a recent poll of 300 executives' exercise habits revealed that 95 run and 127 bike. 49 reported that they bike and run for exercise. if one of these is executives is randomly selected, what is the probability that they run or bike for exercise? leave your answer as a number between 0 and 1. round to two decimal places.

The equation (5 x 10⁶) (9 × 10⁻²) = 6 x 10⁴ when written in scientific notation. The value of b is 5 and the value of n is 4.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in standard decimal form. The number is written in the form of a number between 1 and 10 multiplied by a power of 10.

The value of b in this equation is 5. This is because the decimal points in both terms must be aligned in order to multiply them together.

The decimal points in each term are 6 and 2, respectively.

Since 6 is greater than 2, the decimal point for the total must be aligned with 6.

This means that the number 5 must be multiplied by 10⁶, resulting in b being 5.

The value of n in this equation is 4. This is because when the two terms are multiplied together, the exponents must be added.

The exponents of 10 in each term are 6 and -2, respectively.

When these are added together, they equal 4, resulting in the exponent of 10 in the new term to be 4.

Therefore, the equation (5 x 10⁶) (9 × 10⁻²) = 6 x 10⁴ when written in scientific notation. The value of b is 5 and the value of n is 4.

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In the event that a monopolistic firm takes over superbly competitive advertising, we would anticipate seeing the advertising cost of the great rise and the amount sold drop.

Be that as it may, when a monopolistic firm takes over the showcase, it picks up showcase control and the capacity to impact the cost. The monopolist can charge a better cost than the competitive advertising cost since there are no near substitutes for its item. As the monopolist raises the cost, the amount requested will drop, as customers switch to substitutes or decrease their utilization of the item.

we would anticipate seeing the advertising cost of the great rise and the amount sold fall as the monopolist tries to extend benefits by raising costs. This is often in differentiating from impeccably competitive advertising.

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The quotient function of f(x) and g(x) is given as follows:

(f/g)(x) = 3x^(3/4).

The functions in the context of this problem are defined as follows:

When we want to divide two functions, we just divide each other, hence:

(f/g)(x) = f(x)/g(x) = 3x/x^(1/4).

When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:

x/x^(1/4) = x^(1 - 1/4) = x^(3/4).

Hence the function is:

(f/g)(x) = 3x^(3/4).

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The probability of heads is 3 times that of tails, so the probability of heads is 0.75 and the probability of tails is 0.25.

Assign a probability of 0.5 to heads

Assign a probability of 0.25 to tails

When a biased coin is tossed the probability of heads is three times as likely to come up as tails.

To find the probability that should be assigned to the outcome of heads and tails the first step is to calculate the probability of heads.

Once this is done,

The probability of heads can be assigned a value of 0.5 and the probability of tails can be assigned a value of 0.25.

After that,

The probability of heads and tails can be calculated accordingly.

The probability of heads and tails when a biased coin is tossed, the first step is to calculate the probability of heads.

Once this is done the probability of heads can be set to 0.5 and the probability of tails can be set to 0.25.

With these probabilities assigned the probability of heads is three times that of tails.

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The results are:

7a) Explicit = h(n) = [tex]0.87^{n-1}[/tex] * 200.

Recursive = h(0) = 200 and h(n) = 0.87 * h(n-1)

7b) Rebound height = 99.76 cm (rounded to the nearest hundredth).

8a) Explicit formula: A(n) = 575 + 47.50n

Recursive formula: A(0) = 575, A(n) = A(n-1) + 47.50

8b) 30 weeks to save $2000'

7a) Explicit: h(n) = [tex]0.87^{n-1}[/tex] * 200 (

where h(n) = height of the golf ball after n bounces,

0.87 is the rebound factor,

200 is the initial height)

h(n) = [tex]0.87^{n-1}[/tex] * 200

Recursive:  h(0) = 200

h(n) = 0.87 * h(n-1)

where h(n) = the height after n bounces,

h(n-1) = height after (n-1) bounces,

0.87 = rebound factor.

Apply given values:

h(0) = 200

h(n) = 0.87 * h(n-1)

7b) Rebound height, using recursive formula:

h(0) = 200

h(1) = 0.87 * 200 = 174

h(2) = 0.87 * 174 = 151.38

h(3) = 0.87 * 151.38 = 131.70

h(4) = 0.87 * 131.70 = 114.71

h(5) = 0.87 * 114.71 = 99.76 (rounded to the nearest hundredth)

8a)Explicit: A(n) = 575 + 47.50n,

where A(n) = amount of money Jessica has after n weeks,

575 = initial amount given by grandfather,

47.50 = amount Jessica adds each week.

Recursive: A(0) = 575, A(n) = A(n-1) + 47.50,

where A(n) = the amount of money Jessica has after n weeks,

A(n-1) = amount Jessica has after (n-1) weeks

47.50 = amount Jessica adds each week.

8b) Weeks to save $2000:

A(n) = 575 + 47.50n = 2000

Solving for n:

575 + 47.50n = 2000

47.50n = 2000 - 575

47.50n = 1425

n = 1425 / 47.50

= 30 weeks.

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Joel cannot make a right triangle with the current lengths of fencing.

A right triangle is a triangle that has one angle that measures exactly 90 degrees (a right angle). This means that the other two angles of the triangle are acute (measuring less than 90 degrees). The side opposite the right angle is called the hypotenuse, and it is always the longest side of the triangle. The other two sides are called the legs of the triangle.

To check if Joel can make a right triangle with the current lengths of fencing, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).

So, let's check if the measurements satisfy the Pythagorean theorem:

8²  + 15² = 64 + 225 = 289

20²  = 400

According to the Pythagorean theorem, a triangle with sides of length 8 ft, 15 ft, and 20 ft would be a right triangle if it satisfies the equation a²  + b²  = c² , where a and b are the shorter sides (legs) and c is the longest side (hypotenuse). However, in this case, we can see that the sum of the squares of the shorter sides (8²  + 15² ) is not equal to the square of the longest side (20² ), so the measurements cannot form a right triangle.

Therefore, Joel cannot make a right triangle with the current lengths of fencing.

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Chad drinks  389.28  fluid ounces of water in 6 days.

A unit of weight equal to ¹/₁₂ troy pound see Weights and Measures Table. : a unit of weight equal to ¹/₁₆ avoirdupois pound. : a small amount. an ounce of sense.

An ounce (oz) is a unit of weight that is equal to one-sixteenth of a pound. Items that weigh approximately one ounce include a slice of bread and a pencil. A fluid ounce is a unit of liquid volume that is equal to one-eighth of a cup. A medicine cup has a volume of approximately one fluid ounce.

given that,

chad drinks 64.88 fluid ounces of water per day,

so in 6 days

he will drink = 6 x water drink per day

= 6 x 64.88

= 389.28

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Answer:

B. 12x^2 + 31x + 20

Step-by-step explanation:

Use FOIL (First, Outer, Inner, Last)

(3x + 4)(4x + 5)

12x^2 + 15x +16x + 20

12x^2 + 31x + 20

Answer:

B

Step-by-step explanation:

You are going to want to use the FOIL method. First outer inner last. Multiply 3x*4x to get 12x^2 then multiply 3x*5 to get 15x then multiply 4*4x to get 16x and last multiply 4*5 to get 20. Since 15x and 16x are like terms we add them together to get 31x

Answer:

the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line

Answer: x=23±√609/10

Step-by-step explanation:

Answer:

[tex]\begin{array}{|c|c|c|c|c|c|} \cline{1-6} & \text{Music} & \text{Gov} & \text{Theater} & \text{Sports} & \text{Total}\\\cline{1-6}\text{7th grade} & 42 & 12 & 20 & 58 & 132\\\cline{1-6}\text{8th grade} & 38 & 9 & 45 & 30 & 122\\\cline{1-6}\text{Total} & 80 & 21 & 65 & 88 & 254\\\cline{1-6}\end{array}[/tex]

"Gov" refers to "Student  Government".

==================================================

Explanation:

The rows are labeled "7th grade", "8th grade" and "Total".

The columns are labeled "Music", "Student  Government", "Theater", "Sports", and "Total".

