Scarlett has the deluxe version of the card game Mysterious Monsters of the Deep with 3D images printed on the playing cards. She randomly selects one card from the deck, puts it back in the deck, and picks another card. She repeats this several times and gets 2 anglerfish, 3 vampire squids, 1 viperfish, 4 megamouth sharks, and 5 ghost fish.
Based on the data, what is the probability that the next card Scarlett selects will have an anglerfish on it?

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

edge 2022

the solutions to the equation 8cos^2(x) + 4cos(x) - 4 = 0 are:

x₁ = arccos(1/2) + 2πn (where n is an integer)

x₂ = π + 2πn (where n is an integer)

To solve the equation 8cos^2(x) + 4cos(x) - 4 = 0, we can substitute u = cos(x) and rewrite the equation as 8u^2 + 4u - 4 = 0.

Now, we can solve this quadratic equation for u by factoring or using the quadratic formula. Factoring doesn't yield simple integer solutions, so we'll use the quadratic formula:

u = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 8, b = 4, and c = -4. Substituting these values into the formula, we get:

u = (-4 ± √(4^2 - 4(8)(-4))) / (2(8))

u = (-4 ± √(16 + 128)) / 16

u = (-4 ± √144) / 16

u = (-4 ± 12) / 16

Simplifying further, we have two possible solutions:

u₁ = (-4 + 12) / 16 = 8 / 16 = 1/2

u₂ = (-4 - 12) / 16 = -16 / 16 = -1

Since u = cos(x), we can solve for x using the inverse cosine function:

x₁ = arccos(1/2) + 2πn  (where n is an integer)

x₂ = arccos(-1) + 2πn

Thus, the solutions to the equation 8cos^2(x) + 4cos(x) - 4 = 0 are:

x₁ = arccos(1/2) + 2πn  (where n is an integer)

x₂ = π + 2πn  (where n is an integer)

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The answer is "false". The interval [1, 2] contains all the real numbers between 1 and 2 including the endpoints.

An interval notation is used for representing the continuous set of real values. This is the shortest way of writing inequalities.

Intervals are represented within the brackets such as square brackets or open brackets(parenthesis).

The given interval is [1, 2]

The given statement is - 'the interval [1, 2] contains exactly two numbers - the numbers 1 and 2'

The given statement is 'false'.

This is beacuse, an interval consists set of all the real values in between the two values given.

So, according to the definition, there are not only the end values but also many real values in between them.

Thus, the answer is "false". The interval [1, 2] consists of all the real values between 1 and 2 including 1 and 2.

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The absolute value of x minus one is equal to two. Therefore, x must be either one greater than two (x = 3) or one less than two (x = 1).

One less than x results in a value of two in absolute terms. As a result, x minus 1 has an absolute value of 2, which is a positive number. The separation of an integer from zero is its absolute value. As a result, x minus 1 is two units from zero in absolute terms. As x minus one has an absolute value of two, its real value must either be two or a negative two. That is to say, x must either be one more than two (x = 3) or one less than two (x = 1).In order to confirm this, let's look at a few examples. If x = 3, then |x - 1| = |2 - 1| = |1| = 1 which is not equal to two. Therefore, x = 3 is not the answer we are looking for. On the other hand, if x = 1, then |x - 1| = |1 - 1| = |0| = 0 which is not equal to two. Therefore, x = 1 is also not the answer we are looking for. The only two possible solutions for the equation |x - 1| = 2 are x = 3 and x = 1. Therefore, the result of |x - 1| = 2 is that x must be either one greater than two (x = 3) or one less than two (x = 1)

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Answer:

the diagonal distance from one corner to the opposite is 15 feet.

Step-by-step explanation:

using the pythagorean theorem, we know that a^2 + b^2 = c^2. if a=9 and b=12 we can set up our equation as follows:

9^2 + 12^2 = c^2

81 + 144 = c^2

225 = c^2

the square root of 225 is 15 therefore:

15 = c

If f = q (v x b) and v is perpendicular to b, then the direction of b will be perpendicular to both f and v.

The cross product, also known as the vector product, is a mathematical operation performed between two vectors in three-dimensional space. The result of the cross product is another vector that is perpendicular to both original vectors.

