What is the exact length of the missing side of the triangle if the legs are 12 cm and 13 cm?

Answers

Answer 1

The exact length of the missing side of the triangle is approximately 17.68 cm.

To find the exact length of the missing side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Given that the legs of the triangle are 12 cm and 13 cm, we can label them as 'a' and 'b' respectively, and the missing side as 'c'.

We can set up the equation as follows:

a² + b² = c²

Plugging in the values:

12² + 13² = c²

Simplifying:

144 + 169 = c²

313 = c²

To find the exact length of the missing side, we take the square root of both sides:

√313 = √c²

17.68 ≈ c

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Related Questions

Why do you think the percentage of tax filers has most dramatically increased for the 65+ age group?
-45-54?

Answers

The increase in tax filers in the 65+ age group and the 45-54 age group can be attributed to factors such as the aging population, changes in retirement patterns, economic factors, and increased income levels.

The percentage of tax filers has most dramatically increased for the 65+ age group and the 45-54 age group due to several reasons.

Firstly, the aging population is one of the main factors contributing to the increase in tax filers in the 65+ age group. As people in this age group retire, they may rely on various sources of income such as pensions, social security benefits, and investments. These income sources are taxable, which requires them to file tax returns.

Secondly, changes in retirement patterns and economic factors play a role. With longer life expectancies and improved healthcare, many individuals in the 65+ age group continue to work beyond traditional retirement age. This leads to additional income and tax obligations, resulting in an increase in tax filers.

In the 45-54 age group, the increase in tax filers can be attributed to several factors as well. This age range represents individuals in their peak earning years, with higher incomes compared to other age groups. As their incomes increase, they may reach certain tax thresholds that require them to file tax returns.

Additionally, changes in employment patterns and economic factors can impact the number of tax filers in this age group. For instance, economic downturns or job loss may lead individuals to seek self-employment or other sources of income, increasing the likelihood of filing tax returns.

In conclusion, the increase in tax filers in the 65+ age group and the 45-54 age group can be attributed to factors such as the aging population, changes in retirement patterns, economic factors, and increased income levels.

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A set of data has a normal distribution with a mean of 50 and a standard deviation of 8. Find the percent of data within each interval.

less than 50

Answers

Approximately 50% of the data falls below 50 in a normal distribution with a mean of 50 and a standard deviation of 8.

To find the percentage of data that falls below 50 in a normal distribution with a mean of 50 and a standard deviation of 8, we can use the Z-score formula.

The Z-score is a measure of how many standard deviations an observation is away from the mean. For our case, we want to calculate the Z-score for the value of 50.

Z = (X - μ) / σ

where X is the given value, μ is the mean, and σ is the standard deviation.

Substituting the values into the formula, we have:

Z = (50 - 50) / 8

Z = 0 / 8

Z = 0

A Z-score of 0 indicates that the value of 50 is exactly at the mean.

Now, to find the percentage of data less than 50, we need to determine the area under the normal distribution curve up to the Z-score of 0.

By referring to a standard normal distribution table or using statistical software, we find that the area to the left of the Z-score of 0 is 0.5000 or 50%.

Therefore, approximately 50% of the data falls below 50 in a normal distribution with a mean of 50 and a standard deviation of 8.

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If the probability of finding the first green light is 0.56, find the probability that driver will find the second traffic light green

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Probability refers to the measure of the likelihood or chance of an event occurring, expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty.

To find the probability that the driver will find the second traffic light green, we need to make an assumption that the probability of each traffic light being green is independent of the other traffic lights. This means that the probability of finding the second traffic light green is the same as the probability of finding the first traffic light green.

Since the probability of finding the first green light is given as 0.56, the probability of finding the second green light is also 0.56.

Therefore, the probability that the driver will find the second traffic light green is 0.56.

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Julian needs to spend at least seven hours each week practicing the drums. he has already practiced five and one third hours this week. he wants to split the remaining practice time evenly between the last two days of the week. write an inequality to determine the minimum number of hours he needs to practice on each of the two days. group of answer choices five and one third 2x ≤ 7 five and one thirdx 2 ≤ 7 five and one thirdx 2 ≥ 7 five and one third 2x ≥ 7

Answers

The correct inequality is: six x is greater than or equal to five.

To determine the minimum number of hours Julian needs to practice on each of the two days, we can set up an inequality.

