Find the Mean from the line plot. Show your work and explain how you solved using First, Next, and Last.

Answer:

x=2

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

3x - 9x + 7 - 3 = -8

Combine like terms

-6x +4 = -8

Subtract 4 from each side

-6x +4-4 = -8-4

-6x = -12

Divide each side by -6

-6x/-6 = -12/-6

x = 2

Answer:

1. For the median (as per the question posted): the median of Justin's earnings is more than the median of TJ's earnings

Difference = $3

2. For the mean (as per the requirement in the image): the mean of TJ's earnings is more than the mean of Justin's earnings

Difference = $4

Explanation:

The complete question is shown in the attached image

1. The median:

a. For Justin:

He earned the following: $32, $45, $50, $33 and $50

Arranging the data: $32, $33, $45, $50 and $50

The middle value is: $45

The median is: $45

b. For TJ:

He earned the following: $58, $48, $40, $42 and $42

Arranging the data: $40, $42, $42, $48 and $58

The middle value is: $42

The median is: $42

c. Comparing the medians:

From the above, we can conclude that the median of Justin's earnings is more than the median of TJ's earnings

Difference = $45 - $42 = $3

2. The mean:

a. For Justin:

He earned the following: $32, $45, $50, $33 and $50

Summing the data: $32 + $33 + $45 + $50 + $50 = 210

Number of values in the data= 5

The mean is: [tex]\frac{210}{5}=42[/tex]

b. For TJ:

He earned the following: $58, $48, $40, $42 and $42

Summing the data: $40 + $42 + $42 + $48 + $58 = $230

Number of values in the data: 5

The mean is: [tex]\frac{230}{5} = 46[/tex]

c. Comparing the values:

From the above, we can conclude that the mean of TJ's earnings is more than the mean of Justin's earnings

Difference = 46 - 42 = $4

Hope this helps :)

Answer:

6

Step-by-step explanation:

Answer:

Answer is (2,6) B.

Step-by-step explanation:

A. The perimeter of quadrilaterals are same when x=2.

B. The area of quadrilaterals are same when x=4.6

Step-by-step explanation:

A. Perimeter of the quadrilaterals must be equal.

Perimeter of square = Perimeter of rectangle

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

⇒ 24 = 2(3x+6)

⇒ 24 = 6x + 12

⇒ 6x = 12

⇒ x = 12/6

x = 2

For x=2, the perimeters of both the quadrilaterals are same.

B. Area of the quadrilaterals must be equal.

Area of square = Area of rectangle

(6)² = 2(3x+4)

36 = 6x+8

6x = 28

x = 28/6

x = 4.6

For x=4.6, the area of both the quadrilaterals are same.

The number of students in the class is [tex]s=14[/tex]

Explanation:

It is given that there are 6 girls in a music class.

This represents [tex]\frac{3}{7}[/tex] of the entire class.

To determine the number of students in the class, we need to solve the equation [tex]\frac{3}{7}s=6[/tex]

Let us solve the expression for s.

Multiplying both sides of the equation by [tex]\frac{7}{3}[/tex], we have,

[tex](\frac{7}{3} )\frac{3}{7}s=6(\frac{7}{3} )[/tex]

Simplifying the expression, we have,

[tex]s=\frac{42}{3}[/tex]

Dividing by 3, we have,

[tex]s=14[/tex]

Thus, the number of students in the class are 14.

Answer:

90 degrees pi/2 radians

I think so but i dont know

Step-by-step explanation:

Answer:

12 1/7 cars

Step-by-step explanation:

Let the number of cars she'd wash to earn $63 in spending money be A.

Given she saves $22 of her weekly earnings and wants to have at least $63 for spending money.

That means she’d have to make $63 + $22 = $85

The expression is thus

$85 = A x $7

Where A is the number of cars and $7 is the amount she earns for washing one car and $85 is the total amount she has to make .