If we have the cross product (v x b) v is perpendicular to b, then the direction of b will be perpendicular to both f and v. This is because the cross product of two vectors, v x b, will result in a vector that is perpendicular to both of the original vectors. Therefore, the direction of b will be in a direction that is perpendicular to both f and v.

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The explicit rule for the sequence is f(n) = 4 + 3(n - 1)

From the question, we have the following parameters that can be used in our computation:

a1 = 4

a(n) = a(n - 1) + 3

In the above sequence, we can see that 3 is added to the previous term to get the new term

This means that

First term, a = 4

Common difference, d = 3

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 4 + 3(n - 1)

Hence, the explicit rule is f(n) = 4 + 3(n - 1)

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To solve this problem, we can use the Poisson distribution, which models the number of events that occur in a fixed period of time, given the average rate of occurrence.

a. To find the probability that at most 425 people are struck by lightning in a year, we can use the Poisson distribution with a mean of 400. The formula for the Poisson distribution is:
P(X ≤ k) = e^-λ ∑_(i=0)^k (λ^i/i!)
where X is the random variable (the number of people struck by lightning in a year), λ is the mean (400), and k is the maximum number of people we're interested in (425). Plugging in the values, we get:
P(X ≤ 425) = e^-400 ∑_(i=0)^425 (400^i/i!) = 0.8855
So the probability that at most 425 people are struck by lightning in a year is 0.8855, or about 88.55%.
b. To find the probability that at least 375 people are struck by lightning in a year, we can use the complement rule: the probability of an event happening is 1 minus the probability of the event not happening. So in this case, we want to find the probability that fewer than 375 people are struck by lightning, and subtract that from 1 to get the probability of at least 375 people being struck.
P(X ≥ 375) = 1 - P(X < 375) = 1 - e^-400 ∑_(i=0)^374 (400^i/i!) = 0.9369
So the probability that at least 375 people are struck by lightning in a year is 0.9369, or about 93.69%.
It's important to note that these probabilities are based on the assumption that the number of people struck by lightning in a year follows a Poisson distribution with a mean of 400. This may not be a perfect model, but it's a reasonable approximation based on the available data. Additionally, the chances of being struck by lightning are still relatively low - even at the high end of our estimates, only about 0.1% of the US population would be affected.

Based on the given information of 400 people being struck by lightning in the United States on average each year, we can calculate the probabilities for the scenarios you mentioned.
a. The probability that at most 425 people are struck by lightning in a year:
To calculate this, we'll need to know the distribution of people being struck by lightning, which isn't provided. However, let's assume it follows a normal distribution with a mean of 400 and some standard deviation. In this case, we would calculate the z-score for 425 people and find the corresponding probability from the z-table. Unfortunately, without the standard deviation, we cannot compute the exact probability.
b. The probability that at least 375 people are struck by lightning in a year:
Similarly, to calculate this probability, we'd need the standard deviation to find the z-score for 375 people and then find the corresponding probability from the z-table. Again, without the standard deviation, we cannot compute the exact probability.
In conclusion, without knowing the standard deviation or the distribution of people being struck by lightning, we cannot provide a precise probability for the given scenarios.

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The simplified expression is \(21x^2 - 25x - 28\) in the given case.

An expression in mathematics is a combination of numbers, symbols, and operators (such as +, -, x, ÷) that represents a mathematical phrase or idea. Expressions can be simple or complex, and they can contain variables, constants, and functions.

"Expression" generally refers to a combination of numbers, symbols, and/or operations that represents a mathematical, logical, or linguistic relationship or concept. The meaning of an expression depends on the context in which it is used, as well as the specific definitions and rules that apply to the symbols and operations involved. For example, in the expression "2 + 3", the plus sign represents addition and the meaning of the expression is "the sum of 2 and 3", which is equal to 5.

To simplify the expression, first distribute the -3x and (3x + 4) terms:

\(-3x(4 - 5x) + (3x + 4)(2x - 7) = -12x + 15x^2 + (6x^2 - 21x + 8x - 28)\)

Next, combine like terms:

\(-12x + 15x^2 + (6x^2 - 21x + 8x - 28) = 21x^2 - 25x - 28\)

Therefore, the simplified expression is \(21x^2 - 25x - 28.\)

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the following instructions :

It can be deduced from part a that the final result will be twice the original number 'n'

The number 'n' multiplied by 4 = (4 * n) = 4n

10 added to 4n = 4n + 10

The result of the sum divide by 2 = (4n + 10) / 2

= 2n + 5

5 subtracted from the result of the quotient obtained : 2n +5 - 5 = 2n

Where n is the original number.