I'll abbreviate "Student  Government" to "Gov" so that the table doesn't get too wide.

There are 254 students total. This value goes in the bottom right corner of the table. This is the grand total.

----------

We have 80 students in music. This value goes at the bottom of the "music" column since we're in a "total" row. Basically it's the total of all the music students regardless of grade.

Of those 80 students in music, 42 are in seventh grade. Write 42 in the first row of this column and 38 just underneath it (because 80-42 = 38). The two values 42 and 38 should add to the 80 mentioned.

----------

There are 21 students in student government. This value goes at the bottom of the "student government" column.

9 of these students are in eighth grade, so the remaining 21-9 = 12 must be in seventh grade.

----------

There are 65 students in theater. This value goes at the bottom of the "theater" column.

There are 20 such students in 7th grade and 45 in 8th grade (because 65-20 = 45).

----------

There are 88 students in sports.

30 are in 8th grade, so 88-30 = 58 must be in 7th.

----------

At this point, you should have these values along the bottom row:

80, 21, 65, 88, 254

The first four values (80, 21, 65, 88) should add to the grand total 254.

Along each row, add up the values to get the row total.

7th grade: 42 + 12 + 20 + 58 = 132

8th grade:  38 + 9 + 45 + 30 = 122

There are 132 seventh graders and 122 eighth graders.

Those subtotals add to 132+122 = 254 total students, which helps confirm we did things correctly.

So the transformation is: (x, y) → (x + -8, y - 4) which is equivalent to option B.

In mathematics, a transformation is a process that manipulates the position, size, or shape of a geometric object. Transformations can include translations, rotations, reflections, and dilations. They are used to study geometric properties and relationships and are often used in fields such as geometry, algebra, and computer graphics. Transformations are important in understanding symmetry and congruence, as well as in solving problems involving geometric figures.

Here,

We can see that the transformation takes each point of the form (x, y) in ABC to a corresponding point of the form (x', y') in A'B'C'. To find the correct transformation, we need to determine how the coordinates of the points in ABC are related to the coordinates of the corresponding points in A'B'C'. One way to do this is to use the fact that the transformation should preserve the relative distances and angles between the points. Another way is to use the known coordinates of three corresponding points to determine the transformation directly.

In this case, we can see that the transformation maps (-3,-2) to (5,2), (-1,-4) to (7,0), and (-6,-5) to (2,-1). We can use these points to find the transformation:

(x, y) → (x', y')

To map (-3,-2) to (5,2), we need to add 8 to the x-coordinate and add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-1,-4) to (7,0), we again add 8 to the x-coordinate, but this time we only add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-6,-5) to (2,-1), we subtract 4 from the x-coordinate and subtract 4 from the y-coordinate:

x' = x - 4

y' = y - 4

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The option that best describes the data is the option;

Dependent and independent data refers to the relationship between two sets of data.

The specified data in the table indicates;

The data obtained from an household in January is located directly on top the data obtained from the same household in June.

The heating bill depends on the amount of energy used in an household.

The amount of energy used in each household depends on the heating requirement of the household, such that the heating bill for an household in January is related to the heating bill for the same household in June

The correct option is therefore;

The data are related because the heating bills in January and June came from the same households.

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As per the unitary method, the list shows the number of each type of animal on this farm is

Number of pigs = x

Number of horses = 2x

Number of cows = 8x

Let us start by assigning variables to each type of animal on the farm. Let's say the number of pigs is "x".

From the problem statement, we know that there are twice as many horses as pigs. Therefore, the number of horses would be 2x.

Further, we know that there are four times as many cows as horses. So, the number of cows would be 4 times the number of horses. Mathematically, we can represent it as:

Number of cows = 4 * Number of horses

Or, Number of cows = 4 * (2x) = 8x

Therefore, we have the number of each type of animal on the farm as follows:

Number of pigs = x

Number of horses = 2x

Number of cows = 8x

This is the same ratio as we found using the unitary method.

Therefore, our solution is correct.

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The probability of reaching into the bucket and randomly drawing three balls numbered 4, 9, and 7 without replacement, in that order, is 1/990, which is a decimal rounded to the nearest millionth is 0.001.

The probability of drawing three balls numbered 4, 9, and 7 without replacement, in that order, can be found by multiplying the probabilities of drawing each ball in the correct order.

The probability of drawing the first ball, numbered 4, is 1/11, since there is only one ball numbered 4 out of 11 balls in the bucket.

After the first ball is drawn, there are 10 balls remaining in the bucket, and the probability of drawing the second ball, numbered 9, is 1/10, since there is only one ball numbered 9 remaining out of the 10 balls in the bucket.

After the first two balls are drawn, there are 9 balls remaining in the bucket, and the probability of drawing the third ball, numbered 7, is 1/9, since there is only one ball numbered 7 remaining out of the 9 balls in the bucket.

Therefore, the probability of drawing the balls numbered 4, 9, and 7 without replacement, in that order, is:

(1/11) * (1/10) * (1/9) = 1/990

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The probability that the sample contains exactly two defective parts is 0.0058.

We may utilize the binomial probability formula to resolve this issue:

P(X = k) is equal to (n pick k) * p * k * (1-p) (n-k)

where n is the sample size, k denotes the number of successes, p denotes the likelihood that a success will occur, and (n pick k) denotes the binomial coefficient, which indicates the number of possible ways to select item k from n.

Here, n = 5, k = 2, and p = 0.025 (due to the fact that 2.5% of the pieces are flawed).

P(X = 2) therefore equals (5 pick 2)*0.025*2*(1 - 0.025)*3

We calculate P(X = 2) = 0.0058 using a calculator.

As a result, there is a 0.0058 percent chance that the sample has exactly two defective components.

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The optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.

The initial node represents the decision whether to invest in the development of the microbiological product.

The two possible outcomes are a successful development or failure after 2 years.

(b) To determine the policy that the company should adopt to maximize its expected returns, we need to calculate the expected value at each decision node.

Starting from the end nodes and working backwards, we have:

For large-scale production with high sales:

Expected value = 0.75 x $6m + 0.25 x $1m = $4.25m

For large-scale production with low sales:

Expected value = 0.75 x $1m + 0.25 x $6m = $1.75m

For small-scale production with high sales:

Expected value = 0.75 x $4m + 0.25 x $2m = $3.5m

For small-scale production with low sales:

Expected value = 0.75 x $2m + 0.25 x $4m = $1.75m

At the 2-year node, the expected value for a successful development is:

For large-scale production:

Expected value = 0.75 x $4.25m + 0.25 x $1.75m = $3.5m

For small-scale production:

Expected value = 0.75 x $3.5m + 0.25 x $1.75m = $2.81m

Finally, at the initial node, the expected value for investing in the development is:

Expected value = 0.6 x $3.5m + 0.4 x (-$3m) = $0.1m

Therefore, the policy that the company should adopt to maximize its expected returns is to invest in the development of the microbiological product, choose large-scale production if the development is successful, and choose small-scale production otherwise.

(c) If the probability of a successful development is lower than a certain threshold, the option of not developing the product should be chosen. Let p be this threshold probability. Then the expected value at the initial node is:

Expected value = p x $0m + (1-p) x (-$3m) = -$3m + $3mp

Setting this equal to zero and solving for p, we get:

p = 1

Therefore, if the probability of a successful development is lower than 100%, the company should not invest in the development of the microbiological product.

(d) The new owner's utilities represent their preferences for the sums of money involved in the decision.

The utilities are increasing and concave, indicating diminishing marginal utility of money.

This means that the new owner is risk-averse.

The policy identified in (b) may not be optimal for the new owner because their utilities are different from the present-value net returns.

To determine the optimal policy for the new owner, we need to use the new owner's utility values to calculate the expected utility of each decision branch in the decision tree.

If the company invests in large-scale production and high sales are achieved, the expected utility is 0.75 * 0.95 * 1.0 * $6m = $4.285m.

If the company invests in large-scale production and low sales are achieved, the expected utility is 0.75 * 0.95 * (1 - 0.0) * $1m = $712,500.

If the company invests in small-scale production and high sales are achieved, the expected utility is 0.75 * 0.05 * 1.0 * $4m = $150,000.

If the company invests in small-scale production and low sales are achieved, the expected utility is 0.75 * 0.05 * (1 - 0.0) * $2m = $75,000.

If the company decides not to invest in the product, the expected utility is 0.25 * (1 - 0.6) * $0m + 0.25 * 0.6 * (1 - 0.0) * -$3m = -$450,000.

Therefore, the optimal policy for the new owner is to invest in large-scale production. This decision branch has the highest expected utility of $4.285m.

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The probability of getting a straight in a five-card poker hand is 0.0019, which is calculated by dividing the total number of possible straights by the total number of possible five-card hands.

To calculate the probability of getting a straight in a five-card poker hand, we need to first understand the concept of a straight. A straight is a combination of five cards that are in consecutive ranks, such as 6-7-8-9-10 or 10-J-Q-K-A.

The total number of possible five-card hands is given by the mathematical formula 52 choose 5, which is equal to 2,598,960. To calculate the number of possible straights, we need to consider the number of ways that we can choose five consecutive ranks out of the thirteen ranks available in a standard deck of cards. There are 10 ways to do this, since we can start with each of the 10 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10) and have one unique straight for each.

However, there are different ways to arrange the cards in a straight. For example, the straight 10-J-Q-K-A can be arranged in five different ways (10-J-Q-K-A, A-10-J-Q-K, K-A-10-J-Q, Q-K-A-10-J, J-Q-K-A-10). Therefore, the total number of possible straights is 10 * 5 = 50.

To calculate the probability of getting a straight, we divide the number of possible straights by the total number of possible five-card hands. Thus, the probability of getting a straight in a five-card poker hand is 50/2,598,960, or approximately 0.0019. Therefore, the chances of getting a straight are relatively low, but not impossible.

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The proportional relationship is y = 3x.

What is the proportional relationship?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Here, we have

Given:

x:  2, 6, 8, 10

y:  6, 18, 24, 30

We have to find the proportional relationship between x and y.

So, we can see from inspection and visual observation that there is a proportional relationship between x and y.

6 = 3  2,  18 = 3  6, 24 = 3  8, 30 = 3  10.

Hence, The proportional relationship is y = 3x.

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The exponential function for the new participants is f(x) = 3 * 4^x

Let's start with the initial number of participants who sent selfies on Day 0.

We know that Aliyah, Kim, and Reese each sent selfies to 4 friends, so there are 3 x 4 = 12 participants on Day 1.

On Day 2, each of these 12 participants will send selfies to 4 friends, so we will have 12 x 4 = 48 new participants.

We can see that the number of new participants each day is increasing exponentially. In fact, the number of new participants each day is multiplied by 4, since each participant sends selfies to 4 friends.

Therefore, we can write an exponential function of the form:

f(x)=a * 4^x

Where x is the number of days since the challenge started, and $a$ is the initial number of participants who sent selfies on Day 0.

We know that a = 12 from our earlier calculations.

So, we have

f(x) = 3 * 4^x

Hence, the function is f(x) = 3 * 4^x

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The first step is to find the mean number of incorrect answers. Since there are 11 questions, and each question has a 50/50 chance of being answered incorrectly, we can expect the student to get 5.5 questions wrong on average.

Next, we need to calculate the variance. To do this, we can use the formula:

Variance = p(1-p)n

Where p is the probability of getting a question wrong (0.5), and n is the number of questions (11).

Variance = 0.5(1-0.5)11 = 1.375

Finally, we can find the standard deviation by taking the square root of the variance:

Standard deviation = sqrt(1.375) = 1.17 (rounded to two decimal places)

Therefore, the standard deviation of the number of incorrect answers on the exam is 1.17.

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The absolute deviation for the observation of 16 in the data-set is given as follows:

5.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Hence the mean of the data-set in this problem is given as follows:

(19 + 16 + 4 + 9 + 7)/5 = 11.

The absolute deviation of 16 is given by the difference between 16 and the mean of 11, hence:

16 - 11 = 5.

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Answer:

Step-by-step explanation:

Answer:

17.2 hours, or 17 hours and 12 minutes

Step-by-step explanation:

If she reads 50 pages per hour, then 860/50 = 17.2

The probability that a randomly selected student will be taller than 63 inches tall is 0.9332, to the nearest thousandth.

True. A cartesian join, also known as a cross join, returns all possible combinations of rows between two tables. In this scenario, since table a contains two rows and table b contains eight rows, there will be 2 x 8 = 16 possible combinations or rows in the result set.

When a Cartesian join is used to link two tables, it creates a combination of all possible rows between the two tables. In this case, table A has 2 rows and table B has 8 rows. To calculate the number of rows in the result, you simply multiply the number of rows in each table:

2 rows (table A) x 8 rows (table B) = 16 rows

So, when a Cartesian join is used to link table A with 2 rows to table B with 8 rows, there will be 16 rows in the result.

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The statement "if a cartesian join is used to link table a which contains two rows to table b which contains eight rows, there will be sixteen rows in the results" is a true statement.

What is a Cartesian join?

A Cartesian join, also known as a cross join or a cross product, generates a result set that combines every row from the first table with every row from the second table, with no requirements or limits.

If table A has two rows and table B has eight rows, a Cartesian join between the two tables will yield a result set with 16 rows (the product of the number of rows in each table).

So the statement "if a Cartesian join is used to link table A with two rows to table B with eight rows, the results will have sixteen rows" is valid.

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Answer: The formula for the surface area of a cylinder is:

SA = 2πr^2 + 2πrh

where SA is the surface area, r is the radius, and h is the height.

In this case, we know that the surface area is 936π square meters and the radius is 13 meters. So we can plug those values into the formula and solve for h:

936π = 2π(13^2) + 2π(13)(h)

Simplifying:

936π = 338π + 26πh

936π - 338π = 26πh

598π = 26πh

h = 598/26 = 23

Therefore, the height of the cylinder is 23 meters.

Step-by-step explanation:

Step-by-step explanation:

you made some mistakes with the formula.

the surface area of a cylinder is

the outside mantle area

+

the 2 circle areas on top and bottom.

the outside mantle area is

2×pi×radius×height

the 2 circle areas are

2 × pi×radius²

in total that is

2×pi×radius×height + 2×pi×radius² =

2×pi×radius×(height + radius) = 936pi

2×pi×13×(height + 13) = 936pi

pi×(height + 13) = 36pi

height + 13 = 36

height = 36 - 13 = 23 m

a) The percentage of batteries the company expects to replace is:

0.1271 * 100% = 12.71%

b) The company should guarantee the batteries for 34 months (rounded to the nearest month) to ensure that refunds are not made for more than 9% of its batteries under the full-refund guarantee policy.

(a) Let X be the random variable representing the life of a battery. We want to find the probability that a battery fails within 36 months after purchase, which is equivalent to finding P(X ≤ 36).

Using the normal distribution formula with mean μ = 44 months and standard deviation σ = 7 months, we have:

Z = (X - μ) / σ = (36 - 44) / 7 = -1.14

Using a standard normal table or calculator, we find that the probability of a standard normal variable being less than or equal to -1.14 is 0.1271. Therefore, the percentage of batteries the company expects to replace is:

0.1271 * 100% = 12.71% (rounded to two decimal places)

(b) Let Y be the random variable representing the length of the guarantee period in months. We want to find the value of Y such that P(X ≤ Y) = 0.09, where X has the same normal distribution with mean μ = 44 months and standard deviation σ = 7 months.

Using the inverse normal distribution formula with mean μ = 44 months and standard deviation σ = 7 months, we have:

Z = invNorm(0.09) = -1.34

where invNorm is the inverse normal function. Solving for Y, we have:

(Y - μ) / σ = Z

(Y - 44) / 7 = -1.34

Y - 44 = -1.34 * 7

Y ≈ 34.42

Therefore, the company should guarantee the batteries for 34 months (rounded to the nearest month) to ensure that refunds are not made for more than 9% of its batteries under the full-refund guarantee policy.

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