Hillary gets divorced in 2016 and is required to pay her ex-spouse $200 per month until her son reaches 18 years of age in 7 years and $120 per month thereafter. How much of her 2019 payments are deductible as alimony?

Length of segment HJ is 5√3 units

Step-by-step explanation:

Here, apply the Pythagorean relationship where sum of squares of the sides equals the square of the hypotenuse.

Given that the hypotenuse, c= 10 units, and one of the side, a=5 units, then the other side can be calculated as;

a²+b²=c²

5²+b²=10²

b²=10²-5²

b²=100-25

b²=75

b=√75 = √3*25 = √3 *√25 = √3 *5 = 5√3

Length of segment HJ is 5√3 units

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Answer:

B

Step-by-step explanation:

Answer:

P = 0.1654

Step-by-step explanation:

Binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

P = ₂₅C₁₈ (0.75)¹⁸ (0.25)²⁵⁻¹⁸

P = 480,700 (0.75)¹⁸ (0.25)⁷

P = 0.1654

Answer:

The answer to your question is letter D. x = 64

Step-by-step explanation:

Equation

                                       log x 8  = 0.5

Express the log as a exponential equation

                                        x[tex]x^{0.5}[/tex] = 8

Express the power as a fraction

                                        [tex]x^{1/2} = 8[/tex]

                                        [tex]\sqrt{x^{2}}[/tex]

Look for a number which squared root is 8

                                        [tex]\sqrt{64} = 8[/tex]

Then

                                        x = 64

Answer:

Please mark as brainliest :)

Step-by-step explanation:

Answer:

$149.27

Step-by-step explanation:

18% of $126.50 is $22.77 which then added to 126.50=$149.27

Answer: the company now have 531 employees.

Step-by-step explanation:

The initial number of employees that the company had was 450.

The company began a new project line and must increase their number of employees by 18% . it means that the number of new employees that the company employed would be

18/100 × 450 = 0.18 × 450 = 81

Therefore, the total number of employees that the company have now would be

450 + 81 = 531

Answer:

593,775 ways

Step-by-step explanation:

24 donuts have to be selected from 7 different varieties of donuts

n = 7

r= 24

Repetition is allowed

C(n+r-1, r) = C(7 + 24 - 1 , 24)

= C(30,24)

Recall that C(n,r) = n! /(n-r)! r!

C(30,24) = 30!/(30 - 24)! 24!

= 30!/(6!24!)

= 593,775 ways

Answer: 346,789 ways

Step-by-step explanation:

Using the formular for permutation to calculate :

P= n!/r!(n-r)!

We need to select 24 apples from 7 types of apples

n=24 ,r=7

Permutation =24!/7!(24-7)!

Permutation =6.2×10^23/1.793×10^18

P= 346 ,789 ways

Answer:

the top of the ladder is 27.5ft above the ground.

Step-by-step explanation:

The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.

The length of the ladder represents the hypotenuse of the right angle triangle.

The ground distance from the base of the wall to the foot of the ladder represents the adjacent side of the right angle triangle.

Therefore, to determine how high up is the top of the ladder on the wall, x, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

28² = x² + 5²

784 = x² + 25

x² = 784 - 25 = 759

x = √759 = 27.5ft

Using the Pythagorean theorem, the ladder reaches approximately 27.5 feet up the wall when the base is 5 feet from the wall.

The question involves finding the height up a wall that a 28ft ladder reaches when its base is 5ft from the wall. To solve this, we will use the Pythagorean theorem which relates the sides of a right-angled triangle. The ladder, wall, and ground form a right-angled triangle with the ladder as the hypotenuse and the wall and ground as the other two sides.

Let h be the height the ladder reaches up the wall. Using the Pythagorean theorem, we have:

28² = h² + 5²

Solving for h:

28² - 5² = h²


784 - 25 = h²

759 = h²

h ≈ √759

h ≈ 27.5 (to the nearest tenth)

Therefore, the ladder reaches approximately 27.5 feet up the wall.

Answer:

Option C) [tex]{\{0.5,0}\}[/tex] is correct

The solution to the given equation is [tex]{\{0.5,0}\}[/tex]

Step-by-step explanation:

Given quadratic equation is [tex]-2x^2+x=0[/tex]

To solve the equation by completing the square :

[tex]-2x^2+x=0[/tex]

[tex]-2(x^2-\frac{x}{2})=0[/tex]

[tex]x^2-\frac{x}{2}=0[/tex]

Rewritting the above equation as below :

[tex]x^2-2(x)\frac{1}{4}+\frac{1}{4^2}-\frac{1}{4^2}=0[/tex]

[tex](x-\frac{1}{4})^2-\frac{1}{4^2}=0[/tex]

[tex](x-\frac{1}{4})^2=\frac{1}{4^2}[/tex]

Taking square root on both sides we get

[tex]\sqrt{(x-\frac{1}{4})^2}=\sqrt{\frac{1}{4^2}}[/tex]

[tex](x-\frac{1}{4})=\pm\frac{1}{4}[/tex]

[tex]x=\pm\frac{1}{4}+\frac{1}{4}[/tex]

[tex]x=+\frac{1}{4}+\frac{1}{4}[/tex] and [tex]x=-\frac{1}{4}+\frac{1}{4}[/tex]

[tex]x=\frac{2}{4}[/tex] and [tex]x=0[/tex]

Therefore [tex]x=\frac{1}{2}[/tex] and x=0

[tex]x=0.5[/tex] and x=0

Therefore the solution to the given equation is [tex]{\{0.5,0}\}[/tex]

Option C) [tex]{\{0.5,0}\}[/tex] is correct

Answer:

-1z-3

Step-by-step explanation:

10z-11z = -1z

+2-5= -3

= -z-3

Answer:

-z - 3

Step-by-step explanation:

10z - 11z + 2 - 5

Simplifying:

10z - 11z = -z

+2 - 5 = -3

Theresfore; 10z - 11z +2 - 5 = -z - 3

Joey started his day with $63.

Step-by-step explanation:

Let,

x be the amount Joey started with.

Amount left = 5 cent = $0.05

Amount spent on bus ticket = $0.75

Amount spent on soccer ball = [tex]\frac{1}{2}x[/tex]

Amount spent on lunch = [tex]\frac{1}{4}x[/tex]

Amount spent on soccer tickets = $14.95

According to given statement;

Total amount - bus ticket - soccer ball - lunch - soccer tickets = Amount left

[tex]x-0.75-\frac{1}{2}x-\frac{1}{4}x-14.95=0.05\\\\x-\frac{1}{2}x-\frac{1}{4}x=0.05+0.75+14.95\\\\\frac{4x-2x-x}{4}=15.75\\\\\frac{x}{4}=15.75[/tex]

Multiplying both sides by 4

[tex]4*\frac{x}{4}=15.75*4\\x=63[/tex]

Joey started his day with $63.

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Answer: the total number of distance markers on the trail is 6

Step-by-step explanation:

The total distance that Robert covers in the race is 3 miles.

If a distance marker is placed evenly every 1/2 mile from the beginning of the race until the end, then the total number of distance markers on the trail would be

3/0.5 = 6

Answer: your IQ test score is 117

Step-by-step explanation:

Assume that the mean of a normal distribution of IQ scores is 102 and the standard deviation is 15.

If you have been told that your test score is 1 standard deviation above the mean, it means that your score would be

102 + 15 = 117

According to the empirical rule, 68% of data falls within the first standard deviation from the mean. This means that 117 falls within 68% of the scores.

Answer:

The answer to your question is 10.5 in

Step-by-step explanation:

Data

First triangle

height = x

base = 7 in

Second triangle

height = 12 in

base = 8 in

Process

1.- Use proportions to solve this problem, relates the sides of a triangle with the same sides of the other triangle.

                                   [tex]\frac{x}{7} = \frac{12}{8}[/tex]

2.- Multiply both sides by 7

                                [tex]7\frac{x}{7} = \frac{7(12)}{8}[/tex]

3.- Simplify

                                 x = [tex]\frac{84}{8}[/tex]

4.- Result

                                x = 10.5 in

Answer:

Step-by-step explanation:

1 foot is 0.3048 meters, so ...

  70 m/s = (70 m/s)×(1 ft)/(0.3048 m) ≈ 229.659 ft/s

At that speed, the distance covered in 20 seconds is ...

  (20 s)(229.659 ft/s) = 4,593.18 ft

The parachutist will fall 4593 feet during 20 seconds of free fall at 229.7 ft per second.

_____

Final answers are rounded. Intermediate values are not.

Answer:

That would be the side-side-side (SSS) postulate, which states that if all the sides of a triangle are in a fixed ratio to all the corresponding sides of another triangle, then the two triangles are said to be congruent.

Step-by-step explanation:

Looking at triangles ABC and DEF, we notice that:

[tex]\frac{AB}{DE} = \frac{AC}{DF}=\frac{BC}{EF}[/tex]

since

[tex]\frac{3}{18} = \frac{6}{36}=\frac{7}{42}=\frac{1}{6}[/tex]

Let me know if you have further questions.

Answer:x = 9.01

Step-by-step explanation:

The given triangle is a right angle triangle.

From the given right angle triangle the hypotenuse of the right angle triangle is 17

With 35 degrees as the reference angle,

x represents the adjacent side of the right angle triangle.

The unlabelled side represents the opposite side of the right angle triangle.

θ = 35 degrees

To determine x, we would apply trigonometric ratio

Cos θ = adjacent side/hypotenuse side. Therefore,

Cos 35 = x/11

x = 11 Cos 35 = 11 × 0.8192

x = 9.01

Answer:

9.01

Step-by-step explanation:

The right angle triangle with a focused angle of degree is easily solved using Trig Ratio that can easily be recalled with this word :

SohCahToa.

What it means is:

If the Opposite side to the focused angle is given and also the hypotenuse is given, we use sine

Cosine if Adjacent and Hypotenuse is given.

Tangent if the opposite and Adjacent is given.

Now, to the question:

The Adjacent and the Hypotenuse is given. Therefore we'll use Cosine.

Therefore:

Cos 35 = x / 11

Cross multiplying:

11 cos 35 = x

11 * 0.8192 = x

Theresfore,

x = 9.01

Hope it helped?

Final answer:

The statement forms p → q ∨ r, p ∧ ¬q → r, and p ∧ ¬r → q are shown to be logically equivalent using principles of logical equivalence and contraposition. The original statement 'If n is prime, then n is odd or n is 2' can thus be rephrased in different ways while retaining the same meaning.

Explanation:

Logical Equivalences

To show that the statement forms p → q ∨ r, p ∧ ¬q → r, and p ∧ ¬r → q are all logically equivalent, we need to understand that logical equivalence means that the statements have the same truth value in every possible scenario. The implication p → q is equivalent to p∨ q, as a truth table would confirm. Likewise, by using the principle of contraposition, which states that p → q is equivalent to ¬q → ¬p, we can transform the given implications accordingly.

Considering the sentence "If n is prime, then n is odd or n is 2" and denoting p as "n is prime", q as "n is odd", and r as "n is 2", the original statement can be represented as p → q ∨ r. Using logical equivalences established earlier, two different ways to rewrite this sentence could be:

The logical equivalences show that all these forms express the same condition from different perspectives but with the same meaning.

Answer:

As

30° + 330° = 360°

So, the figure has rotated one complete revolution as

Step-by-step explanation:

Considering the image of triangle XYZ for a composition of a

and a

As

30° + 330° = 360°

It means, the figure has rotated one complete revolution. And now the figure is very much back to starting position.

Keywords: image, triangle, rotation, revolution

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Answer: The first image is the triangle XYZ and the second is the composition of 30° and 330° (360°) as a rotation about point z

Answer:

random variable

Step-by-step explanation:

Random variable also known as stochastic variables are variables that are used in statistics and probability, The value of a random variable must be determined by chance which remain uncertain and depends on the outcome of a random process or experiment.

Unlike algebra, when random variable is introduced into a mathematical model, it is represented by capital letter and it has a single numerical value.

Answer: P(Upper E' prime) = 0.06

Step-by-step explanation:

Not happen:P(Upper E prime) = 0.94

Happen: P(Upper E' prime) = ?

P(Upper E' prime) + P(Upper E' prime) = 1

Therefore

P(Upper E' prime) + 0.94= 1

P(Upper E' prime) =1- 0.94

P(Upper E' prime) = 0.06

Answer: The function will be ODD.

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QuezoMartiinez

The function f(x) = -9x³ + 8x is odd.

Option A is the correct  answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

A function f(x) is even if f(-x) = f(x).

A function is odd if f(-x) = -f(x).

Using the above definition.

f(x) = -9x³ + 8x

Put x = -x

f(-x) = -9 x (-x³) + 8 x (-x)

f(-x) = 9x³ - 8x

f(-x) = - ( -9x³ + 8x)

f(-x) = -f(x)

This means,

The function is odd.

Thus,

f(x) is odd.

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Answer:

3, -2

Step-by-step explanation:

Answer:

Nguyen family uses sprinkler for 35 hours while the Hall family uses sprinkler for 15 hours

Step-by-step explanation:

Let h and n be the number of hours that the Hall and Nguyen family individually use their sprinkler for, respectively. Since they use for a combined total of 50 hours, h + n = 50, or h = 50 - n

Also their total water output is 1050 L, we can have the following equation

35h + 15n = 1050

Substitute h = 50 - n and we have

35(50 - n) + 15n = 1050

1750 - 35n + 15n = 1050

35n - 15n = 1750 - 1050

20n = 700

n = 35 hours

h = 50 - n = 50 - 35 = 15 hours

Answer:

When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do P(A) and P([math] \overline A [/math]) represent?

Step-by-step explanation:

The value of x in the expression will be 36.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is;

⇒ √x - 11 = 5

Now,

Solve the expression for x as;

⇒ √x - 11 = 5

Squaring on both side;

⇒ (√x - 11)² = 5²

⇒ x - 11 = 25

Add 11 both side;

⇒ x - 11 + 11 = 25 + 11

⇒ x = 36

Thus, The value of x in the expression will be 36.

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The correct answer is option D. 36.

We need to solve the equation:

√(x - 11) = 5

To solve this, follow these steps:

Square both sides to eliminate the square root.

√(x - 11)2 = 52

x - 11 = 25

Isolate x by adding 11 to both sides:

x - 11 + 11 = 25 + 11

x = 36

So, the correct answer is 36 (option D).

Answer:

Step-by-step explanation:

figure out the answer by  figuring out how much each bar is

Answer:

2b + 5b = b(2+5) = 7b

Step-by-step explanation:

Have a good day :)

Sam 2 granola bars

ADD

Haley 5 granola bars

Equal 7 granola bars

Answer:

17.B

19. C

20.C

Step-by-step explanation:

17.

[tex]\frac{m^2n^3}{p^3} \div \frac{mp}{n^2}\\=\frac{m^2n^3}{p^3} \times \frac{n^2}{mp}\\=\frac{mn^5}{p^4}[/tex]

19.

[tex]w^{2} +w-20=w^2+5w-4w-20=w(w+5)-4(w+5)=(w+5)(w-4)\\(w-3)(w-4)=w(w-4)-3(w-4)=w^2-4w-3w+12=w^2-7w+12\\reqd.~fraction ~is~ \frac{w^2-7w+12}{w^2+w-20}[/tex]

20.

[tex]\frac{w^2+5w+6}{w^2-w-12} =\frac{w^2+3w+2w+6}{w^2-4w+3w-12} =\frac{w(w+3)+2(w+3)}{w(w-4)+3(w-4)} =\frac{(w+3)(w+2)}{(w-4)(w+3)} =\frac{w+2}{w-4}[/tex]

Answer: Option 'e' is correct.

Step-by-step explanation:

Since we know that

Discrete data are those data which is countable and it is expressed in exact numerical form.

Continuous data are those data which is lie within the interval and it varies so it does not expressed in exact numerical form.

Here, the number of iphones sold today at an Apple store is countable and it can be expressed in exact numbers.

So, it is considered as discrete.

Hence, Option 'e' is correct.

Final answer:

The number of iPhones sold today at an Apple store represents an example of quantitative discrete data.

Explanation:

The number of iPhones sold today at an Apple store is an example of classified as discrete data. This is because the number of iPhones can only take on specific numerical values and cannot be a fraction or a decimal. In other words, you cannot sell half an iPhone, so the data is quantitative discrete.

Answer:

The answer to your question

a) Values excluded = -2, 0

b) solutions = -2/3, 2

Step-by-step explanation:

Equation

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

a) x is restricted when the denominators equal zero, so let's get them.

                 2x + 4 = 0                           2x =  0

                 2x = - 4                                  x = 0 / 2

                 x = -4 / 2                               x = 0

                 x = -2

x must be different to -2, 0

b)                   [tex]\frac{4x}{2x + 4} = \frac{x+ 2}{2x}[/tex]

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

                      4x² = (x + 2)²

                      4x² = x² + 4x + 4

                     4x² - x² - 4x - 4 = 0

                      3x² - 4x - 4 = 0

                      3x² - 6x + 2x - 4 = 0

                     3x(x - 2) + 2(x - 2) = 0

                     (x - 2)(3x + 2) = 0

                      x₁ - 2 = 0                  3x₂ + 2 = 0

                     x₁ = 2                         x₂ = -2/3

20 * (sqrt) 5 is the correct answer or “D”

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Answer:

d

Step-by-step explanation:

using Pythagorean theorem you would do a^2 + b^2 = c^2 so 20^2 + 40^2 = 2000 do the square root of 2000 and you get 20* square-root of 5