A box contains six red pens, four blue pens, eight green pens, and some black pens. Leslie picks a pen and returns it to the box each time. The outcomes are recorded in the table.a. what is the experimental probability of drawing a green pen?b. if the theoretical probability of drawing a black pen is 1/10, how many black pens are in the box

The line segment BD has a length of 18 units

The possible figure is added as an attachment

From the question, we have the following parameters:

The lengths BE and ED implies that the point E is between the endpoints B and D

Since the shape is a parallelogram, then the point E is halfway between the endpoints B and D

So, we have

BE = ED

Substitute the known values in the above equation

6x + 44 = -6x - 16

Evaluate the like terms

So, we have

12x = -60

Divide both sides by 12

x = -5

Substitute x = -5 in BE = 6x + 44

So, we have

BE = 6 x -5  + 44

Evaluate

BE = 14

The length is then calculated as

BD = 2 x BE

So, we have

BD = 2 x 14

Evaluate

BD = 18 units

Hence, the length of BD is 18 units

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Solution:

Given that a value or quantity must not exceed ten, let x represent the value or quantity.

Since it must not exceed 10, this implies that

The second option is the correct answer.

18) the best estimate will be 75 square feet (option G)

18) radius = 10ft

let π = 3.14

We are told the deck will have 1/4 the area of a circle. We need to first find the area of a circle.

Area of circle = πr²

Next, we will divide the area by 4:

From the options, the one close to the result we got is 75 square feet

Hence, the best estimate will be 75 square feet (option G)

x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3

Two or more expressions with an Equal sign is called as Equation.

The given three equations are

-x+y+2z=-5.....(1)

5x+4y-4z=4....(2)

x-3y-2z=3....(3)

Add equations (1) and (3)

-x+y+2z+x-3y-2z=-5+3

Add the like terms

-2y=-2

y=1

Now put value of y in equations (1) and (2)

-x+2z=-6..(4)

5x-4z=0...(5)

Multiply with 5 on equation 4 and add with equation 5

-5x+10z+5x-4z=-30

6z=-30

z=-5

Now put y and z values in equation (1)

-x+1+2(-5)=-5

-x+1-10=-5

-x-9=-5

-x=4

x=-4

Hence x=-4, y=1 and z=-5 are solutions of x+y+2z=-5" 5x+4y-4z=4 x-3y-2z=3

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Given:

A graph

To determine the Mean, Median, and Mode based on the given graph, we first get the data set as shown below:

2,5,5,5,5,6,9,11,12,13,14,15,18,20

Next, we find the Mean by getting the average:

Then, we get the Median by getting the average of the two middle values since there is an even number of data values:

Now, we get the Mode by finding the number that appears most frequently. Hence, the Mode is 5.

Therefore, the answer is:

Mean:10, Median:10, Mode:5

$75 -----> 100%

x ---------> 20%

asnwer 1: they leave her $ 15

answer 2: the total cost of the meal is

$ 90

The value of x in the equation given is x = -4/7.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The information given will be illustrated as:

9 - (9x - 6) - 9 = 3(4x + 6)

9 - 9x + 6 - 9 = 12x + 18

Collect like terms

-9x + 6 = 12x + 18

-9x - 12x = 18 - 6

-21x = 12

Divide

x = 12/-21

x = -4/7

This illustrates the concept of equations.

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SOLUTION

We want to identify the equation that represents the data in the table.

Let's put the first values for x and y from the table, that is x = -2 and y = 11 and see if it works for the first option

This becomes

Since we didn't get y = 11, but we got y = 3, then the first option is wrong.

Let's try the next one

This becomes

So, we got y = 11, this option should be the correct answer, but let us confirm with the next values of x and y which are (0, 5).

So we will put x = 0, if we get y = 5, then the option is correct, so

Since we got y = 5, this option is correct.

Hence, the answer is the 2nd option.

The volume of the cone is 45.28 cubic inches.

The amount of sand inside the cone is measured by its volume.

Based on the numbers for the radius and height, the cone's volume is 45.28 cubic inches.

The volume of a cone is the measure of how much space a cone takes up. Cone height and base radius both affect how much space the cone takes up.

The volume of the cone is given by V = [tex]\frac{1}{3}\pi r^{2} h[/tex]

The value of the radius is r = [tex]3\frac{1}{23} = \frac{70}{23}[/tex]

The value of Height is h = [tex]3\frac{5}{3} = \frac{14}{3}[/tex]

So, the Volume of the cone =[tex]V =\frac{1}{3}\pi r^{2} h[/tex]

[tex]V =\frac{1}{3}\pi r^{2} h\\\\V = \frac{1}{3}\pi (\frac{70}{23}) ^{2} \frac{14}{3} \\\\V = 45.28[/tex]

The volume of the cone is 45.28 cubic. inches

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Considering the given table, it is found that:

a. The exponential regression equation is: P(t) = 2408.80(1.059)^t.

b. The yearly percent increase is of 5.9%.

c. P(13) = 5075.

d. The population of the town after 13 years is of 5075.

