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2 years ago

10

Bailey rolls a pair of dice 12 times, and the sum of 6 came up 5 times to calculate the experimental and theoretical probabiliti

es of rolling a sum of six with a pair of dice

1 answer:

mel-nik [20]2 years ago

3 0

Answers:

Experimental probability = 5/12

Theoretical probability = 5/36

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

Explanation:

The experimental probability, aka empirical probability, is what we observe to happen. The event of rolling a six happens 5 times out of 12 total rolls. That leads directly to the experimental probability of 5/12

----------------------------

The theoretical probability is based on predetermined odds, and can be done on paper rather than actually rolling the dice.

There are 6*6 = 36 ways to roll two dice. Of those 36 ways, we have these cases that add to 6

1+5 = 6
2+4 = 6
3+3 = 6
4+2 = 6
5+1 = 6

There are five ways to add to 6, out of 36 outcomes total.

This means the theoretical probability of getting a sum of 6 is 5/36

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8- (0.75+2). Plzzz explain it

frosja888 [35]

Answer:

5.25

Step-by-step explanation:

ok so first you add 0.75+2 which is equal to 2.75

and now you will have 8-2.75 which is equal to 5.25

3 0

3 years ago

Original price of a CD is $17.50 discount is 50%

ladessa [460]

Answer:

$8.75

Step-by-step explanation:

To calculate this you could use two methods. The first method is to find out what 10% is and multiply it by 5. The second method is to calculate 50% using the formula.

<u>Method 1:</u>

To work this out you would simply divide 17.50 by 10, which is 1.75. This is because percentages are out of 100 and so by dividing by 10 we are finding out what 10% is. Then you would multiply 1.75 by 5, which is 8.75. Then you would minus 8.75 from 17.50, which is 8.75.

<u></u>

1) Divide 17.50 by 10.

$17.50/10=1.75$

2) Multiply 1.75 by 5.

$1.75*5=8.75$

3) Minus 8.75 from 17.50.

$17.50-8.75=8.75$

4) The new price is $8.75

<u>Method 2:</u>

<u></u>

The formula for percentages is.

$\frac{percentage}{100} * amount$

<u></u>

To work this out you would first divide 50 by 100, which gives you 0.5. Then you would multiply 0.5 by 17.50, which is 8.75. Then you would minus 8.75 from 17.50, which is 8.75.

1) Divide 50 by 100.

$50/100=0.5$

2) Multiply 0.5 by 17.50.

$17.50*0.5=8.75$

3) Minus 8.75 from 17.50.

$17.50-8.75=8.75$

4) The new price is $8.75.

7 0

3 years ago

The cost to manufacture x number of chairs can be represented by the function C(x)=36x . In th

bogdanovich [222]

<span>C(x)=2268 means that the cost of </span><span>manufacture 63 chairs is 2268$.

2268/36 = 63 chairs
</span>

4 0

3 years ago

20 points Return to questionItem 4Item 4 20 points Police records in the town of Saratoga show that 13 percent of the drivers st

Sladkaya [172]

Answer:

a) 0.1423

b) 0.2977

c) 0.56

Step-by-step explanation:

For each driver stopped for speeding, there are only two possible outcomes. Either they have invalid licenses, or they do not. The probability of a driver having an invalid license is independent from other drivers. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

13 percent of the drivers stopped for speeding have invalid licenses.

This means that $p = 0.13$

14 drivers are stopped

This means that $n = 14$

(a) None will have an invalid license.

This is $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{14,0}.(0.13)^{0}.(0.87)^{14} = 0.1423$

(b) Exactly one will have an invalid license.

This is $P(X = 1)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{14,1}.(0.13)^{1}.(0.87)^{13} = 0.2977$

(c) At least 2 will have invalid licenses.

Either less than 2 have invalid licenses, or at least 2 does. The sum of the probabilities of these events is decimal 1. Mathematically, this is

$P(X < 2) + P(X \geq 2) = 1$

We want $P(X \geq 2)$

So

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1) = 0.1423 + 0.2977 = 0.44$

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.44 = 0.56$

8 0

3 years ago

Can you help me create a polynomial function matching the criteria on the left please and thanks

Olenka [21]

Answer:

$f(x) = \dfrac{1}{8}(x + 4)^2(x + 1)(x - 3)$

Step-by-step explanation:

From inspection of the graph, we can see that the curve intercepts the x-axis at (-4, 0), (-1, 0) and (3, 0)

Therefore,

x = -4 ⇒ x + 4 = 0

x = -1 ⇒ x + 1 = 0

x = 3 ⇒ x - 3 = 0

Because (-4, 0) touches the x-axis, then (x + 4)² will be a factor

So (x + 4)², (x + 1) and (x - 3) are all factors of the polynomial

$\implies f(x) = \dfrac{1}{n}(x + 4)^2(x + 1)(x - 3)$

If we multiply the constants, this will give us the y-intercept:

⇒ 4² x 1 x -3 = -48

From inspection of the graph, the y-intercept is -6

So to get from -48 to -6 we need to multiply -48 by 1/8

Therefore, n = 1/8

$\implies f(x) = \dfrac{1}{8}(x + 4)^2(x + 1)(x - 3)$

7 0

2 years ago

Read 2 more answers