Solve for v.
-8 = v + 4

ƒ^(-1)(ƒ(x)) ≠ x. In conclusion, we have found the inverse function of ƒ(x) = x^2 - 7 for x ≥ 0 to be ƒ^(-1)(x) = √(x + 7). However, it does not satisfy the property of ƒ^(-1)(ƒ(x)) = x for all values of x

To find the inverse function of ƒ(x) = x^2 - 7 for x ≥ 0, we can follow these steps:

Step 1: Replace ƒ(x) with y:

y = x^2 - 7

Step 2: Swap x and y:

x = y^2 - 7

Step 3: Solve for y:

x + 7 = y^2

√(x + 7) = y

Step 4: Replace y with ƒ^(-1)(x):

ƒ^(-1)(x) = √(x + 7)

Now, let's verify the inverse function:

To verify ƒ(ƒ^(-1)(x)) = x:

ƒ(ƒ^(-1)(x)) = (√(x + 7))^2 - 7

ƒ(ƒ^(-1)(x)) = (x + 7) - 7

ƒ(ƒ^(-1)(x)) = x

Therefore, we have verified that ƒ(ƒ^(-1)(x)) = x.

Now, let's verify ƒ^(-1)(ƒ(x)) = x:

ƒ^(-1)(ƒ(x)) = ƒ^(-1)(x^2 - 7)

ƒ^(-1)(ƒ(x)) = √(x^2 - 7 + 7)

ƒ^(-1)(ƒ(x)) = √x^2

ƒ^(-1)(ƒ(x)) = |x|

The result is the absolute value of x, which is not equal to x for all values of x.

Therefore, ƒ^(-1)(ƒ(x)) ≠ x.

In conclusion, we have found the inverse function of ƒ(x) = x^2 - 7 for x ≥ 0 to be ƒ^(-1)(x) = √(x + 7). However, it does not satisfy the property of ƒ^(-1)(ƒ(x)) = x for all values of x.

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Answer:

r=3.25

Step-by-step explanation:

3 divided by 0.5=6

6-2.75=3.25

r=3.25

Answer:

r = 3.25

Step-by-step explanation:

Isolate the variable, r. Note the equal sign, what you do to one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& roots)

Multiplications

Divisions

Additions

Subtractions

~

First, divide 0.5 from both sides of the equation:

(0.5(r + 2.75))/0.5 = (3)/0.5

r + 2.75 = 3/0.5

r + 2.75 = 6

Next, subtract 2.75 from both sides of the equations:

r + 2.75 (-2.75) = 6 (-2.75)

r = 6 - 2.75

r = 3.25

r = 3.25 is your answer.

~

The probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

Given that Edward works as a waiter, where his monthly tip income is normally distributed with a mean of $2,000 and a standard deviation of $350.

The z score formula is given by;`z = (x - μ) / σ`

Where; x is the raw scoreμ the mean of the populationσ is the standard deviation of the population.

The probability that Edward’s monthly tip income exceeds $2,350 is to be found.`z = (x - μ) / σ``z = (2350 - 2000) / 350``z = 1`

The value of z is 1.

To find the area in the right tail, use the standard normal distribution table.

The table value for z = 1.0 is 0.8413.

Therefore, the probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

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To determine the z-score(s) that cover the "middle 98%" of the normal curve and represent the 98% confidence level (CL), we can use the properties of the standard normal distribution.

The "middle 98%" refers to the area under the normal curve between the z-scores that enclose the central 98% of the distribution. In a standard normal distribution, the mean is 0 and the standard deviation is 1.

Since the distribution is symmetric, we need to find the z-score(s) that correspond to the area of (1 - 0.98) / 2 = 0.01 on each tail of the distribution. The remaining 0.02 is split equally between the two tails.

To find the z-score(s), we can use a standard normal distribution table or a calculator.

Looking up the value of 0.01 in the z-table, we find that the z-score that corresponds to the lower tail is approximately -2.33. This means that 1% of the area lies to the left of z = -2.33.

To find the z-score for the upper tail, we use the symmetry of the distribution. The z-score that corresponds to the upper tail is the negative of the z-score for the lower tail, so it is approximately 2.33.

Therefore, the z-scores that cover the "middle 98%" of the normal curve and represent the 98% confidence level (CL) are approximately -2.33 and 2.33.

