In Rodger's state, unemployment compensation is calculated by finding the total of the quarterly wages of two consecutive quarters and dividing by 26. The weekly unemployment is 65% of that amount. In the quarter including January, February, and March, Rodger made a total of $13,950.80. In the quarter including April, May, and June, he made a total of $14,250.10. Find Rodger's weekly unemployment amount.

Answers

Answer 1

Rodger's weekly unemployment amount is $ 705.0225

Given,

The total of the quarterly wages of two consecutive quarters and dividing by 26.

The weekly unemployment is 65% of that amount.

Rodger made a total of $13,950.80.

and, he made a total of $14,250.10

We have to follow the some steps for solving question:

Step 1:  Find the total of the quarterly wages of two consecutive quarters.

= $ 13,950.80 + $ 14,250.10

= $28,200.90

Step 2 : Divide the total  by 26

  = $28,200.90 / 26

  =  1,084.65

Step 3 : Find the 65%

  =   1,084.65 x 65%

  =  1,084.65 x 65/100

  =   705.0225

Hence, Rodger's weekly unemployment amount is $ 705.0225

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Answer 2

Answer:

$705.02

got it right

Step-by-step explanation:


Related Questions

nathan is making a beaded bracelet. for every 5 red beads there are 3 white beads. what is the ratio of red to white beads?

Answers

Answer:

5;3

Step-by-step explanation:

You start with $100 at a casino and can bet any amount of that money to play a game any amount of times where in each game, you have a 40% chance of winning. If you win, you’ll gain the amount you bet, in addition to being returned the amount you bet. If you lose, you lose your bet. What is your strategy to have the highest chance of getting to $200? (100 - 200 words)

Answers

Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

Given that we start with $100 at a casino and can bet any amount of that particular money to play a game to any amount of times where we have a 40% chance of winning in each game. If we win, we will gain the amount we bet and return the amount that we bet. If we lose, we will lose our bet.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probaility of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probability of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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the temperature has been dropping 2 1/2 degrees every hour and the current tempter is -15 degrees Ferin height how many hours ago was the temperature 0 degrees Ferin height

Answers

The number of hours ago was the temperature 0 degrees is 6 hours.

What is temperature?

Temperature simply means the degree if hotness and coldness in a body.

In this case, the temperature has been dropping 2 1/2 degrees every hour. Let the number of hours be h.

This will be illustrated as:

-15 = -2.5h

where h = number of hours

Divide

h = -15 / -2.5

h = 6

Therefore, the correct option is 6 hours.

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HELP PLS I NEED THIS ANSWERED QUICKLY
A membership at Gym A costs $50 for 5 months. A membership at Gym B down the street costs $40 for 3 months. You write two equations in the form of y=kx to try and figure out which membership would be cheaper for a year. What is the value of k for the cheaper membership?

Answers

The cost for a year is cheaper in the Gym A than Gym B. The value of k for the cheaper membership would be; $10.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables. A linear equation is an equation that increases at a constant rate.

An equation in the form y = kx is called a linear equation.

In the equation of form y = kx

y = dependent variable which is the total cost

x = number of months

k = constant of proportion / cost per month

Thus k = y/x

The Cost per month at Gym A = $50 / 5 = $10

The Cost per month at Gym B = $40 / 3 = $13.33

The Membership cost at Gym A for a year = $10 x 12 = $120

The Membership cost at Gym B for a year = $13.33 x 12 = $160

Hence, The cost for a year is cheaper in the Gym A than Gym B. The value of k for the cheaper membership would be; $10.

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34. G and H are complementary angles.
If the measure of G = (6x-15)° and the measure of H = (3x + 6), find the measure of H.

Answers

Answer: the measure of H is 39 the measure of G is 51

Step-by-step explanation:

6x-15+3x+6=90

9x-9=90

9x=99

x=11

6(11)-15=51

3(11)+6=39

Help please its due tonight

Answers

Answer:

[tex]\sf 12-5x+6x=4[/tex]  (Given)

[tex]\sf 12+x=4[/tex]  (Combine like terms)

[tex]\sf x=-8[/tex]  (Subtraction property of equality)

--------------------------------------------------

Hope this is what you're looking for!

