Among five portable generators produced by an assembly line in one day, there are two defectives. If two generators are selected for sale, find the probability that both will be nondefective. (Assume the two selected for sale are chosen so that every possible sample of size two has the same probability of being selected.)

The probability that fewer than 38 out of 146 eligible voters aged 18-24 voted is approximately 0.8413.

To find the probability that fewer than 38 out of 146 eligible voters aged 18-24 voted, we can use a normal approximation.

First, we need to calculate the mean (μ) and standard deviation (σ) of the distribution. The mean can be calculated by multiplying the total number of eligible voters by the proportion who voted: μ = 146 * 0.22 = 32.12.

Next, we need to calculate the standard deviation using the formula σ = √(n * p * (1 - p)), where n is the sample size and p is the proportion who voted: σ = √(146 * 0.22 * (1 - 0.22)) ≈ 5.868.

Now, we can use the normal distribution to approximate the probability. We want to find P(X < 38), where X follows a normal distribution with mean μ = 32.12 and standard deviation σ = 5.868.

We can standardize the value of 38 using the formula z = (X - μ) / σ, where X is the number of voters.

Calculating z: z = (38 - 32.12) / 5.868 ≈ 1.00.

Finally, we can use a standard normal distribution table or a calculator to find the probability associated with z = 1.00, which is approximately 0.8413.

Therefore, the probability that fewer than 38 out of 146 eligible voters aged 18-24 voted is approximately 0.8413

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To solve for x, we just need to compute the inverse of A (if it exists) and multiply it by b. If A is invertible, then this method will give us the unique solution to the linear system Ax=b.

To solve a linear system of the form Ax=b using inverse matrices, we can first find the inverse of matrix A (if it exists) and then multiply both sides of the equation by \(A^-1\), giving us:

\(A^-1Ax = A^-1b\)

Since\(A^-1A\) is the identity matrix I, we can simplify the left-hand side to just x:

\(x = A^-1b\)

However, it's worth noting that computing the inverse of a matrix can be computationally expensive, particularly for large matrices.

So, while using inverse matrices can be a useful technique for solving small systems, it may not be the most efficient approach for larger systems. In those cases, other techniques such as Gaussian elimination or LU decomposition may be more appropriate.

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Answer:

y = 2x - 3

Step-by-step explanation:

Calculate the gradient of AB.

m = (y2 - y1) / (x2 - x1)

m = (25 - 15) / (9 - 4)

m = 2

The line parallel to AB will have the same gradient.

Use the equation y - y1 = m * (x - x1) and consider the gradient and point C through which the parallel line passes. This is to find the equation of the line parallel to AB in gradient-intercept form y = mx + c.

y + 15 = 2 * (x + 6)

y + 15 = 2x + 12

y - 2x = 12 - 15

y - 2x = -3

y = 2x - 3

Answer: x = - 12

8x + 45 = 10x + 69

⇔ 10x - 8x = 45 - 69

⇔ 2x = -24

⇔ x = -12

Step-by-step explanation:

Answer:

x = -12

Step-by-step explanation:

8x + 45 = 10x + 69

8x = 10x + 24

-2x = 24

x = -12

Answer: x = 3

Step-by-step explanation:

Sqrt(x+7) - 1  = x

Sqrt(x+7) = x + 1

x+7 = x^2 + 1

x = x^2 - 6

x=3

\(126 + 45 = 171\)

\(171\div9 = 9\)

\(\bold{9 \ days}\)

Answer:

D

Step-by-step explanation:

sum of angle in a triangle end up to 180 and the sum of angles in a straight line end up to 180 degrees

Answer:

900

Step-by-step explanation:

a heptagon has 7 sides, so we take the hexagon's sum of interior angles an and add 180 to it's getting us, 720 + 180 = 900 degrees

Other answers are possible.

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

Explanation:

Let's say 10 is the median, and we'll have four values above it and four below. This gives 4+1+4 = 9 total items. One such example could be {6,7,8,9,10,11,12,13,14}. This is the set of whole numbers from 6 to 14 inclusive.

Due to the symmetry of that list, the mean = median = 10

The only problem is the max is 14, when we want it to be 15. We can fix this by adding 1 to each of the upper four values {11,12,13,14} to get {12,13,14,15}.

