the quality control manager at a computer manufacturing company believes that the mean life of a computer is 80 months, with a variance of 64 . if he is correct, what is the probability that the mean of a sample of 77 computers would be greater than 82.59 months? round your answer to four decimal places.

The standard deviation of the ACT scores is approximately 4.2.

Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much the data values deviate, on average, from the mean (or average) of the data set. A higher standard deviation indicates greater variability or spread in the data, while a lower standard deviation indicates less variability or spread.

According to the given information:

To find the standard deviation of ACT scores, we can use the given information about the mean and the percentage of scores above a certain threshold.

Given:

Mean (μ) = 21.4

Percentage of scores above 26 = 15%

Since the distribution is approximately normal, we can use the Z-score formula to find the Z-score corresponding to the given percentage. The Z-score is the number of standard deviations a particular value is from the mean in a normal distribution.

Z-score formula:

Z = (X - μ) / σ

Where:

Z = Z-score

X = Value (in this case, 26)

μ = Mean (21.4)

σ = Standard deviation (to be found)

We can rearrange the formula to solve for σ:

σ = (X - μ) / Z

Substituting the given values:

X = 26

μ = 21.4

Z = Z-score corresponding to 15% (which can be found using a standard normal distribution table or a Z-score calculator)

Assuming a standard normal distribution table or calculator gives us a Z-score of approximately 1.04 for a percentage of 15%, we can plug in the values:

σ = (26 - 21.4) / 1.04

σ = 4.4 / 1.04

σ ≈ 4.2 (rounded to the nearest tenth)

So, the standard deviation of the ACT scores is approximately 4.2.

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Answer:

≈ $26

Step-by-step explanation:

13% = 0.13

199.99 x 0.13 = $25.9987

So, 13% markup is ≈ $26

Answer: To find the new balance including interest, we need to take into account the interest charged on the current balance and the new purchase.

First, let's calculate the interest charged on the current balance. The monthly interest rate is 18.99% / 12 = 1.5825%.

The interest charged on the current balance is therefore:

interest on current balance = 0.015825 * 9160.00 = 144.98

So the total balance including interest for the current month is:

current balance including interest = 9160.00 + 144.98 = 9304.98

Next, let's calculate the interest charged on the new purchase of $1,098.00. The interest charged on the new purchase is:

interest on new purchase = 0.015825 * 1098.00 = 17.39

So the total balance including interest for the new purchase is:

new balance including interest = 1098.00 + 17.39 = 1115.39

Finally, we add the current balance including interest and the new balance including interest to get the total balance including interest:

total balance including interest = current balance including interest + new balance including interest

total balance including interest = 9304.98 + 1115.39

total balance including interest = 10420.37

Therefore, the new balance including interest is $10,420.37.

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

The explanation is in the picture

Answer:

Your answer should be A

The total number of oranges used in Bertha's pyramid is 24 + 6 + 2 + 1 = 33 oranges.

To calculate how many oranges are used in Bertha's pyramid, we first need to find out how many oranges are in each

layer of the pyramid. Since the base of the pyramid is a rectangle that is 4 oranges by 6 oranges, there are a total of 4 x 6 = 24 oranges in the base layer.

For the second layer of the pyramid, each orange rests on 4 oranges below it.

Since the base layer has 24 oranges, there will be 24 / 4 = 6 oranges in the second layer.

For the third layer, each orange again rests on 4 oranges below it.

So there will be 6 / 4 = 1.5 oranges in the third layer.

Since we cannot have half an orange, we round up to 2 oranges.

Finally, the top layer of the pyramid will consist of a single orange.

Therefore, the total number of oranges used in Bertha's pyramid is 24 + 6 + 2 + 1 = 33 oranges.

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Answer: A

Explanation:

True, there exists a function f such that f(x) > 0, f'(x) < 0, and f"(x) > 0 for all x.

An example of such a function is[tex]f(x) = e^(-x)[/tex], where e is the base of the natural logarithm (approximately 2.718).

Let's verify the given conditions:

f(x) > 0:

Since e^(ax) is always positive for any real value of x and any constant a, [tex]e^(-x)[/tex]is also always positive for any real value of x.

f'(x) < 0:

To find the first derivative, apply the chain rule: [tex]f'(x) = -e^(-x). As e^(-x)[/tex] is always positive, the derivative

[tex]f'(x) = -e^(-x)[/tex] is  always negative for all x.

f"(x) > 0:

To find the second derivative, apply the chain rule again:

[tex]f"(x) = e^(-x). As e^(-x)[/tex]is always positive, the second derivative[tex]f"(x) = e^(-x)[/tex] is always positive for all x.

Thus, it is true that there exists a function f with the given conditions.

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The function [tex]f(x) = e^(-x)[/tex] meets all the given conditions.

True. There exists a function f such that [tex]f(x) > 0, f'(x) < 0, and f"(x) > 0[/tex] for all x. One example of such a function is [tex]f(x) = e^(-x)[/tex].
True. There exists a function f(x) that satisfies the given conditions: f(x) > 0, f'(x) < 0, and f''(x) > 0 for all x.

Consider the function [tex]f(x) = e^(-x)[/tex]. This function has the following properties:

1. f(x) > 0 for all x because the exponential function is always positive.
2. [tex]f'(x) = -e^(-x)[/tex]which is always negative because e^(-x) is always positive, and the negative sign in front makes the derivative negative.
3. [tex]f''(x) = e^(-x)[/tex]which is always positive.

Thus, the function [tex]f(x) = e^(-x)[/tex]meets all the given conditions.

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The best prediction possible for the number of times the spinner will not land on yellow is 18.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

Assuming that the spinner is fair and all outcomes are equally likely, we can calculate the probability of the spinner not landing on yellow in one spin by adding up the probabilities of all other outcomes, which are green, blue, and red.

The probability of the spinner not landing on yellow in one spin is:

P(not yellow) = P(green) + P(blue) + P(red)

= 1/6 + 1/3 + 1/6

= 1/2

Therefore, the expected number of times the spinner will not land on yellow in 36 spins is:

E(not yellow) = 36 x P(not yellow)

= 36 x 1/2

= 18

So the best prediction possible for the number of times the spinner will not land on yellow is 18. However, it's important to note that this is just a prediction based on probabilities, and the actual number of times the spinner doesn't land on yellow in 36 spins may vary.

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Systematic sampling is a type of probability sampling method where every nth item in a population is selected for inclusion in the sample.

For example, if a researcher wanted to select a systematic sample of 100 students from a school population of 1,000 students, they would randomly select one of the first 10 students (1/10th of the population) and then select every 10th student thereafter until they reach 100. Systematic sampling is often used when the population is too large to enumerate and it is more efficient than simple random sampling. However, it is important to ensure that the sampling interval is not biased in any way, otherwise the sample may not be representative of the population.

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Systematic sampling is a relatively easy and quick method of sampling, as it requires less effort and time than other methods such as stratified or cluster sampling.

The starting point is truly random, and that the interval selected does not create any bias in the sample.

Systematic sampling is a method of selecting a sample from a population using a system or a pattern.

It involves selecting every nth item or person from the population after a random starting point has been determined.

To perform systematic sampling, the first item or individual in the sample is randomly selected from the population.

Then, the remaining items or individuals are selected at regular intervals, such as every 10th or 20th item or individual.

The interval is calculated by dividing the population size by the desired sample size.

A researcher wants to select a sample of 100 from a population of 1000, the interval would be. [tex]1000/100 = 10.[/tex]

The researcher would randomly select the first item or individual from the population, and then select every 10th item or individual thereafter until the desired sample size is reached.

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The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = (5/2)^x - 5, we need to find the minimum and maximum values of y that can be obtained by plugging in all possible x values.

To find the maximum value of f(x), we can take the limit as x approaches infinity:

The area of the cement part is 24 m².

Area is the region bounded by a plane shape.

To calculate the area of the part with cement. we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area is 24 m².

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If we shuffle a deck of cards ,turn over first card, then

(a) "Sample-Space" of this experiment is set of all 52 cards.

(b) Number of outcomes in event that the first card is a heart is 13 .

Part (a) : The "Sample-Space" of this experiment refers to all possible outcomes that occur when "first-card" from a shuffled deck of cards is turned over.

In a "standard-deck" of 52 playing cards, the sample space consist of all 52 cards, which includes 4 suits (hearts, diamonds, clubs, spades) each with 13 cards (Ace - 10, Jack, Queen, King).

So, the sample space of this experiment will be set of all 52 possible cards that could be turned over as "first-card".

Part (b) : The event that "first-card" is a heart will consist of all outcomes where the first card turned over is a heart.

In a "standard-deck" of 52 "playing-cards", there are 13 hearts (Ace of Hearts, 2 of Hearts, 3 of Hearts, ..., 10 of Hearts, Jack of Hearts, Queen of Hearts, and King of Hearts).

Therefore, there are 13 outcomes in the event .

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The given question is incomplete, the complete question is

Shuffle a deck of cards and turn over the first card.

(a) What is the sample space of this experiment?

