If a shipment has at least 5% defective light bulbs, it will be replaced. If a sample of 60 light bulbs has 2 that are which statement is true? defective,
A The shipment will be replaced.
B The shipment will not be replaced.
C The shipment has 12 defective light bulbs.
D The shipment has 30 defective light bulbs. ​

Answer: If x-1 is a factor of f(x) = 3x^3+kx-13, then f(x) can be written as (x-1)g(x) for some polynomial g(x). This means that f(1) = 0.

We can substitute x = 1 into f(x) to get f(1) = 3(1)^3 + k(1) - 13 = 3 + k - 13 = 0.

Therefore k - 10 = 0, so k = 10

So the value of k is 10.

Step-by-step explanation:

The measurement of ∠1 =  136° and ∠2 = x = 44°, using Vertically opposed angles.

Vertical angles are produced when two lines intersect at a point. They are always on an even playing field. Or, to put it another way, whenever two lines cross or intersect, four angles are formed. As we can see, two opposed angles are equal and are referred to as vertical angles.

They are also referred to as "vertically opposed angles" because of their position directly opposite one another.

∠x = 44

∠2 = x = 44

∠1 + ∠2 = 180

∠1 = 180 - 44 = 136°

Therefore, the angles are 36° and 144°.

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Answer:

y < x + 6

Step-by-step explanation:

The line is broken so that mean that points on the line are not a solution.  The shaded part is below the line so that means that we would use the less than sign.

The slope is 1.  Rise over Run.  We go up 1 and right 1.  1/1 = 1.  The graph crossed the y axis at 6

To find the slope of the line given the points (-6,0) and (0,6), we can use the formula: m = (y2 - y1) / (x2 - x1).

m = (6 - 0) / (0 - (-6)) = 6/6 = 1

Using point-slope form, we can write the equation of the line as:

y - 0 = 1(x + 6)

y = x + 6

To get the inequality we just need to change the equation to the inequality by replacing the equal sign with the inequality sign.

So the linear inequality for the points (-6,0) and (0,6) is:

y > x + 6

Assuming the exponential decay model applies, a similar calculator will cost $10.19 in the year 2023.

Question 2:

Part A:

The amount of caffiene that would still be in her system at bedtime is 28.36 mg

Part B:

The hours before she goes to sleep which she could drink a 16-oz coffee is 6.51 hours.

The average cost of a scientific calculator was $96.50 in 1970 and $22 in 2016. Using the exponential decay model, the cost of a similar calculator in 2023 would be $10.19.

Question 2:

Part A:

Reshanda was invited for coffee at 2:00 pm, and she normally goes to sleep at 10:00 pm. The half-life of caffeine is 5.5 hours. To determine how much caffeine would still be in her system at bedtime, we can use the formula:

C(t) = C0(1/2)^(t/T),

where C(t) is the amount of caffeine in her system at time t, C0 is the initial amount of caffeine (122 mg), t is the time in hours since she consumed the coffee, and T is the half-life of caffeine (5.5 hours).

At 10:00 pm, 8 hours after drinking the coffee, t = 8 hours. Plugging these values into the formula and solving for C(t), we get: C(8) = 122(1/2)^(8/5.5) = 28.36 mg

Part B:

Reshanda cannot sleep if she has 15 or more mg of caffeine in her system. We can use the formula from part A to solve for the time t when the caffeine level drops below 15 mg.

C(t) = 15, C0 = 122, T = 5.5

15 = 122(1/2)^(t/5.5)

then we can isolate t:

t = 5.5 * ln(122/15) = 6.51 hours

So, Reshanda could drink the coffee 6.51 hours before she goes to sleep.

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Answer:

x = -55/7, y = 34/7

Step-by-step explanation:

Solve the following system:

{-7 y - 7 = -41 | (equation 1)

-6 y + x = -37 | (equation 2)

Express the system in standard form:

{0 x - 7 y = -34 | (equation 1)

x - 6 y = -37 | (equation 2)

Swap equation 1 with equation 2:

{x - 6 y = -37 | (equation 1)

0 x - 7 y = -34 | (equation 2)

Multiply equation 2 by -1:

{x - 6 y = -37 | (equation 1)

0 x + 7 y = 34 | (equation 2)

Divide equation 2 by 7:

{x - 6 y = -37 | (equation 1)

0 x + y = 34/7 | (equation 2)

Add 6 × (equation 2) to equation 1:

{x + 0 y = -55/7 | (equation 1)

0 x + y = 34/7 | (equation 2)

Collect results:

Answer: {x = -55/7, y = 34/7

The total surface area and lateral area have a difference of 48 square inches. (Correct choice: D)

In this problem we find a right prism with a rectangular base, of which we must determine its lateral area and its total surface area, both in cubic inches.

Lateral area is the sum of all faces A and C (four rectangles), whereas total surface is the sum of lateral area and all faces B (two rectangles). Area formula for rectangles is shown below:

A = w · l

Where:

Now we proceed to determine the lateral area and the total surface area of the prism:

Lateral area

A' = 2 · (3 in) · (5 in) + 2 · (8 in) · (5 in)

A' = 30 in² + 80 in²

A' = 110 in²

Total surface area

A = A' + 2 · (8 in) · (3 in)

A = 110 in² + 48 in²

A = 158 in²

And the difference between total surface area and lateral area is equal to  48 in².

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Answer:

  (3, 7)

Step-by-step explanation:

Given that points (-4,9), (-6,-5), and (1.-7) are three vertices of a parallelogram with segments connecting them in order, you want the point that is the fourth vertex.

The diagonals of a parallelogram bisect each other, which means they have the same midpoint:

  ((-4, 9) +(1, -7))/2 = ((-6, -5) +(x, y))/2

Multiplying by 2 and subtracting the point on the right side, we have ...

  (-4, 9) +(1, -7) -(-6, -5) = (x, y)

  (-4 +1 +6, 9 -7 +5) = (x, y) = (3, 7)

The fourth vertex is (3, 7).

__

Additional comment

In general three points can define three possible parallelograms. Here, the segments connecting the points are presumed to be the sides of the parallelogram, so reducing the number of possibilities to just one.

The fact that the diagonal midpoints are the same is useful for solving a variety of problems involving parallelograms.

Answer:

(a) 45

(b) 10

(c) 70

Step-by-step explanation:

(a) The number of teachers who teach science but not humanities is:

Number who teach science - Number who teach both subjects

==> 60 - 15 = 45

(b) The number of teachers who teach humanities but not science is:

Number who teach humanities - Number who teach both subjects

==> 25 - 15 = 10

(c) The number who teach humanities or science is Number who teach humanities + number who teach science  - number who teach both

60 + 25 - 15 = 70

There are 30 teachers who teach neither humanities nor science = 100 - 70

Answer:

$18,000

rate of 5 %

Step-by-step explanation:

Answer:

7000 per year. 3000 interest

Step-by-step explanation:

Answer: To find the distance the child travels, we can use the arc length formula: s = r * θ, where s is the arc length, r is the radius of the circle, and θ is the angle of rotation in radians. Since the merry-go-round has a radius of 3m and rotates through 120 degrees, we can convert the angle to radians by multiplying by pi/180.

120 degrees * pi/180 = 2pi/3 radians

Now we can plug in the values into the arc length formula:

s = r * θ

s = 3 * (2pi/3)

s = 2pi

The distance the child travels is 2pi meters, which is the circumference of the circle.

Step-by-step explanation:

The domain and range of the function is input value and output values respectively.

In math function is defined as  a correspondence from one value x of the first set A to another value y of the second set B.

Here we have to state the domain and range of the function.

AS per the definition of the function, we have identified that the domain of a function is the set of values that we are allowed to plug into our function. Which refers that this set is the x values in a function such as f(x).

And the term range of a function is defined as the set of values that the function assumes and which includes the set is the values that the function shoots out after we plug an x value in.

Complete Question:

State the domain and range of the function for the function f. And enter your answers using interval notation. if it is not a function, enter it in all blanks.

Domain: ____

Range: _____

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Answer: B

Step-by-step explanation:

The pumpkin to green bean ratio is 2:1

That means x, the amount of green beans, has to be 1/2 the amount of pumpkin. Therefore the amount of pumkin is 2x.

The total amount of cans would be 3x, which is 114

3x = 114

114/3  = x

x = 38 cans of green beans

According to the given information in the question the mean is 16.71.

A data set's mean (average) is calculated by summing all of the numbers in the set, then reducing by the total number of values within the set. The median is the middle when a data set is sorted from least to greatest. The value that pops up most frequently in a data set is its mode.

The data set's values must first be summed together before being divided by the total number of values to determine the mean. List the data set's values in numerical order to get the median, then note the value that sits in the middle of a list.

mean = (20 + 17 + 19 + 22 + 18 + 17 + 5) / 7

mean = 16.71.

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Based on the data displayed in the histogram, the percentage of students who study 2 or more hours for the midterm is 88%.

A histogram is a graphical representation of data that shows the distribution of a dataset. It is used to show the frequency or the relative frequency of different values within a set of data. It is a bar chart that displays the data in a continuous format, with the bars touching each other.

Based on the histogram, the number of students studying 2 or more hours for the exam are:

= 9 + 6 + 3 + 2 + 1 + 1

= 22 students

While the total number of students studying is :

= 3 + 9 + 6 + 3 + 2 + 1 + 1

= 25 students

The percentage of students study to or more hours can be determined by dividing the number of students studying 2 or more hours with the total number of students studying multiply by 100.

percentage = 22/25 x 100

percentage = 0.88 x 100

percentage = 88%

Therefore, 88% of students study to or more hours for the midterm.

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Jane continues her triathlon training by swimming, then biking 16 miles south and running 12 miles west. Her trainer meets her at the end of the run.

Jane has traveled a total of 28 miles - 16 miles biking and 12 miles running.

Jane is training for a triathlon and is putting in the work to reach her goal. After swimming a few laps in the health club, she bikes 16 miles south. She then runs 12 miles west, bringing her total distance to 28 miles. When she has finished her run, her trainer meets her to check on her progress and offer support for her continued success. Jane's hard work and dedication to her training is admirable and demonstrates her commitment to completing her triathlon. The support from her trainer will be invaluable in helping her reach her goal.

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The amount that you would have to pay in federal income tax if you claim 3 allowances would be:  $65.46

To calculate the amount you will pay in federal income tax using the percentage method of withholding, you will need to know the withholding percentage for your gross pay and the number of allowances you are claiming.

If you claim 3 allowances, each allowance is $80.80, and you gross pay for the week is $710, your taxable income is:

$710 - 3*$80.8 = $710 - $242.4 = $467.6

To find the amount of federal income tax you will pay, you will need to use the withholding percentage for your taxable income. You can find this information by consulting the IRS Circular E (Employer's Tax Guide) or by using an online withholding calculator.

If we use the IRS Circular E, we can find that if you are single and claim 3 allowances, the withholding percentage for a taxable income of $467.6 is 14%.

So the amount you will pay in federal income tax is:

$467.6 * 14% = $65.46

Therefore, you will pay $65.46 in federal income tax if you claim 3 allowances, and your gross pay for the week is $710.

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It is useful to determine the predictive accuracy of a choice model and hence option c is correct for confusion matrix

the misclassification error rate for the following xlminer confusion matrix and the accuracy value of the confusion matrix is 10.82% .

In the field of machine learning, specifically the problem of statistical classification (in unsupervised learning, it is typically referred to as a matching matrix), a confusion matrix, also known as an error matrix, is a specific table structure that enables visualizing the performance of an algorithm.

The literature describes both iterations of the matrix, where each row represents instances in an actual class and each column represents instances in a predicted class. Since it is straightforward to tell whether the system is combining two classes, the name was chosen (i.e. commonly mislabeling one as another).

accuracy is given by the formula :

Accuracy(%) = (true positive + true negative)/(positive + negative)

Here TP true positive =10

and TN true negative is 8.2

hence accuracy = (10+8.2) / (1+0)  %

Accuracy = 10.82%

Therefore the accuracy value of the confusion matrix is 10.82% .

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The sample space for rolling a fair eight-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8}; the correct option is D

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. The likelihood of an event occurring might range from 0 to 1. A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results.

Given;

An eight-sided die,

The sample space=?

Now, when eight sides die is tossed there will be 8 sample spaces that are;

1, 2, 3, 4, 5, 6, 7, 8,

Hence, S = {1, 2, 3, 4, 5, 6, 7, 8}

Therefore, the probability sample space will be S = {1, 2, 3, 4, 5, 6, 7, 8}

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Conducting a simulation can help to establish a cause and effect relationship between two variables is false regarding the use of simulation.

By enabling the testing of various scenarios or process improvements, a simulation is a modeling that replicates the operation of a current or proposed system. It provides evidence for decision-making. This can be integrated with virtual reality technologies for a more engaging experience.

Using simulation modeling, real-world issues can be safely and effectively solved. It provides a crucial analytical method that is easy to verify, interpret, and explain. Through providing precise insights into complex systems, simulation modeling offers beneficial solutions across sectors and disciplines.

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Answer:

The volume of the cubical tank is 42 cm x 42 cm x 42 cm = 84,764 cm^3

If the tank is filled up to the height of its edge, it means that the water filled up to the height of 42cm, and the volume of the water filled is 42cm x 42cm x 42cm = 84,764 cm^3

The volume of 1 jug = 1.3 litres = 1300 cm^3

The total volume of water spilled = 2.45 litres = 2450 cm^3

The total volume of water that can be filled into jugs = total volume of water in tank - volume spilled = 84764 - 2450 = 82314 cm^3

If we divide the total volume of water that can be filled into jugs by the volume of 1 jug, we get 82314/1300 = 63.6

The maximum number of jugs that were fully filled is 63, as the fraction of 0.6 jugs is not possible.

The equation y-4 = 5/3 ( x+3). can be written in standard form as 3y-5x = 15

A linear equation is the equation in which the highest power of it's variable is 1. A linear equation can be with a variable or more. y-4 = 5/3 ( x+3) is an example of linear equation with two variables.

The standard form of writing the linear equation is in the form Ax+By = C

Where C Is the constant and A and B are the coefficient of the variable x and y.

y -4 = 5/3 (x+3)

opening the parentheses

y = (5/3)x +5

y - (5/3)× = 5

multiply both sides by 3

3y -5x = 15

therefore the standard form of writing y-4 = 5/3 ( x+3) is 3y -5x = 15

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The percentage of oak trees in park is 7.14% and there are 14 times more trees in the park than giant oak trees.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

The total number of trees in a park is = 56

The number of giant oak trees in the park is = 4

To find the percentage of oak trees, use the formula -

(Number of Oak Trees/Total number of trees) × 100

Substitute the values into the formula -

(4/56) × 100

(1/14) × 100

7.14%

The number of times (x) that bigger oaks is lesser in comparison to other trees can be found using the arithmetic operation of division.

The equation is -

4x = 56

x = 56/4

x = 14

Therefore, there are 14 times more trees.

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Answer:

12

Step-by-step explanation:

√144 =12 answer

12 is right answer

Answer:

[tex]m=-\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\Delta y=-1,\,\Delta x=2\\\rightarrow \frac{\Delta y}{\Delta x}=\frac{-1}{2}=-\frac{1}{2}[/tex]

[tex]\Delta[/tex] represents change in both variables, so we calculate the slope this way.

Answer:

m=-1/2

Step-by-step explanation:

Use slope formula: [tex]m=\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]

Here is an example of how the code to rotate the cube could be implemented in Python:

class RooCube:

   def __init__(self):

       self.colors = ["w", "b", "o", "g", "y", "r"]

   def left(self):

       self.colors = [self.colors[1], self.colors[5], self.colors[2], self.colors[3], self.colors[0], self.colors[4]]

   def right(self):

       self.colors = [self.colors[4], self.colors[0], self.colors[2], self.colors[3], self.colors[5], self.colors[1]]

   def up(self):

       self.colors = [self.colors[3], self.colors[1], self.colors[0], self.colors[5], self.colors[4], self.colors[2]]

   def down(self):

       self.colors = [self.colors[2], self.colors[1], self.colors[5], self.colors[0], self.colors[4], self.colors[3]]

class RooRunner:

   def __init__(self):

       self.cube = RooCube()

   def rotate(self):

       direction = input("What direction would you like to rotate (left, right, up, down)? ")

       if direction == "left":

           self.cube.left()

       elif direction == "right":

           self.cube.right()

       elif direction == "up":

           self.cube

This would give us the required result.

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3 teragrams is equal to 3 million grams.

The formula to convert teragrams (tg) to grams (g) is: grams = teragrams x 1000000000000. For example, to convert 15 teragrams to grams, we multiply 15 by 1000000000000, which equals 1.5e+13 or 150000000000000 grams. To convert grams to teragrams, we reverse the formula by dividing grams by 1000000000000. For example, to convert 1500000000000 grams to teragrams, we divide 1500000000000 by 1000000000000, which equals 1.5 teragrams.1 tg (teragram) is equal to 1000000 g (grams).

To calculate how many grams are in a teragram, you can use the following formula:

Grams = Teragrams x 1,000,000

For example, let's say you have 3 teragrams. To find out how many grams this is, you would use the formula above:

Grams = 3 tg x 1,000,000

Grams = 3,000,000 g

In other words, 3 teragrams is equal to 3 million grams.

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The average number of text messages that Quentin could have sent is given as follows:

At most 20.

The maximum number of text messages that can be sent on the entire plan is given as follows:

1000.

The amount sent by Sarina is given as follows:

400.

Hence the maximum amount of text messages that Quentin can send is given as follows:

1000 - 400 = 600.

Hence the maximum average over 30 days is given as follows:

600/30 = 20.

Hence the inequality is:

0 ≤ x ≤ 20.

(as the average number of messages cannot be negative).

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Yes this sample(straightforward random sample)representative of the class's performance on the quiz

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values. ​

A teacher randomly selects eight students from the class and averages their test scores to forecast how well her first period class will fare on their upcoming quiz. Is this sample indicative of how the class performed on the test?

Yes, since it is a straightforward random sample. ​

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Answer: There are 120 ways to arrange the letters.

Step-by-step explanation:

The number of unique permutations will be 90720.

To find unique permutations for any word, one needs to break the word into letters,

In the present case the word has 9 letters, out of which 'P' and 'H' are the repeating letters.

The basic method of finding unique permutations for a word is calculating the total number of words and doing its factorial.

for e.g. in the word "WORD"

the number of unique permutations is 4! = 24 unique combinations.

But for the given question the number of unique permutations will be as follows:-

9!/2!*2!= 90720

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Answer:

6 divided by 2/3 = 9

Step-by-step explanation:

Steven cuts the 6 ft long rope by 2/3 to make 9 pieces and the answer is mathematically correct, via calulcator