The line given by y = 1/4x − 1 is dilated by a scale factor centered at the origin. The image of the line after dilation is given by y = 1/4x - 5. What is the scale factor of the
dilation?

The requried factor pair of the sum of the horses and cows is given as 2 × 2 × 2 × 5.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

here,
Some of the cows and horses = 18 + 22 = 40
The required factor pair of the sum can be formed as,
= 2 × 2 × 2 × 5

Thus, the requried factor pair of the sum of the horses and cows is given as 2 × 2 × 2 × 5.

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The pair of angles ∠4 and ∠7 are alternate interior angles.

In Mathematics, parallel lines can be defined as two (2) lines that are always the same distance apart and they never meet.

In Geometry, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent. Additionally, these angles are generally referred to as alternate interior angles in Mathematics, .

In this scenario, we can logically conclude that angle 4 (m∠4) and angle 7 (m∠4) forms a pair of alternate interior angles because line l is parallel to line m.

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The amount of water drank in 12 hours will be 180 ounces.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jim drinks 15 ounces of water each hour. The amount of water drank by Jim in 12 hours will be,

Amount of water = 15 x 12

Amount of water = 180 ounces

Hence, the amount of water drank in 12 hours will be 180 ounces.

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In ΔACE, BG = 7, GE = 14 is the centroid theorem and BE = 21 then BG = 7, GE = 14.

The method for determining a triangle's centroid is called the centroid formula. Any object's centroid is its geometric center. The point that divides the medians in half by two is referred to as a triangle's centroid. The geometric center of any geometric object, whether it be a one-dimensional curve, a two-dimensional region, or a three-dimensional volume, is called the centroid. Centroids can very handy for a variety of tasks in Statics and later courses, such as the study of distributed forces, beam bending, and shaft torsion.

The place where the triangle's three medians intersect is known as the centroid (each median connecting a vertex with the midpoint of the opposite side).

According to the centroid theorem, the centroid is located 2/3 of the way between each vertex and the middle of the opposing side.

Point G is 2/3 of the way from point E, and BE is the median:

GE = 2/3BE = 2/3(21) = 14

BG = BE - GE = 21 - 14 = 7

BG = 7, GE = 14

Therefore, the correct answer is option c) BG = 7, GE = 14.

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To maximize the profit only 52 Tables must be manufactured daily and to minimize the profit only 173 chairs must be manufactured working with the efficiency given.

What is efficiency?

The ratio of work accomplished by a machine or process to total energy expended or heat consumed is known as efficiency.

Efficiency refers to how close we can get to a specific outcome from a given input with the least amount of waste. Efficiency is the capacity to waste as little material, work, energy, and time as possible when executing a task or generating a desired outcome.

The ratio of usable output to total input can be used to calculate efficiency. The efficiency of a device is defined as the ratio of energy transferred to a usable form to the total energy provided originally.

Now

For table,

assembly hours=8

finishing hours = 2

profit/table=$90

For Chairs

assembly hours=2

finishing hours = 1

profit/chair=$25

Total assembly hours in a day=400

Total finishing hours in a day=120

As profit for table is more than profit for chair. Therefore, for maximum profit only Tables will be manufactured and will be

=total hours available/Time taken for one chair

=520/10

Tables manufactured=52

and for minimum profit only chairs will be manufactured

=520/3

chairs manufactured=173

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Answer:

infintely many

Step-by-step explanation:

Answer:

Step-by-step explanation:

The number of cubes that can be filled in the rectangular prism is 720.

Volume of a three dimensional shape is the space occupied by the shape.

Volume of a rectangular prism = Length × Width × Height

Given a rectangular prism with side lengths 3inches by 7.5 inches and 4 inches.

Volume of rectangular prism  = 3 × 7.5 × 4 = 90 inches³

Volume of a cube = (side length)³

Given cube has side length 0.5 inch.

Volume of cube = (0.5)³ = 0.125 inches³

Number of cubes that can be filled in the rectangular box = 90 / 0.125

                                                                                                 = 720

Hence 720 cubes can be filled in the rectangular prism.

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The average participation score after dropping the lowest 4 participation scores is = 83.33%

In order to calculate the average participation score after dropping the lowest 4 participation scores, we need to first calculate the participation score for each class.

For the first class, the student answered 2 out of 3 quizzes correctly, so the participation score is (2/3) x 100 = 66.67%.

For the second class, the student answered 1 quiz correctly, so the participation score is 100%.

Now we need to find the average participation score after dropping the lowest 4 scores. Since the student only participated in 2 classes, we don't need to drop any scores, the average participation score is (66.67 + 100)/2 = 83.33%

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The maximum number of interior angles of a convex n-gon that can have measure 131° is equals to the seven.

A polygon is said to be convex n-gon when no line segments between the points, goes inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°. Sum of interior angles of n sided polygon

= 180(n- 2) degrees

We have, Alex assume that one of interior angle of convex n-gon is 131° . Let total maximum number of interior angles of a convex n-gon or polygon that can have measure 131° be "x".

Total measures of all remaining interior angles, (n - x) of this polygon

= 180(n- 2) - 131x

But for a convex n-gon, interior angles of a convex polygon are less than 180°. So,

180(n- 2) - 131x < (n - x) 180

Now, solve this Inequality,

=> 180n - 360 - 131x < 180n - 180x

=> -360 + 180x - 131x < - 180x + 180x

=> - 360 + 49x < 0

=> 49x < 360

=> x < 360/49

=> x < 7.34 ~ 7

So, the required value of x is 7 .

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The standard deviation of d is 1.27, which is the measure of the variability of a set of data. It tells us how much variation or dispersion exists from the average or mean value.

In other words, it reveals the degree to which the data points deviate from the mean. In this instance, the standard deviation of 1.27 means that, on average, the number of puzzles solved in a 5-minute period by two randomly selected participants differs by 1.27 puzzles. Accordingly, the majority of individuals ought to deviate by an amount that is within 1.27 puzzles of the mean.

Additionally, this implies that some subjects will have differences larger than 1.27 and some lower. We may quantify the level of variability in a data set using the standard deviation, which is a useful measure of variability.

Your question is incomplete but most probably your full question was A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by randomly chosen subject. The psychologist found that X had the following probability distribution_ Value Probability 0.2 0.4 0.3 0.1 Let D be the difference in the number of puzzles solved by two randomly selected subjects in a 5-minute period. What is the standard deviation of D? 0.81  1.8  1.27

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Answer:

9. y=66  x=114

10.y=9  x=16

Step-by-step explanation:

Answer:

5 weeks

Step-by-step explanation:

Let's find how much money she saves a week by multiplying the decimal form of 60% and $70.

To get the decimal form of a percent you have to move the decimal to the left twice, like this: 60 ---> .60

Now that we have the decimal form of the percent we can multiply it by the 70 to find how much she saves a week:(70)(.6) = 42

Therefore, Kendra saves $42 each week. To find how many weeks it will take Kendra to buy the game system you divide $210 by the $42.

Like this:(210)/(42) = 5 All in all, it will take Kendra 5 weeks to save enough money to buy a game system that costs $210. I hope this helps!!

-Hadi

Answer:

Step-by-step explanation:

Answer:

5 weeks

Step-by-step explanation:

Let's find how much money she saves a week by multiplying the decimal form of 60% and $70.

To get the decimal form of a percent you have to move the decimal to the left twice, like this: 60 ---> .60

Now that we have the decimal form of the percent we can multiply it by 70 to find how much she saves a week:(70)(.6) = 42

Therefore, Kendra saves $42 each week. To find how many weeks it will take Kendra to buy the game system you divide $210 by the $42.

Like this:(210)/(42) = 5 All in all, it will take Kendra 5 weeks to save enough money to buy a game system that costs $210. I hope this helps!!

-Raf

Answer:

40 units

Step-by-step explanation:

AB = AC as the opposite angles are equal.

4x + 4 = 6x - 14

2x = 18

x = 9 units

Therfore, AC = 6 x 9 - 14 = 54 - 14 = 40 units

Answer:

1/7

Step-by-step explanation:

The number of people in attendance who would prefer chili on a hotdog is 3,380.

Option B is the correct answer.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of attendance = 8450

Number of people who prefer chili on a hotdog out of 150.

= 60

The percentage of people who prefer chili on a hotdog out of 150.

= 60/150 x 100

= 40%

Now,

The number of people who prefer chili on a hotdog from 8450 attendance.

= 40% of 8450

= 40/100 x 8450

= 3380

Thus,

3,380 in attendance would prefer chili on a hotdog.

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Finn has 3 hamsters and 8 fish at home, the ratio of fish to total number of pets is -  8 : 11

The ratio refers to the number that may be used to represent one quantity as a percentage of another, to put it simply. Only when the ratio's two numbers use the same unit can they be compared. To compare two objects, we utilize ratios. When the second integer in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. A percentage seems to be an equation in which two proportions are made equal to one another. Ratio, which is comfortably pronounced as the ratio, was directly derived from the Latin term. Everything from "reason," "calculation," and "proportion" were all included in the Latin word ratio.

Given that,

Hamsters: 3

Fish: 8

Thus, total = 3 + 8 = 11

Now, ratio of fish total number of pets:

= 8 : 11

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Answer:

Step-by-step explanation:

Then general form of a linear function is:

f(x) = mx + c

where m = the slope and c is the value of f(x) when x = 0 (the y-intersect on a graph)

f(0) = 4, so

f(0)  = m(0) + c

4 = m(0) + c

Giving c = 4.

Slope = -6, so

f(x) = -6x + 4  (answer)

The polynomial:

5x²*y²*z + 10*x²*y²*z

Is a monomial (it can be rewritten as 15*x²*y²*z)

And the degree is 5.

Remember that the degree of a polynomial is equal to the maximum sum of exponents that we have on a single term.

The given polynomial here is:

5x²*y²*z + 10*x²*y²*z

First, notice that we can take "x²*y²*z" as a common factor, then we can rewrite:

5x²*y²*z + 10*x²*y²*z = 15*x²*y²*z

So we have only a term, thus, this is a monomial.

And the degree is the sum of the exponents, we will get:

2 + 2 + 1= 5

So the degree is 5.

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The required value of k will the system of linear equations has infinite number of solutions is -16.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

According to question:

We know that

8x + 5y - 9 = 0 . ..........(1)

KX+10y - 18=0 ..........(2)

Because there are infinity many solutions to linear equations.

[tex]\frac{a_{1}}{a_{2}} =\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}[/tex]

⇒ 8/k = 5/10 = -9/-18

8/k = 1/2

k = 16

Thus,required value of k is -16.

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ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.

What is congruent ?

In geometry, congruent refers to the condition where two or more figures have the same size and shape. Congruent figures have the same dimensions, angles, and proportions. Two figures are congruent if they can be superimposed exactly on each.

1) If, C.) Angle B is congruent to angle E then ∆ABC and ∆DEF are congruent by the ASA criterion.

2) If, D.) Angle A is congruent to angle D then ∆ABC and ∆DEF are congruent by the SAS criterion.

3) ∆ABC and ∆DEF are congruent if B.) AB=DE

ASA criterion: If in two triangles, two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.

ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.

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Answer:

12

Step-by-step explanation:

Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.

Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.

How do equations work?

A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.

Equation symbols (=) are used to represent equations.

A finance charge is what?

The interest and other fees levied on credit cards are included in a finance charge.

Typically, the finance charge is based on a stated APR (annual percentage rate).

The month's billing cycle lasts for 28 days.

Balance at current starting = x.

APR = 24%, or annual percentage rate.

The monthly percentage rate (MPR) equals 2% (24% divided by 12).

The final day's purchase cost $1,400.

$51 is the total finance fee for the month.

($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.

$50 ($51 - $1) serves as the initial balance's finance charge.

The starting balance at this time is x = $2,500 ($50 x 2%).

Current Beginning Balance Equation: x = 51 - 1 0.02

($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.

Finance charge savings from buying on the last day equals $27 ($28 - $1).

By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.

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Derivative of given logarithmic function [tex]log_7x[/tex] is [tex]\frac{1}{xlog(7)}[/tex].

