suppose you have a set of data with a mean of 50 and a standard deviation of 10. if you add 5 to each data point, what will happen to the mean and the standard deviation of the new set of data?

To prove these statements, we will use the formulas for the volume and surface area of a sphere and a cylinder.
The volume of a sphere is given by the formula V = 4/3 πr³, where r is the radius of the sphere.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.

(a) If a sphere is inscribed in a right circular cylinder whose height is equal to the diameter of the sphere, then the height of the cylinder is 2r and the radius of the base is r. Therefore, the volume of the cylinder is
V = πr²(2r) = 2πr³.
Now, we can compare the volume of the cylinder to the volume of the sphere:
V_cylinder/V_sphere = (2πr³)/(4/3 πr³) = (2/4)(3/1) = 3/2.
Therefore, the volume of the cylinder is 3/2 the volume of the sphere.
(b) The surface area of a sphere is given by the formula A = 4πr².
The surface area of a cylinder, including its bases, is given by the formula
A = 2πrh + 2πr², where r is the radius of the base and h is the height of the cylinder.
If a sphere is inscribed in a right circular cylinder whose height is equal to the diameter of the sphere, then the height of the cylinder is 2r and the radius of the base is r. Therefore, the surface area of the cylinder is
A = 2πr(2r) + 2πr² = 4πr² + 2πr² = 6πr².
Now, we can compare the surface area of the cylinder to the surface area of the sphere:
A_cylinder/A_sphere = (6πr²)/(4πr²) = (6/4) = 3/2.
Therefore, the surface area of the cylinder, including its bases, is 3/2 the surface area of the sphere.

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Answer:

subtotal: $23.45

tip: $4.22

total: $27.67

Step-by-step explanation:

7.99+1.00+8.99+2.49+1.99+0.99=$23.45

23.45x0.18=$4.22

23.45+4.22=$27.67

Answer:

A = 45 units²

Step-by-step explanation:

the lined figure is composed of a rectangle and a triangle

area of rectangle WFSC is calculated as

area = length × width

       = FW × WC

      = 2 × 9

     = 18 units²

the area of Δ is calculated as

area = [tex]\frac{1}{2}[/tex] base × perpendicular height

       = [tex]\frac{1}{2}[/tex] × FS × perpendicular length from N to base FS

       = [tex]\frac{1}{2}[/tex] × 9 × 6

      = 4.5 × 6

      = 27 units²

total area (A) is then the sum of the 2 figures , that is

A = 18 + 27 = 45 units²

Answer:

b - a = -5

Step-by-step explanation:

I am not sure if I am right, but I am thinking -5

a = 0 and b - -5

a -b = 5

0 - (-5) = 5

5 = 5  If this is true, then

b - a would be

-5 - 0 = -5

-5 = -5

Helping in the name of Jesus.

Answer:

-5

Step-by-step explanation:

We know that a - b = 5,
so to find b - a, we can rearrange this equation as follows:

a - b = 5

a = b + 5
b = a - 5

Therefore, b - a = (a - 5) - a

= -5

So, b - a = -5.

Answer:

We can use the principle of conservation of momentum to solve this problem. According to this principle, the total momentum of a system of objects remains constant if there are no external forces acting on the system.

Initially, only the cue ball is moving, and the 8 ball is at rest. Therefore, the initial momentum of the system is:

p_initial = m1 * v1 + m2 * v2

= 0.2 kg * 10 m/s + 0.15 kg * 0 m/s

= 2 kg m/s

After the collision, the cue ball is rolling forward at 1 m/s, and the 8 ball is moving in some direction with some velocity v_final. Therefore, the final momentum of the system is:

p_final = m1 * v1 + m2 * v_final

According to the conservation of momentum principle, p_initial = p_final. Therefore,

2 kg m/s = 0.2 kg * 1 m/s + 0.15 kg * v_final

Solving for v_final, we get:

v_final = (2 kg m/s - 0.02 kg m/s) / 0.15 kg

= 13.33 m/s

Therefore, the velocity of the 8 ball after the collision is 13.33 m/s.

Answer:

To find the absolute change in population from 2007 to 2009, we can subtract the initial population in 2007 from the final population in 2009:

Absolute change = Final population - Initial population

= 6,200 - 3,900

= 2,300 people

Therefore, the absolute change in population from 2007 to 2009 is 2,300 people.

To find the percent increase (relative change) in population, we can use the formula:

Percent increase = (Absolute change / Initial population) x 100%

Substituting the values given in the problem, we get:

Percent increase = (2,300 / 3,900) x 100%

= 58.97%

Therefore, the population increased by approximately 58.97% from 2007 to 2009. Rounded to the nearest tenth of a percent, the percent increase is 59.0%.

On answering the provided question, we have got that As a result, the scale factor of the dilatation between triangle  ABC and A′′B′′C′′ is 1/2.

An additional four or so parts make a triangle a polygon. Its shape is a simple rectangle. An edged rectangle with the letters ABC on it is known as a triangle. Euclidean geometry yields a single plane and cube when the sides are actually not collinear. Having three parts and three angles makes a triangle a polygon. The corners of a triangle are where the three edges meet. The sum of the angles of a triangle's sides is 180.

By multiplying the individual scale factors of the two dilations, we can determine the scale factor of the dilation between ABC and A′′B′′C.

Each side of ABC is scaled down by a factor of 1/3 in the first dilation with a scale factor of 3. Thus, the corresponding sides of A, B, and C are a third the length of corresponding s of ABC.

In the second dilation, each side of "A" through "C" is scaled up by a factor of 3/2. As a result, the corresponding sides of A′′B′′C′′ are 3/2 times longer than those of A′B′C′.

1/3 × 3/2 = 1/2

As a result, the scale factor of the dilatation between ABC and A′′B′′C′′ is 1/2.

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Answer: -2

Step-by-step explanation:

Answer:

plot the point at -2

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a geometric means problem. 6 is the altitude, which belongs to both of those smaller triangles; thus, it is the geometric means. We set up the proportion like this:

[tex]\frac{8}{6} =\frac{6}{b+3}[/tex] and we cross multiply to solve.

8(b + 3) = 36 and

8b + 24 = 36 and

8b = 12 so

b = 3/2 or 1.5

Answer:

The volume of the cake is:

12 inches x 9 inches x 2 inches = 216 cubic inches

Dividing the volume of the cake by the number of pieces, we get:

216 cubic inches / 18 = 12 cubic inches per piece

Therefore, the volume of each piece is 12 cubic inches.

Answer:

12 inches cubed

Step-by-step explanation:

First we have to find the total volume so we can split it up. We can do this by using the formula LWD = V, where l = length, w = width, and d = depth.

Here, the length is 12, the height is 2, and the depth is 9. We apply the formula:

(12)(2)(9) = 216

Now, we have to split it into 18 separate pieces. We can do this by dividing the total volume (216 inches cubed) by 18.

216/18 = 12

Therefore, each equal piece will be 12 inches cubed

Answer: 1,368 books

Explanation: To find the total number of science fiction books in the bookstore, you need to multiply the number of bookcases by the number of books in each bookcase. In this case, there are 19 bookcases, each containing 72 books:

19 bookcases × 72 books per bookcase = 1,368 books

So, there are 1,368 science fiction books in the bookstore.

In the illustration, there are 2 9-point stars and 8 5-point stars.

Let x be the number of 5-pointed stars and y be the number of 9-pointed stars. Each 5-pointed star has 5 points and each 9-pointed star has 9 points, so the total number of points in the drawing is:

5x + 9y = 66

There are two variables in the equation, so we need another equation to solve for x and y. The problem states that there are a total of 10 stars in the drawing, so:

x + y = 10

We can represent this system of linear equations using a matrix:

[5 9] [x] [66]

[1 1] [y] = [10]

This is a matrix equation of the form Ax = b, where A is the coefficient matrix, x is the variable matrix, and b is the constant matrix. We can solve for x and y by finding the inverse of the coefficient matrix A:

A^-1 = 1/(5-9) [-9 5]

[ 1 -1]

Multiplying both sides by A^-1, we get:

x = A^-1 b

x = 1/(5-9) [-9 5] [66]

[1 -1] [10]

x = [-3 8]

Therefore, there are 8 5-pointed stars and 2 9-pointed stars in the drawing.

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According to the information, the scale that you would use for the pictogram would be 10 for each symbol.

To choose the most appropriate pictogram for the information in the table, we must take the data into account. In this case, we must find a divisor number of all the numbers to take it as the value of the scale. In this case we can take 10, because it divides all the numbers as shown below:

According to the above, 8 sports symbols, 4 reading symbols, 7 game symbols and 6 music symbols should be used to represent the values, taking into account that each symbol is equal to 10 units.

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The correct option is A. m∠X = 45° as the triangles ABC and XYZ are congruent.

Congruent triangles are two triangles that have the same shape and size. In other words, if two triangles are congruent, then all their corresponding sides and angles are equal. Some methods that allow us to compare the lengths of corresponding sides and the measures of corresponding angles in the two triangles and determine whether they are equal includes: SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle), AAS (angle-angle-side), or HL (hypotenuse-leg).

The angle m∠A corresponds to the angle m∠X given that the triangles ABC and XYZ are congruent.

In conclusion, the correct option for the congruent triangles is A. m∠X = 45°.

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Answer:

After one year, the amount in the bank account will be:

$200 + ($200 x 0.05) = $200 + $10 = $210.

Therefore, the total in the bank account after 1 year is $210.

To flesh out a coordinate descent method : (i) One common approach is to choose coordinate with the largest gradient. (ii) One common approach is to use a line search, where we try out step sizes along the chosen coordinate and select the one that leads to the largest decrease in the function value. (iii) One common stopping criterion is to stop when the change in function value.

This can be done by computing the partial derivatives of the function with respect to each coordinate, and selecting the one with the largest absolute value. This approach is known as "greedy" coordinate descent, and it can help speed up convergence by focusing on the most important directions.

This approach can be more computationally efficient, since it doesn't require computing the gradient at each step. Another approach is to use a fixed step size, which can be simpler to implement but may not always lead to the best results.

By choosing the coordinate to optimize along, determining the step size, and setting a stopping criterion, we can develop a coordinate descent method that is well-suited to our particular optimization problem.

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Answer:

0.177

Step-by-step explanation:

A perfect correlation is 1. So .998 or even .863 is a good correlation.

since our decimal isn't close to that at all, we have a weak positive correlation.

The equation of the quadratic function is f(x) = (x + 5)² - 2

A quadratic function is a second-degree polynomial function of one variable, which can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and x is the variable.

From the question, we have the table of values which represents a quadratic function f(x).

A quadratic equation is represented as

f(x) = a(x - h)² + k

Where, Vertex = (h, k)

If we plot the graph according to the given table, the vertex will be,

(h, k) = (-5, -2)

Substitute, (h, k) = (-5, -2) in f(x) = a(x - h)² + k

So, we have, f(x) = a(x + 5)² - 2

Also, from the graph, we have the point (0, 23)

This means that

a(0 + 5)² - 2 = 23

25a = 25

a = 1

Substitute a = 1 in f(x) = a(x + 5)² - 2

f(x) = (x + 5)² - 2

Hence, the equation is f(x) = (x + 5)² - 2

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The probability that the first customer will sit in a seat in the back row is 4/9.

A customer is a person or business that buys goods or services from another business.

There are a total of 45 seats in the theater. Out of those, 20 seats are in the back row.

So the probability that the first customer who enters the theater will sit in a seat in the back row is:

P(back row) = 20/45

Simplifying the fraction gives:

P(back row) = 4/9

Therefore, the probability that the first customer will sit in a seat in the back row is 4/9.

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Answer: 9.42477796077 square yards

Step-by-step explanation:

Cone Surface Area Calculation

surface area of cone slant height is 2 radius is 1

To find the surface area of a cone, we need to know the radius and slant height of the cone.

In this case, we are given that the radius (r) is 1, and the slant height (l) is 2. We can use the Pythagorean theorem to find the height (h) of the cone:

l^2 = r^2 + h^2

2^2 = 1^2 + h^2

4 = 1 + h^2

h^2 = 3

h = sqrt(3)

Now we can use the formula for the surface area of a cone:

A = πr^2 + πrl

Substituting the values we know:

A = π(1)^2 + π(1)(2)

A = π + 2π

A = 3π

So the surface area of the cone is 3π

3 times Pi = 9.42477796077

ChatGPT

.

Answer:

h=13

Step-by-step explanation:

have a good day

Answer:

13

Step-by-step explanation:

27-h=14

-h=14-27

-h=-13

To get rid of the negative sign, divide both sides by -1

Therefore h=13

Answer:  C $462.50

Step-by-step explanation:

It's $462.50 because since $6 has a higher profit you would want to try and sell more of that product (The football). So $6 times 45 is 270. And the max number of balls the store can have is 80, 80 minus 45 is 35 so there can only 35 baseballs left. 35 times $5.50 is 192.50. Lastly, you add the two products, and you get 462.50.

The maximum profit the store can make from selling footballs and baseballs in a typical month is $462.50.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Let's say the store sells x footballs and y baseballs.

The total number of balls sold can be expressed as x + y ≤ 80.

Also, we know that 35 ≤ x ≤ 45 and 40 ≤ y ≤ 55.

To maximize the profit, the store should sell the maximum number of footballs and baseballs that it can stock.

From the constraints, we see that the maximum number of footballs the store can sell is 45 and the maximum number of baseballs it can sell is 55, which together make a total of 100 balls.

However, this exceeds the 80-ball limit, so we need to adjust the numbers.

Let's say the store sells 45 footballs and y baseballs.

Then, y ≤ 35 since 45 + 35 = 80, which is the maximum number of balls the store can stock.

Similarly, let's say the store sells x footballs and 55 baseballs.

Then, x ≤ 25 since 25 + 55 = 80.

To find the maximum profit, we need to calculate the profit from selling 45 footballs and 35 baseballs, which will give the highest profit among the feasible combinations.

The profit from selling 45 footballs is 45 × $6 = $270.

The profit from selling 35 baseballs is 35 × $5.50 = $192.50.

The total profit is $270 + $192.50 = $462.50.

Therefore,

The maximum profit the store can make from selling footballs and baseballs in a typical month is $462.50.

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The only value of x for which f(x) = 0 is x = 36. So, f(x) = -x + 36 does not have a real root, since there is no value of x that makes the function equal to zero.

What is a function ?

A function is a mathematical concept that describes the relationship between a set of inputs (domain) and a set of outputs (range), such that each input has a unique output. In other words, it is a rule that assigns to each input exactly one output.

A real root of a function refers to a value of x for which the value of the function is equal to zero. So, to determine whether f(x) = -x + 36 has a real root, we need to find the value(s) of x for which f(x) = 0.

Setting f(x) = 0, we have:

-x + 36 = 0

Adding x to both sides, we get:

36 = x

Therefore, the only value of x for which f(x) = 0 is x = 36. So, f(x) = -x + 36 does not have a real root, since there is no value of x that makes the function equal to zero.

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The hotel had 289 guests on the day in question. The z-score is a measure of how many standard deviations a data point is away from the mean of the distribution.

In this case, we are given that the number of guests in a hotel per day follows a normal distribution with a mean of 220 and a standard deviation of 30, and that the z-score of the number of guests on a particular day was 2.3.

Using the formula for z-score, we have:

z = (x - mu) / sigma

where x is the number of guests on the given day, mu is the mean of the distribution, and sigma is the standard deviation of the distribution.

Substituting the given values, we have:

2.3 = (x - 220) / 30

Multiplying both sides by 30, we get:

69 = x - 220

Adding 220 to both sides, we get:

x = 289

Therefore, the hotel had 289 guests on the day in question.

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The product of two binomials is the result of multiplying each term from the first binomial by each term from the second binomial. The product of the two binomials, (-5x-1) and (2x+8), is[tex]0x^2+(-10x-2x)+(-8x-8)[/tex] which simplifies to -18x-10.

To calculate the product of the two binomials, we multiply the coefficients of each term together and add the exponents of the same base together. The coefficients of the first binomial, -5x and -1, are multiplied together to give a coefficient of -5. The exponents of x, 1 and 0, are added together, giving an exponent of 1. Thus, the first term is[tex]-5x^1[/tex]. The coefficients of the second binomial, 2x and 8, are multiplied together to give a coefficient of 16. The exponents of x, 1 and 0, are added together, giving an exponent of 1. Thus, the second term is[tex]16x^1[/tex].The last terms, -1 and 8, are multiplied together to give a coefficient of -8. The exponents of x, 0 and 0, are added together, giving an exponent of 0. Thus, the third term is[tex]-8x^0[/tex], which simplifies to -8.When all the terms are combined, the product of the two binomials, (-5x-1) and (2x+8), is -18x-10.

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The third term of the arithmetic sequence presented is given as follows:

14.

An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a constant value, called the common difference (d), to the previous term.

From the sequence in this problem, the terms are given as follows:

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