#12: If the slope of a linear function is m = 6/5, how much
does the output change, when the input is decreased by 30?
The output changes by:

Answer:

x^2+15x

Step-by-step explanation:

when doing word problems like these, keywords are "sum" and "square" and "times". They help discern the expression.

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The difference between the amounts Julia and Kellen will raise when they both read x pages is represented by the function j(x) - k(x) =  0.75x + 8.03. And if they both read 500 pages, the difference will be 383.03.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given, Julia and Kellen are participating in a read-a-thon to raise money for charity.

The money each of them raises will be a mix of fixed and per-page donations.

Function / models the total amount, in dollars, that Julia will raise if she reads x pages:

j(x) = 1.65x + 17.31.

Function k models the total amount,

in dollars, that Kellen will raise if he reads x pages:

k(x) = 0.90x + 9.28.

To find the difference between the amounts Julia and Kellen will raise when they both read x pages:

j(x) - k(x) =  1.65x + 17.31 - (0.90x + 9.28).

j(x) - k(x) =  1.65x + 17.31 - 0.90x - 9.28.

j(x) - k(x) =  0.75x + 8.03.

If they both read 500 pages, the difference will be;

j(500) - k(500) =  0.75(500) + 8.03 = 375 + 8.03 = 383.03

Therefore, if they both read 500 pages, the difference will be 383.03.

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The complete question is:

Select the correct answer from each drop-down menu.

Julia and Kellen are participating in a read-a-thon to raise money for charity. The money each of them raises will be a mix of fixed and per-page

donations.

Function / models the total amount, in dollars, that Julia will raise if she reads x pages:

j(x) = 1.65x + 17.31.

Function k models the total amount, in dollars, that Kellen will raise if he reads x pages:

k(x) = 0.90x+9.28.

The function

If they both re

h(x)=0.75x+26.59

h(x) = 0.75x+8.03

h(x) = 2.55x+8.03

h(x) = 2.55x+26.59

represents the difference between the amounts Julia and Kellen will raise when they both read x pages.

ence will be $

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Independent-samples t test statistical test is most appropriate for analyzing the results .

What is Independent-samples t test?

To ascertain whether there is statistical support that the linked population means are statistically substantially different, the Independent Samples t Test compares the means of two independent groups.

                     An example of a parametric test is the Independent Samples t Test. The Independent t Test is another name for this test.

What is the difference between a dependent and independent samples t-test?

If the participants in one sample do not influence the participants in the other, then the two (or more) samples are said to be independent.

                                  Dependent samples are two (or more) samples where the members picked for one sample automatically determine the members chosen for the second sample.

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The equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair is A. 35.5w + 136.45 = 455.95; w = 9

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

In this case, a new gaming chair costs $455.95. You have already saved $136.45 and earn $35.50 each week babysitting.

Let the number of weeks be w.

This will be represented as:

136.45 + 35.50w = 455.95

Collect the like terms

35.50w = 455.95 - 136.45

35.50w = 319.50

Divide

w = 319.50 / 35.50

w = 9

The number of weeks is 9.

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The answer is A!

Step-by-step explanation:

It's right can I get brainliest?

Answer:

y≤-3

Step-by-step explanation:

the parabola is negative and the maximum is -3.

The probability that at least one graduate out of the five who were picked at random obtains a job in their chosen area within a year of graduation is 93.96%.

Let X represent a random variable which represents the proportion all school graduates who secure employment in their profession of choice within a year of graduation:

With a binomial distribution,

X has a n = 5 and a p value of 0.57.

n = number of trial.

p = probability of success

x = number of success.

A binomial distribution's probability mass function is provided by:

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

The likelihood that at least one gets employment in their field of choice within a year after graduation:

P(X ≥ 1) = 1 - P(X < 1)

P(X ≥ 1) = 1 - P(X = 0)

P(X ≥ 1) = 1 - ⁵C₀ . (0.57)⁰ . (0.43)⁹⁻⁰

P(X ≥ 1) = 1 - 0.603

P(X ≥ 1) = 0.9396

P(X ≥ 1) = 93.96%

Thus, the probability that at least one graduate out of the five who were picked at random obtains a job in their chosen area within a year of graduation is 93.96%.

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The complete question is-

A study conducted at a certain college shows that 57% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that among 5 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.

