Math 8
3) Determine the total area.
4 in
20 in

Answer:0.04

Step-by-step explanation:

a. The marginal density function for Y2 is fY2(y2) = 3y2², where 0 ≤ y2 ≤ 10.

b. For y2 ≤ y1 ≤ 10 of y2 is the conditional density f(y1|y2) is defined

(a) To find the marginal density function for Y2, we integrate the joint pdf over all possible values of Y1:

fY2(y2) = ∫fY1,Y2(y1,y2) dy1, where the integral is taken over the range where 0 ≤ y2 ≤ y1 ≤ 10, otherwise 0.

fY2(y2) = ∫₀¹⁰3y1 dy1 = 1.5y² |₀y2 = 1.5y2², where 0 ≤ y2 ≤ 10.

So the marginal density function for Y2 is:

fY2(y2) = 3y2², where 0 ≤ y2 ≤ 10.

(b) The conditional density f(y1|y2) is defined as:

f(y1|y2) = fY1,Y2(y1,y2) / fY2(y2), where fY2(y2) > 0.

So the conditional density is defined for all y1 such that 0 ≤ y2 ≤ y1 ≤ 10 and 0 ≤ y2 ≤ 10, i.e.,

y2 ≤ y1 ≤ 10.

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Rewrite the expression for y when x>5 without absolute values: y = 2x + 4

Rewrite the expression for y when -2<x<5 without absolute values: y = 2x - 6

Given the absolute values given:

If we rewrite without the absolute value for the condition, then there would be different values for y as shown above which is:

y = (x-3) + (x+2) - (x-5)

y = 2x + 4

Rewrite the expression for y when -2<x<5 without absolute values:

y = (x-3) + (x+2) - (5-x)

y = 2x - 6

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The United States has a population of about 320 million, so if homicides were proportional to Honduras' rate of homicide, we would expect about 12,800 deaths due to homicides in the United States.

This is calculated by taking the population of the United States (320 million) and multiplying it by the Honduras' homicide rate of 40 per 100,000 people.


To calculate this, we first need to find Honduras' homicide rate. The World Bank has this information, which states that the rate is 40 per 100,000 people. We then need to take the population of the United States (320 million) and multiply it by the rate.

This equals 128 million homicides per 100,000 people in the United States. This comes out to 12,800 deaths due to homicides in the United States. Round this to the nearest person, and you get 12,800.

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Answer:

The answer i got was (x - 5)2

Since

AB/DC = AC /CE - Given; and

AB || CD - Given

Where BCA = DEC = 90°

Therefore, ΔABC ~ ΔCDE - Side-Side-Similarity.

The theorem of Side-Side-Similarity (SSS) states that if in two triangles, the lengths of corresponding sides are proportional, then the triangles are similar. More specifically, if triangle ABC is similar to triangle DEF, then AB/DE = BC/EF = AC/DF.

This theorem is one of the three criteria for similarity of triangles, the other two being Angle-Angle (AA) similarity and Side-Angle-Side (SAS) similarity.

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Step-by-step explanation:

I added a photo of my solution

Answer:

3m+2L = 7

4m + L = 6

Step-by-step explanation:

Let m = cost of the muffins

Let L = cost of the lattes

3m+2L = 7

4m + L = 6

To solve

Multiply the second equation by -2 and add them together.

3m+2L = 7

-8m + -2L = -12

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

-5m  = -5

Divide by -5

-5m/-5 = -5/-5

m = 1

Then

4(1) +L = 6

L = 6-4

L =2

The solution is

muffins cost 1 dollar and lattes cost 2 dollars.

As there are 100 centavos in one Philippine Peso, there are 12,575 centavos in P 125.75.

An arrangement of things in a particular order is known as a permutation in mathematics. A permutation of a group of things is a particular technique to arrange them in a particular sequence, where each object is used exactly once. Consider the trio of letters A, B, and C as an example. This set can be permuted in six different ways: ABC, ACB,BAC, BCA, CAB, and CBA

These combinations each show a different way to arrange the letters in the set.

given

The Philippine Peso, represented by the letter "P," is the official unit of money in the Philippines.

One Philippine Peso is equal to 100 centavos.

We must multiply P 125.75 by 100 to convert it to centavos:

P = 12,575 centavos (125.75 x 100).

As there are 100 centavos in one Philippine Peso, there are 12,575 centavos in P 125.75.

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The surface area of this rectangular prism is equal to 158 ft².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

SA = 2(WH + LW + LH)

Where:

By substituting the given parameters into the formula for the surface area of a rectangular prism, we have the following;

SA = 2(8 × 3 + 5 × 8 + 5 × 3)

SA = 2(24 + 40 + 15)

SA = 2(79)

SA = 158 ft².

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Thus, the system of equation have no solution, solved by the elimination method.

To create an equation from one variable using the elimination approach, you can either add as well as subtract the equations.

To eliminate a variable, add the equations when the coefficients from one variable are in opposition, and subtract the equations when the coefficients from one variable are in equality.

Given system of equations are-

-3x - y = 10 ...eq 1

3x + y = -8  ... eq 2

Add both eq.

-3x - y + 3x + y = 10 - 8

0 = 2

As both value of x and y are getting cancelled.

But, 0 ≠ 2

Thus, the system of equation have no solution, solved by the elimination method.

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The answer to the given problem is x = 3 and y = 1.

Simultaneous equations are a set of equations with multiple variables that must be solved at the same time. In other words, they are equations that have more than one unknown value, and their solutions must satisfy all the equations in the system. These equations are used to model many real-world situations, such as business and engineering problems.

Given equation;

x + y = 4 ...................... (1)

2x - 5y = 1 ..................... (2)

Multiplying by 5 equation (1) we get,

5(x + y = 4)

5x + 5y = 20 ................. (3)

Adding equation (2) and (3) we get,

2x - 5y = 1

5x + 5y = 20

7x = 21

x = 21/7

x = 3

Putting x=3 in equation(2), we get

2x - 5y = 1

2(3) - 5y = 1

6 -5y =-5y = 1 - 6

-5y = -5

y = -5/-5

y = 1

As a result, the equation's answer is x = 3 and y = 1.

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The complete question is:

x+ y = 4 ; 2x - 5y = 1 solve by simultaneous equation

James would pay R77,410.46 in taxes on his R364,321 annual taxable income for the tax year that ends on February 28, 2022.

James's tax bracket, deductions, and credits, among other things, would all affect how much tax he pays. The various income ranges that are subject to various rates of taxation are referred to as tax brackets.

Income up to R216 200: 18% of taxable income

Income from R216 201 to R337 800: R38 916 plus 26% of taxable income above R216 200

Income from R337 801 to R467 500: R70 742 plus 31% of taxable income above R337 800

Income from R467 501 to R613 600: R110 739 plus 36% of taxable income above R467 500

Income from R613 601 to R782 200: R163 335 plus 39% of taxable income above R613 600

Income from R782 201 to R1 656 600: R229 089 plus 41% of taxable income above R782 200

Income above R1 656 601: R587 593 plus 45% of taxable income above R1 656 600

Based on James' annual taxable income of R364,321.

The first R216,200 of James' income would be taxed at 18%, which equals R38,916.

The remaining R148,121 of James' income would be taxed at 26%, which equals R38,494.46.

Therefore, James' total tax liability would be R77,410.46.

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James,67 year old, has an annual taxable income of R364321 per year, What amount of tax he pays?

Answer:

[tex] {x}^{2} + 8x + 16 = 18[/tex]

[tex] {(x + 4)}^{2} = 18[/tex]

x + 4 = +3√2, so x = -4 + 3√2

There can be 78,364,164,096 different license plates created if there are 7 numbers or letters on the plate, determined using the product rule.

