Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Plano Power Plant. Ten percent of all plant employees work in the finishing department; 20% of all plant employees are absent excessively, and 7% of all plant employees work in the finishing department and are absent excessively.
1. If a plant employee is selected randomly, and F is the event "works in the finishing department," then P(F) = ________.
A. 0.07
B. 0.10
C. 0.20
D. 0.13
2. A plant employee is selected randomly; F is the event "works in the finishing department" and A is the event "is absent excessively." The probability of intersection of A and F, (P∩F) = __________.
A. 0.07
B. 0.10
C. 0.20
D. 0.23

1. Jada's data set has a mean of 5, Diego's data set has a mean of 6, and Lin's data set has a mean of 4.

2. The data set that has the greatest variability is Lin's data set because it has the highest standard deviation of 3.6.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Question 1.

In this scenario and exercise, we would determine the mean of the three data sets based on the number of text messages sent by Jada, and Diego, and Lin over 6 days as follows;

Mean number of text for Jada = (4 + 4 + 4 + 6 + 6 + 6)/6

Mean number of text for Jada = 30/6

Mean number of text for Jada = 5.

Mean number of text for Diego = (4 + 5 + 5 + 6 + 8 + 8)/6

Mean number of text for Diego = 36/6

Mean number of text for Diego = 6.

Mean number of text for Lin = (1 + 1 + 2 + 2 + 9 + 9)/6

Mean number of text for Lin = 24/6

Mean number of text for Lin = 4.

Question 2.

In Statistics, variability is a measure of the spread of a data set. Also, we would use standard deviation to determine the variability in each data set as follows;

Standard deviation = √(1/n × ∑(xi - u₁)²)

Standard deviation for Jada = √(1/6 × [(4 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (6 - 5)² + (6 - 5)²]

Standard deviation for Jada = √(6/6) = 1

Standard deviation for Diego = √(1/6 × [(4 - 6)² + (5 - 6)² + (5 - 6)² + (6 - 6)² + (8 - 6)² + (8 - 6)²]

Standard deviation for Diego = √(14/6) = 1.53

Standard deviation for Lin = √(1/6 × [(1 - 4)² + (1 - 4)² + (2 - 4)² + (2 - 4)² + (9 - 4)² + (9 - 4)²]

Standard deviation for Lin = √(76/6) = 3.6

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Missing information:

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

An ellipse's equation has its origin at its center, its foci on the y-axis, and its major axis at x2/16+y2/144, which is three times longer than its minor axis.

In mathematics, an ellipse is a planar curve with two focal points, where the total of the two distances from any point on the curve to the focal points is a constant.

It generalizes the shape of a circle, a unique variety of ellipse in which the two focus points coincide.

The eccentricity of an ellipse,  , which ranges from 0 (the limiting case of a circle) to 1 (the length of the ellipse), is used to determine how long it is (the limiting case of infinite elongation, no longer an ellipse but a parabola).

The area of an ellipse has a straightforward algebraic solution, while the perimeter (also known as circumference), for which integration is necessary to arrive at a precise answer, only has approximations.

According to our question-

M(X0|Y)   M(0|0)

(X-X0)^2/a^2 +(Y-Y0)^2/b^2=1

x2/a2+x2b2=1

a=4 b=3 .a=12

x2/16+y2/144

Hence, An ellipse's equation has its origin at its center, its foci on the y-axis, and its major axis at x2/16+y2/144, which is three times longer than its minor axis.

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Answer:

creo que es 15

Step-by-step explanation:

Answer:

can u translate for english?

Step-by-step explanation:

I can't understand

The possible values of x are 3 and 7

Given the rational expression below;

√60-8x = x - 9

Square both sides to have:

(60-8x)² = (x-9)²

60-8x = x²-18x+81

Equate to zero to have;

x²-18x+81 - 60 + 8x = 0

x² - 10x + 21 = 0

x² -3x-7x +21 = 0

x(x-3)-7(x-3) = 0

x = 3 and 7

Hence the possible values of x are 3 and 7

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The 99% confidence interval for the true population mean backpack weight is approximately (68.15, 71.85) ounces, rounded to two decimal places.

