Fifteen pieces of paper are numbered 1 to 15 and placed in a container. One piece of paper is selected at random, then replaced. The second piece of paper is selected at random. What is the probability that the first piece of paper is marked with a number less than 5 and the second piece of paper is marked with a 12?

Answer:

  No, some of the ordered pair in this graph have the same first element.

Step-by-step explanation:

A vertical line intersects the graph in as many as 3 places. Each of those has coordinates with the same first element. Because the number of points of intersection with a vertical line can be more than 1, the graph is not a function.

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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Answer:

1.11 will be the answer

Step-by-step explanation:

well, let's recall that Profit is Revenue - Costs, in essence, subtracting what you spent to make the product from the amount you charge, whatever the surplus amount is, goes by the name of "profit".

\(P(t)~~ = ~~\stackrel{S(t)}{(-4t^2+48t)}~~ - ~~\stackrel{M(t)}{(-3t^2+36t)} \\\\\\ P(t)=-4t^2+48t+32t^2-36t\implies \boxed{P(t)=-t^2+12t}\)

Check the picture below.

is there a point when Maria is losing money?

well, from the graph, if we to say the origin, that (0,0), there's no profit, profit is 0, now, if we go to the left of that, the line is going to the negative, so we can say if makes "negative t-shirts" hehe, namely, if she starts to give them away like there's no tomorrow, then hell she's in the red ink, now if we go beyond t = 12, the graph goes back down again?  the hell?  well, that just means that if she makes t-shirts for more than 12 days, she's back in the red ink again,.

Janet has 630 options to customize a car based on the given features.

How to solve the question?

To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:

10 car models x 7 exterior colors x 9 interior colors = 630

Thus, Janet has 630 options to customize a car based on the given features.

It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.

Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.

In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.

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Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

On edge

The surface area of the triangular prism is 313.47 cm².

Given is a triangular prism, we need to find the surface area,

A triangular prism is a 3D shape with two identical faces in the shape of a triangle connected by three rectangular faces. The rectangular faces are referred to as the lateral faces, while the triangular faces are called bases. The bases are also called the top and the bottom (faces) of the prism.

Triangular Prism Meaning: A triangular prism is a 3D polyhedron with three rectangular faces and two triangular faces. The 2 triangular faces are congruent to each other, and the 3 lateral faces which are in the shape of rectangles are also congruent to each other. Thus, a triangular prism has 5 faces, 9 edges, and 6 vertices. Observe the following image of a triangular prism in which l represents the length of the prism, h represents the height of the base triangle, and b represents the bottom edge of the base triangle.

so, the surface area of a triangular prism =

perimeter × length + 2 × base area

So,

SA = (4.5+7.2+9) × 8.1 + 2 × 8.1 × 9

= 167.67 + 145.8

= 313.47

Hence the surface area of the triangular prism is 313.47 cm².

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Answer:

Refer to picture.

How to:

Put a dot at (0,2) for the +2 in the equation.

Go three spaces up and one to the right. Repeat this until you can make a line.

Answer:

(15x + 120) ft³

Or

15(x + 8) ft³

Step-by-step explanation:

The prism can be decomposed into a rectangular prism and a triangular prism

The volume of the prism = volume of the rectangular prism + volume of the triangular prism

✔️Volume of rectangular prism = L*W*H

L = 5 ft

W = 4 ft

H = 6 ft

Volume = 5*4*6 = 120 ft³

✔️Volume of triangular prism = ½*b*h*l

b = x ft

h = 6 ft

l = 5 ft

Volume = ½*x*6*5 = 15x ft³

✔️Volume of the prism = (15x + 120) ft³

Answer:

2.970600004839 × 10^5

Step-by-step explanation:

First, we add up these 2 numbers.

297,060 + 0.0004839 = 297060.0004839

Then, we convert that into scientific notation.

297060.0004839 = 2.970600004839 × 10^5

Finally, we check if it's right.

10^5 = 100000

2.970600004839 * 100000 = 297060.0004839

Hope this helps.

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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Answer:

\(54\pi \: {cm}^{2} \)

Step-by-step explanation:

Given:

A cone

l = 15 cm

r (radius) = 3 cm

Find: A (surface area) - ?

\(a(surface) = \pi {r}^{2} + \pi \times r \times l\)

\(a(surface) = \pi \times {3}^{2} + \pi \times 3 \times 15 = 9\pi + 45\pi = 54\pi \: {cm}^{2} \)

After answering the presented question, we can conclude that This is equation true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3): a = 30.8/(11n+3)

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

We are given that the factored form of 30.8n+8.4 is a(11n+3).

To find the value of a, we can expand the product a(11n+3) and equate it to the given expression 30.8n+8.4.

Expanding a(11n+3), we get:

a(11n+3) = 11an + 3a

Equating this to 30.8n+8.4, we have:

11an + 3a = 30.8n + 8.4

We can factor out an "a" from the left-hand side:

a(11n + 3) = 30.8n + 8.4

Now we can see that this is the same as the given factored form, so we can equate the two expressions:

a(11n + 3) = a(11n + 3)

This is true for all values of a and (11n+3), so we can conclude that the value of "a" is simply 30.8 divided by (11n+3):

a = 30.8/(11n+3)

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According to the Angle Addition Postulate, the measure of m∠ABD = 202°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

The angle measures:

m∠ABC=37°,

and m∠⁡C⁣B⁣D= 165⁢°.

So, according to the angle addition postulate;

m∠ABD = m∠ABC + m∠CBD

Substituting the values,

m∠ABD = 37° + 165⁢°

m∠ABD = 202°

Therefore, the angle measure of m∠ABD = 202°.

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Answer:

a. Negation of ∃x ∀y(P(x,y) → Q(x,y)) = ∀x  ∃y P(x,y)  ∧ ¬Q(x,y) ]

b. Negation of ∃x ∀y(P(x,y) → P(y,x)) = ∀x ∃y  [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [P(x,y) ∨ P(y,x)]

c. Negation of ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) = ∀x ∀y ¬ [P(x,y)]  ∨ ∃x ∃y ¬ [Q(x,y)]

Step-by-step explanation:

a.∃x ∀y(P(x,y) → Q(x,y))

Negation = ¬ [ ∃x ∀y(P(x,y) → Q(x,y)) ]

                = ∀x  ¬ [ ∀y(P(x,y) → Q(x,y)) ]

                = ∀x  ∃y ¬ [ (P(x,y) → Q(x,y)) ]

                = ∀x  ∃y ¬ [  ¬P(x,y)  ∨ Q(x,y) ]

                = ∀x  ∃y P(x,y)  ∧ ¬Q(x,y) ]

Negation of ∃x ∀y(P(x,y) → Q(x,y)) = ∀x  ∃y P(x,y)  ∧ ¬Q(x,y) ]

b. ∃x ∀y(P(x,y) → P(y,x))

Negation = ¬ [ ∃x ∀y(P(x,y) → P(y,x)) ]

               = ∀x ¬ [ ∀y(P(x,y) → P(y,x)) ]

               = ∀x ∃y ¬ [ (P(x,y) → P(y,x)) ]

               = ∀x ∃y ¬ [ ( P(x,y) ∧ P(y,x) ) ∨ ( ¬P(x,y) ∧ ¬P(y,x) )]

               = ∀x ∃y ¬ [ P(x,y) ∧ P(y,x) ] ∧ ¬[ ¬P(x,y) ∧ ¬P(y,x) ]

               = ∀x ∃y  [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [ P(x,y) ∨ P(y,x) ]

∴ we get

Negation of ∃x ∀y(P(x,y) → P(y,x)) = ∀x ∃y  [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [P(x,y) ∨ P(y,x)]

c. ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y)

Negation = ¬ [ ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) ]

                = ¬ [ ∃x ∃y P(x,y) ]  ∨ ¬ [ ∀x ∀y Q(x,y) ]

                = ∀x¬ [  ∃y P(x,y) ]  ∨ ∃x ¬ [ ∀y Q(x,y) ]

                = ∀x ∀y ¬ [ P(x,y) ]  ∨ ∃x ∃y ¬ [ Q(x,y) ]

∴ we get

Negation of ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) = ∀x ∀y ¬ [ P(x,y) ]  ∨ ∃x ∃y ¬ [ Q(x,y) ]

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Answer:

-77 + (-46)

=> -77 - 46 (When you add two negative integers, it is the same thing as subtracting a positive integer with a negative integer)

=> -123 (Because a negative + a negative = a negative)

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Thank You!!