Let x represent the number of hours Julian needs to practice on each of the two days.

We know that Julian has already practiced 5 and one third hours, which can be written as 16/3 hours.

So, the total practice time for the remaining two days would be 7 hours (the minimum number of hours he needs to practice each week) minus 16/3 hours.

Thus, the inequality would be:
2x ≥ 7 - 16/3

Simplifying the right side:
2x ≥ 21/3 - 16/3
2x ≥ 5/3

To get rid of the fraction, we can multiply both sides by 3:
3 * 2x ≥ 3 * 5/3
6x ≥ 5

Therefore, the correct inequality is:
six x is greater than or equal to five.

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why is-3^2 -9 not 9?

serious answers pls

Answers

Answer:

Step-by-step explanation: The negative sign needs to be enclosed in parentheses if you want the result to be 9

If you write (-3)^2 the result is 9

and -3^2 = -9 is right

determine whether the reasoning is an example of deductive or inductive reasoning. to find the perimeter p of a square with side of length​ s, i can use the formula p4s. so the perimeter of a square with side of length 7 inches is 4728 inches.

Answers

The correct perimeter of a square with a side length of 7 inches is 28 inches.

Based on the given information, the reasoning used is an example of deductive reasoning.

Deductive reasoning is when a conclusion is drawn based on a set of premises or known facts. In this case, the formula p = 4s is a well-known and accepted formula to calculate the perimeter of a square.

By substituting the side length of 7 inches into the formula, the conclusion is reached that the perimeter is 28 inches. However, the stated perimeter of 4728 inches is incorrect.

To find the correct perimeter, we would use the formula p = 4s, where s represents the side length of the square.

Plugging in 7 inches for s, we get p = 4 * 7, which simplifies to p = 28 inches.

Therefore, the correct perimeter of a square with a side length of 7 inches is 28 inches.

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The reasoning used in this example is deductive because it starts with a general formula and applies it to a specific example to draw a conclusion. The conclusion, however, is incorrect, and the correct perimeter is 28 inches, not 4728 inches.

The reasoning provided is an example of deductive reasoning. Deductive reasoning is a logical process where specific conclusions are drawn from general principles or premises.

In this case, the reasoning starts with the general principle or formula for finding the perimeter of a square, which is p = 4s, where p represents the perimeter and s represents the length of one side of the square. The formula is based on the geometric properties of a square.

Next, the specific example of a square with a side length of 7 inches is given. By substituting the value of s into the formula, we can calculate the perimeter: p = 4 * 7 = 28 inches.

The conclusion that the perimeter of a square with a side length of 7 inches is 4728 inches is incorrect. It seems like there might have been a typo or calculation error in the provided answer.

To find the correct perimeter, we need to use the formula p = 4s again, substituting the correct value of s (7 inches). This gives us: p = 4 * 7 = 28 inches. Therefore, the correct perimeter of a square with a side length of 7 inches is 28 inches.

In summary, the reasoning used in this example is deductive because it starts with a general formula and applies it to a specific example to draw a conclusion. The conclusion, however, is incorrect, and the correct perimeter is 28 inches, not 4728 inches.

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chegg Suppose that you select a random sample of 200 totally random audits and that 90% of all the returns filed would result in no-change audits. What is the probability that the sample has

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You can substitute the value of x into the formula to calculate the probability for any specific number of no-change audits.

To determine the probability that the sample has a specific number of no-change audits, we can use the binomial probability formula.

The binomial probability formula is given by:

[tex]P(X = k) = C(n, k) * p^k * (1 - p)^{(n - k)}[/tex]

Where:

P(X = k) is the probability of having exactly k successes (in this case, no-change audits),

n is the sample size,

k is the number of successes,

p is the probability of success in a single trial (in this case, the probability of a no-change audit), and

C(n, k) is the binomial coefficient, also known as "n choose k," which represents the number of ways to choose k successes from n trials.

In this scenario, n = 200 (sample size) and p = 0.9 (probability of no-change audit). We want to calculate the probability of having a specific number of no-change audits. Let's say we want to find the probability of having x no-change audits.