Therefore,

85 = A x 7

Divide both sides by 7

85/7 = A x 7/7

12 1/7 = A

A = 12 1/7 cars

She must wash 12 1/7 cars to have at least $63 spending money and also have her weekly Savings of $22

Answer:

x=6

Step-by-step explanation:

You are correct. x does equal 6

Answer:

Yes

x = 6

Step-by-step explanation:

Given

2x - 5 = 3(1 - x) + 22

First distribute 3 into (1 - x)

We have

2x - 5 = 3 x 1 -3 x X + 22

2x - 5 = 3 - 3x + 22

The expression can be rearranged as

2x - 5 = 3 + 22 - 3x

2x - 5 = 25 - 3x

Add 3x to both sides

3x + 2x - 5 = 25 - 3x + 3x

5x - 5 = 25

Add five to both sides

5x - 5 + 5 = 25 + 5

5x = 30

Divide both sides by 5

5x/5 = 30/5

x = 6

Answer:

4 days

Step-by-step explanation:

$25 on gas

$415-$25=$390 she still can spend $390

390/100=3.9 days

that means she can go for 3.9 days

so she must go for less than 4 days

Answer:

3

Step-by-step explanation:

18*x=54   (divide both sides by 18)

x = 54 ÷ 18

x = 3

Hello!

The answer to your problem is A) 3

Move all terms to the left

[tex]18x-(54)=0[/tex]

Move all terms containing x to the left, all other terms to the right

[tex]18x=54[/tex]

[tex]x=54/18[/tex]

Get your answer

[tex]x=3[/tex]

Hope This Helps!

A simulation is a mathematical model used to represent a situation.

When we combine two or more simple events we have a compound event

A Tree Diagram is a diagram that shows all the possible outcomes of an event

All the possible outcomes or results is called the sample space

When an event is not affected by a previous outcome we have an independent event

Let me know if you need any clarifications, thanks!

~ Padoru

Answer:

     [tex]25\leq 27[/tex]

Explanation:

1. Starting inequality:

      [tex]-125\geq -135[/tex]

2. Divide both sides by [tex]-5[/tex]

3. Rule

When you divide an inequality by a negative number, the inequality symbol has to be changed:

4. Solution

Thus, when dividing by -5 change the inequality symbol ≤ to ≤

      [tex]\dfrac{-125}{-5}\leq \dfrac{-135}{-5}\\\\\\25\leq 27[/tex]

Answer:

That 1st one will be in the negatine seconw one will de positive

Answer:

D.2.4

Step-by-step explanation:

Because it's a fraction and can be written in fraction as 240/100

Answer:

answer is C

Step-by-step explanation:

4/2 : rational

4/2 = 2 : integer

and When you simplify 4/2 you get 2, 2 is an integer.

Answer:

[tex]512\ m^{3}[/tex]

Step-by-step explanation:

Volume of any cube equals a product of all the edge lengths. Since there are 3 edges:

[tex]V = a^{3} = 8^{3} = 512\ m^{3}[/tex]

The required area of the cube with an edge length of 8 meters is 512 cubic meters.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

here,
A cube has an edge length of 8 meters.
The volume of the cube = a³
The volume of the cube = 8³ = 512 cubic meters

Thus, the required area of the cube with an edge length of 8 meters is 512 cubic meters.

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Answer:

$3600

Step-by-step explanation:

Cost of the car = $8000

The car loses value at 11% each year .

That’s

11% /100% x $8000

0.11 x 8000

$880

11% decrease each year means that the cost of the car is reduced by $880 per year.

Therefore,

Worth of the car in 5 years

= $8000 - ($880 x 5)

= $8000 - $4400

= $3600

The car will be worth $3600 in five years

Answer:

4/12 or 2/6 or 1/3

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The formula is Y-Y1= M(X-X1)

So y-4=3(x+2)

Jim's income tax liability for the $45,000 he earned from his three employers would be $9,500.

To calculate Jim's income tax, we first need to find his total income. Since he worked for three different employers, his total income would be the sum of his earnings from each employer, which is $15,000 * 3 = $45,000.

Next, we need to know the tax rates that apply to Jim's income. Income tax rates are usually progressive, meaning different portions of income are taxed at different rates.

Using the hypothetical tax rates mentioned above, we can calculate Jim's income tax liability:

First $10,000 at 10%: $10,000 * 0.10 = $1,000

Next $20,000 at 20%: $20,000 * 0.20 = $4,000

Remaining $15,000 at 30%: $15,000 * 0.30 = $4,500

Now, summing up the tax amounts from each tax bracket: $1,000 + $4,000 + $4,500 = $9,500.

Therefore, Jim's income tax liability should have been $9,500.

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Final answer:

Jim earned a total of $45,000 from three employers. Using a simplified marginal tax rate example, his total income tax comes to approximately $7,106.25. This calculation method demonstrates how the marginal tax rate system works in a basic form.

Explanation:

To determine how much income tax Jim should have paid on his earnings from three different employers, where each paid him $15,000, we first need to calculate his total income. Jim's total income is $15,000 from each job, multiplied by 3, because he worked for three different employers, resulting in a total income of $45,000.

Assuming a simple tax rate example (for illustrative purposes), let's use the marginal tax rates provided in the reference:

Income from $0 to $9,075 is taxed at 10%

Income from $9,075 to $36,900 is taxed at 15%

Income from $36,900 and beyond is taxed at 25%

Since Jim earns $45,000, here is how his taxes would be calculated:

The first $9,075 is taxed at 10%, amounting to $907.50.

The next $27,825 ($36,900 - $9,075) is taxed at 15%, amounting to $4,173.75

The remaining $8,100 ($45,000 - $36,900) is taxed at 25%, amounting to $2,025.

Add up these amounts to get the total tax:

$907.50 + $4,173.75 + $2,025 = $7,106.25

Therefore, applying this simplified tax calculation, Jim should have paid a total of roughly $7,106.25 in income tax on his total earnings of $45,000 from three different employers.

Solution:

We have to find the height of lamppost

From the figure in question,

Given is a right angled triangle

Where,

base = 40 inches

height = ?

By definition of tan,

[tex]tan\ 70 = \frac{opposite}{base}\\\\tan\ 70 = \frac{height}{40}\\\\height = tan\ 70 \times 40\\\\height = 2.7474 \times 40\\\\height = 109.89 \approx 110[/tex]

Thus height of lamp post to nearest inch is 110 inches

Answer:

They each used 60 dollars in total

Step-by-step explanation:

They each brought 12 dollars and if you multiply it by 5 that's how much they spent in total

Answer:

36 ft. tall

Step-by-step explanation:

We can easily solve this problem with a simple proportion:

12 feet / height    =     2 feet / 6 feet

6 * 12 = 2h

72 = 2h

h = 36 ft.

It's found that the tree is 36 feet tall.

To find the height of the tree using the lengths of the shadows and the person's height, we can use a proportion based on similar triangles. Since the sun's rays hit both the tree and the person at the same angle, the ratio of the height of the tree to the length of its shadow is the same as the ratio of the person's height to the length of their shadow.

Let's let 'h' represent the height of the tree. We can set up the proportion as follows:

Person's height / Person's shadow length = Tree's height / Tree's shadow length

6 feet / 2 feet = h / 12 feet

Now we solve for 'h' by cross-multiplying:

6 feet * 12 feet = 2 feet * h

72 feet2 = 2 feet * h

Divide both sides by 2 feet to get:

h = 36 feet

Therefore, the tree is 36 feet tall.

Answer:

Slope = 2

y-intercept = 1

x-intercept = -0.5

Standard Form ⇒ y - 2x = 1

Step-by-step explanation:

write the equation of the line through (-2 , -3) and (0,1)

The general form of the line is  y = mx + c

Where m is the slope and c is the y-intercept

The slope m = (y₂ - y₁)/(x₂ - x₁) = (1 - [-3])/(0 - [-2]) = 4/2 = 2

∴ y = 2x + c

By substitution with the point (0,1) to find c

1 = 2 *0 + c

c = 1

∴ y = 2x + 1

Or   y - 2x = 1 ⇒Standard Form

Also,

See the attached figure which represents the graph of the line y - 2x = 1

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut point with the y axis

We have the following points:

[tex](x_ {1}, y_ {1}): (0,1)\\(x_ {2}, y_ {2}): (-2, -3)[/tex]

We find the slope:[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-3-1} {- 2-0} = \frac {-4} {- 2} = 2[/tex]

Thus, the equation is of the form:

[tex]y = 2x + b[/tex]

We substitute a point and find b:

[tex]1 = 2 (0) + b\\b = 1[/tex]

Finally, we have:

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

On the other hand, the equation in the standard form is given by:

[tex]ax + by = c[/tex]

So, according to the slope-intersection equation we have:

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

Answer:

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

Answer:

This system has infinitely many solutions because they right on top of each other.

If the lines were perpendicular, then there would be exactly one solution.

If the lines were parallel, there would be no solutions.

Answer:

5.43333 recurring

Step-by-step explanation:

Mean is the average of a set of numbers. That is, the sum of the digits in the set, divided by the number of the digits.

In the question above, we have 9 digits. So we find the sum of the digits divided by 9.

(9.6+2+4.1+8+5.9+2+3.7+6+7.6)/9

48.9/9

5.4333recurring

Answer:

Erwin have 1 [tex]\frac{1}{2}[/tex]   gallons of lemonade left

Step-by-step explanation:

Erwin had 2 5/12 gallons of lemonade. He spilled 11/12 gallon of lemonade. How much lemonade dose he have left? Write in simplest form

All we need to do is to subtract 11/12 from 2 5/12. But to do this, we will convert 2 5/12 to improper fraction

converting 2 5/12 to improper fraction yields : 29/12

Lemonade have left = Total lemonade - lemonade spilled

                         =          29/12 -  11/12

                         =     18/12

Lemonade have left =18/12

But we can reduce 18/12 to its lowest term

18÷6/ 12÷6      =     3/2

       Lemonade have left = 3/2

We can change to 3/2 to a mixed number to give us 1 [tex]\frac{1}{2}[/tex]    

Therefore Erwin have 1 [tex]\frac{1}{2}[/tex]   gallons of lemonade left

Answer:

(3/2) or (1 1/2) gallons of lemonade

Step-by-step explanation:

Erwin had 2 5/12 gallons of lemonade at his disposal which also translate to 29/12 gallons.

If he spills 11/12 gallon of the lemonade,then the quantity left with him will be (29/12) - (11/12) = 18/12(change to proper fraction): 3/2 or 1 1/2 gallons of lemonade

Part A: For 100 miles, the cost will be same for both companies.

Part B: Alex should use Drive and Move company as it will cost him less money.

Step-by-step explanation:

Given,

Starting amount of YMI= $40

Per mile charges = $1.99

Let,

x be the number of miles.

y be the total charges.

y = 1.99x+40    Eqn 1

Starting amount of DM = $60

Per mile charges = $1.79

y=1.79x+60    Eqn 2

Part A:

For same charges;

Eqn 1 = Eqn 2

[tex]1.99x+40=1.79x+60\\1.99x-1.79x=60-40\\0.20x=20[/tex]

Dividing both sides by 0.20

[tex]\frac{0.20x}{0.20}=\frac{20}{0.20}\\x=100[/tex]

For 100 miles, the cost will be same for both companies.

Part B:

Total miles = x = 150

Putting x=150 in Eqn 1

y=1.99(150)+40

y=298.5+40

y=$338.50

Putting x=150 in Eqn 2

y=1.79(150)+60

y=268.5+60

y=$328.50

Alex should use Drive and Move company as it will cost him less money.