A hedge fund returns on average 26% per year with a standard deviation of 13%. Using the
empirical rule, approximate the probability the fund returns over 50% next year.

a) The probability of failing to meet the specification limit of 45-pounds tensile strength 15.87%.

b) The number of parts that would not meet the specification is 7,935.

a) Given that the tensile strength of a metal part is normally distributed with mean 40 pounds and standard deviation 5 pounds.

We have to find the probability of failing to meet the specification limit of 45-pounds tensile strength.

Using the standard normal distribution, we can find the probability of failing to meet the specification limit of 45 pounds as follows:

z = {45 - 40}/{5}

= 1

The probability of failing to meet the specification limit of 45 pounds is the probability that the standardized variable Z is greater than 1, which is given by:

P(Z > 1) = 0.1587

Therefore, the probability of failing to meet the specification limit of 45-pounds tensile strength is 0.1587 or 15.87%.

b) If the probability of failing to meet the specification is 0.1587, the probability of meeting the specification limit is

1 - 0.1587 = 0.8413

.If 50,000 parts are produced, then the expected number of parts that meet the specification limit is:

0.8413* 50,000 =  42,065.

Therefore, the number of parts that would not meet the specification is: 50,000 - 42,065 = 7,935.

Hence, about 7,935 parts would not meet the specification.

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Answer: x ≤ 35x

Step-by-step explanation:

enjoy ;) *debby smirk*

Answer:

?

Step-by-step explanation:

By using the volume of the cylinder, it can be calculated that

Volume of the cylinder is 75.360 cubic inches

What is volume of a cylinder?

Volume of a cylinder is the total space taken by the cylinder.

If r is the radius of the cylinder and h is the height of the cylinder, then volume of the cylinder is calculated by-

V = \(\pi r^2h\)

Here,

Height of the cylinder = 6 inches

Radius of the cylinder = 2 inches

Volume of the cylinder = \(3.14 \times 2^2 \times 6\) = 75.360 cubic inches

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Complete Question

A cylinder has a height of 6 inches and a radius of 2 inches. What is its volume? Use a 3.14 and round your answer to the nearest hundredth.​

Answer:

C

Step-by-step explanation:

I chose C because it more detailed than the rest of the question. Everyone already knows how many months are in a year. What is for lunch today is just a normal question. How many students have a cell phone was not really detailed but it would have been different if they said "How many percentage of college students in math class uses cell phones.  

Hope this helps:)

Answer:

C

Step-by-step explanation:

subtract

Answer: B

It would easily be made into an equation and it’s more simple

Question 1-

To determine which two points would a line of fit go through to best fit the data on the scatter plot, we need to visually analyze the pattern of the data points and choose two points that the line would pass through to represent the overall trend.

Without the actual scatter plot provided, I am unable to directly analyze it. However, based on the given answer choices:

A. (1,9) and (9,5)

B. (1,9) and (5,7)

C. (2,7) and (4,3)

D. (2,7) and (6,5)

Since I don't have the scatter plot, I cannot accurately determine which points would best fit the data. I would recommend carefully reviewing the scatter plot and selecting the two points that seem to represent the general trend or pattern of the data. The two points that form a line that closely follows the general direction of the data points would be the best choices.

Question 2-

To determine the slope of the relationship between the number of hours Laila danced, x, and the money she raised, y, we need to examine the graph and calculate the slope using the formula:

Slope = (change in y) / (change in x)

However, since the graph is not provided, it is not possible to directly calculate the slope. However, we can still evaluate the given answer choices based on their explanations:

A. The slope is 1/4, which means that the amount the student raised increases by $0.75 each hour.

B. The slope is 4, which means that the amount the student raised increases by $4 each hour.

C. The slope is 12, which means that the student will finish raising money after 12 hours.

D. The slope is 20, which means that the student started with $20.

From the explanations provided, it seems that option B would be the most reasonable choice. A slope of 4 would indicate that for each additional hour Laila danced, she raised $4. However, without the actual graph, it is challenging to confirm the accuracy of the answer choice or its real-world interpretation.

Answer:

Ratio: Tan B = 12/5

Exact value in degrees: \(67.38^{o}\)

Step-by-step explanation:

SOH CAH TOA

Means Tan B  means opposite/adjacent.

Tan B = 12/5

B = \(Tan^{-1} (\frac{12}{5})\\\)

B = \(67.38^{o}\)

The mass of the entire archway is 585.32 grams. This is calculated by (275 x 1.2 x 0.1785) + 45 = 585.32 grams.

1. Calculate the mass of the helium in the balloons: (275 x 1.2 x 0.1785) = 49.38 grams

2. Calculate the mass of the string and fixings: 45 grams

3. Add the mass of the helium and the mass of the string and fixings: 49.38 + 45 = 585.32 grams

4. The mass of the entire archway is 585.32 grams.

The mass of the entire archway is 585.32 grams. This is calculated by (275 x 1.2 x 0.1785) + 45 = 585.32 grams.

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Answer:

A, complementary angles sum up to 90°

(i) The null hypothesis is that the mean living area of all single-family homes in the county is equal to or less than 2400 square feet. The alternative hypothesis is that the mean living area of all single-family homes in the county is greater than 2400 square feet.

(ii) The test statistic is calculated using the formula: (sample mean - hypothesized mean) / (standard deviation / square root of sample size). In this case, the test statistic is \(\frac{(2540 - 2400)}{\frac{472}{\sqrt{50} } } =2.44\)

(iii) The p-value is the probability of obtaining a sample mean as extreme or more extreme than the one observed, assuming the null hypothesis is true. Using a t-distribution with 49 degrees of freedom (since we are using a sample size of 50 and estimating the population standard deviation), we can find the p-value to be 0.009.

(iv) Using a significance level of 0.05, we can conclude that the real estate agent's claim is not true, since the p-value is less than 0.05. We reject the null hypothesis and accept the alternative hypothesis that the mean living area of all single-family homes in the county is greater than 2400 square feet. If we use a significance level of 0.01 instead, we still reject the null hypothesis since the p-value is less than 0.01.

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a) To find the equation of the line tangent to the graph of f at x = e^2, we need to find the slope of the tangent line and the y-intercept. The slope of the tangent line is given by the derivative of f evaluated at x = e^2: f'(e^2) = (1 - ln(e^2))/(e^2)^2 = (1 - 2)/e^4 = -1/e^4

The y-intercept is found by plugging x = e^2 into the original function and finding the corresponding y-value: f(e^2) = ln(e^2)/e^2 = 2/e^2

We can use this information to write the equation of the tangent line in point-slope form: y - f(e^2) = -1/e^4(x - e^2)

b) To find the x-coordinate of the critical point of f, we need to find the value of x at which f'(x) = 0 or is undefined.

f'(x) = (1 - lnx)/x^2

When we set f'(x) to 0, we get 1 - lnx = 0 lnx = 1 x = e.

As a result, the critical point is at x = e.To determine whether this point is a relative minimum, a relative maximum, or neither, we need to find the second derivative of f(x) and evaluate it at x = e.

f''(x) = -(1 + lnx)/x^3

Evaluating at x = e, we get: f''(e) = -(1 + ln(e))/e^3 = -(1 + 1)/e^3 = -2/e^3

Since the second derivative is negative, the critical point is a relative maximum.

c) To find the x-coordinate of the point of inflection, we need to find the value of x at which f''(x) = 0.

f''(x) = -(1 + lnx)/x^3

Setting f''(x) = 0, we get 1 + lnx = 0 lnx = -1 x = e^-1

So the point of inflection is at x = e^-1.

d) To calculate f(x) = lnx/x, we need to substitute the value of x into the function. f(x) = lnx/x

For example, if we want to calculate f(2) f(2) = ln(2)/2 = 0.693147180559945/2 = 0.346573590279973

So f(2) = 0.346573590279973

Answer:

V= 452.16

Step-by-step explanation:

V= πr^2h

V= π6^2(4)

V= π x 36 x 4

V= π x 144

π= 3.14

V= 3.14 x 144

V= 452.16

Answer:

x = -1 and y = 5.3

Step-by-step explanation:

4x + 3y = 12

2x - 3y = -18 (× -)

4x+ 2x = 12 + (-18)

6x = -6

x = -6/6

x = -1

4(-1) + 3y = 12

-4 + 3y = 12

3y = 12 + 4

3y = 16

y = 16/3

y = 5.3

Step-by-step explanation:

According to angles of intersecting chords theorem    ( angle S is also 117):

117 = 1/2 (208 + 2x-4)  

so  x = 15

then 2x-4 = 26 degrees

Answer:

They took 3 vans and 3 buses.

Step-by-step explanation:

Given:

To find:

The number of vans and the number of buses they took.

Explanation:

Let the number of vans = v

Let the number of buses = b

The total number of vans and buses is 6:

\(v+b=6\)

⇒\(v=6-b....\)Equation(1)

Each van holds 6 students and each bus hold 50 students.

The number of students on the trip is 168.

\(6v+50b=168\)....Equation(2)

Substitute equation (1) into equation (2):

\(6v+50b=168\)

\(6(6-b)+50b=168\)

Then solve the equation for b:

\(36-6b+50b=168\)

\(44b=168-36\)

\(44b=132\)

\(\frac{44b}{44}=\frac{132}{44}\)

\(b=3\)

Then, solve for v:

\(v=6-b=6-3=3\)

Answer:

They took 3 vans and 3 buses.

After 7 months, there will be approximately 6,622 fish in the lake.To solve the problem, we can use the formula for exponential growth.

Here is the formula for exponential growth:

N(t) = \(N0 e^(^r^t^)\)

where N0 is the initial population, r is the monthly growth rate, and t is the time in months. However, we also need to take into account the loss of fish each month, which can be modeled with a linear function:

L(t) = mt + b

where m is the rate of loss and b is the initial loss (in this case, 300 fish per month).

So the actual population of fish after t months can be modeled with the following equation:

P(t) = N(t) - L(t)

= \(N0 e^(^r^t^)\) - mt - b

Substituting the given values, we have:

N0 = 4500

r = 0.08

m = 300

b = 300

So the equation becomes:

P(t) = \(4500 e^(^0^.^0^8^t^)\) - 300t - 300

To find the population after 7 months, we can simply substitute t = 7 into the equation:

P(7) = \(4500 e^(^0^.^0^8^(^7^))\) - 300(7) - 300

≈ 6621.84

Therefore, after 7 months, there will be approximately 6622 fish in the lake.

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Answer:

x = 10

Step-by-step explanation:

Since the ray AE is an angle bisector, it means that it cuts the angle 50 / 50, or perfectly in half.

This means that angle BAE and angle EAC are actually congruent

∠BAE = ∠EAC

\(x + 30 = 3x - 10\)

Get rid of x on one side. Since you are solving for x, use the more simple x

This becomes this ⇅

\(30 = 2x + 10\)

Subtract 10 from both sides

20 = 2x

20 divided by two

2x divided by two

x = 10

Both series (a) Σ(n = 0 to ∞) (3η)! and (b) Σ(n = 1 to ∞) sin^(-1)(αξ) are divergent. The ratio test was used to determine the divergence of (3η)!, while the divergence test was used to establish the divergence of sin^(-1)(αξ).

(a) The series Σ(n = 0 to ∞) (3η)! is divergent. This can be determined using the ratio test. The series (3η)! diverges, and the ratio test is used to establish this.

To determine the convergence or divergence of the series Σ(n = 0 to ∞) (3η)!, we can apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is greater than 1, the series diverges. Alternatively, if the limit is less than 1, the series converges.

Let's apply the ratio test to the series (3η)!:

lim(n→∞) |((3η + 1)!)/(3η)!| = lim(n→∞) (3η + 1)

Since the limit of (3η + 1) as n approaches infinity is infinity, the ratio test fails to yield a conclusive result. Therefore, we cannot determine the convergence or divergence of the series (3η)! using the ratio test.

(b) The series Σ(n = 1 to ∞) sin^(-1)(αξ) also diverges. The divergence test can be used to establish this.

The series Σ(n = 1 to ∞) sin^(-1)(αξ) diverges, and the divergence test is employed to determine this.

To determine the convergence or divergence of the series Σ(n = 1 to ∞) sin^(-1)(αξ), we can use the divergence test. The divergence test states that if the limit of the series terms as n approaches infinity is not equal to zero, then the series diverges.

