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The linear equation in the slope intercept form that models this situation is y = 9x + 15 .

In the question ,

it is given that ,

a member of hiking club paid $51 for 4 months ,

let the number of months be represented on x coordinate , and

the amount paid be represented on y coordinate .

So , the point becomes (4 , 51).

also given that you pay a total of $105 after 10 months ,

the second point becomes (10 , 105).

to find the equation in slope intercept form , we need slope ,

So , Slope = (105-51)/(10-4)

= 54/6

= 9

So , the equation having the point (4,51) and slope as 9 , in slope intercept form is

(y - 51) = 9(x - 4)

y - 51 = 9x - 36

y = 9x - 36 + 51

y = 9x + 15

Therefore , The linear equation in the slope intercept form that models this situation is y = 9x + 15 .

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The ending inventory cost on December 31 for 21 units, under the three inventory methods, is as follows:

a) first-in, first-out (FIFO) method: $719

b) last-in, first-out (LIFO) method: $661

c) weighted average cost method: $690

The ending inventory cost is the difference between the cost of goods available for sale and the cost of goods sold determined by the various inventory methods.

Some of the inventory methods include:

Date       Activities         Units     Unit Cost   Total

Jan. 1      Inventory           16            $31       $496

Aug. 13   Purchase           14           $33         462

Nov. 30  Purchase           13           $35         455

Available for sale            43                       $1,413

Average cost = $32.86 ($1,413 ÷ 43)

Ending inventory             21

Units sold =                     22 (43 - 21)

a) FIFO:

Ending inventory = $719 (13 x $35 + 8 x $33)

Cost of goods sold = $694 ($1,413 - $719)

b) LIFO:

Ending inventory = $661 (16 x $31 + 5 x $33)

Cost of goods sold = $752 ($1,413 - $661)

c) Weighted Average:

Ending inventory = $690 (21 x $32.86)

Cost of goods sold = $723 (22 x $32.86)

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The gallons of water and gallons of the premium antifreeze solution that must be mixed are 60 gallons and 120 gallons respectively.

In order to solve this word problem, we would assign a variable to the gallons of water and premium 60% antifreeze that is required, and then translate the word problem into algebraic equation as follows:

Since the premium antifreeze solution contains 60% premium antifreeze, we have the following mathematical expression:

w + p = 180      ....equation 1.

0.60p = 0.40(180)    ....equation 2.

From equation 2, we have:

0.60p = 0.40(180)

0.60p = 72

Premium antifreeze, p = 72/0.60

Premium antifreeze, p = 120 gallons.

For the gallons of water, we have:

w + p = 180

Water, w = 180 - p

Water, w = 180 - 120

Water, w = 60 gallons.

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Answer:

[tex]16a^6x^4y^2[/tex]

Step-by-step explanation:

To simplify this expression, use the exponent rule stating that when an exponent is put to an exponent, the exponent values are multiplied (e.g., [tex](x^2)^2 = x^{2 \cdot 2} = x^4[/tex])

Using that rule, we get:

[tex](-4x^2ya^3)^2 = (-4)^2 \cdot x^{(2 \, \cdot \, 2)} \cdot y^2 \cdot a^{(3 \, \cdot \, 2)}[/tex].

This can be simplified to

[tex]16 \cdot x^4 \cdot y^2 \cdot a^6[/tex],

which can be written as:

[tex]16a^6x^4y^2[/tex]

using the commutative property of multiplication.

The correct statement regarding the critical value of the t-distribution is given as follows:

a) [tex]t_{\frac{\alpha}{2}} = 1.6753[/tex]

What defines which distribution should be used is whether the population standard deviation is known, as follows:

As stated in the problem, the population standard deviation is not known, hence the t-distribution is used, as the sample standard deviation can be calculated from the histogram.

The critical value is obtained using a t-distribution calculator, considering that:

Hence it is given as follows:

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Answer:

D

Step-by-step explanation:

Answer: 22 square unit

Step-by-step explanation:

As each small square represents one square unit, we can count the squares and get the answer easily.

The median of the data collected from a track meet  is 2 meters.

The median is the middle number in a sorted, ascending or descending list of numbers.

To calculate the median of the given date, we folloe the steps below.

Collected date: 1, 4, 6, 2, 4, 3, 2/3, 1/3, 1/2

Step 1: Rearreange the date in accending order.

Step 2: Pick the middle of the number in the arranged data

Hence, the median of the data collected is 2 meters.

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Answer:

2.5

Step-by-step explanation:

If you want easy access to your money for paying bills, eating out, etc, it is best to use a checking account.

A checking account is a sort of bank account that enables simple deposits and withdrawals of cash for everyday use.

For instance, you may use your debit card to withdraw cash, deposit a check you receive, or set up direct deposit to get your paychecks.

It is advisable to utilize a checking account if you want quick access to your money for things like paying bills and dining out.

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The population means that the number of years worked is 14, and 73% of employees worked for the company for at least 10 years.

