Rachel lives in state without income tax. Each month, she pays $307 in federal income tax
and $206 in other taxes. Her pay after taxes is $2,040. What are Rachel's monthly earnings?

Answer:

Step-by-step explanation:

Let the number of miles be x.

Total amount of rental is:

Total amount of rental is:

Since A = B, substitute the values and solve the equation:

The option D.15 + 40 = 5(3 + 8); demonstrates the distributive property.

From the given options;

Consider option D; 15 + 40 = 5(3 + 8).

It is the case of distributive addition.

where

5(3 + 8) = 5×3 + 5×8

5(3 + 8) = 15 + 40

Thus, the option D is the correct representation of the distributive law.

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Solution=0.76

How to solve 11/12 - 7/45?

[tex]\frac{11}{12} -\frac{7}{45} \\=\frac{(11*45-7*12)}{540} \\=\frac{411}{540} \\=0.76[/tex]

What is a fraction?

       Ex: 1/2 = 0.5

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we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"

Because one of these solutions does not have a meaning in the given contest.

So we have a square with an area of 16 square units, then the side length of that square will be given by:

S^2 = 16 square units

Now, there are two solutions for the above equation, these are:

S = 4 units

S = -4 units.

But being a solution of the equation does not mean that the solutions have sense in the context of the problem.

When we talk about dimensions of figures, negative numbers are not really well defined. We can't say that a square has a side length of "negative 4 units"

That does not make sense, remember that math is just a language, and it should be used to communicate things to others.

So the logical solutions (4 and -4) is not the only thing we need to look at when we state the solutions of a problem, but also the problem itself.

That is why we can't say that "both square roots for 16, the area of the square, are the length of each side of the square"

Because one of these solutions does not have a meaning in the given contest.

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For the given subscriptions, we have that:

a) The mean is of $6.42.

b) The median is of $5.

c) The modes are of 5 and 10.

d) Marshall would have to add a subscription of $12.25.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

For this problem, the observations are given as follows:

10, 5, 10, 4, 12, 5, 6, 2.75, 3.

Hence the mean is:

M = (10 + 5 + 10 + 4 + 12 + 5 + 6 + 2.75 + 3)/9 = $6.42.

With another observation, we want a mean of $7, hence:

(10 + 5 + 10 + 4 + 12 + 5 + 6 + 2.75 + 3 + x)/10 = 7

57.75 + x = 70

x = 12.25.

Hence, for item d:

Marshall would have to add a subscription of $12.25.

The median of a data-set is the middle value, which is the value that 50% of the data-set is greater and 50% is lesser.

The ordered data-set in this problem is:

2.75, 3, 4, 5, 5, 6, 10, 10, 12.

The middle value is of 5, which is the median.

The mode of a distribution is the observation that appears the most times in the distribution.

In this problem, those observations are 5 and 10, both of which appears twice, hence the distribution is bimodal.

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Answer:

Approximately [tex]0.7\; {\rm ft}[/tex].

Step-by-step explanation:

If the current bounce is of height [tex]h\; {\rm ft}[/tex], the next bounce would be of height [tex](78\%\, h)\; {\rm ft}[/tex], which is equal to [tex](0.78\, h)\; {\rm ft}[/tex].

It is given that the first bounce is of height [tex]6.5\; {\rm ft}[/tex]. Relative to this first bounce:

In general, the [tex]n[/tex]th bounce would have been dampened [tex](n - 1)[/tex] times. The height of that bounce would be [tex]((0.78)^{n - 1}\, 6.5)\; {\rm ft}[/tex].

Thus, the [tex]10[/tex]th bounce would have been dampened [tex](10 - 1) = 9[/tex] times. The height of that bounce would be [tex]((0.78)^{10 - 1} \, 6.5)\; {\rm ft} \approx 0.7\; {\rm ft}[/tex] (rounded to the nearest tenth, one digit after the decimal point.)

Answer:

-4

Step-by-step explanation:

Split the problem into two cases: one positive and one negative

|4x+7| =9

4x+7=9

(4x+7) =9

Subtract 7 from both sides

4x+7 - 7 = 9 - 7

Solution

x = 1/2

x = -4

Answer:

975 lbs.

Step-by-step explanation:

9 3/4 = 9.75

9.75 × 100 = 975

The total area of all the faces of the cube is square feet

The given parameter is

Side length, l = 2 feet

The total area of all the faces of the cube is calculated as

So, we have

Total area = 6 * Side length^2

This gives

So, we have

Total area = 6 * 2^2

Evaluate the exponent

So, we have

Total area = 6 * 4

Evaluate the product

So, we have

Total area = 24

Hence, the total area of all the faces of the cube is 24 square feet

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The equation that is not a power equation is p = v²×i

From the question, we are to determine which of the given equations is not a power equation

Where the Voltage, V, and the Current, I, are given, the power, P is given by

P = IV

When the Voltage and the Resistance, R, are given

P =  V²/R

When the Current and the Resistance are given,

P = I²R

∴ P =  V²/R, P = IV, and P = I²R are power equations.

Hence, the equation that is not a power equation is p = v²×i

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Answer:

Side length of a square game board is 11.916 inches. Explanation: If the area is 142 ∈2 , as area is square of side length of a square,

Step-by-step explanation:

Answer:

Answer C is correct

Step-by-step explanation:

We know that,

[tex] \sf \: {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \\ \sf \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \: \: \: \: \: \: \: \: [/tex]

[tex]\sf (x) ^{0} = 1 \rightarrow \: Any \: number \: to \: the \: power \: 0 \: is \: 1[/tex]

Let us solve it now.