Answer:

(- 2, - 4 )

Step-by-step explanation:

- 4x + 4y = - 8 → (1)

4x - 6y = 16 → (2)

adding (1) and (2) term by term will eliminate x

0 - 2y = 8

- 2y = 8 ( divide both sides by - 2 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (2)

4x - 6(- 4) = 16

4x + 24 = 16 ( subtract 24 from both sides )

4x = - 8 ( divide both sides by 4 )

x = - 2

solution is (- 2, - 4 )

Answer:

$5.50

Step-by-step explanation:

Add 3.00 plus 2.50.Which is 5.50.

The probability of getting a head given that probability of getting a tail is   0. 52 is  0.48.

Probability of getting at least one head is equal to the probability of all events (100 percent, or 1) less the likelihood of receiving all tails .

Therefore the probability of getting a head is ( 1 - 0.52)

= 0.48

A random event's occurrence is the subject of this area of mathematics. The range of the probability is 0 to 1.

The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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The required statment that is true is AC = 12 and BC = 10. Option A is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
A, B and C are Collinear and B lies between A & C.
AC = AB + BC
2x + 4 = 2 + x + 6
2x + 4 = x + 8
x = 4

Now,
AC = 8 + 4 = 12
BC = 4 + 6 = 10

Thus, the required statment that is true is AC = 12 and BC = 10. Option A is correct.

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Answer:

6x + 1

Step-by-step explanation:

When you are finding the perimeter of any shape, you will combine the measurements of each side together. Note any variables when combining. They must have the same amount of the same variables to be combined:

[tex]P = (2x + 1) + (3x) + (x)\\P = (2x + 3x + x) + 1[/tex]

Combine like terms. Add 3x, 2x and x together:

[tex]P = (2x + 3x + x) + 1\\P = (6x) + 1\\[/tex]

The perimeter of the triangle is 6x + 1.

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Waiting time follows an exponential distribution with mean

μ=60

μ=60 seconds. This implies λ=1μ=160λ= μ1= 601

Let X be the waiting time. for first we have to calculate the probability of customers who wait less than 30 secs.

a. X is less than 30 seconds, then we have to find ,

P(X<X1)=1−e−λX1⇒P(X<30)=1−e−λ×0

=1−e−160×30 =1−e−12=1−0.6065

=0.3935P(X<X 1)⇒

P(X<30)

​

=1−e −λX 1=

1−e −λ×30 1−e − 601×30 =

1−e − 21

=1−0.6065

=0.3935

​b. X is more than 120 seconds, then we have to find less than 120 sec

b. X is more than 120 seconds

P(X>X1)=1−P(X<X1)=1−(1−e−λX1)⇒P(X>120)=1−(1−e−λ×120=e−60×120=e−2=0.135

P(X>X 1)⇒P(X>120)=1−P(X<X 1)=1−(1−e −λX 1)=1−(1−e −λ×120= − 601×120 =e −2=0.135

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Answer:

Ellie 69%

Kevin 78%

Therefore Kevin has the redder paint

Hence, the 2 decimal places a possible value of the number is 5.25, 5.26, 5.27, 5.28, 5.29, 5.31, 5.32, 5.33, 5.34

What are upper and lower bounds?

The maximum and smallest values that a number may have before it was rounded are known as upper and lower limits. They are also known as accuracy limits. Error intervals can be utilised to write the upper and lower bounds.

Given, A number truncated to 1 d.p. gives 5.3

And, the number originally had 2 decimal places

Then, the number could have been

5.25, 5.26, 5.27, 5.28, 5.29, 5.31, 5.32, 5.33, 5.34

These are the possible value of the number.

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Explanation about number line is discussed below:

Number lines are horizontal straight lines used in mathematics when integers are spaced at equal intervals. A number line may be used to visualise all the numbers in a succession. Both endpoints of this line continue forever.

Number lines aid in the development of a mental arithmetic approach for addition and subtraction. Research has proved the significance of number lines in fostering sound mental number sense and arithmetic techniques. No one disputes the significance of number lines.

Firstly, start from -3 on the number line.

Then, since we are adding 7, we would add 7 spaces to the right.

That should lead us to our answer; 4.

Another way is: 7 + (-3) or 7-3.

They all equal 4.

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Fatima needs to carry 13 pails to fill the pool to a depth of 18 cm.

