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3 years ago

A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result.

Mathematics

1 answer:

luda_lava [24]3 years ago

5 0

Answer:

Probability (P) (k successes out of n trials) = nCk * p^k * (1-p)^(n-k), where nCk = n! / (k! * (n-k)!)

for this problem n=20, p = 1/6(probability of rolling 1 two) is approximately 0.1667

P ( of getting more that 3 two's) = 1 -P(0 two's out of 20 trials) -P(1 two out of 20 trials) -P(2 two's out of 20 trials) -P(3 two's out of 20 trials)

P ( of getting more that 3 two's) = 1 -0.026 -0.104 -0.198 -0.238 = 0.434

My answer is A

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A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its op

Alina [70]

Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

So, $\dfrac{r}{h}=\dfrac{3}{9}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}h$

Volume of cone is given by

$V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3$

By differentiating with respect to time t, we get that

$\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}$

Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie $\dfrac{dv}{dt}=-4\ in^3$

and h = 2 inches deep.

$-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}$

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

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3 years ago

Lisa claims that when multiplying any number between 0 and 10 by 100, the product is greater than 100. What is a possible number

dlinn [17]

The number is 1. 1 multiplied by 100 gives 100 as answer. Lisa claims that <span>when multiplying any number between 0 and 10 by 100, the product is greater than 100. In this case the answer is equal to 100 not greater than 100.

So this proof shows that Lisa's claim is not correct. </span>

3 0

3 years ago

Figure ABCD is a parallelogram. What is the value of n?

Zigmanuir [339]

Answer

Find out the what is the value of n.

To prove

By using the parallelogram property .

In parallelogram opposite angels are congruent .

As shown in the figure .

∠B = ∠ D

As given

∠B = (2n + 32)°

∠D = (4n - 2)°

(2n + 32) = (4n - 2)

solving the above

4n -2n = 32 +2

2n = 34

$n = \frac{34}{2}$

n = 17

Therefore the value of n is 17 .

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3 years ago

Read 2 more answers

−2x = 4y + 6 2(2y + 3) = 3x − 5 What is the solution (x, y) to the system of equations above

Wewaii [24]

Answer:

(1;-2)

Step-by-step explanation:

x=-2y-3

2(2y+3)=-6y-9-5

10y=-20

y=-2

x=4-3=1

6 0

3 years ago

The base of a triangle is 6 meters longer than the height of the triangle. If the area of the triangle is 108 square meters, wha

Nonamiya [84]

Answer:

36 meters

Step-by-step explanation:

A=1/2b×h

108sq. m=1/2.6m×h

both side canceling meter

h=2×108m/6

h=36m. answer

4 0

3 years ago