Let Z be a standard normal random variable: i. E. , Z ∼ N(0, 1).


(a) Using the distribution method, find the pdf of U = Z 2. (We proved this in class by using the MGF method. )

(b) Using result from previous part, show that pdf of U follows a special case of Gamma distribution and also of χ 2 distribution. Write down the corresponding parameters for each

Pyramids have been a symbol of great architecture inventions of the mankind. Egyptian People were the first once to design pyramids on a very large level.

Let a be the Side of Area of base of Pyramid . The base of a pyramid is a square shaped quadrilateral

The Volume of the Pyramid with base area   and height  is given by the equation (1)

[tex]Volume = (1/3)Ah....(1)[/tex]

[tex]A = a^{2}[/tex]

[tex]a = Side[/tex]

A = [tex]a^{2}[/tex] = [tex]44cm^{2}[/tex]

[tex]h = 12.6[/tex]

Putting these values in equation (1) we get

[tex]Volume = (1/3)X44X12.6[/tex]

[tex]Volume[/tex] [tex]= 184.8cm^{3}[/tex]

Hence , the volume of the pyramid is 184.8cm³

Answer:

Step-by-step explanation:

b

Answer:

23; 11 + 2t

Step-by-step explanation:

So let's start with the equation and then plug in the 6 hours:

Because we start with 11 dollars just to enter, our equation would start like this:

11 +

Also, 2 dollars for every hour. One hour could be represented as 1t, or just t:

11 + 2t (2 dollars for every t, every hour)

So now the equation is 11 dollars starting entry plus 2 dollars every hour

Now all we have to do is replace t with the number of hours:

11 + 2(6) = answer

11 + 12 = answer

23 = answer

Answer:

x ≥ 2

Step-by-step explanation:

the solid circle at 2 indicates that x can equal 2

the arrow points to the right indicating values of x greater than 2 , then the inequality being represented by the number line is

x ≥ 2

draw a line from the starting point of the segment to the endpoint using the same angle and length.

1. Place a ruler or straightedge on the given segment and draw a line along the length of the ruler.

2. Use a compass to create a line segment equal to the given segment. Set the compass to the length of the given segment, place the point of the compass on one end of the segment, and draw an arc to the other end of the segment.

3. Use a protractor to measure the angle and length of the given segment. Then, draw a line from the starting point of the segment to the endpoint using the same angle and length.

The answer explains three methods for drawing a line segment equal to a given segment: using a ruler or straightedge, using a compass, and using a protractor.

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Answer:

---------------------------------

Find the difference in time and the difference in the number of batches.

The two numbers will help to find the rate of change in that time interval.

This is same as finding the slope of a line with points (2.5, 8) and (4, 11):

The commission from selling each pair of shoe is $5 while that from selling each boot is $15

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x represent the commission earned from selling each pair of shoe and y represent the commission from selling each pair of boot.

Cooper sold 2 pairs of shoes and 10 pairs of boots, earning $160 in commission. Hence:

2x + 10y = 160    (1)

Also, he sold 4 pairs of shoes and 10 pairs of boots, earning a total commission of $170, hence:

4x + 10y = 170    (2)

From both equations:

x = 5, y = 15

The commission from selling each pair of shoe is $5

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The dots in the expression - 321⋅35⋅7⋅15 represents multiplication.

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

From higher classes, we write a dot sign in between two terms to represent that the terms are being multiplied.

Given, - 321⋅35⋅7⋅15 this represents multiplication between the numbers

- 321, 35, 7, and 15.

The result of this product is,

- 321×35×7×15

= - 1,179,675.

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Actual length is 5.5m and percentage error is 20%.We can find by using percentage error formula.

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words the percent error is the relative error multiplied by 100.

Subtract the actual value from the estimated value.And then divide the results with the real value. Multiply the results by 100 to find the total percentage.The formula represent it as a percentage of the exact value.Percent error = |Approximate value – Exact Value|/Exact value * 100.

