A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, X, is found to be 100, and the sample standard deviation found to be 8.
Construct a 98% confidence interval about µ, if the sample size n, is 20.
Lower bound ______ Upper bound _______
(Round to one decimal place as needed.)

Answer:

7) b, c, f

8) b, d, e

Step-by-step explanation:

Hope this helps!

An urn contains 4 green balls and 8 red balls. (a) The probability of getting a red ball is 2/3. (b) If you select two balls, the probability that one (but not both) is red is 16/33. (c) The probability that the second ball is red is 14/33.

(a) The probability of getting a red ball = Number of red balls / Total number of balls= 8 / (4 + 8) = 8/12= 2/3

(b) The probability of selecting one red ball out of 2 balls = (Number of ways to select one red ball from 8) × (Number of ways to select one green ball from 4) = (8/12) × (4/11) = 8/33

The probability of selecting one green ball out of 2 balls = (Number of ways to select one green ball from 4) × (Number of ways to select one red ball from 8) = (4/12) × (8/11) = 8/33

Therefore, the probability that one (but not both) is red = 8/33 + 8/33= 16/33

(c) After the first ball is selected, there will be 11 balls left in the urn, including 7 red and 4 green. The probability of selecting a red ball = Number of red balls left / Total number of balls left= 7 / 11

Therefore, the probability that the second ball is red = 8/12 × 7/11= 14/33.

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Answer:

9.5 hours

Step-by-step explanation:

323/34 = 9.5 hours

Answer:

Henry and Valencia are 16 m apart.

Step-by-step explanation:

A sketch to this question shows that their distance apart forms a right angled triangle. So then, we can apply the Pythagoras theorem.

Let the distance between Henry and Valencia be represented by x, so that;

[tex]/hyp/^{2}[/tex] = [tex]/adj 1/^{2}[/tex] + [tex]/adj 2/^{2}[/tex]

[tex]20^{2}[/tex] = [tex]x^{2}[/tex] + [tex]12^{2}[/tex]

400 = [tex]x^{2}[/tex] + 144

[tex]x^{2}[/tex] = 400 - 144

   = 256

x = [tex]\sqrt{256}[/tex]

  = 16

x = 16 m

Therefore, Henry and Valentia are 16 meters apart.

The following statements about the correlation coefficient (rho) between two variables x and y are correct: The value of rho ranges between -1 and 1. If rho = 1, it indicates a perfect positive linear relationship between x and y. If rho = -1, it indicates a perfect negative linear relationship between x and y. If rho = 0, it indicates no linear relationship between x and y.

The correlation coefficient (rho) measures the strength and direction of the linear relationship between two variables x and y. It ranges between -1 and 1. Here's an explanation of each statement:

1. The value of rho ranges between -1 and 1: The correlation coefficient is a standardized measure, and it takes values between -1 and 1, inclusive. A value of -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship.

2. If rho = 1, it indicates a perfect positive linear relationship between x and y: When rho equals 1, it means that the variables x and y have a perfect positive linear relationship. This means that as x increases, y also increases in a consistent manner.

3. If rho = -1, it indicates a perfect negative linear relationship between x and y: When rho equals -1, it means that the variables x and y have a perfect negative linear relationship. This means that as x increases, y decreases in a consistent manner.

4. If rho = 0, it indicates no linear relationship between x and y: When rho equals 0, it means that there is no linear relationship between the variables x and y. In other words, the variables are not linearly associated with each other.

These statements summarize the key properties of the correlation coefficient and its interpretation in terms of the relationship between two variables.

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The probabilistic approach characterized by PERT does not use the median activity times.

The probabilistic approach characterized by PERT stands for Program Evaluation and Review Technique. It is a statistical tool used to evaluate and estimate the time required to complete a project. The PERT method is based on a three-point estimation technique, which takes into account the best case, worst case, and most likely case scenarios for each activity involved in the project management process.

The PERT formula is used to calculate the expected time required to complete a project. The formula is based on the three-point estimation technique used by the PERT method. The formula for calculating the expected time for an activity is as follows:

Expected time = (optimistic time + (4 x most likely time) + pessimistic time) / 6Where,Optimistic time is the shortest possible time required to complete an activityMost likely time is the most probable time required to complete an activityPessimistic time is the longest possible time required to complete an activity

The PERT method is a valuable tool for project managers as it provides a statistical estimation of the time required to complete a project. By using the three-point estimation technique, project managers can evaluate the best case, worst case, and most likely case scenarios for each activity involved in the project management process.

