if f(8)=2, find f^-1(2)

To solve an equation we need to isolate the unkown variable on the left side. To do that we will have to switch terms from one side to another of the equality, this is done by inverting its operations. If the term is adding it'll go to the other side by subtracting and if it is multiplying it will go to the other side by dividing, the oposite is also true.

With this in mind lets solve the expression.

The value of "x" in this expression is 5.

Answer:

3

Step-by-step explanation:

The slope is rise/run and for this case, it is 3/1 which equals 3!!!

Answer:

38

Step-by-step explanation:

Answer:

The integers are -3 and -4.

Step-by-step explanation:

Two consecutive integers are an integer and the one just greater or just less than the4 first one, such as 5 and 6, or -8 and -9.

If the smaller integer is x, then the next greater integer is x + 1.

x + 1 = 4x + 13

-3x = 12

x = -4

x + 1 = -3

Answer: The integers are -3 and -4.

Check:

Smaller integer: -4

Larger integer: -3

4 times smaller integer = 4 * (-4) = -16

13 greater than 4 times smaller = -16 + 13 = -3 = greater integer

-3 and -4 is the correct answer.

Answer:

-3 and -4

They are indeed correct.

The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

The proportion of voters that approve the mayor's work is of 70%.

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The variance of first n even natural numbers is n²-1/12. So, the correct option is (a) .

The first n even natural numbers can be represented as 2, 4, 6, ..., 2n. The mean or expected value of this sequence is given by:

mean = (2 + 4 + 6 + ... + 2n) / n

= 2(1 + 2 + 3 + ... + n) / n

= 2n(n+1)/2n

= n+1

The variance of a sequence is the average of the squared differences from the mean, so we need to calculate:

Var = [(2- (n+1))² + (4- (n+1))² + (6- (n+1))² + ... + (2n- (n+1))²] / n

Simplifying the expression inside the brackets and using the formula for the sum of the first n integers, we get:

Var = [4(1² + 2² + 3² + ... + n²) - 4(n+1)(1 + 2 + 3 + ... + n) + n(n+1)²] / n

Substituting the formula for the sum of the first n squares and the sum of the first n integers, we get:

Var = [4n(n+1)(2n+1)/6 - 4(n+1)n(n+1)/2 + n(n+1)²] / n

Simplifying and factoring out (n+1), we get:

Var = (n+1)(n² - 1) / 3

Thus, the correct option is (a) n²-1/12.

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Answer:bread?

Step-by-step explanation:

Part A: The factored expression is 8x(5x - 2)

Part B: The expression is 4x - 16

Note that algebraic expressions are described as expressions that consists of coefficients, factors, constants, terms and variables.

They are also made up of arithmetic operations such as addition, subtraction, bracket, parentheses, multiplication and division

From the information given, we have that;

40x² and 16x

40x² - 16x

factorize the values

8x(5x - 2)

To add the expressions;

(10x+8) - 3(2x + 8)

expand the bracket, we have;

10x + 8 - 6x - 24

collect the like terms

4x - 16

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The probability that a randomly selecting a college student at Washington who either a male or a female is 33.3%

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).

Subjective Probability. Definition of Relative Frequency.

Considering there are males, females and other genders

The probability that a randomly selecting a college student at Washington who either a male or a female is 33.3%

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The coordinates of Point A are (2, -7). To find the coordinates of Point B, we need to reflect Point A across the y-axis.

When we reflect a point across the y-axis, the x-coordinate changes its sign while the y-coordinate remains the same. So, the x-coordinate of Point B will be the opposite of the x-coordinate of Point A, and the y-coordinate of Point B will be the same as the y-coordinate of Point A.

Therefore, the coordinates of Point B will be (-2, -7). Point B is located 2 units to the left of the y-axis, with the same y-coordinate as Point A.

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Answer:

the market price of the sprinter is 597.06

Answer:

x = 1.27

y = 5.18

Step-by-step explanation:

to solve this system of  equation by simultaneous equation we say that let

3x+y=9.............................. equation 1

-5x+2y=4 .......................... equation 2

from equation 1

3x+y=9.............................. equation 1

y = 9 -3x.............................. equation 3

substitute the value of y = 9 -3x into equation 2

-5x+2y=4 .......................... equation 2

-5x + 2( 9 -3x) = 4

-5x + 18 - 6x = 4

collect the like terms

18 - 4 = 6x + 5x

14 = 11x

divide both side by 11

14/11 = 11x/11

x = 14/11

x = 1.27

put the value of x = 1.27 into  equation 3

y = 9 -3x.............................. equation 3

y = 9 - 3( 1.27)

y = 9 - 3.82

y = 5.18

to check if you are correct put the value of x and y into either equation 1 or equation 2.

3x+y=9.............................. equation 1

3( 1.27) + 5.18 = 9

3.81 + 5.18 = 9

9 = 9

The 19th percentile of x bar is 71.724.

Since the sample size is greater than 30 and the population standard deviation is known, we can use the normal distribution to find the 19th percentile of x bar.

First, we need to find the standard error of the mean (SEM):

SEM = σ/√n = 8/√50 = 1.1314

Next, we need to find the z-score associated with the 19th percentile. We can use a standard normal distribution table or a calculator to find this value, which is approximately -0.877.

Finally, we can use the formula for a confidence interval to find the value of x bar associated with the 19th percentile:

x bar = μ + z*SEM = 73 + (-0.877)*1.1314 = 71.724

Therefore, the 19th percentile of x bar is approximately 71.724.

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The equation of the line that passes through the points (2, 1 ) and (4,5) in the Cartesian coordinate plane is y = (2/3)(x - 4) + 5.

By subtracting the y coordinates [5 - 1] = 4, we get

Subtract the x coordinates in the same order  [4 - (-2)]  = [4 + 2] = 6

The slope is given by  y-coordinate/x-coordinate = 4/6  = 2/3.

Now, just choose one point say (4,5), and substitute the coordinates in this formula-

y - [y-coordinate of our point] - (slope)* [ x - ( the  x-coordinate of our point)]

y - 5  = (2/3)(x - 4)      ...........(adding 5 to both sides)

y = (2/3)(x - 4) + 5    

Hence, the equation of the line in the "slope-intercept" form is y = (2/3)(x - 4) + 5.

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The complete question is -

what is the equation of the line that passes through the points (-2,1) and (4,5) in the cartesian coordinate plane?

Answer:

11

Step-by-step explanation:

Here, we replace x and y with the values given that x = 6 and y = 2:

=\(\frac{3(6)+4}{(2)}\)

= \(\frac{18+4}{2}\)

=\(\frac{22}{2}\)

=11

Answer:

B

Step-by-step explanation:

44/77

=0.55

The critical numbers of the function h(p) = (p - 1) / (p^2 - 5) are "dne" (does not exist).

To find the derivative of h(p), we can apply the quotient rule. Taking the derivative, we have:

h'(p) = \([(p^2 - 5)(1) - (p - 1)(2p)] / (p^2 - 5)^2\)

Simplifying this expression, we get:

h'(p) = \((p^2 - 5 - 2p^2 + 2p) / (p^2 - 5)^2\)

= \((-p^2 + 2p - 5) / (p^2 - 5)^2\)

To find the critical numbers, we set h'(p) equal to zero and solve for p:

\(-p^2 + 2p - 5 = 0\)

However, this quadratic equation does not factor easily. We can use the quadratic formula to find the solutions:

p = (-2 ± √\((2^2 - 4(-1)(-5))) / (-1)\)

p = (-2 ± √(4 - 20)) / (-1)

p = (-2 ± √(-16)) / (-1)

Since the discriminant is negative, the equation has no real solutions. Therefore, the critical numbers of the function h(p) = (p - 1) / (\(p^2\) - 5) are "dne" (does not exist).

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In this problem, we are given the median score for an exam, which is 84%, and the standard deviation of the scores, which is 6%.

a) To find the score above which we would expect 2.5% of the students to score, we can use the concept of the standard normal distribution. First, we need to find the z-score corresponding to the 2.5th percentile, which is -1.96. Using the formula z = (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation, we can rearrange the formula to solve for x. Plugging in the values, we have -1.96 = (x - 84) / 6. Solving for x, we find x ≈ 73.24. Therefore, we would expect 2.5% of the students to score above approximately 73.24%.

b) To determine the percentage of students expected to score below 78%, we can again use the concept of the standard normal distribution. First, we find the z-score corresponding to the 78th percentile, which is approximately -1.33. Using the same formula as before, we can solve for x: -1.33 = (x - 84) / 6. Solving for x, we find x ≈ 76.02. Therefore, we would expect approximately 76.02% of the students to score below 78%.

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The one-sample z-statistic for evaluating the hypothesis that unvaccinated people get COVID-19 is not 0.03 is -85.7. This statistic tested the hypothesis that unvaccinated people do not get COVID-19 at 0.03%.

In order to compute the one-sample z-statistic, we must first do a comparison between the observed proportion of COVID-19 instances in the placebo group and the expected proportion of 0.03. (p - p0) / [(p0(1-p0)) / n is the formula for the one-sample z-statistic. In this formula, p represents the actual proportion, p0 represents the predicted proportion, and n represents the sample size.

The observed proportion of COVID-19 instances among those who received the placebo is 162/18325 less than 0.0088. According to the received wisdom, the proportion that should be anticipated is 0.03. The total number of people sampled is 18325. After entering these numbers into the formula, we receive the following results:

z = (0.0088 - 0.03) / √[(0.03(1-0.03)) / 18325] ≈ (-0.0212) / √[(0.0291) / 18325] ≈ -85.7

As a result, the value of the z-statistic for just one sample is about -85.7. This demonstrates that the observed proportion of COVID-19 cases in the unvaccinated population is significantly different from the expected proportion of COVID-19 cases in that population.

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Required value of s(4), s(7), s(5), s(9) are V(4) + C, V(7) + C, V(5) + C, V(9) + C respectively where c is the constant.

To determine the values of s(t) at different time points, we need to integrate the velocity function v(t) with respect to time. Based on the values you provided, it seems like you have already performed the integration correctly. However, since the values you provided are the definite integrals, we need to find the antiderivative or the indefinite integral of the velocity function to determine s(t) explicitly.

Let's assume the indefinite integral of v(t) is V(t). Then, we have:

s(t) = V(t) + C

where C is the constant of integration. To determine the constant C, we can use the initial condition s(0) = -3. Substituting t = 0 into the equation, we get:

s(0) = V(0) + C

-3 = V(0) + C

Since the constant of integration is the only unknown term, we can solve for C:

C = -3 - V(0)

Now, we can find the position function s(t) for different values of t using the indefinite integral and the constant C:

s(4) = V(4) + C

s(7) = V(7) + C

s(5) = V(5) + C

s(9) = V(9) + C

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Answer:

7 cajas grandes y 3 cajas pequeñas  

Step-by-step explanatio:

Answer:

157

Step-by-step explanation:

The answer is B. The cubed root of -12 is -2.28942848511. That is in between -2 and -3.

Answer: B) -2 and -3

Step-by-step explanation:

the cube root of -12 is about -2.2 which is between -2 and -3.

Substance Gallons         % Fruit Juice

Drink A              x                         20%

Drink B              y                          5%

Total         x + y = 30                  10%

To find the number of gallons of Drink A and Drink B that should be used, we can write two equations based on the percentage of fruit juice.

20% * x = 10% * (x + y)

5% * y = 10% * (x + y)

Simplifying and solving for x and y:

x = 1.5 * y

10% * (x + y) = 10% * 30

y = 15

x = 1.5 * 15 = 22.5

So, we would use 22.5 gallons of Drink A and 15 gallons of Drink B to make a 30 gallon mixture that is 10% fruit juice.

The equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

To find the equation of the line perpendicular to the tangent to the curve at (2,1), we need to first find the slope of the tangent line at that point.

The derivative of y=x^3-4x+1 is y'=3x^2-4, so the slope of the tangent line at (2,1) is y'(2) = 3(2)^2-4 = 8.

Since we want the line perpendicular to the tangent, we know that its slope will be the negative reciprocal of the tangent's slope. Therefore, the slope of the line we're looking for is -1/8.

Next, we use the point-slope form of the equation of a line to write the equation of the line with the slope we found and passing through the point (2,1):

y - 1 = (-1/8)(x - 2)

Simplifying and putting the equation in slope-intercept form:

y = (-1/8)x + 9/8

Therefore, the equation of the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1) is y = (-1/8)x + 9/8.

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Answer:

105⁰

Step-by-step explanation:

Please refer to the attachment.

Hope it helps :)

Based on the rate of decrease and the acres of undeveloped land, the equation to determine the number of years till 900 acres is remaining is B)900 = 3,400(0.827)^t.

As 900 acres is the target number of acres to remain, this will be on the left side of the equation as the y value.

The right side of the equation would be:

= Current number of acres remaining x ( 1 - rate of decrease) ^ number of years

= 3,400 x ( 1 - 17.3%) ^ number of years

Putting them together:

900 = 3,400(0.827)^t.

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To find articles about LeBron James in the NBA finals, Alison should type relevant keywords in her search window. She can use the following terms: "LeBron James," "NBA finals," "basketball," and "sports."

By using these terms, she can filter the results that appear on her screen. Alison can also add other details to her search window to narrow down her search further

.For instance, she can add the year of the NBA finals that LeBron James participated in. For instance, "LeBron James in NBA finals 2021". Additionally, Alison can type the name of the newspaper, magazine, or website she wants to browse.

This tactic ensures that she can find relevant articles from trusted sources. Furthermore, Alison can use search filters such as dates and locations to ensure she finds the most recent articles about LeBron James in the NBA finals.

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First, let's identify the coordinates of the vertices of rhombus WXYZ:
W(1,5), X(6,3), Y(1,1), and Z(4,3)

Now, we will perform a reflection over the x-axis. To do this, we simply need to negate the y-coordinate of each vertex while keeping the x-coordinate the same.

Step-by-step:

1. Reflect point W(1,5):
  The x-coordinate stays the same: 1
  Negate the y-coordinate: -5
  New coordinates for W': W'(1,-5)

2. Reflect point X(6,3):
  The x-coordinate stays the same: 6
  Negate the y-coordinate: -3
  New coordinates for X': X'(6,-3)

3. Reflect point Y(1,1):
  The x-coordinate stays the same: 1
  Negate the y-coordinate: -1
  New coordinates for Y': Y'(1,-1)

4. Reflect point Z(4,3):
  The x-coordinate stays the same: 4
  Negate the y-coordinate: -3
  New coordinates for Z': Z'(4,-3)

The coordinates of the image of rhombus WXYZ under the reflection in the x-axis are W'(1,-5), X'(6,-3), Y'(1,-1), and Z'(4,-3).

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