Write an expression equivalent to (2/5)^4 using a positive exponent.

Answers

Answer 1

According to the given statement the positive exponent is \(\frac{16}{625}\).

What do an exponent and an example mean?

Exponents are a method of expressing enormous magnitudes in terms of their respective powers. The amount of times some number has already been multiplied in itself is the exponent, so to speak. For instance, the result of multiplying the number 6 on it's own four times is 6 6 6 6. This may be expressed as 64. Here, the exponent and base are 4 and 6, respectively.

The solution to powers and exponents.

The exponent is the exact quantity of times that base would be compounded on its own. As a result, if two powers have the same foundation, they can be multiplied. Whenever two powers are multiplied, exponents are added. If necessary, we can also divide the abilities.

Briefing:

= \(( \frac{2}{5} )^{4}\)

= \(\frac{2}{5} \times\frac{2}{5} \times\frac{2}{5} \times\frac{2}{5} \\\\\frac{16}{625}\)

Hence, the required exponent is \(\frac{16}{625}\).

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Related Questions

What will a $160,000 house cost 8 years from now if the price appreciation for homes over that period averages 7​% compounded​ annually?

Answers

Answer:

FV= $274,909.8

Step-by-step explanation:

Giving the following information:

Present value (PV)= $160,000

Interest rate (i)= 7%

Number of periods (n)= 8 years

To calculate the future value (FV) of the home, we need to use the following formula:

FV= PV*(1+i)^n

FV= 160,000*1.07^8)

FV= $274,909.8

What is the domain of the function y=3/x?
O
-00 O 0 0 1

What is the domain of the function y=3/x?O-00O 001

Answers

Answer: Choice A)  \(-\infty < x < \infty\)

We can plug in any x value we want. The domain is the set of all real numbers. We don't have to worry about applying the square root of a negative value since negative values are allowed in cube roots.

For instance, \(\sqrt[3]{-64} = \sqrt[3]{(-4)^3} = -4\)

Use the linear combination method to add the system of equations and create a one-variable equation. x – 5y = 6 –x + 2y = –3 Which solution is correct? 7y = 3 7y = –9 –3y = –9 –3y = 3

Answers

Answer:

D

Step-by-step explanation:

i did the assignment.

The correct solution of the system of the equation is -3y = 3.

The correct option is D.

What is the system of equations?

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A system of equations,

x – 5y = 6    {equation 1}

–x + 2y = –3    {equation 2}

In order to solve the equations, using linear combination method.

Combining the two equations 1 and 2 to eliminate one of the variables x.

Adding both the equations,

-3y = 3

y = -1.

Therefore, –3y = 3 is the solution.

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What will be the average of the first five
consecutive numbers starting from 11

Answers

Answer:

  13

Step-by-step explanation:

The average of any 5 consecutive numbers is the 3rd one (the middle one of the group). The third consecutive number starting from 11 is 13.

The average of {11, 12, 13, 14, 15} is 13.

Determine the value of x.

Determine the value of x.

Answers

i think the answer is d

7) Find the approximate sum (24,687 +38,403 +53,628) to the nearest thousand:​

Answers

The approximate sum of the values to the nearest thousand is 117000

Sum of numbers and rounding up

Any number of digits after that number becomes zero and this is known as rounding down. If the digit in the smallest place is greater than or equal to 5, then the digit is added with +1.

Given the expression below;

24,687 +38,403 +53,628 = 116718

Hence the approximate sum of the values to the nearest thousand is 117000

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1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 QUESTION 1 [24] Gavin Pillay is employed at Maritzburg Engineering, a Steel manufacturing company in Pietermaritzburg. Below is a copy of his Payslip. 1. 3201 Company Maritzburg Engineering cc 21 Halsted Road Pietermaritzburg Employment No 105 Id Number Income Basic Salary Overtime M Gross Salary Maritzburg Engineering cc Employee Name Gavin Pillay Period 31/05/2023 Sex Male 790128514088 R8700 R1200 A Status Married Deductions PAYE UIF Total Deductions Net Pay 1200 87 B C Name the Employee? What does UIF stand for? Show by calculation that the UIF paid by Gavin is calculated correctly Which month is this Payslip for? Calculate the missing values A to C How old is Gavin this year? Give the address of Gavin's work place. Gavin would like to contribute towards a Pension fund (7,5% of his Basic Salary). H would this affect his net salary?​

Answers

If Gavin contributes towards a Pension fund (7,5% of his Basic Salary), then his net salary will be reduced by the amount he contributed towards pension fund i.e. R652.5.

1.1 Name of employee is Gavin Pillay. 1.2 UIF stands for Unemployment Insurance Fund. UIF is a benefit to provide short-term relief to workers who lose their jobs, or can't work due to illness, maternity or adoption leave. 1.3 The UIF paid by Gavin is calculated correctly.

Firstly, we need to calculate Gross Salary of Gavin, which is given as: Basic Salary + Overtime + M = R8700 + R1200 + R3201 = R13101Then, calculate total deductions from gross salary.

Total Deductions = PAYE + UIF = R1200 + 87 = R1287Hence, Gavin's net salary = Gross salary - Total Deductions = R13101 - R1287 = R11814Therefore, UIF paid by Gavin is calculated correctly as R87.1.4 This payslip is for the month of May i.e.

31/05/2023.1.5 Basic salary of Gavin = R8700. Deduct 7.5% of his basic salary to calculate his pension fund contribution. Pension Fund Contribution = 7.5/100 x R8700 = R652.5.1.6

Total deductions of Gavin includes PAYE, UIF and pension fund contribution.

Therefore, Total Deductions = PAYE + UIF + Pension Fund Contribution = R1200 + R87 + R652.5 = R1939.5.1.7

Gavin's age can not be determined as his date of birth is not provided.1.8 Address of Gavin's workplace is 21 Halsted Road, Pietermaritzburg?

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A 2 meter television camera at ground level is filming the lift-off of a space shuttle at a point 750 meters from the launch pad. The camera’s angle of elevation to the shuttle is 32° at this specific time . Find the height of the shuttle.

Answers

To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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Darryl has 2/3 of a bag of dog food. His dog eats 4/9 of a bag per week. How many weeks will the dog food last?

Answers

it should last him 1/3

A fraction is a part of a whole and it can be expressed as a quotient, in which the numerator is divided by the denominator.

The number of weeks the dog will take to finish 2/3 of a bag of dog food is 1 (1/2) weeks.

What is a fraction?

A fraction is a part of a whole and it can be expressed as a quotient, in which the numerator is divided by the denominator.

We have,

The amount of dog food in the bag = 2/3

The amount of dog food the dog eats per week = 4/9

We need to find the number of weeks that the dog finishes 2/3 of dog food.

The number of weeks:

1 week = 4/9 dog food

Multiply both sides by (9/4 x 2/3)

(9/4 x 2/3) x 1 week = (9/4 x 2/3) x 9/4 dog food

3/2 weeks = 2/3 dog food

[ 3/2 = 1 (1/2) ]

1(1/2) weeks = 2/3 dog food

This means in one and a half weeks the dog finished 2/3 of dog food.

Thus the number of weeks the dog will take to finish 2/3 of a bag of dog food is 1 (1/2) weeks.

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I WILL GIVE BRAINLEST ITS A IREADY QUESTION (7TH GRADE)

I WILL GIVE BRAINLEST ITS A IREADY QUESTION (7TH GRADE)

Answers

Answer: 75.67

Step-by-step explanation:

1) Area of a triangle: A=bh/2. Substitute: 12*8/2=96/2=48

2) Area of parallelgram: A=vertical height*base.

Substitute: 19*13= 247

3) Area of rectangle: A=bh. Substitute: 3.5*8.1=28.35

4) Area of penatgon: 5/2 x s x a when s is side of pentagon and a is apothem of pentagon. Substitute: 5/2*4*2.5=25

5) Area of trapezoid: (a+b/2)+h. Substitute: ((18+24)/2)+9=(42/2)+9=21+9=30

Mean formula: all numbers added together/number of values in list.

(48+247+28.35+25+30)/5=75.67

Hope that helps! If you found that helpful feel free to give me Brainliest!

-ax^(2)+2x+2a if a=7 and x=-5

Answers

Answer:  -151

Step-by-step explanation:  

First Plug everything in

-7(5)^(2)+2(5)+2(7)

Then use order of operations and first deal with the exponent

-7(25)+2(5)+2(7)

then multiply left to right

-175+10+14

combine

so the answer is -151

Y (4)
+4y ′′
+4y=0 A general solution with x as the independent variable is y(x)=

Answers

Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

Write down the ratio 240 kg to 6 kg.
Give your answer in its lowest form.

Answers

The ratio of the given 240 kg to 6 kg will be 40:1.

What is Ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."

the ratio 240 kg to 6 kg.

It will be simple 240/6 :: 40 :1

Hence the ratio of the given data will be 40:1

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Find the average rate of change of each function on the interval specified.

i only need #5 thank you :)

Find the average rate of change of each function on the interval specified.i only need #5 thank you :)

Answers

The average rate of change (AROC) of a function f(x) on an interval [a, b] is equal to the slope of the secant line to the graph of f(x) that passes through (a, f(a)) and (b, f(b)), a.k.a. the difference quotient given by

\(f_{\mathrm{AROC}[a,b]} = \dfrac{f(b)-f(a)}{b-a}\)

So for f(x) = x² on [1, 5], the AROC of f is

\(f_{\mathrm{AROC}[1,5]} = \dfrac{5^2-1^2}{5-1} = \dfrac{24}4 = \boxed{6}\)

Deidre bought a car in California. The price of the car was $32,000. California has an 8% sales tax. How much did Deidre pay for the car including sales tax?

Answers

Given:

Price of car = $32,000

Sales tax = 8%

To find:

The price of car including sales tax.

Solution:

We have,

Price of car = $32,000

Salas tax = 8%

Amount of sales tax = 8% of price of car

\(\text{ Sales Tax}=\dfrac{8}{100}\times 32000\)

\(\text{Sales Tax}=2560\)

Now,

Total price of car including tax = Price of car + Sales tax

\(\text{Total price of car including tax}=32000+2560\)

\(\text{Total price of car including tax}=34560\)

Therefore, the price of car including tax is $34560.

For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.

Answers

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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What does m represent in the equation of a line?

Answers

Answer:

m is the slope of the line

Step-by-step explanation:

Equation of a line

The equation of a line can be written in the form:

y = mx+b

Where m is the slope of the line and b is the y-intercept. Both parameters define the behavior of the line in terms of it's increasing/decreasing trend, and where it crosses the y-axis.

As an example, let's consider the line

y =3x-8

Here, the slope is 3 and the y-intercept. It means the line is increasing from left to right and the point where it crossed the y-axis is (0,-8).

m is the slope of the line

Real-life Problems Question 10

Real-life Problems Question 10

Answers

Answer :

a) It is given that

Everyday a machine makes 500000 staples and puts them into the boxes.

The machine need 170 staples to fill a box

One box contans = 170 staples.

Total number of staples = 500000

Number of box required to fill 500000 staples = Total number of staples/No. of staples 1 box contains.

\( \: :\implies \) 500000 /170

\( :\implies \: \) 2941 (approx)

Therefore, 2941 boxes are required to fill with 500000 staples.

b) It is given that,

Each staple is made of 0.21 g of metal .

Total weight of metal = 1 kg = 1000 g

1 staple = 0.21 g

Number of staples = weight of metal/ Weight of 1 staple.

\( \: :\implies \) 1000/0.21

\( \: :\implies \) 4761 (approximately)

Therefore, 4761 staples can be made from 1 kg of the metal.

formula for density
formula for density


Answers

Answer:

The formula for density (ρ) is:

Density (ρ) = Mass (m) / Volume (V)

Step-by-step explanation:

Where:

Density is measured in units such as kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).Mass is the amount of matter in an object and is typically measured in kilograms (kg) or grams (g).Volume is the amount of space occupied by an object and is typically measured in cubic meters (m³) or cubic centimeters (cm³).

Please hurry need help, Answer choices-
A.9
B.-2
C.11
D.3

Please hurry need help, Answer choices-A.9B.-2C.11D.3

Answers

The numerical value of x in angle ABD is 9 as angle ABC is divided into two equal halves.

What is the numerical value of x?

An angle bisector divided an angle into two equal halves.

From the diagram:

Line BD divides angle ABC into two equal halves.

Angle ABD = ( 3x - 7 ) degrees

Angle DBC = 20 degrees

Since angle ABD and DBC are equal haves;

Angle ABD = Angle DBC

Plug in the values:

( 3x - 7 ) = 20

Solve for x:

3x - 7 = 20

Add 7 to both sides:

3x - 7 + 7 = 20 + 7

3x = 27

x = 27/3

x = 9

Therefore, the value of x is 9.

Option A)9 is the correct answer.

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Which of these is NOT a way to show that two figures are congruent?

Answers

If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.

What is Triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

What is the condition to be congruent?

If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

here, we have,

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In Δ PQR and ΔXYZ, as shown in figure,

we can identify that PQ = XY, PR = XZ,

and QR = YZ

and ∠P = ∠X,

∠Q = ∠Y and ∠R = ∠Z.

Then we can say that Δ PQR ≅ ΔXYZ.

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Which of these is NOT a way to show that two figures are congruent?

The table shows the number of one doctor’s patients who caught a cold one week and whether or not they exercised regularly. help me please! ​

The table shows the number of one doctors patients who caught a cold one week and whether or not they

Answers

#2=2 #3=2 I think the questions are the same just said differently so they aren’t meant to trick you Do you need help on #4 too?

2) P(did not exercise | did not catch a cold) = 1/16

3) P(did not catch a cold | did not exercise) = 1/6

4) The events "did not exercise" and "did not catch a cold" are dependent events.

What is probability?

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

The formula of the probability of an event A is:

P(A) = n(A) / n(S)  

where, n(A) is the number of favorable outcomes and n(S) is the total number of events in the sample space.

Conditional probability formula:

For events A, B,

P(A|B) means, event A and event B are depends on each other.

P(A | B) = n(A ∩ B) / P(B)

For given situation:

the total number of doctor’s patients: 8 + 30 + 10 + 2 =50

⇒ n(S) = 50

Let event A: did not exercise

⇒ n(A) = 10 + 2

⇒ n(A) = 12

⇒ P(A) = 12/50

event B: did not catch cold

⇒ n(B) = 30 + 2

⇒ n(B) =32

⇒ P(B) = 32/50

patient who did not catch a cold as well as who did not exercise = A ∩ B

⇒ n(A ∩ B) = 2

⇒  P(A ∩ B) = 2/50

2) To find: P(did not exercise | did not catch a cold)

⇒ P(A | B) = P(A ∩ B) / P(B)

⇒ P(A | B) = \(\frac{\frac{2}{50} }{ \frac{32}{50} }\)

⇒ P(A | B) = 2/32

P(A | B) = 1/16

3) To find: P(did not catch a cold | did not exercise)

⇒ P(B | A) = P(B ∩ A) / P(A)

⇒ P(B | A) = \(\frac{ \frac{2}{50} }{ \frac{12}{50} }\)

⇒ P(B | A) = 2/12

P(B | A) = 1/6

4) Since P(B | A) ≠ P(B)

i.e., P(did not catch a cold | did not exercise) ≠ P(did not catch a cold)

This means, the events "did not exercise" and "did not catch a cold" are dependent.

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A line passes through the point (10, 6) and has a slope of
2
5
Write an equation in point-slope form for this line.

Answers

In point slope it is y-6=2/5(x-10)

What’s 6(x – 1) = 9(x + 2) ?

Answers

Answer:

-8=x

Step-by-step explanation:

6x-6=9x+18

-6-18=9x-6x

-24=3x

x=-8

hope i helped

brainliest pls

im trying to level up

Answer:

x=-8

Step-by-step explanation:

whatre the values of x and y

whatre the values of x and y

Answers

By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

What are the values of two variables associated with two angles from a right triangle?

In this system we have a geometrical system formed by two right triangles with a common hypotenuse. Right triangles are triangles where one of its internal angles are right angles and the sum of the measures of the internal angles within a triangle equals 180°. Then, this geometrical system can be modelled by using the following linear equations:

(x + 20) + 90 + 30 = 180         (1)

20 + 90 + (y + 30) = 180         (2)

By using the concept of internal angles of a triangle, the solution of the system of linear equations related to the geometrical system is (x, y) = (40, 40).

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Need help with finding the mean (MATH 7th GRADE)

Need help with finding the mean (MATH 7th GRADE)

Answers

Answer:

mean = 49.25

Step-by-step explanation:

mean = sum of all the number ÷ amount of number

mean = 56 + 21 +55 + 30 + 34+ 76 + 40 + 82 = 394 ÷ 8

mean = 49.25

mean absolute deviation = (56- 49.25) + (21 - 49.25) + (55 -49.25) + (30 - 49.25) + (34 -49.25) + (76 -49.25) + (40 - 49.25) + (82- 49.25) / 8

mad= 6.75 + -28.25 + 5.75 + -19.25 + -15.25 + 26.75 + -9.25 + 32.75 / 8

mad = 0/8

mad= 0

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Problem 3.4 (Video 2.5 - 2.6, Lecture Problem) You are interested in calculating the probability that your favorite 1
Game of Thrones character is eliminated in episode X. You have decided to model X as a Geometric (1/4) random variable. (a) Unfortunately, you have learned a spoiler: your favorite character does not appear in episode 4 or beyond. What is the conditional PMF P X∣B

(x) of X given the event B={X<4} ? (b) Given this spoiler, what is the probability that your favorite character is eliminated in one of the first two episodes? (c) Given this spoiler, what is the expected value of X conditioned on the event B ? (d) Let's consider yet another scenario: After watching the show for 2 episodes, you are happy to see that your favorite character has not been eliminated yet. What is the conditional PMF P X∣C

(x) of X given the event C={X>2} ? 1
Somehow, you have already managed to decide on a favorite character before watching any episodes. 2 (e) Let Y=X−2 be the number of additional episodes after the 2 nd that it takes for your favorite character to be eliminated. Using part (d), quickly determine the conditional PMF P Y∣C

(y) of Y given the event C={X>2}. Determine the family of random variables this conditional PMF belongs to, along with the associated parameter(s). (f) Using what you learned in part (e), determine the conditional mean E[X∣C].