Now we find

wall is measured 5m to the nearest so

approximate value= 4.5

actual value     =5.5

putting value in the formula

Percentage error  = 5.5- 4.5/5 *100

                              = 20%

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Answer:

Step-by-step explanation:

divide them both by 2

which is 3/ 9

divide them both by 3

whic is 2/6

and finally divide them both by 6

which is 1/3

you can multiply them both by an number as well

take care

Answer:

3/2

Step-by-step explanation:

3/2 is in the simplest form; it can't be decreased any more.

The length of the sides of cube will be;

⇒ 2 cm

A cube is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six squared faces with eight vertices and twelve edges is called cuboid.

Given that;

The surface area of a cube = 24 cm².

We know that;

The surface area of a cube with side 'a' is,

⇒ S.A = 6a²

Here, The surface area of a cube = 24 cm²

Hence, We get;

⇒ 24 = 6a²

⇒ 24/6 = a²

⇒ a² = 4

⇒ a = √4

⇒ a = 2 cm

Thus, The side of cube = 2 cm

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Numbered meridians are semicircles.

On a map of the planet, the Prime Meridian is an illustrative line. It serves as the origin of the longitude system of measurement. Meridians, a system of fictitious north-south lines, make up longitude. The planet Earth rotates like a ball. The Earth's axis serves as the spin's focal point.

The North Pole and the South Pole are where the axis intersects the surface of the planet. The North Pole and the South Pole are the points on each meridian. Meridians are used to calculate how far away from the prime meridian you are in degrees east or west.

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The regular price of a ticket to the game was $204.00.

We can use algebra to solve the problem. Let x be the regular price of a ticket to the game.

We know that the group rate saved Mason $5.75 per ticket, so the regular price of a ticket is x + $5.75.

We know that Mason bought 16 tickets and paid a total of $296.00, so we can set up the following equation:

x + $5.75 = (x + $5.75) * 16 = 16x + $92

So the regular price of a ticket is x = $296.00 - $92 = $204.00

Therefore, the regular price of a ticket to the game was $204.00.

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Answer:

1.

(a) 4y

(b) 5w

(c) 6a

(d) 3s

(e) 2n

(f) 3g

(g) 2y

(h) 0

2.

(a) -2u

(b) -w

(c) -3a

(d) -7y

3.

(a) 7a+3b

(b) 12y+4h

(c) 2g+10a

(d) 15m+10p

(e) 10e+4

(f) 12+5a

Step-by-step explanation:

Don't be intimidated by the "letter" variables. It is really just simple addition and subtraction. Examples:

For Q1=

y + y + y + y = 4y because there are 4 y's, and since we don't know the values of the y, this is the farthest we can simplify it.

For Q2=

4u - 6u = -2u. Since these two numbers have the same variable, this is just a simple subtraction problem. 4 - 6 = -2.

For Q3=

3a + 2b + 4a + b = 7a + 3b.

Look for the numbers with the same variable. 3a and 4a both have a's, so we add the two and get 7a. 2b and b (b is the same thing as 1b) both have b's, so we add them and would get 3b.

Therefore, the answer is 7a + 3b.

I hope this helped! Good luck with future endeavors!!

Step-by-step explanation:

attached the answers below, hope that helps...

This is how the Cluster of sampling technique is best described.

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The response to the given domain range questions is [go f oh]. (9) = 5(18^2 - 1 )

Domain and range. A function's authorised range of values is known as its domain. The x values in a function like f make up this set (x). A function's range is the collection of values that it can take as input. When we enter an x value, the function outputs this set of values.

f(x) = x^5 – 1, g(x) = 5x^2, and h(x) = 2x

[g o f o h](9)=g(f(h(9))

Let's find h(9) first

h(x)= 2x

h(9)= 2(9) =18

Now plug in 18 for h(9)

[g o f o h](9)=g(f(h(9)) = g(f(18))

now we find f(18)

f(x) = x^5 – 1, f(18)= 18^5 -1

Now we plug in 18^5 -1 for f(18)

[g o f o h](9)=g(f(h(9)) = g(18^5 -1)

Plug it in g(x)

g(x)= 5x^2

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In slope-intercept form, the equation of the line passing through the points (5.-4) and (-1,8) is y = -4x + 8 .

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.

given

the points (5.-4) and (-1,8)

slope = [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

slope intercept form = y = mx + c

To find the equation of the line that passes through the points (5, -4) and (-1, 8),

The slope and the intercept by the slope intercept form = y = mx + c .

The slope is -4 and the intercept is 8.

In slope-intercept form, the equation of the line passing through the points (5.-4) and (-1,8) is y = -4x + 8 .

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Using Heron's formula the area of the triangle is 15.78cm²

Heron's formula is a formula for calculating the area of a triangle when the lengths of all three sides are known. It is named after the Greek mathematician and engineer Heron of Alexandria (c. 10–70 AD). The formula is:

Area = √s(s-a)(s-b)(s-c)

Where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter, or half the perimeter, of the triangle, given by:

s = (a + b + c)/2

Let's define the variables as;

s = (5.1 + 7.8 + 6.2) / 2

s = 9.55cm

The area can be calculated as;

A = √s(s - a)(s - b)(s - c)

A = √9.55(9.55 - 5.1)(9.55 - 7.8)(9.55 - 6.2)

A = 15.78cm²

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Answer:

Yes

Step-by-step explanation:

The side lengths are a Pythagorean triple.

Katie is correct. Any number with 4 as a factor will also have 8 as a factor; therefore, any number with 8 as a factor will have 4 as a factor.

Katie is correct. Any number that is a multiple of 8 will also be a multiple of 4 because 8 is divisible by 4. For example, 8 is a multiple of 4 (8 = 2 x 4) and 16 is a multiple of 8 (16 = 2 x 8) and also a multiple of 4 (16 = 4 x 4). So, any number that is a multiple of 8 will also be a multiple of 4.  So any number that is a multiple of 8 will also be a multiple of 4. Note that 80 is a multiple of 8, but not 4.

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Answer:

80

Step-by-step explanation:

80+10=90

90/18 = 5

Answer:

W=80

For both equations, you can substitute W for 80 and it would work/be true.

An absolute value equation is an equation that contains an absolute value expression. An inequality is a mathematical statement that compares algebraic expressions using greater than (>), less than (<), and other inequality symbols.

The absolute number of a number a is written as  |a|

And represents the distance between a and 0 on a number line.

An absolute value equation is an equation that contains an absolute value expression. The equation IxI = a

Has two solutions x = a and x = -a because both numbers are at the distance a from 0.

To solve an absolute value equation as

x+7|=14

You begin by making it into two separate equations and then solving them separately.

x+7=14

x+7−7=14−7

x=7

or

x+7=−14

x+7−7=−14−7

x=−21

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.

The inequality   |x|<2  represents the distance between x and 0 that is less than 2 Whereas the inequality  |x|>2 represents the distance between x and 0 that is greater than 2.

You can write an absolute value inequality as a compound inequality.

$$\left | x \right |<2\: or

−2<x<2

This holds true for all absolute value inequalities.

|ax+ b| < c, where c>0

=−c < ax+ b < c

|ax+ b|> c, where c>0

=ax+ b <−corax+ b>c

You can replace > above with ≥ and < with ≤.

When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.

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An absolute value equation is an equation that contains an absolute value expression. An inequality is a mathematical statement that compares algebraic expressions using greater than (>), less than (<), and other inequality symbols.

The absolute number of a number a is written as  |a|

And represents the distance between a and 0 on a number line.

An absolute value equation is an equation that contains an absolute value expression. The equation IxI = a

Has two solutions x = a and x = -a because both numbers are at the distance a from 0.

To solve an absolute value equation as

x+7|=14

You begin by making it into two separate equations and then solving them separately.

x+7=14

x+7−7=14−7

x=7

or

x+7=−14

x+7−7=−14−7

x=−21

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.

The inequality   |x|<2  represents the distance between x and 0 that is less than 2 Whereas the inequality  |x|>2 represents the distance between x and 0 that is greater than 2.

You can write an absolute value inequality as a compound inequality.

[tex]$$\left | x \right | < 2\[/tex]: or

−2<x<2

This holds true for all absolute value inequalities.

[tex]|ax+ b| < c, where c > 0\\=−c < ax+ b < c\\|ax+ b| > c, where c > 0\\=ax+ b < −corax+ b > c[/tex]

You can replace > above with ≥ and < with ≤.

When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.

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The required probability as calculated from the data given above is found to be as 1 / 9.

Given,

The spinner is having the letters as A, B and C.

The possibility of getting any of these letters when the spinner is rolled is same.

Therefore , the sample space will be as follows ,

6 + 3 = 9

This is due to the fact a die has 6 sides.

Then the probability of getting a B will be ,  1/9

Sample space is known as the collection of all values which are used in an experiments. The total number of favorable outcomes are taken from this sample space only.

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In word variation, we can write as;

⇒ In the equation, A = C + Kx, if K is a nonzero constant and C = 0, then you have the function A = Kx, which is called a direct variation.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The equation is,

⇒ A = C + Kx

Now, We know that;

The direct variation is of the form of y = kx.

Here, The equation is,

⇒ A = C + Kx

Hence, Its words variation is written as;

In the equation, A = C + Kx,

if K is a nonzero constant and C = 0, then you have the function A = Kx, which is called a direct variation.

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It divides by three. According to the law of divisibility for three, a number is fully divisible by three if its digit sum is likewise divisible by three.

The divisibility rule is a clear and useful method for determining if an integer is divisible by a given set of divisors without actually doing division, sometimes simply looking at the integer's digits. The divisibility test allows you to rapidly determine if a given integer can be divided by a specified divisor without actually doing the division process. The quotient must be an integer and the remainder must be zero when dividing two numbers precisely.

here  

add all the numbers,

326 = 3+2+6 = 11

so it is not divisible by 3

327 = 3+ 2 + 7 = 12

so it is divisible by 3

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Short term memory is a response variable as it is dependent. Hence Option C is the answer.

A dependent variable is the response variable. It is reliant on the independent variable, which serves as the explanatory variable.

Explanations for the findings revealed by the response variables are provided by the explanatory or independent variables. Explanatory response is qualitative since it is classified based on a category.

The response variable is what the researcher often measures in research studies. The response variable in the example presented above is short-term memory, which is influenced by exercise.

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The conjugate is -7+6i. The correct option is third.

When two binomials have the same terms but different arithmetic operators in the center of these related words, they are said to be conjugate. For instance, the conjugate of p + q is p - q.

Given:

On a coordinate plane,

the y-axis is labeled imaginary and the x-axis is labeled real.

Point z is at (negative 7, negative 6).

Z(-7, -6)

So, the equation,

-7-6i

So, the conjugate of the equation is,

-7+6i

Therefore, -7+6i is the conjugate of the points.

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The value of x and y in the diagram are 26° and 9° respectively.

Two adjacent angles formed a linear pair.

The linear pair property:

The sum of the angle measure of both the angles is 180°.

Given:

Using linear pair theorem,

(5x - 17)° + (3x - 11)° = 180°.

8x - 28°= 180°

8x = 180° + 28°

8x = 208°

x = 208/8

x = 26°

The value of x is 26°.

Now,

3x - 11° = 3×26°-11°

           = 67°

Linear pair theorem,

67° + 90° + (2y+5)° = 180°

157°+2y+5° = 180°

2y + 162° = 180°

2y = 180° - 162°

2y = 18°

y = 9°

The value of y is 9°.

Therefore, the value of x is 26° and y is 9°.

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The complete question is given in the attached image.

We would require 400 square tiles, each measuring one square foot, to cover the whole surface of the square room.

If the perimeter of the room is 80 feet, we know that all four sides of the square room have the same length. To find the length of each side, we can divide the perimeter by 4: 80 feet / 4 = 20 feet.

Now that we know the length of each side of the room, we can find the area of the room by squaring that measurement: 20 feet x 20 feet = 400 square feet.

To find the number of floor tiles needed to cover the area of the room, we divide the total area of the room by the area of each tile: 400 square feet / 1 square foot/tile = 400 tiles.

So, to cover the entire area of the square room, we would need 400 square tiles of one square foot each.

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