[tex] \sf( {a}^{3} {b}^{12} {c}^{2} ) \times ( {a}^{5} {c}^{2} ) \times ( {b}^{5} {c}^{4} )^{0} \\ \sf( {a}^{3} {b}^{12} {c}^{2} ) \times ( {a}^{5} {c}^{2} ) \times 1 \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{3} \times {a}^{5} \times {b}^{12} \times {c}^{2} \times {c}^{2} \times 1\\ \sf {a}^{3 + 5} \times {b}^{12} \times {c}^{2 + 2} \times 1 \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{8} \times {b}^{12} \times {c}^{4} \times 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{8} {b}^{12} {c}^{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:

47

Step-by-step explanation:

6(7)+5=42+5=47

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The length of MN is 68.

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given:

LN = 6x-5, LM = x + 7, and MN = 3x + 20

As, M is in between L and N.

LM + MN = LN

x+7 + 3x+ 20 = 6x-5

4x + 27 = 6x -5

-2x = -32

x= 16

So, the length of MN = 3x + 20 = 3 * 16 + 20 = 68

Hence, the length of MN is 68.

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The phrase "54 less than twice Chrissy's age" is translated into an algebraic expression as 2x - 54.

Given the phrase in the question;

"54 less than twice Chrissy's age"

Let variable 'c' represent Chrissy's age

Translation

Chrissy's age ⇒ x

Twice Chrissy's age ⇒ 2 × x = 2x

54 less than ⇒ -54

Now combine terms

2x and - 54

2x - 54

Therefore, the phrase "54 less than twice Chrissy's age" is translated into an algebraic expression as 2x - 54.

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The equation of the circle that passes through the point (-6 , -4) and has a center located at the origin is x^2 + y^2 = 52.

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-6 , -4).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(-6 - 0)^2 + (-4 - 0)^2

radius= √36 + 16

radius = √52

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = √52

(x - 0)^2 + (y - 0)^2 = (√52)^2

x^2 + y^2 = 52

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Using supplementary angles, it is found that the value of x is of x = 10.75.

Supplementary angles are angles whose measures add to 180º.

An entire pizza is 360º, hence half the pizza is 180º, meaning that angles AOB and BOD are supplementary.

Their measures are given as follows:

Since they are supplementary, they add to 180º and we can add their measures and solve for x as follows:

2x - 4 + 14x + 12 = 180

16x = 172

x = 172/16

x = 10.75.

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To calculate the geometric mean, we take their product instead: 1 x 5 x 10 x 13 x 30 = 19,500 and then calculate the 5-th root of 19,500 = 7.21. This is equivalent to raising 19,500 to the 1/5-th power. Another way to calculate the geometric mean is with logarithms, as it is also the average of logarithmic values converted back to base 10.

A recursive function allows us to find the value of any term in a geometric sequence by using the previous term in that exact sequence. If the common ratio of that geometric sequence is 9, then each term is nine times the previous term.

The general term for the geometric sequence is

an= a1 * r ^ (n-1)

where an is the nth term, a₁ is the first term, r is the common ratio, and n is its position or number. The term.

where a₁ = 3 and r = 3/2

Sequence: 3, 4.5, 6.75, 10.125, 15.1875, 22.78125, 34.171875, 51.2578125, 76.88671875 ...

3rd value: 6.75.

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Answer:

4.6667

Step-by-step explanation:

The coordinates of the midpoint of a segment with the given endpoints will be (1.5, -2).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints are A(0, 0) and C(3, -4).

Then the coordinates of the midpoint of a segment with the given endpoints will be

(x, y) = [(0 + 3) / 2, (0 - 4) / 2]

(x, y) = (3/2, -4/2)

(x, y) = (1.5, -2)

The coordinates of the midpoint of a segment with the given endpoints will be (1.5, -2).

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Answer:

No decimal: 905

One decimal: 905.3

Answer: 180

Step-by-step explanation: 3 times 6 is 18 so just add a zero

Answer: 180

Step-by-step explanation:

3x60

60+60+60

The total number of seats are there is row 16 is 65.

In Arithmetic Progression, the difference between two different arithmetic orders is a fixed number (AP). Arithmetic Sequence is another name for it.

We'd come along through a few specific terms in AP that had been labeled as:

As shown below, the AP can also be referred to in terms of common differences.

Now, as the values given in the question;

There are total 16 rows in the arena.

Thus, n = 16.

There are 20 seats present in row 1.

Consider the first term as 'a₁' = 20.

Similarly, there are 23 seats present at row 2.

Consider 'a₂' = 23 is the second term.

Now, calculate the common difference;

d = a₂ - a₁  

Put the values in the 'd'.

d = 23 - 20 = 3.

Now, compute the total number of seats in 16th row bu nth formula.

n-th term:  an = a + (n − 1) × d

a₁₆ = a₁ + (n - 1)d

a₁₆ = 20 + (16 - 1)3

a₁₆ = 20 + 45

a₁₆ = 65

Therefore, the total number of seats present in the 16th row is 65.

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Answer: 8/5

Step-by-step explanation:

The value of the expression  is 3 using the concept of the logarithm.

A base must be raised to a certain exponent or power, or logarithm, to produce a specific number. If bˣ=n, then x is the logarithm of n to the base a, which is expressed mathematically as x = logₐ n.

Given the expression log₂√(2+14)(1+3)

Solving the square root we obtain,

[tex]log_{2} \sqrt{(16)(4)}\\[/tex]

Simplifying further we get,

[tex]=log_{2} (4)(2)[/tex]

[tex]=log_{2} (8)[/tex]

We know that the logarithm of 8 with base 2 is 3.

Hence, the given expression can be simplified as 3.

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Answer:

x=7

Step-by-step explanation:

AB is 1 part of the line

BC is the other part of the line

the total length of the line is 50 units

when you add AB to BC you should get 50

5x+2x+1=50

7x+1=50

7x=49

x=7