Factor 6x + 36y using the greatest common factor

The blue graph is a translation of 2 units to the left and 1 unit up of the parent function, thus, the equation is:

g(x) =  |x + 2| + 1

We know that the red graph is an absolute value function, so we have:

f(x) = |x|

And we want to find the equation of the blue absolute value function, which is a translation of the above one.

Notice that the vertex of the blue one is at (-2, 1), so we have a translation of 2 units to the left and one unit up, it is just written as:

y = |x + 2| + 1

We conclude that the translated function is:

g(x) =  |x + 2| + 1

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The 5 number are 25, 25, 35, 45 and 70 that has the mean of 40 and a median and deviation of 35 and a mode of 25.

Mean:

Mean is the sum of all observations divided by the number of observations.

Median:

Median defines the value of the middlemost observation, obtained after arranging the data in ascending or descending order.

Mode:

The value which appears most often in the given data i.e. the observation with the highest frequency is called a mode of data.

Given,

Mean = 40

Median = 35

Mode = 25

We know that the mean value is  is the sum of all observations divided by the number of observations.

So, Let us consider v,w,x,y,z are the five numbers.

So it can be written as,

[tex]Mean=\frac{v+w+x+y+z}{n}[/tex]

We know that,

Mean = 40 and n = 5.

Then,

[tex]40=\frac{v+w+x+y+z}{5}[/tex]

Therefore,

=> v + w + x + y + z = 40 x 5

=> v + w + x + y + z = 200 --------------------------(1)

Here we know that the Median is 35.

The median in equation (1) is x,

So x = 35

And the mode is 25, we know that definition of mode so let us consider it will occurs at least twice,

So, the values of v = 25 and u = 25

Now apply the values on the equation,

=> 25 + 25 + 35 + y + z = 200

=> 85 + y + z = 200

=> y + z = 200 - 85

=> y + z = 115

So, here we have to take the combinations that gives the value of 115 and the values must be greater than 35.

So, the values are 45 and 70.

Therefore, the five numbers are 25, 25, 35, 45 and 70.

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Based on the 1.5 × IQR rule for outliers, there is no evidence to support the student's claim because there is only one outlier at 58 minutes.

An outlier is also referred to as anomalous data and it can be defined as a numerical value that is either unusually too small or large (big) in comparison with the overall pattern of the numerical values contained in a data set.

IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.

Mathematically, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):

IQR = Q₃ - Q₁

Based on the given data set, the following interquartile ranges was calculated by using Excel:

Q₃ = 31.5

Q₁ = 20.5

Now, the interquartile range (IQR) is given by:

IQR = Q₃ - Q₁

IQR = 31.5 - 20.5

IQR = 11

Based on the 1.5 × IQR rule for outliers, we have:

1.5 × IQR = 1.5 × 11 = 16.5

Therefore, our fences will be 16.5 points below Q₁ and 16.5 points above Q₃:

Lower fence = 20.5 - 16.5 = 4.5

Upper fence = 4.5 + 31.5 = 36.

In conclusion, we can reasonably infer and logically deduce that there is no evidence to support the student's claim because there is only one outlier at 58 minutes.

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Complete Question:

The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list.

9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58

One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5 × IQR rule for outliers, is there evidence to support the student's claim?

Answer:

(-6 ÷ 5) × (-6 ÷ 8) = 9/10 or 0.9

Step-by-step explanation:

Carlos took 8 minutes to complete 5 3/4 laps all around school track.

Now, to answer the question

5 3/4 laps = 23/4 laps

= (23/4)/8

Simplifying the equation;

=23/4 × 1/8

=23/32

Therefore, Carlos will take 23/32 laps per minute to running on school track.

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The correct question is-

carlos jogged 5 3/4 laps around the school track in 8 minutes. what was his average speed in laps per minute?

Answer:

c would be the y intercept,

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

A____(6)_____B____(10)_____C

6+10=16

Hope this helps!

Based on the given parameters, there are 1119360 feet in 212 miles

The given parameters are

12 inches = 1 foot

5,280 feet = 1 mile.