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(B) A and B are not independent.

Explanation: Given that Event A has probability of 0.4 to occur and Event B has a probability of 0.5 to occur. Their union (A or B) has a probability of 0.7 to occur. We know that the formula of the probability of union of two events A and B is P(A or B) = P(A) + P(B) - P(A and B).Substituting the values in the formula: P(A or B) = P(A) + P(B) - P(A and B)0.7 = 0.4 + 0.5 - P(A and B)P(A and B) = 0.2Now, we will check whether A and B are independent or not. Two events A and B are independent if and only if P(A and B) = P(A)P(B).Substituting the values: P(A) = 0.4P(B) = 0.5P(A and B) = 0.2P(A)P(B) = 0.4 × 0.5 = 0.2Since, P(A and B) ≠ P(A)P(B) Thus, A and B are not independent, which is option (B).

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Answer: 4a

Step-by-step explanation:

Answer:

4a

Step-by-step explanation:

8 of something minus 4 of something gives you 4 of that thing

Answer:

Step-by-step explanation:

negative

Answer:

x^3 + 1 +  (−7) /  x+3

Step-by-step explanation:

The effective rate of interest for 1 year is 22.14%.

The formula to calculate the effective rate of interest (APY) is:

APY = (1 + r/n)^n - 1

Where:r = annual interest rate as a decimal, n = number of compounding periods per year.

We know that the principal amount is 18,000, the interest rate is 20%, and the interest is compounded quarterly. Therefore, the number of compounding periods per year is:

n = 4

Using the above formula and substituting the given values in it, we get:

APY = (1 + r/n)^n - 1

APY = (1 + 0.2/4)^4 - 1

APY = 1.2214 - 1

APY = 0.2214 or 22.14% (rounded to the nearest hundredth)

Therefore, the effective rate (APY) of interest for 1 year at a 20% interest rate compounded quarterly is 22.14%.

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The differentiated 3-form:

d(sin(x₅x₂ + x₃x₄) dx₁ ∧ dx₂∧ dx₃) = cos(x₅x₂ + x₃x₄) * (d(x₅x₂ + x₃x₄) ∧ dx₁ ∧ dx₂∧ dx₃)

To differentiate the 3-form given by sin(x₅x₂ + x₃x₄) dx₁ ∧ dx₂∧ dx₃,

we need to apply the exterior derivative operator (denoted by d) to each component of the 3-form.

First, let's differentiate the component sin(x₅x₂ + x₃x₄):

d(sin(x₅x₂ + x₃x₄)) = cos(x₅x₂ + x₃x₄) * d(x₅x₂ + x₃x₄)

Next, we need to differentiate the differential forms dx₁, dx₂, and dx₃:

d(dx₁) = 0

d(dx₂) = 0

d(dx₃) = 0

Finally, we can assemble the differentiated 3-form:

d(sin(x₅x₂ + x₃x₄) dx₁ ∧ dx₂∧ dx₃) = cos(x₅x₂ + x₃x₄) * (d(x₅x₂ + x₃x₄) ∧ dx₁ ∧ dx₂∧ dx₃)

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Answer:

Robert

Step-by-step explanation:

If Robert runs 3 miles in 45 minutes, by the end of 90minutes, Robert would have covered 6miles, while Jacob covered 5miles in 90 minutes, therefore, Robert ran faster than Jacob.

Answer:

x=9 im pretty sure

Step-by-step explanation:

Answer:

He has 40$

Step-by-step explanation:

Cuz 100-20=80 then if she has twice as more as him then you divide 80 by 2 then get 40

Answer:

In explanation

Step-by-step explanation:

ln(x) = 5

log (base e) x = 5

exponential form is e ^ 5 = x

you should be able to generate 2 sentences from here, hope it helps!

