The average price of a college math textbook is $151 and the standard deviation is $24. Suppose that 40 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.

What is the distribution of
X? X ~ N( , )

For the group of 40, find the probability that the average price is between $152 and $155.

Find the third quartile for the average textbook price for this sample size. $
(round to the nearest cent)

For part b), is the assumption that the distribution is normal necessary? YesNo

Please upload an image or give a question.

Answer:

0.3947368421 = approx 39%

Step-by-step explanation:

Add up all the number of times rolled on the right column.

=6+3+5+6+9+9

= 38 total rolls

Add up the number of times a 4 or a 5 were rolled:

= 6+ 9 = 15

Divide 15/38

=15/38=0.3947368421 = approx 39%.

The circumference of the given circle is approximately 47.3 inches.

Since the length of the arc KL and the measure of the central angle ∠KOL are known, we can use the formula for arc length to find the circumference of the circle:

arc length = (central angle / 360°) x circumference

Plugging in the known values, we have:

4.6 in = (35° / 360°) x circumference

Solving for the circumference, we get:

circumference = 4.6 in / (35° / 360°)

circumference = 4.6 in x (360° / 35°)

circumference ≈ 47.3 in (rounded to the nearest tenth)

Therefore, the circumference of the circle is approximately 47.3 inches.

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Answer:

[tex]x=(x-3)^{\frac{9}{5}}[/tex]

Step-by-step explanation:

The first thing we are going to do is change both sides of the equation to be base (x-3):

[tex](x-3)^{log_{(x-3)}(x)}=(x-3)^{\frac{9}{5}}[/tex].

Now, since the log is in base (x-3), the base (x-3) and the log cancel out:

[tex]x = (x-3)^\frac{9}{5}[/tex]

This is the final answer.

Part 1a) An exponential function is a better model to represent the data because the rate of change is not constant instead of using a linear function, whose rate of change (slope) is constant.

Part 1b) The slope between each points are different.  So, the data is best represented by an exponential function.

Part 2a) The estimated number of college degrees earned in the United States in 2050 is about 2 million.

Part 2b) The estimated number is more likely to be an under-estimation.

Exponential equations increase by a constant exponent or power, written in the form of $$f(x) = ab{x}$$.

Linear equations or functions increase by a constant slope, written in the form of y = mx + b, where m is the slope.

Year    College degrees

            (  thousands)

1910                37

1930             122

1950            432

1970            792

1990          1,051

2010          1,650

Using exponential smoothing in Excel, the result of the prediction shows that 2,237,000 college degrees will be earned in 2050.

The number of college degrees earned in the United States in 2050 = 2,237,000 ≈ 2 million.

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The shoe sizes that will only have one dot are 5 1/2, 7, 8 and 10 1/2

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

The record of shoe sizes

From the data values, we have the following shoe sizes that appear once

5 1/2, 7, 8 and 10 1/2

These are the data values that will have only one dot  if the data is recorded on a line plot

Hence, the shoe sizes that will only have one dot are 5 1/2, 7, 8 and 10 1/2

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There will be about 21 cm³ of empty space in the cylindrical container.

The formula for the volume of a sphere is V = (4/3)πr³ where r is the radius of the sphere. Since the diameter of each bouncy ball is 3 cm, the radius is 1.5 cm.

V = (4/3)π(1.5)³

= 14.13 cm³

The volume of three bouncy balls is 3 times this amount:

= 3 × 14.13

= 42.39 cm³

Since the diameter of each cylinder is 3 cm, the radius is 1.5 cm. We also know that the height of the cylinder is 9 cm, since each cylinder is 3 cm tall and there are three cylinders stacked on top of each other.

= π(1.5)^2(9)

= 63.62 cm³

Empty space = Vcontainer - Vtotal

= 63.62 - 42.39

= 21.23 cm³

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The solution to the system of equations is given as follows:

Considering the augmented matrix, the system of equations is defined as follows:

Adding the first and third equations, we have that:

-4x - 6y = -36.

From the second equation, we have that:

2x + 3y = 18.

The addition equation is a multiple of this equation, hence the system has an infinite number of solutions.

From the second equation, we have that:

2x + 3y = 18.

x + 1.5y = 9

x = 9 - 1.5y.

The definition for z is given as follows:

z = x + y - 7.

Hence the variable y is:

y = z - x + 7.

The variable x is of:

x = 9 - 1.5(z - x + 7)

x = 9 - 1.5z + 1.5x - 10.5

0.5x = 1.5 + 1.5z

x = 3z + 3.

The variable y is:

y = z - 3z - 3 + 7

y = -2z + 4.

Hence the solution is:

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The angle between the vectors is given as follows:

θ = 60º.

The formula for the angle between the vectors in this problem is given as follows:

cos(θ) = uv/(|u||v|)

The vectors are given as follows:

The dot product between the vectors is given as follows:

uv = <-2,3><1,2> = -2 + 6 = 4.

The norms for each vector are given as follows:

Applying the arccosine function, the angle is given as follows:

[tex]\theta = \arccos{\left(\frac{4}{\sqrt{13} \times \sqrt{5}}\right)}[/tex]

θ = arccos(0.49613893835)

θ = 60º. (approximately).

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The marginal cost (MC) function tells us the additional cost of producing one more unit of the Senior Executive model.

To find the average cost, we need to know the fixed costs, which are not given in the problem. Therefore, we cannot calculate the average cost.

To find the marginal cost, we need to take the derivative of the total cost function with respect to x:

MC(x) = dC(x) / dx

MC(x) = [tex]0.3x^2[/tex] - 16x + 500

Interpreting the results, the marginal cost (MC) function tells us the additional cost of producing one more unit of the Senior Executive model. It is an increasing function, which means that the cost of producing an additional unit increases as the production level increases. When MC is greater than the price of the product, it is not profitable to produce additional units, and the optimal production level is reached when MC equals the price.

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Question

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is represented by the following function:

C(x) = 0.1x^3 - 8x^2 + 500x + 4000

where C(x) is measured in dollars/year.

The measure of angle m∠XKZ is 218°.

An angle is formed when two straight lines or rays meet at a common endpoint.

The six types of angles are,

To find the measure of angle m∠XKZ, we use the formula below

Formula:

From the question,

Given:

Substitute these values into equation 1 and solve for x

Hence, m∠XKZ = [(15×15)-7] = 218°

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Answer:

L'' = (6, - 5 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 3, y - 3 ) means

add 3 to the original x- coordinate and

subtract 3 from the original y- coordinate

then

L (3, - 2 ) → L'' (3 + 3, - 2 - 3 ) → L'' (6, - 5 )

The area of the Japanese garden around the koi pond is 195.74 square feet.

To find the area of the Japanese garden around the koi pond, we need to subtract the area of the circular pond from the area of the rectangular garden. Let's use the given terms and follow these steps:
1. Calculate the area of the rectangular garden.
Area = Length × Width
Area = 16 feet × 14 feet
Area = 224 square feet
2. Calculate the area of the circular koi pond.
Area = π × (radius)^2
Area = 3.14 × (3 feet)^2
Area = 3.14 × 9 square feet
Area = 28.26 square feet
3. Subtract the area of the koi pond from the area of the garden.
Garden area around the koi pond = Area of the rectangle - Area of the circle
Garden area = 224 square feet - 28.26 square feet
Garden area = 195.74 square feet
Your answer: The area of the Japanese garden around the koi pond is 195.74 square feet.

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The cost of one gallon of gas is given as follows:

$2.75.

The cost of one gallon of gas is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per gallon is obtained dividing the total cost by the number of gallons.

The parameters for this problem are given as follows:

Hence the cost of one gallon of gas is given as follows:

22/8 = $2.75.

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By using the given graph of the function​ f, the key features include the following:

​(a) the​ y-intercept is (0, 10).

​(b) its domain is [-∞, ∞] and the range is [0, ∞].

​(c) it is​ increasing over the interval [-∞, ∞].

​(d) The function is​ even.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the graph, we would calculate the value of a and b as follows;

f(x) = a(b)^x

10 = a(b)⁰

a = 10

Next, we would determine value of b as follows;

12 = 10(b)¹

12 = 10b

b = 12/10

b = 1.2

Therefore, the required exponential function is given by;

[tex]y = 10(1.2)^x[/tex]

Part a.

When x = 0, the y-intercept can be determined as follows;

[tex]y = 10(1.2)^0[/tex]

y = 10(1)

y = 10.

Part b.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞].

Range = [0, ∞] or {y | y ≥ 0}

Part c.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce that the exponential function is always increasing over the interval [-∞, ∞].

Part d.

In conclusion, this exponential function is an even function because it is symmetric with respect to the y-coordinate (y-axis).

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This question involves using the binomial distribution.

Let X be the number of male high school lacrosse players who will play at the college level out of the 20 selected players . We can model X as a binomial random variable with parameters n=20 and p=0.128, where p is the probability of success (i.e., a player going on to play at the college level).

The probability of exactly 4 players playing at the college level is given by the formula:

P(X=4) = (20 choose 4) * (0.128)^4 * (1-0.128)^(20-4)

Using a calculator, we can evaluate this expression to find:

P(X=4) = 0.155

Therefore, the probability that exactly four of the 20 male high school lacrosse players selected at random will end up playing at the college level is 0.155, or between C and 1 (inclusive).

Note that we rounded to three decimal places as requested .

Answer:

please see explanation and attachment

Step-by-step explanation:

√16 = 4.

√14 = ?

how do we get from 16 to 14? we subtract 2. r = remainder. denominator is twice √16, ie 8.

so we have 4 r -2 r 8

= 4 r -1 r 4

= 3 r 3 r 4

= 3.75

= 3.8 to nearest tenth

The two numbers are 15 and 15. The product of the two numbers is 225.

Let x and y be the two numbers we are searching for. We know that x + y = 30, so we can settle for y to get y = 30-x. The result of x and y is then, at that point:

[tex]P(x, y) = x(30 - x) = 30x - x^2[/tex]

To find the greatest item, we can take the subsidiary of P(x, y) concerning x and set it equivalent to 0:

dP(x, y)/dx = 30 - 2x = 0

Settling for x, we get x = 15. Subbing x = 15 into y = 30-x, we get y = 15. Hence, the two numbers that have an amount of 30 and produce the biggest conceivable item are 15 and 15.

The result of the two numbers is:

P(15, 15) = 15 * 15 = 225

So the result of the two numbers is 225.

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The height if the squared-based pyramid is given as 34 cm

We have BD / 2

= 10 / 2

= 5 cm

AC = [tex]\sqrt{AB^2-BC^2}[/tex]

= √12² - 5 ²

= 12 cm

The height is given as 10 + 12 + 12

= 34 cm

Hence the height if the squared-based pyramid is given as 34 cm

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The problem asks to convert a volume of 8000 [tex]cm^3[/tex] to [tex]m^3[/tex] which is 0.008 [tex]m^3[/tex].

Unit conversion is the process of converting a quantity expressed in one unit of measurement into another equivalent quantity expressed in a different unit of measurement.

To do this conversion, we need to use the fact that 1 m = 100 cm (or equivalently, 1 cm = 0.01 m) and that volume is a cubic measure.

So, first we need to convert the volume from cubic centimeters to cubic meters. To do this, we can divide the volume in [tex]cm^3[/tex] by the number of [tex]cm^3[/tex] in 1 [tex]m^3[/tex].

1 [tex]m^3[/tex] = (100 cm)^3 = 1,000,000 [tex]cm^3[/tex]

Therefore,

8000 [tex]cm^3[/tex] / 1,000,000 [tex]cm^3/m^3[/tex] = 0.008 [tex]m^3[/tex]

Thus, the volume of 8000 [tex]cm^3[/tex] is equal to 0.008 [tex]m^3[/tex].

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The molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.

To solve this problem, we can use the equation:

M₁V₁= M₂V₂

where M₁ is the initial molarity, V₁ is the initial volume, M₂ is the final molarity, and V₂ is the final volume.

We are given that the initial volume is 50.0 mL and the initial molarity is 1.25 M. We are also told that 100.0 mL of water is added to the solution, so the final volume is 50.0 mL + 100.0 mL = 150.0 mL.

Plugging these values into the equation, we get:

(1.25 M)(50.0 mL) = M2(150.0 mL)

Solving for M₂, we get:

M₂ = (1.25 M)(50.0 mL) / (150.0 mL) = 0.4167 M

Therefore, the molarity of the resulting solution is 0.42 M (rounded to two significant figures), which is option C.

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The likelihood of rain occurring on precisely two out of the four days they are there is 0.323.

The binomial probability formula is given by:

P(X = k) = C(n, k) . [tex]p^k[/tex] . (1 - [tex]p)^(n - k)[/tex]

Where:

P(X = k) is the probability of exactly k successes,

C(n, k) is the number of combinations of n items taken k at a time,

p is the probability of success on a single trial, and

n is the total number of trials.

Using the formula, we can calculate the probability as follows:

P(X = 2) = C(4, 2) x (0.71)² x  (1 - 0.71)²

P(X = 2) = 6 x (0.71)² x (0.29)²

P(X = 2) ≈ 0.323

Therefore, the probability that it will rain on exactly two of the four days they are there is 0.323.

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Answer:

Part A: The point z1 is at (4, 6) and the point z2 is at (-5, 2). The distance between them is √((4-(-5))^2 + (6-2)^2) = √(9^2 + 4^2) = √(81 + 16) = √97.

Part B: The complex conjugate of z2 is (-5, -2). Geometrically, it can be found by reflecting the point z2 across the x-axis.

Part C: To find z2 − z1 geometrically, you can draw a vector from z1 to z2. The coordinates of this vector are (-5-4, 2-6) = (-9, -4). So z2 − z1 = -9 - 4i.

Answer:

10

Step-by-step explanation:

If you multiply the width with the length and height , you will get nine, then add that lonely brick on top to get ten

10.8

.......................................

1. Green Party: Political party prioritizing environmental issues, sustainability, and social justice.

2. The National Environmental Education Act promotes environmental education and awareness.

3.  Urban conditions impact species by habitat loss and fragmentation.

4. Developed countries prioritize environmental conservation; undeveloped countries focus on development.

1.  A green party is a political party that prioritizes environmental issues, sustainability, and social justice. One example of a green party is the Green Party of Germany (Bündnis 90/Die Grünen).

Founded in 1980, they advocate for renewable energy, climate protection, social equality, and grassroots democracy.

They have been part of coalition governments in Germany and have influenced national and European environmental policies.

2. The National Environmental Education Act is a United States federal law that was enacted in 1990 to promote environmental education and awareness among students and the general public.

The Act established the Office of Environmental Education within the Environmental Protection Agency (EPA) to provide funding for environmental education programs and to develop and disseminate environmental education materials.

3. Urban areas can have various negative impacts on species that live in the area. One example is the loss of natural habitat due to urban development.

When forests or wetlands are cleared to make way for buildings or roads, it disrupts the habitat of many species, leading to population declines and biodiversity loss.

4. Societal attitudes in developed countries often prioritize environmental conservation, sustainability, and environmental regulations.

There is generally greater awareness and concern for issues such as climate change, pollution, and resource depletion. In contrast, societal attitudes in undeveloped countries may vary, with more immediate concerns such as poverty and economic development taking precedence over environmental concerns.

5. The global aspect of environmental issues can have both positive and negative impacts on local environmental issues. Positively, global awareness and collaboration can lead to knowledge sharing, resources, and support for local initiatives.

Negatively, global demands and policies may prioritize economic growth, leading to environmental degradation and challenges for local communities.

Regarding the issue with banned questions, I apologize for any inconvenience caused.

The moderation system is in place to ensure compliance with community guidelines and prevent misuse of the platform. It's possible that certain questions may trigger filters due to sensitive topics, inappropriate content, or excessive repetition.

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The total length of the chord PR is 30.

Given a circle Q.

Given a chord named as PR.

We have to find the length of the chord.

Here Q is the center of the circle.

Given that ∠QSP is a right angle.

Then clearly, ∠QSR is also a right angle.

Consider the triangle QSR and QSP.

QP = QR, since they are radius of the circle.

So, QP = QR = 17

QS ia a common side.

So QS = 8

Then it is clear that,

PS = SR

Using Pythagoras theorem,

(PS)² = 17² - 8²

        = 225

PS = √225 = 15

So the length of the chord, PR = 15 + 15 = 30.

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Answer:

Step-by-step explanation:

The equation to solve the problem is:

x + 550 = 750

Explanation:

The manager has already distributed $550, and the remaining amount to distribute is represented by the variable x. Adding the distributed amount to the remaining amount should equal the total amount of tips the manager has, which is $750. Therefore, the correct equation is x + 550 = 750.