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Answer:

you dont really need calculations for this exercise, you just need to think a little logic to find the right answer

Step-by-step explanation:

D. impossible

After Wednesday comes Thursday

B. Certain

After summer comes autumn

E. Evens

they're 3 prime numbers from 1 to 6

A. Likely

there are no numbers smaller than 1 on a dice, the only number that could not be bigger than 1 is 1 itself

C. Unlikely

a leap happens once a 4 years so the chance is 1/4

The vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.

To determine if the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly independent, we need to find the scalars a, b, and c that satisfy the equation:

a * [-5 4 5] + b * [2 -1 5] + c * [-17 16 45] = [0 0 0]

If the only solution is a = b = c = 0, the vectors are linearly independent. If there are other solutions where a, b, and c are not all zero, the vectors are linearly dependent.

Let's form a matrix with these vectors as columns:

|-5  2 -17|
| 4 -1  16|
| 5  5  45|

Now, we can row reduce this matrix to its reduced row echelon form (RREF):

| 1 -2  5|
| 0  1 -3|
| 0  0  0|

From the RREF, we can write the system of linear equations:

x - 2y + 5z = 0
y - 3z = 0

Solving this system, we get:

y = 3z
x = 2y - 5z = 6z - 5z = z

Since z can be any scalar, we have infinitely many solutions where not all of a, b, and c are zero. For example, when z = 1, we get x = 1 and y = 3. So, the scalars (1, 3, 1) make the equation true.

Thus, the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.

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Answer:

Step-by-step explanation:

3 inches is 2 feet

10 inches is 6.66 feet (no this isn't a joke)

A histogram is a univariate display of quantitative data that organizes data into bins and shows the frequency of observations within each bin.


A histogram is a graphical representation that displays the distribution of quantitative data. It consists of a series of contiguous bars, where each bar represents a specific range or bin of values, and the height of the bar corresponds to the frequency or count of observations falling within that range.

Histograms are commonly used to visualize the shape, central tendency, and spread of a dataset. By examining the heights of the bars, one can determine the frequency of values within each bin and identify patterns such as peaks or clusters. This makes histograms an effective tool for exploring the distribution and characteristics of a single variable in a dataset.

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the answer is an percent

To determine the distance between two points in a rectangular coordinate system, we can use the distance formula. Given the coordinates of the points (4.8, 2.5) and (-3.2, 5.0), we can calculate the distance as follows:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values, we get:

Distance = √((-3.2 - 4.8)^2 + (5.0 - 2.5)^2)

Simplifying further:

Distance = √((-8)^2 + (2.5)^2)

Distance = √(64 + 6.25)

Distance = √70.25

Distance ≈ 8.38 centimeters

Therefore, the distance between the points (4.8, 2.5) and (-3.2, 5.0) is approximately 8.38 centimeters.

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Answer:

Y=11x+7

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The graph starts from 55 and stops at 65 and the only answer that is between that range is D.

Hope it helps:-)

To find the maximum likelihood estimator (MLE) for λ, we need to maximize the likelihood function L(λ) with respect to λ of the Poisson distribution

First, let's write the probability density function (PDF) of the Poisson distribution:
P(X = k) = (e^(-λ) * λ^k) / k!

The likelihood function can be defined as the product of the probabilities for each observation in the random sample. Since the sample is independent and identically distributed, we can write the likelihood function as:
L(λ) = P(x1, x2, ..., xn | λ) = P(x1 | λ) * P(x2 | λ) * ... * P(xn | λ)

Taking the logarithm of the likelihood function (log-likelihood) will simplify the calculations. The log-likelihood function is:
log(L(λ)) = log(P(x1 | λ)) + log(P(x2 | λ)) + ... + log(P(xn | λ))

Now, let's calculate the derivative of the log-likelihood function with respect to λ:
d/dλ log(L(λ)) = d/dλ (log(P(x1 | λ)) + log(P(x2 | λ)) + ... + log(P(xn | λ)))
= d/dλ (log(P(x1 | λ))) + d/dλ (log(P(x2 | λ))) + ... + d/dλ (log(P(xn | λ)))

To find the MLE, we set the derivative equal to zero and solve for λ:
d/dλ log(L(λ)) = 0

The derivative of log(P(x | λ)) with respect to λ can be calculated using the logarithmic differentiation technique. After taking the derivative, we equate it to zero and solve for λ.

By solving the equation, we will obtain the MLE for λ.

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Answer:

12.73 mins

Step-by-step explanation:

velocity: 9.9 mi/h

distance: 2.1 mi

d=vt

t = d/v = 2.1/9.9 = 0.21h

convert to minutes: 2.1/9.9 x 60 = 12.73 min

It is given that a set of real numbers s is non-empty and bounded. The objective is to prove that inf s ≤ sup s. This statement can be justified as below.

Firstly, as per the definition of bounded set, it is known that the set s has both lower and upper bounds. Thus, the infimum and supremum of s exist and are denoted as inf s and sup s, respectively.

Since s is non-empty and bounded, it can be observed that every element of the set s is greater than or equal to inf s and less than or equal to sup s.

Therefore, inf s is the greatest lower bound of s and sup s is the least upper bound of s, implying that inf s ≤ sup s. Hence, it is proven that inf s ≤ sup s for a non-empty set s of real numbers that is bounded.

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Answer:

\(\boxed {\tt h=20\ inches}\)

Step-by-step explanation:

The volume of a rectangular prism can be found using the following formula.

\(v=l*w*h\)

We know that the volume is 12,090 cubic inches, the length is 31 inches, and the width is 19.5 inches.

\(v= 12,090 \ in^3\\l=31 \ in \\ w=19.5 \ in\)

\(12,090 \ in^3= 31 \ in * 19.5 \ in * h\)

Multiply 31 inches and 19.5 inches.

\(12,090 \ in^3= 604.5 \ in^2 * h\)

We are trying to find h, therefore we must isolate it. h is being multiplied by 604.5 square inches. The inverse of multiplication is division. Divide both sides of the equation by 604.5 in²

\(\frac{12,090 \ in^3}{604.5 \ in^2}= \frac{604.5 \ in^2 *h}{604.5 \ in^2}\)

\(\frac{12,090 \ in^3}{604.5 \ in^2}=h\)

\(20 \ in =h\)

The height of the shopping basket is 20 inches.

Answer:

81.5

Step-by-step explanation:

<G and <H are congruent

<F and <I are congruent

so the last two angles in both triangles must also be congruent

this means that <K and <J are congruent

so we can create this equation: <K = <J

substitute the angles with what we know: 4\(y^{2}\) = 6\(y^{2}\) - 40

add 40 to both sides and subtract 4\(y^{2}\) from both sides: 40 = 2\(y^{2}\)

you get: 20 = \(y^{2}\)

root square on both sides: \(\sqrt{20}\) = \(\sqrt{y^{2} }\)

you get: y ≈ 4.5

substitute this into one of the equations for a missing variable:

6\(y^{2}\) -----> 6 (4.5 x 4.5) - 40

6 ( 20.25) - 40

121.5 - 40

81.5

Answer:

The other length would be 6.

Step-by-step explanation:

Rectangle area is l times height. So x is either the length for height. So we have 5 times x = 30. To find the other length we have to take 30/5 which equals 6

Answer: Therefore, the truck is 240 inches long.

Step-by-step explanation:

truck = 150 + 60% of 150

        = 150 + 60/100 * 150

        = 150+90

        = 240 inches

Using the triangle sum theorem, x = 7 and y = 18.

The theorem that says that all the interior angles of a triangle will be equal to 180 degrees is referred to as the triangle sum theorem.

In the diagram given, since vertical angles are congruent, therefore:

(11x - 9) + (6x - 2) + 72 = 180 [triangle sum theorem]

Solve for x

11x - 9 + 6x - 2 + 72 = 180

17x + 61 = 180

17x = 180 - 61

17x = 119

x = 7

Also,

(5y - 8) + (11x - 9) + 30 = 180 [triangle sum theorem]

5y - 8 + 11x - 9 + 30 = 180

5y + 13 + 11x = 180

Plug in the value of x

5y + 13 + 11(7) = 180

5y + 13 + 77 = 180

5y + 90 = 180

5y = 180 - 90

5y = 90

y = 90/5

y = 18

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The volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane is V = xyz, where x, y, and z are the lengths of the sides of the rectangular box.

To find the largest volume, we need to maximize x, y, and z. Since we have three faces in the coordinate planes, one vertex will be at the origin (0, 0, 0). The other two vertices will lie on the coordinate axes.

Let's assume the vertex on the x-axis is (x, 0, 0), and the vertex on the y-axis is (0, y, 0). The third vertex on the z-axis will be (0, 0, z). Since the box is in the first octant, all the coordinates must be positive.

To maximize the volume, we need to find the maximum values for x, y, and z within the constraints. The maximum values occur when the box touches the coordinate planes. Therefore, the maximum values are x = y = z.

Substituting these values into the volume formula, we get V = xyz = x³. Therefore, the volume of the largest rectangular box is V = x³.

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What is the maximum volume of a rectangular box situated in the first octant, with three of its faces lying on the coordinate planes, and one of its vertices located in the plane?

The answer to your question is that the random variable x represents the index of the first occurrence of a success domain (i.e., y with value 1) in the sequence of Bernoulli random variables.

let's break down the components of the question. A Bernoulli random variable is a type of discrete probability distribution that represents the outcome of a single binary event (e.g., success or failure). In this case, each yi is a Bernoulli random variable, which means it can take on one of two possible values: 1 (success) or 0 (failure).

The random variable x is defined as the index of the first occurrence of a success in the sequence of yi random variables. For example, if y1 = 0, y2 = 1, y3 = 0, y4 = 0, y5 = 1, then x would equal 2, since y2 is the first yi with a value of 1. To calculate the value of x, we need to examine each yi in the sequence until we find the first success. Once we find the first success, we record the index of that yi as the value of x and stop examining subsequent yis. This means that x can only take on integer values from 1 to infinity (since there may be no successes in the sequence).

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Answer:

66

Step-by-step explanation:

B is 57

C is 57

180 - (57 x 2) =

180 - 114 = 66

- Mean: 119.43- Median: 118.50- Mode: 110 - Count: 28

To find the mean, we add up all the values and divide by the number of observations. In this case, the sum of the values is 3342, and since there are 28 observations, the mean is 3342/28 = 119.43.

The median is the middle value when the data is arranged in ascending order. In this case, there are 28 observations, so the median is the average of the 14th and 15th values. When the data is ordered, the 14th value is 118 and the 15th value is 124. Therefore, the median is (118 + 124)/2 = 118.50.

The mode is the value that appears most frequently in the dataset. In this case, the value 110 appears three times, which is more than any other value. Hence, the mode is 110.

The count simply refers to the number of observations in the dataset, which is 28 in this case.

(b) The data is skewed right.

When data is symmetric, it means that the values are evenly distributed around the mean, resulting in a bell-shaped curve. In this case, the data is not symmetric. Looking at the dataset, we can observe that there are several smaller values on the left side, while the right side has a few larger values. This indicates a right skew or positive skewness.

Skewness refers to the asymmetry of a distribution. In a right-skewed distribution, the tail of the distribution extends towards the right, indicating a longer right tail. Therefore, the correct answer is b. Skewed right, indicating that the data is positively skewed.

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9514 1404 393

Answer:

  15/22 peso/m^2 ≈ 0.68182 peso/m^2

Step-by-step explanation:

The area is the product of the dimensions. 1 km = 1000 m.

  A = (550 m)(550·1000 m) = 302,500,000 m^2

The price per square meter is ...

  206,250,000/302,500,000 peso/m^2

  = 15/22 peso/m^2 ≈ 0.68182 peso/m^2

The statistical measurement that informs a CTRS about how well the assessment results compare to what is being measured is Construct validity.

Construct validity assesses how well the assessment measures the intended construct or trait, and compares the results to other tests or measures of the same construct to determine how accurate and reliable the assessment is.

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For proof of 3 divisibility, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

The proof for divisibility of 3 implies that an integer is divisible by 3 if the sum of the digits is a multiple of 3.

111 = 1 + 1 + 1 = 3  (the sum is multiple of 3 = 3 x 1)  (111/3 = 37)

222 = 2 + 2 + 2 = 6 (the sum is multiple of 3 = 3 x 2)  (222/3 = 74)

213 = 2 + 1 + 3 = 6 ( (the sum is multiple of 3 = 3 x 2)  (213/3 = 71)

27 = 2 + 7 = 9  (the sum is multiple of 3 = 3 x 3)  (27/3 = 9)

Thus, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

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The total amount paid in dollars per hour is $19.

Unitary Method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

It is given that the total amount given by the uncle is $133 for the work done by Barn for 7 hours.

We have to find the amount paid per hour.

Total amount given = $133

Number of hour Barn work = 7 hours

Amount paid per hour = 133/ 7

= $ 19

Therefore the amount paid per hour is $19.

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