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The equation 8n + 2 - 6n = 9 + 2n - 13 has only one solution, n = -3.

To solve the equation 8n + 2 - 6n = 9 + 2n - 13, we need to simplify both sides and combine like terms.
 Starting with the left side of the equation, 8n - 6n can be simplified to 2n. And on the right side, 9 - 13 is -4.  
So, we have 2n + 2 = -4. We can now subtract 2 from both sides to isolate the variable n. This gives us 2n = -6. To solve for n, divide both sides of the equation by 2: n = -3.

Therefore, the equation 8n + 2 - 6n = 9 + 2n - 13 has only one solution, n = -3.

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Answer: Three

Step-by-step explanation:

Given: )Megan is picking out an outfit to wear.

The given list of outfits :-

Red shirt – Black pants

Red shirt – White pants

Red shirt – Blue pants

Pink shirt – Black pants

Pink shirt – White pants

Pink shirt – Blue pants

The name of colors of pants :- Black , White ,  Blue

⇒ The number of different-color pants =3

Therefore, there are three different color pants from which Meghan has to choose .

Answer: 72

Step-by-step explanation: i did it a got it right

We need to find which of the given statements are true.

The system of linear equations has no solutions.

First let us find what type of solution does the system have

The equations are

[tex]5x+2y=-4[/tex]

[tex]5x+2y=1[/tex]

So,

[tex]\dfrac{a_1}{a_2}=\dfrac{5}{5}=1[/tex]

[tex]\dfrac{b_1}{b_2}=\dfrac{2}{2}=1[/tex]

[tex]\dfrac{c_1}{c_2}=\dfrac{-4}{1}=-4[/tex]

So,

[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]

This means the two lines do not intersect and are parallel.

Hence, the system of linear equations has no solutions.

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To solve the coin problem, two equations are set up, one for the total number of coins and another for the total value in dollars. By using the elimination method, we find that Kevin has 8 dimes and 15 quarters in his piggy bank.

To solve this problem, we assign variables to represent the number of each coin type: let 'd' be the number of dimes, and 'q' be the number of quarters.

Now, we can set up our two equations. The first equation represents the total number of coins:

d + q = 23.

The second equation derives from the total value of the coins:

0.10d + 0.25q = 4.55.

Multiplying the second equation by 100 to clear the decimals gives us;

10d + 25q = 455.

To solve the system, we can use either substitution or elimination. Here, we will use elimination.

If we multiply the first equation by 10 (giving 10d + 10q = 230), we can subtract it from the modified second equation to eliminate 'd':

(10d + 25q) - (10d + 10q) = 455 - 230, simplifying to 15q = 225.

Dividing both sides by 15 gives us q = 15, which indicates Kevin has 15 quarters.

Substituting 'q = 15' into the first equation gives us d + 15 = 23, which simplifies to d = 8.

Therefore, Kevin has 8 dimes and 15 quarters.

To find y, first find the measure of the third interior angle. We'll call it x.

The triangle angle sum theorem allows us to create an equation to find x. Set the interior angle values equal to 180 and solve.

180 = 28 + 30 + x

Add the constants.

180 = 58 + x

Subtract 58 from both sides.

122 = x

Now, ∠x (which we now know measures 122°) is supplementary to ∠y. Set them equal to 180 and solve for y.

180 = 122 + y

Subtract 122 from both sides.

58 = y

m∠y = 58°

Answer:

This was the correct answer, I even provided proof from my own test. Hope this helps!

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation P[ 1 + 0.208/12 ]¹² + $60 =  P[ 1 + 0.246/12 ]¹² will be used to solve the given problem so option (D) will be correct.

Compound interest is applicable when there will be a change in principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

For credit card A →

APR = 20.8%

Annual fee = $60

The total amount after 1 year will be = compound interest + annual fee

So,

P[ 1 + 0.208/12 ]¹² + $60

For credit card B →

APR = 24.6%

No annual fee

The total amount after 1 year will be = compound interest

So,

P[ 1 + 0.246/12 ]¹²

Given that all are equal

So,

P[ 1 + 0.208/12 ]¹² + $60 =  P[ 1 + 0.246/12 ]¹²

Hence "The equation P[ 1 + 0.208/12 ]¹² + $60 =  P[ 1 + 0.246/12 ]¹² will be used to solve the given problem".

