Charlene has a monthly salary of $3,410. With her present budget, Charlene has a net income that is 7% of her monthly salary. Charlene is going to reduce her net income by $125 each month and put this money towards paying down her debt. What will Charlene’s new net income be?

1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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Answer:

I think it's 35, because if there's 25 dark and you divide 25 by 5 you get 5, so 1/12 is equal to 5

Option C is  not a criterion for congruence of triangles

What is congruent triangles?

Congruence of triangles: two triangles area unit aforesaid to be congruent if all 3 corresponding sides area unit equal and every one the 3 corresponding angles area unit equal in measure.

Main body:

SAS = If two pairs of  corresponding sides of two triangles are equal in length, and the  corresponding included angles are equal in measurement, then the triangles are congruent.

ASA = If two pairs of  corresponding angles of two triangles are equal in measurement, and the  corresponding  included sides are equal in length, then the triangles are congruent.

SSS = If three pairs of  corresponding sides of two triangles are equal in length, then the triangles are congruent.

SSA =The SSA condition (Side-Side-Angle) which specifies two sides and a non-included angle (also known as A-SS, or Angle-Side-Side) does not by itself prove congruence.

Hence the option C is  not a criterion for congruence of triangles.

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The vertex of the parabola is (5, 4). The solution has been obtained by using quadratic formula.

What is quadratic formula?

The quadratic formula is used to determine an equation's roots. This formula assists in evaluating the solutions of the quadratic equations instead of the factorization approach.

We are given equation as  y = -x² + 10x - 21.

Using quadratic formula, we know that x = -b/2a

So,

x = -10/-2

x = 5

On substituting this in the equation, we get

y = -5² + 10(5) - 21

y = -25 + 50 - 21

y = 4

Hence, the vertex of the parabola is (5, 4).

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Answer: 49

Step-by-step explanation:

28÷8=3.5

3.5 is the number you multiply 14 by to get 49

The elementary skills have used so far in the course is explained below.

What is whole numbers?

An integer is the range zero, a high quality herbal range or a bad integer with a minus sign. The bad numbers are the additive inverses of the corresponding high quality numbers. In the language of mathematics, the set of integers is frequently denoted through the boldface Z or blackboard bold.

The cap potential to define entire numbers and differentiate them from natural numbers is a critical component of math.

complete numbers like 0, 1, and 2 are the constructing blocks to expertise greater complex wide variety identifiers like actual numbers, rational numbers, and irrational numbers.

The subset of numbers within integers is whole numbers. those are numbers that we're maximum used to working with, which include zero. We see entire numbers on nutrients labels, or signs on the toll road telling us how many miles are to the subsequent exit/city.

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Answer:

x = 7°

Step-by-step explanation:

(8x + 6)° + 118° = 180°

8x = 56°

x = 7°

The domain of the quotient function (f/g)(x) consists of all numbers that belong to both the domain of f and the domain of g which is false.

A statement, opinion, or rule that forms a linking of two variables is characterized as a function. Mathematics has functions, which are necessary for the design of meaningful relationships.

The range refers to all potential values of y, and the domain refers to all conceivable values of x.

The denominator of the rational function shouldn't be 0. The function is not defined if the denominator is 0.

Thus, the given statement is false.

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The 12th term of the sequence is:

\(T_{12} = T_{11}*r = -18*3 = -54\)

For a geometric sequence with a common ratio r and a first term T₁, the equation for the n-th term is:

\(T_n = T_1*(r)^{n-1} = T_{n-1}*r\)

Such that the second formula (the right one) is called the recursive formula or recursive relation for the sequence.

We know that r = 3, and T₁₀ = -6, then we can use the recursive relation:

T_{11} = T_{10}*r = -6*3 = -18

T_{12} = T_{11}*r = -18*3 = -54

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Check the picture below.

so we only want the area in pink.

\(\stackrel{\textit{left and right}}{2(4)(11)}~~ + ~~\stackrel{\textit{front and back}}{2(4)(11)}\implies \text{\LARGE 176}~cm^2\)

Answer:

2

5

Step-by-step explanation:

Answer: 2/3

Step-by-step explanation:

    We will turn all of these fractions into decimals by dividing to compare them easier.

3/5 ➜ 0.6

20/100 ➜ 0.2

6/10 ➜ 0.6

1/2 ➜ 0.5

2/12 ➜ 0.16666

2/3 ➜ 0.6666

    0.6666 > 0.6, so 2/3 > 3/5

    This means our answer is 2/3

Answer:

volume = 41,472 in³

Step-by-step explanation:

volume = 24 x 48 x 36 = 41,472 in³

Answer:

32x – 72

OR

–72 + 32x

Step-by-step explanation:

To use the Distributive Property, just simply follow my steps:

Write the equation:

–8(9 – 4x)

To distribute, multiply the numbers inside the parenthesis by the number outside of the parenthesis SEPARATELY. It should look like this:

(–8 • 9)(–8 • –4x)

(–72)(32x)

Since the 32 is positive, the equation could be written either way:

–72 + 32x

OR

32x – 72

If you want the equation to be fully solved...

Set the equation equal to zero:

32x – 72 = 0

Isolate the variable. Subtract 72 from both sides:

32x – 72 + 72 = 0 + 72

32x = 0 + 72

32x = 72

Divide:

32x/32 = 72/32

x = 9/4 (Improper Fraction Form)

OR

x = 2 (and) 1/4 (Mixed Number Form)

Convert 9/4 to a decimal:

x = 9/4

x = 2.25

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Many ways can 3 baseball players and 5 basketball players be selected from 12 baseball players and 12 basketball players are 173040 ways.

This is a combination problem, and we want to find the number of ways to choose 3 baseball players and 5 basketball players from a pool of 12 baseball players and 12 basketball players.

The formula for combinations is: C(n, k) = n! / (k! (n - k)!).

The total number of combinations is the product of the number of combinations for each group, so 220 * 792 = 173040.

Therefore, there are 173040 ways to choose 3 baseball players and 5 basketball players from a pool of 12 baseball players and 12 basketball players.

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Answer:

2,-2

you just have to look at the "menu" of choices and determine which one of the choices

fits the question... the f(-4) says you have to see which one of the three

choices has -4 in it ...

the middle one does -4≤x≤1 -4 is for sure in the range

this question #1 answer is "2" because the result is always a 2 for that choice...

the next question put in 3 ... three is greater than 1 (that is the third choice)

so the result is -(3) + 1 = -2

your answers are 2, and -2

Step-by-step explanation:

To complete the table of values for the rational function f(x) = 8x/(x-4), we need to plug in different values of x and evaluate the function.

x | f(x)
--|----
-3| 24
-2| -16
0 | 0
2 | 16
4 | undefined
6 | -24
Let me explain how I arrived at each value. When x=-3, we get f(-3) = 8(-3)/(-3-4) = 24. Similarly, when x=-2, we get f(-2) = 8(-2)/(-2-4) = -16. When x=0, we get f(0) = 8(0)/(0-4) = 0. When x=2, we get f(2) = 8(2)/(2-4) = 16. However, when x=4, we get f(4) = 8(4)/(4-4) = undefined, since we cannot divide by zero. Finally, when x=6, we get f(6) = 8(6)/(6-4) = -24.I hope this helps you understand how to evaluate a rational function for different values of x. Let me know if you have any other questions!

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The Population set for a sample of 28 percent is a reasonable estimate sample of the percentage of those who have taken one or more courses in statistics is "all mathematics teachers who have taken one or more courses in statistics".

So, Correct option is option (C) .

We have given that ,

There is a large conference of teachers from a variety of subjects.

Random sample size = 50 mathematics teachers who attended the conference is selected.

Population set : A population is the entire group that you want to draw conclusions about, that is here population set contains all teachers who attand the conference .

Sample : It is defined as subset of population set in a representative manner. It is taken from large population.

here, sample is 50 selected mathematics teachers.

