calculate each value for P

The circumference of the 13cm circle is 40.846 cm.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The circumference of a circle is expressed mathematically as;

C = 2πr

Where r is radius and π is constant pi ( π = 3.142 )

Given that; the diameter is 13 cm, the radius is half of that:

radius r = diameter / 2

radius r = 13m / 2

radius r = 6.5 cm

Substituting this into the formula, we get:

C = 2 × π × r

C = 2 × 3.142 × 6.5cm

C = 40.846 cm

Therefore, the circumference is 40.846 cm.

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The solution is:

b. The function has a maximum value. The maximum value of the function is 18.5.

Here, we have,

Let's consider the equation of a parabola.

f(x) = -2x² + 10x + 6

where,

a: -2

b: 10

c: +6

The sign of "a" determines the openness of the parabola. Since a < 0, the parabola is open downwards and has a maximum.

We can find "x" of the vertex using the following expression.

x(v) = -b/2a = -10/2.(-2) = -2.5

We can find the "y" of the vertex by replacing this x in the equation

y(v) = -2.(2.5)² + 10.(2.5) + 6 = 18.5

The vertex (maximum) is (2.5, 18.5).

Hence, The solution is:

b. The function has a maximum value. The maximum value of the function is 18.5.

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The graph of the inequality expression x > -4 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

x>

–

4

Express the inequality properly

So, we have

x > -4

Next, we plot the graph using a graphing tool

The graph is added as an attacment

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The main answer is: d. true. All matrices with orthonormal columns are orthogonal matrices.

An orthogonal matrix is a square matrix with orthonormal columns or rows. In other words, if the columns of a matrix are orthonormal, then it is an orthogonal matrix. This is because the dot product of any two distinct columns of the matrix is 0, which means they are perpendicular to each other.

On the other hand, if the matrix has orthonormal rows, then it is still an orthogonal matrix, but the columns may not necessarily be orthonormal.

Therefore, option d is the correct answer, as all matrices with orthonormal columns are orthogonal matrices.

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The head of hr in a 50,000 person pharmaceutical company wanted to determine if she should implement a work at home policy for the company.

The HR analyst made an error in assuming that correlation implies causation. Just because there is a correlation between marital status and commuting times.

Additionally, the sample size of 15 employees may not be representative of the entire population of the company, which has 50,000 employees. The small sample size may have introduced sampling bias or sampling error, which could affect the generalizability of the findings.

Hence, the HR analyst should not make a decision about implementing a work at home policy based solely on this small and potentially biased sample.

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Answer:

Step-by-step explanation:

Assuming Lauren's speed started at 20 miles per hour , and decreased linearly to zero in a straight line as she applied the brakes, the domain of her graph would be the range of time it takes her to come to a complete stop. In this case, it is 0 seconds to 4.5 seconds.

So the domain of her graph would be [0, 4.5] seconds.

It's worth noting that without more information about the specifics of the braking process, such as the exact shape of the deceleration curve, this is an approximation.

Answer:

Step-by-step explanation:

a. To compute M₁ for y = f(x) on the interval [2, 5], we need to divide the interval into n = 3 subintervals of equal width Δx = (5 - 2)/3 = 1. Then, we can evaluate f(x) at the endpoints and midpoints of the subintervals to get the heights of the corresponding rectangles.

The values of Ax and the locations of the subintervals are:

Ax = Δx [f(2) + f(3) + f(4)] = 1[22 + 25 + 28] = 75

The sketch of the function and the rectangles is shown below:

            |

            |      ___

            |     |   |

            |     |   |

            |     |___|

_____________|___________

   2   3   4   5

b. The area of the region bounded by y = f(x) and the x-axis on [2, 5] is given by the definite integral:

∫[2,5] f(x) dx

= ∫[2,5] (3x + 4) dx

= [3/2 x^2 + 4x] from 2 to 5

= (3/2 (5)^2 + 4(5)) - (3/2 (2)^2 + 4(2))

= 37.5

c. The values computed in (a) and (b) turn out to be the same because the function f(x) = 3x + 4 is a linear function, which means that the area under the curve between any two points is the same as the area of the corresponding trapezoid with height equal to the average of the function values at those points. This is true regardless of the number of subintervals used in the approximation.

If we use a number different than n = 4 and compute M, we will get a different value for the area approximation. However, if the function is continuous and integrable on the interval, the exact area will still be given by the definite integral.

L4 and R4 will not have the same value as the exact area of the region found in (b) because they use the left and right endpoints of each subinterval to determine the height of the corresponding rectangle, which can overestimate or underestimate the true area. M4, on the other hand, uses the midpoint of each subinterval, which tends to give a better approximation to the true area.

Answer: Not enough information.

Step-by-step explanation: To find the value of point B on a number line, you need to figure out where it is. Each point on the line represents a value, with bigger values to the right and smaller ones to the left, assuming zero is on the left. You can find B's value by counting the units from zero to B, or by comparing it to the values of A and C. If you know the values of A and C and where B is between them, you can find B's value.

Median = 23

Q1 = 11.5

Q3 = 42

Minimum = 7

Maximum = 49

We have,

To construct a box-and-whisker plot for the given data, we first need to find the five-number summary, which consists of the minimum, lower quartile (Q1), median, upper quartile (Q3), and maximum values.

Arrange the data in order from smallest to largest:

7, 8, 15, 19, 22, 24, 31, 35, 49, 49

Find the median, which is the middle value of the data:

Median = (22 + 24) / 2 = 23

Find Q1, which is the median of the lower half of the data:

Q1 = (8 + 15) / 2 = 11.5

Find Q3, which is the median of the upper half of the data:

Q3 = (35 + 49) / 2 = 42

Find the minimum and maximum values:

Minimum = 7

Maximum = 49

Thus,

Median = 23

Q1 = 11.5

Q3 = 42

Minimum = 7

Maximum = 49

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The question "How many pages are in the favorite books of students your age?" is a statistical question. This is because the question is asking about a characteristic of a population (students of a certain age group), and the answer will likely vary from person to person. The response to the question is also numerical, which is another characteristic of a statistical question. Therefore, the correct responses are "Statistical; Pages of books have a numerical value" and "Statistical; There are many different answers."

The probability that someone who buys 3 packages will return exactly 1 of them is approximately 0.2448, or 24.48%.

Let's start by calculating the probability of finding at most 1 defective diskette in a single package. We can use the binomial distribution formula for this:

P(X ≤ 1) = P(X = 0) + P(X = 1) = (0.99)¹⁰ + 10(0.01)(0.99)⁹

The first term represents the probability of finding 0 defective diskettes in the package, and the second term represents the probability of finding exactly 1 defective diskette in the package. We can use the formula for combinations to calculate the second term: 10 choose 1.

Using a calculator, we can simplify this expression to:

P(X ≤ 1) = 0.9044

Now, let's consider the three packages. We want to find the probability that exactly one of them will be returned. This means that two of the packages will have at most 1 defective diskette, and one of them will have more than 1 defective diskette.

We can use the binomial distribution again to calculate this probability. Let's define a success as a package with at most 1 defective diskette, and a failure as a package with more than 1 defective diskette. The probability of success is 0.9044, as we calculated earlier, and the probability of failure is 1 - 0.9044 = 0.0956.

Using the binomial distribution formula, we can calculate the probability of exactly one failure in three trials:

P(X = 1) = (3 choose 1)(0.0956)¹(0.9044)²

Using a calculator, we can simplify this expression to:

P(X = 1) = 0.2448 or 24.48

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Answer:

c. There is no ideal debt-equity ratio, because it varies as per the industry.

Step-by-step explanation:

The correct answer is C. Systematic sampling because it is the mechanical sampling of one unit at a certain number of units in a certain order.

In statistical sampling, there is a methodology called systematic sampling wherein items or individuals are picked from a larger population regularly at predetermined intervals.

The reason this method exists is to analyze the smaller representative sample as it's overly ambitious to assess the entire population. It involves computing the interval at which the samples must be taken.

To compute such an interval, all one has to do is divide the size of the population with the desired sample size to get the answer.

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Answer:23

Step-by-step explanation:

Answer:

c=100, d=40

Step-by-step explanation:

Answer:

3.75n + 5.4 is the required answer

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: im ok at these i beleve its Y = 4'2

The team that has best overall record for the season is the falcons because they have a larger mean value of 20.9 points

The mean is the sum of all values divided by the total number of values. Therefore mean can be expressed as;

mean = sum of item /number of item

The mean value of Eagles = (3+24+14+27+10+13+10+21+24+17+27+7+40+37+55)/15

= 310/15 = 20.67

The mean value of falcons = (24+24+10+7+30+28+21+6+17+16+35+30+28+24+14)/15

= 314/15 = 20.93

Therefore since the mean value of falcons is higher than eagles, falcons has the best overall performance.

