X is distributed with mean 6 and standard deviation 2 and Y=2X+5. Find the mean and standard deviation of the Y distribution.

Answer:

[tex]x=20[/tex]

Step-by-step explanation:

We have been a triangle has one angle measuring [tex]3x[/tex] degrees the second angle measures [tex]2x+20[/tex] degrees and the third angle measures [tex]4x-20[/tex] degrees. We are asked to find the value of x.

We know that all interior angles of a triangle add up-to 180 degrees.

[tex]3x+2x+20+4x-20=180[/tex]

Combine like terms:

[tex]3x+2x+4x-20+20=180[/tex]

[tex]9x=180[/tex]

Divide both sides by 9:

[tex]\frac{9x}{9}=\frac{180}{9}[/tex]

[tex]x=20[/tex]

Therefore, the value of x is 20 for our given triangle.

Final answer:

To express 28 as a product of its prime factors, you would write [tex]28 = 2^2 \times 7[/tex], where 2*2 represents 2 multiplied by itself and 7 is a prime number.

Explanation:

To write 28 as a product of its prime factors, we begin by finding the smallest prime number that divides 28. Since 28 is an even number, we know it's divisible by 2. So we start with 2 and keep dividing:

28 ÷ 2 = 14

14 ÷ 2 = 7

Now, 7 is a prime number and cannot be divided further except by 1 and itself. So, we end up with:

28 = 2 × 2 × 7

We can also express this using exponents:

28 = 2² × 7

These are the prime factors of 28, written in order from smallest to largest.

The given equation is

   [tex]\rightarrow 9r+16=\frac{\pi}{5}[/tex]

The value of π is 3.14 or [tex]\frac{22}{7}[/tex] that is a fixed Value.

   [tex]\rightarrow 9r +16=\frac{3.14}{5}\\\\9r+16=0.628\\\\9r=0.628-16\\\\9r=-15.372\\\\r=\frac{-15.372}{9}\\\\r=-1.708[/tex]

So, the given equation is Literal ,because variable value is Known.

A literal equation is an equation that has at least one letter or one unknown variable.

[tex]9r + 16= \frac \pi 5[/tex] is a literal equation because it has letter r

Given that:

[tex]9r + 16= \frac \pi 5[/tex]

By analyzing the equation, we have:

[tex]9, 16, 5 \to[/tex] number

[tex]r \to[/tex] letter

[tex]\pi \to[/tex] constant

Because r is a letter, then the equation is a literal equation

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The average height of the ocean is -2.

Average The arithmetic mean is calculated by adding a set of integers, dividing by their count, and then taking the result.

For instance, the result of 30 divided by 6 is 5, which is the average of 2, 3, 3, 5, 7, and 10.

Averages are used to condense a vast number of data points into a single value. It is a visual depiction of all the data set's accessible numbers.

Given data:

Monday a.m.: −4

Monday p.m.:​ −6 ​

Tuesday a.m.: ​ −3 ​

Tuesday p.m.: ​ −1 ​

Wednesday a.m.: 0

Wednesday p.m.: 2

Thursday a.m.:​ −1 ​

Thursday p.m.:​ −3 ​

So, the average height of the ocean at low tide

=(-4 + (-6)+ (-3)+ (-1) + 0+ 2 + (-1) + (-3))/8

= (-18 + 2 ) / 8

= -16 /8

= -2

Hence, the average height of the ocean is -2.

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Answer:

243 ft2

Step-by-step explanation:

9*3= 27

3*3= 9

27*9=243 ft2

The area of the rectangular flower bed is 243 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

Given that a flower bed has the shape of a rectangle 9 yards long and 3 yards wide.

Length = 9 yards = 9 x 3 feet = 27 feet

Width = 3 yards = 3 x 3 feet = 9 feet

The area of the rectangular flower bed will be calculated as,

Area = L x W

Area = 27 x 9

Area = 243

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Answer:

$29 million is spent more by each person for dogs than cats.

Step-by-step explanation:

Amount spent on visits for the dogs = $7,737.6 millions.

Number of dogs owned = 31.2 millions (by bar graph)

∴ On average amount spent on each person = [tex]\frac{7,737.6}{31.2} = $248 millions [/tex]

Amount spent on visits for the cats = $7,737.6 millions.