[tex]P(X = x) = C(200, x) * 0.9^x * (1 - 0.9)^{(200 - x)}[/tex]

Now, let's calculate the probability of having a specific number of no-change audits for different values of x. For example, if we want to find the probability of having exactly 180 no-change audits:

[tex]P(X = 180) = C(200, 180) * 0.9^{180} * (1 - 0.9)^{(200 - 180)}[/tex]

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Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Answers

Juan and Ben have been negotiating the purchase of Juan's car. Juan receives a new and higher offer from someone else. The negotiations between Juan and Ben can be renegotiated based on the new offer.

In this scenario, Juan and Ben have been negotiating the purchase of Juan's car. However, Juan receives a new and higher offer from someone else. This new offer changes the dynamics of the negotiation between Juan and Ben. Since Juan now has a better offer, he can choose to renegotiate the terms of the deal with Ben. Juan may use the new offer as leverage to potentially get a higher price or better terms from Ben. The negotiation process can be restarted based on the new information. The dynamics of the negotiation change as a result of the new offer.

When Juan receives a new and higher offer for his car while negotiating with Ben, he can use it as leverage to reopen the negotiation and potentially obtain a better deal.

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Focus20 applicants from a pool of 90 applications will be hired. How many ways are there to select the applicants who will be hired

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There are 13,749,669,792,000 ways to select the applicants. To calculate the number of ways to select applicants who will be hired, we can use the combination formula. The formula for calculating combinations is:

C(n, r) = n! / (r!(n - r)!)

Where n is the total number of applicants (90 in this case), and r is the number of applicants to be hired (20 in this case). Plugging in the values, we get:

C(90, 20) = 90! / (20!(90 - 20)!)

Calculating the factorial terms:

90! = 90 × 89 × 88 × ... × 3 × 2 × 1

20! = 20 × 19 × 18 × ... × 3 × 2 × 1

70! = 70 × 69 × 68 × ... × 3 × 2 × 1

Substituting these values into the combination formula:

C(90, 20) = 90! / (20!(90 - 20)!)

= (90 × 89 × 88 × ... × 3 × 2 × 1) / [(20 × 19 × 18 × ... × 3 × 2 × 1) × (70 × 69 × 68 × ... × 3 × 2 × 1)]

Performing the calculations, we find: C(90, 20) = 13,749,669,792,000

Therefore, there are 13,749,669,792,000 ways to select the applicants who will be hired from a pool of 90 applications.

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remember to round off the answer to the nearest whole number, because fractions of a drop are to be avoided when calculating iv drip rates. order: 1000 ml to be infused for 12 hours on micro drip, gtt per minute.

Answers

The IV drip rate for this order is 83 gtt/minute. The order is for 1000 mL to be infused over 12 hours using a micro drip set. First, let's find the number of drops per mL for a micro drip set.

To calculate the IV drip rate in gtt per minute, we need to determine the number of drops per mL and then multiply it by the mL per hour. In this case, the order is for 1000 mL to be infused over 12 hours using a micro drip set.
First, let's find the number of drops per mL for a micro drip set. A micro drip set usually has a drop factor of 60 gtt/mL.
Next, we need to find the mL per hour. Since we have a total of 1000 mL to be infused over 12 hours, we divide 1000 by 12 to get 83.33 mL/hour. Remember to round off to the nearest whole number, which is 83 mL/hour.
Finally, to calculate the drip rate in gtt per minute, we multiply the mL per hour (83 mL) by the drop factor (60 gtt/mL) and divide it by 60 minutes to get 83 gtt/minute.
Therefore, the IV drip rate for this order is 83 gtt/minute.

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your community wants to put a square fountain in a park. around the fountain will be a sidewalk (hat is 3.5 ft wide. the total area that the fountain and sidewalk can be is 700 ft2, are the dimensions of the fountain?

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The dimension of the fountain will be 20ft x 20ft x 2.5ft. Let the width of the fountain be x ft. The length of the fountain will be x ft as well. The height of the fountain will be 2.5 ft.

Therefore, the volume of the fountain will be:V = (length) × (width) × (height)

V = (x) × (x) × (2.5)

V = 2.5x²

Now, let us calculate the area of the sidewalk. The area of the sidewalk is a rectangular region with the dimensions (length + 2) × (width + 2). This is because there are two additional feet on both sides of the length and width of the fountain. Therefore, we can represent the area of the sidewalk as follows: A = (length + 2) × (width + 2)

A = (x + 2) × (x + 2)

A = (x + 2)²

Now, since the total area of the fountain and sidewalk is 700ft², we can write an equation as follows: 2.5x² + (x + 2)² = 700 Expanding and solving the quadratic equation

we get,x² + 4x - 348 = 0

(x + 19)(x - 15) = 0

Since the width of the fountain cannot be negative, we will only consider the positive root, x = 15 feet.

Therefore, the dimensions of the fountain will be 20ft x 20ft x 2.5ft.

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Suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. She figures her t score to be -.20. What decision should she make regarding the null hypothesis

Answers

Without additional information such as the significance level or p-value, it is not possible to make a definitive decision regarding the null hypothesis based solely on the t-score of -0.20.

Based on the given information, the counselor obtained a t-score of -0.20. To make a decision regarding the null hypothesis, we need to compare this t-score to a critical value or determine the p-value associated with it.

If the counselor has a predetermined significance level (α), she can compare the t-score to the critical value from the t-distribution table. If the t-score falls within the critical region (beyond the critical value), she would reject the null hypothesis. However, without knowing the significance level or degrees of freedom, we cannot make a definitive decision based solely on the t-score.

Alternatively, if the counselor has access to the p-value associated with the t-score, she can compare it to the significance level. If the p-value is less than the significance level (typically α = 0.05), she would reject the null hypothesis.

Without more information about the significance level or p-value, it is not possible to determine the decision regarding the null hypothesis based solely on the t-score of -0.20.

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Write six different iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane xyz. Evaluate the first integral. Question content area bottom Part 1

Answers

Using triple integration, the volume of tetrahedron cut from the plane 2x + y + z = 4 is [tex]\frac{16}{3}[/tex].

A tetrahedron is nothing but a three dimensional pyramid.

To find the volume of tetrahedron cut from the plane 2x + y + z = 4, we need to first take one of the three dimension as base. Let as take xy plane as base.

XY as plane implies z = 0, equation becomes 2x + y = 4. To find the limits of X and Y, we put y = 0.

Thus, 2x + 0 = 4 , implying, x = 2.

Thus the range of x is : [0,2]

Putting the value of x in the given equation, the range of y is [0, 4 - 2x]

Similarly, range of z becomes: [0, 4 - 2x - y]

Since z is dependent upon y and x, and, y is dependent on x, Therefore the order of integration must be z, then y and then x.

The volume of tetrahedron becomes:

[tex]=\int\limits^0_2 \int\limits^{4-2x}_0 \int\limits^{4-2x-y}_0 {1} \, dz \, dy \, dx \\\\=\int\limits^0_2 \int\limits^{4-2x}_0 4-2x-y \, dy \, dx \\\\=\int\limits^0_2[ (4-2x)y - \frac{y^2}{2}]^{4-2x}_0 dx\\ \\=\int\limits^0_2 (4-2x)^2 - \frac{1}{2} (4-2x)^2 dx\\\\[/tex]

[tex]=\int\limits^2_0 {\frac{1}{2}(16+4x^2-16x )} \, dx \\\\=\int\limits^2_0(8+2x^2-8x)dx\\\\=[8x+\frac{2}{3} x^3-4x^2]^2_0\\\\=\frac{16}{3}[/tex]

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The complete question is given below:

Use triple integration to find the volume of tetrahedron cut from the plane 2x + y + z = 4.  



In a recent telephone survey, respondents were asked questions to determine whether they supported the new that required every passenger to wear a seat belt while in a moving vehicle. The first question was, "According to the National Highway Traffic Safety Administration, wearing seats belts could prevents 45% of the fatalities suffered in car accidents .Do you think that everyone should wear safety belts?" Does this question introduce a bias into the survey? Explain

Answers

Yes, the question "According to the National Highway Traffic Safety Administration, wearing seat belts could prevent 45% of the fatalities suffered in car accidents. Do you think that everyone should wear safety belts?" introduces a bias into the survey.

The question introduces a bias because it presents information about the effectiveness of seat belts in preventing fatalities before asking for the respondents' opinion. By providing the statistic that 45% of fatalities can be prevented by wearing seat belts, the question already influences the respondents' perception and frames the issue in a positive light.

This framing can potentially lead respondents to feel pressured or compelled to agree with the statement due to the presented statistic. It may not give an unbiased opportunity for respondents to express their own opinions or consider alternative viewpoints.

To avoid bias, it is important to ask questions in a neutral and unbiased manner, allowing respondents to form their own opinions without being influenced by pre-presented information or statistics.

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Redesign of entrance a
entrance a
3x + y = 5
key
0
fountain
= path a
---- = path b
- 2x + 5y8
wao
entrance bc
how does the redesigned equation of the path from entrance a affect the coordinates of the fountain? show your
work and explain your reasoning.

Answers

In summary, the redesigned equation of the path from entrance a affects the coordinates of the fountain by changing the coefficients of x and y in the equation. This change in coefficients results in a different slope for the path.

The redesigned equation of the path from entrance a affects the coordinates of the fountain by changing the values of x and y in the equation of the path.


The original equation of the path from entrance a is 3x + y = 5. To redesign the equation, we need to analyze the changes mentioned in the question: "path a ---- = path b - 2x + 5y8 wao entrance bc".

From this information, we can deduce that the new equation of the path from entrance a is given by: 3x + y = -2x + 5y + 8.

To understand how this redesigned equation affects the coordinates of the fountain, we can compare it to the original equation.

By rearranging the terms in both equations, we can see that the coefficients of x and y have changed. In the original equation, the coefficient of x is 3 and the coefficient of y is 1. However, in the redesigned equation, the coefficient of x is now -2 and the coefficient of y is 5.

These changes in the coefficients affect the slope of the path. The slope of the original equation is -3 (the coefficient of x divided by the coefficient of y), while the slope of the redesigned equation is -2/5.

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Assume the following for this question. Lower and Upper specification limits for a service time are 3 minutes and 5 minutes, respectively with the nominal expected service time at 4 minutes. The observed mean service time is 4 minutes with a standard deviation of 0.2 minutes. The current control limits are set at 3.1 and 4.9 minutes respectively.

Answers

The observed mean service time falls within the current control limits. We can conclude that the process is stable, the service time is in control, and it meets the required specifications.


1. Calculate the process capability index (Cpk) using the formula: Cpk = min((USL - mean)/3σ, (mean - LSL)/3σ), where USL is the upper specification limit, LSL is the lower specification limit, mean is the observed mean service time, and σ is the standard deviation.
2. Plug in the values: USL = 5 minutes, LSL = 3 minutes, mean = 4 minutes, σ = 0.2 minutes.
3. Calculate Cpk: Cpk = min((5-4)/(3*0.2), (4-3)/(3*0.2)) = min(0.556, 0.556) = 0.556.
4. Since the calculated Cpk is greater than 1, the process is considered capable and the service time is in control.
5. The current control limits (3.1 and 4.9 minutes) are wider than the specification limits (3 and 5 minutes) and the observed mean (4 minutes) falls within these control limits.
6. Therefore, the process is stable and meets the specifications.

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Let x1, . . . , xn denote a sequence of numbers, y1, . . . , yn denote another sequence of numbers, and a, b, and c denote three constants. Show that:

Answers

The expression is [tex]∑(i=1 to n) (a * x_i + b * y_i + c) = a * ∑(i=1 to n) x_i + b * ∑(i=1 to n) y_i + c * n[/tex]

To show that the given expression is true, we will use the properties of summation notation. Let's break it down step-by-step:

1. Start by expanding the left side of the equation using the properties of summation:
[tex]a * x_1 + b * y_1 + c + a * x_2 + b * y_2 + c + ... + a * x_n + b * y_n + c[/tex]

2. Now, group the terms together based on their constants (a, b, and c):
[tex](a * x_1 + a * x_2 + ... + a * x_n) + (b * y_1 + b * y_2 + ... + b * y_n) + (c + c + ... + c)[/tex]

3. Observe that each sum within the parentheses represents the summation of the sequences x_i, y_i, and a sequence of c's respectively:
[tex]a * ∑(i=1 to n) x_i + b * ∑(i=1 to n) y_i + c * n[/tex]

4. This matches the right side of the equation, which proves that the given expression is true.

Therefore, we have shown that:
[tex]∑(i=1 to n) (a * x_i + b * y_i + c) = a * ∑(i=1 to n) x_i + b * ∑(i=1 to n) y_i + c * n.[/tex]

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HELP PLEASEEEE!!!!! I WILL MARK!!!!!!

If y = 3x2 − 9, what is its inverse?

A. inverse of y is equal to negative square root of the quantity x plus 9 over 3 end quantity such that x is greater than or equal to negative 9
B. inverse of y is equal to negative square root of the quantity x plus 9 over 3 end quantity such that x is less than or equal to negative 9
C. inverse of y is equal to negative square root of the quantity x over 3 end quantity plus 9 such that x is less than or equal to 0
D. inverse of y is equal to negative square root of the quantity x over 3 end quantity plus 9 such that x is greater than or equal to 0

Answers

Answer:

A

Step-by-step explanation:

Given quadratic function:

[tex]y=3x^2 - 9, \qquad x \leq 0[/tex]

The domain of the given function is restricted to values of x less than or equal to zero. Therefore:

The domain is x ≤ 0.

As 3x² ≥ 0, then range of the given function is restricted to values of y greater than or equal to -9.

The range is x ≥ -9.

[tex]\hrulefill[/tex]

To find the inverse of the given function, first interchange the x and y variables:

[tex]x = 3y^2 - 9[/tex]

Now, solve the equation for y:

[tex]\begin{aligned}x& = 3y^2 - 9\\\\x+9&=3y^2\\\\\dfrac{x+9}{3}&=y^2\\y&=\pm \sqrt{\dfrac{x+9}{3}}\end{aligned}[/tex]

The range of the inverse function is the domain of the original function.

As the domain of the original function is restricted to x ≤ 0, then the range of the inverse function is restricted to y ≤ 0.

Therefore, the inverse function is the negative square root:

[tex]f^{-1}(x)=-\sqrt{\dfrac{x+9}{3}}[/tex]

The  domain of the inverse function is the range of the original function.

As the range of the original function is restricted to y ≥ -9, then the domain of the inverse function is restricted to x ≥ -9.

[tex]\boxed{f^{-1}(x)=-\sqrt{\dfrac{x+9}{3}}\qquad x \geq -9}[/tex]

So the correct statement is:

A)  The inverse of y is equal to negative square root of the quantity x plus 9 over 3 end quantity such that x is greater than or equal to negative 9.

Which expression is equivalent to ? a 2x3+122x^{3}+122x 3 +12 b 2x2+11x+122x^{2}+11x+122x 2 +11x+12 c 2x3+6x2+4x+122x^{3}+6x^{2}+4x+122x 3 +6x 2 +4x+12 d 2x3+8x2+3x+122x^{3}+8x^{2}+3x+122x 3 +8x 2 +3x+12

Answers

the expression c) [tex]2x^3 + 6x^2 + 4x + 12 + 122x^3 + 6x^2 + 4x + 122x^3 + 6x^2 + 4x + 12[/tex] is equivalent to [tex]6x^3 + 18x^2 + 12x + 36.[/tex]

The equivalent expression is:

c) [tex]2x^3 + 6x^2 + 4x + 12 + 122x^3 + 6x^2 + 4x + 122x^3 + 6x^2 + 4x + 12[/tex]

Simplifying it further:

[tex]2x^3 + 2x^3 + 2x^3 + 6x^2 + 6x^2 + 6x^2 + 4x + 4x + 4x + 12 + 12 + 12[/tex]

Combining like terms:

[tex]6x^3 + 18x^2 + 12x + 36[/tex]

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Manu has invested 30% of his capital in petro bonds and rest in a life insurance plan

Answers

Manu invested 30% of his capital in petro bonds, and the remaining 70% of his capital was invested in a life insurance plan.

Manu has invested 30% of his capital in petro bonds and rest in a life insurance plan.

Let's find out how much Manu has invested in petro bonds and life insurance plans.

Suppose the total capital is x.

Then, according to the problem, Manu has invested 30% of x in petro bonds.

So, the amount he has invested in petro bonds = 30% of x = 0.3x

And he has invested the remaining amount in a life insurance plan.

So, the amount he has invested in a life insurance plan = 100% - 30% = 70% of x = 0.7x

Therefore, Manu has invested 0.3x in petro bonds and 0.7x in a life insurance plan.

Therefore, the answer is:Manu invested 30% of his capital in petro bonds, and the remaining 70% of his capital was invested in a life insurance plan.

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Choose all the inequalities for which the solution set is x < 2.


A. X-1 <1


B. X2 <0


C. X 3 < 1


D. X+4 < 6


HELP PLS

Answers

The correct options are A)  X-1 <1 and D) X+4 < 6.