Cube and cuboid are three-dimensional shapes that consist of six faces, eight vertices and twelve edges. The primary difference between them is a cube has all its sides equal whereas the length, width and height of a cuboid are different. Both shapes look almost the same but have different properties. The area and volume of cube, cuboid and also cylinder differ from each other.

Volume of a circular pool to a depth of 18cm = Area of circular pool x depth

π[tex]r^{2}[/tex]h

where r = radius of circular pool which is 120/2 = 60cm

h = depth which is 18cm, [tex]\pi[/tex]( constant) = 3.14

Volume (V) = 3.14 x 60^2 x 18  which is  203472 cubic centimeters

volume of each rectangular pail = 30 x 22 x 24 which is 15840 cubic centimeters

If the volume of 1 rectangular pail is 15840 cubic centimeters then the number of pails to fill 203472 cubic centimeters will be

203472/15840 = 12.84 approximately 13 pails

In conclusion 13 pails is needed to fill the pool to the depth of 18cm

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a. The constant of variation is 1.3.

b. Initially the tree is  29.1 cm.

c. The equation showing this relationship is y = 1.3x + 29.1.

d. After  12.2 weeks many weeks will the plant be 45 cm tall.

e. 16.85 weeks of time has gone by when the plant is 51.3 cm tall.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at

x = 0.

a. The constant of variation is (y₂ - y₁)/(x₂ - x₁) = (38.2 - 33)/(7 - 3).

= 1.3.

∴ 38.2 = (1.3)7 + b.

38.2 = 9.1 + b.

b = 29.1.

y = mx + 29.1.

b. Now initial constant of variation m = 0.

So, y = 29.1 (cm).

c. The equation showing this relationship is y = 1.3x + 29.1.

d. 45 = 1.3x + 29.1.

1.3x = 15.9.

x = 15.9/1.3.

x = 12.2 weeks.

e. 51 = 1.3x + 29.1.

1.3x = 21.9

x = 16.85 weeks of time have gone.

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Answer:

12 miles in 15 minutes

Step-by-step explanation:

To find the car's rate in miles per minute, we can divide the rate in miles per hour by the number of minutes per hour. There are 60 minutes in an hour, so the car's rate in miles per minute is 48 miles per hour / 60 minutes per hour = 0.8 miles per minute.

To find the number of miles the car will travel in 15 minutes, we can multiply the rate in miles per minute by the number of minutes. The car will travel 0.8 miles per minute * 15 minutes = 12 miles in 15 minutes.

The value of that maximize the profit, und determine the corresponding price and total profit for the level of production is $52,500

Given,

Suppose that the demand equation for a monopolist is p=100−.02x and the cost function is C(x)=20x+10,000. Find the value of x that maximizes the profit and determine the corresponding price and total profit for this level of production.

Here we need to find the value of that maximize the profit.

As per the Monopolist maximizes profit by setting marginal costs (MC) equal to marginal revenue (MR).

Here the Marginal revenue is the first partial derivative of Total revenue (TR) function.

And the total revenue is the quantity (X) times price (P):

TR = P⋅X

=> (100−0.01X) X

=> 100X−0.02X

Then we get get marginal cost, take the partial derivative of the cost function with respect to x:

=> MC=∂c(X)/∂X:50

=> MR=MC/100−0.02X=50/100−50

=> 0.02X

=> 2500units

Then the price of X, plug in the value of x in the inverse demand function and solve for price:

=> P=100−0.01(2500)=$75

And the profit is the difference between Total revenue and Total costs:

=> ∏=TR−TC/TR = P⋅X

=> $75 × 2500 = $187,500

Finally, the total costs, plug in the value of x in the total cost function:

=> TC = 50(2500)+10,000

=> $135,000

=> ∏ = $187,500−$135,000

=> $52,500

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The student can select 1 bill or more than one bill. The student could make 15 different sum of money.

What is permutation?

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.

Given that a student has a $50 bill, a $10 bill, a $5 bill, and a $1 bill.

He must select at least one bill.

To find the number of ways where the order does not matter is nCr.

The number of bills is 4.

Case 1:

Assume that he select 1 bill.

The number of ways to select one bill is ₄C₁ = 4!/1!(4-1)! = 4

Case 2:

Assume that he select 2 bill.

The number of ways to select two bill is ₄C₂ = 4!/2!(4-2)! =6

Case 3:

Assume that he select 3 bill.

The number of ways to select two bill is ₄C₃ = 4!/3!(4-3)! =4

Case 4:

Assume that he select 4 bill.

The number of ways to select two bill is ₄C₄ = 4!/4!(4-4)! =1

The total number of ways is 4 + 6 + 4 + 1 = 15

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Answer:

Adult:19

Child:18

Step-by-step explanation:

Adults: x

Children:y

Equation 1: 3x+4y=129

Equation: 2x+3y=92

Let's now graph our equations on the desmos graphing calculator!!!

Look for the points that meet each other on the graph which is (19,18)

So $19 for an adult and $18 for children

The total displacement in km and vector form in the form of i and j is 35.8 a[x] km + 0 a[y] km.

According to the question,

We have the following information:

A cyclist rode his bike for 169 min at an average velocity of 3. 53 m/s on a bearing of 450.

Now, we know that the following formula is used to find the velocity:

Velocity = displacement/time

(We will convert time from minutes into seconds.)

Displacement = 3.53*(169*60)

Displacement = 35794.2 m

Now, the displacement in km will be 35.8 km approximately.

Now, let's take that the bike is moving along the positive x-axis. So, it would be written in the following expression:

Displacement = 35.8 a[x] km + 0 a[y] km

Hence, the total displacement in km and vector form in the form of i and j is 35.8 a[x] km + 0 a[y] km.

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Speed of Santa 's sleigh in air (X) is 6 units and the speed of the wind (Y) is 1 unit.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical operation, and extraction of roots.

Main body:

Let 'y' stand for the speed of the wind and 'x' stand for the speed of Santa. We will use the general equation (distance)=(rate)(time) to write two equations from the given information:

With the wind:

35=(x+y)(5)                -------(1)

Against the wind:

35=(x-y)(7)                 --------(2)

using equation 1  ,we have

x+y = 7

using equation 2  ,we have

x- y = 5

now solving both equations , we get

x = 6 and y = 1

Hence , speed of Santa 's sleigh in air (X) is 6 units and the speed of the wind (Y) is 1 unit.

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Answer:

Step-by-step explanation:

Oh I don't really know but I will find it out for you right now

All the points that will lie on the median through the point (7,4) are given as follows:

The median that passes through the point (7,4) is a linear function that also passes through the midpoint of the vertices (1,4) and (7,-2).

The midpoint of two points is given by the mean of it's coordinates, hence the midpoint of the vertices (1,4) and (7,-2) is calculated as follows:

Then the two points on the line are given as follows:

(4,1) and (7,4).

Given two points, the slope is calculated as the division of the change in y by the change in x, hence:

m = (4 - 1)/(7 - 4)

m = 1.

Hence:

y = x + b

When x = 4, y = 1, hence the intercept b is obtained as follows:

1 = 4 + b

b = -3.

Then the function is given as follows:

y = x - 3.

And the points that lie on the median are all the points for which the x-coordinate is 3 less than the y-coordinate.

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Answer:

B Not a Function. They are Coordinates

(i) 263.9 meters sheet of metal is required.

(ii) 1847.25 liters of water can this tank hold.

(iii) Rupees 27841.45 cost of whitewashing this tank at the rate of rupees 105.5 per 2.

Given that,

A open cylindrical tank of radius 14 meters and height 3 meters is made of sheet metal.

We have to find

(i) The quantity of metal sheet needed.

(ii) How much water this tank is capable of holding.

(iii) How much would it cost to whitewash this tank at a rate of 105.5% per square foot?

We know that,

(i) To find the sheet required of metal is

Curved surface area of cylinder =2πrh

Here,

r is 14 and h is 3

=2π(14)(3)

=84π

=263.9

Therefore, 263.9 meters sheet of metal is required.

(ii)To find how much liters of water can tank hold.

Volume of the cylinder =πr²h

=π(14)²(3)

=588π

=1847.25

Therefore, 1847.25 liters of water can this tank hold.

(iii) To find the cost of whitewashing this tank at the rate of rupees 105.5 per 2.

=263.9×105.5

=27841.45

Therefore, Rupees 27841.45 cost of whitewashing this tank at the rate of rupees 105.5 per 2.

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Answer:

160

Step-by-step explanation:

163

if the number was 5 and over, it'd be 170. But since the number is less than 5, the answer is 160.