(80i) – (80 + 101) =
Express your answer in the form (a + bi).

Answer:

28.72

Step-by-step explanation:

The area for the 8 inch diameter cake is 50.27

1/4·π·8^2

but the area for the 10 inch diameter cake is 78.54

1/4·π·10^2 = 78.54

All you do to find the difference is

78.54 - 50.27 which is 28.72

Answer:

3x²

im lazy to solve right now

hope it helps

Answer:

Step-by-step explanation:

half of the circle is 180 degrees

so x + 3x = 180

4x = 180

x = 45

4/11

The probability of choosing a green marble followed by a brown marble is 4/11. Simple probability is the likelihood that an event occurs, and in this case the likelihood is 4/11. This is calculated by taking the total number of green marbles (4) divided by the total number of marbles in the jar (11).

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Answer:

16+13+12=41

Step-by-step explanation:

it is acute

Answer:

\(a_{n}\) = 6n - 4

Step-by-step explanation:

There is a common difference between consecutive terms in the sequence, that is

8 - 2 = 14 - 8 = 6

This indicates the sequence is arithmetic with n th term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = 6 , thus

\(a_{n}\) = 2 + 6(n - 1) = 2 + 6n - 6 = 6n - 4

Thus the formula representing the sequence is

\(a_{n}\) = 6n - 4

The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).


To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.

Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.

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The values of x and y are: 24° and 58° respectively.

We know that vertically opposite angles are equal, so:

(5x+20) = (6x-4)

5x-6x = -4-20

-x=-24

x=24

hence x=24°

also, angles on a straight line adds up to 180°, so:

5x+20+y-18=180°

using x=24

5(24)+20+y-18=180°

120+20+y-18=180

140+y-18=180

y+122=180

y=180-122

y=58°

Hence the values of x and y are 24° and 58° respectively.

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The expression 2 sin(4x) cos(9x) can be written as the difference of two functions using trigonometric identity as: sin(13x) - sin(5x).

To write the expression 2 sin(4x) cos(9x) as the sum or difference of two functions, we can use the trigonometric identity:

sin(A) cos(B) = (1/2)[sin(A + B) + sin(A - B)]

Applying this identity to the given expression:

2 sin(4x) cos(9x) = 2 * (1/2)[sin(4x + 9x) + sin(4x - 9x)]

Simplifying:

= sin(13x) + sin(-5x)

Note that sin(-θ) = -sin(θ), so we can rewrite sin(-5x) as -sin(5x):

= sin(13x) - sin(5x)

Therefore, the expression 2 sin(4x) cos(9x) can be written as the difference of two functions: sin(13x) - sin(5x).

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Answer:

C

This is the answer

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

Answer:  See the image below.

Formulas are already included that will calculate the totals for you.

Factorial notation is used to represent the product of a series of descending positive integers, and is denoted by an exclamation mark.

For example, 5! represents 5 x 4 x 3 x 2 x 1, which equals 120. If the study involves counting the number of ways a certain group of items can be arranged, factorial notation may be used to express the total number of possible arrangements. However, without knowing the specifics of Dr. Elder's study, it is impossible to provide the correct factorial notation. Therefore, I would recommend providing more details about the study in order to receive a more accurate answer.

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The most complete and accurate choice is (a).

To prove the inequality, we break down the integral into three parts: ∫[-∞, ∞] |F(x) - G(x)| dx = ∫[-∞, -1] |F(x) - G(x)| dx + ∫[-1, 1] |F(x) - G(x)| dx + ∫[1, ∞] |F(x) - G(x)| dx.

For the first part, ∫[-∞, -1] |F(x) - G(x)| dx, we can use the fact that |F(x) - G(x)| ≤ 1 for all x, so the integral is bounded by the length of the interval, which is 2.

For the second part, ∫[-1, 1] |F(x) - G(x)| dx, we use Chebyshev's inequality to bound it by ∫[-1, 1] (F(x) + G(x)) dx. Since F(x) and G(x) are cumulative distribution functions, they are non-decreasing and bounded by 1. Thus, the integral is bounded by 2.

For the third part, ∫[1, ∞] |F(x) - G(x)| dx, we can use the fact that |F(x) - G(x)| ≤ x^2(E(X^2) + E(Y^2)) for all x ≥ 1. Therefore, the integral is bounded by ∫[1, ∞] x^2(E(X^2) + E(Y^2)) dx, which is finite.

Adding the three parts together, we have ∫[-∞, ∞] |F(x) - G(x)| dx ≤ 2 + ∫[1, ∞] x^2(E(X^2) + E(Y^2)) dx. The right-hand side of the inequality is finite and can be further simplified as c∫[1, ∞] x^2 dx, where c ≤ 2(E(X^2) + E(Y^2)).

