Hamid is playing a trivia game with multiple choice questions. Each question has 222 correct answers among 555 answer choices. Hamid has no idea what the answers to a certain question are, so he needs to choose two different answers at random. What is the probability that hamid guesses both answers correctly?.

Answer:

D.   \(x^4-x^3+x^2-x+1-\frac{6}{5x+5}\)

Step-by-step explanation:

Volume of a rectangular box = Base Area x Height

V = Ah

Here we are give V and h and asked to compute A

From the equation for V, dividing both sides by h gives
V/h = A

A = V/h

V = 5x⁵ - 1
h = 5x + 5

\(V = \dfrac{5x^5-1}{5x + 5}\)

The simplified result is \(x^4-x^3+x^2-x+1-\frac{6}{5x+5}\)

I solved this using synthetic division and can provide the steps if you want

Regardless of what the Inspector chooses, the Owner's expected payoff is the same (33.33). The Owner does not have a better option than waiting for the Inspector to choose container B.

This problem can be modeled as a game of incomplete information. The Inspector and Owner are players in the game, and each has two possible strategies: either choose container B, or switch to container C. The payoffs for each player depend on the strategy they choose and which container contains the counterfeit goods.

To solve this game, we can use backward induction. We start by considering the final decision point: whether to switch to container C after seeing that container A does not contain the counterfeit goods. Let's consider the two cases:

If the counterfeit goods are in container B, then the Inspector knows that container C also does not have the counterfeit goods. In this case, the payoff for choosing container B is 100 (if they find the counterfeit goods) or -100 (if they do not).

If the counterfeit goods are in container C, then the Inspector knows that container B does not have the counterfeit goods. In this case, the payoff for switching to container C is 100 (if they find the counterfeit goods) or -100 (if they do not).

Since the Inspector does not know which container has the counterfeit goods, they should choose the strategy with the higher expected payoff. To calculate the expected payoffs, we need to consider the probability that the counterfeit goods are in each container. Since the owner chose one container at random, each container has a 1/3 chance of containing the counterfeit goods.

If the Inspector chooses container B, the expected payoff is:

Expected payoff (choose container B) = (1/3) * 100 + (2/3) * (-100) = -33.33

If the Inspector switches to container C, the expected payoff is:

Expected payoff (switch to container C) = (1/3) * 100 + (2/3) * (-100) = -33.33

Therefore, regardless of what the Inspector chooses, their expected payoff is the same (-33.33). This means that the Inspector does not have a better option than choosing container B, and switching to container C does not improve their chances of finding the counterfeit goods.

For the Owner, if the Inspector chooses container B, then the Owner's expected payoff is:

Expected payoff (Inspector chooses container B) = (1/3) * (-100) + (2/3) * 100 = 33.33

If the Inspector switches to container C, then the Owner's expected payoff is:

Expected payoff (Inspector switches to container C) = (1/3) * (-100) + (2/3) * 100 = 33.33

Therefore, regardless of what the Inspector chooses, the Owner's expected payoff is the same (33.33). The Owner does not have a better option than waiting for the Inspector to choose container B.

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Answer:

7040

Step-by-step explanation:

first find how many are in 1 mile by doing 5280/3 to get 1760.

second multiply 1760x4 to get 7040

If 1 yard = 3 feet and 1 mile = 5,280 feet, then there are 7,040 yards in 4 miles.

To convert miles to yards, we can use the given conversion factors:

1 mile = 5,280 feet

1 yard = 3 feet

We need to find how many yards are there in 4 miles.

Convert 4 miles to feet using the conversion factor:

4 miles × 5,280 feet/mile

= 21,120 feet

Now, Convert the 21,120 feet to yards using the yard-to-feet conversion factor:

21,120 feet / 3 feet/yard

= 7,040 yards

Therefore, there are 7,040 yards in 4 miles.

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A set of transformations that have been performed on the graph of f(x) = ∛x to obtain the graph of g(x) = 1/4(∛(x + 3) + 6 include the following:

A. Translate the graph up

B. Stretch the graph away from x-axis

E. Translate the graph to the left

In Mathematics, the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate of the pre-image or function.

In Mathematics, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

In conclusion, we can logically deduce that the graph of the parent function was stretched away from x-axis.

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She purchased a cellphone using a simple interest loan of $40,000 with an interest rate of 7%. She'll pay a total interest amount of $67,200 over the course of the 2-year loan repayment period for her cellphone purchase.

The amount of interest paid can be calculated using the formula:

Interest = Principal × Rate × Time

First, we need to convert the interest rate to a decimal. In this case, 7% is equivalent to 0.07. The principal amount borrowed is $40,000, and the time period is 2 years, which equals 24 months.

Using the formula mentioned above, the interest paid can be calculated as follows:

Interest = $40,000 × 0.07 × 24 = $67,200.

Therefore, Jacqueline will pay a total interest amount of $67,200 over the course of the 2-year loan repayment period for her cellphone purchase.

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Answer:

12? or 6-

Step-by-step explanation:

6 * 2

6*1

Step-by-step explanation:

You can choose from four main ways to detect outliers:

1.Sorting your values from low to high and checking minimum and maximum values.

2.Visualizing your data with a box plot and looking for outliers.

3.Using the interquartile range to create fences for your data.

4.Using statistical procedures to identify extreme values

please make me brainilist

The dimensions for which the printed area is maximized are 16.432 × 10.954 in².

let the height of the poster = x inches

area of the poster = 180 in²

thus, its width is 180/x inches.

The printed area has a height of x - 3 inches due to the 1-inch bottom margin and 2-inch top margin.

The sides have a margin of 1 inch, so the width of the printed area is:

180/x - 2

the area of printed area A is given by the formula of a rectangle,

A = height × width

A = (x-3)(180/x - 2)

A = 180 - 2x - 540/x + 6

the maximized area is when dA/dx = 0

dA/dx = - 2 - 540(- 1/x²) = 0

540/x² = 2

x = √270

hence height = √270 = 16.432 inches,

and width = 180/√270 = 10.954 inches.

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Hi!

55<35+10x

Move 35 to the left, using the opposite operation:

55-35<10x

20<10x

Divide both sides by 10:

2<x

Since 2 is greater than x, x is less than 2:

x<2 (Answer)

Hope it helps!

Enjoy your day!

~Misty~

Answer:

Step-by-step explanation:

Ok

Answer:

what

Step-by-step explanation:

:(

The length of each side of the square is 7 yards.

The square sides are equal in a square. So, we wuill find the square root of the number to get what make one side length.

To get length of each side of the square, we will divide perimeter by 4 since a square has four equal sides.

The formula is: Perimeter = 4 * Side Length

Plugging the values:

28 yd = 4 * Side Length

Side Length = 28 yd / 4

Side Length = 7 yd.

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Answer:

the answer is:

997+2=999 so all you would have to do is multiply 997 and 2

Answer:

24 x 2.5 = 60...

Step-by-step explanation:

sorry if this is wrong...

have a good day

let x ,y be lengths of sides of base , z be height of box

amount of cardboard used =surface area s=xy +2xz +2yz

volume v= x y z =27436

==>z=27436/xy

s=xy +2x*27436/xy   +2y*27436/xy

s=xy +54872/y   +54872/x

minimum amount ==>ds/dx=0 ,ds/dy =0

==>ds/dx= y-54872/x^2 =0 ,ds/dy= x-54872/y^2 =0

==> yx^2=54872 ,xy^2 =54872

xy^2 -yx^2 =0 ==>xy(y-x)=0 ==>y=x

yx^2=54872==>y=54872/x^2

xy^2 =54872==>x(54872/x^2)^2 =54872 ==>x^3 =54872 ==>x=38

==>y=38

xyz=27436 ==>z=27436 /xy ==>z=27436 /(38*38) ==>z=19

dimensions of box are 38x38x19

(largest side)38  (smallest side)19

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The mood of the categorical syllogism in example 2 is AIO.

In your example, we have the following premises and conclusion:

1. Major Premise: No dogmatists are scholars who encourage free thinking.
2. Minor Premise: Some theologians are scholars who encourage free thinking.
3. Conclusion: Some theologians are not dogmatists.

The major premise in example 2 is an A proposition (All S are not P). The minor premise in example 2 is an I proposition (Some S are P). The conclusion in example 2 is an O proposition (Some S are not P).

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Answer:

Moore's Law states that the number of transistors on a microchip will double approximately every two years. So, if a microchip in a given year could hold 922,200 transistors, 19 years later, it could hold approximately 922,200 * 2^(19/2) = 922,200 * 2^9.5 = 922,200 * 15,564,224 = 14,225,067,008,000 transistors.

Answer:

A and E

Step-by-step explanation:

This is an example of the distributive property.

28n-25 is the base

E shows 7(4n-5)

7*4=28=28n

7*5=35

7(4n-5)=28n-35

The mass of a plate with radius 4 and a radial density given by rho(x)=e^(x2−12) is b. π(e^4-e^(-12) ).

To find the mass of the plate, use the formula for the mass of a plate with radial density:
M = ∫∫ρ(r) r dr dθ
Where M is the mass of the plate, ρ(r) is the radial density, r is the radius, and θ is the angle.

Given that the radial density is ρ(x)=e^(x2−12) and the radius is 4, we can plug these values into the formula:
M = ∫∫e^(r2−12) r dr dθ

We can solve this integral by first integrating with respect to r:
M = ∫(1/2)(e^(r2−12))(r^2) dθ

Integrate with respect to θ:
M = (1/2)(π)(e^(r^2−12))(r^2)

Finally, we can plug in the value of r=4 and simplify:
M = (1/2)(π)(e^(4^2−12))(4^2)
M = (1/2)(π)(e^4-e^(-12))(16)
M = π(e^4-e^(-12))

Therefore, the mass of the plate is b. π(e^4-e^(-12) ).

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Answer:

Most of the musicians started to play at age 9 or older

Answer:

Yup, same.

Step-by-step explanation:

Answer:

(keyboard spam, nice)

a. the equation for the object's velocity is v(t) = -6 cos(t) - 1. b. the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

a) To find the equation for the object's velocity, we need to integrate the acceleration function with respect to time.

The integral of a(t) = 6 sin(t) with respect to t gives us the velocity function v(t):

v(t) = ∫(6 sin(t)) dt

Integrating sin(t) gives us -6 cos(t), so the equation for the object's velocity is:

v(t) = -6 cos(t) + C

To find the constant C, we use the initial velocity v(0) = -7 m/s:

-7 = -6 cos(0) + C

-7 = -6 + C

C = -1

Therefore, the equation for the object's velocity is:

v(t) = -6 cos(t) - 1

b) To find the object's displacement from time 0 to time 3, we need to integrate the velocity function over the interval [0, 3]:

Displacement = ∫[0,3] (-6 cos(t) - 1) dt

Integrating -6 cos(t) gives us -6 sin(t), and integrating -1 gives us -t. Applying the limits of integration, we have:

Displacement = [-6 sin(t) - t] from 0 to 3

Plugging in the upper and lower limits:

Displacement = [-6 sin(3) - 3] - [-6 sin(0) - 0]

Displacement ≈ -6 sin(3) + 3

Therefore, the object's displacement from time 0 to time 3 is approximately -6 sin(3) + 3 meters.

c) To find the total distance traveled by the object from time 0 to time t, we need to integrate the absolute value of the velocity function over the interval [0, t]:

Total Distance = ∫[0,t] |(-6 cos(t) - 1)| dt

Since the absolute value function makes the negative part positive, we can rewrite the equation as:

Total Distance = ∫[0,t] (6 cos(t) + 1) dt

Integrating 6 cos(t) gives us 6 sin(t), and integrating 1 gives us t. Applying the limits of integration, we have:

Total Distance = [6 sin(t) + t] from 0 to t

Plugging in the upper and lower limits:

Total Distance = [6 sin(t) + t] - [6 sin(0) + 0]

Total Distance = 6 sin(t) + t

Therefore, the total distance traveled by the object from time 0 to time t is 6 sin(t) + t meters.

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Answer:

3/10+4/10=7/10

Step-by-step explanation:

Answer:

The answer is C, I had this same quiz today and I got 100%

Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

We must conclude that there are infinitely many primes of the form 3k + 2, where k is a non-negative integer.

To adapt the proof:

We can use a similar contradiction argument.

Suppose that there are only finitely many primes of the form 3k + 2, say p1, p2, ..., pn.

Let N = 3p1p2...pn + 2. Note that N is of the form 3k + 2 for some non-negative integer k.

Now, let's consider the prime factorization of N. Either N is prime and of the form 3k + 2, in which case we have found a new prime of the desired form, contradicting our assumption that there are only finitely many such primes. Or, N is composite and has a prime factorization consisting only of primes of the form 3k + 1 (since any prime of the form 3k + 2 would divide N). But this implies that N itself is of the form 3k + 1.

Now, let's consider the number M = 3N + 2. M is also of the form 3k + 2, and so must have a prime factorization consisting only of primes of the form 3k + 1. But since N is of the form 3k + 1, we have

M = 3(3p1p2...pn + 1) + 2 = 9p1p2...pn + 5. This means that M has a prime factorization consisting of primes of the form 3k + 2, which contradicts our assumption that there are only finitely many such primes.

Therefore, we must conclude that there are infinitely many primes of the form 3k + 2, where k is a non-negative integer.

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Answer:

2261612416

Comment if you need help with this still

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

36 ft squared

Step-by-step explanation:

12*5=60 Original Size

12+25% of 12= 16

5+ 20% of 5= 6

6*16=96

The difference between the two:

96-60=36 ft squared difference

Answer: Each student will pay about $4.78

Step-by-step explanation: You have to add 76.50 and 23.95 and you will get 100.45 then divide by 21 and your product is $4.78. Hope it helped.