The exponential regression equation is found inserting the points into a calculator.

The points are given as follows:

(0, 2400), (3, 2801.27), (7, 3608.71), (12, 4974.15), (14, 5426.17), (19, 6898.37).

Using a calculator, the function is:

2408.80(1.059)^t.

The yearly percent increase rate is calculated as follows:

1 + r = 1.059

r = 1.059 - 1

r = 0.059

r = 5.9%.

Then in 13 years, the population will be given as follows:

P(13) = 2408.80(1.059)^13 = 5075.

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Answer:

22 feet

Explanation:

The area of a triangle can be calculated using the following equation:

Where b is the base and h is the height.

We know that the area is 330 square feet and the base is 30 ft, so we can replace these values to get:

Now, we can solve the equation for h. First, multiply both sides by 2:

Then, divide both sides by 30:

Therefore, the height of the triangle is 22 feet.

Answer:

(10, -3)

Step-by-step explanation:

[tex]-\frac{7}{2}x+32=\frac{4}{5}x-11 \\ \\ -35x+320=8x-110 \\ \\ -43x=-430 \\ \\ x=10 \\ \\ \therefore y=-\frac{7}{2}(10)+32=-3[/tex]

Find the inverse of:

The variable x can take any real value and the function f(x) exists. This means

the domain of f(x) is (-∞, +∞).

Now find the inverse function.

Swapping letters, we get the inverse function:

For each value of x, we get two values of y, thus this is not a function.

The domain of the inverse is restricted to values of x that make the square root exist, thus the domain is x ≥ 0, or [0, +∞)

The range of the inverse is the domain of the original function, that is, (-∞, +∞)

Function: No

Domain: [0, +∞)

Range: (-∞, +∞)

The choice to select is shown below.

The Solution.

Monday's sales is $3459.00

The food cost for Monday is

Tuesday's sales is $2976.81

The food cost for Tuesday is

Wednesday's sales is $3185.32

The food cost for Wednesday is

Thursday's sales is $3562.91

The food cost for Thursday is

Friday's sales is $4582.13

The food cost for Friday is

Saturday's sales is $4820.36

The food cost for Saturday is

A rational number

The perimeter of a rectangle is given by the formula:

Perimeter = 2(Length + Width)

The Length = 6 units

Perimeter = 2 (6 + Width)

Perimeter = 12 - 2 Width

2 Width = 12 - Perimeter

Width = (12 - Perimeter)/2

Note that a rational number is a number that can be written as a fraction of two integers.

Since the perimeter is said to be a rational number, any rational number substituted into the formula equation for the width above will give a rational number.

The width of the rectangle is therefore a rational number

In general, an inverse variation relation has the form shown below

It is given that x=16, then y=5/4; thus,

Therefore, the equation is y=20/x

2) Set x=4 in the equation above; then

When x=4, y=5.

Answer:120 inches per second

Step-by-step explanation:120 inches per second this is because 1 ft= 12 inches so you can multiply 10 x 12 which is 120 inches.

Given the equation (x + y)³ + 1 , we can assume we have two terms here. These are (x + y)³ and 1. Since both terms are perfect cubes, we can use the sum of cubes formula which is:

where a = (x+y) and b = 1.

Therefore, the factors of (x + y)³ + 1 is:

The factor of (x + y)³ + 1 is (x + y + 1)(x² + 2xy + y² - x - y +1).

Answer: x 0 1 2 3

p(x) 0.011 0.170 0.279 0.539

Given that the values of x =

Television 0 1 2 3

Household 30 443 727 1401

Let television be = x

Household = frequency = distribution

Firstly, we need to find the interval of x

The interval of x = Range between two numbers

1 - 0 = 1

2 -1 = 1

3 - 2 = 1

Hence, the interval is 1

Where N = total frequency

w = interval

Total frequency = 30 + 443 + 727 + 1401

Total frequency = 2601

when x = 1

When x = 2

when x = 3

Therefore,

x 0 1 2 3

p(x) 0.011 0.170 0.279 0.539

Answer:

y = 1/10x + 9/10

Step-by-step explanation:

Find slope intercept form: –2x = –20y + 18

slope intercept form: y = mx + b

_______________________________

–2x = –20y + 18

add 20y to both sides:

–2x + 20y = –20y + 18 + 20y

–2x + 20y = 18

add 2x to both sides:

–2x + 20y + 2x = 18 + 2x

20y = 18 + 2x

divide all terms by 20:

20y/20 = 18/20 + 2x/20

y = 9/10 + 1/10x

reorder terms for slope intercept form:

y = 1/10x + 9/10

Answer:

[tex]y=\dfrac{1}{10}x+\dfrac{9}{10}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]-2x=-20y+18[/tex]

To write the given equation in slope-intercept form, make y the subject.

Add 20y to both sides:

[tex]\implies 20y-2x=-20y+18+20y[/tex]

[tex]\implies 20y-2x=18[/tex]

Add 2x to both sides:

[tex]\implies 20y-2x+2x=2x+18[/tex]

[tex]\implies 20y=2x+18[/tex]

Divide both sides by 20:

[tex]\implies \dfrac{20y}{20}=\dfrac{2x+18}{20}[/tex]

[tex]\implies \dfrac{20y}{20}=\dfrac{2x}{20}+\dfrac{18}{20}[/tex]

[tex]\implies y=\dfrac{1}{10}x+\dfrac{9}{10}[/tex]

Therefore, the given equation in slope-intercept form is:

[tex]\boxed{y=\dfrac{1}{10}x+\dfrac{9}{10}}[/tex]

The problem is;

-2(x-1) - 2 > 8 - 5x +4+ x

open the parenthesis

-2x + 2 -2 > 8- 5x + 4+ x

collect the like-term

-2x+5x-x > 8+4

2x > 12

divide both-side of the inequality by 2

x>6

The first mistake that was made is adding of the x-variables

It is 2x and not -6x

ANSWER

z = 1.88

EXPLANATION

We have to find z such that the area under the normal curve to the right of that value is 0.03,

This is the same as finding z such that the area to the left of that value is 1 minus 0.03,

These are the values that z-score tables show. So, we have to find a z-score where the value in the table is 0.97,

The z-score whose area to its left is closest to 0.97 is z = 1.88.

Hence, for z = 1.88, the area under the curve to its right is 0.03.

Firstly, we need to know the number of boxes they both filled per hour.

From the question, we are told that 126 boxes were filled in six hours; thus in an hour, the number of boxes filled will be 126/26 = 21 boxes

Now in an hour, Nicholas filled 9 boxes; the number of boxes that will be filled is clearly the remainder of the 21 boxes.

The number of boxes filled by Jack is thus; 21 - 9 = 12 boxes

Jack fills 12 boxes in an hour

x > -8

Let the number be represented by x:

Three times the number = 3x

Six minus three times the number = 6 - 3x

Six minus three times the number is less than 30:

That can be interpreted mathematically as:

6 - 3x < 30

To find the value of x:

Step 1: Collect like terms

- 3x < 30 - 6

-3x < 24

Step 2: Divide both sides by 3:

-x < 8

Multiply both sides by (-1) and change the < sign to >

(-1) (-x) > 8 x(-1)

x > -8

Givens.

• The total number of laps is 14.

• The total distance is 30.8 miles.

First, divide the total distance by the number of laps.

Each lap length is 2.2 miles.

Let's transform it to yards using the conversion factor 1 mile = 1760 yards.

Therefore, each lap length is 3872 yards.

38

1) Starting from the first equation

3x +6 = 18 Subtract 6 from both sides

3x = 18 -6

3x = 12 Divide both sides by 3

x =4

2) Since x =4, let's plug that into the second expression 10x -2 to find out "what is 10x -2"

10x -2 Replace x, by 4

10(4) -2 Effectuate the multiplication

40 -2

38

Hence, the answer is 38

Answer:

B. the cost to enroll in the file-sharing service

Explanation:

The y-intercept is the cost when x = 0. It means that it is the cost of the service when the customer uploads 0 Mb, so it should represent the cost to enroll in the file-sharing service.

A graph of the proportional relationship is given by: D. graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30.

A graph can be defined as a type of chart that's commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Mathematically, a proportional relationship can be modeled by the following linear equation:

y = kx

Where:

Furthermore, the graph of any proportional relationship is characterized by a straight line with data points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) decreases or increases, the values on the y-coordinate (y-axis) decreases or increases simultaneously.

In this context, we can reasonably infer and logically deduce that the relationship between the values on the x-coordinate (x-axis) and y-coordinate (y-axis) of this graph is proportional and given by this equation:

y = 3x

Where:

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Answer:

A graph of the proportional relationship is given by: D. graph with x axis labeled time seconds and y axis labeled sit ups, with a line from 0 comma 0 going through 90 comma 30.

Step-by-step explanation:

Let's begin by listing out the given information:

A fair dice has 6 sides

The dice has its sides numbered from 1-6

The number of sides with even numbers (2, 4 & 6) equals 3

The number of sides with odd numbers (1, 3 & 5) equals 3

The probability of rolling an even number is given as shown below:

The probability of rolling an odd number is given as shown below:

The probability of rolling an even number followed by an odd number is obtained by the product of the probabilities above. We have:

Therefore, the probability of rolling an even number and then an odd number is 1/4