How to do variable expression

Answer:

Below

Step-by-step explanation:

See diagram

.158384 = height/x      <======   x = height/.15838

.061162 = height /(11+x)    <====sub in x from above into here

.061162 = height /(11+height/.158384)      solve for height

.672789 + .386163 height = height

height = 1.1 mi high

Answer: 1

               _

               32

Step-by-step explanation: because the are skip count and adding the number every single time .

Answer:

588

Step-by-step explanation:

Answer:

Step-by-step explanation:

If 3<y<7 then,

0 < 14-2y < 8

14 - 2(3) = 8

14 - 2(7) = 0

Answer:

$2938.66

Step-by-step explanation:

2000x1.08(to the power of 5) = 2938.656154

rounded to 2s.f is $2938.66

The likelihood of randomly selecting a chocolate chip cookie from the batch is unlikely

From the question, we have the following parameters that can be used in our computation:

P(chocolate chip) = 0.25

Probability values less than 0.5 are unlikely

0.25 is less than 0.5

This means that the likelihood is unlikely

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If you would like to have $500,000 when you retire in 30 years.
a. Amount earned  $2,322.76.

b. Total money  $2,322.76

c. Total interest earned $225,268.80

a) To calculate the amount you need to deposit each quarter to reach $500,000 in 30 years, you can use the formula:

P = A / (1 + r/n)^(nt)

P = $500,000 / (1 + 0.066/4)^(4 * 30)

P = $2,322.76

b) Total money

 Total money = $2,322.76 * 4 quarters/year * 30 years

Total money = $2,322.76

c) Total interest earned

Total interest earned = $274,731.20 - $500,000

Total interest earned = $225,268.80

Therefore the amount earned is  $2,322.76.

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Step-by-step explanation:

To solve the inequality |2x + 5| < 2 - x, we need to split it into two cases:

When 2x + 5 > 0:

In this case, the absolute value is positive, so we can simplify the inequality as follows:

2x + 5 < 2 - x

Expanding the left side:

3x + 5 < 2

Subtracting 5 from both sides:

3x < -3

Dividing both sides by 3:

x < -1

So the solution for this case is x < -1.

When 2x + 5 < 0:

In this case, the absolute value is negative, so we can simplify the inequality as follows:

(2x + 5) < 2 - x

Expanding the left side:

-2x - 5 < 2 - x

Adding x to both sides:

-2x - 5 + x < 2

Combining like terms:

-x - 5 < 2

Adding 5 to both sides:

-x < 7

Dividing both sides by -1:

x > -7

So the solution for this case is x > -7.

Taking the union of the two solutions, we get:

-7 < x < -1.

This means that x is between -7 and -1, excluding -7 and -1.

7/3 in four different ways is 7/12

Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division. The main goal of dividing is to see how many equal groups are formed or how many are in each group when sharing fairly.

If 100 apples are to be shared by 20 girls equally. The number of apple each girl will get is 100/20 = 5 apples each.

Similarly to put 7/3 in four different ways we have to divide 7/3 by 4

7/3 ÷ 4 = 7/3 × 1/4

= 7/12

therefore 7/12 of the four places will give 7/3

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Answer:

121

Step-by-step explanation:

The formula for calculating the sum of interior angles is ( n − 2 ) × 180

so you have 5 sides n=5

so total is 3*180 = 540

there are 3 right angles = 3/90 = 270

so 540-270 = 270 = angle B+ angle C

so 6x+1 +8x-11 =270

14x-10 = 270

14 x =280

x=20

B =6x+1 =121

The eigen values of matrix A  [tex]\left[\begin{array}{ccc}1&2&1\\0&2&1\\0&0&3\end{array}\right][/tex] are respectively, 1, 2, 3

In mathematics, the eigen values are characteristic roots of the equation

| A - λI |,

where,  A is matrix and λ is eigen value of the matrix

Properties of matrix,

1.  Sum of diagonal elements = Sum of eigen values

2. Determinant of matrix  = Product of eigen values

Given that,

Matrix A =    [tex]\left[\begin{array}{ccc}1&2&1\\0&2&1\\0&0&3\end{array}\right][/tex]

The eigen values of A = ?

It is known that,

For the upper and lower triangular matrix, eigen values of the matrix are diagonal elements,

given matrix is, upper triangular,

Diagonal elements are  1, 2, 3

So, The eigen values will be 1, 2, 3

Thus, the eigen values are  1, 2, 3

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The domain and range are x >= 3 and y >= 0

From the question, we have the following parameters that can be used in our computation:

The graph

The domain is the set of the input values

On the graph, we have

Input values start from x = 3 and increases

So, the domain is x >= 3

The range is the set of the output values

On the graph, we have

output values start from y = 0 and increases

So, the range is y >= 0

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Two lines that are perpendicular to one another have a slope product that is negative one. If m1 and m2 are the slopes of the two lines, then m1.m2 = -1.

As a result, we may state that m1 = 4, which is the slope of this line.

As a result, m2 = -1/4 is the slope of the line perpendicular to this line.

Now, the 2nd line's general equation can be expressed as

y = (-1/4)x + c —— 1)

Since point (-12,4) is located on this line, we may solve for c by substituting y = -12 and x = 4 in the equation above.

We may finish the equation for the line perpendicular to the line y = 4x+3 once we know the value of c.

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The equation of line is y = -2x + 9 , where the slope is m = -2

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 , the value of A is

Let the point be represented as P ( 1 , 7 )

Let the slope of the line be m = -2

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

Substituting the values in the equation , we get

y - 7 = -2 ( x - 1 )

On simplifying the equation , we get

y - 7 = -2x + 2

Adding 7 on both sides of the equation , we get

y = -2x + 9

Hence , the equation of line is y = -2x + 9

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The solution for the One-Variable Addition Equations is,

1: d = 0.6,  2:  k = 11,  and 3: y = 3.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given 1: d  + 3.2 = 6.3 - 2.5

subtract 3.2 from both sides

d = 6.3 - 2.5 - 3.2

d = 0.6

2: 25 + k + 4(1/4) = 37

divide 4/4 = 1

25 + k + 1 = 37

k = 37 - 26

k = 11

3: 4(1/2) + y = 10(1/2)

so 4/2 = 2 and 10/2 = 5

2 + y = 5

y = 3

Hence d  = 0.6, k = 11,  and y = 3.

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The probability of the winner is 1/8100. And the probability of losing is 8099/8100.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Let A signify the occasion of putting down a $1 straight bet on a specific lottery and winning. Assume that, for this specific lottery, there are 8,100 unique ways that you can choose the four digits (with reiteration permitted) in this lottery, and only one of those four-digit numbers will be the victor.

Then the probability of the winner is given as,

P(A) = 1 / 8,100

The probability of losing is given as,

Q(A) = 1 - P(A)

Q(A) = 1 - 1/8100

Q(A) = 8,099 / 8,100

The probability of the winner is 1/8100. And the probability of losing is 8099/8100.

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The maximum value of the function z = 5x + 3y subjected to the constraints is given as follows:

48.1665.

The function for this problem is defined as follows:

z = 5x + 3y.

The constraints are given as follows:

x has a higher multiplier than y, hence the value of y should be minimized to obtain the maximum value, hence:

y = 3.

Then the value of x is obtained as follows:

6x + 7(3) = 68

6x = 47

x = 7.8333.

Then the maximum value of the function is given as follows:

z = 5(7.8333) + 3(3)

z = 48.1665.

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The Canal's price/earnings ratio is 2.92.

To calculate Canal's price/earnings ratio, we need to find the earnings per share (EPS) first. The EPS can be calculated by dividing the net income by the weighted average number of common shares outstanding.

The weighted average number of common shares outstanding can be calculated as follows:

Weighted average number of common shares outstanding = Total number of common shares - Weighted average number of treasury shares

Weighted average number of common shares outstanding = 24,200 - 4,200 = 20,000

EPS = Net income / Weighted average number of common shares outstanding

EPS = $260,000 / 20,000 = $13

Finally, the price/earnings ratio can be calculated by dividing the market price per share by the EPS:

Price/earnings ratio = Market price per share / EPS

Price/earnings ratio = $38 / $13 = 2.92

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The solution of the inequality 3x < 13 is x < 4.33.

None of the given option is correct.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality,

3x < 13.

Simplifying,

x < 4.33

The graph is given in the attached image.

Therefore, the solution is x < 4.33.

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The three statements about his solution that are true include the following:

1. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

2. He did not multiply the numerator and denominator by the correct number to equal 1,500.

5. He should have multiplied the numerator and denominator by 75, not 30,  because 20 × 75 = 1,500.

Based on the information provided, a mathematical expression which models the number of songs of each genre on Josiah's MP3 player to be 300 songs:

here, we have,

10/20 = x/1500

Multiplying the mathematical expression by 75, we have the following:

75 × (10/20) = x/1,500

750/1500 = x/1500

1,500x = (750 × 1,500)

x = (750 × 1,500)/1,500

x = 750.

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Answer:

The range of acceptable length is between 35.28 inches and 36.72 inches.

To calculate the range of acceptable length:

Lower bound: 36 in. - (36 in. x 0.05) = 35.28 in.

Upper bound: 36 in. + (36 in. x 0.05) = 36.72 in.

The fraction equivalent of 7/8 + 5/12 is 31/24

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: Two fractions 7/8 and 5/12

Now sum of the two fractions are 7/8+5/12

We know When two or more fractions with different denominators are added together, then we cannot the numerators directly. Thus Make the denominators of the fractions same, by finding the LCM of denominators and rationalising them with LCM(8,12)=24

Thus, 7/8+5/12= 21+10  /24

                        = 31/24

Hence, The fraction equivalent of 7/8 + 5/12 is 31/24

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The value of x in the parallelogram is calculated to be 11

The value of x is solved using the property of a parallelogram which says that the opposite angles are equal

Applying this mathematically gives

7x - 2 = 75

collecting like terms

7x = 75 + 2

7x = 77

Isolating x by dividing through by 7

7x / 7 = 77 / 7

x = 11

so we found the value of x to be 11

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Answer:

C. a quadratic function with a negative value of a

Step-by-step explanation:

It is likely that a quadratic function with a negative value of a would be the best model for this data, as it would represent a parabolic shape that can accommodate a downward trend, followed by an upward trend, in the stock price. The value of "a" determines the direction of the parabola, with a negative value resulting in a downward-facing parabola, which is appropriate for a stock price that starts low and increases over time. This type of function would provide a good fit for the data, especially if there are fluctuations or ups and downs in the stock price over time.

31/6 or 5.167 feet of lumber was left.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given,  Peter cut a piece of lumber 9 5/6 feet long from a piece that was 15 feet long.

Since the total length of wood is 15 feet

Thus,

The remaining wood = 15 - (9 5/6)

The remaining wood = 6 - 5/6

The remaining wood = 31/6

therefore, 31/6 or 5.167 feet of the lumber was left.

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Answer:

5/12

Step-by-step explanation:

Find the LCM for denominators 3 and 4, this would be 12.

[tex]\frac{1*3}{4*3} = \frac{3}{12}[/tex]

[tex]\frac{1*4}{3*4} = \frac{4}{12}[/tex]

Add both fractions together:

3/12 + 4/12 = 7/12

Subtract 7 from 12 to find the remaining amount to make 12:

12 - 7 = 5

Therefore, the fraction that remains for other expenses is [5/12]

Answer:

Fred spent $3.18 on brownies.

The equation that models the product is 5 × 5 = 25

In mathematics, a numerical expression is a combination of numbers or integers combined using mathematical operators like addition, subtraction, multiplication, division, etc. In this, we don't use variables like x, y, etc., or any unknown quantity.

Here we have

Jonathan uses the area model to show the product of two mixed numbers  

The equation that models the product can be formed as follows

Here number of units along length = 5 units

Number of units along breadth = 5 units

Area = 5 × 5 = 25

Therefore,

The equation that models the product is 5 × 5 = 25

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Answer:

a) C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)
b) 39.22
c)  143.69

Step-by-step explanation:

(a) We can write a piecewise function to describe the cost C(n) of n CDs purchased:

C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)

(b) The cost of 53 CDs is:

C(53) = 0.74 * min(53, 100) + 0.69 * max(53 - 100, 0) = 0.74 * 53 = 39.22

(c) The cost for 201 CDs is:

C(201) = 0.74 * min(201, 100) + 0.69 * max(201 - 100, 0) = 0.74 * 100 + 0.69 * 101 = 74 + 69.69 = 143.69