Someone has the answer?

Find the value of x so that the function has the given value. j(x) = 3-x;j(x) = -5

During the problem disaggregation process, the logic trees should have branches that are both mutually exclusive and collectively exhaustive.

Problem disaggregation refers to the process of breaking down the larger higher-level operation into smaller plans and shorter periods. It refers to the use of analysis, logic, and facts to evaluate and understand each element of the problem in terms of causes and driver of the situation using logic trees. Logic trees improve the problem definition and aid in understanding an issue in more detail. There are different types of logic trees used in the process – factor logic tree, inductive logic tree, deductive logic tree, hypothesis tree, and decision tree. The logic trees should have branches that are MECE – mutually exclusive and collectively exhaustive. It is the second and an important step in the seven steps bulletproof problem-solving process used for complex solving.

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The number of dime and the number of quarters that Aiden have are 10 and 8 respectively.

Aiden ha $3 worth of dime and quarter. Aiden has 2 more dime than quarter. The number of dime and the number of quarter that Aiden has can be calculated as follows:

let

x =  number of quarter

y = number of dime

Therefore,

y = 2 + x

y - x = 2

0.1y + 0.25x = 3

Multiply equation(ii) by 10

y - x = 2

y + 2.5x = 30

subtract equation(i) from equation(ii)

3.5x = 28

x = 28 / 3.5

x = 8

Hence,

y = 2 + 8

y = 10

Therefore,

number of dime  = 10

number of quarters = 8

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Applying the definition of linear pair angles, the measures are:

y = 10

m∠JKM = 106°

m∠MKL = 74°

A linear pair involves two angles that lie adjacent to each other on a straight line. The sum of their measures is equal to 180 degrees, this is because linear pair angles are supplementary to each other.

Given the following:

Measure of angle JKM = (10y + 6)°

Measure of angle MKL = (8y - 6)°

Therefore:

m∠JKM + m∠MKL = 180 [linear pair angles are supplementary]

Substitute

10y + 6 + 8y - 6 = 180

Combine like terms

18y = 180

18y/18 = 180/18

y = 10

Plug in the value of y to find the measures:

Measure of angle JKM = (10y + 6)° = 10(10) + 6 = 106°

Measure of angle MKL = (8y - 6)° = 8(10) - 6 = 74°

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Using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.

So, the distance of the building from John and Fred is:

Now, we get the formula:

Calculate as follows:

John's distance:

Fred's distance:

Therefore, using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.

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The area of the largest rectangle is 25 square units.

It is given that the radius of the semicircle is [tex]4[/tex].

It is required to inscribe a rectangle of maximum area.

Consider a rectangle of sides [tex]x[/tex], [tex]y[/tex] as shown in the given figure.

From the attached figure,[tex]AB=x[/tex], [tex]OB=r[/tex] and [tex]OB=\frac{y}{2}[/tex].

Now, in the triangle OAB, apply Pythagoras' theorem as,

[tex](OA)^{2}=(OB)^{2}+(AB)^2[/tex]

[tex]r^2=(\frac{y}{2} )^2+x^2\\\\[/tex]

[tex]16=\frac{y}{4}+x^2[/tex]

[tex]y^2=4(16-x^2)[/tex]

[tex]y=2\sqrt{16-x^2}[/tex]

So, the area of the rectangle will be,

Area,

[tex]A = 2x \times y[/tex]

= [tex]2x \times \sqrt{(16 - x^2)}[/tex]

Differentiate the area with respect to ,

[tex]A' = 2 \times \sqrt{(16 - x^2)} - 2x^2/(16 - x^2)[/tex]

Differentiate the area twice as,

When[tex]x = 0, y = 5[/tex] and when [tex]x = 5, y = 0[/tex], [tex]area = 0[/tex].

It implies that area is maximum when the value of x lies between 0 and 5.

This will occur where [tex]A'= 0[/tex].

⇒ [tex]2 \times \sqrt{(16 - x2) }- 2x^2/(16 - x^2) = 0[/tex]

⇒[tex]2 \times \sqrt{(16 - x^2)} = 2x^2/(16 - x^2)[/tex]

On simplification, we get,

⇒ [tex]2 \times (16 - x^2) = 2x^2[/tex]

⇒ [tex]16 - x^2 = x^2[/tex]

⇒ [tex]2x^2= 16[/tex]

⇒ [tex]x^2 = 16/2[/tex]

⇒ [tex]x = \sqrt{8}[/tex]

Now, [tex]y = \sqrt{(16 - x^2)}[/tex] becomes

⇒[tex]y = \sqrt{(16 - (\sqrt8)^2)}[/tex]

⇒ [tex]y = \sqrt{(16 - 8)}[/tex]

[tex]y =\sqrt{8}[/tex]

Maximum area = 2xy

[tex]=2(\sqrt{8)}(\sqrt{8})[/tex]

[tex]=16[/tex]

Therefore, the area of the largest rectangle is 16 square units.

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40 freezers could be shipped in the container.

What is a variable?

A variable is a quality that may be measured and take on several values.

We are given that

A railroad container can hold weight=42,000 pounds

Total number of ovens for ship=90

Weight of each oven=200 lbs

Weight of each freezer=600 pounds

We have to find the number of freezers that can be shipped in the container.

Let x be the number of freezers that can be shipped in the container.

According to the question,

42000=90(200)+600x

42000=18000+600x

600x=42000-18000=24000

x=24000/600=40

Hence, 40 freezers can be shipped in the container.

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17576000 courses can be given unique catalog numbers.

There are three numbers and three English letters.

Each of three numbers can be chosen from 0 to 9, so the ways to choose each number is  = 10

So the total number to choose three numbers = 10*10*10 = 1000

Each of letters can be chosen from A to Z.

Number of choice for the each letter = 26

So, the outcomes of letter combination = 26*26*26 = 17576

Hence the total possible catalog numbers = 1000*17576 = 17576000

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Answer: What do you need the total or the equation? I am going to write the equation.

Step-by-Step Solution: (5)(d)+(5)(d)(2.5)+ (5)(d)-4

The pool will have 14, 477 gallons of water.

The amount of water that has leaked in 91 days = rate of leakage × number of days

Keep the values in formula

The amount of water that has leaked in 91 days = 11 × 91

Performing multiplication

The amount of water that has leaked in 91 days = 1001 gallons

Amount of water remaining after 91 days = total amount of water - the amount of water that has leaked in 91 days

Amount of water remaining after 91 days = 15,478 - 1001

Performing subtraction

Amount of water remaining after 91 days = 14, 477 gallons

Hence, after 91 days there will be 14, 477 gallons of water in the pool.

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Answer:

0.86 pounds of fruit is left.

Step-by-step explanation:

If Stacey bought 8.3 pounds and the class ate 7.44 pounds, the amount of fruit that's left is 8.3-7.44=0.86      

17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.

A percentage is a number or ratio expressed as a fraction of 100.

Given that, there are 14 litres of a solution which is 90% acidic,

Let water added be x, then according to question,

0.90*14 = 0.40(x+14)

12.6 = 0.40x + 5.6

0.40x = 7

x = 17.5

Hence, 17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.

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Answer:

Decagon

Step-by-step explanation:

Because it has 10 sides.

Answer:

Its a Decagon

Step-by-step explanation:

Answer:

0.538 as a fraction in its simplest form is 269/500

Step-by-step explanation:

We all know that 0.538 can be written as 0.538/1

Multiply the numerator and denominator by 1000 which comes out to 538/1000

Divide the numerator and denominator by 2 which comes out to 269/500

Since 269 is a prime number 269/500 is 0.538 in its simplest form

The equation of a line in point- slope form, that passes through (1, -7) and has a slope of -2/3 is (y + 7) = -2/3 (x - 1)

Information gotten from the question include

a slope of -2/3

points (1, -7)

A linear function consists of functions where the variables has exponents of 1.

The equation of a line in point- slope form is expressed in the form.

(y - y₁) = m (x - x₁)

Definition of variables

(y and y₁) = refers to variables in the y direction

m = slope

x and  x₁ = refers to variables in the x direction

substituting into the slope and point (1, -7) equation gives

()y + 7) = -2/3 (x - 1)

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The required answer in mixed number for a given operation is [tex]8\frac{4}{9}[/tex]

What are mixed numbers?

A whole number and a proper fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it.

Given,     [tex]2\frac{8}{9} + 5\frac{5}{9}[/tex]

             [tex]= \frac{(2*9)+8}{9} +\frac{(5*9)+5}{9}[/tex]

             [tex]= \frac{18+8}{9} +\frac{45+5}{9}[/tex]

              [tex]= \frac{26}{9} +\frac{50}{9}[/tex]

               [tex]= \frac{26+50}{9} = \frac{76}{9} = 8\frac{4}{9}[/tex]

Hence, the required answer for the given term is  [tex]8\frac{4}{9}[/tex] .