Multiply both sides of 5,280 feet = 1 mile by 212

So, we have

212 * 5,280 feet = 1 mile * 212

Evaluate the product

1119360 feet = 212 miles

The above means that there are 1119360 feet is 212 miles

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The final step to be performed in the mathematical expression, (Σx)2 is square the sum of the scores

Sum of squares is a statistical method for calculating the dispersion of data points in regression analysis. By deviating the least from the data, the sum of squares can be used to identify the function that fits the data the best. The purpose of a regression analysis is to assess how well a data series can be fitted to a function that could provide insight into the process by which the data series was created. In the world of finance, the sum of squares can be used to calculate the variation in asset values.

A statistical measure of departure from the mean is the sum of squares. Variation is another name for it. The squared differences of each data point are added together to calculate it. The sum of squares is calculated by squaring the separation between each data point and the line of best fit, then adding the results. The line of greatest fit will reduce this value to the minimum.

We first find the sum, and then square the sum.

ΣX = 1 + 0 + 2 + 4 = 7

So,  ΣX + 1 = 8

Mean = ( 4+6+14 )/3 = 8

Mean =  ΣX*f /  Σf = (5*2 + 4*1 + 3*3 + 2*2 + 1*2) / (2+1+3+2+2) = 29/10

Subtract 3 points from the score X=3

Changing the lowest score to a lower one will increase the range.

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The final step to be performed in the mathematical expression, (Σx)2 is square the sum of the scores

Sum of squares is a statistical method for calculating the dispersion of data points in regression analysis. By deviating the least from the data, the sum of squares can be used to identify the function that fits the data the best. The purpose of a regression analysis is to assess how well a data series can be fitted to a function that could provide insight into the process by which the data series was created. In the world of finance, the sum of squares can be used to calculate the variation in asset values.

A statistical measure of departure from the mean is the sum of squares. Variation is another name for it. The squared differences of each data point are added together to calculate it. The sum of squares is calculated by squaring the separation between each data point and the line of best fit, then adding the results. The line of greatest fit will reduce this value to the minimum.

We first find the sum, and then square the sum.

ΣX = 1 + 0 + 2 + 4 = 7

So,  ΣX + 1 = 8

Mean = ( 4+6+14 )/3 = 8

Mean =  ΣX*f /  Σf = (5*2 + 4*1 + 3*3 + 2*2 + 1*2) / (2+1+3+2+2) = 29/10

Subtract 3 points from the score X=3

Changing the lowest score to a lower one will increase the range.

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The inverse of the given function,f(t) = 100 . 2^(t/4) is 4 * log2(x/100).

What is the inverse of a function?

An inverse of a function f(x), is defined as another function that undoes the operations performed on the function. It is denoted by f^(-1).

Calculation of the inverse of a function

We are given a function,

f(t) = 100 . 2^(t/4)

Let us assume that f^(-1) represents the inverse of a function

Replacing f(t) with y, we get,

y = 100 . 2^(t/4)

Now, replace further t with y and y with x

x = 100 . 2^(y/4)

Rearranging, we have,

2^(y/4) = x / 100

Taking log both sides, we get,

(y/4) log 2 = log (x/100)

y/4 = log2(x/100)

y = 4 * log2(x/100)

Further, replace x with t and y with f^(-1), i.e.

f^(-1) = 4 * log2(t/100)

Hence, the inverse of the given function, f(t) = 100 . 2^(t/4) is 4 * log2(x/100).

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The numbers in the equations are -4 and -26

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

Let the numbers be x and y

A system of linear equations is a collection of at least two linear equations. So, we have the following linear equations

y = 5x - 6

x - y = 22

Substitute y = 5x - 6 in x - y = 22

x -5x + 6 = 22

Evaluate the like terms

-4x = 16

Divide both sides by -4

x = -4

Substitute x = -4 in y = 5x - 6

y = 5 * -4 - 6

Evaluate

y = -26

Hence, the numbers are -4 and -26

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Answer: 0.2121...=7/33     ≈943 hits

Step-by-step explanation:

a.