Let's apply the divergence test to the series Σ(n = 1 to ∞) sin^(-1)(αξ):

lim(n→∞) sin^(-1)(αξ) ≠ 0

Since the limit of sin^(-1)(αξ) as n approaches infinity is not equal to zero, the series Σ(n = 1 to ∞) sin^(-1)(αξ) diverges.

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If  n(E1 and E2) = 3 and n(E1) = 12, then  P(E2|E1) = 1/4. To find the probability P(E2|E1), given that n(E1 and E2) = 3 and n(E1) = 12, we'll use the conditional probability formula. The formula is P(E2|E1) = P(E1 and E2) / P(E1).

Step 1: Find the probabilities of the events.
P(E1) = n(E1) / total outcomes = 12 / total outcomes
P(E1 and E2) = n(E1 and E2) / total outcomes = 3 / total outcomes
Step 2: Plug the probabilities into the conditional probability formula.
P(E2|E1) = P(E1 and E2) / P(E1)

Step 3: Substitute the values from Step 1 into the formula.
P(E2|E1) = (3 / total outcomes) / (12 / total outcomes)
Step 4: Simplify the expression.
P(E2|E1) = 3/12
Step 5: Reduce the fraction to the simplest form.
P(E2|E1) = 1/4
So, the probability of event E2 occurring given that event E1 has occurred is 1/4 or 0.25.

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Answer:

(8,2)

Step-by-step explanation:

The rule is (x,y) becomes (-x, y).  You can visualize this.  (-8,2) is 8 units to the left of the origin (0,0) and two units up from the origin (0,0).  Now, it we flip it so that is is on the other side of the y axis, it is still two units above the origin(0,0), but it is now 8 units to the right of the origin.

Answer: Did it in ways that are different.

Step-by-step explanation:

35.25 hours

2115 minutes

5 3 minutes + 5 7 hours

You must count the instances of each rule and the instances of each item in each rule separately using the data in the Excel file in order to determine the support, confidence, and lift of a rule.

Open the Excel file and look for the information on the options ordered for the specific model of car. This information will probably be presented as a table or a group of columns, where each row represents a distinct order and each column a different choice.

You must count the instances of the rule's components occurring together in the data in order to calculate the support for a rule. You would need to track how frequently the fastest engine choice and the traction control option are selected together, for instance, if the rule is "If the quickest engine, then traction control." This can be accomplished by counting the number of cells in a range that satisfy a specific condition using Excel's COUNTIF function.

The confidence in a rule is calculated by dividing the total number of times the items in the premise (the "if" component of the rule) occur by the total number of times the items in the rule. The number of times the fastest engine and traction control options are selected together must be divided by the total number of times the fastest engine option is ordered, for instance, if the rule is "If the fastest engine, then traction control."

You must divide the rule's confidence by the support of the item in the rule's conclusion to determine the lift of a rule (the "then" part of the rule). You would need to divide the rule's confidence by the support for the traction control option, for instance, if the rule is "If the quickest engine, then traction control."

To calculate the support, confidence, and lift for each of the rules, you can use the Excel formulas indicated above together with any other Excel functions or tools you are familiar with.

It is crucial to keep in mind that the precise formulas and processes you will need to follow will depend on the exact data and rules you are working with, so you might need to modify the following instructions to suit your personal needs.

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Answer:

Its G

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

12 C 2  = 12! / ( 10! 2!) = 66 ways

F(1) is the value of the function F(x) when x is equal to 1. To evaluate F(1), we substitute x = 1 into the given equation: F(1) = f * 7 sin(u * 1). The result will depend on the specific values of f and u. Without knowing these values, we cannot determine the numerical value of F(1).

In the given equation, F(x) = f * 7 sin(ut), where f and u are constants. To evaluate the expression F(1), we substitute x = 1 into the equation. The value of F(1) will depend on the specific values of f and u, as well as the angle measure in radians for sin(ut). Without these specific values, it is not possible to determine the exact numerical result.

Regarding the derivative of F(x), denoted as F'(x), we need to find the rate of change of F(x) with respect to x. Taking the derivative of F(x) with respect to x will involve applying the chain rule, as the function includes a composition of multiple functions. However, without further information or the specific form of f and u, we cannot determine the derivative F'(x) analytically.

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