Find the inverse of the following functions. Assume we are using valid domains. Round numerical answers to two decimal places if needed. If f(x)=
3
2
​
x+4 then f
−1
(x)=x+ If g(x)=
x+8
​
then g
−1
(x)=x
2
+ x+

The value of x in the right triangle is 15√2.

A right triangle is a triangle that has one of its angles as 90 degrees.

The sides of a right triangle can be named base on the angle position. This includes hypotenuse side, opposite side and adjacent side.

Therefore, the side x of the right triangle can be found using trigonometric ratios as follows:

cos 45 = adjacent / hypotenuse

cos 45° = x / 30

cross multiply

30 cos 45° = x

Therefore,

x = 30 × 1 / √2

x =  30 / √2 × √2 / √2

x = 30√2 / 2

x = 15√2

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Answer:

1200?

Step-by-step explanation:

Answer: The Answer Is 23

Step-by-step explanation:

Answer:

the answer is 23,

Step-by-step explanation:

i took the test and got it right!!!

The area of the rectangular parking lot is 929.03 square meters.

Use the formula for the area of a rectangle to calculate the area of the rectangular parking lot, which is given as:

Area = length × width

We know that the parking lot is 67.5 ft wide and 148 ft long, the area can be calculated as follows:

Area = 67.5 ft × 148 f

t= 9990 sq. ft

However, the question asks for the area in square meters, so we need to convert square feet to square meters. 1 square foot is equal to 0.092903 square meters, so we can use this conversion factor to convert square feet to square meters.

Area in square meters = Area in square feet × 0.092903

= 9990 sq. ft × 0.092903

= 929.03 sq meters

Therefore, the area is 929.03 square meters.

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Answer:

12.04

Step-by-step explanation:

7) The transformation is a dilation by a scale factor of 1.5.

8) The transformation here is; Rotation 180° about the origin.

7) We are told that ABCG is transformed to KHIJ.

Coordinates of ABCG are;

A(-2, -3), B(0, 5), C(6, 0), G(1, -3)

Now, coordinates of KHIJ are;

K(-3, -4.5), H(0, 7.5), I(9, 0), J(1.5, -4.5)

Now, from the transformed shape, we see that its' coordinates are 1.5 times that of the original shape coordinates. Thus, we can say that the transformation is a dilation by a scale factor of 1.5.

8) We are told that ABC is transformed to KLJ.

Coordinates of ABC are;

A(-9, 8), B(-4, 7), C(-7, 1)

Now, coordinates of KLJ are;

K(9, -8), L(4, -7), J(7, -1)

It is clear that the transformation here is;

(x, y) → (-x, -y)

From transformation rules, we can say that the transformation here is;

Rotation 180° about the origin.

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Increasing the sample size for a chi-square test for independence, while holding other factors constant, increases the likelihood of rejecting the null hypothesis because as the sample size increases, the test becomes more sensitive to detecting small deviations from the expected frequencies.

In a chi-square test for independence, the null hypothesis assumes that there is no association between two categorical variables.

The test compares the observed frequencies in a contingency table to the expected frequencies under the assumption of independence. The chi-square test statistic measures the discrepancy between the observed and expected frequencies.

When the sample size is small, the test may not have enough power to detect a significant departure from the null hypothesis, even if such a departure exists in the population.

However, as the sample size increases, the test becomes more capable of detecting smaller deviations from independence, increasing the likelihood of rejecting the null hypothesis when there is a true association between the variables.

Therefore, increasing the sample size can improve the statistical power of the chi-square test and increase the likelihood of rejecting the null hypothesis, assuming other factors remain constant.

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The two best examples of long-term needs that people need to save for includes:

This refer to those needs that one will be will be needing in the future or for a very long time.

The need to saving up for college is important if one want to have a bright future or a better salary.

The need to saving up for medical emergencies is also crucial because we're all human beings who, at some point, will deteriorate physically.

Therefore, the Option A and C is correct,

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To determine the complex exponential Fourier series representation for each of the given signals, we can use the formula:

X(t) = ∑[n=-∞ to ∞] Cn * e^(jnω0*t)

where Cn represents the complex Fourier coefficients and ω0 is the fundamental frequency.

