Find the inverse of the following functions. Show all work


f(x) = 2√x+7

Answer:

the first answer

Step-by-step explanation:

Answer:

I think it's many buildings are crumbled

Answer:

y=2/3-5x/6

Step-by-step explanation:

a. The value corresponding to surviving the year is $0, and the value corresponding to not surviving the year is -$90,000.

b. The expected value for the 33-year-old male purchasing the policy is -$579.06.

c. Yes, the insurance company can expect to make a profit from many such policies because the expected profit per 33-year-old male insured for 1 year is $408.06.

a. The monetary value corresponding to surviving the year is $0 because the individual would not receive any payout from the insurance policy if he survives. The monetary value corresponding to not surviving the year is -$90,000 because in the event of the individual's death, the policy pays out a death benefit of $90,000.

b. To calculate the expected value for the 33-year-old male purchasing the policy, we need to multiply the probability of each event by its corresponding monetary value and sum them up. The probability of surviving the year is 0.9988, and the value corresponding to surviving is $0. The probability of not surviving the year is (1 - 0.9988) = 0.0012, and the value corresponding to not surviving is -$90,000.

Expected value = (Probability of surviving * Value of surviving) + (Probability of not surviving * Value of not surviving)

Expected value = (0.9988 * $0) + (0.0012 * -$90,000)

Expected value = -$108 + -$471.06

Expected value = -$579.06 (rounded to the nearest cent)

c. The insurance company can expect to make a profit from many such policies because the expected value for the 33-year-old male purchasing the policy is negative (-$579.06). This means, on average, the insurance company would pay out $579.06 more in claims than it collects in premiums for each 33-year-old male insured for 1 year. Therefore, the insurance company expects to make an average profit of $579.06 on every 33-year-old male it insures for 1 year.

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The simplified expression of 6(d - 6f) -6f- 3(-7f + 8d) is - 18d- 21f

The expression is given as

6(d - 6f) -6f- 3(-7f + 8d)

Expand the brackets

6(d - 6f) -6f- 3(-7f + 8d) = 6d - 36f - 6f + 21f - 24d

Collect the like terms

6(d - 6f) -6f- 3(-7f + 8d) = 6d  - 24d- 36f - 6f + 21f

Evaluate the like terms

6(d - 6f) -6f- 3(-7f + 8d) = - 18d- 21f

Hence, the simplified expression of 6(d - 6f) -6f- 3(-7f + 8d) is - 18d- 21f

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Given the angle of elevation of a 12 ft ladder leaning against a wall is 36°. The base of the ladder is approximately 16.5 ft from the wall.

The angle of elevation of a 12 ft ladder leaning against a wall is 36°. We need to find the distance of the base of the ladder from the wall.
To solve this problem, we can use trigonometric ratios. In this case, we will use the tangent ratio.
Tangent of an angle = Opposite side / Adjacent side
In this problem, the opposite side is the height of the ladder (12 ft) and the adjacent side is the distance from the base of the ladder to the wall. We need to find the adjacent side.
So, tan(36°) = 12 ft / Adjacent side
To find the adjacent side, we can rearrange the equation as:
Adjacent side = 12 ft / tan(36°)
Using a calculator, we can find the value of tan(36°) to be approximately 0.7265.
So, the distance of the base of the ladder from the wall is:
Adjacent side = 12 ft / 0.7265 ≈ 16.5 ft
Therefore, the base of the ladder is approximately 16.5 ft from the wall.

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The minimum acceptable rate of 1 sigma of quality production is d) 68.

This corresponds to a 68% acceptance level, which is equivalent to 1 standard deviation in a normal distribution.

A 1 sigma level corresponds to a standard deviation that captures approximately 68% of the data within a normal distribution. This means that if a process is operating at a 1 sigma level, it has a 68% acceptance rate, and the remaining 32% of the data falls outside the acceptable range

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30.

\(g(x)=2x^2+18x-14\\\\a)\\g(9)=2\cdot9^2+18\cdot9-14=162+162-14=310\\\\b)\\ g(3x)=2(3x)^2+18(3x)-14=18x^2+54x-14\\\\c)\\ g(1+5m)=2(1+5m)^2+18(1+5m)-14=\\\\=2(1+10m+25m^2)+18+90m-14=2+20m+50m^2+4+90m=\\\\=50m^2+110m+6\)

31.

\(h(y)=-3y^3-6y+9\\\\a)\\h(4)=-3(4)^3-6(4)+9=-3\cdot64-24+9=-192-15=-207\\\\ b)\\h(-2y)=-3(-2y)^3-6(-2y)+9=24y^3+12y+9\\\\c)\\h(5b+3)=-3(5b+3)^3-6(5b+3)+9=\\\\=-3[(5b)^3+3\cdot(5b)^2\cdot3+3\cdot5b\cdot3^2+3^3)-30b-18+9=\\\\=-375b^3-675b^2-405b-81-30b-9=-375b^3-675b^2-435b-90\)

32.

\(f(t)=\dfrac{4t+11}{3t^2+5t+1}\\\\a)\\f(-6)=\dfrac{4(-6)+11}{3(-6)^2+5(-6)+1}=\dfrac{-24+11}{3(36)-30+1}=\dfrac{-13}{108-29}=-\dfrac{13}{79}\\\\b)\\f(4t)=\dfrac{4(4t)+11}{3(4t)^2+5(4t)+1}=\dfrac{16t+11}{48t^2+20t+1}\\\\c)\\f(3-2a)=\dfrac{4(3-2a)+11}{3(3-2a)^2+5(3-2a)+1}=\dfrac{12-8a+11}{3(9-12a+4a^2)+15-10a+1}=\\\\=\dfrac{-8a+23}{27-36a+12a^2+16-10a}=\dfrac{-8a+23}{12a^2-46a+43}\)

33.

\(g(x)=\dfrac{3x^3}{x^2+x-4}\\\\a)\\g(-2)=\dfrac{3(-2)^3}{(-2)^2+(-2)-4}=\dfrac{3(-8)}{4-2-4}=\dfrac{-24}{-2}=12\\\\b)\\g(5x)=\dfrac{3(5x)^3}{(5x)^2+(5x)-4}=\dfrac{3(125x^3)}{25x^2+5x-4}=\dfrac{375x^3}{25x^2+5x-4}\\\\c)\\g(8-4b)=\dfrac{3(8-4b)^3}{(8-4b)^2+(8-4b)-4}=\dfrac{3[8^3-3\cdot8^2\cdot4b+3\cdot8\cdot(4b)^2-(4b)^3]}{64-64b+16b^2+8-4b-4}=\\\\=\dfrac{3(512-768b+384b^2-64b^3)}{16b^2-68b+68}=\dfrac{3\cdot4(128-192b+96b^2-16b^3)}{4(4b^2-17b+17)}=\\\\=\dfrac{384-576b+288b^2-48b^3}{4b^2-17b+17}\)

Answer:

Step-by-step explanation:

Var(x)  is equals to 13.

Variance is a measure of the spread or dispersion of a set of data from its mean. It is calculated by taking the differences between each data point and the mean, and then squaring the differences. The larger the variance, the more spread out the data is from the mean.

The formula for variance is Var(x) = E(x^2) - (E(x))^2.

Given that E(x) = 1, Var(x^2) = 5, and E(x^2) = 14, we can plug these values into the formula and solve for Var(x).

Var(x) = E(x^2) - (E(x))^2
Var(x) = 14 - (1)^2
Var(x) = 14 - 1
Var(x) = 13

Therefore, the variance of x is 13.

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The water in the aquarium tank will rise by 0.05 cm when the brick is placed in the bottom of the tank.

The volume of the brick is calculated as 40 cm x 20 cm x 10 cm = 8000 cm^3. Since the brick is submerged in the water, the amount of water displaced by the brick is equal to the volume of the brick. Therefore, the water level will rise by the same amount as the volume of the brick, which is \(8000 cm^3\).

To calculate the rise in water level, we need to divide the volume of the brick by the area of the rectangular base of the tank. The area of the rectangular base is calculated as 100 cm x 400 cm = \(40000 cm^2\). Dividing the volume of the brick (\(8000 cm^3\)) by the area of the rectangular base \(40000 cm^2\) gives us 0.2 cm. However, the brick is not placed at the bottom of the tank, but rather at a height of 40 cm. Therefore, we need to divide the calculated value by the height of the tank, which is 40 cm. This gives us a final result of 0.2 cm / 40 cm = 0.05 cm, which is the rise in water level when the brick is placed in the bottom of the tank.

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We can substitute back in for u to get our final terms of t:(2/3)(1 - t^10)^(3/2) + CThis is our final answer for the integral, with C representing the constant of integration.

To evaluate the integral, we will use substitution method. Let's begin by assigning a variable to the expression inside the square root. Let's assign u = 1 - t^10. Now, we can rewrite the integral in terms of u:\inttegral ^4 / sqrt. u duNow, we can use the power rule for integration to find the integral of this expression:\inttegral ^4 / sqrt. u du = \inttegral u^(-1/2) du = (2/3)u^(3/2) + CNow, we can substitute back in for u to get our final terms of t:(2/3)(1 - t^10)^(3/2) + CThis is our final answer for the integral, with C representing the constant of integration.

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Given statement solution is :- a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

a) Power set for two sets A and B with any 2 elements:

Set A: {1, 2}, Set B: {3, 4}

Power set of A: {{}, {1}, {2}, {1, 2}}

Power set of B: {{}, {3}, {4}, {3, 4}}

Set A: {apple, banana}, Set B: {cat, dog}

Power set of A: {{}, {apple}, {banana}, {apple, banana}}

Power set of B: {{}, {cat}, {dog}, {cat, dog}}

Set A: {red, blue}, Set B: {circle, square}

Power set of A: {{}, {red}, {blue}, {red, blue}}

Power set of B: {{}, {circle}, {square}, {circle, square}}

b) Power set for two sets A and B with any 3 elements:

Set A: {1, 2, 3}, Set B: {4, 5, 6}

Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}

Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}

Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}

Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}

Set A: {red, blue, green}, Set B: {circle, square, triangle}

Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}

Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}

c) Power set for two sets A and B with any 4 elements:

Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}

Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}

Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},

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The probability density function (pdf) of the largest of the five waiting times is given by: f(x) = 4/10^5 * x^4, where x is a real number between 0 and 10. The expected value of the largest of the five waiting times is 8.33 minutes.

The pdf of the largest of the five waiting times can be found by considering the order statistics of the waiting times. The order statistics are the values of the waiting times sorted from smallest to largest.

In this case, the order statistics are X1, X2, X3, X4, and X5. The largest of the five waiting times is X5.

The pdf of X5 can be found by considering the cumulative distribution function (cdf) of X5. The cdf of X5 is given by: F(x) = (x/10)^5

where x is a real number between 0 and 10. The pdf of X5 can be found by differentiating the cdf of X5. This gives: f(x) = 4/10^5 * x^4

The expected value of X5 can be found by integrating the pdf of X5 from 0 to 10. This gives: E[X5] = ∫_0^10 4/10^5 * x^4 dx = 8.33

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Answer:

180

Step-by-step explanation:

to work out all possibilities you multiple the amount of options.

4x5x9=180

Answer:

A = |A| = 5 units. We know, negative Y-axis is an angle 270° counterclockwise with positive X-axis. θ = Angle of vector A with positive X-axis = (270°

Step-by-step explanation:

points

(2,10), (3,15), and (4,20)

as x increases by 1, y increases by 5

rise / run

5 / 1, 5

slope is 5

IDFT can completely reproduce the input sequence.

Given data sequence (5, 2, -2, 4) and time interval [0, 1], we need to obtain the DFT of the data and then its IDFT.

Following is the DFT of the data sequence: [Image attached]

Following is the IDFT of the data sequence: [Image attached]

The input sequence of length N = 4 is given in the time interval [0, 21]. The values of the input sequence are given by a function f(x) = cos(t x = k t / N; k = 0, 1, 2, 3).

Following is the DFT of the input sequence: [Image attached]

Comparing the angular frequency represented by the original function giving the input sequence with the spectrum of angular frequencies obtained by DFT, we can see that both the graphs overlap perfectly. Hence, the input sequence can be completely represented by the given DFT and the spectrum of angular frequencies obtained by DFT.

The following is the IDFT of the input sequence: [Image attached]

We can observe that the IDFT and the original function match completely. Hence, the input sequence can be completely reproduced by IDFT.

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Answer: none of these

Step-by-step explanation:

They are not supplementary because 101+77 = 178 and not 180.

They are not complementary because 101+77 = 178 and not 90.

They are not vertical because there are no intersecting lines and the two angle measures are not equal.

Therefore, none of these are true.

Answer:

11i= √-1

Step-by-step explanation:

So first take 1 to the other side so we can leave the numbers with I on one section. So when we take 1 to the other side it becomes negative so 0-1 = -1. Since the 8 is squared to get rid of it were going to put a square root on the whole equation. √8i² + 9i = √-1 and we have to put the square root on the other side of the equation to make it equal. So on the other side we now have 8i + 3i *because the square root of 9 is 3* and then the -1 stays like that so its 11i= √-1 because we combine the 8i and 3i. Happy I could help!!!

The equation in point-slope form is y - 5 = (5/3)(x + 5). The general form of the equation is 5x - 3y + 40 = 0.

To find the equation of a line parallel to the given line and passing through the point (-5,5), we can use the point-slope form of a linear equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line. First, we need to find the slope of the given line, and then we can substitute the values into the point-slope form to obtain the equation. Additionally, we can convert the equation to the general form, which is Ax + By + C = 0, by rearranging the terms.

The given line has the equation 5x - 3y - 2 = 0. To find the slope of this line, we can rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope. Rearranging the equation gives us:

-3y = -5x + 2

y = (5/3)x - 2/3

From the equation, we can see that the slope of the given line is 5/3. Since the line we want to find is parallel to this line, it will have the same slope.

Now, using the point-slope form with the point (-5,5) and the slope 5/3, we can write the equation:

y - 5 = (5/3)(x - (-5))

y - 5 = (5/3)(x + 5)

This is the equation of the line in point-slope form.

To convert it to general form, we can multiply through by 3 to eliminate the fraction:

3y - 15 = 5x + 25

5x - 3y + 40 = 0

This is the equation of the line in general form.

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Answer:

74

Step-by-step explanation:

All the angles of a triangle add up to 180

66+40 = 106

To find the missing angle...

180-106 = 74

Answer:

ANGLE A=74

Step-by-step explanation:

LET ANGLE A BE X

ANGLE B=40°

ANGLE C=66°

SUM OF ADJACENT ANGLE IS 180°

SO, WHEN:

40+66+X=180

X=180-106

ANGLE A=74°

HAVE A NICE DAY!!

False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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The set of polynomials is not closed under division.

A set is said to be closed under an operation if the result of that operation on elements of the set is always an element of the set. For example, the set of natural numbers is closed under addition because the sum of two natural numbers is always a natural number.

In the case of polynomials, the set of polynomials is closed under addition, subtraction, and multiplication. This means that if you have two polynomials, you can add, subtract, or multiply them and the result will be another polynomial.

However, when it comes to division, the set of polynomials is not closed. When you divide two polynomials, the result is not always a polynomial. The result can be a polynomial plus some remainder. For example, dividing x^2 + 2x + 1 by x + 1 will give you x + 1 with a remainder of 1.

Therefore, the set of polynomials is not closed under division because the result of dividing two polynomials is not always a polynomial.

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The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

-6x + 2y = 8 ---(1)

y = 3x + 4 ---(2)

Substitute equation (2) into equation (1):

-6x + 2(3x + 4) = 8

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

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its just -1/2 tho or -0.5

It takes approximately 26.56 seconds for the ferris wheel to make one revolution.

so, the correct option is: e) 26.56 seconds

Here, we have,

The ferris wheel makes one complete revolution when the distance of the person above the ground returns to the original value after completing a full circle.

This occurs when the sine function returns to its maximum value, which is 1.

Thus, we have the following equation:

20 * sin(π/30 * t) + 10 = 20

Solving for t,

we will get:

sin(π/30 * t) = 0.5

Taking the inverse sine of both sides:

(π/30 * t) = sin^-1(0.5)

Multiplying both sides by 30/π,

we will get the following:

t = (30/π) * sin^-1(0.5)

Now solving the value of t

We will get it as: t ≈ 26.56 seconds.

so, the correct option is: e) 26.56 seconds

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complete question:

the distance from the ground of a person riding on a ferris wheel can be modeled by the equation d equals 20 times the sine of the quantity pi over 30 times t end quantity plus 10 comma where d represents the distance, in feet, of the person above the ground after t seconds. how long will it take for the ferris wheel to make one revolution?

a) 10 seconds

b) 20 seconds

c) 30 seconds

d) 60 seconds

e) 26.56 seconds

Answer:

3x + y = 19

Here to answer any questions as well

Answer:

6

Step-by-step explanation:

\(\sf 4-(-2)=4+2=\bf{6}\)

The answer is 6.

SOLUTION-

plotting on number line-

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