The mean is calculated by dividing the number of employees by the number of years of service. The total number of years of service is 417, hence the average will be

The average years worked = 417/30 = 13.9 ≈ 14 years

The % of workers who have worked there for at least ten years is calculated by calculating the number of employees who have ten or more years of service and dividing that number by the total number of employees.

The final result is presented as a percentage will be:

(10 years or more)/(total number) = 22/30 = 0.73 = 73%

Thus, the population means that the number of years worked is 14, and 73% of employees worked for the company for at least 10 years.

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The width or short side is 12 feet

The length or long side is 18 feet

What is Area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares. The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some common units for measuring area include square cms, square feet, square inches, square meters, etc.

Let Width= x feet

so, as per question Length = x+6 feet

Area = Length x Width = x(x+6) = [tex]x^{2} +6x[/tex]

According to the question each side is increased 6 feet

New Length = x+12 feet

New Width = x+6 feet

New Area = Length x Width[tex]= 2x(x+6)[/tex] <the area is multiplied by 2>

Length x Width=[tex](x+6)(x+12) = 2x(x+6)[/tex]

x+12=2x

x=12 feet

so, original width = 12 feet

original length = 18 feet

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The customer have to pay $87.9 for the watch.

A customer at the store wanted to buy a different watch that was listed at $88 but had a 15% discount.

Given the information is

Watch is listed at $88 and had a discount of 15%

The customer had to pay a sales tax of 5%

Than, by reducing the discount from the price listed

= $88 - 15%

= 88 - [tex]\frac{15}{100}[/tex]

= 87.85

Now we have to add 5% tax to the discounted price

= 87.85+5%

= $87.9

Hence the answer is the customer have to pay $87.9 for the watch.

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If two points on the map measures 10 cm, with a scale of 1 : 1000 the actual distance is 10 000 cm

information gotten from the question

a scale of 1:1000

2 points on the map 10 cm = ?

Scale factors refer to the amount or the factor the image on a map was increased or reduced in comparison with the actual dimension of the image

A map has a scale of 1 : 1000

the scale factor is 1/1000 then 10/?

1/1000 = 10/?

cross multiplying gives

? = 10 000 cm

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Answer:

r = 20/7

x = 13.5

Step-by-step explanation:

Hello!

Solve for r by cross-multiplying:

The value of r is 20/7.

Solve for x by cross-multipying:

The value of x is 13.5.

Answer:

Step-by-step explanation:

7) r/2 = 10/7, value of r?

→ r/2 = 10/7

→ r = (10/7) × 2

→ r = (10 × 2)/7

→ [ r = 20/7 ]

Hence, value of r is 20/7.

8) 9/4 = x/6, value of x?

→ 9/4 = x/6

→ x/6 = 9/4

→ x = (9/4) × 6

→ x = (9 × 6)/4

→ x = 54/4

→ [ x = 27/2 ]

Hence, value of x is 27/2.

The hopper will empty all of the grain in approximately 48.2 seconds .

Total amount of grain in the hopper = 2024.5 cubic feet

Rate at which the grain is emptied = 42 cubic feet /second.

Time taken to empty the grain

= 2024.5 / 42

= 48.202...

≈ 48.2 seconds

The ratio of two related quantities represented in several units is known as a rate. The numerator of something like the ratio expresses the rate of change for the other dependent variable if the denominator of both ratios is expressed as a single unit of each of these quantities and it is assumed that even this quantity can also be changed in a predictable way.

Hence the hopper will empty all the grain in about 48.2 seconds.

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The slope of the function A which is presented as an equation and the slope of function B presented as a table are presented as follows;

The slope of function A is 4

The slope of function B are;

Between f(0) and f(1), the slope is 1

Between f(1) and f(2), the slope is 3

Between f(2) and f(3), the slope is 5

The slope is found by the ratio of the rise to the run of the graph.

The function A is; y = 4·x - 5

Function A is of the form y = m·x + c

Where;

m = The slope of the function = 4

Therefore;

The slope of function A is 4

The first difference of the values of function B is not a constant.

The value of f(0) in function B is 0

The value of f(1) in function B is 1

The slope between f(0) and f(1) is m = (f(1) - f(0))/(1 - 0)

Which indicates that m = (1 - 0)/(1 - 0) = 1

The slope of function B between f(1) and f(2) is found as follows;

f(2) = 4, f(1) = 1, from which we get;

m = (4 - 1)/(2 - 1) = 3

The slope between f(2) and f(1) is 3

The slope of the function B between f(2) and f(3) is found as follows;

f(2) = 4, f(3) = 9, from which we get;

m = (9 - 4)/(3 - 2) = 5

The slope of the function B between f(2) and f(3) is 5

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Answer:

2 and 43.5

Step-by-step explanation:

Answer:

[tex]-1.7f+-25[/tex]

Step-by-step explanation:

1 ) To simplify combine like terms...

[tex]=-2.5f+0.8f+-16+-9[/tex]

[tex]=(-2.5f+0.8f)+(-16+-9)[/tex]

[tex]=-1.7f+-25[/tex]

Hope this helps! :)

The ratio of males to females in the cage is 2:3.

According to the question,

We have the following information:

For every 4 male birds in a cage there are 6 females.

The ratio of males to females = Number of males in the cage: number of females in the cage

Ratio of males to females = 4:6

We can convert this ratio into the simplest form by dividing both the numbers by 2 and this will also be the equivalent ratio of this obtained ratio.

Ratio of males to females = 2:3

Hence, the ratio of males to females in the cage is 2:3.

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According to the given distance, the dog can run on 22.5 miles

Distance:

Distance refers the the length of the line joining the two points. Here the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.

Given,

On his trip to meet Clare, Kiran brought his dog with him.

Here at the same time Kiran and Clare started walking, the dog started running 6 miles per hour.

When they got to Clare it turned around and ran back to Kiran. And when it got to Kiran, it turned around and ran back to Clare, and continued running in this fashion until Kiran and Clare met.

Here we know that they meet after 3.75 hours.

And we know that the dog was running 6 miles per hour

So, for 3.75 hours, it can be calculated as,

=> 3.75 x 6

=> 22.5

Therefore, then the dog can ran 22.5 miles.

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If no withdrawals were made from the accounts. The total interest earned at the end of 1 year is $230 and the percent interest for the total deposited is 5.75%.

a. Total interest earned  :

Total interest earned  = (0.02)($1000)+(0.07)($3000)

Total interest earned =$20+$210

Total interest earned =$230

b. Percent interest amount deposited

Percent interest amount deposited = Total interest earned / Total amount deposited

Percent interest amount deposited = $230 /( $1,000 + $3,000)

Percent interest amount deposited = $230 / $4000

Percent interest amount deposited = 0.0575 × 100

Percent interest amount deposited =5.75%

Therefore $230 is the interest earned and 5.75 is the percent interest.

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9.5 is the largest number

Consecutive numbers are the number will follow each other in order.

The difference between every two numbers is one. if n is the number so, the consecutive number will be n+1,n+2 , . . . . . .

Let four consecutive numbers be a , a+1 , a+2 , a+3

where a+3 will be largest number

Given the sum of these is 32

a + a +1 +a + 2 + a +3 = 32

=> 4a + 6 = 32

=>4a = 26

=> a= 26/4

=> a = 6.5

putting the values,

consecutive number will be = 6.5 , 7.5 , 8.5 , and 9.5

9.5 is the largest number

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The overall weighted average grade for this student in the class is 83.5%.

The weighted average grade is a function of the multiplication of each rate by the average score for each grading category.

The class grades are added to obtain the total grade that the student received for the different categories, involving class participation, classwork/homework, and tests/projects.

                                      Grade   Average    Class Grade

Participation                    10%        100          10% (10% x 100%)

Classwork/Homework   30%         95          28.5% (30% x 95%)

Test/projects                  60%         75          45% (60% x 75%)

Total grade in class                                      83.5%

Thus, from the student's participation, classwork/homework, and tests/projects, we can summarize that they scored an average weighted grade of 83.5%.

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The function of f(0) =7.0710.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

f(x) = 2(x)² +5√(x+2)

f(0) = 2*0 +5√2

f(0) =  7.0710

Hence the value will be 7.0710.

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Dwayne have to complete the race in 11.53 second or the speed of Dwayne  is 11.53 second/ 100 meter.

What is speed of an object?

Speed, expressed in terms of meters per second, is the rate at which an object's location changes. An item moves one meter in one second, for instance, if it starts at the origin and moves three meters in three seconds. The formula for speed is straightforward: time divided by distance.

Given that Chris, Kiona, Seiko, and Dwayne each run 100 meters in a relay

race. Chris runs his part of the race in 12.35 seconds, Kiona takes

13.12 seconds, and Seiko takes 11.91 seconds.

The total time that is taken by Chris, Kiona, and Seiko is (12.35 + 13.12 +  11.91) seconds = 37.38 seconds.

The team wants to break the record of 48.92 seconds.

To break the record, they should complete the race in 48.91 seconds.

Thus Dwayne have to run 100 meters in ( 48.91 - 37.38) = 11.53 seconds.

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The balance on the loan after a month is $623389.25.

The following can be deduced from the information given:

Principal = $250000

Time = 25

Rate = 6%

Interest = (Principal × Rate × Time) / 100

Interest = (250000 × 6 × 25) / 100

Interest = $375000

The total amount will be:

= Principal + Interest

= $250000 + $375000

= $625000

The balance of the loan will be:

= Amount - One month payment

= $625000 - $1,610.75

= $623389.25

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The percentage of the campers prefer outdoor activities and reading is A. 24%.

From the information, the tree diagram shows campers branching off into two categories, prefer outdoor activities is labeled 80%, and those who prefer reading, which is labeled 30%.

Therefore, percentage of the campers prefer outdoor activities and reading will be:

= Percentage for outdoor × Percentage of reading

= 80% × 30%

= 24%

In conclusion, the correct option is A.

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Answer: 56% i did the test

Step-by-step explanation: