A car's value is $9,800.A sales person receives 5% commission if he
sells the car. How much would he obtain in commission from the sale of
that car.

Answers

Answer 1

The commission the salesperson would receive is $490.

What is a commission?

A commission is a payment made to an individual, such as a salesperson or agent, for services rendered or a good sold. The commission is typically a percentage of the sale or revenue generated. This percentage is known as the commission rate.

To find the commission a salesperson would receive from selling a car, we need to multiply the commission rate (5%) by the car's value ($9,800).

The commission rate is given as a percentage, so we need to convert it to a decimal to do the calculation. We can do this by dividing the percentage by 100.

So 5% = 5/100 = 0.05

Then to find the commission the salesperson would receive we multiply:

Commission = 0.05 * $9,800

Commission = $490

Hence, the commission the salesperson would receive is $490.

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Related Questions

-1=1/3v
show work
∨=









Answers

Answer:

v = 1/-3

Step-by-step explanation:

cross multiply

-3v = 1

then:

divide through by the coefficient of v which is -3

-3v/-3 = 1/-3

[tex]-1=\dfrac{1}{3} v[/tex]

Flip:

[tex]\dfrac{1}{3} v=-1[/tex]

Multiply both sides by 3:

[tex]3\times(\dfrac{1}{3} v)=3\times(-1)[/tex]

[tex]\fbox{v = -3}[/tex]

In a market survey, 100 traders sell fruits. 40 sell apples, 46 oranges, 50 mangoes, 14 apples and oranges, 15 apples and mangoes and 10 sell all three fruits each of the 100 traders sell at least one of the three fruits. (A) how many traders sell only one fruit. (B) how many traders sell only two fruits.

Answers

a) The number of traders who sell only one fruit is given as follows: 88.

b) The number of traders who sell only two fruits is given as follows: 9.

How to obtain the amounts?

The amounts are obtained using Venn sets in the context of this problem.

The sets are given as follows:

Set A: sells apples.Set B: sells oranges.Set C: sells mangoes.

10 sell all three fruits, hence:

A ∩ B ∩ C = 10.

15 vendors sell apples and mangoes, hence:

(A ∩ C) + (A ∩ B ∩ C) = 15

(A ∩ C) = 5.

14 vendors sell apples and oranges, hence:

(A ∩ B) + (A ∩ B ∩ C) = 14

(A ∩ B) = 4.

Hence the number who sell two of them is of:

(A ∩ B) + (A ∩ C)  = 4 + 5 = 9.

50 vendors sell mangoes, hence:

C + (A ∩ C) + (A ∩ B ∩ C) = 50

C = 35.

46 vendors sell oranges, hence:

B + (A ∩ B) + (A ∩ B ∩ C) = 46

B = 32.

40 vendors sell apples, hence:

A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 40.

A + 9 + 10 = 40

A = 21.

Hence the number of vendors who sell only one fruit is given as follows:

A + B + C = 21 + 32 + 35 = 88.

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Write and solve an equation to find the value of x.

Answers

Answer:

x = 60°

Step-by-step explanation:

opposite angle = congruent

so

120 = 2x

x = 120 : 2

x = 60

check

120 = 2 x 60

120 = 120

the answer is good

Using a number line, find both the intersection and the union of the following
intervals:
(-∞,2) and [0,∞)

Answers

The answer choice which represents a number line for the intersection of the given intervals is; (-∞, 2).

The answer choice which represents a number line for the union of the given intervals is; (-∞, ∞).

What is the number line representation of the intersection and union of the given intervals?

It follows from the task content that the number line which represents the intersection and union of both intervals given is to be determined.

Since the given intervals are; (-∞, 2) and [0,∞).

It follows that the intersection of both intervals is the interval; (-∞, 2).

Also, the interval which represents the union of both intervals is; (-∞, ∞).

Hence, the image which represents both scenarios is attached.

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Hello. Please answer!

Answers

✓=correct

X=wrong

Answer:


X 3x+1=9

✓ 25/x+4=9

X 11+6x=22

✓ x/5+5=6

✓ 32-4x=12

X 18-2x=9





Does 5 12 13 make a right triangle?

Answers

The sides of the triangle having length as  5 units , 12 units and 13 units make a Right Triangle because the condition to form a right triangle is satisfied by the given sides .

The Pythagoras Theorem is used to check whether the sides form a right triangle or not , it  states that square of the lonest side (hypotnuse) of the triangle is equal to  sum of  square of other two sides ( perpendicular and Base) ,

The side lengths of  triangle = 5 units , 12 units and 13 units ,

By  Pythagoras theorem , we have  [tex]13^{2} = 12^{2} + 5^{2}[/tex]

On simplifying ;

we get ;

[tex]169 = 144 + 25[/tex] ;

[tex]169 = 169 ;[/tex]

the condition of Pythagoras theorem is satisfied ,

that means the sides form a right triangle .

Therefore , the side 5 units , 12 units and 13 units  make a right triangle .

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Please help ASAP!


Solve the inequities:


k^2-7k+12. 25>0


2. 25y^2-3y+1<0

Answers

It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression

Solve the inequities:

k^2-7k+12. 25>0

2. 25y^2-3y+1<0

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression

So Whenever you find two conclusions which are false Just check for these two symbols . In Most of the case where two conclusions are false and these two signs are not there respectively than that statement, you can call it as Neither Nor.

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How many minutes will a bus take to cover 5 km travelling at 9 km/h?

Answers

Answer:

the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.

Step-by-step explanation:

To find out how many minutes it will take for a bus to cover 5km at a speed of 9km/h, we need to use the formula:

time = distance / speed

In this case, the distance is 5 km, and the speed is 9 km/h. To convert the speed to km/min we can divide 9 by 60.

9 km/h = 0.15 km/min (by dividing 9 by 60)

Now we can substitute the distance and speed into the formula:

time = 5 km / 0.15 km/min = 33.33 min

So, the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.

It's important to note that in this problem km/h is the speed and the distance is given in km, so you need to convert it to km/min in order to find the time. Also the time you get will be in minutes.

Estimate how many times larger 1.9 • 10^-8 is than 4.2 • 10^-13

Answers

Answer:

Step-by-step explanation:

a.[tex]1.9[/tex]·[tex]10^{-8}[/tex]=190000·[tex]10^{-13}[/tex]

b.so 190000÷4.2=4523

c.finally, about 4523 times

To compare the two numbers, we need to compare the ratio of 1.9 • 10^-8 to 4.2 • 10^-13.

The first number, 1.9 • 10^-8, can be written as 0.00000019.
The second number, 4.2 • 10^-13, can be written as 0.000000000000042.

We can see that 1.9 • 10^-8 is much larger than 4.2 • 10^-13, as it has more trailing zeros. We can estimate that 1.9 • 10^-8 is about 45 times larger than 4.2 • 10^-13.

We can confirm this by counting the difference in the number of trailing zeros in both numbers. 1.910^-8 has 8 trailing zeroes and 4.210^-13 has 13 trailing zeroes, meaning 1.910^-8 is 8-13= -5 orders of magnitude larger than 4.210^-13

Find the missing term in the arithmetic sequence −14, _, _, 46

Answers

In an arithmetic sequence, the difference between consecutive terms is constant. In this case, the difference between −14 and 46 is 60, so we can say that the common difference is 60.

To find the missing terms, we can use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference.

Plugging in the values from the given sequence, we have:

a_2 = -14 + (2 - 1) * 60 = -14 + 60 = 46

a_3 = -14 + (3 - 1) * 60 = -14 + 120 = 106

So, the missing terms are 46 and 106.

Why parallel algorithm is better than a sequential algorithm?

Answers

The capacity to complete complex tasks quickly enough to make them useful is the main benefit of choosing a parallel algorithm over a sequential algorithm.

What is the differences between parallel algorithm and sequential algorithm?

The differences between parallel algorithm and sequential algorithm are-

Sequential algorithm

One by one, each instruction is carried out in order. It only has one processor.Due to the single processor, it performs poorly and puts a heavy burden on the processor.The format utilized for data transport is bit-by-bit.The entire process takes longer to finish.Low price

Parallel algorithm

Every command is carried out simultaneously.There are several processors in it.Due to the several processor, it performs very fast and puts no burden on the processor.Transfers of data occur in bytes.The entire process takes less time to finish.Price is expensive.

