A video store has 6 new comedies, 4 new action movies, and 2 new dramas available to rent. If you choose 1 of each type of movie, how many combinations are there?

In spherical coordinates (ρ, θ, ϕ), the point (0, -5, 0) can be represented as (5, π/2, π/2).

To convert from rectangular coordinates to spherical coordinates, we use the following formulas:

ρ = √(x² + y² + z²)

θ = arctan(y / x)

ϕ = arccos(z / √(x² + y² + z²))

In this case, since the point lies on the negative y-axis, the x-coordinate is 0, and the y-coordinate is -5. Therefore, we have:

ρ = √(0² + (-5)² + 0²) = √25 = 5

Since the point lies in the negative y-axis, the angle θ is π/2.

Since the point lies on the xz-plane, the z-coordinate is 0. Therefore, we have:

ϕ = arccos(0 / √(0² + (-5)² + 0²)) = arccos(0 / 5) = arccos(0) = π/2

Combining these values, the point (0, -5, 0) in rectangular coordinates is equivalent to (5, π/2, π/2) in spherical coordinates.

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Answer:

Step-by-step explanation:

b

The scale factor of a dilation is the ratio of the corresponding side lengths of the image triangle to the original triangle. In this case, the image triangle is triangle A' B' C' and the original triangle is triangle ABC.

To find the scale factor, we can compare the corresponding side lengths of the two triangles. Let's denote the lengths of the corresponding sides as follows:

Side AB corresponds to side A'B'

Side BC corresponds to side B'C'

Side CA corresponds to side C'A'

The scale factor is then given by:

Scale factor = Length of corresponding side in image triangle / Length of corresponding side in original triangle

To find the scale factor, you can calculate the ratio of the corresponding side lengths. For example, if the length of AB is 4 units and the length of A'B' is 8 units, then the scale factor would be 8/4 = 2.

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Answer: (a) $424.8

Step-by-step explanation:

Step-by-step explanation:

Surface Area of Figure = Area of 4 triangular sides + Area of Base

=

[tex]4 \times ( \frac{1}{2} \times base \times height) + (length \: \times \: width) \\ = 4 \times ( \frac{1}{2} \times 10 \times 12.1) + (10 \times 10) \\ = 4 \times 60.5 + 100 \\ = 242 + 100 \\ = 342 {yd}^{2} [/tex]

The statement  if /[tex]\sqrt{25}[/tex]∉Q, then it is the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q is false.

To disprove the statement, we need to provide a counter example where [tex]\sqrt{25}[/tex] ∉ Q (irrational) and [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∉ Q (also irrational).

Let's consider [tex]\sqrt{25}[/tex] = 5, which is a rational number since it can be expressed as a ratio of two integers (5/1).

In this case, [tex]\sqrt{25}[/tex] ∉ Q is false since it is a rational number.

Furthermore, [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] = 5 - [tex]\sqrt{17}[/tex] is also irrational since it cannot be expressed as a ratio of two integers.

Therefore, we have found a counterexample that disproves the statement, showing that if [tex]\sqrt{25}[/tex] ∉ Q, then it is not necessarily the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q.

Hence, the statement is false.

Question: Prove or disprove, using any method, that if /[tex]\sqrt{25}[/tex]∉Q, then it is the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q.

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The question is incomplete:

Two ovens have measurements as shown. Which oven has a greater volume? How much greater is its volume?

The image with the information is below.

Answer:

-Oven B has a greater volume.

-Its volume is greater by 768 in³.

Step-by-step explanation:

First, you have to calculate the volume of each oven by multiplying the area of the base by the height:

Oven A: 576 in²*15 in= 8640 in³

Oven B: 672 in²*14 in= 9408 in³

Now, you have to calculate the difference between the volumes:

9408-8640=768

According to this, the answer is that oven B has a greater volume. Its volume is greater by 768 in³.

Answer:you cross multiply

Step-by-step explanation:

i hate tacos

Answer:

20

Step-by-step explanation:

Find the difference of the smallest value and the largest value.

Answer:

30 minus 10 then the range is 20

Answer:

(0,6), (6,0)

Step-by-step explanation:

Answer:

Whatttttttttttttttttt

After 1 minute, the mass of salt in the tank will be 3.072 kg. The concentration of salt in the tank will reach 0.01 kg/L after approximately 31 minutes.

To determine the mass of salt in the tank after 1 minute, we need to consider the inflow and outflow of the brine solution. The rate of inflow is 8 L/min, and the initial concentration of salt in the solution is 0.03 kg/L. Therefore, after 1 minute, 8 L of brine solution with a concentration of 0.03 kg/L will enter the tank, resulting in an additional mass of salt of 0.24 kg (8 L * 0.03 kg/L).

Since the solution inside the tank is well stirred and flows out at the same rate, the outflow rate is also 8 L/min. Thus, after 1 minute, 8 L of the brine solution will leave the tank, taking away 0.24 kg of salt.Considering the initial mass of salt in the tank (3 kg) and the change in mass due to the inflow and outflow after 1 minute, the mass of salt in the tank after 1 minute will be 3 kg + 0.24 kg - 0.24 kg = 3.0 kg.

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Answer:

y - 6 = -1 (x+5)

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1} \\[/tex]. Substitute the x and y values of (-5,6) and (0,1) into the formula and simplify like so:

[tex]m = \frac{(1)-(6)}{(0)-(-5)} \\m = \frac{1-6}{0+5} \\m = \frac{-5}{5} \\m = -1[/tex]  

So, the slope of the line is -1.

2) Now we have enough information to write the equation of the line in point-slope form. Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute real values for the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].

Since [tex]m[/tex] represents the slope of the line, substitute -1 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (-5, 6) in those places as well. This gives the following equation and answer:

[tex]y-6 = -1(x+5)[/tex]

Answer:

The answer is A. y <= -3x + 3

Answer: C

Step-by-step explanation:

21x+9-3x = 18x + 9

If you factor out the 9, you would be left with

9 (2x+1)

Answer: A. 9(2x - 1)

Step-by-step explanation:

combine like terms

21x+9-3x

21x-3x

18x+9

Factor the expression

factor out 9 from the expression

you get 9(2x - 1)

Answer:

B is not true

Step-by-step explanation:

8+7= 15 and 14+3= 17

15 is not equal to 17

Answer:

B is the one equation that is NOT true.

Step-by-step explanation:

A: 9+4 is 13, and 17-4 is 13 as well. This equation is true, 13=13.

B: 8+7 is 15, and 14+3 is 17. This equation is false, because 15 is not equal to 17. Although we have our answer, we need to still check the other equations.

C: 11 is, well, 11, because nothing changed on that side of the equation. 19-8 is 11, so this is true because 11=11.

D: 5+8 is 13, and 20-7 is 13. This equation is also true, because 13=13.

The only equation that is not true, is B. (8+7 = 14+3)

Answer:

The median of plot A is greater that the median of plot B

Step-by-step explanation: the median on plot A is 45 and the median on plot B is 15

1)The mean of the data in plot A is greater than the

mean of the data in plot B.

2) The median of the data in plot A is greater than the

median of the data in dot plot B.

3) The range of the data in plot A is greater than the

range of the data in plot B.

The median is the middle number in a sorted, ascending, or descending, list of numbers.

Let us arrange the data of plot A in ascending order:

30,35,35,40,40,40,40,45,45,45,45,50,55,55,60

Number of observations = 15

Mean of the plot A = 44

Median will be the middle observation i.e. 8th observation i.e. 45

Let us arrange the data of plot A in ascending order:

5,5,5,10,10,10,10,15,15,15,20,20,25,30,35

Number of observations = 15

Mean of the plot B = 15.33

Median will be the middle observation i.e. 8th observation i.e. 15

Therefore,1)The mean of the data in plot A is greater than the

mean of the data in plot B.

2) The median of the data in plot A is greater than the

median of the data in dot plot B.

3) The range of the data in plot A is greater than the

range of the data in plot B.

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Answer:

3 units down

Step-by-step explanation:

got it right on edg

Answer:

1 km

Step-by-step explanation:

According to the unit of conversion in every 1 kilometer, there is a total of 100 000 centimeters. Now, the given value of centimeters is equals to 52 800 => 1 km = 100 000 cm => 52 800 cm is less than the value of 100 000 cm which is equivalent to 1 km. Thus, the given is not correct.

Question

Marcus asked 10 people at a juggling festival what age they were when they started to juggle. Which interval contains the median age?

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]n = 10[/tex]

Required

The median interval

The question is incomplete, as the required data is not given.

To solve this question, I will use the following assumed dataset.

[tex]Age:17\ 17\ 18\ 20\ 21\ 22\ 22\ 24\ 28\ 28[/tex]

First, calculate the median position.

[tex]Median = \frac{n+1}{2}\ th[/tex]

[tex]Median = \frac{10+1}{2}\ th[/tex]

[tex]Median = 5.5\ th[/tex]

This implies that the median is the mean of the 5th and 6th data

So, we have the interval to be.

[tex]Median = [5th, 6th][/tex]

[tex]Median=[21,22][/tex]

Generally, the median of 10 data set is located at interval 5 to 6

Answer:

[tex]4\frac{5}{12}[/tex]

Step-by-step explanation:

[tex]4\frac{3}{4} -\frac{1}{3} \\\\\frac{19}{4} -\frac{1}{3} \\\\\frac{57}{12} -\frac{4}{12} \\\\\frac{53}{12} \\\\4\frac{5}{12}[/tex]

Answer:

leon's older brother is 4 5/12 feet tall

Step-by-step explanation:

4 3/4 - 1/3

= 4 5/12

Answer:

3x=105,x°+2x°+75°=180°,and 3x°+75°=180°

Step-by-step explanation:

no explanation sorry,your welcome

Step-by-step explanation:

We first Find the Slope of the line y=2x+3

The Slope Intercept Form of the equation of a given line is:

y=mx+c

where m is the Slope of that line, and c is the Y intercept.

For this line, the Slope is 2

So the Slope of the line PARALLEL to y=2x+3 will also be 2. And we are given that it passes through the point (2,6)

The Point-Slope form of the Equation of a Straight Line is:

(y−k)=m⋅(x−h)

m is the Slope of the Line

(h,k) are the co-ordinates of any point on that Line.

Here, we have been given the coordinates (h,k) of 1 point on that line as (2,6)

And the Slope m is 2

Substituting the values of h,k and m in the Point-Slope form, we get

(y−2)=(2)⋅(x−6)

(y−2)=2⋅(x-6)

y−2=2x -12

y=2x -12 +2

y=2x-10

The graph will look like

graph{y=2x -10 10 [10, -10, 5, - 5]}

Answer:

17/27

Step-by-step explanation:

Since there are 10 blue marbles, and 27 total marbles, the probability of not choosing a blue marble is 17/27 because you subtract the amount of blue marbles (10) from the amount of total marbles (27).

The probability of not choosing a blue marble is 17/27.

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the given situation,

Number of red marbles = 4

Number of blue marbles = 10

Number of green marbles = 7

Number of yellow marbles = 6

The event is the probability of not choosing a blue marble is

⇒ [tex]\frac{red+green+yellow}{Total marbles}[/tex]

⇒ [tex]\frac{4+7+6}{27}[/tex]

⇒ [tex]\frac{17}{27}[/tex]

Hence we can conclude that the the probability of not choosing a blue marble is 17/27.

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We need to determine whether an 8x8 matrix A exists that satisfies three conditions:

(i) having zeros below the main diagonal,

(ii) having a non-zero entry in the first row and eighth column, denoted as a18

(iii) being diagonalizable. In the second paragraph.

we will either provide an example of such a matrix and prove that it satisfies the conditions, or prove that no such matrix exists.

To provide an example of an 8x8 matrix A that satisfies the given conditions, we need to construct a matrix that satisfies each condition individually.

Condition (i) requires that all entries below the main diagonal of A are zero. This condition can easily be satisfied by constructing a matrix with zeros in the appropriate positions.

Condition (ii) states that a18, the entry in the first row and eighth column, must be non-zero. By assigning a non-zero value to this entry, we can fulfill this condition.

Condition (iii) requires that the matrix A is diagonalizable. This condition means that A must have a complete set of linearly independent eigenvectors. If we can find eigenvectors corresponding to distinct eigenvalues that span the entire 8-dimensional space, then A is diagonalizable.

If we are able to construct such a matrix that satisfies all three conditions, we can provide it as an example and prove that it fulfills the given conditions. However, if it is not possible to construct such a matrix, we can prove that no such matrix exists by showing that the conditions are mutually exclusive and cannot be satisfied simultaneously.

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Answer:

6 and 2/5

Step-by-step explanation:

Answer:

Decimal form: 6.4

Fraction form: 32/5

Step-by-step explanation:

of = times

2/5 x 16 = 6.4

The mean value is 6.5.

Given, z = 2.25, x = 14.6, σ = 3.6

The formula to calculate the z-score is,

z-score, z = (x - μ) / σOn

substituting the given values in the above formula, we get

2.25 = (14.6 - μ) / 3.6

Multiplying both sides by 3.6, we get,

2.25 * 3.6 = 14.6 - μ8.1 = 14.6 - μ

Subtracting 14.6 from both sides, we get,

-6.5 = -μOn multiplying both sides by -1, we get,

μ = 6.5

Hence, the mean value is 6.5.

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The decimal place z -score formula, z=x−μσ z = x − μ σ the mean (μ) is 6.5.

To find the mean (μ) using the z-score formula the Solve for μ

z = (x - μ) / σ

substitute the given values into the equation

2.25 = (14.6 - μ) / 3.6

solve for μ:

2.25 × 3.6 = 14.6 - μ

8.1 = 14.6 - μ

To isolate μ, subtract 14.6 from both sides:

8.1 - 14.6 = -μ

-6.5 = -μ

multiplying both sides by -1 gives

6.5 = μ

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