of strawberries cost £4.10.

Work out the total cost of 200 g of raspberries and 200 g of strawberries.

Answer:

Hope I helped you with this. Everything is explained in the photo

The value of the expression 2y + 2y² when y = 4 is 40.

It should be noted that in Mathematics, an expression simply means the finite combination that is formed according to a specific rule. It should be noted that an expression must have variables that are connected by the operator.

In this case, the expression given in the question is:

2y + 2y².

where y = 4

We have to put y = 4 into the expression. This will be:

2y + 2y².

2(4) + 2(4)²

= 8 + 32

= 40

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Step-by-step explanation:

pure acid is a 100% acid solution.

x = ml of 100% solution

1×x + 0.3×400 = 0.75×(400 + x)

x + 120 = 300 + 0.75x

0.25x = 180

x = 720 ml

we must add 720 ml of pure acid to the 400 ml of 30% solution to create a 75% solution (1,120 ml in total).

Answer:

4(x+

Step-by-step explanation:

8(x+3)^2/2(x+3)

[8(x + 3)(x + 3)]/2(x + 3)

8 ÷ 2 = 4

(x + 3)(x + 3) ÷ (x + 3) = (x + 3). In other words, we cancel one of the numerator factors.

Answer: 4(x + 3).

Answer:

4(x + 3)

or 4x + 12.

Step-by-step explanation:

8(x + 3)^2/ 2(x + 3)

x + 3 is common to both numerator and denominator of the fraction so they simplify to (x + 3)^2 / (x + 3) = (x+3).

the answer is 8 * (x + 3) / 2

= 4(x+ 3).

If a cylindrical barrel has a radius of 5.7 ft and a height of 8.4 ft, tripling the height of the concerned barrel will triple up its current volume.

As per the question statement, a cylindrical barrel has a radius of 5.7 ft and a height of 8.4 ft.

We are required to determine the dimension or dimensions which on tripling, will triple up the current volume of our question-mentioned barrel.

To solve this question, first we need to know the formula to calculate the volume of a cylinder, which goes as (π * r² * h)

Where [π = (22/7)], (r = radius of the cylinder)

And, (h = height of the cylinder).

Here, (r = 5.7 ft) and (h = 8.4 ft).

Now, considering [V = (π * r² * h)], where, ["V" is the volume]

if we triple our radius "r", our Volume "V₁" will become {π * (3r)² * h}

or, V₁ = 9πr²h

or, V₁ = 9(π * r² * h)

or, V₁ = 9V,

That is, 9 times the current volume. Hence, tripling the radius will not triple up the current volume of our concerned barrel.

Now, considering we triple our height "h", our Volume "V₂" will become {π * r² * 3h}

or, V₂ = 3πr²h

or, V₂ = 3(π * r² * h)

or, V₂ = 3V,

That is, 3 times the current volume. Hence, tripling the height will triple up the current volume of our concerned barrel.

As Proof,

Current Volume of our barrel = [(22/7) * (5.7)²* (8.4)]

                                                 = 857.74 ft²

And Volume of our barrel tripling the height = [(22/7) * (5.7)²* (3*8.4)]

                                                                          = 2573.21 ft²

And, (2573.21/857.74) = 3.

Therefore,  tripling the height of the concerned barrel will triple up its current volume, thus Proved.

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Answer:

x ≈ 15

Step-by-step explanation:

using Pythagoras' identity in the right triangle

a² + b² = c²

with a = 8, b = x , c = 17

8² + x² = 17²

64 + x²  = 289 ( subtract 64 from both sides )

x² = 225 ( take square root of both sides )

[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{225}[/tex]

x = 15

Based on the first entry level web developer salary paid, and the new work year, the amount the web developer can expect his annual pay to decrease by is $2,190

First, find the weekly pay of the web developer in the first salary:

= 56,940 / 52

= $1,095 per week

The new salary of the web developer as a result of the work week becoming 50 weeks is:
= 1,095 x 50

= $54,750

The decrease in this annual pay to the web developer is:

= 56,940 - 54,750

= $2,190

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The solution to the given inequalities is -7 < x ≤ 6. The graph of the inequality is shown below on a number line.

From the question, we are to solve the given inequalities

The given inequalities are

-3x - 7 < 14 and -25 ≤ -3x - 7

Solving -3x - 7 < 14

-3x - 7 < 14

Add 3x to both sides of the inequality

-3x + 3x - 7 < 14 + 3x

-7 < 14 + 3x

Subtract 14 from both sides

-7 - 14 < 14 - 14 + 3x

-21 < 3x

Divide through by 3

-21/3 < 3x/3

-7 < x

Solving -25 ≤ -3x - 7

-25 ≤ -3x - 7

Add 3x to both sides

-25 + 3x ≤ -3x + 3x - 7

-25 + 3x ≤ - 7

Add 25 to both sides

-25 + 25 + 3x ≤ - 7 + 25

3x ≤ 18

Divide through by 3

3x/3 ≤ 18/3

x ≤ 6

Thus,

The solutions to the inequalities are

-7 < x and x ≤ 6

That is,

-7 < x ≤ 6

The number line is shown below

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Answer:

-1

Step-by-step explanation:

You just have to divide the change in the x axis by change in the y axis on any arbitrary interval.

Answer:

-1

Step-by-step explanation:

Do rise-over-run for linear equations. Its the vertical change over the horizontal change between two points. Ex. between (-2,0) and (-1,-1) the line drops 1 unit horizontally (-1) and moves to the right one unit (1) so the slope would be -1/1 = -1

Answer: L - 7 because 35/5

Answer:

The length is 7 cm

Step-by-step explanation:

The area of a rectangle is given by

A = l*w  where l is the length and w is the width

35 = l*5

Divide each side by 5

35/5 = l*5/5

7 = l

The length is 7 cm

By using the equation for the line of best fit, the salary for an employee who has seven (7) years of experience is: D. $55,573.

