Determine whether each expression can be used to find the length of side RS.

To find the inverse do these steps

1- Put f(x) = y

2- Switch x and y

3- solve to find the new y

Let us do that

Switch x and y

Now square the two sides to cancel the root

Multiply both sides by 3 to cancel the denominator

Subtract 4 from both sides

The rule is the answer D

Using the binomial distribution, the measures are given as follows:

a) Expected value: 28.

b) Variance of 16.8 and standard deviation of 4.099.

The formula for the probability of x successes is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

Hence, in the context of this problem, the values of these parameters are given as follows:

p = 0.4, n = 70.

The expected value of the distribution is calculated as follows:

E(X) = np.

Hence:

E(X) = 70 x 0.4 = 28.

The variance of the distribution is calculated as follows:

V(X) = np(1 - p) = 70 x 0.4 x 0.6 = 16.8.

The standard deviation of the distribution is calculated as follows:

sqrt(V(X)) = sqrt(16.8) = 4.099.

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We are given a triangle and three possible transformations performed on it. The first transformation shows that the triangle has no change in orientation, therefore, this transformation is a translation only.

For image 2 we notice that the orientation of the triangle changes. If we draw a horizontal line in the middle of the shaded triangle and image 2 we notice that these two images are related by a reflection, also after this reflection the image was translated therefore, for image two we have reflection across a horizontal line followed by a translation.

For image 3 we can draw a vertical line in the middle of the shaded triangle and image 3 and we do a reflection across this vertical line since there is a change in the orientation of the figure.

If a figure has a vertex, (x, y) and it is rotated 180 degrees counterclockwise, the corresponding vertex of the new image would have a coordinate of (- x, - y)

Looking at the given figure, we would compare the corresponding coordinates of a given vertex. Looking at vertex A,

For the original figure, the coordinate is (1, 3)

For the ratated figure, the coordinate of A' is (- 1, - 3)

This corresponds to what was we stated earlier

Thus, it was rotated 180 degrees in the counterclockwise direction

From the graph, we can see that the town that had most sunny days was Shiny Twon.

So, between this town and Sun City, we have Bright Viallge, that had a number of sunny days between Sun City and Shiny Town.

So the answer is Bright Village.

The amount of interest paid is $21000

What is interest?

In finance and economics, interest is the payment of an amount over repayment of the principle sum (that is, the amount borrowed) by a borrower or deposit-taking financial institution to a lender or depositor at a certain rate by a borrower or deposit-taking financial institution. It differs from a charge that the borrower may pay to the lender or a third party. Interest is also distinct from a dividend, which is given by a firm to its shareholders (owners) from its profit or reserve, but not at a fixed rate, but rather on a pro rata basis as a portion of the reward achieved by risk-taking entrepreneurs when revenue exceeds total expenditures.

Total amount paid = $11000x3 = $33000

Interest paid = $(33000-12000) = $21000

Hence, the amount of interest paid is $21000

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Given:

The Radius of the circle: 2.5 inch

To find:

The area of the circle

Step-by-step solution:

We know that:

The Area of the circle = π(r)²

The Area of the circle = π(2.5)²

The Area of the circle = 3.14 × (2.5)²

The Area of the circle =

Answer:

Step-by-step explanation:

The number is 2.

222x4=888

Hence, the number am I is [tex]888[/tex].

What is the even number?

A number that is divisible by [tex]2[/tex] and generates a remainder of [tex]0[/tex] is called an even number.

Here given that,

I am an even number. I have three digits and they are all the same.

If you multiply me by [tex]4[/tex], all of the digits in the product are [tex]8[/tex].

The number is [tex]2[/tex] sp ot would be

[tex]222[/tex]x[tex]4=888[/tex]

Hence, the number am I is [tex]888[/tex].

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SOLUTION

Given the question in the question tab, the following are the solution steps to answer the question.

STEP 1: Define the variation that occurs in the Question.

Inverse Variation: Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.

STEP 2: Interpret the statements in the question tab

STEP 3: Get the constant of variation

STEP 4: Use the given values to get the equation relating x and y

Hence, the equation relating x and y is:

STEP 5: Find y when x=-1

Hence, the value of y when x=-1 is 3/2

110,169 is larger than 110,72​

This is false as the first decimal of 110.169 is 1 and the first decimal of 100,72 is 7.

110,169 is larger than 110,72​

This is false as the first decimal of 110.169 is 1 and the first decimal of 100,72 is 7.

Answer

Domain is all real numbers except x ≠ 0, -4, and 4

Vertical asymptote at x = 0, -4, and 4

Explanation

Given function:

Note: The domain of a function is a set of input or argument values for which the function is real and defined.

For the function to be real; the denominator must not be equal zero, i.e.

Hence, the domain is all real numbers except x ≠ 0, -4, and 4.

Note: A vertical asymptote with a rational function occurs when there is division by zero.

Hence, the vertical asymptote at x = 0, -4, and 4

We will have the following:

Now, we will solve for the following:

This value in degrees is:

So, the solution is located in the interval:

1) When we need to round up or down to the nearest tenth, it's necessary to consider the hundredth's place.

2) Note this number:

We can see that 13.496 is greater than 13.45 so it is closer to 14 than 13, then we can round it off to the nearest greater number than 4.

3) Thus, we can round it off to:

We have to identify the translation.

We can see that the green triangle represents the transformation of triangle ABC after a dilation with a scale factor of 1/2 and a reflection across the x-axis.

We can then find the translation in each axis from the image as:

Triangle is DEF is translated 3 units to the left (and none in the vertical axis).

We can express this translation as this rule:

Answer: (x+3, y+0)

Answer: 75

Step-by-step explanation:

So first, we need to divide 125 by 5

125÷5=25

Next we need to multiply 3 by 25.

25×3=75

The printer can print 75 pages in 125 seconds.

Assume the height of the box is x.

5 reams of paper have 5 x 500 = 2500 sheets of paper.

This means that each sheet of paper has a thickness of x/2500.

Two sheets of paper have a thickness of 2 times x/2500.

Simplifying the fraction:

Two sheets of paper have a thickness of 1/1250th of the height of the box.

Assume the height is x = 20 cm, then two sheets are 20/1250 = 0.016 cm thick.

The domain of an ordered pair are its first elements and its range are all the second elements of the ordered pair.

So, the domain ={0,2,4,9}

Range={1,4,7,1}

The value of x is 10.04 using log properties.

The power to which a number must be increased in order to obtain another number is known as a logarithm. The exponential function is thought of as the inverse of the logarithmic function because of their close relationship. The logarithmic function logₐN = x is created from the exponential function [tex]a^{x}[/tex] = N. For instance, since ten raised to the power of two equals 100, the base ten logarithms of 100 is 2: log 100 = 2.

logₐ xy = logₐ x + logₐ y (product property)

logₐ x/y = logₐ x - logₐ y (quotient property)

logₐ [tex]x^{y}[/tex] = ylogₐ x (power property)

log2x = 3

2x = e³

x = e³/2

= 10.04

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For variables to be related proportionally, the relationship must have a constant of proportionality. In our case we will represent the constant of proportionality as k. Therefore,

Now lets find y when x = 18

w=2

All real numbers are solutions

1) In this question, let's solve each equation, and then we can check whether there are solutions, which one would be.

2) Let's begin with the first one, top to bottom

Note that we distributed the factors outside the parenthesis over the terms inside.

So for the first one, we can check w=2

3) Moving on to the 2nd equation, we can state:

So, there are infinite solutions for this equation, or All real numbers are solutions

The given expression is

To factorize this, we find the square root of each term.

Then, we use the difference of perfect square which states

So, we have

-3(1+6r) = 14 -r

-3-18r = 14 - r

-3-14 = -r +18r

-17 = 17r

17r/17 = -17/17

r = -1

Answer:

The slope of (-3, -2) and (5, -8) is -3/4

The slope of (6, 10) and (-2, 10 ) is 0

Step-by-step explanation:

[tex]\frac{-8 - (-2)}{5 - (-3)} = \frac{-6}{8} = -\frac{3}{4}[/tex]

and

[tex]\frac{10 - 10}{-2 - 6} = \frac{0}{-8} = 0[/tex]

Since both inequalities include the less than symbol, <, the shaded region must be below the two lines.

The intersection (common) of the shaded regions, which are both below the two lines, is region D.

We have to use the conditional probability formula:

Where P(A|B) is the probability that A occurs given that B occurs, P(B) is the probability that B occurs, and P(A∩B) is the probability that both events A and B occur.

In this case, since we are asked for the probability that events A and B both occur, we need to solve the equation for P(A∩B):

And the information we have about the problem is:

We substitute this into the formula for P(A∩B):

Solving the multiplication of fractions:

And finally, we simplify the fraction by dividing both numbers in the fraction by 3:

Answer: 2/21

The amount of freight transported by rail was 580 billion ton-miles in 1960.

The amount increased at a rate of 2.32% per year.

a. The growth in freight transport with respect to the passing years can be expressed as exponential growth. The general form of this equation is

Where

y represents the final number after "x" periods of time

a represents the initial number at x=0

r represents the growth rate, expressed as a decimal value

x represents the number of time intervals that have passed

For this example, the initial amount is a=580 billion

The growth rate is r=2.32/100=0.0232

You can determine the equation as follows:

b. This function is of exponential increase, its domain is all real numbers and its range is all positive real numbers, you can symbolize it as y > 0, it's increasing, and it has a horizontal asymptote as x approaches -∞

To graph it, you have to determine at least two points of the graph, I will determine 3

For x=-100

For x=0

For x=10

The points are

(-100,58.53)

(0,580)

(10,729.51)

Plot the points and then draw an increasing line from -∞ to +∞

c. To determine the time when the freight transported will exceed 1000 billion tom-miles, you can use the graph, just determine the value of x, for which y=1000

This value is approximate x=23.57

This means that counting from 1960 will take 23 and a half years to reach over a trillion ton-miles transported.

Add the number of years to the initial year to determine the date:

By 1983 the number of ton-miles transported will exceed the trillion.

For the intersection operation we have to look what elements both sets have in common, in this case both E and L has the number 8. Then the second answer is:

Now, the union operation adds the all elements into a single set without repetition, in this case the first answer is:

We are asked to find which of the measurements form a right triangle.

A right triangle is a triangle that has an angle of 90°, and also we can use the Pythagorean theorem in them.

The Pythagorean theorem tells us that the sum of the two legs of the triangle squared is equal to the hypotenuse squared:

Where a and b are the legs of the triangle and c is the Hypotenuse. Also, in the right triangle, the hypotenuse is the longest side of the triangle.

We will use the Pythagorean theorem formula on all of the options using the first two given measures as a and b, and check that we the third measure as the value of c.

Option A. 7in, 24in, and 25 in.

We define:

And apply the Pythagorean theorem:

And we solve for c. If the result for x is 25, the triangle will be a right triangle, if not, this will not be an answer.

-Solving for c:

Taking the square root of both sides we find c:

Since we get the third measure as the value of c option A is a right triangle.

Option B. 18ft, 23ft, and 29 ft.

we do the same as did with option A. First, define a and b:

Apply the Pythagorean theorem:

And solve for c:

We get 29.2 instead of just 29, thus option B is NOT a right triangle.

Option C. 10in, 24in, and 26 in.

Define a and b:

Apply the Pythagorean theorem:

Solve for c:

We get 26 which is the third measure given, thus, option C is a right triangle.

Option D. 10yd, 15yd, and 20yd.

Define a and b:

Apply the Pythagorean theorem:

We don't get 20yd as the value of c, thus, option D is NOT a right triangle.

Option E. 15mm, 18mm, and 24 mm

Define a and b:

Apply the Pythagorean theorem

We don't get 24 as the value of c, thus, option E is Not a right triangle.

Answer:

Option A and Option C are right triangles.

The ways to select the winning numbers is 286

From the question, we have

The winning numbers could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 13 and r = 3

Substitute the known values in the above equation

Total = ¹³C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 13!/10!3!

Evaluate

Total = 286

Hence, the number of ways is 286

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Answer: 9.5112

Step-by-step explanation:

There are 0.2642 gallons in a liter. So, in 36 liters, there are [tex]36(0.2642)=9.5112 \text{ gal }[/tex]