[tex]99n=100n-n\\[/tex]

Divide both parts of the equation by 99:

[tex]\displaystyle\\n=\frac{100n-n}{99} \\\\n=\frac{100*0.2121...-0.2121...}{99} \\\\n=\frac{21.2121...-0.2121...}{99}\\\\n=\frac{21}{99} \\\\n=\frac{7*3}{33*3}\\\\n=\frac{7}{33}[/tex]

b.

[tex]\displaystyle\\200:\frac{7}{33}=\\\\200*\frac{33}{7} =\\\\\frac{200*33}{7}=\\\\\frac{6600}{7}=\\\\ \approx943[/tex]

Answer:

==============================

Identity of the square of a sum of two numbers:

Given equation:

We can see one of the numbers is y, and the second one is 15 as twice the product is 30y.

Add 15² = 225 to both sides to complete the square, then solve it:

Answers:

y = ± 221.47, y = -0.24, y = -29.76

Step-by-step explanation:

y^2 + 30y = -7

Move -7 over to the other side

y^2 + 30y +7 = 0

This takes form of a quadratic equation of ax^2 + bx + c = 0, where y = x

Quadratic formula is x = (-b ± (sqrtb^2 - 4ac)/2a and replace everything so it's y = (-30 ± (sqrt30^2 - 4*1*7)/2*1. Once solved, the answer choices are y = ± 221.47, y = -0.24, or -29.76.

5x + 23

Step-by-step explanation:

[tex]{ \purple{ \tt{3(x + 1)}}} - { \purple{ \tt{4(2x - 5)}}} + { \purple{ \tt{10x}}}[/tex]

[tex] = { \purple{ \tt{3x + 3 - 8x + 20 + 10x}}}[/tex]

[tex] = { \purple{ \tt{3x + 2x + 23}}}[/tex]

[tex] = { \purple{ \tt{5x + 23}}}[/tex]

The group given the treatment being studied during an experiment, such as medication, fertilizer, or exposure to some other variable, is called the (A) test group.

Therefore, the group given the treatment being studied during an experiment, such as medication, fertilizer, or exposure to some other variable, is called the (A) test group.

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The correct question is given below:

The group given the treatment being studied during an experiment, such as medication, fertilizer, or exposure to some other variable, is called the _____?

(A) test group

(B) placebo group

(C) control group

(D) variable group

Hi!

Use the Slope Formula:

[tex]\begin{gathered}\\\bullet\implies\boldsymbol{\displaystyle\frac{y_2-y_1}{x_2-x_1}} \\\\\boldsymbol{Setting\:the\:Values}\\\bullet \boldsymbol{y_2=3}\\\bullet\boldsymbol{x_2=8}\\\bullet\boldsymbol{y_1=3}\\\bullet\boldsymbol{x_1=-2}\\\\\boldsymbol{Solving\:for\:the\:slope}\\\boldsymbol{\displaystyle\frac{3-3}{8-(-2)}}\\\boldsymbol{\dfrac{0}{8+2}}\\\boldsymbol{Slope\longrightarrow0}\end{gathered}[/tex]

I hope I helped! ^^

A pair of intersecting lines that forms a pair of complementary angles is as drawn below.

Remember that complementary angles are defined as angles which sum is equal to 90°.

Besides, each of the pairs of opposite angles made by two intersecting lines are called vertical angles. Now, from congruent proofs, we know that that vertical angles are congruent. In another words, they have the same measure.

Thus, we have to draw two vertical angles that measure:

90° ÷2 = 45°

This image is as drawn below in the attached file.

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Answer:

Answers will be. ............ 36+38

Step-by-step explanation:

Try it on calculator

The term that best represents the intersection of two pages of an open book is point.

A third item made up of everything that is simultaneously contained in all of the other things is called an intersection of two or more objects in mathematics. In Euclidean geometry, for instance, the intersection of two lines in a plane that are not parallel is where they come together. More broadly, the set of elements that are a part of all of the sets is what is meant by the intersection of sets in set theory. The items being considered do not need to be in a shared space, unlike the Euclidean concept.