A line of best fit is a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between a data.

In this scenario, the employee's salary would be plotted on the y-axis of the scatter plot while the years of experience would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the data in the given table, an equation for the line of best fit is given by:

y = 2233.3x + 39940

Next, we would use the above equation for the line of best fit to predict the salary for an employee with 7 years of experience:

y = 2233.3(7) + 39940

y = 15,633.1 + 39940

y = 55,573.1 ≈ $55,573.

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The scale factor that is used for student is running for president of student government is 1:54.

From the information, her friend has designed a campaign poster that measures 27 feet by 14 feet and she duplicated the poster on a

rectangular button measuring 6 inches by 3 1/9 inches.

1 feet = 12 inches

27 feet = 27 × 12 = 324 inches.

The scale factor will be the division of the values and this will be:

= 6/324

= 1/54

The scale factor is 1:54.

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Probability for the sample mean to have been 18.2 ounces or larger = 0.0003

Sample size, n = 30 boxes

Sample mean, [tex]\bar x[/tex] = 18.2 ounces

Population mean, μ = 18 ounces

Standard deviation of the population, σ = 0.32 ounces

We assume that this follows normal distribution.

Then the z-score, z = [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

                                = [tex]\frac{18.2-18}{\frac{0.32}{\sqrt{30}} }[/tex]

                                = 3.42

This z-score follows Standard Normal Distribution with mean = 0 and standard deviation = 1

Probability for the sample mean to have been 18.2 ounces or larger =

P(z ≥ 3.42) = 0.5 - P(0 < z < 3.423)

                  = 0.5 - 0.4997

                  = 0.0003

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Answer:Two lines are parallel if the have the same slope. To find the slope of the line parallel to the line y=4/7x-2 we need to get the line into slope-intercept form (y = mx + b), but the line is already in that form, so the slope is m = 4/7.

Step-by-step explanation:

Answer:

rational

number

Step-by-step explanation:

because any decimal number that repeats forever can be written as a fraction and any number that can be written as a fraction is rational

a number is any value that has no variables

a whole number is a positive value that is not a decimal

an integer is also any whole value

Answer:

6

Step-by-step explanation:

Answer: x=5/2

Step-by-step explanation:

JK=NO

2x+6=11

2x+6-6=11-6

2x=5

x=5/2

The probability of someone being 5 feet and 4.2 inched tall is 0.2877

Probability:

Probability means the possibility of occurring the specific even across the total number of event.

Given,

100 people where sampled and their heights were recorded, it was discovered the mean height was 5 feet and 6.3 inches with a standard deviation of 3.75 inches.

Here we need to find the the probability of someone being 5 feet and 4.2 inches tall.

From the given details, we know that,

n = 100

mean (ч) = 5 feet and 6.3 inches

standard deviation (σ) = 3.75 inches

We know that the formula to find the probability is,

P = (x - ч)/σ

But here we have used the different measurement for each. So, the first step is convert them into inches.

So,

5 feet and 6.3 inches = 60 + 6.3 inches = 66.3 inches.

Similarly 5 feet and 4.2 inches = 64.2 inches.

So, the probability is,

P (X < 64.2) = (64.2 - 66.3)/3.75

P (X < 64.2) = -0.56

Based on the standard normal table to conclude that:

P (X < 64.2) = -0.56 = 0.2877

Therefore, the probability of someone being 5 feet and 4.2 inches tall is 0.2877.

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Check the picture below.

Answer:

88

Step-by-step explanation:

[tex]\frac{u}{8}-4=7 \\ \\ \frac{u}{8}=11 \\ \\ u=88[/tex]

Answer:u=88

Step-by-step explanation:

The distance between the sides of the right-angled triangle is given as follows:

Recall that a right-angled triangle is one that has at least one side equal to 90°

In the question, we know the endpoints and the line hypothenus. To find the length of the hypothenuse, we can state:

Distance = [tex]\sqrt{(x2 - x1)^{2} +(y2 - y1)^{2} }[/tex]

Recall that the distance between the two points is given as (−2,4) for first point and (7,−8) for the second point.; Hence:

Distance = √[(-2+7)²+ (4+-8)²]

Distance = √(5²) + (-4)²
Distance = √(25+16)
Distance  = √41

Hence the third point is (-2-8).

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Main Answer:

Number of students in Lincoln high school is [tex]4w-75[/tex]

Explanation:

Number of students in Washington high school = w

Number of students in Lincoln high school = 75 less than four times number of students in Washington high school

Therefore, number of students in Lincoln high school = [tex]4w-75[/tex]

Answer:

2/5

Step-by-step explanation:

40%= 40/100 = 4/10 = 2/5

Answer:

2/5

Step-by-step explanation:

Simplest form:

       [tex]\sf 40 \%= \dfrac{40}{100}=\dfrac{4}{10}=\dfrac{2}{5}[/tex]

The angle B has a measure of  121 degrees

Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines

The angles are given as

A = 2x + 29

B = 3x - 17

Also, we have:

The angles are vertical angles

Vertical angles are congruent angles

This means that

A = B

So, we have

2x + 29 = 3x - 17

Evaluate the like terms

x = 46

Substitute x = 46 in B = 3x - 17

B = 3 x 46 - 17

Evaluate

B = 121

Hence, the measure of the angle B is 121 degrees

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Answer:

Step-by-step explanation:

b=(3x-17) degrees.