Answer:

1. given

2. combine like terms,

3. subtraction property of equality

Step-by-step explanation:

a 8-meter ladder is leaning against the wall of a building, and the base of the ladder is sliding away from the building at a rate of 5 meters per second. how fast is the top of the ladder sliding down the wall when the base of the ladder is 6 meters from the wall?

Answers

Height of the ladder on the wall in decreasing at the rate of ≈ 6m/s

What is differentiation ?

Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation can be performed utilizing only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.

Calculation

let ym be the height of wall at  which ladder touches

Also let the foot of ladder be xm away from the wall

then by the pythagoras theorem we have ,

[tex]x^{2} +y^{2} =[/tex] 64 [ length of ladder = 8 m ]

⇒ y = [tex]\sqrt{64 - x^{2} }[/tex]

then , the rate of change of height (y) with respect to time (t) is given by

[tex]\frac{dy}{dt}=\frac{-x}{\sqrt{64 - x^{2} }} . \frac{dx}{dt}[/tex]

it is given that [tex]\frac{dx}{dt}[/tex] = 5 m/s

∴ [tex]\frac{dy}{dt}=[/tex] [tex]\frac{-5x}{\sqrt{64 - x^{2} }}[/tex]

now when x = 6m , we have :

[tex]\frac{dy}{dt} = \frac{-5 * 6}{\sqrt{64 - 6^{2} }}[/tex]

  = -30 / 5 .3

  = -5.660377358490566

therefore height of the ladder on the wall in decreasing at the rate of ≈ 6m/s

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Alex and Patty are tracking the number of steps they walk. Alex records that he can walk 5750 steps in 50 minutes. Patty
writes the equation y = 1142, where y is the number of steps and x is the number of minutes she walks, to describe her
step rate. This week, Alex and Patty each walk for a total of 4 hours. Who walks more steps? How many more?
walks
more steps.

Answers

By solving the equation we can conclude that Andre (36,000 steps) walks more than Priya (35,400 steps).

What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this article, let's learn more about math equations.

So, the distance that Andre traveled.

He demonstrated his ability to take 6000 steps in 50 minutes.

The pace at which Andre can walk is:

= 6000/50= 120 steps per minute

The 5 hours in minutes conversion: 5  × 60 minutes = 300 minutes

Then,

The distance traveled by Andre is:

120 × 300 = 36000 stepsSo, Andre walks 36000 steps.And, Priya enters the formula y = 118x.

Where x represents the number of minutes and y is the number of steps.

The formula to convert 5 hours to minutes is:

x = 5 × 60 minutesx = 300 minutes

Replace x with its value in the equation:

y = 118xy = 118 × 300y = 35400 steps

35400 steps are taken by Priya.

Therefore, by solving the equation we can conclude that Andre (36,000 steps) walks more than Priya (35,400 steps).

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The correct question is given below:

Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walked for a total of 5 hours. Who walks more steps?

The diagram shows the positions of three turbines A, B and C.
A is 6 km due north of turbine B.
C is 4.5 km due west of turbine B.
(a) Calculate the distance AC.

Answers

the distance AC is 7.5cm


XYZ and LMN are complementary angles. XYZ = (3x+14)° and LMN= (5x+24)°. What is LMN in degrees?
Write your answer as a decimal.

Answers

Answer:

6.5°

Step-by-step explanation:

We know that both XYZ and LMN are complementary angles.

Complementary angles add up to 90°.

So,

we can simply add both of the expressions and set it equal to 90 (degrees).

(3x+14) + (5x+24) = 90

-> add the variables and constants

8x+38=90

-> subtract the 38 from both sides (90-38)

8x=52

-> divide out the coefficient to isolate the variable

x=6.5

So, the answer is 6.5 degrees.

Hope this helped :)

The graph shows y varying directly as x according to the equation y = kx. What is the value of d?
A d = kb + kdd = kb + kd
B d = ka + kcd = ka + kc
C d = b + kdd = b + kd
D d = kb

Answers

The equation that represents the value of d is d = b + kc

How to determine the value of d?