To balance things out, subtract 1 from each of the lower four values. So we go from {6,7,8,9} to {5,6,7,8}. This balancing is to keep the mean the same at 10.

Therefore, the set  {6,7,8,9,10,11,12,13,14} becomes {5,6,7,8,10,12,13,14,15} which is one possible answer.

There are infinitely many other possible answers. The data set does not have to be symmetric like this.

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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A nation cannot have a comparative advantage in the production of every good. Alpha can produce either 18 oranges or 9 apples an hour, while Beta can produce either 16 oranges or 4 apples an hour. The opportunity cost of producing 1 orange for Alpha and Beta, respectively, are: 0.5 apples; 0.25 apples.

A percentage is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province.

Here,

A country cannot have a competitive advantage in producing every good. Alpha can generate 18 oranges or 9 apples per hour, whilst Beta can produce 16 oranges or 4 apples per hour. The opportunity cost of producing one orange for Alpha and Beta is 0.5 apples and 0.25 apples, respectively.

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Answer: 6 cm, 11 cm, 12 cm

Step-by-step explanation:

The value 30 is not present in the given data set.The given data set is: 67,38,21,89,23,36,82,11,53,77,29,17

In order to search for the values 29 and 30 in the data set using binary search algorithm, the given data set should be sorted in ascending order.

Arranging the given data set in ascending order, we get11, 17, 21, 23, 29, 36, 38, 53, 67, 77, 82, 89

a) Search for value 29 Binary search algorithm for the value 29:

Step 1: Set L to 0 and R to n - 1, where L is the left index, R is the right index, and n is the number of elements in the data set.

Step 2: If L > R, then 29 is not present in the data set. Go to Step 7.

Step 3: Set mid to the value of ⌊(L + R) / 2⌋.Step 4: If x is equal to the value at index mid, then return mid as the index of the element being searched for.

Step 5: If x is less than the value at index mid, then set R to mid - 1 and go to Step 2. This sets a new right index that is one less than the current mid index.

Step 6: If x is greater than the value at index mid, then set L to mid + 1 and go to Step 2. This sets a new left index that is one more than the current mid index.

Step 7: Stop. The algorithm has searched the entire data set and 29 was not found in the given data set. The recursion diagram for the binary search algorithm for the value 29 is:We can see that the binary search algorithm for the value 29 has terminated in the fifth iteration.

Thus, the value 29 is present in the given data set.b) Search for value 30Binary search algorithm for the value 30:

Step 1: Set L to 0 and R to n - 1, where L is the left index, R is the right index, and n is the number of elements in the data set.

Step 2: If L > R, then 30 is not present in the data set. Go to Step 7.

Step 3: Set mid to the value of ⌊(L + R) / 2⌋.

Step 4: If x is equal to the value at index mid, then return mid as the index of the element being searched for.

Step 5: If x is less than the value at index mid, then set R to mid - 1 and go to Step 2. This sets a new right index that is one less than the current mid index.

Step 6: If x is greater than the value at index mid, then set L to mid + 1 and go to Step 2. This sets a new left index that is one more than the current mid index.

Step 7: Stop. The algorithm has searched the entire data set and 30 was not found in the given data set. The recursion diagram for the binary search algorithm for the value 30 is:

We can see that the binary search algorithm for the value 30 has terminated in the fifth iteration.

Thus, the value 30 is not present in the given data set.

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Answer:

7+n

Step-by-step explanation:

More indicates that we are adding an amount to n.

So since it is 7 more, we need to add 7 to n.

Note that an expression does not include an equal sign, so we are done.

Other commonly seen phrases are:

less than ->  indicates subtraction

product of -> indicates multiplication

divided by -> division

The required inequality is 3.5x > 63 oz, where x represents windows Savannah cleans.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let x be the number of windows Savannah cleans.

The amount of window cleaner Savannah uses can be represented by the equation:

3.5x = oz

To represent the inequality that Savannah uses more than 18 windows, we can write:

x > 18

This inequality states that the number of windows Savannah cleans (x) is greater than 18.

Combining both the equation and the inequality we can write

3.5x > 63 oz

It tells us that the amount of window cleaner Savannah uses (3.5x) is greater than 63 oz when she cleans more than 18 windows.

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There are approximately 0.0012 ways (or about 1 way in every 833 attempts) for the person to get 1616 heads out of 2222 tosses.

To calculate the number of ways a person can get 16 heads out of 22 coin tosses, we need to use the binomial probability formula:

P(x) = (nCₓ) * p^x * (1-p)^(n-x)

where:

n = number of trials (coin tosses)

x = number of successful outcomes (heads)

p = probability of success (getting a head on a single toss)

(1-p) = probability of failure (getting a tail on a single toss)

nCₓ = number of combinations of n things taken x at a time

In this case, n = 2222, x = 1616, p = 0.5 (since the coin is fair and has an equal chance of landing on heads or tails), and (1-p) = 0.5.

Therefore, the formula becomes:

P(1616) = (2222C1616) * 0.5^1616 * 0.5^(2222-1616)

where 2222C1616 represents the number of ways to choose 1616 heads out of 2222 tosses.

Using a calculator or a computer program, we can calculate:

P(1616) = (2222C1616) * 0.5^2222 ≈ 0.0012

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Answer:

2,672.45475 (round if needed)

Step-by-step explanation:

44 percent to a decimal is 0.44

2.5 percent to a decimal is 0.025

6,439.65 × 0.44 = 2833.446 (within 15 days)

6,439.65 × 0.025 = 160.99125 (within 30 days)

2833.446 - 160.99125 = 2,672.45475

The area of the triangle with vertices (2, 2), (11, 0), and (5, 7) is 25.5 square units.

To find the area of a triangle with the given vertices, we can use the formula for the area of a triangle:

Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Given the vertices:

A = (2, 2)

B = (11, 0)

C = (5, 7)

Substituting the coordinates into the formula:

Area = 1/2 * |2(0 - 7) + 11(7 - 2) + 5(2 - 0)|

Simplifying the expression:

Area = 1/2 * |-14 + 55 + 10|

Area = 1/2 * 51

Area = 25.5

Therefore, the area of the triangle with vertices (2, 2), (11, 0), and (5, 7) is 25.5 square units.

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a) Contribution (objective value) = $132.14

b) The firm earns $132.14 at the optimal solution.

c) An additional hour of time available for the third machine is worth $0.14 to the firm.

d) An additional 5 hours of time available for the second machine will increase the objective value by $3.69.

The best result obtained from using computer software to solve the LP problem is: X1 = 11.43, X2 = 12.86, X3 = 5.71

b) The number of unused hours at the ideal solution is:

Machine 1 still has 8.57 hours of time left.

There are no hours left on Machine 2 at the moment.

There are still 94.29 hours left on Machine 3.

c) The shadow price of the third limitation is worth an extra hour of time available for the third machine. With the exception of increasing the right-hand side of the third constraint by one unit, we can solve the LP problem using the same constraints to determine the shadow price. Using LP to solve this issue, we discover that the shadow price for the third constraint is

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Given:

Total number of students = 10

To find:

How many was can you award first, second, and third place?

Solution:

Total number of students is 10. So, the total possible ways for the first award is 10.

We know that one student can hold only one place. So, after giving the first award, the number of remaining students is 9 and the total possible ways for the second award is 9.

Similarly, the total possible ways for the third award is 8.

Now, the total number of ways to award first, second, and third place is:

\(10\times 9\times 8=720\)

Therefore, the total number of ways to award first, second, and third place is 720.

To find the estimated project completion time for the given project activities, we need to first calculate the earliest start and earliest finish times and then the latest start and latest finish times.

Using the activity times given, we can calculate the earliest start and earliest finish times for each activity as follows: Activity A: Earliest start time = 0

Earliest finish time = 1

Activity B: Earliest start time = 2

Earliest finish time = 5

Activity C: Earliest start time = 5

Earliest finish time = 11

Activity D: Earliest start time = 11

Earliest finish time = 17

Activity E: Earliest start time = 5

Earliest finish time = 8 Activity F:

Earliest start time = 8

Earliest finish time = 17

Now we can calculate the latest start and latest finish times for each activity using the backward pass.

