assume that the amount of time that it takes an employee to service a car at an oil change facility follows the uniform probability distribution between 21 and 38 minutes. what is the standard deviation of this distribution? group of answer choices

EXPLANATION

Given the line on the graph, we need to find the slope and the y-intercept.

Considering two ordered pairs, as for instance (x₁,y₁)=(50,-90) and (x₂,y₂)=(80,90)

The slope-equation is:

Replacing terms:

The point-slope form of the line is:

y-y₁= m(x-x₁)

Finally, we need to represent as a point-slope form considering either one ordered pair, as for instance, (x₁,y₁)=(50,-90)

y-(-90) = 6(x-50) [Simplifying terms]

y + 90 = 6(x-50) [ANSWER]

sin t = -7/25, cos t = 24/25, sec t = 25/24, csc t = -25/7, and cot t = -24/7.

Given, tan t = -7/24 and π/2 < t < π.

We can use the fact that tangent is negative in the second quadrant (π/2 < t < π) and draw a right-angled triangle with angle t in the second quadrant, opposite side -7 and adjacent side 24.

Using Pythagoras theorem, we can find the hypotenuse of the triangle, which is √(24² + 7²) = √(576 + 49) = √625 = 25.

So, sin t = -7/25 (opposite/hypotenuse)
cos t = 24/25 (adjacent/hypotenuse)
sec t = 25/24 (hypotenuse/adjacent)
csc t = -25/7 (hypotenuse/opposite)
cot t = -24/7 (adjacent/opposite)

Therefore, sin t = -7/25, cos t = 24/25, sec t = 25/24, csc t = -25/7, and cot t = -24/7.

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The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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Dilation and rotation transformation produces shapes that are not congruent.

Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.

Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.

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The 7th term of the geometric sequence is 3675/64.

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant called the common ratio.

The 7th term of a geometric sequence can be found using the formula:

a_n = a_1 * (r)^(n-1) where a_1 is the first term of the sequence, r is the common ratio, and n is the position of the term in the sequence.

Given that the common ratio is 3/2 and the first term is 5, we can substitute these values into the formula:

a_7 = 5 * (3/2)^(7-1)

After solving the expression we get:

a_7 = 5 * (3/2)^6 = 5* (243/64) = 15*243/64 = 3675/64

So the 7th term of the geometric sequence is 3675/64.

Therefore, the 7th term of the geometric sequence is 3675/64.

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Answer:

is closer to the club José

is looking for a common denominator

Juan 5/6 = 10/12

Pedro 2/3 = 8/12

Luis 1/2 = 6/12

José 11/12

the largest is chosen

Pirya needs 1 1/2 cups of raspberries for 3/4 of a cake, so she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.

A fraction is a numerical representation of a portion of a total. It consists of two integers, a numerator and a denominator, separated by a line or slash. The numerator reflects the number of equal portions of the whole that are being considered, while the denominator represents the total number of equal parts in the whole. For instance, the fraction "1/2" denotes one of two identical pieces, or half, of the whole. Mathematicians frequently utilize fractions to represent quantities, ratios, and proportions. They are also used in everyday life to signify amounts, such as one-half of a pizza or one-third of a cups of sugar.

How to solve?

she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.

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The solution set to the given inequality is

(-∞, -4) U (2,∞)

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

5(x – 2)(x + 4) > 0

First we solve for x, we replace the inequality sign by = sign

5(x – 2)(x + 4) = 0

Divide both sides by 5

(x – 2)(x + 4) = 0

Now we set each factor =0  and solve for x

x-2 =0 , so x= 2

x+4 =0, so x= -4

Now we use number line and make three intervals

First interval -infinity to -4

second interval -4 to 2

third interval 2 to infinity

Now we check each interval with our inequality

First interval -infinity to -4, pick a number in this interval and check with our inequality. lets pick -5

5(-5 – 2)(-5 + 4) > 0

35>0 is true

second interval -4 to 2, pick a number in this interval and check with our inequality. lets pick 0

5(0– 2)(0 + 4) > 0

-40>0 is false

Third interval 2 to infinity, pick a number in this interval and check with our inequality. lets pick 3

5(3 – 2)(3 + 4) > 0

35>0 is true

solution set are the intervals that make the inequalities true

(-∞, -4) U (2,∞)

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Question:

What is the solution set to the inequality 5(x – 2)(x + 4) > 0?