To construct a 99% confidence interval for the true population mean backpack weight, we can use the formula:Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √Sample Size).

Since the population standard deviation is known, we can use the z-distribution and find the critical value corresponding to a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576.

Given that the sample mean weight is 70 ounces, the population standard deviation is 6.4 ounces, and the sample size is 48, we can calculate the confidence interval:

Confidence Interval = 70 ± (2.576 * 6.4 / √48).

Simplifying the expression, we get:

Confidence Interval ≈ 70 ± 1.855.

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\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22\)

A member of the senate will serve for (h+4) years.

An expression, in mathematics, is a finite set of combinations and/ or numbers and variables that accurately represents the the context in question. When two or more expressions are connected using the equality sign then an equation is formed.

Here, we are given that in the US government a member of the senate serves for 4 years longer than a member of the House of Representatives.

Also the House of Representatives serves for- h years

Thus, the number of years a member of the Senate will serve will be 4 more than the number h

= h + 4

Thus, a member of the senate serves for (h+4) years.

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Step-by-step explanation:

288 is girl in the class......

The number of total girls students in school is 288 students out of total students.

What information do we have?

Number of total students = 1200

Percentage of girls = 24%

Number of total girls students in school = Number of total students × Percentage of girls

Number of total girls students in school = 1200 × 24%

Number of total girls students in school = 1200 × 0.24

Number of total girls students in school = 288 students

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Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

We have ,

Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.

The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.

Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.

Hence, Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

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complete question:

A. What was Watson’s actual check average? Was this higher or lower than the original budget and flexible budget check average?

b. Were Watson’s actual food sales higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?

c. Was Watson’s actual food cost higher or lower than the original budget? Why do you think this is so?

d. Was Watson’s actual food cost higher or lower than the flexible budget? By how much? Was this favorable or unfavorable? How can Watson use this information in his report to his general manager?

e. Were Watson’s variable salaries, wages, and benefits higher or lower than the original budget?

f. Were Watson’s variable salaries, wages, and benefits higher or lower than the flexible budget? By looking at both the original budget and the flexible budget, what conclusion can you draw about Watson’s ability to control his labor costs?

g. Was Watson’s actual net income higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?

h. Overall, how do you think Watson is doing at meeting the budget goals set by the general manager? How should he respond to his general manager’s claim that his department is operating at a “sub-par” performance level?

Answer:

a) 0.7847 = 78.47% probability that no samples are mutated.

b) 0.9769 = 97.69% probability that at most one sample is mutated.

c) 0% probability that more than half the samples are mutated.

Step-by-step explanation:

For each sample, there are only two possible outcomes. Either they are mutated, or they are not. The probability of a sample being mutated is independent of any other sample, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

2% of cases.

This means that \(p = 0.02\)

12 samples are studied

This means that \(n = 12\).

(a) No samples are mutated.

This is \(P(X = 0)\). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847\)

0.7847 = 78.47% probability that no samples are mutated.

(b) At most one sample is mutated.

This is:

\(P(X \geq 1) = P(X = 0) + P(X = 1)\)

Then

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{12,0}.(0.02)^{0}.(0.98)^{12} = 0.7847\)

\(P(X = 1) = C_{12,1}.(0.02)^{1}.(0.98)^{11} = 0.1922\)

\(P(X \geq 1) = P(X = 0) + P(X = 1) = 0.7847 + 0.1922 = 0.9769\)

0.9769 = 97.69% probability that at most one sample is mutated.

(c) More than half the samples are mutated.

This is:

\(P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)\)

So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{12,7}.(0.02)^{7}.(0.98)^{5} \approx 0\)

So the others(greater than 7) wil be 0 too

0% probability that more than half the samples are mutated.

The nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.

The percentage decrease theory suggests that a decrease in the price of a product or service will lead to an increase in demand for that product or service.

This theory is based on the idea that consumers are more likely to buy a product or service if its price is lower. This theory can be applied to both new and existing products or services.

For example, a retailer may decide to decrease the price of a product in order to attract more customers and increase sales. Similarly, a company may choose to reduce the cost of a service in order to make it more attractive to potential customers.

This question is using the percentage decrease theory. According to this theory,

you can calculate the percentage decrease by subtracting the current value from the original value and then dividing by the original value.

Step 1: Subtract the current number of wild tigers (3200) from the original number of wild tigers (20 years ago).

Original - Current = Change

120,000 - 3200 = 116,800

Step 2: Divide the change (116,800) by the original number of wild tigers (120,000)

Change / Original = Percentage Change

116,800 / 120,000 = 97%

Step 3: Multiply the percentage change (97%) by the original number of wild tigers (120,000)

Percentage Change x Original = Estimated Original

97% x 120,000 = 116,400

Therefore, to the nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.

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Answer:

"B".  Domain is all real numbers, and the Range is all positive real numbers

Step-by-step explanation:

It is important to recognize that this function is an exponential function, either by the graph (observe a horizontal asymptote on the x-axis, and increasing exponentially), or more importantly by the equation which is in exponential form \(y=a*b^x\) where "a" is a non-zero real number, and "b" is a positive real number not equal to 1.

Observe that for the given function, a=4 (a real number not equal to zero), and b=2 (a positive real number that is not 1).

The domain for all exponential functions is all real numbers, so this function's domain is all real numbers.

The Range for exponential functions depends on "a", where if "a" is a positive number the Range is positive numbers only, and if "a" is a negative number, the Range is negative numbers only.

Since "a" is positive, the Range is positive numbers only.

Writing the Domain in "set-builder notation" (since all of the choices are given using that notation), the Domain is "all real numbers" put into curly brackets, so {all real numbers}.

Writing the Range in "set-builder notation", recall that the Range is the outputs of the function, so the Range is "y values such that y is greater than zero".  There is some shorthand used, where the phrase "such that" is symbolized using a short vertical line (common in set-builder notation), and the phrase "y is greater than zero" is shortened using inequality symbols "y>0".  So, the Range is written as { y | y>0 }.

Further, the "Domain" and "Range" are abbreviated with "D" and "R" respectively.

Therefore, the final answer would be D = {all real numbers}; R = { y | y>0 }, which is answer "B"

Answer:

2.7 x 10 7

Step-by-step explanation:

This is the correct answer !

The value of x is 14.

We know in an isosceles triangle an isosceles polygon is a polygon with at least two sides of equal length.

We have two sides measured 2x-9 and x+ 5.

From the figure the length of sides are equal then

2x-9 = x+ 5

2x- 9- x = 5

x-9 = 5

Add 9 to both sides of the equation:

x - 9 + 9 = 5 + 9

x= 14

Thus, the value of x is 14.

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Answer:

71

Step-by-step explanation:

The square represents 90 degrees.

A triangle’s three angles ALWAYS adds up 180.

To find the missing angle:

180 - 90 = 90

90 - 19 = 71.

Therefore, the answer is 71

Answer: If your looking for the slope Intercept form, the answer is y=1x+7

I hope this answer helps you, and Happy Holidays! :)

Answer:

coochieman is different

Step-by-step explanation:

you

must

be

different

too

The particle travels approximately 45.63 units along the path. The displacement is the straight-line distance between the initial and final positions of the particle is 2781.

To find the distance the particle travels along the path, we can integrate the speed over the interval of time. The speed of the particle is given by the magnitude of its velocity vector.