On reading the provided data we conclude that The required population set for given sample is All mathematics teachers who have taken one or more course in statistics.

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Complete question:

At a large conference of teachers from a variety of subjects, a random sample of 50 mathematics teachers attending the conference was selected. Among the selected mathematics teachers, 28 percent had taken one or more courses in statistics. For which of the following populations is 28 percent a reasonable estimate of the percentage of those who have taken one or more courses in statistics?

A. All mathematics teachers

B. All mathematics teachers who attended the conference

C. all mathematics teachers who have taken one or more courses in statistics

D. All teachers who attended the conference

E. All teachers

Answer:

  (y -12)(y -4)

Step-by-step explanation:

This can be factored as the difference of squares:

  (y -8)² -16 = (y -8)² -4² = (y -8 -4)(y -8 +4) = (y -12)(y -4)

Answer:

x ≤ $30

Step-by-step explanation:

Including the $15 for flowers, there is a budget of $45. Josh cannot spend more than $30 on a gift.

x can be less than or equal to $30

The inequality for the $x of gift x≤ 30.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

For example, In the 12U Softball division, Olivia gets chosen. What is Olivia's age?

Olivia's age is unknown to you since the word "equals" is missing. However, because you are aware that she should be under or equal to 12, you can write Olivia's Age ≤ 12.

Given:

Total amount spend on gift = $45

price of flower= $15

So, the amount of gift only is

=45- 15

=$30

Thus, Josh can only spend $30 for the gift not more than that.

Hence, the inequality for the $x of gift

x≤ 30

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Answer:

She should cut 1.21 inches (or a square of area 1.46 inch²) from 4 corners to get the maximum volume

Step-by-step explanation:

Length = L = 10 inches

Width = W = 6 inches

Suppose x is cut from the 4 corners to make a box.

Dimensions of the Box:

L= 10 - 2x

W = 6 - 2x

H = x

Volume of the Box:

V = (L)(W)(H)

V = (10-2x)(6-2x)(x)

V = 4x³ -  32x² + 60x

For Maximum value:

\(\frac{dV}{dx}=0\)

\(\frac{dV}{dx}=\frac{d}{dx}(4x^3-32x+60x)\\\frac{dV}{dx}=12x^2-64x+60\\12x^2-64x+60 = 0\)

The values of x found are:

x= 4.12 , x = 1.21

If we put x= 4.12 in W= 6-2x , the value of width becomes negative, so that is not possible.

We discard 4.12. Now x=1.21

So,

If 1.21 inches are cut from 4 corners, or a square of 1.21*1.21 = 1.46 inch² is cut from 4 corners, we get the maximum value of V

The sector is mapped onto the region bounded by the rays with argument 0 and π/4 and the ray with argument π.

To, Sketch the region onto which the sector r≤1,0≤θ≤π/4 is mapped by the following transformations: (a) f(z)=1​/z (b) f(z)=z^2 (c) f(z)=z^4 (d) f(z)=ez.

(a) f(z) = 1/z, Here, when we calculate the product of r and θ, we get that the product lies between 0 and 1/4π .

So, when we apply the transformation f(z) = 1/z, we see that the sector is mapped onto the interior of the circle |z| = 1.  Also, all the points on the sector except 0 are mapped on to the interior of this circle.

(b) f(z) = z^2, Here, when we calculate the product of r and θ, we get that the product lies between 0 and 1/2.

So, when we apply the transformation f(z) = z^2, we see that the sector is mapped onto the region bounded by the rays with argument 0 and π/2 and the ray with argument π.

We see that all the points in the sector are mapped into this region.

(c) f(z) = z^4, Here, when we calculate the product of r and θ, we get that the product lies between 0 and 1/8.

So, when we apply the transformation f(z) = z^4, we see that the sector is mapped onto the region bounded by the rays with argument 0 and π/4 and the ray with argument π.

We see that all the points in the sector are mapped into this region.

(d) f(z) = ez, Here, when we calculate the product of r and θ, we get that the product lies between 0 and e^π/4 .

So, when we apply the transformation f(z) = ez, we see that the sector is mapped onto the region bounded by the rays with argument 0 and π/4 and the ray with argument π.

We see that all the points in the sector are mapped into this region. This region extends beyond the point at infinity.

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The monic cubic polynomial with integer coefficients is x³ - 3x² + 3x + 2 with the leading coefficient as 1.

In order to find a monic cubic polynomial with integer coefficients, we can use the following method:

Let us assume that the cubic polynomial is of the form:x³ + bx² + cx + d

We need to find the values of b, c, and d such that the polynomial is monic and has integer coefficients.

Since the polynomial is monic, the coefficient of x³ is 1.

Therefore, we can write the polynomial as:x³ + bx² + cx + d = (x - r)(x² + px + q)

Where r is the root of the cubic polynomial, and p and q are constants to be determined.

We know that the sum of the roots of a cubic polynomial is equal to -b/1 = -b.

Therefore, the sum of the roots of our cubic polynomial is equal to:r - p/1 = -bOr,r + p = -b ...(1)

Also, we know that the product of the roots of a cubic polynomial is equal to -d/1 = -d.

Therefore, the product of the roots of our cubic polynomial is equal to r(q - r).

Thus,r(q - r) = -d ...(2)

Solving equations (1) and (2) for r and q, we get:

r = -b/3q = b²/3 - d

Hence, we can write the cubic polynomial as:

x³ + bx² + cx + d = (x + b/3)(x² + (b²/3 - d)x + r(b²/3 - d))

Let us choose d = 2 and r = 1, then we have:b = -3

Substituting these values, we get:x³ - 3x² + 3x + 2 = (x - 1)(x² - 2x - 2)

Therefore, the monic cubic polynomial with integer coefficients is x³ - 3x² + 3x + 2.

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Answer:

A black hole

Step-by-step explanation:

take my word for it it is A!

Have a fantastico day!  

The measure of angle ∠4 is 115°, we can conclude that the measure of corresponding angle ∠2 is also 115°.

Corresponding angles are formed when a transversal intersects two parallel lines. In the given figure, if the lines on either side of the transversal are parallel, then angle ∠4 and angle ∠2 are corresponding angles.

The key property of corresponding angles is that they have equal measures. In other words, if the measure of angle ∠4 is 115°, then the measure of corresponding angle ∠2 will also be 115°. This is because corresponding angles are "matching" angles that are formed at the same position when a transversal intersects parallel lines.

Therefore, in the given figure, if the measure of angle ∠4 is 115°, we can conclude that the measure of corresponding angle ∠2 is also 115°.

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Since line G has a slope of 7/5 and line H is parallel to line G, the slope of line H is 7/5.

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

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂

This ultimately implies that, the slope of these two lines are equal and the same:

Slope of line G = Slope of line H

7/5 = 7/5

In conclusion, we can reasonably infer and logically deduce that the slope of line H is equal to 7/5.

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An equation for the function g(x) when g(x) = f(-x) is g(x) = -x/3 - 6, which is shown in the graph attached below.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By reflecting the given function across the across the y-axis (y = x), we have the following:

f(x) = x/3 - 6

g(x) = f(-x)

g(x) = -x/3 - 6.

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Integers are numbers without decimals

The integers could you have multiplied are 9 and 2

Let the numbers be x and y

So, we have:

\(\mathbf{x \times y}\)

Increase x by 1 and reduce y by 1.

So, we have

\(\mathbf{(x +1) \times (y -1) = 6 + xy }\)

Open brackets

\(\mathbf{xy -x + y - 1 = 6 + xy}\)

Subtract xy from both sides

\(\mathbf{ -x + y - 1 = 6}\)

Collect like terms

\(\mathbf{ -x + y = 6 + 1}\)

\(\mathbf{ -x + y = 7}\)

Rewrite as:

\(\mathbf{ y -x= 7}\)

The above means that, the difference between the integers is 7.

There are several integers that fit the above description;

One possibility is: 9 and 2

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To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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