Answer:

6

Step-by-step explanation:

answer:

so there isnt such thing as a hertergon but if your looking for how much sides does a heptagon have

the answer is 7 !

ill add a photo here for you to see just in case i got the shape you were looking for wrong

but there isnt really any way to see how much sides a shape does have, the easiest way is to count the sides!

hope this help you and your problem! if you need anything else or if i didn't explain it well enough then please ask! hope you have a good rest of your day :)

Answer:

y = -0.25x + 40 ; $26,000

Step-by-step explanation:

From the graph attached ;

The regression equation, y could be obtained :

y = mx + c

m = slope = Rise / Run = (y2 - y1) / (x2 - x1)

Slope = (15 - 40) / (100 - 0)

Slope = - 25 / 100

Slope = - 0.25

c = intercept, where the regression line crosses the y-axis, from. The graph, c = 40

The regression equation goes thus :

y = -0.25x + 40 ; y = price of car ; x = number of miles driven

Price of car that has been driven for 56000 miles

y = - 0.25(56) + 40

y = - 14 + 40

y = 26

Hence, price of car is $26,000

If they make additional payments of $3,000 every four months for the first five years, it will reduce the outstanding balance on the mortgage.

To calculate the values requested, we'll need to perform various calculations based on the given information. Let's go step by step:

Monthly Interest Rate:

The mortgage rate provided is 4.9% compounded semi-annually. To calculate the monthly interest rate, we need to convert the semi-annual rate to a monthly rate. Since there are two compounding periods per year, we divide the annual interest rate by two and then convert it to a decimal:

Monthly interest rate = (4.9% / 2) / 100 = 0.0245

Monthly Payments:

To calculate the monthly payments, we can use the formula for the monthly payment of a mortgage:

Monthly Payment = (Loan Amount - Down Payment) * (Monthly Interest Rate / (1 - (1 + Monthly Interest Rate)^(-Number of Months)))

Loan Amount = $460,000 - (10% * $460,000) = $414,000

Number of Months = 25 years * 12 months/year = 300 months

Substituting these values into the formula, we can calculate the monthly payments:

Monthly Payment = ($414,000) * (0.0245 / (1 - (1 + 0.0245)^(-300)))

Amount Owed after 5 Years:

After five years, the number of months remaining on the mortgage is 25 years - 5 years = 20 years = 240 months. To find out how much they owe after the first five years, we need to calculate the remaining balance on the mortgage:

Remaining Balance = Loan Amount * (1 + Monthly Interest Rate)^Number of Months - Total Payments

In this case, the Loan Amount is $414,000, the Monthly Interest Rate is 0.0245, and the Number of Months is 240. To calculate the Total Payments, we can multiply the Monthly Payment by the number of months paid during the first five years (5 years * 12 months/year = 60 months).

Interest Paid in the First Five Years:

To determine the interest paid in the first five years, we can subtract the remaining balance after five years from the initial loan amount:

Interest Paid = Loan Amount - Remaining Balance

New Semi-Monthly Payments after Renegotiation:

If they renegotiate the mortgage at a new rate of 5.9%, compounded semi-annually, and plan to pay off the remaining balance from part c, we need to recalculate the monthly payments.

We can use a similar formula as in part b, substituting the remaining balance (from part c) as the new loan amount, and the semi-monthly interest rate based on the new mortgage rate.

Payments of $3,000 every Four Months in the First Five Years:

To calculate the new interest paid in the first five years, we need to consider the reduced balance resulting from the additional payments and then subtract this balance from the initial loan amount.

Now, let's perform the calculations and find the values for each part.

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Using the law of sines, the value of q is: D. 72.7.

The law of sines is given as: sin A/a = sin B/b = sin C/c.

Thus, given △PQS, where:

m∠Q = 22°

m∠S = 65°

s = 176

Applying the law of sines, we have:

sin Q/q = sin S/s

Substitute

sin 22/q = sin 65/176

q = (sin 22 × 176)/sin 65

q = 72.7

Therefore, using the law of sines, the value of q is: D. 72.7.

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Answer:

A vertical line

c × c = c²

c × -5 = -5c

8 × c = 8c

8 × -5 = -40

arrange

c² -5c +8c -40

c² +3c -40

answer is B

Answer:

c^2 + 3c - 40

Step-by-step explanation:

seriously dude all you have to do is use an online calculator or something

The P94 value is the 35th value in the sorted data set, which is 8600.

To obtain the 94th percentile (P94) from the given data, you need to identify the value that separates the top 94% of the data from the remaining 6%.

First, arrange the data in ascending order:

1000 1100 1800 1900 2100 2400 2600 2700 2800 2900 3100 3200 3300 3500 3700 3800 3900 4000 4300 4400 4700 5100 5200 5300 5800 6100 6400 7100 7200 7400 7700 7900 8200 8300 8400 8600 8700 8800 8900

Since there are 36 data points, the 94th percentile corresponds to the 94th percentile rank, which can be calculated as (94/100) * (36 + 1) = 34.56. Since this is not a whole number, we need to round up to the next whole number, which is 35.

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Answer:

8???????

Step-by-step explanation:

Suppose you have 10 black, 10 white, 10 blue, and 10 brown socks. The minimum number of socks to pick that all 3 brothers wear the same color socks is 4 of the same color.

You are required to determine how many socks to pick blindly since there is no light in the room so all three brothers wear the same color socks. In this question, we have 4 types of socks. Therefore, we can apply Pigeonhole Principle here. Pigeonhole Principle states that If n+1 items are put into n boxes, then at least one box must contain two or more items.

Assuming that a brother needs to wear 3 socks of the same color. Therefore, for all 3 brothers to wear the same color socks, we must pick 4 socks of the same color. Therefore, the minimum number of socks that needs to be picked = 4.  

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The circle's radius is:

(33.912 : 3.14) : 2 = 5.4 (inches)

Answer:

The letter is choose from set of vowels i.e. {a, e , i , o, u}.

Step-by-step explanation:

(a) The trigonometric form of 8 is 8, the trigonometric form of 6i is 6i, and the trigonometric form of cos(-i sin 5) is 1(cos(-i sin 5) + isin(-i sin 5)).

(b) The simplified expression ([tex]\[(1^* - \frac{1+2}{2} + 2) + 3 + 1 = 5\][/tex]) is 4.5, and the simplified expression 2i(i - 1) + (7 + 3i) + (1 + i)(1 + i) is 7 + i.

(a) To write the complex number 8 in trigonometric form, we convert it to the form r(cosθ + isinθ). In this case, r = 8 and θ = 0 since 8 lies on the positive real axis. Therefore, the trigonometric form of 8 is 8(cos0 + isin0), which simplifies to 8.

(b) To write the complex number 6i in trigonometric form, we convert it to the form r(cosθ + isinθ). In this case, r = 6 and θ = π/2 since 6i lies on the positive imaginary axis. Therefore, the trigonometric form of 6i is 6(cos(π/2) + isin(π/2)), which simplifies to 6i.

(c) To write the complex number cos(-i sin 5) in trigonometric form, we convert it to the form r(cosθ + isinθ). In this case, r = 1 and θ = -i sin 5. Therefore, the trigonometric form of cos(-i sin 5) is 1(cos(-i sin 5) + isin(-i sin 5)).

5. Simplify ([tex]\[(1^* - \frac{1+2}{2} + 2) + 3 + 1[/tex]

To simplify this expression, we perform the operations step by step:

([tex]\[(1^* - \frac{1+2}{2} + 2) + 3 + 1\][/tex]

We perform the multiplication and division:

([tex]\[-\frac{3}{2}[/tex] + 2) + 3+1

Finally, we combine like terms:

[tex]\[-\frac{3}{2} + 6\][/tex]

To further simplify, we can convert -3/2 to a decimal:

[tex]\[-\frac{3}{2}[/tex] = -1.5

Therefore, the simplified expression is:

-1.5 + 6 = 4.5

(b) Simplify 2i(i - 1) + (7 + 3i) + (1 + i)(1 + i)

First, let's simplify each term separately:

2i(i - 1) = 2i² - 2i = -2i - 2i = -4i

(1 + i)(1 + i) = 1 + i + i + i² = 1 + 2i - 1 = 2i

Now, let's combine all the terms:

-4i + (7 + 3i) + 2i

Combine the real and imaginary parts separately:

(7 + 0) + (-4i + 3i + 2i) = 7 + i

So the simplified expression is 7 + i.

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