The velocity vector is the derivative of the position function r(t):

\(v(t) = (d/dt)(t^3/3, t^2, 2t)\)

\(= (t^2, 2t, 2)\)

The speed of the particle at any given time t is:

|v(t)| = √((t^2)^2 + (2t)^2 + 2^2)

= √(t^4 + 4t^2 + 4)

= √((t^2 + 2)^2)

To find the distance traveled along the path, we integrate the speed function over the given interval of time. The particle travels from t = -1/3 to t = 9.

distance = ∫[from -1/3 to 9] |v(t)| dt

= ∫[from -1/3 to 9] |t^2 + 2| dt

= ∫[from -1/3 to 0] -(t^2 + 2) dt + ∫[from 0 to 9] (t^2 + 2) dt

= [-1/3 * t^3 - 2t] (from -1/3 to 0) + [1/3 * t^3 + 2t] (from 0 to 9)

Evaluating the definite integrals:

distance = [-1/3 * 0^3 - 2 * 0 - (-1/3 * (-1/3)^3 - 2 * (-1/3))] + [1/3 * 9^3 + 2 * 9 - (1/3 * 0^3 + 2 * 0)]

= [0 - (1/3 * (-1/27) + 2/3)] + [1/3 * 729 + 18]

= [1/27 + 2/3] + [729/3 + 18]

= 1/27 + 2/3 + 729/3 + 18

= 1/27 + 18/27 + 729/3 + 18

= (1 + 18 + 729)/27 + 18

= 748/27 + 18

= 27.63 + 18

= 45.63 units (approximately)

Therefore, the particle travels approximately 45.63 units along the path.

To find the average speed, we divide the distance traveled by the time taken. The time taken is 9 - (-1/3) = 9 1/3 = 28/3.

average speed = distance / time

= 45.63 / (28/3)

= 45.63 * (3/28)

= 4.9179 units per unit time (approximately)

The displacement is the straight-line distance between the initial and final positions of the particle.

displacement = |r(9) - r(-1/3)|

= |(9^3/3, 9^2, 2 * 9) - ((-1/3)^3/3, (-1/3)^2, 2 * (-1/3))|

= |(27, 81, 18) - (-1/27, 1/9, -2/3)|

= |(27 + 1/27, 81

= 2781.

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Answer:

Answer:

Ans. The greates present value is the one that pays 1,000 at the beginning of each year, for 10 years. Assuming a 10% effective annual rate, this present value is equal to1,000atthebeginningofeachyear,for10years.Assuminga106,759.02

Explanation:

Hi, in order to find the present value of an annuity, first we have to take into account if this annuity is paid at the beginning or at the end of each period. This is the formula for an annuity that pays at the beginning of each year.

PresentValue=A+\frac{A((1+r)^{n-1}-1) }{r(1+r)^{n-1} }PresentValue=A+

r(1+r)

n−1

A((1+r)

n−1

−1)

In the case of an annuity that pays at the end of each year is:

PresentValue=\frac{A((1+r)^{n}-1) }{r(1+r)^{n} }PresentValue=

r(1+r)

n

A((1+r)

n

−1)

Where:

A= annuity

r= rate of return

n= periods that will be paid

But, there are 2 types of annuities here(that pay at the beginning of the period), one is paid every year and other that pays every 6 months. Since we are going to assume a rate of return of 10% effective annually, for the first type (pays every year at the beginning) r=10% and n=10, and for the second one (pays at the beginning of every 6 months) r=4.8809% and n=20.

Let me show you the formula to turn an annual effective rate into a semi-annual effective rate.

r(semi-annual)=(1+r(annual))^{\frac{1}{2} } -1=(1+0.1)^{\frac{1}{2} } -1=0.048809r(semi−annual)=(1+r(annual))

2

1

−1=(1+0.1)

2

1

−1=0.048809

Let´s find each present value.