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The distance from checkpoint B to the starting line for the given right-angle triangle will be 16 yards.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

As per the given right angle triangle,

Suppose the missing length is x.

By Pythagoras' theorem,

x = √(20² - 12²)

x = √(400 - 144) = √256 = 16

Hence "The distance from checkpoint B to the starting line for the given right-angle triangle will be 16 yards".

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Answer:

Batch 1:  Pineapple = 3 1/2; Banana = 1 2/5

Batch 2:  Pineapple = 8; Coconut = 4 4/5

Batch 3:  Banana = 1; Coconut = 1 1/2

Step-by-step explanation:

For Batch 1:

We know that coconut is 3/10 of the mixture, and we have 2 1/10 coconut:

3/10x = 2 1/10

Converting 2 1/10 to an improper fraction, we have

3/10x = 21/10

Divide both sides by 3/10:

3/10x ÷ 3/10 = 21/10 ÷ 3/10

To divide fractions, flip the second one and multiply:

x = 21/10 × 10/3 = 210/30 = 7

This means we have 7 total of the mixture.

1/2 of this is pineapple:  1/2(7) = 7/2 = 3 1/2

1/5 is banana:  1/5(7) = 7/5 = 1 2/5

For Batch 2:

1/5 of the total is banana; we have 3 1/5 banana:

1/5x = 3 1/5

Convert the second fraction to an improper fraction:

1/5x = 16/5

Divide both sides by 1/5:

1/5x÷1/5 = 16/5÷1/5

Flip the second fraction and multiply:

x = 16/5×5/1 = 80/5 = 16

We have 16 of the total shampoo.

Pineapple is 1/2 of this:

1/2(16) = 8

Coconut is 3/10 of the total:

3/10(16) = 48/10 = 4 8/10 = 4 4/5

For Batch 3:

Pineapple is 1/2 of the total.  We have 2 1/2 pineapple:

1/2x = 2 1/2

Convert the fraction on the right to improper:

1/2x = 5/2

Divide both sides by 1/2:

1/2x÷1/2 = 5/2÷1/2

Flip the second fraction and multiply:

x = 5/2×2/1 = 10/2 = 5

We have 5 total shampoo.

Banana is 1/5 of this:

1/5(5) = 1

Coconut is 3/10 of this:

3/10(5) = 15/10 = 1 5/10 = 1 1/2

Mr. Vitorello spends $10,500 on rent annually, which is calculated by multiplying the monthly rent expense ($875, which is 35% of his monthly salary) by 12.

Mr. Vitorello spends 35% of his monthly salary on rent, which is $2,500 each month. To calculate how much he spends on rent each year, we first need to determine the monthly rent expense.

Monthly rent expense = 35% of monthly salary

= 0.35  imes $2,500

= $875

Now that we have the monthly rent expense, we can calculate the annual rent expense by multiplying the monthly amount by the number of months in a year.

Annual rent expense = Monthly rent expense  imes 12

= $875  imes 12

= $10,500

Therefore, Mr. Vitorello spends $10,500 on rent each year.

Probability is the likelihood, or chance, that a certain event will occur. The easiest way to understand probability is with coin tosses. Probability can also be applied in various fields such as medicine and stock market.

Probability is the likelihood, or chance, that a certain event will occur. The easiest way to understand probability is with coin tosses.

When you toss a coin, the chance of a head turning up is 50 percent. This is because a coin has only two sides, so there is an equal chance of a head or tail turning up on any given toss.

Probability can also be applied in various fields. For example, doctors use probability to determine the chance of a vaccination causing the disease the vaccination is supposed to prevent.

Stockbrokers use probability to determine the rate of return on a client's investments. In statistics, we study populations and use a sample to gain information about the larger population. Data are the result of sampling from a population.