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dimaraw [331]
3 years ago
9

A game is played with a spinner on a circle, like the minute hand on a clock. The circle is marked evenly from 0 to 100, so, for

example, the 3:00 position corresponds to 25, the 6:00 position to 50, and so on. The player spins the spinner, and the resulting number is the number of seconds he or she is given to solve a word puzzle. If 100 players are selected randomly, what is the probability that the avearge time these players will get to solve the word puzzle will exceed 50 seconds?
Mathematics
1 answer:
zheka24 [161]3 years ago
8 0

Answer:

The probability is 1/2

Step-by-step explanation:

The time a person is given corresponds to a uniform distribution with values between 0 and 100. The mean of this distribution is 0+100/2 = 50 and the variance is (100-0)²/12 = 833.3.

When we take 100 players we are taking 100 independent samples from this same random variable. The mean sample, lets call it X, has equal mean but the variance is equal to the variance divided by the length of the sample, hence it is 833.3/100 = 8.333.

As a consecuence of the Central Limit Theorem, the mean sample (taken from independant identically distributed random variables) has distribution Normal with parameters μ = 50, σ= 8.333. We take the standarization of X, calling it W, whose distribution is Normal Standard, in other words

W = \frac{X - \mu}{\sigma} = \frac{X - 50}{8.333} \simeq N(0,1)

The values of the cummulative distribution of the Standard Normal distribution, lets denote it \phi , are tabulated and they can be found in the attached file, We want to know when X is above 50, we can solve that by using the standarization

P(X > 50) = P(\frac{X-50}{8.33} > \frac{50-50}{8.33}) = P(W > 0) = \phi(0) = 1/2

Download pdf
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Classify each pair of angles as Complementary, Supplementary or neither.
stellarik [79]

Answer:


Step-by-step explanation:

1. Supplementary

2. complementary

3. neither

4. These two are vertically opposite so neither.

5. Supplementary

6. They add to 90 so they are complementary

7. They add to 180 so they are supplementary.

8. These 2 are equal and vertically opposite. They are neither for this exercise.

9. Complementary: they add to 90.

8 0
3 years ago
Plz answer ASAP with work ty!
horsena [70]

Answer: 8\sqrt{6}

Step-by-step explanation:

\frac{2^4\sqrt{3}}{\sqrt{2}}

2^{\frac{7}{2}}\sqrt{3}

2^{\frac{7}{2}}=2^{3+\frac{1}{2}}

2^3\cdot \:2^{\frac{1}{2}}=

2^3\sqrt{2}

= 2^3\sqrt{2}\sqrt{3}=

2^3\sqrt{2\cdot \:3}

=2^3\sqrt{6}

2^3=8

Answer- 8\sqrt{6}

7 0
3 years ago
A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The sec
DochEvi [55]

The statements that are true about the intervals of the continuous function are Options 2, 4  and 5

  • f(x) ≤ 0 over the interval [0, 2].
  • f(x) > 0 over the interval (–2, 0).
  • f(x) ≥ 0 over the interval [2, ).

<h3>What is the statement about?</h3>

Looking at the values given, the intervals which satisfies the condition are known to be:

f(x)<=0 over the interval [0,2]

f(x)>0 over the interval (-2,0)

f(x)>=0 over the interval [2,∞)

Because:

Since the table with x  and f(x) values, we have to examine analyze the table and see the each option that is in line with f(x) or not .

Examine the values of x that is from -3 to 3, the f(x) values are both positive and negative . hence f(x)>0 is false over the interval (-∞,3)

Looking at the the interval from 0 to 2, the f(x) values are 0 and negative. Hence, f(x)<=0 over the interval [0,2]

When you look over the interval (-1,1), the f(x) values are said to be both positive and negative and as such, f(x)<0 is false over the interval (-1,1)

When you look at the interval (-2,0) , the f(x)  is positive and as such, f(x)>0 over the interval (-2,0)

Looking at the interval  [2,∞), f(x) is positive and as such, f(x)>=0 over the interval [2,∞)

Therefore, Option 2, 4 and 5 are correct.

Learn more about interval from

brainly.com/question/14454639

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6 0
2 years ago
What is the surface area of a right circular cylindrical oil can, if the radius of its base is 4 inches and its height is 11 inc
Alla [95]

Step-by-step explanation:

Given

Radius (r) = 4 inches

height (h) = 11 inches

Total surface area of cylindrical oil can is

= 2πr ( r + h)

= 2 * 22 / 7 * 4 ( 4 + 11)

= 2 * 22/7 * 4 * 15

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4 0
3 years ago
Read 2 more answers
What is the LCM of x^2+5 and x^2+10x+25?
avanturin [10]

Answer:

(x+5)²(x²+5)

Step-by-step explanation:

Given two functions x²+5 and x²+10x+25, to get their Lowest common factor, we need to to first factorize x²+10x+25

On factorising we have:

x²+5x+5x+25

= x(x+5) +5(x+5

= (x+5)(x+5)

= (x+5)²

The LCM can be calculated as thus

| x²+5, (x+5)²

x+5| x²+5, (x+5)

x+5| x²+5, 1

x²+5| 1, 1

The factors of both equation are x+5 × x+5 × x²+5

The LCM will be the product of the three functions i.e

(x+5)²(x²+5)

This hives the required expression.

5 0
3 years ago
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