Logarithmic differentiation is a method for figuring out the derivatives of some difficult functions. In some cases, it is simpler to distinguish between a function's logarithm and function itself. The derivatives are made simple with the right application of logarithm characteristics and chain rule discovery. Nearly any non-zero functions with differentiable nature can be applied with this approach.

Thus, in calculus, some complex functions are differentiated by calculating logarithms, and these complex functions are subsequently solved using the logarithmic derivative.

[tex]y=log_7x[/tex]

[tex]y'=\frac{1}{xlog(7)}[/tex]

Here, differentiation of logarithmic function for different base is different.

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The function g(x) = 2/(x^2 - 1) can be represented as a power series by finding its Taylor series expansion about the point x = 1.

We know that the power series representation of the function 1/(1-x) is given by the summation from n=0 to infinity of x^n.

So we can write:

g(x) = 2/(x^2 - 1) = 2*(1/(1-x))(1/(1+x)) = 2(1/(1-x^2))

We can use the formula for the Taylor series of a function:

f(x) = SUM(n=0 to infinity) (f^n(a)/n!) * (x-a)^n

where f(x) is the function, a is the point about which we are expanding, and n! is the factorial of n.

So we have:

g(x) = 2* SUM(n=0 to infinity) ( (1/(1-x^2))^n * (x-1)^n )

g(x) = 2* SUM(n=0 to infinity) ( (1/(1-x^2))^n * SUM(k=0 to n) (nCk * x^k * (-1)^(n-k) ) )

g(x) = 2* SUM(n=0 to infinity) ( SUM(k=0 to n) ( (1/(1-x^2))^n * (nCk) * x^k * (-1)^(n-k) ) )

where nCk is the binomial coefficient which is equal to n!/(k!(n-k)!).

So we have the power series representation of the function g(x) = 2/(x^2 - 1) as:

g(x) = 2 * SUM(n=0 to infinity) SUM(k=0 to n) ( (nCk) * ((-1)^(n-k) * (1/(1-x^2))^n) * x^k )

It's important to note that this power series is only valid for |x| < 1.

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The circumference of the grain bin with radius 20 feet is 125.6ft.

The distance around the boundary of a circular object is referred to as a circumference.

The formula for calculating circumference is expressed as;

C = 2 × π × r

Given the data in the question;

Plug in the given values into the above formula

C = 2 × π × r

C = 2 × 3.14 × 20ft

C = 125.6ft

Therefore, the circumference is 125.6ft.

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In the year 2046 the price of the stamp will reach 75 cents. The solution has been obtained using linear function.

What is a linear function?

A linear function is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear function with exponents greater than 1. Such a function on the graph, forms a straight line.

We are given y= -0.71 + 0.86x, where y represents the predicted price , in cents of a stamp and x represents the number of years since 1958

We need to find the year in which the price of the stamp will reach 75 cents. This means that

y = 75

Putting this in the equation, we get

⇒75= -0.71 + 0.86x

⇒x= 75.71/0.86

⇒x= 88.03

This means that after around 88 years from 1958 i.e. in 2046 the price of the stamp will reach 75 cents.

Hence, in the year 2046 the price of the stamp will reach 75 cents.

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Since, the question is incomplete, the complete question is attached below

The interest after three years is $117.711 and new balance after three years is $1347.711

Simple interest is a type of interest calculated on the initial principal or starting amount of a loan or investment.

The formula for simple interest is:

I = PRT/100

Where:

I = Interest

P = Principal or starting amount

R = Interest rate

T = Time

a. Interest after three years:

I = PRT/100

P = $1,230, R = 3.19% and T = 3 years

I = (1,230 ×3.19 × 3)/100

I =  $117.711

b.  New balance after three years:

New balance = P + I

New balance =  $1,230 + $117.711 = $1347.711

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Answer:

2.475

Step-by-step explanation:

12 divide into 29.7 goes 2.475 times

use the illustration from the other example and you should be able to do it

12 into 29 goes twice

subtract 29-24 to get 5

bring down the 7 to get 57

12 into 57 goes four times

57-48 = 9

bring down a zero to get 90

12 into 90 goes seven times

90-84 = 6

12 into 60 is 5

18÷29.70= 0.40

that should be right