Number of cats owned = 27 millions (by bar graph)

∴ On average amount spent on each person = [tex]\frac{5913}{27} = $219 millions [/tex]

Thus, on average, by each person amount spent for dogs than cats = $248 millions - $219 millions = $29 millions.

The numbers are 41,43,45,47.

Given that,

Based on the above information, the calculation is as follows:

x + x + 2 + x + 4 + x + 6 = 176

4x + 12 = 176

4x = 164  

x = 41

So, the four consecutive odd numbers are 41, 43, 45, 47

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The length of a side of the patio, rounded to the nearest tenth of a yard, is 7.5 yards.

To find the length of a side of the patio, we need to find the square root of the area. The area of the patio is given as 56 square yards.

To find the length of a side, let's take the square root of 56. The square root of 56 is approximately 7.48.

Therefore, the length of a side of the patio, rounded to the nearest tenth of a yard, is 7.5 yards.

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Answer:

f(x)=11 and f(x)=16

Step-by-step explanation:

f(x)=5(2)+1

f(x)=11

f(x)= 5(3)+1

f(x)=16

The slope is undefined for figure 2.

In general, when the x-values or x-coordinates is the same for both points, the slope is undefined.

For example, let us try to get the slope for a line passing through the points  (1, 3) and (1, 9)

Let x₁ = 1 , y₁ = 9 and x₂ = 1 and y₂ = 3

Slope, m = (y₂ − y₁)/((x₂ − x₁)

m = (3 − 9)/(1 − 1)

m = -6/0, which is undefined.

The greater number between 1/3 and 0.33 is 1/3

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

1/3 or 0.33

Express them as decimals

So, we have

1/3 = 0.333..

0.33 = 0.33

By comparison

0.333.. is greater than 0.33

This means that the greater number is 1/3

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Answer:

26.25 ft.

Step-by-step explanation:

The general form of a parabola is [tex]y = a(x - h)^2 + k[/tex], where the vertex of the parabola is (h,k).

Given that

[tex]y = a(x - h)^2 + k[/tex]

A. The quadratic equation

The lowest point (which stands for the vertex) is given as:

[tex](h,k) = (90,6)[/tex]

So, we have:

[tex]y = a(x - 90)^2 + 6[/tex]

From the question, we understand that:

At a horizontal distance of 30ft, the cable is at 15ft. This means:

[tex](x,y) = (30,15)[/tex]

Substitute these values in: [tex]y = a(x - 90)^2 + 6[/tex]

So, we have:

[tex]15 = a(30 - 90)^2 + 6[/tex]

[tex]15 = a(- 60)^2 + 6[/tex]

[tex]15 = a \times 3600 + 6[/tex]

Collect like terms

[tex]3600a = 15 - 6[/tex]

[tex]3600a = 9[/tex]

Make a, the subject

[tex]a = \frac{9}{3600}[/tex]

[tex]a = 0.0025[/tex]

Substitute [tex]a = 0.0025[/tex] in [tex]y = a(x - 90)^2 + 6[/tex].

[tex]y = 0.0025(x - 90)^2 + 6[/tex]

B. The horizontal distance at a height of 26.25ft.

This means that, y = 26.25

So, we have:

[tex]26.25 = 0.0025(x - 90)^2 + 6[/tex]

Collect like terms

[tex]-6 + 26.25 = 0.0025(x - 90)^2[/tex]

[tex]20.25= 0.0025(x - 90)^2[/tex]

Divide both sides by 0.0025

[tex]8100 = (x - 90)^2[/tex]

Take square roots of both sides

[tex]\±90 = x - 90[/tex]

Solve for x

[tex]x = 90 \± 90[/tex]

To the left of the cable, the horizontal distance is:

[tex]x_1 = 90 - 90[/tex]

[tex]x_1 = 0[/tex]

To the right of the cable, the vertical distance is:

[tex]x_2 = 90 + 90[/tex]

[tex]x_2 = 180[/tex]

So, the coordinates of the left and right support at a height of 26.25 is:

(0,26.25) and (180, 26.25)

The distance (d) between them is calculated using:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]

[tex]d = \sqrt{(180- 0)^2 + (26.25-26.25)^2}[/tex]

[tex]d = \sqrt{180^2 + 0^2}[/tex]

[tex]d = \sqrt{180^2}[/tex]

[tex]d = 180[/tex]

The distance between them is 180ft

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