The weight of an object is given by the formula weight = mass * gravity, where gravity is approximately 9.8 m/\(s^2\). So, in this case, the weight of the object is 10 kg * 9.8 m/\(s^2\) = 98 N.

Since the displacement of the object from its equilibrium position is 9.8 cm = 0.098 m, we can set up the equation:

98 N = K * 0.098 m

Solving for K, we find:

K = 98 N / 0.098 m = 1000 N/m

Now, let's formulate the initial value problem for y(t). The displacement of the object from its equilibrium position is denoted by y(t), and we need to find the equation involving y(t), its first derivative y'(t), its second derivative y''(t), and time t.

Using Newton's second law, the sum of the forces acting on the object is equal to the mass of the object times its acceleration. The forces acting on the object are the force exerted by the spring, given by -K * y(t), and the force F(t) given in the problem. So, we have:

m * y''(t) = -K * y(t) + F(t)

Substituting the values for m and K, we have:

10 kg * y''(t) = -1000 N/m * y(t) + 70 N * cos(8t)

This is the initial value problem for y(t).

To solve the initial value problem for y(t), we need to find the equation of motion for y(t). This is a second-order linear non-homogeneous differential equation. The general solution to this type of equation is a sum of the complementary solution (the solution to the homogeneous equation) and a particular solution (any solution that satisfies the non-homogeneous part).

The complementary solution is found by setting F(t) to zero:

10 kg * y''(t) = -1000 N/m * y(t)

The characteristic equation for this homogeneous equation is:

10\(r^2\) + 1000 = 0

Solving for r, we find r = ±sqrt(-100) = ±10i

So, the complementary solution is:

y_c(t) = c1 * cos(10t) + c2 * sin(10t)

Now, we need to find a particular solution. In this case, since F(t) is of the form A * cos(8t), a particular solution can be assumed to be of the form:

y_p(t) = A * cos(8t)

Substituting this into the differential equation, we get:

-1000 N/m * (A * cos(8t)) = 70 N * cos(8t)

Simplifying, we find A = -0.07 m.

Therefore, the particular solution is:

y_p(t) = -0.07 * cos(8t)

The general solution is the sum of the complementary and particular solutions:

y(t) = y_c(t) + y_p(t)

     = c1 * cos(10t) + c2 * sin(10t) - 0.07 * cos(8t)

To determine the maximum excursion from equilibrium made by the object, we need to find the maximum value of |y(t)|.

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Answer:9

Step-by-step explanation:

the square root of 87 is 9.32737905309 which rounds to 9

Note that function f'(x) is always positive for x > 1 because ln(x) > 0. Therefore, f(x) is strictly increasing for x > 1 and has only one root on its entire domain.

To find an interval of length 1 which has integer endpoints on which the function has a root, we can check the function values at integer points starting from 1.

f(1) = ln(1) - 1/1 = -1

f(2) = ln(2) - 1/2 > 0

f(3) = ln(3) - 1/3 < 0

Since f(1) is negative and f(3) is positive, there must be a root of f(x) between x = 1 and x = 3. Let's check the derivative to prove that there is only one root on the entire domain.

f'(x) = 1/x^2 - 1/x^2 * ln(x)^2 = 1/x^2 * (1 - ln(x)^2)

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Answer:

Perímetro = 8.925 metros

Step-by-step explanation:

La formula del perímetro de un rectángulo es:

perímetro = 2(ancho + largo)

en este caso:

p = 2(a+b)

a = 3b/4

b = 2.55m

a = ancho del rectángulo

b = largo del rectángulo

entonces:

sustituyendo el valor de la segunda ecuación

p = 2((3b/4)+b)

p = 2((3b/4)+(4b/4))

p = 2(7b/4)

p = 14b/4

p = 7b/2

p = 7*2.55/2

p = 8.925m

The tendency to perceive meaningful patterns in random sequences of outcomes often leads us to underestimate the extent to which outcomes result from CHANCE .

The word "chance" describes unpredictability or the unexpected in relation to things like events that happen without a clear reason why and without human intention.

The conclusion is that chance is the tendency of people to recognize different kinds of significant patterns in a random order or sequence in addition to evaluating any kind of outcome. Because chance can also result in an underestimating of a system's conclusion or result, it is crucial to consider it when conducting an investigation.

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There are 5040 possible combination of 7 letter words using 3 vowels and 4 consonants.

We know that the word must have 4 consonants and 3 vowels. We have the following vowels in "mathisfun" : i, a, and u.

We have 7 letters that can be used as consonants: m,t,h,s,f,n.

First we need to find the number of ways to choose the 4 consonants out of 7 possible letters, which is 7C4 = 35.

Then we need to find the number of ways to arrange the 4 consonants and 3 vowels, which is 4!*3! = 144

Finally, we multiply those two values together: 35 * 144 = 5040.

So there are 5040 7 letter words that can be made from "mathisfun" if each word must have 4 consonants and 3 vowels.

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Answer:

1 baseball cost $4

1 ping pong cost $1.5

Step-by-step explanation:

let the cost of baseball be b and the cost of ping pong be p

10 baseballs = 10b

4 ping pong = 4p

Adding both gives total $46

10b + 4p = 46 •••••••••(i)

baseball costs 1 dollar more than 2 ping pong

b = 2p + 1 •••••••(ii)

Substitute ii into i

10(2p + 1) + 4p = 46

20p + 10 + 4p = 46

24p = 46-10

24p = 36

p = 36/24

p = $1.5

b = 2p + 1

b = 2(1.5) + 1

b = 3 + 1 = $4

Answer:

1 1/6

Step-by-step explanation:

10/12 = 5/6

1/3 = 2/6

2/6 + 5/6 = 7/6

7/6 = 1 1/6

When one zero of the polynomial p(x) = x^2 + 3x + k is 2, the value of k is -10.

If one zero of the polynomial p(x) = x^2 + 3x + k is 2, it means that when we substitute x = 2 into the polynomial, the result is zero.

Let's substitute x = 2 into the polynomial p(x) and set it equal to zero:

0 = (2)^2 + 3(2) + k

0 = 4 + 6 + k

0 = 10 + k

To solve for k, we subtract 10 from both sides of the equation:

k = -10

Therefore, when one zero of the polynomial p(x) = x^2 + 3x + k is 2, the value of k is -10.

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When the increment operator precedes its operand, as

++num, the expression is in prefix mode.

When the increment or decrement operator is placed before the operand ( to the operand's left), the operator is being used in prefix mode.

A prefix is defined by specifying its name with the name= keyword, its optional short name with the sname= keyword, optional input names with iname=, and the keyword prefix.

During an assignment of one variable to other the prefix mode of increment and decrement first increments or decrements the variable's value then updated value of the variable is used in assignment.

Postfix mode on the other hand is when the increment or decrement operator is placed after the operand (or to the oper and's right) .

Pre-increment, (for example, ++n) increments the value first, and then performs the specified operation.

Therefore, When the increment operator precedes its operand, as ++num, the expression is in prefix mode.

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Answer:

answer =3/2 or x = -7/2

Step-by-step explanation:

....

Virtual reality" is the appropriate answer.

The utilization of technological advances gives the impression of a 3D interactive environment wherein the things that have such a perception of space embodiment or involvement, are considered as Virtual reality.

Virtual reality implementations often include:

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Answer:

27 meters

Step-by-step explanation:

Given

\(Fishing\ Line =12m\) ----- from hook

\(Andy =15m\) ---- from the fishing line

Required

Distance between Andy and the hook

The scenario can be represented as:

Hook ----------------------- Fishing Line ----------------------------- Andy

Using the above representation, the distance (d) between Andy and the hook is:

\(d = Andy + Fishing\ Line\)

\(d = 15m + 12m\)

\(d = 27m\)

The probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.

The probability mass function (PMF) and cumulative mass function (CMF) for the random variable x, which denotes the number of parts correctly classified in an optical inspection system, can be determined.

Since the classifications of the parts are independent, we can use the binomial probability distribution to model this scenario. The PMF gives the probability of obtaining a specific value of x, and the CMF gives the probability of obtaining a value less than or equal to x.

The PMF of x is given by the binomial probability formula:

P(x) = (n C x) * p^x * (1 - p)^(n - x)

where n is the number of trials (number of parts inspected), x is the number of successes (number of parts correctly classified), and p is the probability of success (probability of correct classification of any part).

In this case, n = 3 (three parts inspected) and p = 0.98 (probability of correct classification).

Let's calculate the PMF for x:

P(x = 0) = (3 C 0) * (0.98^0) * (1 - 0.98)^(3 - 0) = 0.0004

P(x = 1) = (3 C 1) * (0.98^1) * (1 - 0.98)^(3 - 1) = 0.0588

P(x = 2) = (3 C 2) * (0.98^2) * (1 - 0.98)^(3 - 2) = 0.3432

P(x = 3) = (3 C 3) * (0.98^3) * (1 - 0.98)^(3 - 3) = 0.941192

The PMF for x is:

P(x = 0) = 0.0004

P(x = 1) = 0.0588

P(x = 2) = 0.3432

P(x = 3) = 0.941192

To calculate the CMF, we sum up the probabilities up to x:

F(x) = P(X ≤ x) = P(x = 0) + P(x = 1) + ... + P(x = x)

Using the calculated probabilities, the CMF for x is:

F(x = 0) = 0.0004

F(x = 1) = 0.0592

F(x = 2) = 0.4024

F(x = 3) = 1.0

Therefore, the probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.

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Step-by-step explanation:

p + p + 7 = p + 5 + 4

2p + 7 = p + 9

2p - p = 9 - 7

p = 2

\( ({10}^{2} ) {}^{4} = {10}^{2 \times 4} = {10}^{8} \)

I hope this can help you ^_^

Answer:

Only n if 2n is/3 when 2nis divide by 3

Answer:3

Step-by-step explanation:

you could only divide 2n in 3 was there so it would be three

Answer:

r = 7 cm

Step-by-step explanation:

Given that,

Volume of the packing tube, V = 1761 cm²

The altitude of the tube, h = 11 cm

We need to find the radius of the packing tube. The volume of the the cylindrical shaped object is given by :

\(V=\pi r^2 h\\\\r^2=\dfrac{V}{\pi h}\\\\r^2=\dfrac{1761}{\pi \times 11}\\\\r=7.13\ cm\)

or

r = 7 cm

So, the radius of the packing tube is 7 cm.

The number of edges that the prism has is

When a plane intersects a prism, the shape formed is known as the cross section. The cross section of the prism will have the same form as the base if it is divided by a plane that runs horizontally and parallel to the base.

A prism is a 3-dimensional object with two congruent and parallel bases (which are polyggonal) connected by rectangular lateral faces. The number of edges of a prism is equal to the sum of the number of edges of the two bases and the number of lateral faces.

Each base of the prism has n edges, so the two bases together have 2n edges. The number of lateral faces of the prism is equal to the number of edges of one of its bases, so there are n lateral faces. Each lateral face has 4 edges, so the total number of edges of the lateral faces is 4n.

Therefore, the total number of edges of the prism is equal to the sum of the number of edges of the two bases (2n) and the number of lateral faces (4n), which is 2n + 4n = 6n.

In conclusion, the cross section of a prism is an n-sided polygon and the prism has n + 2 edges.

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Answer:

68.9

Step-by-step explanation:

     Let's take the formula: (C*9/5)+32=F

     Now let's substitute C for 20.5:

(20*9/5)+32=F

36.9+32=F

68.9=F

     So, 20.5 centigrade/celsuis is 68 temperature in fahrenheit.

The width of the rectangle is 9 meter.

Now, According to the question:

The perimeter of a rectangle is defined as the sum of all the sides of a rectangle. For any polygon, the perimeter formulas are the total distance around its sides. In case of a rectangle, the opposite sides of a rectangle are equal and so, the perimeter will be twice the width of the rectangle plus twice the length of the rectangle and it is denoted by the alphabet “p”.

Now, Solving the problem:

Perimeter of rectangle is 50 meter sq.

Length of the rectangle(L) is 16 meter.

We have to find the width (W) of the rectangle.

We know that,

Perimeter of rectangle is = 2 (L + W)

50 = 2(16 + W)

50 = 32 + 2W

2W = 50 - 32

2W = 18

W = 18/2

W = 9

Hence, The width of the rectangle is 9 meter.

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