Due to capacity to complete complex tasks quickly enough to make them useful is the main benefit of choosing a parallel algorithm over a sequential algorithm.

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3x -y=-2y solve for y pls help me

Answers

Answer:

-x

Step-by-step explanation:

3x - y = -2y

add y to both sides

3x = -3y

divide both sides by -3

-x = y

Jackson picked apples for his family. He picked a total of 6 pounds. He took 2

3

4

pounds to his aunt and 1

7

8

pounds to his mother. How many pounds of apples were left to give to his grandmother? Use the numbers and symbols to write an equation that represents the problem, then solve the equation. Symbols may be used more than once or not at all.


2

3

4

1

7

8

6 y + =


PLEASE HELPPPPPPPP

Answers

"17/8" pounds of apples were left to give to his grandmother.

Since we have given that

The quantity of apples he picked is given by 6.1/2⇒13/2 pounds.

The quantity of apples he picked for his aunt is given by 2.3/4⇒11/4 pounds.

The quantity of apples he picked for his mother is given by 1.5/8⇒13/8 pounds.

So, the total quantity left for his grandmother is given by

first we have to add the quality of apples he picked for his aunt and the number of apples he picked for his mother.

After subtracting from what he picked.

⇒13/2-(11/4+13/8)

⇒13/2-(22+13/8)

⇒13/2-(35/8)

⇒52-35/8

⇒17/8

Hence, 17/8  pounds are left for his grandmother.

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At a certain university, the average attendance at basketball games has been 2,925. This year the attendance for the first 15 games has been 2,515 with a standard deviation of 585. The athletic director claims that the attendance is the same as last year. If what are the critical values for this two-tailed t test

Answers

The absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.

population mean assumed to be 2925

sample mean = 2515

standard deviation of sample = 585.

sample size = 15

t-score is indicated because the standard deviation is taken from the sample rather than from the population.

t-score = (x - m) / s

x is the raw score

m is the raw mean of the population

s = standard deviation of sample/sqrt (sample size) = 585/sqrt(15) = 151.6217 rounded to 4 decimal places.

degrees of freedom = 15 minus 1 = 14.

t-score = (2515 - 2925)/151.6217 = -2.7123 rounded to 4 decimal places.

you need to know the confidence level.

at a 95% confidence level, the two-tailed critical t-score with 14 degrees of freedom = plus or minus 1.7613 rounded to 4 decimal places.

since the absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.

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Donny is raising money for the school charity drive by mowing lawns for $9.75 per lawn. How much will he raise for the drive?

is this proportional or non proportional and why.

Answers

What does it mean to be proportional?

For two numbers to be proportional, they need to be directly increasing or decreasing in a constant ratio.

If Donny makes $9.75 per lawn, we can make a table that looks like this:

1 Lawn = $9.95

2 Lawns = $19.90

3 Lawns = $29.85...

And so on.

You can see this is proportional because it has a constant ratio between both elements.

(1 to 9.95)

So, it is proportional.

Translate the triangle.
The enter the new coordinates.
A (-2,4)
C
(-3,2)
B
(1,1)
<-4, -1 >
A'(-6, [?])
B'([ ], [ ])
C'([], [])

Answers

Therefore , the solution of the given problem of triangle comes out to be  A'(1, 0) (1, 0) , B'(1, 2) (1, 2) and C'(3,-2) (3,-2).

Explain the triangle.

The fact that a triangle has four segments or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with endpoints A, B, then C is Triangle ABC. A singular plane and square are obtained in Euclidean geometry when the edges are not collinear. Any triangle that has three sides and three corners is a polygon. The triangle's corners are the spots at which its three sides intersect. 180 degrees is the result of three triangle angles.

Here,

The image A'B'C' is formed by our transformation rule, (+3,y-2)

So:

1. Describe the updated coordinates for points A', B', and C'?

In order to locate these new positions, we have:

A' (-23, 2-2)  =>    A'(1, 0) (1, 0)

B' => (-23, 4-2)    =>   B'(1, 2) (1, 2)

C'=> (0+3,0-2) => C'(3,-2) (3,-2)

2. Explain the qualities that would emerge if the respective vertices were linked together by lines.

We can notice the two triangles on the First Figure if we look closely. The green one is A'B'C, while the red one would be the triangle ABC.

The equivalent vertices with in second figure have been joined together by line segments, as shown by the green lines.

Two things can be said about those three lines: first, they are parallel, and second, they are all the same length.

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What is the difference of the polynomials 5x 3 4x 2 )-( 6x 2 2x 9?

Answers

The Solving we get the difference of the given polynomials [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] as [tex]5x^{3} - 2x^{2} + 2x + 9[/tex]   .

What is a Polynomial ?

The polynomial is defined as the expression that is composed of variables, constants and exponents, which are combined by using mathematical operations such as addition, subtraction, multiplication and division .

Based on number of terms present in polynomial , they can be classified as  monomial, binomial, and trinomial .

For Example : [tex]3x^{2} +4x[/tex]  .

The polynomial is given as : [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] ;

On simplifying the above given polynomial ,

we get ,

= [tex]5x^{3} + 4x^{2} - 6x^{2} + 2x + 9[/tex]

On subtracting the like terms together  in above equation ,

we get ;

= [tex]5x^{3} - 2x^{2} + 2x + 9[/tex]

Therefore , the difference of the polynomials is (d)  [tex]5x^{3} - 2x^{2} + 2x + 9[/tex] .

The given question is incomplete , the complete question is

What is the difference of the polynomials?

[tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex]

A. –x³ + 6x² + 9

B. –x³ + 2x² – 9

C. 5x³ – 2x² – 2x – 9

D. 5x³ – 2x² + 2x + 9

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how do i do this question

Answers

The slope of the line is given by the equation slope m = 3/2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , let the first point be P = P ( 0 , 1 )

Let the second point be Q = Q ( 2 , 4 )

Now , the slope of the line between the two points is

Slope m =  ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 4 - 1 ) / ( 2 - 0 )

On simplifying the equation , we get

Slope m = ( 3 / 2 )

Therefore , the value of m is 3/2

Hence , the slope of the line is 3/2

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Mr. Starnes and his wife have 6 grandchildren: Connor, Declan, Lucas, Piper, Sedona, and Zayne. They have 2 extra tickets to a holiday show, and will randomly select which 2 grandkids get to see the show with them.
a. Give a probability model for this chance process.
b. Find the probability that at least one of the two girls (Piper and Sedona) get to go to the show.

Answers

Probability that one of the girls (Piper as well as Sedona) will be able to attend the performance is one in five.

Explain the term Probability?Any probability is a mathematical representation of the likelihood or chance that a specific event will take place. All these proportions ranging from 0 to 1 and percentages varying from 0% through 100% can be used to describe probabilities.

For the stated question-

There are 6 grandkids.There are two girls.

Out of the six grandchildren, two are to be chosen.

There are 6C2 different ways to choose 2 out of 6 grandchildren.

6C2  = 6! / (6 - 2)!*2!

6C2  = 15

There are 15 different ways to choose two grandchildren out of six.There are 2C1 different ways to choose 1 of the 2 girls.

   

2C1 = 2

There are two different ways to choose one of the two girls.

Number of methods for choosing both girls = 2C2

Number of methods for choosing both girls equals one.

Probability of choosing 1 of the 2 grandchildren is 1/15.

The likelihood of choosing both girls is 2/15.

Probability that one of the females (Piper and Sedona) will be able to attend the performance is:

=  1/15 + 2/15.

= 3/15.

Thus, Probability that atleast one of girls (Piper as well as Sedona) will be able to attend the performance is one in five.

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Suppose the average score on a national test is 600,with a standard deviation of 50. If each score is increased by 10, what are the new mean and standard deviation

Answers

On solving the provided question we can say that the new Mean = 610 mean .

What is mean?

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). is 50.

What is mean?

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean).

The mean score is calculated by dividing the total number of tests taken by all of the scores. The mean will therefore rise if you give each test a higher mark. The standard deviation is calculated as the square root of the product of the power of two of all test results, multiplied by the number of tests, and then subtracted from the mean.

Each score you raise by 10 will result in a 10 change in the mean. But as there will be no change in the distance between each score and the mean, the standard deviations will also not change.

Mean = 600

Average deviation is 50.

Scores went up by 10

Mean = 610

Average deviation is 50.

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What is quadrant 3 on a graph?

Answers

The lower left-hand corner of the graph is the third quadrant.

It contains the negative values of both x and y.

Quadrant

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions called quadrants, each bounded by two half-axes.

Cartesian system

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

coordinates

Coordinates are numbers which determine the position of a point or a shape in a particular space.

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The times taken by 25 people to complete a puzzle are shown. Draw a frequency polygon for data.

Answers

To create a frequency polygon calculate the midpoint,  locate the midpoints and connect them with lines.

What is a frequency polygon?

A frequency polygon is a form of graph that shows how frequently a particular variable—in this case, the amount of time it takes for people to finish a puzzle—occurs.

So, we must determine the midpoint or average of the range for each category.

0 < t < 10 = 5

10 < t < 20 = 15

20 < t < 30 = 25

30 < t < 40 = 35

2. Add a point where the data of the axis Y and X form an intersection.

3. Connect the points.

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What is the sum of all the positive two-digit integers where one of the digits is three times the other

Answers

The sum of all the positive two-digit integers where one of the digits is three times the other is 630.

To arrive at this result, the numbers can be broken down into two groups. The first group consists of numbers with 3 as the first digit, and the second group consists of numbers with 3 as the second digit.

For the first group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9. This gives a sum of 3+6+9+12+15+18+21+24+27 = 135.

For the second group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9 and then reversing the digits. This gives a sum of 30+60+90+12+51+81+21+42+72 = 495.

The total sum of all the positive two-digit integers where one of the digits is three times the other is 135+495 = 630.

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At the opening session of the United States Supreme Court, each justice shakes hands with all the others. There are nine justices that sit on the Supreme Court. How many handshakes do they make during the opening session

Answers

According to probability, total number of handshakes will be 36.

How many handshakes are possible?

Handshakes equal n * (n - 1)/2. This is the case because a handshake between two people is not counted twice and each of the n people can shake hands with n - 1 people (they wouldn't shake their own hand). Any number of people can be calculated using this formula.

The first person will need to shake eight (8) people's hands. Only seven (7) hands will need to be shook by the second person because the first handshake will not be repeated. Due to the same factors as mentioned above, only six (6) people will require a handshake from the third person. This continues until the final person has no one left to shake hands with because everyone has already done so.

The formula to calculate how many handshakes were exchanged is n = 8 + 7 + 6 +... + 1 = 36.

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How do you draw a logarithmic graph?

Answers

Choose the range of values for the x-axis and the y-axis , Plot the points on the graph, using the logarithmic formula , Connect the points with a smooth curve and Label the axes and add any other details you want to include.

1. Choose the range of values for the x-axis and the y-axis. Select the minimum and maximum values for both the x-axis and the y-axis.

2. Plot the points on the graph, using the logarithmic formula. Use the formula log(x) = y to calculate the points that should be plotted on the graph. For example, if the x-axis range is from 1 to 10, and the y-axis range is from 0 to 10, then the first point would be (1,0).

3. Connect the points with a smooth curve. Once all the points have been plotted, use a ruler or a graphing calculator to connect them with a smooth curve.

4. Label the axes and add any other details you want to include. Use a ruler or a graphing calculator to label the axes and add any other details you want to include, such as a title, a legend, or a grid.

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Angles A and B are complementary. If sin A = 4x + 10 and cos B = 2x + 16, what is the value of x?

Answers

The value of x is 10.66

What is complementary angles?

Complementary angles  is when the sum of two angles is equal to 90 degrees. for example, 30 degrees and 60 degrees are complementary angles.

If the sum of two angles is 90 degrees then we say that they are complementary. Thus, the complement of an angle is obtained by subtracting it from 90. for example the complement of 40° is 90° - 40° = 50°

So we have Sin A and Cos B

4x + 10+ 2x + 16= 90

Collect like terms

6x+ 26= 90

6x= 90-26

6x= 64

x= 64/6

x= 10.66

Therefore, the value of x is 10.66

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Complete the table with the perimeter for each given side length. Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is l. Use function notation. ​

what does P(11) represent in this situation? What is its value?

Answers

For a roll of paper with dimensions 3 feet cut to any desire length,

a) The value of perimeter when cut to 2.5 feet is 11 feet.

b) The complete table with filled perimeter column is present above . The function notation for perimeter is , P =2(L+ W)

c) P(11) , represents the length of paper cut to 11 feet in this situation. It's value i.e., P(11) = 28 feet .

