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An ordinary Fair die is a cube with the numbers 1 through 6 on the sides represented by painted spots imagine that such a die is

Hoochie [10]

Answer: Probability of, Event A = 5/18

Event B = 1/2

Step-by-step explanation:

Since, The probability of an event = Number of outcomes of the event/ total number of outcomes.

Since, If a fair dire rolled two times then the total number of outcomes, n(S) = 6 × 6 = 36

And, Event A: The sum is greater than 8.

So, possible outcomes are, ( 3,6), (4,5), (4,6), (5,5), (5,6), (5,4), (6,6), (6,5), (6,4), (6,3)

Thus, n(A) = 10

Since, Probability of event A,

P(A) = n(A)/n(S) = 10/36 = 5/18

Therefore, P(A)= 5/18

Now, Event B: The sum is an even number.

So, possible outcomes are, (1,1),(1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,6), (4,2), (4,4), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)

Thus, n(B)= 18

Since, Probability of event B,

P(B)= n(B)/n(S) = 18/36 = 1/2

Therefore, P(B)= 1/2

7 0

3 years ago

What value of x is in the solution set of 3(x – 4) ≥ 5x + 2? –10 –5 5 10

emmasim [6.3K]

Answer:

The value of x is in the solution set of 3(x – 4) ≥ 5x + 2 is -10

Solution:

Need to determine which value of x from given option is solution set of 3(x – 4) ≥ 5x + 2

Lets first solve 3(x – 4) ≥ 5x + 2

3(x – 4) ≥ 5x + 2

=> 3x – 12 ≥ 5x + 2

=> 3x – 5x ≥ 12 + 2

=> -2x ≥ 14

=> -x ≥ 7

=> x ≤ -7

All the values of x which are less than or equal to -7 is solution set of 3(x – 4) ≥ 5x + 2. From given option there is only one value that is -10 which is less than -7

Hence from given option -10 is solution set of 3(x – 4) ≥ 5x + 2.

7 0

3 years ago

Read 2 more answers

Among freshman at a certain university, scores on the Math SAT followed the normal curve, with an average of 550 and an SD of 10

lina2011 [118]

Answer:

a) 6.68th percentile

b) 617.5 points

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 550, \sigma = 100$

a) A student who scored 400 on the Math SAT was at the ______ th percentile of the score distribution.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{400 - 550}{100}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

So this student is in the 6.68th percentile.

b) To be at the 75th percentile of the distribution, a student needed a score of about ______ points on the Math SAT.

He needs a score of X when Z has a pvalue of 0.75. So X when Z = 0.675.

$Z = \frac{X - \mu}{\sigma}$

$0.675 = \frac{X - 550}{100}$

$X - 550 = 0.675*100$

$X = 617.5$

6 0

3 years ago

Solve the following word problem: Kay made 5 less phone calls today than Stephanie. If together they made 21 calls, how many cal

professor190 [17]

Answer:
Kay made 8 phone calls
Stephanie made 13 phone calls

Explanation:
Assume the number of phone calls that Stephanie made is x.
We are given that:
Kay made 5 phone calls less than Stephanie.
This means that:
Kay made x-5 phone calls

We know that the total number of phones is 21.
This means that:
21 = x + x - 5

Now we solve for x as follows:
21 = x + x - 5
21 = 2x - 5
2x = 26
x = 26/2
x = 13

This means that:
Stephanie made x = 13 phone calls
Kay made x - 5 = 13 - 5 = 8 phone calls

Hope this helps :)

5 0

3 years ago

Question 2

choli [55]

%6 of the sixth graders are left handed

8 0

3 years ago