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Events A and B are non-overlapping. Option(2) is correct.

When two sets A and B have at least one element in common, they are said to be overlapping.

The sets of photographs that don't overlap are the sets where no two pictures (correctly) don't overlap. They are the expansion of the cross-bifix-free sets of strings to two dimensions is called non-overlapping.

A red die and a blue die are rolled.

Assume that Event A is receiving the number 9.

Event B: You receive a double.

Whether events A and B overlap or not is what we want to determine.

When two red dice and two blue dice are thrown, a sample space is then provided by,

S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5),(3,6), (4,1), (4,2), (4,3), (4,4),(4,5),(4,6) (5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2),(6,3)(6,4),(6,5),(6,6)}

The two dice are rolled, and there are a total of 36 outcomes.

n(S)=36

Assume that Event A is receiving the number 9.

The probable results for A = (3,6), (4,5), (5,5), (5,6), (6,3)

And let's say that you receive a double in Event B.

The events that may occur if B=(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)

We can observe that the two events are distinct from one another since there is no overlap in the potential outcomes of the two events.

Therefore events A and B are non-overlapping

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The corresponding estimate for numbers in 1,2,3 and 4 are 10, 24, 21 and 153

Estimation and approximation is the process of using rounded values when presenting numerical data and making rough calculations.

The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up

1.  2.1 x 5.12 =  2 x 5 = 10

Explanation: The number after the digit 2 in 2.1 is 1, we will round down 2.1 to 2. Also, the number after the digit 5 in 5.12 is 1, we will round down 5.12 to 5

2. 12.3 x 1.6 = 12 x 2 = 24

Explanation: The number after the digit 12 in 12.3 is 3, we will round down 12.3 to 12. Also, the number after the digit 1 in 1.6 is 6, we will round up 1.6 to 2

3. 6.5 x 3.1 = 7 x 3 = 21

Explanation: The number after the digit 6 in 6.5 is 5, we will round up 6.5 to 7. Also, the number after the digit 3 in 3.1 is 1, we will round down 3.1 to 3

4. 51.3 x 2.7 = 51 x 3 = 153

Explanation: The number after the digit 51 in 51.3 is 3, we will round down 51.3 to 51. Also, the number after the digit 2 in 2.7 is 7, we will round up 2.7 to 3

Therefore, the estimate for 1,2,3 and 4 are 10, 24, 21 and 153 respectively

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A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.

Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] have a strong, negative correlation

What is a correlation coefficient?

A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.

The variables may be two columns of a given data set of observations, often called a sample or two components of a multivariate random variable with a known distribution.

As we know that the correlation coefficient is a measure of the strength of the straight line or linear relationship between two variables. Correlation coefficients are expressed as values between [tex]+1[/tex] and [tex]-1[/tex].

So,

[tex](1,8),(2,3),(3,0),(4,1),(5,2),(6,1)[/tex]

As per the Excel tools i.e., CORREL function the correlation coefficient is [tex]-0.9[/tex].

Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] has a strong, negative correlation.

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Answer:

(8, 9 000)

Step-by-step explanation:

The cost of the gas will be equal to £67.81 p.

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,

Initial gas reading = 8247

Final gas reading = 8631

The total consumed gas is given by,

Final gas reading - Initial gas reading  → 8631 - 8247 = 384

Since the cost of gas is 11p per unit we have, the total cost of the gas consumed is given by

Cost of consumed gas = Units of gas consumed × Unit cost of gas

= 384 × 11p = 4224 p

100 p ≡ £ 1

4224 p  = £42.24 p

The total cost of the gs is obtained by adding the fixed charge to the cost of gas consumed as follows,

£25.57 + £42.24 = £67.81 p

The cost of the gas = £67.81 p

The complete question is given below,

The gas meter readings at the beginning and end of a period were: 8247 = 8631 the cost of the gas is 11p for each unit. there is also a fixed charge of £25.57. calculate the cost of the gas. you must show your working

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The answer is 4/15

2/5 * 2/3 = 2 · 2/5 · 3 = 4/15

Multiply the numerators and denominators together. Keep the result fraction to the smallest possible denominator GCD(4, 15) = 1. It cannot further simplify the fraction result by canceling in the following intermediate step.

In other words, two fifths times two thirds equals four fifteenths.

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Answer:

5/3

Step-by-step explanation:

"of" means times so so so often. It is not a hard math rule/definition. But more like a soft English-Math translation.

So, "2/5 of what"

means 2/5x (but make sure the 2/5 is a fraction beside the x, NOT the x on the bottom with the 5)

"is" means equals.

2/5x = 2/3

Multiply both sides by 5/2.

5/2 • 2/5x = 2/3•5/2

x = 2/3 • 5/2

x = 5/3

You get 5/3 either by "cancelling" the 2's OR by

fraction multiplication where you times top×top and bottom×bottom and simplify.

x = 10/6

x = 5/3

2/5 of 5/3 is 2/3.

The "what" in the question is 5/3.

Answer:

He has to sell 5000 to earn $1000

Step-by-step explanation:

1000/0.2 = 5000

Answer:

c) x+4

Step-by-step explanation:

1. The original expression can be re-written as (I just rewrote each fraction so that there are no mixed numbers):

[tex]\frac{x}{2}+\frac{9}{2}+\frac{x}{2}-\frac{1}{2}[/tex]

2. Next, you want to group all the terms with the variable x, and all the terms without a variable. All the fractions should be rearranged:

[tex]\frac{x}{2}+\frac{x}{2}+\frac{9}{2}-\frac{1}{2}[/tex]

3. You can now simplify and add the variable terms and the non-variable terms.

[tex]\frac{x+x}{2}+\frac{9-1}{2}[/tex]

Simplify further:

[tex]\frac{2x}{2}+\frac{8}{2}[/tex]

[tex]x+4[/tex]

So your answer is choice c

Answer:

Step-by-step explanation:

Let's find the equation in the form of y=mx+b that fits the data.  m is the slope and b is the y-intercept (the value of y when x=0).  Slope, m, the the Rise/Run of the line.  It can be found by taking any two points from the table.  Let's choose (0,15) and (2,35), although any two will work.

x    y

0   15

1    25

2   35

3   45

4   55

(0,15)   (2,35)

The Rise is the change in y:  (35 - 15) = 20.

The Run is the change in x for the same points:  (2 - 0) = 2

The slope is the Rise/Run = (20/2) or 10.

The equation has the form y = 10x + b.

Let's find b.  Just enter any of the points in the above equation and solve for b.  I'll choose (3,45).

  y = 10x + b

  45 = 10*(3) + b

b = 45 - 30

b = 15

[Note:  since b is the value of y when x equals zero, we really didn't need to calculate b as we just did.  There is a data point already that tells us the value of y when x = 0:  (0,15)]

The two positive numbers are 5 , 5.

Given:

Product of two positive numbers = 25

sum of these number is minimum.

Let a and b be the two positive numbers.

a*b = 25

b = 25/a

sum s = a+b

= a + 25/a

apply derivation on both sides.

ds/da = 1 - 25/[tex]a^{2}[/tex]= 0.

1 = 25/[tex]a^{2}[/tex]

a = [tex]\sqrt{25}[/tex]

a = 5 , -5

since given are positive numbers so 5 is considered.

b = 25/5

b = 5

Therefore the two positive numbers are 5 , 5.

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a) These ramp dimensions do not meet the ADA guidelines.

b) A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.

The slope of a situation is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

For the ramp in this problem, we have that the vertical change and the horizontal change are given as follows:

The ratio between the vertical change to the horizontal change is of:

3/15 = 1/5.

Which is greater than 1/12, hence the ramp does not meet the ADA guidelines.

If the horizontal change was 13 times the vertical change, it would meet the ratio, hence a possible measurement is of:

As the ratio would be of:

3/39 = 1/13 < 1/12.

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Using percentages we calculate in the beginning there were 125 jellybeans in the jar.

Let the number of jellybeans in the jar was x.

Now student ate 20% of the jellybeans.

Number of jellybeans students ate = 20% of x = 0.2x

Number of jellybeans left = x - 0.2x = 0.8x

But the number of jellybeans is given as 100.

Therefore 0.8x = 100

or, x = 100 /0.8 = 125

Hence there were 125 jellybeans in the jar.

The English word "percentage" derives from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100.

In other words, that is a relationship where it is always assumed that the value of the whole is 100.

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