A point is the most frequent shape for an intersection in plane geometry, while there are other shapes that can be used as well. An intersection is an item of lesser dimension that is incident to each in incidence geometry, which is typically applied to flats.

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The area of triangle par on the grid is the vertex p is on ordered pair 7 and 6.

Soccer on CBS Sports is various TV programs that have broadcasted soccer matches in the US on CBS, CBS Sports Organization, and Paramount+. These matches are from Global, European, and American contests. Affiliation football, all the more usually known as just football or soccer, is a group activity played between two groups of 11 players who essentially utilize their feet to impel the ball around a rectangular field called a pitch. Soccer, or football as it's known beyond North America, is the most famous game on the planet. Thus, how could it be played, who plays it, and a lot more inquiries are responded to here.

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Answer:

The ideal starting count for your shrimp colony will be around 10 to 20 shrimp. 

Step-by-step explanation:

Answer:

Step-by-step explanation:

20 to 10

Answer:

1/2

Step-by-step explanation:

- find the least common denominatir for the two. (12)

-multiply 4 and 3

-multiply 6 and 2

- Add 1 and 5

-Keep the denominator.

-simplify if needed

Answer:

Step-by-step explanation:

answer 1 1/12 hours

Answer:

I think it’s 4.

Answer: 53/30

Step-by-step explanation:

4/6 + 2/4 + 3/5 =

2/3 + 1/2 + 3/5 =      ==> Simplify Denominators

30/30 * (2/3 + 1/2 + 3/5)=  ==> Have matching denominators by multiplying by the LCM (Least common multiple) of the denominators

(2*30/3 + 1*30/2 + 3*30/5)/30=

(60/3 + 30/2 + 90/5)/30=

(20 + 15 + 18)/30=

(35 + 18)/30=53/30

Using simple interest, Alice need to invest 25000 now in order to get 12 000 saved in 4 years' time at 12% simple interest.

The daily interest rate, the principle, and the number of days between payments are multiplied to determine simple interest. Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest. Simple interest loans are frequently used for auto loans and short-term personal loans.

Given,

simple interest = 12000

rate of interest = 12%

time  = 4 years

Simple interest = P × R × T / 100

12000 = P × 12 × 4 / 100

P = 25000

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The numbers given in scientific notation will be arranged from least to greatest as: 7.6×10⁻²⁰, 5.5×10⁻¹¹, 2.4×10², 8.9×10², 9.2×10⁴, 7.6×10²⁰.

Scientific notation of numbers may be defined as the way of representation of bigger numbers into powers of 10. This helps in reducing space as well as it helps in conveniently solving the problem. For example, scientific notation of 92000 may be written as 9.2×10⁴.

Here in the number 7.6×10⁻²⁰ the power of 10 is maximum but with a negative value so it is the least number. Then comes the number 5.5×10⁻¹¹ as its power are also negative but greater than the previous number. Similarly using the above logic, the other numbers will be placed, and the greatest number would be 7.6×10²⁰ as it has the maximum power of 10 that too with a positive sign.

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The amount that Rebecca will be paid for overtime work is $12.75.

From the information, Rebecca's boss pays her time and a half for overtime work at the comic book store. Her regular wage is $8.50.

The amount for overtime will be:

= (1.5 × $8.50)

= $12.75

Therefore, the amount that Rebecca will be paid for overtime work is $12.75.

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The inequality that is equivalent to the given inequality is -10x + 10 < 13  

From the question, we are to determine the inequality that is equivalent to the given inequality

The given inequality is -10(x - 1) < 13

To determine the inequality that is equivalent to this inequality, we will solve the given inequality

Solving the inequality

-10(x - 1) < 13

Apply the distributive property

-10x + 10 < 13

Subtract 10 from both sides of the inequality

-10x + 10 - 10 < 13 - 10

-10x < 3

Divide both sides by -10 and reverse the sign

x > -3/10

From the steps of solving the inequality, the inequality that is equivalent to the given inequality is -10x + 10 < 13  

Hence, the inequality that is equivalent to the given inequality is -10x + 10 < 13  

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Answer:

C. -10x + 10 < 13