Perimeter is defined as the sum of all boundary length of any geometry. We have a roll of paper with dimensions 3 feet ( i.e, width) is cut to any length. From, it we conclude that that paper is like quadrilateral shape but not square.

a) when the paper cut in a length of 2.5 feet , so, length (L) = 2.5 feet

The perimeter of quadilateral ( rectangle in this case ) is 2(L+W) so, perimeter

= 2( 2.5 + 3)

= 11.0 feet

b) Now, we have to complete "perimeter coulmn ," in the table and side lengths are provided.

Width (w) = 3 feet

length (l) = 1 feet

perimeter = 2(4) = 8

similarly, side lengths (ft.) perimeter ( ft.)

2.5 11

1 8

2 10

11 28

L 2( L + W)

The functional notation for perimeter is

P = 2(L+W) .

c) P(11) represents the length of paper in feet when the paper is cut at a length of 11 feet . It's value is 28 feet . So, the value of P(11) is 28 feet.

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Complete question:

A roll of paper that is 3 feet wide can be cut to any length.

a. If we cut a length of 2.5 feet, what is the perimeter of the paper?

b. Complete the table with the perimeter for each given side length. Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is L, use a function notation.

c) what does P(11) represent in this situation? What is its value?

does multiplying 2 numbers together always give the first common multiple of the numbers? explain using examples

Answers

No. Let’s use 2 and 8
2 x 8 = 16

But the first common multiple is 8

2, 4, 6, 8, 10, 12, 14, 16…
8, 16, 24…

frank weighs 160 lbs gains 2 lbs a week, john weighs 208 lbs and loses 3 lbs a week


A. when will they weigh the same, and how much will they weigh

B. Explain clearly

Answers

If frank weighs 160 lbs gains 2 lbs a week, john weighs 208 lbs and loses 3 lbs a week.

a. When they will weigh the same is  9.6 dieting days and the amount is 179.2lbs.

b. Based on the calculation both of them has the same amount of weight.

How to find the amount of weight?

a. Weight

Let d represent the number of dieting days for this happen.

Since Frank gains 2 lb a day or a total of 2d lbs and John loses 3 lb a day for a total of 3d lbs

So,

John's weight = Frank's weight

Hence,

208 - 3d = 160 + 2d

Combine like terms

208 - 160 = 2d + 3d

48 = 5d

Divide both side by 5d

d = 48/5

d = 9.6 dieting days

The amount the weigh

Using John equation

Weigh = 208 - 3(9.6)

Weigh = 208 - 28.8

Weigh = 179.2 lbs

b. The amount they both weigh is the same as John weigh 179.2ilb and Frank as weigh the same.

Using Frank's equation

Weigh = 160 + 2(9.6)

Weigh = 160 + 19.2

Weigh = 179.2 lbs

Therefore when they will weigh the same is  9.6 dieting days and the amount is 179.2lbs.

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Every tread of a staircase is 8 in.​ deep, and every riser is 6 in. high. How would you find the angle the staircase makes with the​ floor? Explain.

Answers

Answer:

  36.9°

Step-by-step explanation:

You want to know the pitch angle of a staircase with a riser height of 6 inches and a tread depth of 8 inches.

Tangent

The tangent of an angle is the ratio of the side opposite to the side adjacent:

  Tan = Opposite/Adjacent

Application

The tangent of the staircase angle to the floor will be the ratio of the riser height to the tread depth:

  tan(α) = (6 in)/(8 in) = 3/4

The angle is found using the inverse tangent function.

  α = arctan(3/4) ≈ 36.9°

__

Additional comment

You need to be a little bit careful here. Different authors define "tread depth" differently. For the purpose of this question, it must be defined as the horizontal distance between corresponding points on adjacent treads, as shown in the attached illustration.

Some authors define tread depth as the distance from the nosing to the riser. If that definition is used, the "run" of the step will be the tread depth less the nosing depth. The pitch angle will be the arctangent of the ratio of riser height to "run".

The tread depth of 8 inches is a little too narrow to be in compliance with some building codes. A more usual minimum is about 10 inches with a riser height of 7 1/2 inches.

Answer:

0.75 tangent 0.75

Step-by-step explanation:

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