The graph that completes the question is added as an attachment

The equation of the graph is given as

y = kx

Because the graph shows a direct variation, the equation can be illustrated as

y = mx

Where m represents the slope of the line

By comparing the equation y = mx and y = kx, we can conclude that

m = k

This means that the slope of the equation y = kx is k

From the graph, we have the points

(x, y) = (a, b) and (a + c, d)

The slope of a line is calculated using

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

Slope = k

(x₁, y₁) = (a, b) and (x₂, y₂) = (a + c, d)

So, we have

k = (d - b)/(a + c - a)

Evaluate the like terms

k = (d - b)/(c)

Multiply both sides by c

d - b = kc

Add b to both sides

d = b + kc

Hence, the value of d is d = b + kc

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Calculator
What is the area of a rectangle with vertices at
ter your answer in the box.
(0,-4).(-1, -3) (2, 0), and (3, − 1)?

Answers

Answer:

The answer to your question is: 6 units

Step-by-step explanation:

Data

A (-4, 0)

B (-3,1)

C (0,-2)

D (-1,-3)

Formula

d = √((x2 - x1)² + (y2 - y1)²)

Process

dAB = √((x2 - x1)² + (y2 - y1)²)                 dAC = √((0 + 4)² + (-2 + 0)²)

      = √((-3 + 4)² + (1 - 0)²)                      dAC = √((4)² + (-2)²)

      = √((1)² + (1)²)                                    dAC = √(16 + 4)

      = √1 + 1                                             dAC = √20

dAB = √2  = dCD

dAD = √((-1 + 4)² + (-3 - 0)²)                    

dAD = √((3)² + (-3)²)

dAD = √9 + 9

dAD = √18 = dBC

reactangle's area = base x height = √18 x √2 = √18 x 2 = √36

                                                       = 6 units

The answer is six units

Measure of angle 1 = 110 degrees. You only need to type 110.

Answers

The unknown angles are as follows:

∠1 = 110°∠2 = 70°∠3 = 110°∠4 = 70°∠5 = 110°∠6 = 70°∠7 = 110°∠8 = 70°How to find angles?

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, linear angles, alternate angles etc.

Therefore,

∠1 = 110 degrees

∠2 = 180 - 110 (sum of angles on a straight line)

∠2 = 70°

∠3 = ∠1 (vertically opposite angles)

Vertically opposite angles are congruent. vertically opposite angles share the same vertex

Therefore,

∠3 = 110°

∠2 = ∠4 (vertically opposite angles)

∠4 = 70°

∠1 = ∠5 (corresponding angles)

Corresponding angles are congruent

∠5 = 110°

∠6 = ∠4(alternate angles)

Alternate angles are congruent.

∠6 = 70°

∠1 = ∠7 (alternate exterior angles)

∠7 = 110°

∠2 = ∠8(alternate exterior angles)

∠8 = 70°

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a sunflower is planted in a garden and the height of the sunflower increases by 10% per day. 2.66 days after being planted the sunflower is 10.3 inches tall. what is the 1-day growth factor for the height of the sunflower? 0.10 incorrect how tall is the sunflower 3.66 days after being planted? incorrect inches how tall is the sunflower 4.66 days after being planted? incorrect inches what is the 2-day growth factor for the height of the sunflower?

Answers

Two day growth factor for the height of the sun flower is 1.1449

Take the current number and subtract it from the prior value to determine the growth rate. The growth rate is then expressed as a percentage by multiplying the difference by the previous number and dividing by 100.

A height increases by 7% per day

So the growth factor for height of sun flower is  107/100 =1.07

For 2.7 days - 12 inch

3.74 days increase by 7% by day

⇒ 12 + 7/100 x 12

⇒ 12 ( 107/100 )

⇒ 12.84 inches

3.74 days 12.84 inches

4.74 days increase by 7 % by day

⇒ 12.84 + 7/100 x 12.84

⇒ 12.84 x 107/100

⇒ 13.73 inches

Two days growth factor

⇒ 107/100 x 100/107

⇒ 1.1449

Hence Two day growth factor for the height of the sun flower is 1.1449

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Please see image below I am checking my wirk I think the answer is -119

Answers

-119

1) Let's evaluate that polynomial when y=4, note that to evaluate is to find out the corresponding value when we plug into that another one:

[tex]\begin{gathered} -5y^2-8y-7,y=4 \\ -5(4)^2-8(4)-7 \\ -5(16)-32-7 \\ -119 \end{gathered}[/tex]

2) Hence, the answer is -119

Select the correct answer.
This table represents function f.

