What is the value of x in the right triangle below, rounded to the near-
est hundredth?

The general solution to the given differential equation is y(t) = C * e^(3t).

To find the general solution to the inhomogeneous first-order linear differential equation y'(t) - 3y(t) = 0, follow these steps:

Step 1: Identify the homogeneous equation, which is y'(t) - 3y(t) = 0.

Step 2: Solve the homogeneous equation by finding the general solution. In this case, it is y_h(t) = C * e^(3t), where C is a constant.

Step 3: Identify the inhomogeneous part of the equation, which is missing in this case. Since the given equation is already homogeneous, there is no need to find a particular solution.

Step 4: Combine the homogeneous solution and the particular solution (if present) to form the general solution. In this case, the general solution is y(t) = y_h(t) = C * e^(3t).

So, the general solution to the given differential equation is y(t) = C * e^(3t).

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Answer:

What is the probability of rolling an odd product? 1/4

What is the probability of rolling a product that is greater than or equal to 20? 2/9

What is the probability of rolling a product that is less than 10? 17/36

What is the probability of rolling a product that is a multiple of 10? 1/6

The amount of simple interest owed for the loan is $30,010.00.

A method for determining the proportion of interest paid on a sum over a predetermined period of time at a predetermined rate is called simple interest. In simple interest, the principal amount remains unchanged. A straightforward and simple method for calculating money interest is simple interest.

To calculate the simple interest, we use the formula:

Simple Interest = P * r * t

where P is the principal amount, r is the interest rate as a decimal, and t is the time period in years.

Substituting the given values, we get:

Simple Interest = $15,400 * 0.15 * 13

= $30,010.00

Therefore, the amount of simple interest owed for the use of the loan is $30,010.00.

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The winner of the election got 26320 votes.

Let's first find the total number of votes cast in the election. We know that 2/3 fraction of the electors voted for the first candidate and 1/4 of the electors voted for the second candidate. Therefore, the remaining 1/12 of the electors voted for the third candidate. So, we have:

2/3 + 1/4 + 1/12 = 8/12 + 3/12 + 1/12 = 12/12 = 1

This means that all the electors voted, and the total number of votes cast is equal to the total number of electors.

Now, let's find the number of votes the third candidate got, which is 1/12 of the total number of votes. We know that this is equal to 3290. So, we have

1/12 x Total Number of Votes = 3290

Multiplying both sides by 12, we get:

Total Number of Votes = 3290 x 12 = 39480

Now, we can find the number of votes the first candidate got, which is 2/3 of the total number of votes. We have:

2/3 x Total Number of Votes = 2/3 x 39480 = 26320 votes

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The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.

In this situation, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success, p, is the probability that a single lightbulb is not defective, and the probability of failure, q, is the probability that a single lightbulb is defective. The probability of selecting 5 lightbulbs with no defective bulbs is then given by the equation:

P(x=0) = (p^5)*(q^0) = p^5

In this case, p is the probability of not having a defective bulb, and q is the probability of having a defective bulb. The probability of selecting 5 lightbulbs without any defective bulbs is then given by p^5.

For example, if the probability of not having a defective bulb is 0.95 and the probability of having a defective bulb is 0.05, then the probability of selecting a sample of 5 lightbulbs without any defective bulbs is 0.95^5 = 0.7737. This means that there is a 77.37% chance of selecting a sample of 5 lightbulbs without any defective bulbs.

To sum up, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success is the probability of not having a defective bulb, and the probability of failure is the probability of having a defective bulb. The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.

The correct question is:

A box contains 100 bulbs, out of which 10 are defective. If a sample of 5 lightbulbs is selected, find the probability that none in the sample are defective

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The composite function (f + g)(3) when evaluated from f(x) = −3x² + 3x and g(x) = 2x+5 is -7

Given that

f(x) = −3x² + 3x and

g(x) = 2x+5

To perform the operation (ƒ + g)(3), we need to add the functions ƒ(x) and g(x) first, and then evaluate the sum at x = 3.

ƒ(x) = −3x² + 3x

g(x) = 2x + 5

To add the functions, we simply add their corresponding terms:

(ƒ + g)(x) = ƒ(x) + g(x) = (−3x² + 3x) + (2x + 5)

When the like terms are evaluated, we have

(ƒ + g)(3) = −3x² + 5x + 5

Now, we can evaluate the sum at x = 3:

(ƒ + g)(3) = −3(3)² + 5(3) + 5

So, we have

(ƒ + g)(3) = −27 + 15 + 5

Lastly, we have

(ƒ + g)(3) = -7

Therefore, (ƒ + g)(3) = -7.

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Proportionately, the cost of the board game without the sales tax is $28.00.

The sales tax is the levy imposed by the government on the consumption and production of certain goods and services.

The purposes of imposing sales taxes are to discourage consumption and to increase governmental revenue.

Proportion refers to the equation of two ratios.

In this situation, we can equate the value of the sales tax with its percentage to determine the cost of the board game.

The sales tax in dollars = $1.54

The sales tax rate = 5.5%

Proportionately, the value of the board game without the sales tax = $28.00 ($1.54/5.5%).

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How how is the cost?

When a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will shift towards the left side of the body.

Explanation:

The point at which the weight of a body or an object is concentrated, that is, the point at which the mass of the body or the object is focused is known as the center of gravity. The center of gravity (CG) is the point where the weight of the body is supposed to act, which is the point about which the body remains in balance. The body's center of gravity is important because it affects its balance and stability

                             .When a person is standing in a neutral position, the center of gravity is in the midline of the body. When the person flexes their right shoulder and holds their arm horizontally, the center of gravity will shift towards the left side of the body. This is because the weight of the arm is now being supported by the left side of the body. The shift in the center of gravity will cause the person to adjust their posture to maintain balance and stability.

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Option B, The fact that this survey question is a double-barreled question makes it problematic.

A survey question known as a double-barreled question has two questions inside one, making it challenging for respondents to give truthful and insightful responses.

The offered inquiry, in this instance, combines two distinct inquiries: if the phone was acquired within the last two years and whether it has recently had an upgrade.

Inconsistent answers might result from a person who bought their phone more than two years ago but only recently upgraded it, or vice versa. In order to prevent double-barreled questions and guarantee that responders can give precise and complete replies, each question should be isolated and posed independently.

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The question is -

What is the problem with this question item that appeared in a survey? was your phone purchased in the last two years and have you recently updated it?

a. It is a leading question

b. It involves negative wording

c. It is a double-barreled question

d. It is not on a Likert Scale

the answer is below with full explanation

Answer:

i'm pretty sure it's 33

Step-by-step explanation:

6^= 36

36-3= 33

1. The quotient in lowest terms of the given rational division is (x+2)/(3x-9).

2. The values of r is A. x=-2 and B. x=0.

Factor is a quantity which when multiplied by another quantity, produces a given product. Factors are used to simplify and solve equations, as well as in other areas of mathematics. Factors can be numbers, variables, and expressions.

To find the lowest terms, we must divide the numerator and denominator by the same number. The largest common factor of the numerator and denominator is 3. Dividing both the numerator and denominator by 3, we get (x+2)/(3x-9) = (x+2)/(x-3).

The values of r that must be excluded from the domains of the expressions are x=0 and x=3. x=0 must be excluded because it will create a zero in the denominator which is not allowed. x=3 must also be excluded because it will create a zero in the numerator, and thus make the entire expression equal to 0. Thus, the correct answer is A. x=-2 and B. x=0.

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The fence ought to be cut into 12 pieces, every one of length 28 m, to make three squares, each with a side length of 28 m. This will limit the total area encased by the fence.

To limit the total area encased by the fence, the three squares ought to have equivalent areas. Let x be the length of each side of the squares. Then the perimeter of each square is 4x, and the total length of the fence is 3(4x) = 12x. Since the total length of the fence is given to be 336 m, we have:

12x = 336

Addressing for x, we get:

x = 28

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Answer:

We can solve the inequality by adding 4 to both sides:

2b - 4 + 4 ≥ 3 + 4

2b ≥ 7

b ≥ 7/2

The values in the replacement set that are greater than or equal to 7/2 are {3, 4, 5}. Therefore, the solution set is:

{3, 4, 5}

So the answer is B. {3, 4, 5}.

The sector area of a circle is quadrupled when the radius is doubled. When the radius is doubled, the arc length of a circle is also doubled. This happens because the sector area and arc length are both dependent on the radius of a circle. Therefore, any change in the radius of a circle affects both its sector area and arc length.

Let us understand both these concepts in detail:

Sector area of a circle: A sector is a region of a circle, and the area enclosed by two radii and an arc is known as a sector area. The formula for the sector area of a circle is given by:

Sector Area = (θ/360)πr²

where θ is the central angle in degrees,

r is the radius of the circle,

and is a constant value.

If we double the radius of a circle, the sector area increases by a factor of 4. This is because the sector area is directly proportional to the square of the radius.

Hence, doubling the radius of a circle results in an increase in the sector area by a factor of 22 (four).

Arc length of a circle: The length of an arc is the distance between two points on a circle. The formula for the arc length of a circle is given:

Arc Length = (θ/360)2πr

where θ is the central angle in degrees,

r is the radius of the circle,

and 2pie is a constant value.

If we double the radius of a circle, the arc length also doubles.

This is because the arc length is directly proportional to the radius.

Hence, doubling the radius of a circle results in an increase in the arc length by a factor of 2.

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Therefore, the teacher must initially invest at least $7,725 to retire with at least $125,000 in the account after 40 years at a 6.95% annual interest rate compounded continuously.

Percent is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". Percentages are commonly used to describe proportions or rates, such as the percentage of students who passed a test, the percentage of a population that belongs to a certain group, or the percentage increase or decrease in a quantity over time. Percentages are also used in calculations involving discounts, taxes, interest rates, and other financial applications.

Here,

The formula for the continuous compounding interest is given by:

[tex]A = Pe^{rt}[/tex]

where A is the final amount, P is the principal amount (initial investment), e is the constant 2.71828..., r is the annual interest rate as a decimal, and t is the time in years.

In this case, we want to solve for the initial investment P, given that the teacher wants to retire with at least $125,000 in the account after 40 years, and the annual interest rate is 6.95% compounded continuously. Therefore, we have:

A = $125,000

r = 0.0695 (annual interest rate as a decimal)

t = 40 years

Substituting these values into the formula, we get:

$125,000 = [tex]Pe^{0.0695*40}[/tex]

Dividing both sides by [tex]e^{0.0695*40}[/tex], we get:

P = $125,000 / [tex]e^{0.0695*40}[/tex]

Using a calculator, we find that [tex]e^{0.0695*40}[/tex] is approximately 16.173, so:

P = $125,000 / 16.173

P ≈ $7,725.32

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It took 5 seconds for the thunder to be heard, the lightning was 343 * 5 = 1715 meters away.

The distance between the lightning flash and hearing the thunder can be calculated using the speed of sound. The speed of sound in air at 20°C is 343 meters/second.

Explanation: When lightning strikes, the initial flash travels at the speed of light, which is 299,792,458 meters per second. The sound wave created by the flash, however, travels at a much slower speed.

The speed of sound in air at 20°C is 343 meters per second.

To calculate the distance of the lightning, we multiply the speed of sound by the amount of time it took to hear the thunder. In this case, the amount of time was 5 seconds, so the lightning was 1715 meters away (343 * 5 = 1715).

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To compute a 90% confidence interval for the population proportion with a margin of error of 0.08 and no prior estimate for the population proportion, a sample size of 181 is needed.

To determine the sample size needed to compute the 90% confidence interval for the population proportion with a margin of error of 0.08, we can use the formula:

n = (z^2 * p * (1 - p)) / E^2

where n is the sample size needed, z is the z-score for the desired confidence level (90% confidence level has a z-score of 1.645), p is the estimated proportion (since no prior estimate is available, we use 0.5 as a conservative estimate), E is the margin of error (0.08)

Substituting the given values, we get:

n = (1.645^2 * 0.5 * (1 - 0.5)) / 0.08^2

n = 180.99

Rounding up to the nearest whole number, we get:

n = 181

Therefore, a sample size of 181 is needed to compute the 90% confidence interval for the population proportion with a margin of error of 0.08, when no prior estimate for the population proportion is available.

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According to the given exponential equations it is proved that b = (ac) / (a+b) where a+b ≠ 0.

We are given the first equation as [tex]3^{a} = 21^{b}[/tex] ----(1) i.e 3 to the power a is equal to 21 to the power b.

The next exponential equation is [tex]7^{c} = 21^{b}[/tex] ----(2)

We know, 21 can be written as 3*7 because they are the factors of 21. Therefore, [tex]21^{b} = (3*7)^{b} = 3^{b}7^{b}[/tex]

Substituting equations (1) and (2), we get:

[tex]3^{a}= 3^{b} *7^{b}[/tex]

Taking logarithm base 3 on both sides:

a = blog3(37)

a = b*(log3(3) + log3(7))

a = b*(1 + log3(7))

b = a / (1 + log3(7)) ------ (3)

Similarly, taking logarithm base 7 on both sides of equation (2):

c = b*log7(21)

c = b*(log7(3) + log7(7))

c = b*(1 + log7(3/7))

b = c / (1 + log7(3/7)) ------ (4)

Substituting (3) and (4) in the given equation, we get:

a / (1 + log3(7)) = (ac) / (a+b) * (1 + log7(3/7))

After cross-multiplying and simplifying the equations,

b = (ac) / (a+b)

Hence,b = (ac) / (a+b)

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The airplane's average rate in calm air is 600 mph.

What is an average?

In mathematics, the average is a measure of the central tendency of a set of numerical values, which is computed by adding all the values in the set and dividing them by the total number of values. The average is also known as the mean, and it is one of the most commonly used measures of central tendency in statistics

Let's denote the airplane's average rate in calm air by x mph.

When the airplane is flying with the jetstream, its ground speed (speed relative to the ground) is x + 300 mph. We know that it can fly 3000 miles in the same amount of time it takes to fly 1000 miles against the jetstream, so we can set up the following equation:

3000 / (x + 300) = 1000 / (x - 300)

We can cross-multiply to simplify:

3000(x - 300) = 1000(x + 300)

Expanding the brackets gives:

3000x - 900000 = 1000x + 300000

Simplifying and rearranging terms gives:

2000x = 1200000

x = 600

Therefore, the airplane's average rate in calm air is 600 mph.

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The smallest value of x in the Poisson distribution is 0, which means that no cars can pass through the intersection in a given minute.

For explain further, a Poisson distribution is a statistical model that describes the probability of a given number of events occurring in a fixed period of time, such as cars passing through an intersection in a minute.

In a Poisson distribution, the probability of x events occurring in a given minute is given by the equation P(x) = e-λλx/x!, where λ is the average number of events in a given minute. In this case, λ would be the average number of cars that pass through the intersection per minute.

The probability of 0 cars passing through the intersection in a given minute is e-λλ0/0! = 1, which is the highest probability in the distribution. Therefore, the smallest value of x in a Poisson distribution is 0.

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We have 6 red and 1 blue marble thus the probability of drawing blue marble = 1/7

To understand probability as a concept, pay attention to the steps below.

Step 1. Multiply the individual probabilities to obtain the chance of numerous separate events.

Step 2. As there are two separate events in this scenario, double the probabilities of each.

Step 3. Add the individual probabilities to obtain the chance of several events that are mutually exclusive.

In this bag of 7 marbles, there is 1 blue one. Assume that each is marked with a number. Choosing blue-1 has a 1/7 chance of happening. (Why? As there are 7 marbles that may be chosen, each with an equal probability, and since those 7 occurrences are mutually exclusive, the 7 probabilities total up to 1.)

The probability of choosing blue-2 is similarly 1/7; the same goes for blue-3,..., and blue-8. To determine the likelihood of picking a blue, add those up (and blue).

Step 4. Do the same for red next.

Thus the probability of drawing blue marble =  1/7

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A female student's probability of not receiving an A is 0.56, or 56%.

Probability and probability, as well as its cognates in various modern languages, come from the educated Latin of the Middle Ages called probabilis, which Cicero used to refer to a viewpoint as being plausible or generally accepted. Ancient French probabilite is where the word probability came from (14 c.)

We must utilise the data in the table to determine the likelihood that a female student will not receive an A.

There are 16 male students and 9 female students in the class, according to the table. Of the nine female students, four received As compared to five Bs.

Hence, the The likelihood that a female student won't receive an A is: P (Female student does not have an A) = Total number of female students / Number of female students without an A

P

Female student does not have an A (Female student does not have an A) = 5/9 P(Female student does not have an A) = 0.56 or 56%.

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Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο. ,then ∠SGM = 84°.

Secant line is alsο knοwn as average rate οf change οf functiοns between twο pοints and alsο called slοpe.

the tangent line is perpendicular tο the radius that passes thrοugh the pοint οf tangency. Therefοre, we have:

m∠MGS = 90°

Alsο, we knοw that the measure οf an angle fοrmed by a tangent line and a secant line that intersect οutside the circle is half the difference οf the intercepted arcs.

m∠SGM = 1/2 (mSE - mGE)

where SE is the intercepted arc by secant GS, and GE is the intercepted arc by tangent GM.

Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο.

mSE = 2mGS

mSE = 2(84°) = 168°

m∠SGM = 1/2 (mSE - mGE) = 1/2 (168° - 0°) = 84°

Therefοre, m∠SGM = 84°.

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Answer:

y=5x-7

Step-by-step explanation:

The nurse will administer 3 tablets of Coreg to meet the prescribed dosage of 9.375 mg PO daily.

The prescription order is for the nurse to administer 9.375mg of Coreg tablets orally each day. The Coreg tablets have a dosage strength of 3.125mg per tablet. To calculate the number of tablets the nurse needs to administer, we can divide the total dosage needed (9.375mg) by the dosage strength per tablet (3.125mg per tablet).

This results in the nurse administering 3 tablets to meet the prescribed dosage. Therefore, the nurse should give 3 tablets of Coreg to the patient each day to ensure they receive the correct amount of medication.

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The given question is incomplete, the complete question is:

the pharmacy sends the nurse the following coreg tablets. the order is to administer 9.375 mg po daily. how many tablets will the nurse administer? enter only the numeral (not the unit of measurement) in your answer.