Latest finish time = 5

Latest start time = 2

Activity A: Latest finish time = 1

Latest start time = 0

Now we can calculate the slack time for each activity as follows:Activity A:

Slack time = 0

Activity B: Slack time = 0

Activity C: Slack time = 0

Activity D: Slack time = 0

Activity E: Slack time = 3

Activity F: Slack time = 0

The critical path for this project is A -> C -> D, since these activities have zero slack time. Therefore, the estimated project completion time is 17 units of time.

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The time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom cannot be determined without additional information.

To calculate the time taken, we need to know the flow rate or discharge rate of the water from the tank. This information is not provided in the question. The time taken to drain the tank depends on factors such as the diameter of the outlet pipe, the pressure difference, and any restrictions or obstructions in the flow path.

If we assume a known discharge rate, we can use the principles of fluid mechanics to calculate the time. The volume of water that needs to be drained is the difference in the volume of water between 3 meters and 0.5 meters above the bottom of the tank. The flow rate can be determined using the pipe diameter and other relevant factors. Dividing the volume by the flow rate will give us the time taken.

However, since the discharge rate is not given, we cannot perform the calculation and determine the time taken accurately.

Without knowing the discharge rate or additional information about the flow characteristics, it is not possible to calculate the time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom.

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Answer:

A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.

Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).

To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:

1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.

2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.

3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.

Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.

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The average temperature in December is 0 degrees Celsius.

We have in July, the average temperature in one US city equals to 29 degrees Celsius and by December ,the average temperature had fallen by 29 degrees Celsius.

We have investigate why the average temperature in dec was 0 degrees Celsius.

Degree of hotness or coldness measured on a definite scale is called Temperature. When the temperature of the body is high it is called hot body and when it is low it is called cold body.

According to question, we have -

Average temperature in July = 29 degrees Celsius.

The fallen average temperature =  29 degrees Celsius.

Let the average temperature of December be x. Then -

x = Average temperature in July - fallen average temperature

x = 29 - 29 = 0

Hence, the average temperature in December is 0 degrees Celsius.

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You can find factorials by simply taking the whole numbers and multiplying each of the numbers that are less than and equal to the given number upto the number 1.

In case of a sequence of multiplication operations, you can multiply the numbers by taking the first two numbers and multiplying the result with the third one and carrying on with the sequence.

Finally, you can calculate the logarithms by using the method called logarithmic log divisions.

The product of a whole number n with each subsequent whole number that is less than or equal to n up to 1 is known as its factorial. *As an illustration, the factorial of 4 is 4* 3 *2 *1, which is 24. It is symbolized by the letter "!"

A logarithm is a mathematical formula that calculates how many times the base, or initial number, must be multiplied by itself to get the target number. Examples of geometric progressions that are related to arithmetic progressions in nature and art include the spacing between guitar frets, the hardness of minerals, the intensity of sounds, stars, windstorms, earthquakes, and acids. Even the way that humans naturally think about numbers is described by logarithms.

To find the factorials of a number let us take an example of number 5, as per the definition of the factorial we first take all the whole numbers less than the number 5 till the number 1, which would be 5,4,3,2,1 and multiply them to get the factorial , i.e 5*4*3*2*1 = 120

Similarly to multiply a sequence of numbers, we can take first two number , calculate their multiplication and multiply the outcome with the third and continue the same with the sequence, for eg, 55*62*63*2 ,

first let us take 55*62 which is 3410

now multiply 3410 by 63 , i.e 3410 * 63 = 214830

and finally calculate , 214830 *2= 429660

And, To find  the logarithms, you can use a technique called logarithmic long divisions which involve following steps:

Write the logarithm as: log(N) = x

Rewrite the logarithm as: 10^x = N

Rewrite the equation as: N = 10^x

Write the number N as a product of prime factors.

Rewrite the equation as: (2^a)(5^b)(p^c) = 10^x, where p is any prime other than 2 or 5

Find the largest power of 10 that is less than or equal to the number N. This is the power of 10 that will be in the final answer.

Divide the power of 10 found in step 6 into the number N. The result will be a quotient and a remainder.

If the remainder is not equal to 0, divide the remainder by the next highest power of 10 and repeat the process until the remainder is equal to 0.

The final result will be the sum of the powers of 2, 5, and any other prime factor that was divided out in the process.

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Answer:

with the Math & Trig function

Step-by-step explanation: