H⊃I
J⊃K
~K
H∨J
. Show that each of the following arguments is valid by
constructing a proof
I

The expression for the amount earned in one week per hour is 18 x $10

The expression for the amount earned in four weeks is 18 x $10 x 4

An expression is when numbers or letters are connected together by a mathematical operation without an equal to sign. An example of an expression is a + 3b.

The amount earned in one week = total number of hours worked in a week x amount earned per hour

18 x $10

The amount earned in four weeks = total number of hours worked in a week x amount earned per hour x 4

18 x $10 x 4

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The  length of the radius of a circle with a center at 2 – i and a point on the circle at 8 + 7i is: 10.

Using distance between points formula

Distance=√[(x2-x1)²+(y2-y1)²]

Let plug in the formula

Distance=√[(8-2)² +(7+1)²]

Distance=√6²+8²

Distance = √36+64

Distance=√100

Distance=10

Therefore the  length of the radius of a circle with a center at 2 – i and a point on the circle at 8 + 7i is: 10.

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Answer:

as shown in underline ^^

Step-by-step explanation:

Fill in the missing words:

When a solid mixes with a liquid and becomes part of the liquid it dissolves.

A solid that dissolves in a liquid is soluble.

A solid that does not dissolve in a liquid is insoluble.

2.426

Step-by-step explanation:

0 2. 4 2 6

6 1 4. 5 6 0

− 0

1 4

− 1 2

2 5

− 2 4

1 6

− 1 2

4 0

− 3 6

4

Answer as a fraction: \(\frac{75}{182}\)

Answer as a decimal: 2.42

Step-by-step explanation:

Hope it helps and have a great night! =D

~shining stars~

Answer:

Step-by-step explanation:

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Answer=4/5

The fraction of his original money does he have left = 4/5 .

What is a fraction in math?

A boy has = 800 and spends = 160

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Therefore, his original money left =4/5

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When you cube root a number, the answer is always smaller. This is true.

The cube root, denoted by, is the inverse of the cube of a number. For example, 216, or the cube root of 216, equals 6 because multiplying 6 three times yields 216. In other words, because 6³ = 216.

A number's cube root is a value that, when multiplied by itself three times, yields the original value. For example, the cube root of 27 is 3, denoted as 3³ because multiplying 3 by itself three times yields 3 x 3 x 3 = 27.

In this case, we have showed that the answer will be smaller than the original number.

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Answer:

A (3; 4)

B (5; 2)

C (4; 0)

D (-6; -2)

E (-2; -5)

I hope this helps!

Answer:

D) Factors of the polynomial

Step-by-step explanation:

Example: If the polynomial 10x² represents the area of the rectangle, then

2x and 5x will be the dimensions of the rectangle. Thus they will be factors of the polynomial.

So, dimensions of the rectangle represents the factors of the polynomial.

The number of waffles can be made from 15 eggs are, 20 waffles.

the waffles can be calculates as follows

4 cups of fluor + 6 eggs +2 tbsp oil = 8 waffles

we need 6 eggs to make 8 waffles

So, the waffles can we make from 15 eggs = \(\frac{8}{6} X 15 = 20\) waffles

Hence, the number of waffles can be made from 15 eggs are 20 waffles.

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The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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Answer:

Use the straightedge to draw GK−→−. Place the point of the compass on point H and draw an arc in the interior of the angle. Label the intersection of the arcs in the interior of the angle as point K. Place the point of the compass on point G and draw an arc that intersects the sides of ∠G.

Answer:

D

Step-by-step explanation:

Answer:

-4.5

Step-by-step explanation:

-12-3x=x+6

-4x=18

x=-4.5

Answer:

-4.5=x

Step-by-step explanation:

First you would distribute the -3 to the 4 and x inside the parentheses

It would be -3 x 4= -12

Then  -3 x X= -3x

So your equation would now be -12+ -3x = x + 6

Now you add  3x to the -3x to cancel it out and then add it to the x

So your equation now looks like -12=4x +6

Then you subtract 6 from the 6 to cancel it out and add it to the -12

Now your equation looks like -18=4x

Then you divide 4 from the 4x to cancel it out and then divide 4 from the -18

Finally you have  -4.5=x

I'm unsure if this is correct but hopefully this helps :)

The is a large sample necessary to conduct a hypothesis test about the mean age is definitely saying about the age of 80, for the person in histogram.

You want to do is visually investigate whether or not the facts factors comply with the directly line. If the factors music the directly line, your facts comply with the regular distribution. It's very straightforwardhistogram skewed to the proper way that the height of the graph lies to the left facet of the center.

On the proper facet of the graph, the frequencies of observations are decrease than the frequencies of observations to the left facet.

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Answer:

yes of course you can make a triangle

Answer:

No

Step-by-step explanation:

A triangle has ALL equal sides but since it's 3,8,8 you can't because not all side are equal

The net profit margin for this shirt is 55%.

What is net profit?

Net profit is the amount of money your business earns after deducting all operating, interest and tax expenses over a period of time. To arrive at this value, you need to know the company's gross profit. If the value of net profit is negative, it is called net loss.

Net profit is another important parameter that determines the financial health of your business. It shows whether the company can earn more than it spends. Net profit helps you decide when and how to expand your business and when to cut costs.

It is important for a business owner to know the difference between profit and profitability. Profit is an absolute number equal to revenues minus expenses. Profitability, on the other hand, is a relative number (percentage) that equals the ratio of profit to revenue.

Profitability is a measure of efficiency and is useful in determining the success or failure of a business.

Given,

Revenue = $12

Cost of goods sold = $3

Operating expenses = 20% of revenue = 20/100 x $12 = $2.4

We know,

Net Profit = Revenue - Cost of goods sold - Operating expenses

\(Net \: Profit = 12 - 3 - 2.4\)

Hence, Net Profit = $6.6

Again,

Net Profit Margin = (Net Profit / Revenue) x 100%

Net Profit Margin \(= ( \frac{6.6}{ 12}) \times 100\%\)

SO, Net Profit Margin = 55%

Therefore, the net profit margin for this shirt is 55%.

So, it is clear that choice A is correct.

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Answer:

6

Step-by-step explanation:

for this I simply divided that numbers and I got my answer as 5.77 and I turned as 6

Answer:

Step-by-step explanation:

For every 3 quetzals there are four axolotls and for every 8 axolotls there are 5 Mexican wolves, if there is a population of 150 quetzals, how many axolotls are there? And how many Mexican wolves are there?

Is the ratio 5:6 equivalent to 3:4

We can write the given expression as -

(x² + y²)(x² + y²- 2z²) + z² - 4x²y²

Factors of a number are numbers that divide evenly into another number. Factorization writes a number as the product of smaller numbers

Given is the expression -

{(x² + y²) - z²}² - 4x²y²

(x² + y²)² + z² - 2(x² + y²)z² - 4x²y²

(x² + y²) {(x² + y²) - 2z²} + z² - 4x²y²

(x² + y²)(x² + y²- 2z²) + z² - 4x²y²

Therefore, we can write the given expression as -

(x² + y²)(x² + y²- 2z²) + z² - 4x²y²

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Answer:

the first half of the play is 95 minutes long

Step-by-step explanation:

155-35= 120 (you subtract 35 so you get the number if both plays lasted the same time )

120/2= 60 (you get the amount of time one play lasted without extra 35 minutes)

60+35=95 (then add 35 minutes to one play because 1 one is longer than the other one)

the first half of the play is 95 minutes long.

If your commission for the month is $512.50 then total sales were $4659.1

Given,

Commission = 11%

Amount of commission = $512.50

Let,

total sales = x

Therefore,

11% of x = 512.50

11/100 x = 512.50

0.11x = 512.50

Divide both sides by 0.11

x = 4659.1

hence total sales = $4659.1

Therefore, we get the total sales as  $4659.1

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Answer: give me the context please

Step-by-step explanation:

  3/4÷ 2/3=   3/4*3/2= 9/8= mixed fraction 1  1/8 pounds.

Step-by-step explanation:

We have (n + 2)/5 = 14.

=> (n + 2) = 14 * 5 = 70 (multiply 5 on both sides)

=> n = 70 - 2 = 68. (subtract 2 on both sides)

Hence the number n is 68.

Using the given information, the values of the trigonometrical ratios are:

sin(θ) = 12/13

cos(θ) = 5/13

sec(θ) = 13/5

From the question, we are to determine the value of the given trigonometrical ratios

From the given information, we have that

tan(θ) = 12/5

From SOH CAH TOA,

We know that

sin(θ) = Opposite / Hypotenuse

cos(θ) = Adjacent / Hypotenuse

tan(θ) = Opposite / Adjacent

Thus,

We can create a right triangle such that the opposite side is 12 and the adjacent is 5

Using the Pythagorean's theorem, we can find the hypotenuse

|Hyp|² = |Opp|² + |Adj|²

|Hyp|² = 12² + 5²

|Hyp|² = 144 + 25

|Hyp|² = 169

|Hyp| = √169

|Hyp| = 13

Now,

Also from SOH CAH TOA

We can write that

sin(θ) = 12/13

cos(θ) = 5/13

But sec(θ) = 1/cos(θ)

Thus,

sec(θ) = 13/5

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Answer: -5/3

Step-by-step explanation:

Answer: m = -4/3

Step-by-step explanation:

If you're given two different coordinates, and you want to find the slope, the general rule is that you subtract the first coordinates from the first. The formula for these kinds of problems is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) .