Therefore, the most complete and accurate choice is (a) because it correctly breaks down the integral into three parts and provides the correct bounds for each part, leading to the final result.

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The most complete and accurate choice is (a).

To prove the inequality, we break down the integral into three parts: ∫[-∞, ∞] |F(x) - G(x)| dx = ∫[-∞, -1] |F(x) - G(x)| dx + ∫[-1, 1] |F(x) - G(x)| dx + ∫[1, ∞] |F(x) - G(x)| dx.

For the first part, ∫[-∞, -1] |F(x) - G(x)| dx, we can use the fact that |F(x) - G(x)| ≤ 1 for all x, so the integral is bounded by the length of the interval, which is 2.

For the second part, ∫[-1, 1] |F(x) - G(x)| dx, we use Chebyshev's inequality to bound it by ∫[-1, 1] (F(x) + G(x)) dx. Since F(x) and G(x) are cumulative distribution functions, they are non-decreasing and bounded by 1. Thus, the integral is bounded by 2.

For the third part, ∫[1, ∞] |F(x) - G(x)| dx, we can use the fact that |F(x) - G(x)| ≤ x^2(E(X^2) + E(Y^2)) for all x ≥ 1. Therefore, the integral is bounded by ∫[1, ∞] x^2(E(X^2) + E(Y^2)) dx, which is finite.

Adding the three parts together, we have ∫[-∞, ∞] |F(x) - G(x)| dx ≤ 2 + ∫[1, ∞] x^2(E(X^2) + E(Y^2)) dx. The right-hand side of the inequality is finite and can be further simplified as c∫[1, ∞] x^2 dx, where c ≤ 2(E(X^2) + E(Y^2)).

Therefore, the most complete and accurate choice is (a) because it correctly breaks down the integral into three parts and provides the correct bounds for each part, leading to the final result.

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True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer: A range of values, created using sample, within which population parameter has a certain probability of occurring.

Reason: E.g. P(a<x>b) = 0.95

confidence interval is A range of values, is created using a sample, within a population parameter that has a certain probability of occurring.

A sampling method's degree of certainty or uncertainty is measured by confidence intervals. In statistics, the probability that a population parameter will fall between a set of values for a certain percentage of the time is referred to as a confidence interval. Confidence intervals that contain either 95% or 99% of expected observations are frequently utilized by analysts. To comprehend the statistical significance of their estimates, inferences, or predictions, statisticians and other analysts employ confidence intervals.

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Answer:

7.8

Step-by-step explanation:

because if you square 5 and 6 you get 25 and 36. Add them together and you get 61. Square 61 to get 7.8102... which you can round to 7.8

The equation to find the hypotenuse of a right triangle is a^2+b^2=c^2

Answer:

4+7x=32

7x=32-4

7x=28

x=4

Step-by-step explanation:

Answer:

This is how I calculated it.

If the total is $912

And the equipment costs $612.

I did $912- 612= $300 (There's only $300 remaining after purchasing the equipment)

Each uniform costs $25

So I did $300:25= 12

The School purchased 12 uniforms.

Have a nice day.

Answer:

I hope this image will help u....

have a marvelous day a head...

The equation which can be used to find the number of sides of a polygon when the sum of the interior angles is given is n = (s + 360) / 180

s = 180n – 360

s + 360 = 180n

(s + 360) / 180 = n

n = (s + 360) / 180

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Answer:

\(M=\frac{280}{140} =2\)

\(C=2+5=7\)

(2 Movies and 7 Commercials)

Step-by-step explanation:

Let's represent every time Carson's songs are played in a commercial as C and in movies as M.

Set up the following equations:

\(20C+120M=380\)  (1)

\(C=M+5\)   (2)

Substitute equation 2 for equation 1:

\(20(M+5)+120M=380\)

Distribute:

\(20M+100+120M=380\)

Simplify:

\(140M=280\)

Divide both sides by 140:

\(M=\frac{280}{140} =2\)

Substitute 2 as M back into either original equation, I will use (2):

\(C=2+5=7\)

Answer:

Step-by-step explanation:

Given:

The arrow diagram of a relation.

To find:

Whether the given relation is a function or not.

Solution:

A relation is a called a function it there exist a unique y-value or unique output value for each x-value or input value.

From the given arrow diagram it is clear that y=2 and y=-1 for x=-1.

Since we have more than one value of y at x=-1, therefore, the given relation is not a function.

Hence, the correct option is B.

probability that the audience member chooses the number the magician has in mind is 1/10

possible outcomes -

6,7,8,9,10,11,12,13,14,15

ten TOTAL possible numbers= denominator

chance of picking the ONE possible number in mind= numerator

1/10

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

Probability = the number of ways of achieving success / the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

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a) Anaiah currently spending $150 on these goods

b) His behavior is irrational because,

option (1) He is not spending his entire income, option (2) He is spending too much on kiwis and option (3) He is not balancing his spending on each good to achieve maximum total utility.

Based on the given information, Anaiah is currently spending $150 on these goods, which is calculated by adding the total cost of eggplants and kiwis as follows:

Cost of 20 eggplants = 20 x $3 = $60

Cost of 30 kiwis = 30 x $3 = $90

Total cost = $60 + $90 = $150

Anaiah is behaving irrationally because he is not spending his entire income of $180, which means he is not maximizing his utility. Additionally, he is spending too much on kiwis, as indicated by the higher marginal utility per dollar spent on the 30th kiwi compared to the 20th eggplant.

This suggests that he would derive more satisfaction from spending more on eggplants and less on kiwis. Lastly, his marginal utility per dollar spent is not the same for both goods, which implies that he is not balancing his spending on each good to achieve the maximum total utility. Therefore, Anaiah could improve his spending behavior by adjusting his purchases to reflect a better balance of marginal utility per dollar spent on each good.

Therefore, the correct options are  option (1) He is not spending his entire income, option (2) He is spending too much on kiwis and option (3) He is not balancing his spending on each good to achieve maximum total utility.

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If the data supports the research question, the results would have important implications for understanding and addressing the obesity epidemic.

If the data supports the research question of how child obesity is related to adult obesity, the results would indicate a positive correlation between the two. This means that as a child's body mass index (BMI) increases, so does the likelihood that they will develop obesity as an adult.

The results may also show that certain factors, such as genetics, lifestyle habits, and socioeconomic status, can impact the likelihood of a child developing obesity and how that translates into adult obesity.

For example, if the research finds that children who are overweight or obese are more likely to come from lower-income families, this would indicate that economic factors play a role in the development of obesity.

In addition to identifying risk factors for adult obesity, the results may also suggest possible interventions or prevention strategies for child obesity that could have long-term benefits for reducing adult obesity rates.

For example, if the research finds that physical activity and healthy eating habits are important for preventing child obesity, this could inform public health policies and educational programs aimed at promoting healthy behaviors in children.

Overall, if the data supports the research question, the results would have important implications for understanding and addressing the obesity epidemic.

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hope this helps

I really tried my best to give you a very direct answer

TRUE. As one performs multiple separate hypothesis tests, the risk of committing a Type I error (rejecting a true null hypothesis) accumulates.

This overall risk is referred to as the experiment-wise alpha level or family-wise error rate (FWER). It represents the probability of making at least one Type I error among all the conducted tests.

When multiple hypothesis tests are performed simultaneously or sequentially, the individual alpha levels (typically set at 0.05) for each test may no longer be appropriate. This is because if we conduct, for example, 20 separate tests with an alpha level of 0.05 for each test, the cumulative chance of committing at least one Type I error can be much higher than the desired 5%.

To control the experiment-wise error rate, various multiple comparison procedures and adjustments can be employed, such as the Bonferroni correction or the Holm-Bonferroni method. These methods aim to maintain a desired level of significance for the entire set of tests, reducing the risk of accumulating Type I errors.

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Answer:

3 square centimeter = .0003 square meters

Answer:

x is less than or equal to 0

Step-by-step explanation:

- you need to multiply both sides of the inequality by 5/2

- then you reduce the numbers with the greatest common factor 5

- then you reduce the numbers with the greatest common factor 2

- any expression multiplied by 0 equals 0

- so you get x is less than or equal to 0

^^^ hope this helps! :)

Some acceptable board lengths are: 15.8 ft, 16.20 ft and 16.10 feet

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

Length = 16 ft

Percent error = 1.5%

This means that the acceptable lengths are

Acceptable = Length ± Percent error * Length

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

Acceptable = 16 ± 1.5% * 16

So, we have

Acceptable = 16 ± 0.24

Evaluate

Acceptable = 15.76 to 16.24

Some board lengths that should be accepted are 15.8 ft, 16.20 ft and 16.10 feet

In (a), we have

Acceptable = 15.76 to 16.24

Some board lengths that should be rejected are 14.8 ft, 17.20 ft and 12.10 feet

Here, we have

Lengths = 10, 12 and 14 feet

Length too long = 2.3 inches

Convert to inches

Length too long = 0.19

So, we have

Intended lengths = (10, 12 and 14 feet) + 0.19

Evaluate

Intended lengths = 10.19, 12.19 and 14.19 feet

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