2n = twice the original number.

When you develop an argument with a major premise, a minor premise, and a conclusion, you are using deductive reasoning. When constructing an argument using deductive reasoning, three components are involved: a major premise, a minor premise, and a conclusion.

Deductive reasoning is a logical process where the conclusion is derived from the major and minor premises. The major premise is a general statement or principle that establishes a broad context or rule.

The minor premise is a specific statement or evidence that relates to the major premise. Finally, the conclusion is the logical inference or outcome that follows from the combination of the major and minor premises.

Deductive reasoning allows for the logical progression from general principles to specific conclusions, making it a valuable tool in fields such as mathematics, logic, and philosophy.

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The line integral is approximately equal to 0.2675 or 6/5, depending on the method used.

To evaluate the line integral y³ds along the curve C given by x=t³, y=t, 0<=t<=2, we can use either the parameterization method or the line integral formula.

Using the parameterization method, we first find the parametric equations for C:

x = t³
y = t

Then, we can express ds in terms of dt:

ds = √((dx/dt)² + (dy/dt)²) dt
  = √((3t²)² + (1)²) dt
  = √(9t⁴ + 1) dt

Therefore, the line integral can be written as:

integral(y³ ds) = integral(y³ √(9t⁴ + 1) dt)
                 = integral(t³ √(9t⁴ + 1) dt)
                 = 0.2675 (approx.)

Alternatively, we can use the line integral formula:

integral(y³ ds) = integral(y³ dx) - integral(y'² dx)
                 = integral(t³ 3t² dt) - integral(1 9t⁴ dt)
                 = 2 - 32/5
                 = 6/5

Therefore, the line integral is approximately equal to 0.2675 or 6/5, depending on the method used.

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Answer:

B. RZ =R BZ

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisectors of both sides. Therefore, CZ and SZ are perpendicular bisectors of AB and ST, respectively.

Option B is true because point R lies on the perpendicular bisector of AB, and therefore RZ = RB.

Answer: vv

Step-by-step explanation:

Since point Z is equidistant from the sides of ARST, it lies on the perpendicular bisector of the sides ST and AR.

Therefore, we can draw perpendiculars from point Z to the sides ST and AR, which intersect them at points T' and R', respectively.

Now, let's examine the options:

A. SZ & TZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distance from Z to S and T could be different.

B. RZ = RB: This is true, as point Z lies on the perpendicular bisector of AR, and is therefore equidistant from R and B.

C. CTZ = ASZ: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of AR, and the distances from Z to C and A could be different.

D. ASZ = ZSB: This is not necessarily true, as we do not know the exact location of point Z. It could lie anywhere on the perpendicular bisector of ST, and the distances from Z to A and B could be different.

Therefore, the only statement that must be true is option B: RZ = RB.

Answer:

Step-by-step explanation:

It is solved for C unless you C = 5/9 * F - 32*5/9

C = 5/9F - 17.8

=================

If you mean F, then Multiply both sides by  9/5

9/5 * C = F - 32

9/5  * C + 32 = F

=====================

A quick way to do this is to multiply by 2 and add 32

F = 2*C + 30

My wife, an American, always had to do this when she heard the daily temperatures in Canada.

first multiply both sides by 9/5 to get:

9/5C= F -32

Add 32 to both sides and transpose to get:

F=9/5C + 32

these are the formulas to translate between Fahrenheit and Celsius temperatures

Fahrenheit and Celsius meet at - 40 degrees

that is - 40 Fahrenheit = - 40 Celsius    

So alternitive formulas for the conversations can be written:

F=9/5 (C+40) - 40

C=5/9 (F+40) - 40

The equation of the line that is perpendicular to x - 6y = 5 and passes through the y-intercept (0, -6) is y = -6x - 6.

The equation of line in slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line:

x - 6y = 5

Rewrite this equation in slope-intercept form.