= -77 + ( - 46 )

= - 77 - 46 ( a positive integer and a negative integer makes a negative integer )

= -123 ( two negative signs resulted in the usage of addition )

Therefore , -77+ (-46) = -123

Answer:

It's be 60 because 30% of 60 is 18. Hope that helped :)

Answer:

150.72

Step-by-step explanation:

3² × 3.14 × 6 - 1² × 3.14 × 6 = (3² - 1²) × 3.14 × 6 = 150.72

Answer:

The least expensive cost = $245.32

Step-by-step explanation:

From the information:

Volume of the rectangular container = 10 m²

Assume the width of the container is = w

The base = 2 × width

= 2(w)

Volume = height × base × width

10 = h × 2w × w

\(h = \dfrac{10}{2w^2}\)

\(h = \dfrac{5}{w^2}\)

Now, to calculate the area of the base; we have:

\(Area = length \times width\)

\(Area = 2w \times w\)

\(Area = (2w^2) \ m^2\)

\(Cost \ of \ base = 15 * 2w^2\)

Cost of base = \(30w^2\) --- (1)

\(Area \ of \ side = 2 ( height \times length ) + 2( height \times width) \\ \\ = 2 (h \times 2w) + 2(h\times w) \\ \\ = 4hw + 2hw \\ \\ = 6 hw \\ \\ = 6 \times \dfrac{5}{w^2} \times w \\ \\ Area = \dfrac{30 }{w} \ m^2\)

Let's not forget that the cost of the sides = $9 per m²

Thus; the cost of the sides will be \(= \$ 9 \times \dfrac{30}{w}\)

the cost of the sides \(= \dfrac{\$270}{w}\)

Thus the total cost = cost of base = cost of sides

\(C(w) = 30w^2 + \dfrac{270}{w}\)

By differentiation;

\(C'(w) = \dfrac{dC}{dw} \\ \\ = 30 \times 2w + 270 ( \dfrac{-1}{w^2}) \\ \\ C'(w) = 60 w - \dfrac{270 }{w^2} \\ \\\)

\(\text{To determine the minimum cost:} \\ \\ C'(w) = 0 \\ \\ So, 60 w - \dfrac{270}{w^2}= 0 \\ \\ \text{By integrating w.r.t w} \\ \\ w ( 60 - \dfrac{270}{w^3}) =0 \\ \\ \implies 60 - \dfrac{270}{w^3} \\ \\ w^3 = \dfrac{270}{60} \\ \\ w^3 = \dfrac{9}{2} \\ \\ w = (\dfrac{9}{2})^{1/3} \\ \\ w = 1.6509 \ m\)

From; \(C(w) = 30w^2 + \dfrac{270}{w}\)

\(Cos t = \dfrac{30 w^3+ 270}{w} \\ \\ =\dfrac{30 (\dfrac{9}{2})+ 270}{1.6509} \\ \\ = \dfrac{135+270}{1.6509} \\ \\ = \dfrac{405}{1.6509} \\ \\ \mathbf{Cost = \$245.32}\)

The mean and median of the given data are 718.72, and 719.5 respectively, and have no mode. The range is 87 and the standard deviation is 26.26. The interval that includes about 95% of the observations is between $666.20 and $771.24.

Mean - The mean is calculated by summing up all the observations and dividing by the number of observations.

mean = (684 + 710 + 688 + 711 + 722 + 698 + 723 + 743 + 738 + 722 + 696 + 721 + 685 + 763 + 681 + 731 + 736 + 771 + 693 + 701 + 737 + 717 + 752 + 710 + 697) / 25

mean = 718.72

Media -: The median is the middle value in a set of data when the data is arranged in order. With 25 observations, the median will be the average of the 13th and 14th observations when the data is sorted in ascending order.

median = (717 + 722) / 2

median = 719.5

Mode - The mode is the value that occurs most frequently in a set of data. In this case, there is no single value that occurs most frequently, so the data has no mode.

Range - The range is the difference between the largest and smallest values in a set of data.

range = 771 - 684

range = 87

Standard Deviation - The standard deviation is a measure of the spread of the data. It is calculated using the following formula -

\(\sqrt{((684-718.72)^2 + (710-718.72)^2 + (688-718.72)^2 + ... + (697-718.72)^2) / 25)\)

The standard deviation of this sample is approximately 26.26.

Empirical Rule - The Empirical Rule states that approximately 68% of the observations are within one standard deviation of the mean, approximately 95% of the observations are within two standard deviations of the mean, and approximately 99.7% of the observations are within three standard deviations of the mean.

Using the Empirical Rule, we can establish the interval which includes about 95% of the observations:

[718.72 - 2 * 26.26, 718.72 + 2 * 26.26] = [666.2, 771.24]

So, approximately 95% of the observations are between $666.20 and $771.24.

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The complete question is -

A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year: 684 710 688 711 722 698 723 743 738 722 696 721 685 763 681 731 736 771 693 701 737 717 752 710 697 Find the mean, median and the mode of the data. Calculate the range and standard deviation. Use the Empirical Rule to establish an interval that includes about 95 percent of the observations.

The solution to the quadratic equation 2x² - 7x - 4x is x = 0 and x = 11/2.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, y = 2x² - 7x - 4x.

y = 2x² - 11x.

y = x(2x - 11).

Or,

x(2x - 11) = 0.

x = 0 Or 2x - 11 = 0 ⇒ 2x = 11 ⇒ x = 11/2.

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Thus, the  image after the dilation of scale factor of 2/3 with origin for quadrilateral CDEF the are C'(0,0), D'(2, 4),  E'(6, 6),  F'(15, 3).

The ratio between comparable dimensions of an object and a representations of that object is known as a scale factor in mathematics. The copy will just be larger if the scaling factor comprises an entire number. A fractional scaling factor means that the duplicate will be smaller.

For the given coordinates quadrilateral CDEF, to find the coordinates of the image after the dilation of 2/3 with origin are-

Multiply each coordinate with 2/3:

Thus, the image after the dilation of scale factor of 2/3 with origin for quadrilateral CDEF the are C'(0,0), D'(2, 4),  E'(6, 6),  F'(15, 3).

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Answer:

Basically put the definitions as two separate sentences and then random facts that I remember.

Step-by-step explanation:

A terminating decimal is a decimal that has an end.

A repeating decimal is a decimal fraction in which a number, or a group of numbers, is repeated indefinitely.

Most repeating decimals contain a nine in the denominator, when written in fraction form.

Both can be written in fraction form.

Both can have a positive or negative value that can be both large and small.

Answer:

C. Through a given point not on a given line, there is exactly one line parallel to the given line.

Step-by-step explanation:

hope i helped

Answer:

Look down

Step-by-step explanation:

Thanks for reaching out for assistance! Based on the context you provided, it seems like the correct answer is C. Playfair's axiom states that there is exactly one line parallel to a given line that can be drawn through a point not on it. I hope this helps! Let me know if there's anything else I can do for you.

Answer:

88.9

Step-by-step explanation:

The function that correctly defines S(x) is S(x) = 5x - 2(20 - x) + 20

We have the following definitions in the question

If the total questions is 20, then

Incorrect answers = 20 - x

So, the points gained/lost are

Gained = 5 * x = 5x

Lost = -2 * (20 - x) = -2(20 - x)

Bonus = 20

Add the above points to get the function S(x)

S(x) = 5x - 2(20 - x) + 20

Hence, the definition is S(x) = 5x - 2(20 - x) + 20

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