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Step-by-step explanation:

Three reasonable routes :

92 + 49 + 37 = 178 mi

58+74+37 =169

58+125= 183

Shortest is Beginster - Alswell - Fulby - Endswell   = 169 miles

Answer: The midpoint is at (-0.5, 2.5)

Explanation:

You are given a line segment with two points,

point 1: (-4,3)

point 2: (3,2)

To find the midpoint [tex](x_m,y_m)[/tex] of a line segment, we use these:

[tex]x_m=(\frac{x_1+x_2}{2})[/tex]

[tex]y_m=(\frac{y_1+y_2}{2})[/tex]

So, to solve:

[tex]x_m=(\frac{-4+3}{2})=(\frac{-1}{2})=-0.5[/tex]

[tex]y_m=(\frac{3+2}{2})=(\frac{5}{2})=2.5[/tex]

Answer: 248.846m^3

Step-by-step explanation:

Volume of a cone=1/3pir^2h. The r would be 4.45 because diameter=2r. So, 8.9/2. Then plug everything in the equation, 1/3 pi (4.45)^2 (12) which is 248.846m^3

The statements that are true from the list of options are x = 7, y = 10 and QM = 38

Given that

This means that

NM = LM

So, we have

7x - 18 = 31

This gives

7x = 49

So, we have

x = 7

Next, we have

QM = PM

So, we have

6x - 4 = 5y - 12

So, we have

6(7) - 4 = 5y - 12

This gives

5y = 50

So, we have

y = 10

Calculating the lengths, we have

QM = 6(7) - 4

QM = 38

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If some bags contain 9 "yellow-beads' and rest contain 4 "red-beads", then Cassie has 10 bags of yellow beads and 6 bags of red beads.

Let Cassie has "x" bags which contain 9 yellow beads and "y" bags which contain 4 red beads.

So, the total number of "yellow-beads" is 9x, and the total number of red beads is 4y.

We know that Cassie has 16 bags of beads in total, so we have:

x + y = 16 ...equation(1),

We also know that the total number of beads Cassie has is = 114,

So, 9x + 4y = 114   ...equation(2)

Now, we solve for x and y,

We first solve equation(1) for y,

We get,

y = 16 - x

Substituting this into equation(2),

We get,

9x + 4(16 - x) = 114,

5x = 50

x = 10

Substituting x = 10 into equation(1),

We get,

10 + y = 16

y = 6

Therefore, There are 10 bags of "yellow-beads" and 6 bags of "red-beads".

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Answer:

Step-by-step explanation: 15

Mean means average, add all numbers and divide by amount

Mean= (15+12+14+19+x)/5

        =(60+x)/5

Median means to list numbers in order and pick the middle one

12 14 15 19       x is somewhere in the list in middle

Mode means the number that occurs the most, so 1 of these numbers is repeated

It must be 14 or 15 because the median must be the same as the mean

let's try both

(60+14)/5 =14.8                  (60+15)/15=15

The answer is 15.

The median of the data is M = 15 and the value of x = 15

The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points

Arrange the data points from smallest to largest.

If the number of data points is odd, the median is the middle data point in the list.

If the number of data points is even, the median is the average of the two middle data points in the list.

Given data ,

The mean is calculated by summing all the numbers and dividing by the total count of numbers. In this case, we have 5 numbers, including x.

Mean = (15 + 12 + 14 + 19 + x) / 5

Since the mean is also equal to the median, we can rearrange the numbers in ascending order:

12, 14, 15, 19, x

The median is the middle number in a sorted list of numbers. In this case, the median is 15.

Since the mode is also equal to the mean and median, and we can see that 15 is the only number that appears more than once in the list, we can conclude that 15 is also the mode.

Setting the mean equal to 15 and solving for x:

15 = (15 + 12 + 14 + 19 + x) / 5

Multiplying both sides by 5 to eliminate the fraction:

75 = 15 + 12 + 14 + 19 + x

Subtracting the known numbers from both sides:

75 - (15 + 12 + 14 + 19) = x

15 = x

Hence , the value of x is 15 and median is 15

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The calculated value of x in the circle is 18 degrees

From the question, we have the following parameters that can be used in our computation:

The circle

The angle at a semicircle is 90 degrees

using the above as a guide, we have the following:

5x = 90

Divide by 5

So, we have

x = 18

Hence, the solution for x is 18 degrees

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The coordinates of A' are (5, -3).

Since the reflected quadrilateral A'B'C'D' is then translated 3 units right and 2 units up to form quadrilateral A"B"C"D, the coordinates of A" are (8, -1).

In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

Since quadrilateral A'B'C'D' underwent a reflection across the x-axis to form quadrilateral AB'CD', the original coordinates of triangle NLM can be calculated as follows;

(x, y)            →      (-x, y)

A (-5, -3)      →     A' (5, -3)

By applying a translation, we have:

A' (5, -3)  →      (5 + 3, -3 + 2) = A" (8, -1).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

__________________________________

__________________________________

Answer:

-2, -1/2, 0, 1/4

Step-by-step explanation:

As an = n - 3

when n = 1

then we get

a = 1 - 3

a = -2

when n = 2

then we get

2a = 2 - 3

2a = -1

a = -1/2

when n = 3

then we get

3a = 3 - 3

3a = 0

a = 0

when n = 4

then we get

4a = 4 - 3

4a = 1

a = 1/4

so the first four terms of the sequence are: -2, -1/2, 0, 1/4