-6y = -x + 5

y = (1/6)x - (5/6)

The slope of this line is (1/6).

To find the slope of the perpendicular line, we take the negative reciprocal of (1/6), which is -6.

Now, plug the slope m = -6 and point (0,-6) into the point-slope form and simplify:

( y - y₁ ) = m( x - x₁ )

( y - (-6) ) = -6( x - 0 )

y + 6 = -6x + 0

y = -6x - 6

Therefore, the equation of the perpendicular line is y = -6x - 6.

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The discount amount is $29. The sale price of the scooter is $116.

What is the percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol "%" represents it.

Given that, the market price of a scooter is $145.

The discount on the scooter is 20%.

The discount amount is $145×20%

                                        = 145 × (20/100)

                                        = 145 × (1/5)

                                         = 29

The sale price is Marke price - discount

= $(145 - 29)

=$116

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When an upper outlier is added to the dataset, the mean and median will increase. This means that the analyst's decision to add the upper outlier will have a positive effect on the dataset.

The mean will increase and the median will increase.

The mean and median are the two measures of central tendency, and they are calculated to represent the dataset as a whole.

Mean and median are determined by removing or adding the outliers, which are numbers that are either too high or too low. median was 26, the effects are likely to be positive.

However, when the analyst decides to include the upper outlier in the calculations, it will lead to an increase in the mean and median.The effect of outliers on the mean and median is different.

The mean is greatly influenced by outliers. The median is not affected as much by outliers as the mean because it is calculated by arranging the dataset from lowest to highest and selecting the middle value of the dataset.

When an upper outlier is added to the dataset, the mean and median will increase. This means that the analyst's decision to add the upper outlier will have a positive effect on the dataset.

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The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.

Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s

Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s

Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².

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The probability is approximately 0.7745 for the Gaussian random variable and approximately 0.4323 for the Laplace random variable.

Let's first find the probability P(-1 < Y < 2) when Y is a Gaussian random variable with mean 1 and variance 0.5.

We can standardize the random variable Y as follows:

Z = (Y - μ) / σ

where μ is the mean and σ is the standard deviation.

In this case, we have:

μ = 1 and σ²

= 0.5, so σ

= sqrt(0.5)

= 0.7071.

Substituting these values, we get:

Z = (Y - 1) / 0.7071

Now, we can find the probability P(-1 < Y < 2) in terms of Z as follows:

P(-1 < Y < 2) = P((-1 - 1) / 0.7071 < (Y - 1) / 0.7071 < (2 - 1) / 0.7071)

P(-2.8284 < Z < 1.4142)

Using a standard normal table or calculator, we can find that this probability is approximately 0.7745.

Now, let's find the probability P(-1 < Y < 2) when Y is a Laplace random variable with pdf \(0.5e^-|y|\).

We can integrate the pdf between -1 and 2 as follows:

P(-1 < Y < 2) = \(∫₋₁² 0.5e^-|y| dy\)

Since the pdf is even, we can simplify this as:

P(-1 < Y < 2) = \(2∫₀² 0.5e^-y dy\)

P(-1 < Y < 2) =\(e^-1 - e^-2\)

Using a calculator, we can find that this probability is approximately 0.4323.

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Answer:

1.0,1,3,-5

2.2,-2,4,-1

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

3x = 15 (you add the 6 over)

x = 5 (you divide by 3)

Answer:

2 x 7

Step-by-step explanation:

4 x 7 = 28

Since you want doubled, we have to half to find start.

28/2 = 14

Only solid equation that equals 14 is 2 x 7

And since 4 is a double of 2, the answer checks out

The multiplication fact that can be doubled to find 4 x 7 is

2 x 7.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

4 x 7 = 28

Now,

The multiplication of 2 x 7 = 14.

If 2 x 7 is double we get,

2 x (2 x 7) = 2 x 14 = 28

Thus,

The multiplication fact is 2 x 7.

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SOLUTION

We want to solve

To do this, change the mixed fraction into improper fraction.

We say, 2 multiplied by 12, then plus 1. We write the result as the numerator over the denominator which is 2. That is

We then multiply by 4, we have

Hence the answer is 50

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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The hypotenuse of the triangle is 29.2 centimeters.

