Factor the trinomial and show your work..
2x^2 + 22x + 60

If the sphere has radius of 5 units, then the volume of that sphere will be  523.4 cubic units.

The "Volume" of a sphere is a measure of the amount of space enclosed by the sphere and is defined as the amount of three-dimensional space occupied by the sphere.

The formula for volume of "sphere" is represented as : V = (4/3)πr³;

Where V is = volume and r is = radius of sphere,

Substituting value of radius, "r = 5",

We get,

⇒ V = (4/3)π(5)³,

⇒ V = (4/3) × π × (125),

⇒ V ≈ 523.4 cubic units.

Therefore, the required volume of sphere is 523.4 cubic units.

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There are no values of c that satisfy the conclusion of Rolle's Theorem. Thus, the answer is N.

To apply Rolle's Theorem, we need to check if the function satisfies the following conditions:

f(x) is continuous on the closed interval [a, b].

f(x) is differentiable on the open interval (a, b).

f(a) = f(b).

The function f(x) = x² - 9x + 2 is a polynomial, so it is continuous and differentiable everywhere. We need to check the third condition.

f(0) = (0)² - 9(0) + 2 = 2

f(9) = (9)² - 9(9) + 2 = -61

Since f(0) is not equal to f(9), we can't apply Rolle's Theorem to this function on the interval [0, 9].

Therefore, there are no values of c that satisfy the conclusion of Rolle's Theorem. Thus, the answer is N.

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It is not possible to reach the top of the ladder to the edge of the roof.

We can solve this problem using the Pythagorean theorem, which states that for a right triangle, the sum of the squares of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side).

In this case, the ladder is the hypotenuse of a right triangle, and the distance from the base of the ladder to the house and the distance from the top of the ladder to the edge of the roof are the two shorter sides.

Let x be the distance from the top of the ladder to the edge of the roof. Then, we can write:

[tex]10^{2}[/tex] = [tex](1.5)^{2}[/tex] + [tex]x^{2}[/tex] + [tex]12^{2}[/tex]

Simplifying and solving for x, we get:

100 = 2.25 +[tex]x^{2}[/tex] + 144

[tex]x^{2}[/tex] = 100 - 2.25 - 144

[tex]x^{2}[/tex] = -46.25

Since x represents a distance, which must be positive, this means that there is no solution to the equation. Therefore, it is not possible for Sammy to reach the edge of the roof with his 10-foot ladder while keeping the base of the ladder at least 1.5 feet from the base of the house.

Correct Question :

Sammy has a 10-foot ladder, which he needs to climb to reach the roof of his house. the roof is 12 feet above the ground. the base of the ladder must be at least 1.5 feet from the base of the house. how far is it from the top of the ladder to the edge of the roof?

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The piecwise function in the graph  is written as:

We can see that the piecewise function is:

First a constant at y = -2, which ends at x = -2, so this is the first piece.

Then a line x = y, it starts at x = -2 and ends at x = 2, this is the second piece of our function.

Finally, another constant line at y = 2, it starts at x = 2.

Then the piecwise function is written as:

f(x) = -2  if x < -2

f(x) = x   if -2 ≤ x ≤ 2

f(x) = 2  if  2 < x

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Answer:

Step-by-step explanation:
A, III quadrant

An image that has reflectional, rotational, and point symmetry is a regular polygon. I can explain the terms and help you identify the symmetries in the images.

1. Reflectional symmetry: An image has reflectional symmetry if it can be reflected over a line (called the "line of symmetry") and still look the same as the original image.

2. Rotational symmetry: An image has rotational symmetry if it can be rotated around a point (called the "center of rotation") by a certain angle (less than 360°) and still look the same as the original image.

3. Point symmetry: An image has point symmetry if it looks the same when rotated by 180° around a central point (also called the "point of symmetry").

To determine which image has all three types of symmetry, examine each image and check if it meets the criteria for reflectional, rotational, and point symmetry. Once you identify an image that satisfies all three criteria, you have found the correct image.

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To differentiate the expression Y(X) = 2V*-1, we can use the power rule of differentiation. First, we need to consider that V* is a variable and treat it as a constant when differentiating with respect to X.