If function g is a quadratic function that contains the points (-3, 5) and (0, 14), which statement is true over the interval (-3, 0]?
The average rate of change of f is less than the average rate of change of g.
The average rates of change of f and g cannot be determined from the given information.
Te average rate of change of f is the same as the average rate of change of g
The average rate of change of f is more than the average rate of change of g

Answers

The average rate of change of f is less than the average rate of change of g.

What is average rate ?

This expression represents the average rate of change of the function f over the range a≤x≤b is less than or equal to x, and is less than or equal to b:

f(b)−f(a) / b - a

It is the average amount by which the function changed per unit throughout that time period.

Here, in Average rate of change in function g over [-3, 0]

=> a = -3, b = 0

=> f(a) = 5 , f(b) = 14

Average rate of change = (14 - 5) / (0 - (-3))

                                        = 3

Now, in Average rate of change in function f over [-3, 0]

=> a = -3, b = 0

=> f(a) = -3, f(b) = 0

Average rate of change = (0 - (-3)) / (0 - (-3))

                                        = 1

Therefore, The average rate of change of f is less than the average rate of change of g.

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You buy a container of cat litter for $13.75 and a bag of cat food for x dollars. The total purchase is $20.80, which includes 4% sales tax. Write and solve an equation to find the cost of the cat food.

Answers

The cost of the bag of cat food is $6.22

What is cost prize ?

The prize at which the good and services have been bought is known as cost prize.

here, the given information is :

Cost of a container of cat liter = $13.75

Cost of a bag of cat food = X dollars

Total amount of money required to purchase the items = $20.80

Percentage of sales tax that had to be given = 4%

Then,

Amount of sales tax given = (4/100) * 20.8 dollars

                                            = 20.8/25 dollars

                                            = 0.83 dollars

Then the total purchase price for the two items = 20.80 - 0.83 dollars

                                                                               = 19.97 dollars

Now we can easily find the cost of the cat food by subtracting the cost of the liter from the total purchase amount :

Cost of the cat food = 19.97 - 13.75 dollars

                                = 6.22 dollars

Therefore, the cost of the bag of cat food is $6.22

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A local jewelry store sells class rings, which it purchases for $60 each. The store engraves a name and date on the ring and sells it using a markup rate of 340%.

Answers

Class rings are sold by a nearby jewelry store, which buys them for $60 each. The amount of markup is y=204.

Given that,

Class rings are sold by a nearby jewelry store, which buys them for $60 each. The ring has a name and date engraved on it, and the retailer markup it up by 340% before selling it.

We have to find the equation that can be used to find the amount of markup y.

So,

We can write the equation as

Amount of markup=340% of the purchases amount

Taking amount of the markup as y and purchases amount is $60.

y=340%×60

y=340/100×(60)

y=34×6

y=204

Therefore, The amount of markup is y=204.

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Gabriel practices for a local marathon. If the
marathon is 42.195 kilometers long, how
many miles does Gabriel need to run in order
to condition himself? Round the answer to
the nearest tenth.
(1 mile ≈ 1.61 kilometers)

Answers

Answer:

26.208 miles

Step-by-step explanation:

42.195 / 1.61 = 26.208 miles

⦁ At store A, 3 pounds of apples cost $12. ⦁ At store B, the cost is given by y = 2x where y is the cost in dollars and x is the number of pounds of apples. ⦁ The cost of apples at store C is shown in the graph. Answer the questions to find out which store's apples are the least expensive. 1. What is the unit price of apples at store A? Explain how you found this unit price. (2 points) 2. What is the unit price of apples at store B? How did you use the equation to find the unit price? (2 points) 3. What is the unit price of apples at store C? How did you use the graph to find the unit price? (3 points) 4. Which store has the lowest unit price for apples? (3 points)

Answers

1. The unit price of apple in store A is $4

2. The unit price of apple in store B is $2

3. The unit price of apple in store C is $3

4. The store with the lowest unit price is store B

1. How to determine the unit price at store A

We can obtain the unit price at store A by doing the following:

3 pounds of apples cost $12.