(b) How many outcomes are in the event that the first card is a heart?

The value of x is approximately 10.57 and the value of y is approximately 15.25.

In mathematics, a chord is a straight line segment that connects two points on a curve. More specifically, a chord is a line segment that has its endpoints on the curve.

The term "chord" is most commonly used in the context of circle geometry, where a chord is a line segment that connects two points on the circumference of a circle. In this context, the length of a chord can be calculated using the Pythagorean theorem, given the lengths of the radii of the circle and the distance between the endpoints of the chord.

In a circle, if four chords are connected to form a quadrilateral, then opposite angles of the quadrilateral are supplementary. Using this property, we can set up the following equation:

105 + (7y + 1) + (7x + 1) + (4y + 14) = 180

Simplifying and solving for x and y, we get:

7x + 4y + 122 = 180

7x + 4y = 58 ......(1)

Also, we know that the opposite angles of a cyclic quadrilateral are supplementary. Therefore, we can set up the following equations:

105 + (4y + 14) = 180 ......(2)

(7y + 1) + (7x + 1) = 180 ......(3)

Simplifying and solving for y in equation (2), we get:

4y + 119 = 180

4y = 61

y = 15.25

Substituting this value of y in equation (3) and solving for x, we get:

(7x + 1) + (7*15.25 + 1) = 180

7x + 106 = 180

7x = 74

x = 10.57

Therefore, the value of x is approximately 10.57 and the value of y is approximately 15.25.

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Answer:

To graph this inequality, you can start by graphing the related function y = -x^2 - 1. This is a downward-facing parabola that opens downwards and has a vertex at (0, -1).

To graph the inequality y ≥ -x^2 - 1, you need to shade the region above the graph of the parabola. This is because any point above the parabola will have a y-coordinate that is greater than or equal to the corresponding y-coordinate on the parabola.

So, to graph the inequality, you can shade the region above the parabola. You can use a dotted line to represent the boundary of the inequality, since the inequality includes the possibility of equality (y = -x^2 - 1).

I hope this helps!

The upper control limit for the p-chart is 0.111, and the lower control limit is 0.003.

To calculate the upper and lower control limits for a p-chart, we need to use the following formula:

UCL = p' + 3√(p'(1-p')/n)

LCL = p' - 3√(p'(1-p')/n)

Where p' is the mean proportion of defective pots, n is the sample size (in this case, 120), and UCL and LCL are the upper and lower control limits, respectively.

Given that the proportion of defective pots is believed to be 0.05, we can calculate the mean proportion of defective pots as:

p' = 0.05

Substituting this value in the above formula, we get:

UCL = 0.05 + 3√(0.05(1-0.05)/120) = 0.111

LCL = 0.05 - 3√(0.05(1-0.05)/120) = 0.003

Any sample proportion of defective pots falling outside these limits would be considered statistically significant and warrant further investigation to identify the root cause of the defects in the production process.

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Complete question is:

A random sample of 120 cast aluminum pots is taken from a production line once every day. the number of defective pots is counted. the proportion of defective pots has been closely examined in the past and is believed to be 0.05. what are the upper and lower control limits for the p' chart.

The granite countertop would cost $783.00.

Finding the cost of granite:

To find the cost of granite find the amount of granite that can be used for the entire kitchen.  

Since the kitchen floor is in a rectangle shape find the area of the kitchen floor using the area of a rectangle. Which will equal the amount of granite used for the kitchen.  

Use the formula for the cost of the countertop, which is the product of the area, and the cost per square meter, to determine the total cost.

Here we have

A counter in Adriana's kitchen is 1 m wide and 3 m long.

Hence, the area of the countertop can be found by multiplying the length and the width:

Area of kitchen = length x width = 3 m x 1 m = 3 m²

The cost of the granite is given by $ 261.00 per square meter

The cost of the granite countertop will equal the product of the area and the cost per square meter:

Total Cost = 3 m² x $261.00/m² = $783.00

Therefore,

The granite countertop would cost $783.00.

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Answer:

2.36 miles

Step-by-step explanation:

radius, r = 3 miles∅ = 45°Length of an arc = ∅/360 * 2πr= 45/360 * 2 * 3.14 * 3= 2.36 miles

The "possible-sources" of in the measurement error of an experiment are Instrument error, Human error, sampling error and environmental factors, these sources "may" or "may-not" be enough to account for the percent differences calculated from the data.

There are several possible sources of "measurement-error" in an experiment which affect the accuracy and precision of the results.

These sources include instrument error, human error, environmental factors, and sampling error.

(i) "Instrument-Error" : is defined as inaccuracies in the measuring instruments used in the experiment. This include issues such as calibration errors, sensitivity of the instruments.

(ii) "Human-Error" can arise from mistakes made by experimenters during data collection or analysis, such as misreading measurements or recording data incorrectly.

(iii) "Environmental-Factors", such as temperature, humidity, or electromagnetic interference, can also cause error into experiment if they affect performance of measuring instruments.

(iv) "Sampling-Error" occur when a subset of the population is used for the experiment, and the results are generalized to the entire population.

Depending on the magnitude of these sources of error, they may or may not be enough to account for the percent differences calculated from the data.

If the measurement errors are small and within an acceptable range for the experiment, they may not significantly impact the results.

If the errors are large or systematic, they can introduce significant bias into the data and affect the percent differences calculated.

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The given question is incomplete, the complete question is

Discuss the possible sources of measurement error in an experiment. Are these sources of error enough to account for the percent differences you calculated from your data? write out your answer in a clear and well supported paragraph.

The means of a stock that has a beta measure of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a measure of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the average stock in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

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The greatest common factor of 90 and 315 when divided by the least common multiple of 5 and 15 is 45.

When we multiply all the common prime factors, we get the greatest common factor of the numbers.

These prime factors should come from the prime factorization of the numbers given. These should be in all the unique combinations possible.

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Answer:

25

Step-by-step explanation:

The population of your friend's town is 300,000 if the population of your town is about 30,000.

To solve this problem, we can use the fact that if one quantity is a fraction of another quantity, we can multiply or divide the given quantity by that fraction to find the other quantity. In this case, we know that the population of your town is 1/10th of your friend's town's population, so we can multiply your town's population by 10 to get your friend's town's population.

If the population of your town is about 30,000, and it's about 1/10 the population of your friend's town, we can calculate your friend's town's population by multiplying your town's population by 10.

So, the population of your friend's town is

30,000 x 10 = 300,000

Therefore, your friend's town has a population of about 300,000.

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The expression used  to calculate the surface area of the rectangular prism is given by option b. 2×6 + 2×10 + 2×15.

Let us consider 'l' be the length of the rectangular prism.

'w' be the width of the rectangular prism .

'h' be the height of the rectangular prism.

From the attached figure we have,

Length of the rectangular prism l = 3 units

Width of the rectangular prism w = 2 units

Height of the rectangular prism h = 5 units

Surface of the rectangular prism = 2(lw + wh + hl )

Substitute the values in the formula we get,

⇒Surface of the rectangular prism = 2 (3×2 + 2×5 + 5×3 )

⇒Surface of the rectangular prism = 2 ( 6 + 10 + 15)

⇒Surface of the rectangular prism = 2×6 + 2×10 + 2×15

Therefore, the surface area of the rectangular prism with given dimensions is equal to option b. 2×6 + 2×10 + 2×15.

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The above question is incomplete, the complete question is:

Which expression can be used to find the surface area of the following rectangular prism?

Attached figure.

Answer: If you want me to evaluate its 18x - 2

Hope it helped :D

Answer: question#7 is 7/12

question#8 is 1  3/8

question#5 is 1/2

question#6 is 12

question#9 is 1  1/6

question#10 is 31/40

question#11 is 3/4

Step-by-step explanation: give brainliest

Question #5: Option A, [tex]\frac{1}{2}[/tex]

Question #6: Option A, 12

Question #7: Option A, [tex]\frac{7}{12}[/tex]

Question #8: Option D, [tex]1\frac{3}{8}[/tex]

Question #9: Option D, [tex]1\frac{1}{6}[/tex]

Question #10: [tex]\frac{31}{40}[/tex]

Question #11: [tex]\frac{3}{4}[/tex]

Pls mark brainliest

Answer:

d. 1 7/30...............

Answer:

D

Step-by-step explanation:

2/5 + 5/6

Make the denominator same

(2×6)/30 + (5×5)/30

12+25/30

37/30

1 7/30

The number of ways to arrange the letters of PENCIL when the first letter can't be N or L is option (B) 480.

The word PENCIL has 6 letters, here we have to use permutation method.  If all the letters are used, there are 6! = 720 ways to arrange them. However, the first letter can’t be N or L. This means that there are only 4 choices for the first letter (P, E, C, or I). After choosing the first letter, there are 5 letters left to arrange,

So there are 5! = 120 ways to arrange them.

Therefore, the total number of ways to arrange the letters of PENCIL when the first letter can’t be N or L is

4 x 5! = 4 x 120 = 480

Therefore, the correct option is (B) 480.

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