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Answer: 3.75

Step-by-step explanation:

P=0.50, n=15

np= 0.5x15 gives 7.5

n(1-p)= 15x(1-0.5)=7.5

Both are greater than 5

Then Mean, u=np;15x0.5=7.5

Standard deviation, √np(1-p)

15x0.5(0.5)= 3.75

The number of manually filed returns containing errors will there be than electronically filed returns containing errors is: = 658,350

We have the information available from the question is:

0. 05% of all tax returns filed electronically contain errors, but 20% of all tax returns filed manually contain errors.

and, 3. 3 million tax returns are filed each way.

We have to find the Number of manually filed return.

Now, According to the question:

We have to use the formula;

Number of manually filed returns=(Tax returns filed manually contain errors ×Tax return)- (Tax returns filed electronically contain errors× Tax return)

Plug all the values in above formula, we get;

Number of manually filed returns=(20%×3.3 million)-(0.05%×3.3 million)

Number of manually filed returns=660,000-1650

Number of manually filed returns=658,350

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Answer: (-2;8)

\(\left \{ {{3x+3y=18} \atop {2x+y=4}} \right. \\\\<=>\left \{ {{x+y=6} \atop {2x+y=4}} \right. \\\\=>\left \{ {{x=4-6} \atop {x+y=6}} \right. \\\\<=>\left \{ {{x=-2} \atop {x+y=6}} \right. \\\\<=>\left \{ {{x=-2} \atop {y=6-(-2)=8}} \right.\)

Step-by-step explanation:

All people come very close to being able to float in water. therefore, 0.007 is the volume (in cubic meters) of a 50-kg woman.

Correct answer will be a. 0.007

The volume of a person in water is determined by their body density and the amount of air in their lungs. The volume can be estimated using the principle of buoyancy, which states that a body floating in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.

In this case, we are given the weight of a 50-kg woman and asked to determine her volume in cubic meters. To do this, we can use the formula for buoyancy: Fb = ρf * V * g, where Fb is the buoyant force, ρf is the density of the fluid (water), V is the volume of the woman, and g is the acceleration due to gravity.

Since the woman is floating, the buoyant force is equal to her weight, so we can set these two equal to each other: ρf * V * g = 50 kg * 9.8 m/s^2. Solving for V, we find that V = 50 kg / (ρf * g) = 50 kg / (1000 kg/m^3 * 9.8 m/s^2) = 0.005 m^3.

Comparing this answer to the options given, we can see that the closest option is 0.007 m^3 (choice a), which is our final answer.

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The break-even point is 20 units.

The cost and revenue at the break-even point is $4600.

The break-even point is the point at which the cost and revenue are equal. Thus, we can say:

R(x) = C(x)

230x = 220x + 200

230x - 220x = 200

10x = 200

x = 200/10

x = 20

Thus, the break-even point is 20 units

cost and revenue at the break-even point:

Put x = 20 into the C(x) and R(x) respectively

C(x) = 220x + 200

C(20) = 220(20) + 200

C(20) = $4600

R(x) = 230x

R(20) = 230 * 20

R(20) = $4600

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In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown." x is a variable in x + 2 = 7, but we can figure it out.

Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.

To determine the value of X in a multiplication operation, the usual form is

Product = Multiplicand x Multiplier

Consider Multiplier as x.

Product = Multiplicand x

The equation to determine the value of x is then

X = product/multiplier

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Answer:

There are several ways to look at this

Consider the interior angles of a triangle:

33 + A = 90

52 + B = 90

85 + A + B = 180       interior  angles of a triangle must sum to 180

So 180 - 85 = 95     which completes the triangle and would be EKD

Or 33 counterclockwise + X clockwise + 52 counter clockwise = 0

X must be 85 and is exterior to EKD and again

EKD = 180 - 85 = 95

If you consider the geometry and the corresponding angles you should be able to get a satisfactory answer

One can draw the line ED and consider the angles involved

it is not clear whether the data is related to proportions or not. Therefore, the statement that "the Success/Failure Condition is satisfied for sample sizes of at least 75" may not be applicable in this context.

In statistics, the normal distribution or Gaussian distribution is a continuous probability distribution that is commonly used to approximate the distribution of many random variables. One of the main applications of the normal distribution is to model the sampling distribution of the sample mean. However, the accuracy of the normal approximation depends on the sample size.

To determine the smallest sample size that would be reasonable to use the normal model as an approximation for the sampling distribution, we need to look at the histograms of the data. If the histograms are approximately bell-shaped and symmetric, the normal model is likely to be a good approximation.

In this case, it is stated that the normal model would be reasonable to use for a sample size of at least 75. This means that if the sample size is 75 or larger and the histogram is approximately bell-shaped and symmetric, we can use the normal model to approximate the sampling distribution of the sample mean.

Regarding the Success/Failure Condition, it is a condition that applies when we are using the normal model to approximate the sampling distribution of a proportion. The condition states that if np and n(1-p) are both at least 10, where n is the sample size and p is the probability of success, then we can use the normal model to approximate the sampling distribution of the proportion.

However, in this case, it is not clear whether the data is related to proportions or not. Therefore, the statement that "the Success/Failure Condition is satisfied for sample sizes of at least 75" may not be applicable in this context.

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The number of plants Ethan has are 5.

Two or more expressions with an Equal sign is called as Equation.

Let x be the number of plants Ethan has.

Ethan uses 3.5 ounces of water for each plant, so he will use a total of 3.5p ounces of water.

If he starts with 32 ounces of water and ends up with 14.5 ounces

Total of 32 - 14.5 = 17.5 ounces of water.

As given the amount of water used is equal to the amount of water per plant times the number of plants:

3.5x = 17.5

Divide both sides by 3.5

x=5

Hence, , Ethan has 5 plants.

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The height of the building is 71 meters.

We can solve this problem using the similar triangles. The height of the building can be determined by setting up the following proportion:

(the height of pole) / (length of pole's shadow) = (height of building) / (length of building's shadow)

Substituting the given values:

2.8 / 1.49 = (height of building) / 37.5

To find the height of the building, we can cross-multiply and solve for it:

(2.8 * 37.5) / 1.49 = height of building

Calculating the expression on the right side:

(2.8 * 37.5) / 1.49 ≈ 70.7013

Rounding to the nearest meter, the height of the building is approximately 71 meters.

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Answer:

I don't recognize this problem, please make sure the input is complete.

Is this 3 different problems or 1 big problem?

Step-by-step explanation:

In the case above, the correct vectors are:

The solution for the Ship's vector are:

Note that the Horizontal aspect = 30 cos 30  

                                                   = 25.98.

For the  Vertical aspect = 30 sin(-30)

                                        = -15.

Hence it will be  <25.98, -15>.

In regards to the current's vector:

The Horizontal aspect=  5 sin 20

                                       = 1.71.

The Vertical aspect = 5 cos 20

                                     = 4.7.

Hence it will be <1.71, 4.7>.

Therefore, In the case above, the correct vectors are:

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Answer:

c= sqrt149; 12.2 rounded

Step-by-step explanation:

Pythagorean Theorem to find c(hypotenuse): a^2+b^2=c^2

7^2+10^2=149

sqrt149= 12.2 rounded

Answer:

Length = 6.25 feet

Step-by-step explanation:

Your dad is designing a new garden for your backyard. He has 20 feet of fencing to go around the garden.

Let the width is x.

Length is 2 1/2 feet longer than the width i.e. (x+2 1/2) = (x+2.5) feet

Perimeter = 20 feet

2(l+b) = 20

(l+b) = 10

(x+2.5+x) = 10

2x+2.5 = 10

2x = 7.5

x = 3.75 feet

Length = (x+2.5)

= (3.75+2.5)

= 6.25 feet

So, the length of the garden is 6.25 feet.

True

In a symmetrically shaped distribution of scores, regardless of whether it has one mode or two modes, the mean value tends to be similar to the median value.

When a distribution is symmetric, it means that the data is evenly distributed around the central point, resulting in a bell-shaped curve. In such cases, the mean, median, and mode are typically close to each other.

The mean is the arithmetic average of all the scores in a distribution, while the median represents the middle value when the scores are arranged in ascending or descending order. In a symmetric distribution, the mean and median are located at the exact center of the distribution.

If the distribution has only one mode, it means that there is one prominent peak or high point in the data. In this case, the mean and median will coincide with the mode and will be similar.

If the distribution has two modes, it means that there are two prominent peaks in the data, but they are symmetrical around the center. Even though there are multiple modes, the mean and median will still be similar and tend to be located between the two modes.

In summary, in symmetrically shaped distributions, regardless of the presence of one or two modes, the mean and median values are expected to be close to each other.

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Answer:

7 yd

Step-by-step explanation:

The diameter of a circle is two times the radius.

3.5 x 2= 7 yd

The diameter of the given circle is given by d=7 yards

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circumference of the circle. The diameter is also known as the longest chord of the circle.

Given here: Radius of the circle is 3.5 yards

Now diameter of any circle is twice its radius

Thus since the radius is 3.5 yards the diameter would be d=2×3.5

                                                                                           =7 yards

Hence, The diameter of the given circle is given by d=7 yards

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The monthly payment amount is $217.42 and the finance charge is $413.02.

The payment amount and finance charge can be found by using the formula below

Payment amount formula: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

Finance charge formula: Finance charge = Total payment - Loan amount

Where P = Loan amount

R = Interest rate per period

N = Number of periods

Given that a loan is made for $4800 with an APR of 12% and payments made monthly for 24 months

Therefore,P = $4800R = 12% / 12 = 1% per month

N = 24

Using the Payment amount formula above: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

PMT = ($4800 x 0.01 x (1 + 0.01)^24) / ((1 + 0.01)^24 - 1)

PMT = $217.42

Hence, the monthly payment amount is $217.42 (rounded to two decimal places).

Using the finance charge formula above: Finance charge = Total payment - Loan amount

Total payment = Payment amount x Number of periods

Total payment = $217.42 x 24 = $5213.02

Finance charge = $5213.02 - $4800

Finance charge = $413.02

Hence, the finance charge is $413.02 (rounded to two decimal places).

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The minimum distance the annihilation event could have occurred from the center of the machine is approximately 98.94 nanometers.

To determine the minimum distance the annihilation event could have occurred from the center of the machine, we can use the speed of light as a constant and the time difference between the collisions of the gamma rays.

The speed of light in a vacuum is approximately 299,792,458 meters per second (m/s).

Since the time difference between the collisions of the gamma rays is given as 0.33 nanoseconds, we need to convert this time to seconds. One nanosecond is equal to 1 × 10⁻⁹seconds.

0.33 nanoseconds is equal to 0.33 × 10⁻⁹ seconds.

Now, we can calculate the minimum distance using the equation:

Distance = Speed of light × Time

Distance = 299,792,458 m/s × 0.33 × 10⁻⁹ seconds

Distance ≈ 98.94 nanometers

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Answer:

7.07

Step-by-step explanation:

Draw a horizonal line and a vertical line to creat a right triangle.  The horizontal measurement would be 5 and so would the horizontal measurement.

Use the Pythagorean theorem

\(a^{2}\) + \(b^{2}\) = \(c^{2}\)  The c side is the length that you are looking for

\(5^{2}\) + \(5^{2}\) = \(c^{2}\)

25 + 25 = \(c^{2}\)

50 = \(c^{2}\)

\(\sqrt{50}\) = \(\sqrt{c^{2} }\)

7.07 = c  Rounded to the nearest hundredths

Answer:

(i) 5/2 mod 6

5/2 = x

( cross multiply )

2x = 5

( Find the smallest multiple of 5 that can go in both 2 and 5)

The number = 10

2x = 10

(divide both sides by 2 to make x the subject)

x = 5

Ans: 5 mod 6

(ii) 9/7 mod 7

9/7 = x

( cross multiply )

7x = 9

( Find the smallest multiple of 9 that can go in both 7 and 9)

That no = 63

7x = 63

Divide both sides by 7 to make x the subject)

x = 9

Ans: 9 mod 7

(iii) 6/5 mod 7

6/5 = x

( cross multiply )

5x= 6

( Find the smallest multiple of 5 that can go in both 6 and 5)

No: 30

5x = 30

(D.B.S by 6 to make x subject of the formula)

x = 6

Ans: 6 mod 7

The power of substitutes is one of the five forces in Porter's Five Forces framework and it is a measure of how easy it is for customers to switch to alternative products or services. The higher the power of substitutes, the more competitive the industry and the lower the profitability.

The power of substitutes is based on the premise that when there are readily available alternatives to a product or service, customers can easily switch to those alternatives if they offer better value or meet their needs more effectively. This poses a threat to the industry as it reduces customer loyalty and puts pressure on pricing and differentiation strategies.

The availability and quality of substitutes influence the degree to which customers are likely to switch. If substitutes are abundant and offer comparable or superior features, the power of substitutes is strong, increasing the competitive intensity within the industry. On the other hand, if substitutes are limited or inferior, the power of substitutes is weak, providing more stability and protection to the industry.

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we have the expression

2(m + 11)

Apply distributive property

2(m + 11)=2(m)+2(11)=2m+22

The answer is

Answer:

B

Step-by-step explanation:

Here, we want to find the point-slope equation of the line

We start by getting the y-intercept of the line which is y = 3

The general equation of a straight line is;

y = mx + b

where b is the y-intercept

So, we have;

y = mx + 3

Now, to get m , we insert the point given on the like which is (2,-5)

x = 2 and y = -5

-5 = 2m + 3

-8 = 2m

m = -8/2

m = -4

So the equation of the line is;

y = -4x + 3

This is same as option B

I would switch my selection. The reason is that switching provides a higher probability of winning the money. This is known as the Monty Hall Paradox.

Initially, when we choose one box out of three, the probability of selecting the box with the money is 1/3. The remaining two boxes have a combined probability of 2/3 of containing the money.

When the host opens one of the empty boxes, it doesn't change the fact that the initial probability of our selected box having the money is still 1/3. However, the information revealed by the host's action increases the probability of the other unopened box containing the money to 2/3.

By switching our selection, we essentially transfer our initial 1/3 probability to the other unopened box, which now has a probability of 2/3 of containing the money. Thus, switching increases our chances of winning to 2/3, while sticking with our initial selection keeps the probability at 1/3.

Therefore, to maximize our chances of winning, it is advantageous to switch our selection.

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Complete question:

This is the Monty Hall Paradox problem, stated in the lecture note

1. a) There are three empty boxes. I will put $100 in a box and close them. Now you will select a box containing money.

b) First, you will select one of boxes.

c) Then, I will open one box that does not contain the bill (I already know which box has the money).

d) Now, there are two closed boxes, and one of them will have the money.

e) You will be asked to change your mind if you want.

If you have a chance to switch your selection, do you want to switch? Or keep your first selection? What is your decision? Why?

The missing number in the unit conversion problem is composed as follows:

9 ft = 108 inches.

The missing number is obtained applying the proportions in the context of the problem.

The unit conversion rate between ft and inches is given as follows:

1 feet = 12 inches.

Hence the number of inches in 9 feet is obtained multiplying 9 by 12, as follows:

9 x 12 = 108 inches.

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The equation of the parabola that has its focus at (0, -2) and directrix at y = 4 is presented as follows;

\(y = 1 - \frac{ x² }{12}\)

The focus of the parabola, obtained from a similar question posted online is (0, -2)

The given directrix is y = 4

From the definition of the directrix, we have;

(x - 0)² + (y - (-2))² = (y - 4)²

Which gives;

x² + (y + 2)² = (y - 4)²

4•y = y² - 8•y + 16 - (x² + y² - 4)

12•y = 12 - x²

The equation of the parabola is therefore;

\(y = 1 - \frac{ x² }{12}\)

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Answer:

Answer is 28 and no remainder

Answer:

28 with remainder 0

Step-by-step explanation:

The seventh term of the geometric sequence is -7/32. The nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term

To find the seventh term of a geometric sequence, we can use the formula:

\(an = a1 * r^(n-1),\)

where an represents the nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term we want to find.

In this case, we are given a2 = -7 and r = 1/2.

Using the formula, we can find a1 by substituting n = 2:

a2 = a1 * (1/2)^(2-1).

We know that a2 = -7, so we can rewrite the equation:

-7 = a1 * (1/2)^1,

-7 = a1 * (1/2).

Now, let's solve for a1:

a1 = -7 * (2/1),

a1 = -14.

We have found that the first term, a1, is equal to -14.

Now, we can find the seventh term, a7, by substituting n = 7 into the formula:

a7 = (-14) * (1/2)^(7-1),

a7 = (-14) * (1/2)^6,

a7 = (-14) * (1/64),

a7 = -14/64,

a7 = -7/32.

Therefore, the seventh term of the geometric sequence is -7/32.

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