Therefore,

1 pound will cost = (1 × pound $12) / 3 pounds = $4

Thus, the unit price is $4

2. How to determine the unit price at store B

We can obtain the unit price at store B by doing the following:

y = 2x

Number of pound (x) = 1Cost (y) = ?

y = 2x

y = 2 × 1

y = $2

Thus, the unit price is $2

3. How to determine the unit price at store C

We can obtain the unit price at store C by obtaining the slope of the graph. This can be obtaioned as follow:

x coordinate 1 (x₁) = 1x coordinate 2 (x₂) = 3y coordinate 1 (y₁) = 3y coordinate 2 (y₂) = 9Slope (m) =?

m = (y₂ – y₁) / (x₂ – x₁)

m = (9 – 3) / (3 – 1)

m = 6 / 2

m = 3

Thus, the unit price is $3

4.How todetermine the store with the lowest unit price

Unit price at store A = $4Unit price at store B = $2Unit price at store A = $3

From the above, we can conclude that store B has the lowest unit price

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Simplify: 4/x-2/x^2+1-2/x+1

Answers

On simplifying the given expression 4/x-2/x^2+1-2/x+1 we get solution as (2x^2 + 2x - 2)/x^2.

What is the meaning of simplifying a n equation?

To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.

We have given:

[tex]\frac{4}{x} - \frac{2}{x^2} +1 - \frac{2}{x} + 1[/tex]

Adding the numbers:

[tex]\frac{4}{x} - \frac{2}{x^2} - \frac{2}{x} + 2[/tex]

Making a common denominator:

[tex]\frac{4x}{x^2} - \frac{2}{x^2} - \frac{2x}{x^2} + \frac{2x^2}{x^2}[/tex]

Combining the values with common denominator:

[tex]\frac{2x^2 + 2x - 2}{x^2}[/tex]

This the the simplified result of the given expression.

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Tell whether it shows growth or decay and graph by using a table of values

Answers

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given exponential function

[tex]f(x)=0.5^x[/tex]

STEP 2: Compare with the standard exponential function to determine whether it shows growth or decay.

If a is positive and b is greater than 1 , then it is exponential growth.

If a is positive and b is less than 1 but greater than 0 , then it is exponential decay.

[tex]\begin{gathered} f(x)=a\cdot b^x_{} \\ \text{Comparing with }f(x)=0.5^x,\text{ it can be written as }f(x)=1\times0.5^x, \\ It\text{ can be se}en\text{ that }a=1,b=0.5 \\ \text{ Since }a\text{ is positive and b is less than 1 but greater than 0, then it is an exponential decay.} \end{gathered}[/tex]

Hence, the given function shows an exponential decay.

STEP 3: Graph the values by using a table of values

We generate a table of values first

STEP 4: Plot the graph of the data values

A building is in the shape of a square pyramid. each side of the base is 54 meters long and the height is 260 meters. what is the volume of the building? enter your answer in the box. m³

Answers

The volume of the building in the shape of a square pyramid is 252720 m³

In terms of geometry, a square pyramid is a pyramid with a square base and four lateral faces. A pyramid is a type of polyhedron with three or more triangle faces that meet above its base (the apex).

The building is in the shape of a square pyramid.

The base of the building is 54 meters long.

The height of the building is 260 meters.

The volume of the right square pyramid is given as:

V = ( 1/3)a²h

Where a is the base and h is the height.

Now we have,

a = 54 meters and h = 260 meters

Then the volume of the building is:

V = ( 1/3)a²h

V = ( 1/3 ) × ( 54 )² × 260

V = ( 1/3 ) × 54 × 54 × 260

V = 758160/3

V = 252720 m³

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a professor wants to study the effectiveness of a new study tool for a course. there are 150150150 students registered for the course. the professor ranks the students according to cumulative average in the prerequisite course. for every 222 students, in order, from the list, the professor flips a coin to assign one student to use the new study tool and the other to use the previous study tool. what type of experiment design is this?

Answers

It is a completely randomized design.

What is completely randomized design ?