A) Pays 1,000 at the beginning of each year

PresentValue=1,000+\frac{1,000((1+0.1)^{9}-1) }{0.1((1+0.1)^{9} } =6,759.02PresentValue=1,000+

0.1((1+0.1)

9

1,000((1+0.1)

9

−1)

=6,759.02

B) Pays at the beginning of every six months

PresentValue=500+\frac{500((1+0.048809)^{19}-1) }{0.048809((1+0.048809)^{19} }=6,601.75PresentValue=500+

0.048809((1+0.048809)

19

500((1+0.048809)

19

−1)

=6,601.75

C) Pays 1,000 at the end of each year

PresentValue=\frac{1,000((1+0.1)^{10}-1) }{0.1(1+0.1)^{10} }=6,144.57PresentValue=

0.1(1+0.1)

10

1,000((1+0.1)

10

−1)

=6,144.57

D) Pays 500 at the end of every six months

PresentValue=\frac{500((1+0.048809)^{20}-1) }{0.048809(1+0.048809)^{20} }=6,294.52PresentValue=

0.048809(1+0.048809)

20

500((1+0.048809)

20

−1)

=6,294.52

So the answer is A) the one that pays 1,000 at the beginning of each year.

Best of luck.

The distance AB between the two points is 5.7 units

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

A = (2, 2) and B =(-2, -2)

The distance between the two points can be calculated using the following distance equation

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where

(x, y) = (2, 2) and (-2, -2)

Substitute (x, y) = (2, 2) and (-2, -2) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

distance = √[(2 + 2)² + (2 + 2)²]

Evaluate

distance = 5.7

Hence, the distance is 5.7 units

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Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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Answer:

35

Step-by-step explanation:

35 is the answer, it cant be 15 due to red being 21 MORE  

On simplifying the given equation, the value of x = -7/2.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Variables, constants, and mathematical operations including addition, subtraction, multiplication, and division are frequently used in it. Equations can be solved to get the values of the variables that make the equation true. Equations are frequently symbolised with the equals sign (=).

Given,

\((1/4) ^{x+1} =32\)

1/4 can be simplified as\((1/2)^{2(x+1)\)

or it can be written as \(2^{-2x - 2}\)

32 can be expressed as 2⁵

⇒ \(2^{(-2x - 2)} = 2^5\)

As base is same, power will be same,

⇒ -2x - 2 = 5

⇒ 2x + 2 = -5

⇒ 2x = -7

⇒ x = -7/2

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Correct question -

What is the solution to this equation? \((1/4) ^{x+1} =32\)

a: 3/2b: 2c: -2d: -7/2

Answer:

the corect option is c

Step-by-step explanation:

The measure of the angle 4 is 42°.

A pair of angles formed on a straight line are said to be a linear pair. The sum of angles of a linear pair is always 180 degrees.

Given that, the measure of angle 3 is (23x)°, and the measure of angle 4 is (7x)°, we need to find the measure of angle 4,

Since, angle 3 and angle 4 are linear pair angles, therefore,

∠3 + ∠4 = 180°

23x + 7x = 180°

30x = 180°

x = 6

Therefore, ∠4 = 7 × 6

∠4 = 42°

Hence, the measure of the angle 4 is 42°.

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Based on the dimensions of the parallelogram, it can be concluded its area would be 84 square meters.

The area of a parallelogram can be calculated using the following formula:

Area = base x height

This formula is the same that you would use for calculating the area of a rectangle due to the similarities between these two shapes. Now, let's use the formula to know the area:

Area = 12  meters x 7 meters

Area = 84 square meters

This means the total area is 84 square meters.

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4 yr to 6 yr to the lowest term is 2/3.

A fraction represents the parts of a whole or collection of objects e.g 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

A fraction is in its lowest terms if the numerator and denominator have no common factors other than 1. A fraction in lowest terms is also known as a fraction in the simplest form.

4 yr to 6 yr can be written as:

4/6 = 2/3

Note: The numerator and denominator is divided by 2 in order to write 4/6 in lowest term.

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Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x=5/2

Decimal Form:

x=2.5

Mixed Number Form:

x=2 1/2

Step-by-step explanation: