Point R is the center of both circles seen below. What is the area of the shaded regions?

36 pi
20 pi
18 pi
16 pi
4 pi

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Fred should apply to at least 22 long-shot universities in order to have a greater than 90% chance of getting into at least one of them.

Let p be the probability that Fred is NOT admitted to a particular university.

Since he has a 10% chance of being admitted, we have,

⇒ p = 1 - 0.1

       = 0.9.

Now,

Consider the probability that Fred is NOT admitted to any of the n universities he applies to.

Since the events are independent, this is simply the product of the probabilities that he is not admitted to each one,

⇒  P(F1' and F2' and ... and Fn') = P(F1') P(F2') ... P(Fn')

Using the multiplication rule of probability, we can simplify this to,

⇒ P(F1' and F2' and ... and Fn') = \(0.9^n\)

Then, we want to find the probability that Fred is admitted to at least one university, which is the complement of the probability that he is NOT admitted to any university,

⇒ P(at least one admission) = 1 - P(F1' and F2' and ... and Fn')

                                               = 1 -  \(0.9^n\)

We want this probability to be greater than 0.9,

so we set up the inequality,

⇒ 1 -  \(0.9^n\) > 0.9

Solving for n, we get,

⇒ n > log(0.1) / log(0.9) ≈ 22

⇒ n > 22

So, To have a better than 90% chance of getting into at least one of the remote universities, Fred needs apply to at least 22 of them.

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The value of x would be -1 and the point D lies in the second quadrant and has coordinates (-1, 5).

The distance between two points is defined as the length of the line segment between two places represents their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.

The formula of distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².

We have been given as C is the point (1, -2)

The point D lies in the second quadrant and has coordinates (x, 5)

The Length of CD is the square root of 53 units.

Length of CD = √ (x – 1)² + (5 – (-2)) ²

√(53) = √ (x – 1)² + (5 – (-2))²

53 =  (x – 1)² + (5 + 2)²

53 = x² - 2x + 1 + 49

x² - 2x -3 = 0

x = 3, -1

Since D lies in the second quadrant, so x-coordinate will be negative.

Therefore, the value of x would be -1.

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______________________________

 - This is an optional step. I prefer the numbers to be on the left hand side, but it's not necessary.

Equation at the end of Step 1:

 - We combine like terms because there is 2 x's, and we need 1 x.

Equation at the end of Step 2:

 - When solving problems like this, to get x alone you have to do the opposite of what you see.

 - In this case, we have a positive 9. So to get rid of 9 we do the opposite: -9 on each side.

Equation at the end of Step 3:

 - When solving problems like this, to get x alone you have to do the opposite of what you see.

 - In this case, we have 12 being multiplied by x. So to get rid of the 12 we do the opposite: Divide by 12 on each side.

______________________________

Answer: x = 16

Step-by-step explanation:

Supplementary means when the two angles are added together they equal 180 degrees.

(6x+8) + (4x+12) = 180

10x + 20 = 180

10x = 160

X = 16

The present value of a cash inflow of 1250 four years from now, given a required rate of return of 8%, is 918.79, rounded to 2 decimal places. Therefore, option (c) is the correct answer.

To find the present value of a future cash inflow, we need to discount the future value by a factor that takes into account the time value of money, or the opportunity cost of waiting for the money.

This factor is determined by the required rate of return, which is the minimum rate of return that an investor expects to earn on an investment with a similar level of risk.

In this case, we have a cash inflow of 1250 that will be received four years from now, and a required rate of return of 8%. To find the present value, we can use the formula for the present value of a single cash flow:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the required rate of return, and n is the number of years.

Plugging in the values, we get:

PV = 1250 / (1 + 0.08)^4

PV = 918.79

Therefore option (c) is the correct answer.

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There are 26^7 * 21 number of ways to create an 8-letter word using the 26-letter alphabet that begins or ends with a vowel, where 26 is the number of letters in the alphabet, and 21 is the number of consonants.

To find the number of 8-letter words that either begin or end with a vowel, we need to consider two cases: words that begin with a vowel and words that end with a vowel.

For words that begin with a vowel, we have one vowel as the first letter and any of the 26 letters of the alphabet for the remaining 7 letters. Hence, there are 26^7 ways to create an 8-letter word that begins with a vowel.

For words that end with a vowel, we have 21 consonants for the first letter and any of the 26 letters of the alphabet for the remaining 7 letters, followed by one of the five vowels. Hence, there are 21 * 26^7 * 5 ways to create an 8-letter word that ends with a vowel.

Therefore, the total number of 8-letter words that either begin or end with a vowel is the sum of the two cases: 26^7 + 21 * 26^7 * 5, which simplifies to 26^7 * 21.

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Answer:

4 miles, 0.375 inches.

Step-by-step explanation:

1:80

2:350

If the scale is 1:80, that means it is already in the simplest form, so all that is needed is for you to do 350/80 to get 4.375.   4 miles, 0.375 inches.

The best value to use as x0 when determining the value of f(5.5) by the method of linear approximation The method of linear approximation is based on the fact that for small changes in x, the change in f(x) is approximately proportional to the change in x, and this relationship can be expressed using the derivative of f(x) at x0.

The power rule tells us that the derivative of 2x^2 is 4x, and the chain rule tells us that the derivative of √(8) is 1/(2√(8)). So, the derivative of f(x) is:
f'(x) = 4x - 1/(2√(8))


Based on these calculations, the best value to use as x0 is 5.495, since f'(5.495) gives us the closest estimate to f(5.5). Therefore, we can use the equation of the tangent line to f(x) at x=5.495 to estimate f(5.5):
f(x) ≈ f(5.495) + f'(5.495)(x - 5.495)
Plugging in the values we know, we get:
f(5.5) ≈ f(5.495) + f'(5.495)(5.5 - 5.495)
f(5.5) ≈ (2(5.495)^2 - 8√(5.495)) + (4(5.495) - 1/(2√(8)))(0.005)
f(5.5) ≈ 5.506

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Answer:

C. From a starting point of 5 meters below sea level, the whale is descending 9 meters per second.

Step-by-step explanation:

Which statement best describes the depth of the whale, given this equation?

A. From a starting point of 9 meters below sea level, the whale is descending 5 meters per second.

B. From a starting point of 9 meters below sea level, the whale is ascending 5 meters per second.

C. From a starting point of 5 meters below sea level, the whale is descending 9 meters per second.

D. From a starting point of 5 meters below sea level, the whale is ascending 9 meters per second.

Solution:

A linear equation is an equation in the form y = mx + b, where m is the rate of change (slope) and b is the initial value of y when x = 0, y is a dependent variable and x is an independent variable.

Given that: y = -9x - 5

Comparing with the equation of a straight line, m = -9 and b = -5

Since m = -9, The negative sign means descending, therefore the whale is descending at 9 meters per second.

b = -5, the negative sign means below sea level, hence the starting point of the whale is 5 meters below sea level,

Answer:

1.58

Step-by-step explanation:

Answer:

\( { \tt{8 \sqrt{2} + 2 \sqrt{8} }}\)

separate the biggest root ( √8 ):

\({ \tt{ = 8 \sqrt{2} + 2 \sqrt{4 \times 2} }} \\ = { \tt{ 8 \sqrt{2} + (2 \times 2) \sqrt{2} }} \\ = { \tt{8 \sqrt{2} + 4 \sqrt{2} }}\)

factorise √2 out:

\( = { \tt{(8 + 4) \sqrt{2} }} \\ \\ = { \bf{12 \sqrt{2} }}\)

Answer:

The answer is $2.04 i dont know what the silver coin is.

Step-by-step explanation:

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Answer:

4x + (x + 1) / (x^2 + 1)

Explanation:

We perform the long division

The result of the above long division tells is that

If we now divide both sides by x^2 + 1, we get

Hence,

Therefore, the first choice from the options is the correct answer!

The probability that a randomly selected Christian living in the United States would identify as Catholic can be calculated by dividing the number of Catholics in the US by the total number of Christians in the US.

To do this calculation, we need to know the accurate data on the number of Catholics and the total number of Christians in the US. Let's assume that there are X Catholics and Y total Christians in the US.

The probability of a randomly selected Christian being Catholic would be:

P(Catholic) = X/Y

Without the accurate data on the number of Catholics and total Christians in the US, it is not possible to calculate the exact probability. However, if we assume that the data provided is accurate and stable, we can use the formula above to calculate the probability.

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(a)the body temperature of the 1601 lb man will increase by approximately 3.0 °C.(b)the body temperature of the 160 lb man will increase by approximately 2.4 °C.

The specific heat of a human is given as 3.47 J/°C. Using this information, we can calculate the increase in body temperature when a certain number of calories are converted into heat energy. In the first scenario, a 1601 lb man consumes a candy bar containing 287 Cal. In the second scenario, a 160 lb man consumes a roll of candy containing 41.9 Cal. We will calculate the increase in body temperature for each case.

(a) To calculate the increase in body temperature for a 1601 lb man who consumes a candy bar containing 287 Cal, we need to convert calories to joules. Since 1 Calorie (Cal) is equal to 4184 joules, we have:
Energy = 287 Cal × 4184 J/Cal = 1.2 × \(10^6\) J
Now, using the specific heat formula Q = mcΔT, where Q is the energy, m is the mass, c is the specific heat, and ΔT is the change in temperature, we can rearrange the formula to solve for ΔT:
ΔT = Q / (mc)
Assuming the mass of the man is converted to kilograms, we have:
ΔT = (1.2 × \(10^6\) J) / (1601 lb × 0.4536 kg/lb × 3.47 J/°C) ≈ 3.0 °C
Therefore, the body temperature of the 1601 lb man will increase by approximately 3.0 °C.
(b) For a 160 lb man who consumes a roll of candy containing 41.9 Cal, we repeat the same calculation:
Energy = 41.9 Cal × 4184 J/Cal = 1.75 × \(10^5\) J
ΔT = (1.75 × \(10^5\) J) / (160 lb × 0.4536 kg/lb × 3.47 J/°C) ≈ 2.4 °C
Thus, the body temperature of the 160 lb man will increase by approximately 2.4 °C.

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2.18 is the right z-value to utilize for a level of confidence of 98.54%.

Assuming a two-sided confidence interval,

(100-98.54)/2 = 1.46

Lower percentile = 1.46%

In terms of the information that is provided, we have that the percentile is the 3-th percentile.

We need to find the z-score associated to this percentile. How do you we do so? We need to find the

value z* that solves the equation below.

P(Z < z*) = 0.0146

The value of z" that solves the equation above cannot be made directly, it solved either by looking at

a standard normal distribution table or by approximation (the way Excel or this calculator does)

Then, it is found that that the solution is z* = -2.18

Therefore, it is concluded that the corresponding z-score associated to the given 2nd percentile is

Z =-2.18

The results found above are depicted graphically as follows:

The Z-score z = -2.18 is associated to the 2nd percentile

Hence, lower interval Z-score =-2.18

Since the standard normal distribution is symmetric around 0,

Therefore, upper interval Z-score = 2.18

Appropriate z-value =2.18

Hence, the appropriate z-value to use for a 98.54% level of confidence is 2.18

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Answer: B

Step-by-step explanation:

Substituting in the coordinates into the lines which they lie on,

\(r=p+b\\\\5r=4p+b\)

Subtracting the equations,

\(-4r=-3p \implies \frac{r}{p}=\frac{3}{4}\)

If we remove an arbitrary edge from a tree, the resulting graph will still be connected and acyclic (meaning it does not contain any cycles). This is because a tree is defined as a connected and acyclic graph. Removing an edge will not disconnect the graph since there is always at least one path between any two vertices in a tree. However, the resulting graph will no longer be a tree, as a tree must have exactly one fewer edge than vertices.

If we remove an arbitrary edge from a tree, then the resulting graph will be:

1. A disconnected graph: Since a tree is a connected graph with no cycles, removing an edge will separate it into two components.
2. The components will be trees: Each component will still have no cycles and will remain connected.

So, when you remove an arbitrary edge from a tree, the resulting graph will be a disconnected graph with two tree components.

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Answer:

The slope is 2.

Step-by-step explanation:

You can see on the intercepts that it goes rise 2 and run over 1 which would basically equal to 2.

Step-by-step explanation:

I don't know if it help but here.It's the one that says slope of a line.

Answer:

Scale factor = \(\frac{1}{2}\)

Step-by-step explanation:

From the picture given in the question,

If the larger figure is dilated to form the smaller figure,

Scale factor by which a figure is dilated with is determined by the expression,

Scale factor = \(\frac{\text{Measure of one side of the smaller figure}}{\text{Measure of the corresponding side of the larger figure}}\)

                    = \(\frac{3}{6}\)

                    = \(\frac{1}{2}\)

Answer:

2+3

Step-by-step explanation:

We know that function f(x) is given by

where the slope is the coefficient of the variable x, that is, the slope,m, is

Since g(x) is given by

we have that

where the slope is equal to 6, in other words

Therefore, the slope of the graph of g(x) is 6 times the slope of the graph of f(x).

Since the y-intercept of f(x) is zero, then the y-intercept of g(x) is zero too. Then, the answer is: the y-intercept does not change.

F(51)

===========================================================

Explanation:

The very large numbers are likely put there as a distraction. They aren't needed. Adding any two adjacent Fibonacci numbers will lead to the next term in the sequence. This is simply based on how the special number sequence is defined or set up.

This means F(49)+F(50) = F(51) i.e. adding the 49th and 50th terms will generate the 51st term.

In general,

F(n) + F(n+1) = F(n+2)

where n is a positive integer.

Answer:

C

Step-by-step explanation:

5/2=15=6=2.5

Answer:

2.5

Step-by-step explanation:

Since there is 5 cups of flour for 2 cups of vanilla, then all you need to do is divide 5 by 2.

5/2 is 2.5

Hope this helped :)

Answer:

x = 12

Step-by-step explanation:

Answer:

21.15  550 divided by 26 = 21.15.

Step-by-step explanation:

I did the work on my paper. =)

The Newton-Raphson method approximates the roots of a function. So, we need a function whose root is the cube root we're trying to calculate.

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Answer:

a. \(g(0)=9\)

b. \(g(\frac{9}{8} )=0\)

c. \(g(s+1)=-8x+1\)

Step-by-step explanation:

The parent function is \(g(y)=9-8y\). You "plug in" the value inside the parentheses into the equation.

a. \(g(0)=9-8(0)\)

\(g(0)=9-0=9\)

b. \(g(\frac{9}{8} )=9-8(\frac{9}{8} )\)

\(g(\frac{9}{8} )=9-9=0\)

c. \(g(s+1)=9-8(s+1)\)

\(g(s+1)=9-8s-8=-8s+1\)