So, differentiating the expression Y(X) = 2V*-1 with respect to X, we get:

dY/dX = d/dX (2V*-1)
= 2dV*/dX

We can simplify this expression by storing the result in a variable called "firstder":

import sympy as sp
Vstar = sp.Symbol('V*')
X = sp.Symbol('X')

firstder = 2*sp.diff(Vstar,X)

Now, the variable "firstder" contains the symbolic expression for the derivative of Y with respect to X.

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The given series 2/8 + 4/9 + 6/10 + 8/11 + 10/12 + ..... is a divergent series.

The given series is:

2/8 + 4/9 + 6/10 + 8/11 + 10/12 + .....

Here,

t₁ = 2/8 = (2*1/(1 + 7))

t₂ = 4/9 = (2*2/(2 + 7))

Proceeding in this manner we get the n th term of the given series,

tₙ = (2*n)/(n + 7)

So, now the limit of n th term of the series is given by,

[tex]\lim_{n \to \infty}[/tex] tₙ = [tex]\lim_{n \to \infty}[/tex] (2*n)/(n + 7)) = [tex]\lim_{n \to \infty}[/tex] 2/(1 + 7/n)

Since n tends to infinity

So, 1/n tends  to 0. Let 1/n = y

So, 'y' tends to 0.

= [tex]\lim_{y \to 0}[/tex] 2/(1 + 7y) = 2 ≠ 0

Now, difference between (n+1)th and n th term is

= [tex]b_{n+1} - b_n[/tex]

= 2(n+1)/(n +1 +7) - 2n/(n + 7)

= (2(n + 1 + 7) - 14)/(n +1 +7) - (2(n + 7) - 14)/(n + 7)

= 2 - 14/(n + 8) - 2 + 14/(n +7)

= 14/(n +7) - 14/(n +8)

= 14(n + 8 - n - 7)/(n +7)(n +8)  

= 14/(n + 7)(n+8) > 0

So, [tex]b_{n+1}\geq b_n[/tex]

Hence the given series diverges.

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Answer:

Step-by-step explanation:

The statement is partially correct. because, If the study used volunteers who self-selected to participate, then it may not be a representative sample of the entire population with a moderate case of the disease, and therefore the results may not be generalizable to the population.

However, it is important to note that not all studies need to use random sampling in order to draw meaningful conclusions. In some cases, non-random samples may still provide valuable insights into the topic of interest.

In any case, if the study did use volunteers who self-selected to participate, it is important for the researchers to acknowledge this limitation in their conclusions and to avoid overgeneralizing the findings beyond the sample they studied.

The statement is partially correct. because, If the study used volunteers who self-selected to participate, then it may not be a representative sample of the entire population with a moderate case of the disease, and therefore the results may not be generalizable to the population.

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The derivative of F(x) is F'(x) = 3x² - 8x.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] (t³ - 4t² + 6) dt

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] (t³ - 4t² + 6) dt

According to the Leibniz integral rule, if the upper limit of the integral is a function of x, we need to apply the chain rule. The lower limit of the integral is a constant, so it will not affect the differentiation.

F'(x) = (d/dx)(x³ - 4x² + 6)  [applying the chain rule]

F'(x) = 3x² - 8x

Therefore, the derivative of F(x) is F'(x) = 3x² - 8x.

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The probability that a 5-digit pin number has no repeated digits is approximately 0.302.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

To calculate the probability that a 5-digit pin number has no repeated digits, we can use the following formula:

P(no repeated digits) = (number of 5-digit numbers with no repeated digits) / (total number of 5-digit numbers)

The total number of 5-digit numbers is simply 10^5, or 100,000, since we have 10 choices for each of the 5 digits (0-9).

To count the number of 5-digit numbers with no repeated digits, we can use the permutation formula:

nPr = n! / (n - r)!

where n is the total number of elements, and r is the number of elements we are choosing.

In this case, we want to choose 5 digits out of the 10 available, and the order of the digits matters. So the number of 5-digit numbers with no repeated digits is:

10P5 = 10! / (10 - 5)! = 10 * 9 * 8 * 7 * 6 = 30,240

Putting it all together, we have:

P(no repeated digits) = 30,240 / 100,000 = 0.3024

Hence, the probability that a 5-digit pin number has no repeated digits is approximately 0.302.

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The possible values of the sum of a, b and c is (c) - 14

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

Vertex = (9, -14)

It intersects the x-axis at two points.

So, we have (x₁, 0) and (x₂, 0)

The equation of a parabola in vertex form is represented as

y = a(x - h)² + k

Where

Vertex = (h, k)

So, we have

y = a(x - 9)² - 14

Expanding the equation, we have

y = a(x² - 18x + 81) - 14

Open the brackets

This gives

y = ax² - 18ax + 81a - 14

Set a = 0

So, we have

y = (0)x² - 18(0)x + 81(0) - 14

Evaluate

y = 0x² - 0x - 14

This means that

a = 0

b = 0

c = -14

Add the constants a, b and c

So, we have

Sum of constant = 0 + 0 - 14

Evaluate the sum

Sum of constant = - 14

Hence, the possible value of a + b + c is -14

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We have the height of the rectangle equal to h = 37.5 inches.

A rectangle is actually about a right triangle. We can use the Pythagorean theorem to generate an expression to find the height of the rectangle.

We know that:

[tex]c^2=a^2+b^2[/tex] so replacing it with the width and length of the rectangle, we get :

[tex]c^2=h^2+w^2[/tex]

We were not given values for the width and length, just their relationship to each other, and we can use that to find an equation in the variable h:

So, [tex]c^2=h^2+w^2[/tex]

[tex](56)^2=h^2+(h+4)^2[/tex]

[tex]3136=h^2+h^2+8h+16[/tex]

[tex]0=2h^2+8h+16-3136[/tex]

[tex]0=2h^2+8h-3,120[/tex]

Since we cannot factor this, we can use the quadratic formula to solve for the height h, where, a = 2 , b = 8, c = -3,120

h = (-b ±[tex]\sqrt{b^2-4ac}[/tex]) /2a

Now, Plug all the values:

h = (-8 ± [tex]\sqrt{8^2-4(2)(-3120)})/4[/tex])

h = -8 ± [tex]\sqrt{64+24,960}/4[/tex]

h =( -8 ± [tex]\sqrt{25,024})/4[/tex]

h = (-8 ± 158.180)/4

There are two possible solutions, so we have:

[tex]h_1=\frac{-8+158.180}{4}[/tex]                      [tex]h_2=\frac{-8-158.180}{4}[/tex]

[tex]h_1 = 37.545[/tex]                           [tex]h_2=-41.545[/tex]  

[tex]h_1[/tex] ≈ 37.5 in.                          [tex]h_2[/tex] ≈ -41.5 in.

We cannot use [tex]h_2[/tex] because a negative height is absurd and undefined. Thus, we have the height of the rectangle equal to h = 37.5 inches.

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This inference procedure allows you to compare the sample mean to the recommended minimum and determine if there is a statistically significant difference.

To answer this question, we would use a hypothesis test. Specifically, we would set up a null hypothesis that the average math achievement score for eighth-graders in Maryland is equal to or less than 76%, and an alternative hypothesis that the average score exceeds 76%.

We would then collect a sample of math achievement scores from eighth-graders in Maryland and use a t-test or z-test to determine if the sample mean is significantly different from 76%.

To answer the question of whether eighth-graders in Maryland exceed the recommended minimum of 76% on a test of math achievement, you should use a one-sample t-test. This inference procedure allows you to compare the sample mean to the recommended minimum and determine if there is a statistically significant difference.

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The interval that does not describe the number of hours for about 50 % of the students is B. 9 to 14.

In order to gain a proper insight into the dataset, a holistic five-number summary is employed that accounts for the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value. Of these key components, Q1 defines the 25th percentile of the data while Q3 exhibits the 75th percentile.

As it stands, the median of this particular collection - 14 - denotes that half of the students are studying for less than 14 hours per week and the other half above the same timeframe.

This means that the interval that does not show 50 % would be 9 - 14 as this only shows 25 %.

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Options include:

A. 9 - 20

B. 9 - 14

C . 2 - 14

From the given decimals which are 0.2, 0.019, 0.12, 0.02, the smallest number is 0.019.

To compare the given decimals, we need to look at the digits to the right of the decimal point. Starting from the left, the first decimal is 0.2, which has one decimal place. The second decimal is 0.019, which has three decimal places. The third decimal is 0.12, which has two decimal places. Finally, the fourth decimal is 0.02, which has two decimal places.

To compare them, we can line them up vertically by decimal place and see which one has the smallest value in the first decimal place. In this case, the smallest value in the first decimal place is 0.019. Therefore, 0.019 is the smallest decimal among the given options.

In summary, the decimals listed from smallest to largest are: 0.019, 0.02, 0.12, 0.2.

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The appropriate test statistic for analyzing the mean difference between more than two levels of one factor for data that are on an interval or ratio scale of measurement is the analysis of variance (ANOVA).

ANOVA assesses whether there is a statistically significant difference in the means of three or more groups by comparing the variability within each group to the variability between the groups. The F-test is used to calculate the test statistic, which compares the mean differences between groups to the variability within groups. If the F-test produces a significant result, it indicates that at least one of the group means is significantly different from the others.
To analyze the mean difference between more than two levels of one factor for data that are on an interval or ratio scale of measurement, the appropriate test statistic is the Analysis of Variance (ANOVA) test. ANOVA allows you to compare the means of multiple groups and determine if there is a significant difference between them.

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The Pythagorean Theorem is used to show that the hypotenuse has a length of sqrt(2).

In a unit circle, the radius is always equal to 1 unit. Now, consider an isosceles right triangle with two equal sides of length 1 unit

By the Pythagorean Theorem, the length of the hypotenuse (c) of this triangle can be found as:

[tex]c^2 = 1^2 + 1^2[/tex]

[tex]c^2 = 2[/tex]

[tex]c = sqrt(2)[/tex]

Now, let's consider a circle centered at the origin with a radius of sqrt(2) units. Any point on this circle has coordinates (x, y) such that:

[tex]x^2 + y^2 = (sqrt(2))^2[/tex]

[tex]x^2 + y^2= 2[/tex]

This equation represents the unit circle, and any point on the isosceles right triangle we considered earlier also satisfies this equation. Therefore, the isosceles right triangle is inscribed in the unit circle.

In summary, the isosceles right triangle is inscribed in the unit circle because its hypotenuse has a length of sqrt(2) units, which satisfies the equation of the unit circle [tex](x^2 + y^2 = 1)[/tex]. The Pythagorean Theorem is used to show that the hypotenuse has a length of sqrt(2).

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The music box has a surface area of 1350 square cm.

A cube has six square faces that are all the same size. The length of each side of the cube is given as 15 cm. Therefore, the surface area of the cube can be found by calculating the area of one square face and then multiplying it by 6:

Area of one square face = (15 cm) x (15 cm) = 225 square cm

The surface area of the cube = 6 x (Area of one square face)

= 6 x 225 square cm

= 1350 square cm

As a result, the music box has a surface area of 1350 square cm.

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A sample obtained in such a way that every element in the population has an equal chance of being selected is called a random sample.

In a random sample, each member of the population is selected independently and randomly, which means that each member has an equal chance of being included in the sample. Random sampling is a fundamental method used in statistical analysis, and it helps ensure that the sample is representative of the population.

By obtaining a representative sample, we can draw accurate conclusions about the population and make statistical inferences with confidence. Common methods of random sampling include simple random sampling, stratified sampling, and cluster sampling, among others.

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Complete Question:

a sample obtained in such a way that every element in the population has an equal chance of being selected is __.

Answer:

2, 3, 1, 3, 5, 4---->1, 2, 3, 3, 4, 5

The median is 3.

This hypothesis test is two-tailed because no direction is specified in the claim made by the social worker.

A two-tailed test means that the alternative hypothesis is that the population parameter is different from the specified value (in this case, 15 children dropping out of high school each day). So, the null hypothesis would be that the population parameter is equal to 15, while the alternative hypothesis would be that it is either greater than or less than 15. Therefore, we need to conduct a two-tailed test to determine whether the social worker's claim is statistically significant. The correct answer to your question is: This is a two-tailed test because no direction is specified.

In this scenario, the social worker at the community development organization wants to test the claim that the average number of children who drop out of high school each day in a particular city is different than 15 children. The hypothesis test is two-tailed because there is no specified direction for the population parameter (whether it's greater than or less than 15 children). Instead, the test simply seeks to determine if the average number of dropouts is different from 15, which could be in either direction.

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Answer:

B No solution

Step-by-step explanation:

The volume of the empty space inside Container A is given as follows:

703.4 ft³.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

For Container A, the dimensions are given as follows:

r = 8 feet, h = 8 feet.

(radius is half the diameter)

Hence the volume is given as follows:

V = 3.14 x 8² x 8

V = 1607.7 ft³.

For Container B, the dimensions are given as follows:

r = 4 feet, h = 18 feet.

Hence the volume is given as follows:

V = 3.14 x 4² x 18

V = 904.3 ft³.

Then the volume of the empty space is given as follows:

1607.7 - 904.3 = 703.4 ft³.

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There are 662 union members working for the company.

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

Let's use "x" to represent the ratio multiplier, which will allow us to find the actual number of union and nonunion members.

According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that for every 4 union members, there are 5 nonunion members.

We can set up a proportion to find the value of x:

4/5 = x/207

To solve for x, we can cross-multiply:

4 × 207 = 5 * x

828 = 5x

x = 828/5

x = 165.6

Since we cannot have a fraction of a person, we must round this value to the nearest whole number.

Now we can use x to find the actual number of union members:

Number of union members = 4x

Number of union members = 4 × 165.6

Number of union members = 662.4

hence, Rounding this value to the nearest whole number, we can say that there are 662 union members working for the company.

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The best option for the car deal is option B.

The composite function represented by g(f(x)) = 0.9(x - 2000), is option a.

The best possible deal for the car is determined from the final price in each case.

If you apply $2000 first, then the price becomes

= $22,500 - $2000

= $20,500

Then apply 10% discount, the final price becomes;

= (100% - 10%) x  $20,500

= 0.9 x  $20,500

= $18,450

For option b, we will apply the 10% discount first,;

=  (100% - 10%) x  $22,500

= 0.9 x $22,500

= $ 20,250

The apply a rebate of $2000, the final price becomes;

= $ 20,250 - $2,000

= $18,250

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The axis of symmetry of a parabola with vertex (5, -10) is x = 5, which is a vertical line passing through the vertex.

The axis of symmetry of a parabola is a vertical line that passes through its vertex and divides the parabola into two mirror-image halves. In this case, the vertex of the parabola is given as (5, -10), which means the vertex lies on a horizontal line passing through the axis of symmetry.

The equation of the axis of symmetry can be written as x = h, where (h, k) is the vertex of the parabola.

As from the given points h corresponds to value '5'. Therefore, the axis of symmetry for this parabola is x = 5, which is a vertical line passing through the point (5, -10).

To visualize this, you can imagine folding the parabola along its axis of symmetry. The left and right halves of the parabola will overlap perfectly, creating a symmetrical shape.

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Yes.

The data are from a random sample, meeting the Randomization Condition.

The data have at least 10 successes and 10 failures, meeting the Success/Failure Condition.

The population is much larger than the sample, meeting the 10% Condition. A

It is reasonable for the research team to use a Normal model for the sampling distribution of the sample proportion.

A Normal model for the sampling distribution of a sample proportion, three conditions must be met:

The Randomization Condition, the Success/Failure Condition, and the 10% Condition.

The Randomization Condition is met as the sample is selected randomly from a much larger population of adults.

The Success/Failure Condition is also met because the sample size is large enough (n = 1900) for us to expect at least 10 successes (those who are pessimistic about the future of marriage and family) and 10 failures (those who are optimistic about the future of marriage and family).

The sample proportion of pessimistic adults is 34%, which corresponds to 646 successes in the sample.

The 10% Condition is also met as the sample size (n = 1900) is less than 10% of the total population of adults.

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The cost of walking this guest is $190.

The cost of walking the guest can be calculated by adding up the expenses incurred by the hotel.

The guest was walked to another hotel that charged a room rate of $150. Therefore, the hotel incurred a cost of $150 for the room.

In addition to the room cost, the hotel also paid for the guest's Uber ride to the new hotel, which was $15.

Furthermore, the overbooked hotel gave the guest a gift card worth $25. Although the gift card does not directly represent an expense, it can be considered as an opportunity cost for the hotel, as they could have used that money to cover other costs.

Therefore, the total cost incurred by the hotel for walking the guest is:

$150 (room cost) + $15 (Uber cost) + $25 (gift card cost) = $190

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