if x and y are independent random variables does it mean x^2 and y are also independent random variables?

Answer:

We can solve for x by using logarithms.

9^(x + 10) + 3 = 92

9^(x + 10) = 89

Take the log base 9 of both sides:

x + 10 = log9(89)

x = log9(89) - 10

To find the value of log9(89), you can use a logarithm table or calculator.

The solution for x is:

x = log9(89) - 10

The graph which represents the linear equation y = 1/2 x + 2 is the graph of a line passing through the points (-4, 0) and (0, 2).

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

The slope intercept form of a line is,

y = mx + c,

m : slope and c : y intercept

y intercept is the y coordinate of a point when x coordinate equals 0.

Given linear equation is y = 1/2 x + 2.

m = 1/2 and c = 2

Find the slope and y intercept of each of the line in the options given.

In the first option, we have the point (0, -2).

y intercept of this line = -2, which is not the required y intercept.

In the second option, points given are (-4, 0) and (0, 2).

Since we have the point (0, 2), y intercept = 2

m = (2 - 0) / (0 - -4) = 2 / 4 = 1/2

So the line in the second option is the required line.

Hence the graph of the line represented in the second option is the required line.

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The expression is obtained on subtracting 4x + 6 from 7 + 2x is -2x + 1

Given the two expressions in the question;

( 4x + 6 ) and ( 7 + 2x )

To subtract  4x + 6 from 7 + 2x simply means ( 7 + 2x ) - ( 4x + 6 ).

Now, simplify

( 7 + 2x ) - ( 4x + 6 )

Distribute the negative sign to all the terms in the second expression.

( 7 + 2x ) -4x - 6

Now collect and add like terms

2x - 4x - 6 + 7

Add 2x and -4x

-2x - 6 + 7

Add -6 and 7

-2x + 1

Therefore, the resulting expression is -2x + 1.

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Answer: 30 ft

Let's assume the original dimension of the carpet was LxW. Now let's have Lin cut a 1 foot wide strip from the length. That gives her a strip that's L feet long. She then cuts a strip from the other side, giving her another strip that L feet long. She then cuts a strip from the width, giving her a 3rd strip that's (W-2) feet long. And finally, she cuts a 4th strip that's also W-2 feet long. So the total length of all those strips is L + L + W - 2 + W - 2 = 2L + 2W - 4 feet long. And since all the strips are 1 foot wide, they cover 2L + 2W - 4 square feet. So: 2L + 2W - 4 = 26 2L + 2W = 30 Now the original perimeter of the carpet is 2L + 2W, therefore the original perimeter is 30 feet.

By applying linear equation concept, it can be concluded that the number of stamps in the 25th month is 990 stamps

Linear equation is equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.

y = mx + C where

m = Δy / Δx = slope of the line

C = constant

We have the following data:

Month    Number of stamps

   1                      30

   2                     70

   3                     110

   4                     150

   5                     190

As we look at the attached graph, this data is depicted as a linear graph. Thus we want to find the linear equation.

First, we calculate the m:

m = Δy / Δx

   = (70 - 30) / (2 - 1)

   = 40 / 1

   = 40

To find C, we pick one point, let say point (1,30) and input it into the equation:

 y = mx + C

30 = 40*1 + C

30 = 40 + C

 C = -10

Now we have the linear equation:

y = mx + C

y = 40x - 10

We want to know the number of stamps in the 25th month, so we input this value into the equation:

y = 40x - 10

   = 40*25 - 10

   = 1000 - 10

   = 990

Thus, the number of stamps in the 25th month is 990 stamps.

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To find C the Pythagorean formula is used which would be = 7.6

The formula for the Pythagorean theorem is given as follows:

c² = a²+b²

where;

a = 7

b = 3

C = ?

c² = 7²+3²

c² = 49+ 9

c² = 58

C= √ 58

C = 7.6

Therefore, when the Pythagorean formula is being used, the value of the missing side of the triangle = 7.6.

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The hypotenuse of the right triangle is:

C = 7.6

On the image we can see a right triangle where C is the hypotenuse of said triangle.

Remember the Pithagorean's theorem, it says that if A and B are the two legs of the right triangle, then C can be written as:

C = √(A² + B²)

Here we can see that:

A = 3

B = 7

Replacing that we will get:

C = √(3² + 7²) =7.6

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A frequency table is a simple tabular representation of the number of times a particular value or range of values appears in a data set.

It lists the values in one column and the corresponding frequencies in another column. For example, if we have data on the heights of a group of people, a frequency table could list the heights (in cm) in one column and the number of people with that height in the other column.

A frequency distribution is a graphical representation of the same information as a frequency table. It shows the number of occurrences of values in a data set by grouping the values into classes or intervals, and then plotting the frequency of each class or interval. For example, a histogram is a type of frequency distribution where the data is divided into equal-width intervals and the height of each bar represents the frequency of the data that falls within that interval.

A frequency table can be used for both qualitative and quantitative data, whereas a frequency distribution can only be used for quantitative data. This is because the classes or intervals used in a frequency distribution require a numerical representation of the data, which is not possible for qualitative data.

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Answer:400

Step-by-step explanation:

The lateral Surface Area of ​​a Cylinder  is is 345  cm²  

What are solids ?

A three-dimensional object that is closed (which may, according to some terminology conventions, be self-intersecting). A solid is any constrained area of space that is bounded by surfaces, according to Kern and Bland (1948, p. 18). The sphere, cube, cone, and cylinder, as well as the polyhedra more broadly, are some of the most basic solids.

lateral Surface Area of ​​a Cylinder  is :

L= 2 × π × r × h

where, r = base radius,

and h = height of the cylinder

L= 2 × 3.14 × 4.9 × 11.2

=> L=  344.646  cm²

Nearest whole number: 345  cm²

The lateral Surface Area of ​​a Cylinder  is is 345  cm²  

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Alfred sold 98 + the minimum required tickets, so the total number of tickets he sold is 98 + the minimum required.

1. Alfred reported that he raised 98 dollars more than the minimum required.

2. To get the total number of tickets he sold, we will need to add the 98 dollars more than the minimum required to the minimum required amount.

3. Therefore, the total number of tickets Alfred sold is 98 + the minimum required.

Alfred sold 98 + the minimum required tickets, so the total number of tickets he sold is 98 + the minimum required.

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Answer:

[tex] - \frac{8}{7} - ( - \frac{6}{5}) \\ \\ \longrightarrow \: - \frac{8}{7} \: \: + \: \: \frac{6}{5} \\ \\ taking \: LCM \\ \\ \longrightarrow \: \frac{ - 40 + 42}{35} \\ \\ \longrightarrow \: \boxed{ \frac{2}{35} }[/tex]

hope helpful! :-;

The solution is (-5,0), the interval in which the function is increasing.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

In case when you tracking the finger across the line, at which there is an increase or decrease in y axis so this is we called intervals. Moreover, the interval notation is also necessary as it depicts the beginning and ending points. In this, the first number denotes the minimum number while the second number denotes the maximum number

For Decreasing:

(-8,-5)

(4,8)

For Increasing:

(-5,0)

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For the above system of equations 2x+4y+3z=11, 2y+5z=-9, x=11+6z,The value of y=-8, z=7/5, x=97/5.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol.

Here,

x-6z=11

2x+4y+3z=11

2y+5z=-9

x=11+6z

substitute and calculate,

y=-8

z=7/5

x=97/5

The value of y=-8, z=7/5, x=97/5 for the given system of equation: 2x+4y+3z=11, 2y+5z=-9, x=11+6z.

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The gallons of water used column should have four entries: 0, 20, 40, andTo plot the point, you need to plot the values from the table on a graph.

Time (minutes): 0, 2, 4, 6

Gallons of Water Used: 0, 20, 40, 60

Plot: (0, 0), (2, 20), (4, 40), (6, 60)

To complete the table, you need to fill in the time (minutes) and gallons of water used columns.

The time column should have four entries: 0, 2, 4, and 6.

The gallons of water used column should have four entries: 0, 20, 40, andTo plot the point, you need to plot the values from the table on a graph.

The point (0, 0) represents 0 minutes and 0 gallons of water used.

The point (2, 20) represents 2 minutes and 20 gallons of water used.

The point (4, 40) represents 4 minutes and 40 gallons of water used.

The point (6, 60) represents 6 minutes and 60 gallons of water used.

The complete question is :

A shower used 60 gallons of water in 6 minutes. Complete the table and plot the point.

Time (minutes): 0, 2, 4, 6

Gallons of Water Used: 0, 20, 40, 60

Plot: (0, 0), (2, 20), (4, 40), (6, 60)

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The denominator of the formula for the variance of a sample is given as follows:

N - 1.

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

The terms are named as follows:

The formula for the variance of a sample is given as follows:

[tex]s^2 = \frac{sum (X - \overbar{X})^2}{N - 1}[/tex]

Hence the denominator is the bottom term, which is of N - 1.

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The required consumer surplus for the given question is $1000.

The consumer surplus can be calculated by finding the difference between the maximum price the consumers are willing to pay and the actual market price.

Given the demand equation QD = 800 - 100P and the supply equation QS = -100 + 200P, we can find the market equilibrium price and quantity by setting QD = QS and solving for P

800 - 100P = -100 + 200P

900 = 300P

P = 3

So, the market equilibrium price is P = 3, and the market equilibrium quantity is Q = QD = QS = 800 - 100P = 800 - 100 * 3 = 500.

To find the consumer surplus, we need to find the area between the demand curve and the market price. The demand curve can be represented by a linear equation: QD = 800 - 100P. The maximum price the consumers are willing to pay for each quantity can be found by substituting the quantity into the demand equation:

Q = 500: 800 - 100P = 500 => P = 5

So, the maximum price the consumers are willing to pay for Q = 500 is P = 5. The consumer surplus can be found by calculating the area of the triangle between the market price P = 3 and the maximum price P = 5:

Consumer Surplus = 1/2 * (5 - 3) * 500 = 1000

So, the consumer surplus is $1000.

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Answer: 1. No, because figure 1 is 5 squares and figure 2 is 6 squares

Step-by-step explanation:

The perimeter of the rectangle ABCD is 22 cm.

What is the perimeter of a rectangle?

In order to find the perimeter or distance around the rectangle, we need to add up all four side lengths. This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length.

Perimeter = (length+width)×2 is the formula for the perimeter.

The perimeter of a rectangle is the sum of the lengths of all four sides.

If the sides of a rectangle have lengths of 6 cm and 5 cm, then the perimeter can be calculated as follows:

6 cm + 6 cm + 5 cm + 5 cm = 22 cm

The perimeter of a rectangle with sides 6 cm and 5 cm is 22 cm (2 * 6 cm + 2 * 5 cm = 22 cm).

Hence, the perimeter of the rectangle ABCD is 22 cm.

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The discrete probability distribution of the number of successes in a series of n independent experiments is called the binomial distribution with parameters n and p in probability theory and statistics.

What is the binomial distribution?

The binomial distribution formula aids in determining the likelihood that "x" successes will occur in "n" separate trials of a binomial experiment. Recall that there are two possible outcomes for the statistics probability distribution known as the binomial distribution. The binomial distribution in probability theory has two parameters, n and p. When the probability distribution satisfies the following conditions, it becomes a binomial probability distribution. Each experiment may only yield two results, or results that can be reduced to two results. These results could result in success or failure. There must be a specific number of trails. Each trial's results must be distinct from one another.

Additionally, each trial's likelihood success rate must remain constant.

Using binomial probability formula,

k P(X = k)

0 0.0001

1 0.0020

2 0.0236

3 0.1355

4 0.3899

5 0.4489

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The website is advertising a 46% discount on the jacket, meaning that Farah will pay 46% less than the original price if she decides to buy it now.

A discount is a reduction in the original price of an item, allowing the customer to purchase it for less than the original price.

To calculate the discount mathematically, we can use the following formula:

Discounted price = Original price * (1 - discount percentage)

Let's assume the original price of the jacket is P dollars.

The discount percentage is 46%, which can be written as a decimal 0.46. To find the discounted price, we need to multiply the original price by (1 - discount percentage), which is (1 - 0.46) = 0.54.

So, the discounted price after the 46% saving will be P * 0.54 dollars.

In other words, Farah will pay 0.54 times the original price, P, to buy the jacket with the advertised 46% saving.

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She will travel a distance of 62.8 feet × 5 revolutions = 314 feet.

Calculate the circle of the carousel (the distance around the outside) and multiply it by the number of revolutions to determine how far Sierra will move after five rotations.

The following equation can be used to determine the carousel's circumference:

Circumference = 2πr

Where "radius" refers to the carousel's radius and "" is an irrational integer roughly equivalent to 3.14. (in this case, 10 feet).

Substitute the values in the above equation, we get

Circumference = 2 × 3.14 × 10 feet

Circumference = 62.8 feet

Since Sierra will make five revolutions, she will travel a distance

= 62.8 feet × 5 revolutions = 314 feet.

Remember that this is only an estimate because the precise distance may have varied slightly depending on the carousel's speed and Sierra's position on it, among other things.

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The value of x is 6 using logarithmic properties.

The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.

The Scottish mathematician John Napier reported his findings on logarithms in 1614. He was there to aid with the multiplication of quantities known as sines at the time.

Given,

Log2+ log3= logx

To find= We need to find the value of x

The value of log2=  0.301

The value of log 3= 0.477

Now, putting the value in the given expression, we get:

0.301+ 0.477= logx

logx= 0.778

Now, taking the antilog os=f x:

x= antilog(0.778)

x= 5.99=6

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The equation  models the problem is 54

The given parameters that will help us to determine the number are

During the first weekend of December, 43 pine trees were sold. The farm sold 97 trees in all that weekend.

There are two kinds of trees

Tir and Pine.  On the farm and in the weekend as 97 trees were sold with 43 pine tress.

Let f represent fir trees

This implies that f+43 = 97

⇒f= 97-43

f=54 tress

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Answer:

X=. 1. X=. 2

Step-by-step explanation:

The first story (movie theater) has the equation 6(x+3)= 24. The equation for the juice story is 3(x+6)=24 . The x in the move theater story is the cost of each ticket. The x in the juice story is the amount of juice poured to each friend originally (before the extra 6 ounces). The solution to the movie theater story is 6((1)+3)=24. So x is one is the first story.In the juice story, 3((2)+6)= 24. So x is two. The solution tells me that in the movie theater story that each ticket cost 1 dollar. In the second story, it tells me that 2 ounces of juice where poured to each freind originally. So each freind got a total of 8 ounces of juice.

Step-by-step explanation:

I see only 2 stories and equations.

a.

6(x + 3) = 24

is for the first story (6 show tickets and snacks).

3(x + 6) = 24

is for the second story (juice for 3 friends).

b.

in the first story it is the price of one ticket to the show.

in the second story it is the original amount of juice each friend gets before adding 6 oz.

c. and d.

6(x + 3) = 24

6x + 18 = 24

6x = 6

x = 1

each ticket to the show was $1.

3(x + 6) = 24

3x + 18 = 24

3x = 6

x = 2

each of the 3 friends got first 2 oz of juice, before they each got additional 6 oz. so, ultimately, each friend got 8 oz.

How to solve you question!

First, combine multiplied terms into a single fraction.

Like this! (click first file)

sorryyy, i had to do it virtually bc i couldnt find a pencil -.-

then, multiply it by 1.

Like dis! (click second file)

Then, find the common denominator. :>

like dis!!

(obvi, click the third file)

Then, your solution will be dis. (click fourth file.)

Now that we know our solution for the first one, lets do the second one now.

now, if you have the same answers for both, that means, yes, they are equivalent. If no, they are not. If this helped you, please answer my one question of my profile. Thanks!!

The total amount when $9500 is invested at 10% simple interest for 5 years is $14, 250

It is important to note that the formula for simple interest is expressed mathematically with the equation;

I = PRT/100

The parameters are given;

From the information given, we have the values of the principal amount, time and the interest rate

Substitute the values, we get;

Simple interest, I = $9500 × 10×5/100

Multiply the values

Simple interest, I = $475, 000/100

Divide the values

Simple interest, I = $4, 750

Thus, the total amount is $14, 250

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The measure of ∠K is 72°.

To find the measure of ∠K in ΔJKL, we can use the Law of Cosines. The formula is:

cos C = (a^2 + b^2 - c^2) / 2ab where C is the angle opposite the side of length c.

In this case,

Plugging in the values, we get:

cos C = (720^2 + 640^2 - 520^2) / 2 * 720 * 640

cos C = 0.4756

Finally, to find the measure of ∠K, we use the inverse cosine function:

∠K = cos^-1 (0.4756)

∠K = 72.22°

Rounding to the nearest degree, ∠K = 72°.

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In ΔJKL, j = 520 inches, k = 730 inches, and l=640 inches. Find the measure of ∠K to the nearest degree.

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The height of the arch at a distance of 7.5 m from the center is 7m

It's important to keep in mind that a parabola has the usual form of y = a(x - h)2 + k, where (h, k) denotes the vertex and a determines the shape and vertical orientation. x and y are (100, 0) in. You are then provided with the parabola's equation.

What height of the arch, as measured from a point on the water 40 meters from the center of the arch, would sustain a bridge over a river?

The arch is 200 meters wide at water level and 80 meters tall at its tallest point

The peak of the arch might serve as the vertex and be located at position y0 on the y-axis if we wish to plot this on a graph or represent it in an equation

The equation of the parabolic arch is

x² = - 4ay

Lets take x and y for first case as (14, 30)

⇒ 14² = - 4a(30)

⇒ a = −49/30

Now we have a so lets put the formula for another variable to find height

Here, y = 7.5

​x² = - 4ay

⇒ ​x² - 4(-49/30)(7.5)

x = 7

Thus, The height of the arch at a distance of 7.5 m from the center is 7m.

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