X(t) = cos(ωt):

The complex exponential Fourier series representation for X(t) = cos(ωt) is:

X(t) = C0 * e^(j0ω0t) + C1 * e^(j1ω0t) + C(-1) * e^(j*(-1)ω0t)

= C0 + C1 * e^(jω0t) + C(-1) * e^(-jω0t)

x(t) = -cos(0.5 * ωt):

The complex exponential Fourier series representation for x(t) = -cos(0.5 * ωt) is:

x(t) = C0 * e^(j0ω0t) + C0 * e^(j0ω0t) + C1 * e^(j1ω0t) + C(-1) * e^(j(-1)ω0t)

= C0 + C0 + C1 * e^(j0.5ω0t) + C(-1) * e^(-j0.5ω0t)

x(t) = cos(2t + 1):

The complex exponential Fourier series representation for x(t) = cos(2t + 1) is:

x(t) = C0 * e^(j0ω0t) + C2 * e^(j2ω0t) + C(-2) * e^(j*(-2)ω0t)

= C0 + C2 * e^(j2ω0t) + C(-2) * e^(-j2ω0t)

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Answer:

90 miles per hour is the average speed.

Step-by-step explanation:

The formula for Average Speed can be given as follows:

\(\text{Average Speed}= \dfrac{\text{Total Distance Traveled}} {\text{Total Time Taken}}\)

Here time taken is from 1 PM to 4 PM i.e.

Total Time taken = (4-1) hours = 3 hours

Also, it is given that the Total distance covered = 270 miles

As per the formula above:

\(\text{Average Speed} = \dfrac{270}{3}\\\Rightarrow \text{Average Speed} = 90\ miles/hour\)

So, answer is: 270 miles/ hour is the average speed of the train from Philadelphia to Boston.

Answer:

x- intercept = - 1, y- intercept = 2

Step-by-step explanation:

The x- intercept is where the graph crosses the x- axis

The graph crosses the x- axis at x = - 1 ← x- intercept

The y- intercept is where the graph crosses the y- axis

The graph crosses the y- axis at y = 2 ← y- intercept

Answer:

Angle BEA

Step-by-step explanation:

They share the same straight line and their degrees add to 180

Answer:

A vector graphic consists of a set of instructions for creating a picture is a true statement.

Step-by-step explanation:

A vector graphic is an image format that represents images as a set of mathematical instructions or geometric primitives such as lines, curves, and shapes. Instead of using a grid of pixels like raster graphics, vector graphics define images based on mathematical formulas and coordinates.

These instructions or mathematical representations describe the shapes, colors, and other visual attributes of the image. They allow the image to be scaled, resized, and manipulated without loss of quality since the instructions can be recalculated and redrawn at any resolution or size.

Vector graphics are often created and edited using specialized software such as Adobe Illustrator, CorelDRAW, or Inkscape. They are commonly used for logos, illustrations, diagrams, typography, and other graphical elements where scalability and flexibility are important.

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To represent the solution set of a linear equation parametrically, we introduce other parameters like s and t for the free variables.

Every linear equation has n - 1 free variables where n is the number of variables.

For x + y + z = 2, we have 3 variables and 3 - 1 = 2 free variables.

First, let y and z be the free variables, we first solve the linear equation for x to get:

x = 2 - y - z

Therefore , the parametric representation of the solution set is given by :

x = 2 - s -t

y = s

z = t

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Answer:

10.0625 pounds exactly. I'm assuming that's what this question is asking, or 161 ounces.

Step-by-step explanation:

First, multiply 7 by 23, we get 161 ounces. Assuming the question is asking for pounds, and then we divide by 16. As there are 16 ounces in a pound. 161/16 = 10.0625.

Not sure the rounding so this is the number you get from a calculator exactly.

The linear function is y = (-1/2)x + 4.

What is a linear function?

A linear function whose graph is a straight line and which is represented by an equation of the form y = ax + b where a and b are constants, a does not equal zero, and x is any real number.

Here, we have

Given,

A linear function has an x-intercept of 8 and a y-intercept of 4.

So, The two points on the line are (8, 0) and (0, 4).

Now, slope(m) = (4 - 0)/(0 - 8).

slope(m) = -4/8.

slope(m) = -1/2.

As it has a y-intercept of 4 it is the value of b, In y = mx + b.

Hence, the linear function is y = (-1/2)x + 4.

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The permutations of four objects m, I, n, and k taken two at a time without repetition are: mn, mk, mi, nm, nk, ni, km, kn, ki, in, im, ik.

P is the total number of permutations, which is equal to 12.

The correct answer is OB, which lists all 12 permutations.

P2 is the number of permutations taken two at a time with repetition allowed. This means that we can repeat the same object in a permutation.

There are 16 possible permutations with repetition allowed: mm, ml, mn, mk, ll, ln, lk, nn, nk, kk, ii, ik, nn, ni, nk.

Therefore, P2 is equal to 16.

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Answer:

x=-9 mark me brainliest

Step-by-step explanation:

Answer:

no it is not possible

Step-by-step explanation:

Answer:

S=2t

or

T=1/2 S

Answer:

f(x) = x² + 8 - 16x

= x² - 16x + 8

= (x² - 16x + 64) - 64 + 8

= (x - 8)² - 56

Answer:

A.    f(x) = (x – 8)2 – 56

Step-by-step explanation:

so much for expert verified, huh.. -_-

Answer:

I really don't know sorry

The value of the missing leg using Pythagoras theorem is 12.5.

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“

To calculate the missing leg, we use Pythagoras theorem.

Where:

Substitute these values into equation 1 and solve for c

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Answer: The value of x is 7

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

x= -2

Answer:

• The amount invested at 6% is $1,150.

• The amount invested at 12% is $1,750.

Explanation:

Let the amount invested at 6% = x

Kelvin has $600 more in the 12% account, therefore:

The amount invested at 12% = $(x+600).

The total interest is $279.

We solve the equation for x.

The amount invested at 6% is $1,150.

The amount invested at 12% is:

The amount invested at 12% is $1,750.

The probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

Let's use the following notation:

P(TB) represents the probability that an adult has tuberculosis, which is given as 0.05.

P(POS|TB) represents the probability that the test is positive given that an adult has tuberculosis, which is given as 0.746.

P(NEG|TB) represents the probability that the test is negative given that an adult has tuberculosis, which is 1 - P(POS|TB) = 0.254.

We are asked to find the probability of an adult getting a NEG result and truly having tuberculosis, which can be calculated using Bayes' theorem as follows:

P(TB|NEG) = P(NEG|TB) * P(TB) / P(NEG)

We can calculate P(NEG) using the law of total probability, which considers the two possible cases for an adult: having tuberculosis (TB) or not having tuberculosis (TB').

P(NEG) = P(NEG|TB) * P(TB) + P(NEG|TB') * P(TB')

= 0.254 * 0.05 + 0.7653 * 0.95

= 0.7352

Now we can substitute the values into Bayes' theorem:

P(TB|NEG) = 0.254 * 0.05 / 0.7352

= 0.01725

Therefore, the probability of an adult getting a NEG result and truly having tuberculosis is 0.01725, which is closest to option (A) 0.0373.

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E(y) = Var(y) for a Poisson distribution, the variance of y is equal to the value of E(y) .

To calculate the variance of y, follow these steps:

Recall that for a Poisson distribution, the mean (first moment) is equal to the variance. So, if the first moment of x is less

than the first moment of y by 8, we can write: E(x) = E(y) - 8.

We are also given that the second moment of x is 60% of the second moment of y:

\(E(x^2) = 0.6 × E(y^2).\)

Recall that for a Poisson distribution, the second moment is given by \(E(X^2) = E(X)² + E(X)\). Thus, we can write equations

for x and y using this relationship: \(E(x^2) = E(x)² + E(x) and E(y^2) = E(y)² + E(y).\)

Plug the expressions from step 1 into the equation from  \(E(x^2) = (E(y) - 8)² + (E(y) - 8).\)

Plug the expressions from step 2 into the equation from\(0.6 × E(y^2) = (E(y) - 8)² + (E(y) - 8).\)

Solve for \(E(y^2)\) from the equation in  \(E(y^2) = (10/6) × ((E(y) - 8)² + (E(y) - 8)).\)

Substitute \(E(y^2)\) back into the equation for the second moment of y from \(E(y^2) = E(y)² + E(y).\)

Solve for E(y) from the equation in

Since E(y) = Var(y) for a Poisson distribution, the variance of y is equal to the value of E(y) .

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