gina wilson quiz 4-3

There are 36 males and 45 females in the sales field.

Ratio of the number:

Ratios compare two numbers, usually by dividing them.

For example,

If you are comparing one data point (A) to another data point (B), your formula would be

=> A/B.

This means you are dividing information A by information B.

Given.

Suppose that the ratio of males to females in the sales field of a large company is 4:5.

Total number of representatives = 81.

Now, we need to find the number of males and number of females.

Let x be the number of representatives.

So, based on the ratio we have written this as,

=> 4x : 5x = 81

So, the total number of representatives is,

=> 4x + 5x = 81

=> 9x = 81

=> x = 81/9

=> x = 9

So, the number of males is

=> 4x => 4(9) = 36

And the number of females is,

=> 5x => 5(9) = 45

Therefore, there are 36 males and 45 females in the sales field.

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The fraction of a bag that you can put on each plate is 3 /16.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator and the denominator are divided by a line. An example of a fraction is 1 / 2.

The fraction of the cheese that you can put on each plate can be determined by dividing the amount of cheese left by the number of plates. Division is the process of grouping a number into equal parts using another number.

Amount that can be put on each plate = fraction left / number of plates

3 /4 ÷ 4

3/4 × 1/4 = 3 /16.

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Answer: x=6.5

Step-by-step explanation:

3(2x - 4) = 8 + 2x + 6

6x-12=14+2x

4x-12=14

4x=26

x=26/4

x=6.5

Answer:

16 1/4

Step-by-step explanation:

4*10=40, add one more 1/4 and you get 41. So simplified, 41/4 = 10 1/4

Add the 6 and you get 16 1/4

Using the given equation, the missing values in the table are:

x            y

32         14

12          9

0           6

-8          4

-36       -3

Given the equation, y - 6 = x/4, we can rewrite the equation as:

y = x/4 + 6

For x = 12, we have:

y = 12/4 + 6 = 3 + 6

y = 9

For x = 0, we have:

y = 0/4 + 6 = 0 + 6

y = 6

For y = 4, we have:

4 = x/4 + 6

4 - 6 = x/4

-2 = x/4

-8 = x

x = -8

For y = -3, we have:

-3 = x/4 + 6

-3 - 6 = x/4

-9 = x/4

-36 = x

x = -36

Thus, using the given equation, the missing values in the table are:

x            y

32         14

12          9

0           6

-8          4

-36       -3

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The circumference of the circle with arc AB as 22 cm and C as the center will be 176 cm.

We are given that:

Length of the shorter arc forming an angle of 45° with the center = 22 cm

AB = 22 cm

C is the center of the circle.

We know that the length of the arc is calculated as:

Length of an Arc = θ × (π / 180) × r

22 = 45 × (3.14 / 180) × r

22 = 0.785 r

r = 22 / 0.785

r = 28.0255

Circumference = 2 π r

Circumference = 2(3.14) (28.0255)

C = 176 cm

Therefore, we get that, the circumference of the circle with arc AB as 22 cm and C as the center will be 176 cm.

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Answer:

493%

Step-by-step explanation:

To convert a decimal to percentage, muiltiply the decimal by 100.

The probability that one green and one yellow is selected (without replacement) is 3/7.

What are examples and probability?

Probability that one green and one yellow is selected (without replacement).

Since the cellphone is not replaced, the probability is calculated as follows

Pr = [tex]\frac{G}{n} * \frac{Y}{n - 1 } + \frac{Y}{n} * \frac{G}{n- 1}[/tex]  The subtraction means the cellphones are not replaced

This gives

[tex]Pr = \frac{6}{8} * \frac{2}{8 - 1} + \frac{2}{8} * \frac{6}{8 - 1}[/tex]

[tex]Pr = \frac{3}{4} * \frac{2}{7} + \frac{1}{4} * \frac{6}{7}[/tex]

[tex]Pr = \frac{3}{14} + \frac{3}{14}[/tex]

take lcm

[tex]Pr = \frac{3}{7}[/tex]

Hence, the probability that one green and one yellow is selected (without replacement) is 3/7.

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Answer:

32 is it

Step-by-step explanation:

Answer:

7.25 feet

Step-by-step explanation:

Dilation involves changing the size of a quadrilateral or any shape

The coordinates of the image of the dilation are: [tex]W^{\prime}=(1 / 4,-3), X^{\prime}=(10,0)$, $Y^{\prime}=(7,-9)$[/tex] and [tex]$Z^{\prime}=(4,-9)$[/tex]

This is further explained below

The vertices of the pre-image are given as:

W=(0,-4)

X=(13,0)

Y=(9,-12)

Z=(5,-12)

The scale factor is given as:

k=3 / 4

The center of dilation is given as:

(a, b)=(1,0)

To calculate the vertices of the image, we make use of the following formula [tex]$\left(x^{\prime} y^{\prime}\right)=(k(x-a)+a, k(y-b)+b)$[/tex]

So, we have:

W'=(3 / 4(0-1)+1,3 / 4(-4-0)+0)

W'=(1 / 4,-3)

X'=(3 / 4(13-1)+1,3 / 4(0-0)+0)

X'=(10,0)

Y'=(3 / 4(9-1)+1,3 / 4(-12-0)+0)

Y'=(7,-9)

Z'=(3 / 4(5-1)+1,3 / 4(-12-0)+0)

Z'=(4,-9)

Hence, the coordinates of the image of the dilation are:

W'=(1 / 4,-3),

X'=(10,0),

Y'=(7,-9)

Z'=(4,-9)

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Answer:42

Step-by-step explanation:

Answer:

You would need 9 liters of pure acid and 72 liters of 10% acid to make a mixture of of 81 liters of 20% acid.

Step-by-step explanation:

See attached picture.

Answer:

15

Step-by-step explanation:

[tex]-10+\left|6+\left(-17\right)\right|-\left(-14\right)[/tex]
[tex]=-10+\left|6-17\right|+14[/tex]
Subtract.
[tex]=-10+\left|-11\right|+14[/tex]
Now, add.
[tex]=4+\left|-11\right|[/tex]
Apply absolute rule.
[tex]=4+11[/tex]
= 15

Answer: 2000π mm^2

Step-by-step explanation:

A=area of entire circle. B=Area of Inside circle. C=Area of shaded region

A-B=C

π(120/2)^2 -π(80/2)^2=

π(60)^2 -π(40)^2=

3600π-1600π=2000π mm^2

The correct graph of the ellipse is identified and attached below.

Given the equation is (x₋3)²/16 ₊ (y₋4)²/9 = 1

step 1: identify the center (h,k) of the ellipse in standard form:

(x₋h)²/a² ₊ (y₋k)²/b² = 1

In the standard form of an ellipse, notice that there is a minus sign in front of the h and k.

In our equation  (x₋3)²/16 ₊ (y₋4)²/9 = 1 , we have:

h = 3 and k = 4

Therefore, center (h,k) = (3,4)

Step 2: Identify the orientation by determining the major axis and minor axis in (x₋h)²/a² ₊ (y₋k)²/b² = 1

if a>b, the major axis is horizontal and the minor axis is vertical, making the ellipse a horizontal ellipse.

if a<b, the minor axis is horizontal and the major axis is vertical, making the ellipse a vertical ellipse.

For  (x₋3)²/16 ₊ (y₋4)²/9 = 1

a² = 16, a = 4 and b² = 9 , b = 3

so, 4>3, the major axis is horizontal and the minor axis is vertical, making the ellipse a horizontal ellipse.

Step 3:

Plot the co-vertices along the minor axis and the vertices along the main axis (endpoints). No matter which way around, draw points a horizontal distance of a to the left and right from the center and points b above and below the center.

Therefore the vertices are marked along the major axis.

vertices are (3,7) and (3,1)

and co vertices are marked along the minor axis

co vertices are (₋1,4 ) and (7,4)

step 4: connect the vertices and co vertices making a smooth horizontal ellipse.

Hence a horizontal ellipse is made.

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5/6 - 1/9=?/? - ?/? = ?/? , value of each (?/?) is

5/6 -1/9 =15 /18 -2/18 =13 /18.

As given,

5/ 6 - 1/9 =?/? -?/? =?/?

Convert the given terms into like terms

Least common multiple of (6,9)=18

Value of each ( ?/?)

(5/6 ) × ( 3/3) -(1/9) × (2/2)

= 15 /18 - 2/18

= 13 /18

Therefore,5/6 - 1/9 = ?/? - ?/? = ?/? , value of each (?/?) is equal to

5/6 -1/9 = 15 /18 -2/18 = 13/18.

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In 25.76 seconds we will fill the total volume of the cylinder.

The total volume of the cylinder is given by the equation:

V = pi*R^2*H

Where pi = 3.14, R is the radius and H is the height.

Here we know that the diameter is 6 inches, then the radius is:

R= 6in/2 = 3in

And the height is 8 inches, then the volume is:

V = 3.14*(3in)^2*8in = 226.08 in^3

We already have 20 cubic inches of water there, so what we need to fill is:

226.08 in^3 - 20in^3 = 206.08in^3

If we fill it at a rate of 8in^3/s, the time in which we will completely fill the cylinder is:

T = 206.08in^3/8in^3/s = 25.76s

In 25.76 seconds we will fill the total volume of the cylinder.

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The difference quotient of the function g(x) = √x is  [√(x+h) -√x]/h

Difference quotient of the function:

Difference quotient of the function means a measure of the average rate of change of the function over an interval.

The difference quotient formula of a function y = f(x) is,

[ f(x + h) - f(x) ] / h

where

f (x + h) is obtained by replacing x by x + h in f(x)

f(x) is the actual function

Given,

Function g(x) = √x where x≥0.

Here we need to find the difference of the quotient of the function.

For that,

First we have to calculate the value of g(x + h),

By simply replacing the value of x as x + h,

So,

g(x + h) = √(x+h)

Now apply the values on the formula in order to solve it,

=> [√(x+h) -√x]/h

We can't simplify it further.

So, the difference quotient of function is,

=> [√(x+h) -√x]/h

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Answer: D

Step-by-step explanation:

took one for the team

The annuity could pay $221.19 per month.

ANNUITY FORMULA: [tex]P_t=\frac{d\left[\left(1+\frac{s}{n}\right)^{n t}-1\right]}{\frac{s}{n}}[/tex]

Where,

So,

Loren anticipates having $500,000 when he retires.

He establishes a 30-year payout annuity at a 10%interest.

Each month, the annuity could provide

In the formula, replace the above values as follows:

Now, divide both sides by: 2260.487925

Therefore, the annuity could pay $221.19 per month.

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Answer:

y = -2x + 9

Step-by-step explanation:

The standard form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

The line intersects the y-axis at 9, thus b = 9.
The slope formula is rise/run. The line falls 2 and runs 1, thus m = -2/1, or -2.

y = -2x + 9

Answer:

x − 4y = −20x − 4y = −26

Step-by-step explanation:

Answer:£1500

7500 divided by 10=750. £750 is 10% so 750x2 which is 1500, is 20%. Therefore, it is reduced by £1500

Answer:

£1500

Step-by-step explanation:

20% = 20/100 = 0.2

7500 - (7500*0.2)

= 7500 - 1500

= 6000

The reduction in price is:

£ 1500

A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160feett/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute

Given that 1)A gull can fly at a speed of 22 miles per hour and asked to convert its units to  foot/hour

2)An AMTRAK train travels at 125 miles per hour and is asked to convert its units to  miles/minute

1 mile=5280 feet

22 miles/hour=22 × 5280 foot/hour

22 miles/hour=116,160 foot/hour

1 hour=60 minute

125 miles/hour= 125/60 miles/minutes

125 miles/hour= 2.083 miles/minutes≈ 2.1miles/minutes

Therefore, A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160 feet/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute

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The branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.

It is required to find the statement.

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.

Descriptive statistics refers to the summary of important aspects of a data set.

Therefore, the branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.

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Answer: y=-8x+3

Step-by-step explanation:

Parallel lines have the same slope.

y=-8x+b

-5=-8(1)+b

-5=-8+b

b=3

y=-8x+3

Bonjour,

Answer:

16 2/3 = 50/3

Step-by-step explanation:

16 2/3 = 16.6666666…

Change the percent to a decimal number by moving the decimal two places to the left.

Call this x = 0.16666666…

10x = 1.66666666…

100x 16.66666666…

Subtract 100x - 10x = 15

90x = 15

x = 15/90 = 1/6

16 2/3 % = 1/6

The total cost of the brackets before tax = $89.70

Height = 9 feet

length = 10 feet

Wall brackets come in 48-in cost $12.95 and 60-in costing $16.95

Distance of brackets from ends = 1 foot

Maximum distance between brackets = 24 inches

The brackets are:

  48/12= 4feet, and 60/12 = 5feet

One of each must be used to cover the height of the shelf.

The length of the shelf is 60 inches

On subtracting 1 foot from each side of the allowance we get, 60-2 = 58-in

Then dividing by 24 we get

58/24 ≈3

The Total cost = (12.95 + 16.95)×3

                        = $89.70

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