A right triangle is a three-sided polygon. The longest side is called the hypotenuse. It has a 90 degree angle and the sum of angles is 180 degrees.

In order to determine the length of the hypotenuse, the SOHCAHTOA would be needed. Sine would be used because we have the opposite side and we need to determine the value of the  hypotenuse.

Sine = opposite / hypotenuse

sin 20 = 10 / h

0.3420 = 10/h

h = 10 / 0.342

h = 29.2 cm

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A plasmid used in both yeast and bacteria requires two different selection markers because the same selection may not work for both hosts and bacteria and yeast recognize different promoters.

When using a plasmid in both yeast and bacteria, it is important to have two different selection markers for several reasons. First, the same selection, such as the presence of an antibiotic, may not be effective in both hosts. Different organisms have varying sensitivities to antibiotics, so a marker that works in bacteria may not work in yeast or vice versa. Therefore, two different selection markers are needed to ensure successful selection in both hosts.

Additionally, bacteria and yeast recognize different promoters, which are DNA sequences that control the initiation of gene expression. Promoters are specific to each organism and play a crucial role in regulating gene expression. By incorporating two different selection markers into the plasmid, each marker can be driven by a promoter recognized specifically by the corresponding host. This ensures that the selection marker is effectively expressed in the appropriate host organism, enabling accurate selection and maintenance of the plasmid.

In summary, using two different selection markers in a plasmid intended for both yeast and bacteria is necessary because the same selection may not be effective in both hosts, and different promoters are recognized by bacteria and yeast. This approach allows for successful selection and maintenance of the plasmid in both organisms.

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Answer:

  neither exponential nor linear

Step-by-step explanation:

A linear relationship will show a common difference between adjacent value. Here, the first differences between the first three values are 5 and 33. They are not the same, so the relation is not linear.

__

An exponential relationship will show first differences that are continuously increasing or decreasing by increasing or decreasing amounts (respectively).

As we showed, the difference between May 28 and May 27 is 33. This is more than the previous difference. However, the difference between May 30 and May 31 is only 28, which is less than a previous difference.

The relation is not exponential.

__

A graph points up the non-linearity of the relation.

Given: AQ ≅ RQ, it should be noted that AQY ≅ RQF based on SAS Congruence. Therefore, AQY ≅ RQF.

Given: AQ ≅ RQ

∠YAF and ∠FRY are right angles.

Prove: AQY ≅ RQF

1. AQ ≅ RQ (Given)

2. ∠YAF and ∠FRY are right angles (Given)

3. ∠AQY = ∠RQF (Vertical angles are congruent)

4. AQ = RQ (Given)

5. AY = RY (Side-Angle-Side Congruence)

6. ∠QYA = ∠RFQ (Angle-Side-Angle Congruence)

7. AQY ≅ RQF (SAS Congruence)

Therefore, AQY ≅ RQF.

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Given: AQ ≅ RQ

∠YAF and ∠FRY are right angles.

Prove: AQY ≅ RQF

The solution to the equation (80/4) = 14d is d = 1, indicating that when 80 divided by 4 is equal to 14 times d, the value of d is 1.

To solve the equation (80/4) = 14d, we begin by simplifying the left side of the equation. 80 divided by 4 equals 20, so the equation becomes 20 = 14d. Next, we isolate the variable d by dividing both sides of the equation by 14. This gives us (20/14) = (14d/14), which simplifies to 10/7 = d. Therefore, the solution to the equation is d = 10/7 or d ≈ 1.428. This means that when we substitute 10/7 for d and multiply it by 14, we obtain the value of 20, satisfying the equation.

In summary, the equation (80/4) = 14d is solved by determining that the value of d is 10/7 or approximately 1.428, indicating that when 80 divided by 4 is equal to 14 times d, the value of d is 10/7.

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Answer:

New cut off salary = 30,592

Step-by-step explanation:

Given:

Normal distributed mean = $37,000

Standard deviation = $5000

Cut off salary = 10%

Find:

New cut off salary

Computation:

Z - left tale value of 10% is -1.2816

Corresponding x-value using x = zs + u

New cut off salary = (-1.2816)(5,000) + 37,000

New cut off salary = -6,408 + 37,000

New cut off salary = 30,592