Answers

(a) The conditional PMF P X∣B (x) of X given the event B={X<4} can be calculated using the formula

P(X=x|B) = P(X=x and B)/P(B).

Since the event B={X<4} includes the events X=1, X=2, and X=3, we can calculate P(B) as the sum of the probabilities of these events:

P(B) = P(X=1) + P(X=2) + P(X=3) = (1/4) + (3/4)(1/4) + (3/4)^2(1/4) = 13/16.

Therefore, the conditional PMF P X∣B (x) is given by:

P(X=1|B) = P(X=1 and B)/P(B) = (1/4)/(13/16) = 4/13
P(X=2|B) = P(X=2 and B)/P(B) = (3/4)(1/4)/(13/16) = 3/13
P(X=3|B) = P(X=3 and B)/P(B) = (3/4)^2(1/4)/(13/16) = 6/13

(b) The probability that your favourite character is eliminated in one of the first two episodes given the spoiler is P(X=1|B) + P(X=2|B) = 4/13 + 3/13 = 7/13.

(c) The expected value of X conditioned on the event B can be calculated using the formula E[X|B] = sum(x*P(X=x|B)) for all x in the support of X. Therefore, E[X|B] = 1*(4/13) + 2*(3/13) + 3*(6/13) = 20/13.

(d) The conditional PMF P X∣C (x) of X given the event C={X>2} can be calculated using the formula P(X=x|C) = P(X=x and C)/P(C). Since the event C={X>2} includes the events X=3, X=4, ..., we can calculate P(C) as the sum of the probabilities of these events: P(C) = P(X=3) + P(X=4) + ... = (3/4)^2(1/4) + (3/4)^3(1/4) + ... = (3/4)^2/(1-(3/4)) = 12/16. Therefore, the conditional PMF P X∣C (x) is given by:

P(X=3|C) = P(X=3 and C)/P(C) = (3/4)^2(1/4)/(12/16) = 1/3
P(X=4|C) = P(X=4 and C)/P(C) = (3/4)^3(1/4)/(12/16) = 1/4
...

(e) The conditional PMF P Y∣C (y) of Y given the event C={X>2} can be obtained by shifting the conditional PMF P X∣C (x) of X given the event C={X>2} by 2 units to the left. Therefore, P Y∣C (y) = P X∣C (y+2) for all y in support of Y. This conditional PMF belongs to the family of geometric random variables with parameter 1/4.

(f) The conditional mean E[X|C] can be calculated using the formula E[X|C] = sum(x*P(X=x|C)) for all x in the support of X. Since the conditional PMF P X∣C (x) is a geometric distribution with parameter 1/4 shifted by 2 units to the right, we can use the formula E[X|C] = 2 + 1/(1/4) = 6.

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if you invest $550.00 and your annual interest is 4%, what will be the interest

Answers

The annual interest is $22.

What is simple interest?

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Given;

Amount invested= $550

Annual interest= 4%

SI= 550*4*1/100

=5.5*4

=22

Therefore, the simple interest will be $22.

Learn more about simple interest here;

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A movie with an aspect ratio of 1.8:1 is shown as a letter-boxed image on a newer 48-
inch 16:9 television. Calculate the percent of the screen's area that is occupied by the
image.

Answers

Answer: 1.25%

Step-by-step explanation:

Given: A movie with an aspect ratio of 1.8:1  shown as a letter-boxed image.

Since a for l:b , Area = l x b

Area of letter box = 1.8 x 1 = 1.8 sq. units

Screen's ratio= 16:9

Area of screen = 16 x 9 = 144 sq. units

The percent of the screen's area that is occupied by the  image =\(\dfrac{1.8}{144}\times100=1.25\%\)

Hence, the percent of the screen's area that is occupied by the

image. =1.25%

Dividing by a Monomial
What is (9x^3-6x^2+15x) ÷ 3x^2?

Answers

Answer:
\(3x-2+\frac{5}{x}\)

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

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