We can use the product rule to determine the number of different license plates that can be created if there are 7 numbers or letters on the plate.

Assuming that each position on the license plate can be filled with any number or letter, we can use the multiplication principle to find the total number of possibilities. For each position, there are 26 letters and 10 digits to choose from (assuming the use of the English alphabet), so there are 36 choices for each position.

Therefore, the total number of different license plates that can be created is:

36 x 36 x 36 x 36 x 36 x 36 x 36 = 36^7

This simplifies to:

78,364,164,096

So there are 78,364,164,096 different license plates that can be created if there are 7 numbers or letters on the plate.

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--The given question is incomplete, the complete question is given

" which of these numbers of different license plates can be determined if there are 7 numbers or letters on the plate? using only the product rule (without the use of the sum rule or some other rule)?

The solution of the system of linear equations determines if the system has no solution, one solution, or an infinite number of solutions

2·x - 3·y = 3 and -4·x + 6·y = 6

3·x - 2·y = 3 and x + 2·y = 5

-8·x + 12·y = -12 and 2·x - 3·y = 3

y = -x + 2 and y = 3·x - 2

A system of equations is a set of two or more equations that are formed by the same variable.

Each of the equations are solved as follows to determine whether it has no solution, one solution, or an infinite number of solutions

1. 2·x - 3·y = 3 and -4·x + 6·y = 6

Multiplying the first equation by 2, we get; 4·x - 6·y = 6.

Adding the above equation to the second equation,we get;

4·x - 6·y + (-4·x + 6·y) = 6 + 6 = 12

0 = 12 (False)

Therefore, the system has no solution

2. 3·x - 2·y = 3 and x + 2·y = 5

Adding the two equations, we get;

3·x - 2·y + (x + 2·y) = 3 + 5 = 8

4·x = 8

x = 8/4 = 2

Substituting x = 2 into the second equation, we get;

x + 2·y = 5

2 + 2·y = 5

2·y = 5 - 2 = 3

y = 3/2 = 1.5

y = 1.5

Therefore, the system has one solution

3. -8·x + 12·y = -12 and 2·x - 3·y = 3

Multiplying the second equation by 4, we get; 8·x - 12·y = 12

Adding the product of the second equation and 4 to the first equation we get;

8·x - 12·y + (-8·x + 12·y) = 12 + (-12) = 0

0 = 0

Therefore, the system has infinite number of solutions

4. y = -x + 2 and y = 3·x - 2

Substituting y = -x + 2 into the second equation, we get;

-x + 2 = 3·x - 2

3·x - 2 = -x + 2

3·x + x = 2 + 2 = 4

4·x = 4

x = 4/4 = 1

x = 1

y = -x + 2

y = -1 + 2 = 1

y = 1

Therefore, the system has one solution.

Therefore, the first system has no solution, the second system has one solution, the third system has an infinite number of solutions, and the fourth system has one solution.

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The values in the table represent a linear function with the function rule y = 3x + 6, where x is the input value and y is the output value.

To determine if the values in the table represent a linear function, we can check if there is a constant rate of change between the input and output values. This means that for every increase or decrease in the input value, there is a constant increase or decrease in the output value.

Looking at the input and output values in the table, we can see that for every increase of 1 in the input value, the output value increases by 3. This constant rate of change indicates that the values in the table represent a linear function.

To find the function rule, we can use the slope-intercept form of the equation for a linear function, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, we can find the slope by dividing the change in output values by the change in input values:

slope = change in output / change in input = 3/1 = 3

Therefore, the slope of the function is 3. To find the y-intercept, we can use one of the points in the table. For example, we can use the first row, which gives an input value of 0 and an output value of 6:

y = mx + b

6 = 3(0) + b

b = 6

Therefore, the y-intercept of the function is 6. Combining the slope and y-intercept, we can write the function rule as:

y = 3x + 6

This means that for any input value x, the output value y is equal to three times x plus six.