Given, we need to find all the inequalities for which the solution set is x < 2. We know that if x < a then the solution set will lie on the left side of a in the number line. Therefore, for x < 2 the solution set will be on the left side of 2 on the number line. So, let's check each option:

A. X-1 <1 - Adding 1 to both sides of the inequality we get: X < 2

Here, the solution set is x < 2. So, option A is correct.

B. X2 <0 - There is no real value of x for which x² < 0. So, the solution set is null. Therefore, option B is incorrect.

C. X 3 < 1 - Subtracting 3 from both sides we get: X < -2. The solution set is x < -2. So, option C is incorrect.

D. X+4 < 6 - Subtracting 4 from both sides we get: X < 2. Here, the solution set is x < 2. So, option D is correct.

Therefore, the correct options are A and D.

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Vocabulary Which type of multiplication, scalar or matrix, can help you with a repeated matrix addition problem? Explain.

Answers

Scalar multiplication can help with a repeated matrix addition problem. Scalar multiplication involves multiplying a scalar (a single number) by each element of a matrix.

In a repeated matrix addition problem, if we have a matrix A and we want to add it to itself multiple times, we can use scalar multiplication to simplify the process. Instead of manually adding each corresponding element of the matrices, we can multiply the matrix A by a scalar representing the number of times we want to repeat the addition.

For example, if we want to add matrix A to itself 3 times, we can simply multiply A by the scalar 3, resulting in 3A. This operation scales each element of A by 3, effectively repeating the addition process. Thus, scalar multiplication can efficiently handle repeated matrix addition problems by simplifying the calculation.

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Determine the quartiles of the following dataset which represents total points scored during recent football games. 12, 14, 15, 17, 17, 21, 24, 25, 27, 31, 33

Answers

The dataset representing total points scored during recent football games is as follows: 12, 14, 15, 17, 17, 21, 24, 25, 27, 31, 33 so  the quartiles of the given dataset are Q1 = 15, Q2 = 21, and Q3 = 27.

To determine the quartiles of this dataset, we need to find the values that divide the dataset into four equal parts. The first quartile (Q1) represents the 25th percentile, the second quartile (Q2) represents the 50th percentile (also known as the median), and the third quartile (Q3) represents the 75th percentile.

To find the quartiles, we first need to arrange the dataset in ascending order: 12, 14, 15, 17, 17, 21, 24, 25, 27, 31, 33.

There are a total of 11 data points in the dataset. To find the median (Q2), we take the middle value. Since there are 11 data points, the middle value is the 6th value, which is 21. Therefore, Q2 (the median) is 21.

To find Q1, we need to locate the 25th percentile. This means that 25% of the data points in the dataset should be below Q1. Since 25% of 11 is 2.75, we round it up to 3. The third value in the dataset is 15, so Q1 is 15.

To find Q3, we locate the 75th percentile, which means that 75% of the data points should be below Q3. 75% of 11 is 8.25, which we round up to 9. The ninth value in the dataset is 27, so Q3 is 27.

Therefore, the quartiles of the given dataset are Q1 = 15, Q2 = 21, and Q3 = 27.

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A die is rolled. Find the probability of the following outcome.

P (integer)

Answers

The probability of an event is determined by the number of favorable outcomes divided by the total number of possible outcomes. In this case, we need to find the probability of rolling an integer on a die.

A standard die has six sides, numbered 1 through 6. Out of these six possible outcomes, the favorable outcomes are the integers 1, 2, 3, 4, 5, and 6. Therefore, the total number of favorable outcomes is 6.

Since there is only one die being rolled, the total number of possible outcomes is also 6, as each side has an equal chance of landing facing up.

To find the probability of rolling an integer, we divide the number of favorable outcomes (6) by the total number of possible outcomes (6):

P(integer) = Number of favorable outcomes / Total number of possible outcomes

P(integer) = 6 / 6

Simplifying this fraction, we get:

P(integer) = 1

Therefore, the probability of rolling an integer on a die is 1. This means that it is guaranteed that the outcome will be an integer when rolling a standard die.

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Find the sum of the measures of the interior angles of each convex polygon.

32 -gon

Answers

To find the sum of the measures of the interior angles of a convex polygon, we can use the formula:

Sum of Interior Angles = (n - 2) * 180 degrees

Where "n" represents the number of sides (or vertices) of the polygon.

For a 32-gon, substituting n = 32 into the formula, we have:

Sum of Interior Angles = (32 - 2) * 180 degrees

                      = 30 * 180 degrees

                      = 5400 degrees

Therefore, the sum of the measures of the interior angles of a 32-gon is 5400 degrees.

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John wanted to bring attention to the fact that litter was getting out of hand at his neighborhood park. He created a poster where giant pieces of trash came to life and stomped on the park. Which typ
did he use?
Exaggeration
Incongruity
O Parody
Reversal

Answers

John wanted to bring attention to the fact that litter was getting out of hand at his neighborhood park. He created a poster where giant pieces of trash came to life and stomped on the park. The type of humor that he used in the poster is exaggeration.

What is exaggeration?

Exaggeration is the action of describing or representing something as being larger, better, or worse than it genuinely is. It is a representation of something that is far greater than reality or what the person is used to.

In this case, John used an exaggerated approach to convey the message that litter was getting out of hand in the park.

Incongruity: This is a type of humor that involves something that doesn't match the situation.

Parody: This is a type of humor that involves making fun of something by imitating it in a humorous way.

Reversal: This is a type of humor that involves changing the expected outcome or situation.

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Answer:


The type of satire that John used in his poster is exaggeration.Exaggeration is a technique used in satirical writing, art, or speech that highlights the importance of a certain issue by making it seem bigger than it actually is. It is used to make people aware of a problem or issue by amplifying it to the point of absurdity.In the case of John's poster, he exaggerated the issue of litter by making it appear as if giant pieces of trash were coming to life and stomping on the park, which highlights the importance of keeping the park clean.

Dropped 1. 50 inches raising the seasonal total to 26. 42 inches what was the seasonal total prior to the recent storm?

Answers

The seasonal total prior to the recent storm was 76.42 inches.

To calculate the seasonal total prior to the recent storm, we need to subtract the rainfall from the recent storm (50 inches) from the updated seasonal total (26.42 inches).

Let's assume that the seasonal total prior to the recent storm is represented by "x" inches.

So, we can set up the equation:

x - 50 = 26.42

To solve for x, we can add 50 to both sides of the equation:

x - 50 + 50 = 26.42 + 50

This simplifies to:

x = 76.42

Therefore, the seasonal total prior to the recent storm was 76.42 inches.

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Select the correct answer from each drop-down menu. Zahid started the construction of an equilateral triangle inscribed in a circle. Which segments need to be drawn to create the triangle

Answers

To construct an equilateral triangle inscribed in a circle, Zahid would need to draw three specific segments.

First, Zahid would need to draw the radius of the circle, which is a line segment connecting the center of the circle to any point on its circumference. This segment serves as the base of the equilateral triangle.

Next, Zahid would draw two more line segments from the endpoints of the base (radius) to another point on the circumference of the circle. These segments should be of equal length and form angles of 60 degrees with the base. These segments complete the equilateral triangle by connecting the remaining two vertices. Zahid needs to draw the radius of the circle (base of the equilateral triangle) and two additional line segments connecting the endpoints of the radius to other points on the circle's circumference. These line segments should be equal in length and form angles of 60 degrees with the base.

It is important to note that an equilateral triangle is a special case where all sides are equal in length and all angles are 60 degrees. In the context of a circle, an equilateral triangle is inscribed when all three vertices lie on the circumference of the circle.

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Player A has a higher batting average than player B for the first half of the baseball season. Player A also has a higher batting average than player B for the second half of the season. Is it necessarily true that player A has a higher batting average than player B for the entire season

Answers

No, it is not necessarily true that Player A has a higher batting average than Player B for the entire season, even if A outperforms B in both the first and second halves.


The batting average is calculated by dividing the number of hits by the number of at-bats. Player A could have a higher batting average in the first and second halves while accumulating more hits than Player B in those respective periods.

However, if Player B had significantly more at-bats in the overall season or had a higher number of hits relative to their at-bats in the remaining games, it is possible for Player B to surpass Player A’s cumulative batting average for the entire season. The final season batting average depends on the performance in all games played, not just individual halves.

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ben has bbbb dollars. cam has 7777 fewer dollars than ben. how many dollars does cam have? write your answer as an expression. dollars

Answers

The expression for Cam's amount would be: bbbb dollars - 7777 dollars.

To find the number of dollars Cam has, we need to subtract 7777 from Ben's amount.

Let's represent Ben's amount as "bbbb dollars."
The expression for Cam's amount would be: bbbb dollars - 7777 dollars.

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