Completely randomized designs are used in experiment design to explore the effects of a single primary factor without taking additional nuisance variables into account. This article describes single-factor, entirely randomized designs. On the basis of the various levels of that primary factor, the experiment compares the values of a response variable. The levels of the main factor are given at random to the experimental units in fully randomized designs.

Objects or subjects are assigned to groups in a completely random design at random. Labeling each subject before choosing from the labeled participants in a table of random numbers is one common practice for allocating subjects to treatment groups. Computers can be used to accomplish this as well.

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Jocelyn has a points card for a movie theater.
. She receives 25 rewards points just for signing up.
• She earns 12.5 points for each visit to the movie theater.
. She needs at least 170 points for a free movie ticket.
Write and solve an inequality which can be used to determine v, the number of visits
Jocelyn can make to earn her first free movie ticket. Inequality?

Answers

Answer: 25 + 12.5v ≥ 170

Step-by-step explanation:

We already have the 25 reward points; it also gives the information that she gets 12.5 points for each visit. Because we don't know the amount she has gone to the theater or will go we have to use a variable; 12.5v. When we add them, we get 25 + 12.5v. The inequality we use is ≥ because it says "at least". When this is used that means it has to be equal to or greater and that is why use that sign and get the full equation;

5 + 12.5v ≥ 170

Answer:

55

Step-by-step explanation:

A cookie factory uses 1/3 of a barrel of oatmeal in each batch of cookies. The factory used 2/3 of a barrel of oatmeal yesterday. How many batches of cookies did the factory make?

Answers

Answer:

it would be 89

Step-by-step explanation:

Evaluate the following expressions picture attached 100 POINTS

Answers

Answer:

3 5/14 (second choice)

Step-by-step explanation:

c = -3 1/7

d = 6.5 (6 1/2 as fraction)

-3 1/7 as improper fraction: -22/7

6 1/2 as improper fraction: 13/2

Now put both fractions into a common denominator

-22/7 = -44/14

13/2 = 91/14

Now add:

-44/14 + 91/14 = 47/14

Change 47/14 back to fraction

47/14 = 3 5/14


Given that f(x)=x²+3+2 write the formula defining the following function:
h if h can be formed by a horizontal translation of f right 4 units followed by a vertical translation up 7 units.
H(X)=?

Answers

The new function that can be formed after f(x) transforms horizontally 4 units to the right and then vertically 7 units upwards is
H(x) = h(x) = x² + 11x + 37.

How to shift an equation horizontally?
For a function, f; a brand new function d(x) = f(x - h), where h is a constant, is a horizontal shift of the function f; for positive 'h' the graph shifts right and for negative 'h' the graph shifts left.
How to shift an equation vertically?
For a function, f; a brand new function d(x) = f(x) + k, where k is a constant, is a vertical shift of the function f; for positive 'h' the graph shifts up and for negative 'h' the graph shifts down.

Given, the equation is f(x) = x² + 3x + 2
The new equation formed will be = h(x)
Also, the function horizontally shifts 4 units to the right.
Therefore, h(x) = f(x + 4) = (x + 4)² + 3(x + 4) + 2 = x² + 11x + 30
Again, the function formed in h(x) vertically shifts up by 7 units.
Thus, new equation for h(x) is = h(x) + 7 = x² + 11x + 37
Therefore, the required equation for H(x) = h(x) = x² + 11x + 37

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Juanita wants to buy a computer. She needs to earn at least 400 dollars. If she makes 9 dollarsan hour and has already saved 40 dollars, how many hours does she need to work? Write an inequality and solve.

Answers

Problem

Juanita wants to buy a computer. She needs to earn at least 400 dollars. If she makes 9 dollars an hour and has already saved 40 dollars, how many hours does she need to work?

Solution

Let x the number of hours required we can set up the following inequality:

40 + 9x > 400

And now we can solve for x we can subtract 40 and we got:

9x > 360

And then we got:

x> 40

So then Juanita needs to work at least 40 hours

And the graph of the inequality is given by:

to collect these data, the researchers randomly selected american households to visit and interviewed the adult member of the household whose birthday was nearest. is this an experiment or an observational study?

Answers

In an observational study, we measure or survey members of a sample without trying to affect them. In an experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.

This is clearly an observational study

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