Heights of four-year-olds are Normally distributed, with a mean of 40 inches and a standard deviation of 3 inches. At his four-year checkup, Marlon’s height is measured as taller than 70% of boys his age. How tall is Marlon?


38. 4 inches

41. 6 inches

42. 5 inches

43. 8 inches

Answer: 18 years

Step-by-step explanation:

The Rule of 72 is a way to calculate how long it will roughly take for an investment to double in size.

It works by dividing 72 by the interest rate as a whole number:

= 72/ interest rate

= 72 / 4

= 18 years

Answer:

13 over 22

Step-by-step explanation:

because you want to change the denominator to where they can match. So 22 is where 11 and 2 can match. then you want to multiply the amount you multiplied with the denominator so 1 over 11 would be 2 over 22. And 1 over 2 would be 11 over 22. and then you can add. 11 plus 2 is 13 and you can keep the denominator the same. Therefore, the answer would be 13 over 22

hope i helped.

Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

Answer:

3/8

Step-by-step explanation:

3 1/3 = 10/3

1 1/4 = 5/4

Remember when dividing by a fraction you can also multiply by its reciprocal meaning flip the numerator and denominator.

so

(3 1/3) / (1 1/4) = (10/3) / (5/4) = (10/3) x (4/5) which is the same as (3/10) x (5/4)

= (3 x 5) / (10 x 4) = 15 / 40

the numerator and denominator have a common factor of 5 so divide the  numerator and denominator by 5

15 / 40 = 3/8

Answer:

A

Step-by-step explanation:

I hope I got it right. If I didn't I'm sorry.

x=-.7+1.8734994i  and x=-.7-1.8734994i

Step-by-step explanation:

2x+5x² +7x+10+6+4+-2x=(5x²)+(2x+7x-2x)+(10+6+4)=5x²+7x+20

quadratic equation

x=(-b±√(b²-4ac))/2a

where a=5, b=7, c=20

x=(-7±√(7²-4(5)(20)))/(2(5))

x=(-7±√((49-400))/10

x=(-7±√(-351))/10

x=(-7±18.734994i)/10

x=-.7+1.8734994i  and x=-.7-1.8734994i

Answer:

12

Step-by-step explanation:

Time=D/S

T1=PQ/20

T2=PQ/30

Total Time=T1+T2

1=PQ/20+PQ/30

PQ=12

The Reagan doctrine of American activism in the Third World was most particularly exercised in Nicaragua and Grenada. These countries became focal points of U.S. involvement and intervention.

The Reagan doctrine, implemented during the presidency of Ronald Reagan in the 1980s, aimed to counter Soviet influence and promote American interests in the Third World. This doctrine was characterized by a strong anti-communist stance and support for anti-communist governments and movements. Among the various countries where the Reagan doctrine was applied, Nicaragua and Grenada stand out as prime examples.

In Nicaragua, the Reagan administration actively supported the Contras, a rebel group fighting against the Sandinista government. The Contras were seen as a counterforce to the left-wing Sandinistas, who were aligned with the Soviet Union and Cuba. The United States provided financial and military assistance to the Contras, including covert operations, in an effort to undermine the Sandinista regime.

Grenada, a small island nation in the Caribbean, also witnessed American intervention under the Reagan doctrine. The United States launched Operation Urgent Fury, invading Grenada and overthrowing the government, with the stated objective of protecting American citizens and restoring democracy.

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Answer: I am going to evaluate this question. The anwser is 99

Answer:

answer below

Step-by-step explanation:

f(x) = 2x - 10    ... by graph, slope = 2 and y intercept=-10

g(x) = 2x + 6

transformation 1: horizontal translation LEFT 8 units

f(x+8) = 2 (x+8) - 10 = 2x + 6 = g(x)

transformation 2: vertical translation UP 16 units

f(x) + 16 = 2x - 10 + 16 = 2x + 6 = g(x)

The magnitude of vector A of the following components AX and AY is 88.95m

In this question we will apply the pythagoras theorem which will be depicted as

\(R = \sqrt{AX^{2} + AY^{2} }\) . . . . . . . . . (1)

where , R = resultant magnitude of vector

            AX and AY are the components of vector

As per the question

AX = 83m

AY = 32m

Putting the values in the equation (1) we get

                               \(R= \sqrt{83^{2} +32^{2} }\)

                               \(R =\sqrt{6889+1024}\)

                               \(R=\sqrt{7913}\\\)

                               R  =  88.95m

Thus the magnitude of vector A for the following components is 88.95m

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(a) The rejection region based on Z would be Z < -1.28.

(b) For n=2000 and 8 defectives, Z = -1.29.

(c) To calculate the p-value for n=2000 and 8 defectives based on the normal approximation (ignoring continuity correction), we need to find the area to the left of the calculated Z-score (-1.29) on the standard normal distribution. Using a standard normal table or calculator, we find that the area to the left of -1.29 is approximately 0.0985. Therefore, the p-value is 0.0985.



To answer this question, we need to use the formula for calculating the Z-score:

Z = (p - pi0) / sqrt(pi0(1-pi0) / n)

where p is the sample proportion (number of defectives divided by sample size), pi0 is the hypothesized proportion, and n is the sample size.

(a) To find the rejection region based on Z, we need to look at the standard normal distribution and find the Z-score that corresponds to a significance level of 10%. From a standard normal table, we can see that the Z-score for a 10% significance level is -1.28. Therefore, the rejection region based on Z would be Z < -1.28.

(b) To find the Z-score for n=2000 and 8 defectives, we first need to calculate the sample proportion:

p = 8/2000 = 0.004

Then, we can plug in the values into the formula for Z:

Z = (0.004 - 0.007) / sqrt(0.007(1-0.007) / 2000) = -1.29

(c) To calculate the p-value for n=2000 and 8 defectives based on the normal approximation (ignoring continuity correction), we need to find the area to the left of the calculated Z-score (-1.29) on the standard normal distribution. This area represents the probability of observing a sample proportion as extreme or more extreme than 0.004, assuming that the true proportion is 0.007. Using a standard normal table or calculator, we find that the area to the left of -1.29 is approximately 0.0985. Therefore, the p-value is 0.0985.


In summary, the rejection region based on Z for a 10% significance level would be Z < -1.28. For a sample size of 2000 and 8 defectives, the calculated Z-score is -1.29. The p-value for this sample based on the normal approximation (ignoring continuity correction) is 0.0985.

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"Acquisitions, according to research, usually result in value destruction rather than value creation for acquiring firms." This is true.

Numerous studies conducted over the years have revealed that the majority of mergers and acquisitions do not produce the expected synergies—in fact, many do the opposite and reduce value. Managing the process from merger preparation to post-merger integration is key to the idea of wealth creation through mergers and acquisitions.

The procedure entails a careful evaluation of whether a transaction is worthwhile to pursue or not, a solid strategy, and an M&A methodology. Before engaging in a deal or dealing with a cultural problem that might undermine the real value of their long-term strategy, acquirers must have their value creation strategy in place.

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The complete question is:

Acquisitions, according to research, usually result in value destruction rather than value creation for acquiring firms. True or False.

On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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Answer:

-11 F

Step-by-step explanation:

So we need to just add or decrease the temperature.

-5 + 14

9 - 20

-11

Answer:

-5 + 14 = 9

9 - 20 = -11

the answer is -11°f

Answer:

C) P = 12H

Step-by-step explanation:

This is because she makes 12 dollars every hour so it'll be 12 times the number of hours.

Answer:

D. 8.5

Step-by-step explanation:

The full value of √8 is 8.48528137...

Hope this helped!

The value of y = -651. To find the value of y when x = -10 and z = 20, given that y varies jointly as x and z and y = 179 when x = -5 and z = -11, follow these steps:

Step 1: Understand that "y varies jointly as x and z" means y = kxz, where k is the constant of variation.

Step 2: Use the given values (y = 179, x = -5, z = -11) to find k. Substitute these values into the equation:
179 = k(-5)(-11)

Step 3: Solve for k:
179 = 55k
k = 179 / 55
k = 3.2545 (rounded to the nearest hundredth)

Step 4: Use the found value of k (3.2545) and the new values of x (-10) and z (20) to find the new value of y:
y = (3.2545) (-10)(20)
Step 5: Calculate y:
y = -651
So, when x = -10 and z = 20, y = -651.

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Answer:

Actual SAT Score = 815.284

Equivalent ACT Score = 15.811

The equivalent ACT Score = 29.95

Step-by-step explanation:

From the given information:

Scores on the SAT test are normally distributed with :

Mean = 982

Standard deviation = 198

If a student gets an SAT score that is the 20-percentile

Then ;

P(Z ≤ z ) = 0.20

From the standard z-score for percentile distribution.

z = -0.842

Therefore, the actual SAT Score can be computed as follows:

Actual SAT score = Mean + (z score × Standard deviation)

Actual SAT score =  982 +  (- 0.842 × 198)

Actual SAT score = 982 + ( - 166.716)

Actual SAT score =  982  - 166.716

Actual SAT Score = 815.284

Scores on the ACT test are normally distributed with a mean of 19.6 and a standard deviation of 4.5.

Mean = 19.6

Standard deviation = 4.5

Equivalent ACT Score = 19.6 +  (- 0.842 × 4.5)

Equivalent ACT Score = 19.6 +  ( - 3.789)

Equivalent ACT Score = 15.811

If a student gets an SAT score of 1437, find the equivalent ACT score.

So , if the SAT Score = 1437

Then , using the z formula , we can determine the equivalent ACT Score

\(z = \dfrac{X - \mu}{\sigma}\)

\(z = \dfrac{1437 - 982}{198}\)

\(z = \dfrac{455}{198}\)

z =2.30

The equivalent ACT Score = 19.6 + (2.30 × 4.5)

The equivalent ACT Score = 19.6 +  10.35

The equivalent ACT Score = 29.95

Answer:

31

Step-by-step explanation:

Square both sides of the equation to get

x+5 = 36

x = 31

Given: A function y,

Required: To find the zeroes of the given function.

Explanation: For finding the zeroes of the function put y=0 i.e.,

which gives the value of x as

Final Answer: Option C is correct.

353.25

a=(3.14*15^2)/2

a=706.5/2

a=353 sq in

The image of the point (0,4) after a 180° counterclockwise rotation about the origin is (0, -4).

To find the image of a point (0,4) after a 180° counterclockwise rotation about the origin, we can follow these steps:

Therefore, the image of the point (0,4) after a 180° counterclockwise rotation about the origin is (0, -4).

By performing a 180° counterclockwise rotation, we essentially mirror the point across the origin, with the y-coordinate changing sign while the x-coordinate remains unchanged.

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Answer:

18 is the number good luck

Step-by-step explanation:

18+25=43

Answer:

18,25

Step-by-step explanation:

Answer:

Exponential decay

Step-by-step explanation:

Because the values are exponentially decreasing.

Answer: -1/28 gallon

Step-by-step explanation:

divide both numbers by 4 since its 1/4 a minute (-5/7 ÷ 4 and 4/7 ÷ 4) then add them, (-5/28 + 4/28= -1/28)

Answer: -1/28 gallon

Step-by-step explanation:

Answer:

Step-by-step explanation:

y+1 =(3/4)x+9/4

y=(3/4)x+1/4

Answer:

3x - 4y + 5 = 0

Step-by-step explanation:

The equation of a line in general form is

Ax + By + C = 0 ( A, B, and C are integers )

Given

y + 1 = \(\frac{3}{4}\) (x + 3) ← multiply through by 4 to clear the fraction

4y + 4 = 3(x + 3)

4y + 4 = 3x + 9 ( subtract 4y + 4 from both sides )

0 = 3x - 4y + 5 , that is

3x - 4y + 5 = 0 ← in general form