The formula T=26x² +814x+15,118 models
the average cost of tuition and fees, T. at
private colleges for the school year ending x
years after 2000. The graph to the right shows
average cost of tuition and fees at private
four-year college.
Answer parts a through c
Tuition and Fees
30000
15000-
$22,090
$23,294
$24,550
$25,818
2007 2008 2009 2010
Ending Year in the School Year
a. Use the formula to find the average cost of tuition and fees at private colleges for the school year ending in 2010.
Using the formula, the tuition and fees for the school year ending in 2010 was S
(Simplify your answer. Do not include the S symbol in your answer.)

Answer:

The area of half of the garden in square meters.

Answer:

558.75

Step-by-step explanation:

Answer:

option 1. 2/3x-2

Hope this helps! :)

Answer:

2/3x-2

Step-by-step explanation:

If b = the number of boys, which alg expression represents the phrase. The sum of the number of boys and 15 girls is b+15.

Always solve equations for such questions using the information provided in the question. Then, as stated in the solution, we may locate the two unknown variables using the two equations that were created.

This kind of question can be answered by assuming any two numbers, x and y, and then applying the condition specified in the question. We know quite well that any equation that can be written in the form ax+by+c=0, where a, b, and c are real integers, and a and b are not zero, is known as a linear equation in two variables. When we apply the condition, we obtain two linear equations with two variables.

Given that the number of boys is b,

Number of girl = 15 girls

Thus the sum of noys and girls is b+15.

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Precision and confidence are statistical concepts that influence sample size in research studies. Precision refers to the level of variability or margin of error in the measurements or estimates obtained from a sample. Confidence, on the other hand, refers to the degree of certainty or reliability associated with the results obtained from the sample.

Precision refers to the level of accuracy or consistency in the measurements or estimates obtained from a sample. It reflects the degree of variability or margin of error in the data. A high precision indicates low variability and a small margin of error, while low precision indicates high variability and a larger margin of error. Confidence, on the other hand, relates to the level of certainty or reliability in the results obtained from the sample. It represents the degree to which the sample results can be generalized to the population.

In statistical analysis, increasing precision often requires a larger sample size. A larger sample reduces the margin of error and increases the accuracy of the estimates. However, increasing the sample size also requires more resources, time, and effort. Therefore, there is a trade-off between precision and sample size.

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To determine the probabilities, we need to consider the number of favorable outcomes for each situation divided by the total number of possible outcomes.

1.Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)

2. Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7%

3. Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)

4.Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)

1. Salmon chooses a composite number, a cool color (G, B, I, or V), and an A:

a) Composite numbers between 1 and 100: There are 57 composite numbers in this range.

b) Cool colors (G, B, I, or V): There are 4 cool colors.

c) The letter A: There is 1 A in "INDIANA."

Total favorable outcomes: 57 (composite numbers) * 4 (cool colors) * 1 (A) = 228

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 1 (possible letter) = 700

Probability: 228/700 = 0.3257 ≈ 32.57% ≈ 32.6% (rounded to one decimal place)

2. Federico chooses a prime number, a color starting with a vowel (E or I), and a consonant:

a) Prime numbers between 1 and 100: There are 25 prime numbers in this range.

b) Colors starting with a vowel (E or I): There are 2 colors starting with a vowel.

c) Consonants in "INDIANA": There are 4 consonants.

Total favorable outcomes: 25 (prime numbers) * 2 (vowel colors) * 4 (consonants) = 200

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 5 (possible letters) = 3500

Probability: 200/3500 = 0.0571 ≈ 5.71% ≈ 5.7% (rounded to one decimal place)

3. Either chooses a number divisible by 7 or 8, any color, and a vowel:

a) Numbers divisible by 7 or 8: There are 24 numbers divisible by 7 or 8 in the range of 1 to 100.

b) Any color: There are 7 possible colors.

c) Vowels in "INDIANA": There are 3 vowels.

Total favorable outcomes: 24 (divisible numbers) * 7 (possible colors) * 3 (vowels) = 504

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 3 (possible letters) = 2100

Probability: 504/2100 = 0.24 ≈ 24% (exact fraction)

4. Either chooses a number divisible by 5 or 4, blue or green, and L or N:

a) Numbers divisible by 5 or 4: There are 45 numbers divisible by 5 or 4 in the range of 1 to 100.

b) Blue or green colors: There are 2 possible colors (blue or green).

c) L or N in "INDIANA": There are 2 letters (L or N).

Total favorable outcomes: 45 (divisible numbers) * 2 (possible colors) * 2 (letters) = 180

Total possible outcomes: 100 (possible numbers) * 7 (possible colors) * 2 (possible letters) = 1400

Probability: 180/1400 = 0.1286 ≈ 12.86% ≈ 12.9% (rounded to one decimal place)

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The solution of the function is as follows:

(f + g)(3) = 9

(f.g)(-1) = -8

(f o g)(2)  = 8

(g o f)(0) = 2

(g o g)(3) = - 1

A function relates input and output. In other words, a function is an expression that defines a relationship between one variable (the independent variable) and another variable(dependent variable).

Therefore, let's solve the function as follows:

(f + g)(3) = f(3) + g(3) = 8 + 1 = 9

(f.g)(-1) = f(-1) × g(-1) = -2 × 4 = -8

(f o g)(2) = ƒ(g(2)) = f(3) = 8

(g o f)(0) = g(f(0)) = g(0) = 2

(g o g)(3) = g(g(3)) = g(1) = - 1

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Based on the information above, the car with 1,000 pounds more will only go 1,194 miles, and the one with 2,000 pounds more will only go 1,188 miles.

MPG stands for miles per gallon, and refers to the distance in miles a vehicle travels for each gallon of fuel in its tank.

In general, a car consumes about 1,200 miles per gallon. However, when you add load to it, its fuel consumption is higher because it requires more force to move.

Additionally, some studies state that for every 1,000 pounds of weight added to the car, it will yield 0.5% less. So if the car has 1,000 more pounds, it's not going to go 1,200 miles per gallon, it's going to go 1,194 miles.

On the other hand, if 2,000 pounds of weight were added, the fuel economy would be 1% less, that is, it would travel 1,188 miles per gallon.

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Answer:

9 times

Step-by-step explanation:

The value of the constant "a" in the inequality P(|Mn - μ| ≥ ε) ≤ aσ^2/n is 1.

The value of "n" can remain the same when changing ε from 0.1 to 0.1/k, as long as the desired upper bound remains unchanged.

To determine the value of the constant "a" in the inequality P(|Mn - μ| ≥ ε) ≤ aσ^2/n, we can use Chebyshev's inequality. Chebyshev's inequality states that for any random variable with mean μ and variance σ^2, the probability that the random variable deviates from its mean by at least k standard deviations is at most 1/k^2.

In our case, we have ε = 0.1 and we want to find the value of "a" for this specific value. Since ε is the desired accuracy, we are interested in the probability of the sample mean Mn deviating from the true mean μ by at least ε. Using Chebyshev's inequality, we have:

P(|Mn - μ| ≥ ε) ≤ 1/k^2

We can rewrite this inequality as:

P(|Mn - μ| ≥ 0.1) ≤ 1

Therefore, the value of "a" for ε = 0.1 is 1.

For the second part of the question, where ε = 0.1/k, we want to determine how to change the value of "n" so that the upper bound remains the same. Substituting ε = 0.1/k into the inequality, we have:

P(|Mn - μ| ≥ 0.1/k) ≤ 1

To keep the upper bound unchanged, we need to ensure that the right-hand side of the inequality remains 1. Since the right-hand side does not depend on "n", changing ε to 0.1/k does not require any adjustment in the value of "n".

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Answer:

c.

$475.67

Step-by-step explanation:

#4, #1, #3, #2

We will calculate the total amount for each of the credit card and then arrange them in descending order according to their interest after 36 months (3 years)

Interest on Credit card 1 =

                                       = $2233

Interest on credit card 2 =

                                       = $778

Interest on credit card 3 =

                                       = $1656

Interest on credit card 4 =

                                       = 2250

Hence the correct order to pay off all the credit card balances is

#4, #1, #3, #2

Her total monthly credit card payment will be $561.05.

Given that Michelle has four credit cards with the balances and interest rates listed below, if Michelle wanted to pay off all four credit cards in 36 months, to determine what would her total monthly credit card payment be, calculate the total amount of each card of credit including interest, add all the amounts, and then divide the result by 36:

Therefore, her total monthly credit card payment will be $561.05.

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Answer:

19.95 + .71 × x = 125.74

x = 141.053

x is the answer

The amount of juice the cup can hold given that the cup has diameter of 8 centimeters and a height of 12 centimeters is 602.88 cm³

To know the amount of juice the cup can hold, we shall obtain the volume of the cup.

We shall use the formula for obtaining volume of cylinder to obtain the volume of the cup. Details below:

Volume = πr²h

Volume = 3.14 × 4² × 12

Volume = 3.14 × 16 × 12

Volume = 602.88 cm³

Thus, we can conclude from the above calculation that the amount of juice the cup can hold is 602.88 cm³

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For the given geometric sequence we have:

a) R = 3/4

b) 243/256

c) Aₙ = 3*(3/4)⁽ⁿ⁻¹⁾

The common reason is given by the quotient between two consecutive terms, so using the first two, we will get:

R = (9/4)/3

R = 3/4

That is the common reason.

b) To find the fifth therm, we need to take the fourth one and multiply it by the common reason, so we will get:

81/64*(3/4) = 243/256

c) The n-th term of the sequence is the first term of the sequence multiplied by the common reason (n - 1) times, it gives:

Aₙ = 3*(3/4)⁽ⁿ⁻¹⁾

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Answer: 8 times

Step-by-step explanation:

Im right

The value of the variable I (i.e interest) is $9

From the question, we have the following parameters that can be used in our computation:

Principal, P =$400

Rate, R = 9%

Time, T = 0.25 years

The equation to calculate the interest is given as

I = PRT

Where

P, R and T are defined above

And I represents the interest

Substitute the known values in the above equation, so, we have the following representation

I = 400 * 9% * 0.25

Evaluate the products

I = 9

Hence, the interest is $9

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Answer:

Q1) x = 17    ||     Q2) x = 21

Step-by-step explanation:

Q1. \(\frac{x-2}{3} =5\)

\(x-2 = 5*3\)

\(x-2=15\)

\(x=15+2\)

\(x=17\)

Q2. \(\frac{x}{3} -2= 5\)

\(\frac{x}{3}=5+2\)

\(\frac{x}{3} =7\)

\(x=3*7\)

\(x=21\)

Answer:

x = 46°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:

⇒ 180° - 130° = 50°

The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:

⇒ 180° - 96° = 84°

The interior angles of a triangle sum to 180°. Therefore:

⇒ 50° + 84° + x = 180°

⇒ 134° + x = 180°

⇒ 134° + x - 134° = 180° - 134°

⇒ x = 46°

Therefore, the size of angle x is 46°.

Answer:

D

Step-by-step explanation:

the sum of the 3 angles in Δ DEF = 180° , that is

∠ D + 90° + 35° = 180°

∠ D + 125° = 180° ( subtract 125° from both sides )

∠ D = 55°

------------------------

using the tangent and cosine ratios in the right triangle

tan35° = \(\frac{opposite}{adjacent}\) = \(\frac{DE}{EF}\) = \(\frac{DE}{12}\) ( multiply both sides by 12 )

12 × tan35° = DE , then

DE ≈ 8.40 ( to 2 dec. places )

--------------------------

cos35° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{EF}{DF}\) = \(\frac{12}{DF}\) ( multiply both sides by DF )

DF × cos35° = 12 ( divide both sides by cos35° )

DF = \(\frac{12}{cos35}\) ≈ 14.65 ( to 2 dec. places )

The range is the possible y-values of a function.

Based on the graph, the possible values are from 0 to positivity infinity,

In interval notation, the range is (0, ∞).

We want to write in decimals the following fraction

To write this as a decimal number, first we need to convert the denominator to a power of 10. We can do that by multiplying both the numerator and denominator by 4.

Now, we just effectuate the division

0.76 is our answer.

According to the information given in the exercise, you know that the 100% is 80.

Let be "x" the number that is the 53% of 80.

By definition, you can write 53% as a Decimal number by dividing it by 100. Then, this is:

You can write 100% as a Decimal number:

Knowing the above, you can set up the following proportion:

Now you must solve for "x":

The answer is:

Answer: 46

Hope this helps

The result of dividing 1334 by 29 is 46 with no remainder.

The long division work for the division problem 29 ÷ 1334:

        46

  ___________

29 | 1334

 -    116

     _______

        174

        174

       ______

          0

Start by dividing the leftmost digit of the dividend (1) by the divisor (29). Since 1 is smaller than 29, you bring down the next digit (3) to the right of 1, making the new dividend 13.

Next, divide 13 by 29. The quotient is 0, so you bring down the next digit (4) to the right of 13, making the new dividend 134.

Now, divide 134 by 29. The quotient is 4 (29 × 4 = 116), so you write down 4 above the line.

Multiply 29 by 4 and subtract the result (116) from 134, giving you a new remainder of 18.

Finally, divide 18 by 29. The quotient is 0, so you bring down the next digit (4) to the right of 18, making the new dividend 184.

Since the dividend is smaller than the divisor, you can't divide further.

Therefore, the final quotient is 46, and the remainder is 0.

So, 1334 ÷ 29 = 45 with no remainder.

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Answer:

d. h(x) = 4x + 48

Step-by-step explanation:

\(f(x) = \frac{1}{4} x - 12\)

\(y = \frac{1}{4} x - 12\)

\(x = \frac{1}{4} y - 12\)

\( \frac{1}{4} y - 12 = x = 4( \frac{1}{4} y - 12) = 4x\)

\(4 \times \frac{1}{4} y - 4 \times 12 = 4x\)

\(y - 48 = 4x\)

\(y = 4x + 48\)

\(\boxed{\green{= h(x) = 4x + 48}}\)

Answer:

100: x

70 : 12.6

7x=1260

x=1260/70

x or original price= $18

Step-by-step explanation:

Answer:

Increase in percent = 4%

Step-by-step explanation:

Given:

Present population = 130,000

Future population = 135,200

Find:

Increase in percent

Computation:

Increase in population = Future population - Present population

Increase in population = 135,200 - 130,000

Increase in population = 5,200

Increase in percent = [Increase in population / Present population]100

Increase in percent = [5,200/130,000] 100

Increase in percent = 4%

Tri-County will have to charge approximately $83.1 per MWh to break even.

To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.

The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.

To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.

Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.

Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh

Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.

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Answer:where are the numbers

Step-by-step explanation:

Answer:

B     y=15x

Step-by-step explanation:

y=money she makes total

15=money per hour

x=hours

Answer:

C

Step-by-step explanation: