The length of a rectangle is 3 inches greater than the width.
A. Write a polynomial that represents the area of the rectangle.
B. Find the area of the rectangle when the width is 4 inches.

The Correct Option is C that 71 x 10-² of the following gives the value of the expression below written in scientific notation.

The basic objective of scientific notation is to make computations with unusually big or small numbers simpler. The following examples demonstrate how all of the digits in a number in scientific notation are relevant because zeros are no longer utilised to set the decimal point.

The statement for a number n in scientific notation is of the type a10b, where an is an integer such that 1|a|10. B is also an integer. Multiplication: To get the full amount in scientific notation, multiply the decimal values. Add the 10 power exponents after that.

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Answer:

Bond

Step-by-step explanation:

A promissory note or a promise to repay a certain amount of money at some point in the future is basically a bond.

A bond is a debt security that represents a loan made by an investor to a borrower, which is usually a corporation or government agency. It is a fixed-income investment, meaning that the borrower promises to pay a specific amount of interest over a set period of time and return the principal amount of the loan on the date of maturity. Bonds are issued for various purposes, such as raising capital, funding new projects, or refinancing debt.

CD (Certificate of Deposit) is a savings instrument issued by a bank or credit union that generally pays a fixed rate of interest over a set term. Mutual fund is an investment vehicle that pools money from multiple investors to purchase a portfolio of securities, such as stocks, bonds, or both. Stock is an ownership share in a company that represents a claim on part of the company's assets and earnings.

The correct statements regarding the given derivative of function f are explained. The correct option is (e) I, II, and III.

The derivative of function f is defined by `f'(x) = 2(x - 1)(x - 3)`

The derivative of f is given by:f'(x) = 2(x - 1)(x - 3)

The derivative of f is a quadratic function with zeros at x = 1 and x = 3.

Therefore, the derivative of f is positive on the intervals (-∞, 1) and (3, ∞) and negative on the interval (1, 3).

We can use this information to determine properties of the function f.

I. f is decreasing for all x < 4: Since the derivative is positive on the interval (-∞, 1) and negative on the interval (1, 3), it follows that f is decreasing on (-∞, 1) and (1, 3).

Therefore, I is true.II. f has a local maximum at x = 1:

Since the derivative changes sign from positive to negative at x = 1, we know that f has a local maximum at x = 1.

Therefore, II is true.III. f is concave up for all 1 < x < 3:Since the derivative of f is positive on (1, 3), it follows that the function f is concave up on (1, 3).

Therefore, III is true.The statements I, II, and III are all true about the function f if its derivative is defined by f'(x) = 2(x - 1)(x - 3). Therefore, the correct option is (e) I, II, and III.

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Answer: yes  9/30 is a  terminating decimal.

The given probability of having six girls in a six-child family is 0.015625. To determine the method used to compute this probability, we need to analyze the information provided.

The Classical method is based on theoretical assumptions and probabilities calculated using mathematical principles. It assumes equally likely outcomes and relies on counting favorable outcomes over the total number of possible outcomes.

The Empirical method involves gathering data from observations or experiments to estimate probabilities. It relies on observed frequencies and relative frequencies to compute probabilities. However, the given probability does not suggest a sample or data collection, making it unlikely that the Empirical method was used.

The Subjective method involves assigning probabilities based on personal judgment or opinions. Individuals subjectively evaluate the likelihood of an event based on their own beliefs or knowledge.

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To solve a first order linear equation, we can use an integrating factor to make the left side of the equation into the product of the integrating factor and the dependent variable. The integrating factor is given by μ(x)=exp(∫p(x)dx).

Given the equation xy′+(1+4x)y=10x^2−4x, we can find the integrating factor by first identifying p(x) and then finding the integral of p(x). In this case, p(x)=-(1+4x)/x. So, the integrating factor is:

μ(x)=exp(∫-(1+4x)/xdx)=exp(-∫(1/x)dx-∫(4)dx)=exp(-ln|x|-4x)=x^(-1)e^(-4x)

Now we can multiply both sides of the equation by the integrating factor to get:

x^(-1)e^(-4x)(xy′+(1+4x)y)=10x^2e^(-4x)−4xe^(-4x)

This simplifies to:

(ye^(-4x))′=10x^2e^(-4x)−4xe^(-4x)

Now we can integrate both sides of the equation to find the general solution:

ye^(-4x)=∫(10x^2e^(-4x)−4xe^(-4x))dx+C

Using integration by parts and the arbitrary constant C, we can find the general solution:

y(x)=e^(4x)(-5/8x^2e^(-4x)-1/4xe^(-4x)+1/16e^(-4x)+C)

To solve the initial value problem with y(1)=3−4, we can plug in the initial values and solve for the arbitrary constant C:

3−4=e^(4)(-5/8e^(-4)-1/4e^(-4)+1/16e^(-4)+C)

-1=(-5/8-1/4+1/16)+Ce^(4)

C=(-1+5/8+1/4-1/16)e^(-4)=(-1/8)e^(-4)

So the solution to the initial value problem is:

y(x)=e^(4x)(-5/8x^2e^(-4x)-1/4xe^(-4x)+1/16e^(-4x)+(-1/8)e^(-4))

Using the properties of exponents, we can simplify the solution to get:

y(x)=-5/8x^2-1/4x+1/16+(-1/8)e^(4x-4)

This is the solution to the initial value problem.

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The production cost of company 1 is higher than company 2, and when producing the same number of units, company 2 has a lower production cost than company 1. This indicates that when producing the same number of units, company 2 has a lower production cost than company 1.

The given function represents the production cost f(x), in dollars, for x number of units produced by company 1:f(x) = 0.25x² − 8x + 600

The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:x     g(x)6     862.28     856.810   85512   856.814   862.2

To determine whether the production cost of company 1 is less than the production cost of company 2 when producing the same number of units, we must find the production cost of both companies for each given value of x and then compare them. Using the formula above, the production cost of company 1 for each given value of x is:

f(6) = 0.25(6)² − 8(6) + 600= 81 dollars

f(8) = 0.25(8)² − 8(8) + 600= 88 dollars

f(10) = 0.25(10)² − 8(10) + 600= 95 dollars

f(12) = 0.25(12)² − 8(12) + 600= 100 dollars

f(14) = 0.25(14)² − 8(14) + 600= 103 dollars

The production costs of company 2, which are given in the table, are:g(6) = 862.2 dollars

g(8) = 856.8 dollars

g(10) = 855 dollars

g(12) = 856.8 dollars

g(14) = 862.2 dollars

We can see that for each value of x, the production cost of company 1 is higher than the production cost of company 2. Therefore, when producing the same number of units, the production cost of company 2 is less than the production cost of company 1.

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Answer:

21 ft

Step-by-step explanation:

Tan(32) = x/34

34tan(32)=x

x= 21.245...

x=21

Answer:

Its 22

Step-by-step explanation:

x is 19

so 3+19 is 22

There are 2 students who used none of the above-mentioned means of transportation.

There were 2 students who used none of the above-mentioned means of transportation.

A poll was conducted on 100 students at a commuter campus to determine how they got to school.

The following are the results: 36 people drove alone.

34 people carpooled.30 people used public transportation.

5 people used both carpools and public transportation.8 people used both a carpool and their own car.

7 people used buses and their own cars.

4 people used all three modes of transportation.

Now, let us calculate the number of students who didn't use any of the above means of transportation:

Number of students who drove alone = 36

Number of students who carpooled = 34

Number of students who used public transport = 30

Number of students who used carpool and public transport = 5

Number of students who used carpool and their own car = 8

Number of students who used buses and their own car = 7

Number of students who used all three modes of transportation = 4

Thus, the total number of students who used one or more means of transportation =36+34+30+5+8+7+4 = 124

Now, subtracting the number of students who used one or more means of transportation from the total number of students polled will give us the number of students who used none of the means of transportation.

100 - 124 = -24

But, negative values are meaningless in this context.

Hence, the answer is 2.

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The probability that the 3-card hand contains only face cards is 1/100 or 0.01.

To find the probability that the 3-card hand contains only face cards, we'll follow these steps:
1. Determine the total number of ways to draw 3 cards from a deck of 52 cards.
2. Determine the total number of ways to draw 3 face cards from the deck.
3. Divide the number of ways to draw 3 face cards by the total number of ways to draw 3 cards.
Calculate the total number of ways to draw 3 cards from a deck of 52 cards.
This can be found using the combination formula,

which is C(n, k) = n! / (k!(n-k)!),

where n is the total number of cards and k is the number of cards drawn.

In this case, n=52 and k=3.
C(52, 3) = 52! / (3!(52-3)!)

= 22100
Calculate the total number of ways to draw 3 face cards from the deck.
There are 12 face cards in the deck (4 suits with 3 face cards each: Jack, Queen, and King).

We need to find the number of ways to choose 3 face cards from these 12.
C(12, 3) = 12! / (3!(12-3)!) = 220
Divide the number of ways to draw 3 face cards by the total number of ways to draw 3 cards.
Probability = (Number of ways to draw 3 face cards) / (Total number of ways to draw 3 cards)

= 220 / 22100

= 1/100
The probability that the 3-card hand contains only face cards is 1/100 or 0.01.

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Answer:

I think its -y

Step-by-step explanation:

Answer:

x is my answer

Step-by-step explanation:

i don't know sorry

Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

Answer:

answred by G a u t h m a t h

If it helped you pls mark it as brainliest & thank the answer!

Answer:

32 Students

Step-by-step explanation:

3/5 = 12/20

This means you add the boys and girls to get 32.

The probability that the proportion of overweight or obese children in the sample will be greater than 0.57 is less than 50%.

The first paragraph summarizes the answer, stating that the probability is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

In the second paragraph, we can explain the reasoning behind this conclusion. The Central Limit Theorem states that for a large sample size, the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. In this case, the sample was taken in a way that meets the conditions for using the Central Limit Theorem.

Since the population proportion of overweight or obese children is 0.60, any sample proportion below this value is more likely to occur. Therefore, the probability of obtaining a sample proportion greater than 0.57 would be less than 50%. This is because the resulting z-score, which measures how many standard deviations the sample proportion is away from the population proportion, would be negative.

To summarize, the probability of the proportion of overweight or obese children in the sample being greater than 0.57 is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

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a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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Answer:

what are you asking???

Step-by-step explanation:

Answer:

x \(\leq\) -6

Step-by-step explanation:

3x - 2 \(\leq\) -20

Solve for x:

3x \(\leq\) -18

x \(\leq\) -6

After solving the given expression we get  a = b = 12 and q = r = 24.

A fractiοn is a numerical quantity that represents a part οf a whοle οr a ratiο between twο quantities. It is written as a tοp number (numeratοr) οver a bοttοm number (denοminatοr), separated by a hοrizοntal line.

Tο subtract 2/3 - 1/4, we need tο find a cοmmοn denοminatοr fοr the twο fractiοns. The smallest cοmmοn denοminatοr is 12, sο we'll cοnvert each fractiοn tο an equivalent fractiοn with a denοminatοr οf 12:

2/3 = 8/12 (multiply bοth numeratοr and denοminatοr by 4)

1/4 = 3/12 (multiply bοth numeratοr and denοminatοr by 3)

Nοw we can subtract the twο fractiοns:

8/12 - 3/12 = 5/12

Sο 2/3 - 1/4 = 5/12.

Tο express the result as a fractiοn in the fοrm x/y, we can simply use the answer we fοund: x = 5, y = 12, sο:

2/3 - 1/4 = 5/12 = 5/12

Similarly, tο express the result as a fractiοn in the fοrm a/b, we need tο find anοther equivalent fractiοn with a cοmmοn denοminatοr. We can use 24 as a cοmmοn denοminatοr this time:

2/3 = 16/24 (multiply bοth numeratοr and denοminatοr by 8)

1/4 = 6/24 (multiply bοth numeratοr and denοminatοr by 6)

Nοw we can subtract the twο fractiοns:

16/24 - 6/24 = 10/24

Sο 2/3 - 1/4 = 10/24.

Tο express the result as a fractiοn in the fοrm a/b, we can simplify the fractiοn by dividing bοth numeratοr and denοminatοr by their greatest cοmmοn factοr, which is 2:

10/24 = (10 ÷ 2) / (24 ÷ 2) = 5/12

Sο we get a=b=12 and q=r=24.

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Answer: 4

Step-by-step explanation:

so you basically make the + sign into a - sign as when there is a + and - sign next to each other it will always change into a - sign so once you do that it will look like this

11+(-7)

11-7

4

The exact value of the trigonometric expression \(tan(\theta/2)\) is \(-\sqrt{2/5}.\)

Trigonometric Identities:

Trigonometric identities are mathematical equations that relate the angles and ratios of trigonometric functions. They are used to simplify expressions, prove equalities, and solve trigonometric equations. Here are some common trigonometric identities:

To find the exact value of \(tan(\theta/2)\), we can use the half-angle identity for a tangent:

\(tan(\theta/2) = \pm \sqrt{(1 - cos\theta) / (1 + cos\theta)}\)

Given that \(cos\theta\) = 3/5, we can substitute this value into the formula:

\(tan(\pm/2) = \pm \sqrt{(1 - 3/5) / (1 + 3/5)}\)

\(= \pm \sqrt{2/5}\)   (simplifying the expression)

Since \(\theta\) is in the fourth quadrant (\(270^\circ < \theta < 360^\circ\)), the value of  \(tan(\theta/2)\) will be negative. Therefore, we can write:

\(tan(\theta/2) = -\sqrt{2/5}\)

So, the exact value of \(tan(\theta/2)\) is \(-\sqrt{2/5}.\)

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The residual if you know the actual number is 3 and the predicted value is 1.6l is 1.4.

The residual is a measure of the difference between the predicted value and the actual value. In this case, the actual number is 3, and the predicted value is 1.6. To find the residual, we subtract the predicted value from the actual value:

Residual = Actual Value - Predicted Value

= 3 - 1.6

= 1.4

Therefore, the residual in this case is 1.4.

The residual represents the error or the amount by which the predicted value differs from the actual value.

A positive residual indicates that the predicted value is lower than the actual value, while a negative residual indicates that the predicted value is higher than the actual value.

In this case, the positive residual of 1.4 indicates that the predicted value of 1.6 underestimates the actual value of 3 by 1.4.

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Answer: The value is always positive with absolute value, so that is incorrect. Just take away all negative symbols and compare the numbers.

The total number of people is given as follows:

5 + 16 + 27 + 19 + 18 + 3 = 88.

Out of these people, 3 are females with green eyes, hence the percentage is given as follows:

p = 3/88 x 100%

p = 3.4%.

Out of these 88 people, 16 + 27 = 43 are males without green eyes, hence the percentage is given as follows:

p = 43/88 x 100%

p = 48.9%.

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If w1, w2, w3 is a linearly independent set, then w2 - w3, w1 - w3, w1 - w2 is a linearly dependent set.

We can prove this statement by showing that there exist constants c1, c2, and c3, not all zero, such that c1(w2 - w3) + c2(w1 - w3) + c3(w1 - w2) = 0.

Expanding the left-hand side, we get c1w2 - c1w3 + c2w1 - c2w3 + c3w1 - c3w2 = 0.

Rearranging the terms, we get (c2 + c3)w1 + (-c1 - c3)w2 + (c1 + c2)w3 = 0.

Since w1, w2, w3 is a linearly independent set, the coefficients of w1, w2, and w3 in the above equation must all be zero. Thus, we have the system of equations:

c2 + c3 = 0

-c1 - c3 = 0

c1 + c2 = 0

Solving this system of equations, we obtain c1 = -c2 and c3 = -c2. Thus, the only non-zero coefficient is c2, and we have c1(w2 - w3) + c2(w1 - w3) + c3(w1 - w2) = -c2(w2 - w3) + c2(w1 - w3) + (-c2)(w1 - w2) = c2(w1 - w2 - w2 + w3 - w1 + w3) = 0.

Therefore, the set {w2 - w3, w1 - w3, w1 - w2} is linearly dependent.

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Answer:

13 inches

Step-by-step explanation:

A clarinet case is shaped like a rectangular prism the case is 8 inches tall 3 inches wide and has a volume of 312 cubic inches what is the length of the clarinet case

The volume of a rectangular prism = Length × Width × Height

Length of the rectangular prism = Volume/ Width × Height

= 312 in³/ 3 in × 8 in

= 312 in³/24 in²

= 13 in

Length = 13 inches