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Applying the linear pair theorem, the measures of the angles in degrees are:

m<ABD = 112°; m<DBC = 68°

The Linear Pair Theorem, also known as the Linear Pair Postulate, is a basic postulate in geometry that describes the relationship between two adjacent angles that form a straight line.

According to the Linear Pair Theorem, if two angles are adjacent and form a straight line, then they are supplementary. In other words, their measures add up to 180 degrees.

Therefore, according to the linear pair theorem, we have:

m<ABD + m<DBC = 180°

Substitute:

7x + 196 + 9x + 176 = 180

16x + 372 = 180

16x = 180 - 372

16x = -192

x = -192/16

x = -12

m<ABD = 7x + 196 = 7(-12) + 196 = 112°

m<DBC = 9x + 176 = 9(-12) + 176 = 68°

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Answer:

65%

Step-by-step explanation:

Given data

Cost price= £4000

Selling price=  £1400

% loss= cost price-selling price/cost*100

% loss= 4000-1400/4000*100

% loss= 2600/4000*100

% loss= 0.65*100

% loss= 65%

Hence the %loss is 65%

Answer:

probability of getting a red ball= 6/11

Step-by-step explanation:

we know, to find a probability of a event

1st we have to get the total number of events that can occur,i.e

6+4=11

and

the total probability of getting a red ball is 6/11

which is the required answer..

A statement about the model that is true include the following: A. the number of customers visiting the bodega decrease by 25 for every inch of rainfall.

In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Based on the information provided above, an equation that models the situation is given by;

y = 90 + (-25)x

y = 90 - 25x

By comparison of the two equations, we have:

mx = -25x

Slope, m = -25.

In conclusion, the rate of change is -25 customers per inch of rain.

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A height of 25.6 feet above the earth is required of the diver. So , the correct choice is C )  25.6.

Assumed: A diver descends 25.6 feet below sea level.

He would be at sea level at that point, therefore the distance would be 0.

As a result, he must ascend 25.6 feet from sea level to reach 0 feet.

In order to descend to the sea level, the diver must ascend 25.6 feet.

As a result, in order to return to sea level from the diver's current depth of 25.6 feet below it, they must climb 25.6 feet. 25.6 feet is the correct answer.

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[tex]\cos( 50^o )=\cfrac{\stackrel{adjacent}{MN}}{\underset{hypotenuse}{MO}}[/tex]

keep in mind that the opposite side is the side "facing off" the angle, and the adjacent is the one "not" facing it off.

Using the volume formula:

1. 904.32m³.

2. 226.08in³.

3. 392.50cm³.

4. 4186.66in³.

5. 395.64ft³

6. 235.50cm³.

A three-dimensional solid shape's volume is the area it takes up in space. Though it is challenging to picture in any shape, it can be contrasted with others. A compass box, for example, has a bigger volume than one that has an eraser inside of it.

The area of every two-dimensional form is calculated by dividing it into equal square units. We will do something similar to calculate the volume of solid things by dividing it into equal cubical units.

In the given question,

Volume of the sphere is: 4/3πr³.

Radius, r is = 6m.

Volume = (4× 3.14 × 6³)/3

= 904.32m³.

Volume of the cylinder is: πr²h.

Radius, r = 3in.

Height, h = 8in.

Volume = 3.14 × 3² × 8

= 226.08in³.

Volume of cone = 1/3 πr²h

Radius, r = 5cm.

Height, h = 15cm.

Volume = (1 × 3.14 × 5² × 15)/3

= 392.50cm³.

Again, we have a sphere, with d = 20in.

R = d/2

= 20/2

=10in

Volume = 4/3πr³.

= (4 × 3.14 × 10³)/3

= 4186.66in³.

Again, we have a cylinder with r = 3ft and h = 14ft.

Volume =  πr²h.

= 3.14 × 3² × 14

= 395.64ft³

Lastly, we have another cone of r = 5cm and h = 9cm.

Volume = 1/3 πr²h

= (1 × 3.14 × 5² × 9)/3

= 235.50cm³.

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In 1st part expression there is a subtraction of 75% of 0.75d from orignal price and  in 2nd expression the discount of 75% of the orignal price.

In mathematics, an expression is a combination of symbols, numbers, and operators (such as +, −, ×, ÷, etc.) that represent a quantity or a mathematical operation.

Expressions can be simple or complex, and they can involve variables, constants, and functions. Expressions can be evaluated or simplified to obtain a numerical or symbolic result.

d: This represents the original price of the video game in dollars.

0.75d: This represents the price of the video game after the 75% discount has been applied. It is equivalent to subtracting 75% of the original price (0.75 times d) from the original price (d).

0.25d: This represents the amount of the original price that is discounted by 75%. It is equivalent to subtracting the sale price (d - 0.75d) from the original price (d), since the discount is 75% or 0.75 of the original price (d).

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The scale of the map is 1:2, the distance from Averton to Charlbrough is 12 kilometers, and the distance in the map is 6.25 cm.

We know that 25 kilometers are represented in the map using only 12.5 centimeters. Now, let's simplify this:

25 kilometers / 12. 5 cm = 2

This can be expressed as a scale of 1:2 in which each centimeter represents 2 kilometers.

We know the distance on the map is 6 cm, let's now convert this to kilometers:

6cm x 2 = 12 kilometers

We know the distance is 12.5, using this information let's find out the distance on the map.

12.5/ 2 =6.25 cm.

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Range because it measures the difference between the highest and lowest values in a dataset, provides a clear measure of variability for both sets of data. It is not affected by skewness or symmetry, which makes it a useful measure of variability for comparing the temperature consistency between Beach Town and Sunny Town.

What is the range?

A function's range can be used to describe one of two related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is exactly one y in Y such that f connects x to y for every x in X.

Here, we have

Given: A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks for every unit up to 14.

We have to determine which measure of variability should be used for both sets of data to determine the location with the most consistent temperature.

We concluded that Range because it measures the difference between the highest and lowest values in a dataset, provides a clear measure of variability for both sets of data. It is not affected by skewness or symmetry, which makes it a useful measure of variability for comparing the temperature consistency between Beach Town and Sunny Town.

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 Dylan  initial investment was £1200

Interest are of two types :- 1. Simple interest

                                             2.Compound interest

Here Dylan has invested on yearly terms therefore , We need to need to calculate the simple interest here

Given ,

          Principal = ?

           Interest= £72

           Time = 2 years

            rate = 3%

Formulae  for simple interest is=( Principal * (Rate/100) *Time)

Therefore

                 72 = (Principal *(3/100) *2)

                  72 = ( Principal* 0.06)

                  Principal= 72/0.06

                  Principal= £1200

Therefore the initial investment was £1200 by dylan

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Therefore, Dylan's initial investment was £1200.

Simple interest is a type of interest that is calculated on the principal amount of a loan or investment. It is a fixed percentage of the original amount borrowed or invested that is added to the principal at regular intervals, usually monthly, quarterly or annually. The interest rate remains constant throughout the loan or investment term, and the interest earned or paid is calculated solely on the initial principal amount. Simple interest is commonly used for short-term loans or investments, and the formula for calculating it is straightforward:

by the question.

we can start by using the formula for simple interest:

Simple interest = Principal x Rate x Time

Where the Principal is the initial investment, the Rate is the annual interest rate, and the Time is the number of years.

We know that the Rate is 3% per annum and the Time is 2 years, so we can write:

Simple interest = Principal x 0.03 x 2

Since we are given that the value of the investment increased by £72 at the end of the 2-year period, we can set up an equation:

Value of investment - Initial investment = Simple interest

£72 = Principal x 0.03 x 2

£72 = Principal x 0.06

Principal = £72 / 0.06

Principal = £1200

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