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3 years ago

(20 POINTS!!) Find the probability that a multiple of 3 or an odd number is rolled on a number cube.

Mathematics

1 answer:

Anettt [7]3 years ago

7 0

Answer:

1/8

Step-by-step explanation:

A “standard number cube” has six sides, marked 1 2 3 4 5 and 6. Of those, exactly half are even and exactly half are odd, so we can dispense with the 6 part and just go 1/2 (the same as 3/6, after all)

So the first roll is even half the time. If it is, the second roll is odd half the time, so the chances of an even then odd pair are 1/2*1/2=1/4.

If those two happen in the correct order, the chances of the third roll being even are again 1/2… so we have 1/2*1/2*1/2=1/8

Hope it helps

You might be interested in

What is the exact value of the expression the square root of 486. − the square root of 24. + the square root of 6.? Simplify if

kenny6666 [7]

Sqrt(486) - sqrt(24) + sqrt(6)

find the factors of 486 that we can remove from under the square root sign
2 * 243
2 * 3 * 81
2 * 3 * 9 * 9 (we have 2 nines, we can move a 9 outside the sqrt sign)
sqrt(486) = 9 sqrt(6)

Repeating for sqrt(24)
2 * 12
2 * 2 * 6
2 * 2 * 2 * 3 (we can move a 2 outside the sqrt
sqrt(24) = 2 sqrt(6)

Finally, add all 3 terms together

9 sqrt(6) - 2 sqrt(6) + sqrt(6)
8 sqrt(6)

8 times square root of 6 is the final answer

8 0

3 years ago

Construction worker’s planned to secure a tall pole using two cables attached to the pole at a point 12 m above the ground as sh

padilas [110]

Answer:(24+12\3)m

Step-by-step explanation:

6 0

2 years ago

It takes 36 nails to weigh one pound. How many nails would it take to weigh 7 wholes and 2/3 pounds?

o-na [289]

36 * 7 gives you the number of nails in the whole pounds
36 * 2/3 gives you the fraction part

7 * 36 = 252
2/3 * 36 = 24

Total nails = 252 + 24 = 276 nails

5 0

3 years ago

Sunspots have been observed for many centuries. Records of sunspots from ancient Persian and Chinese astronomers go back thousan

Lunna [17]

Answer:

(a) Null Hypothesis, $H_0$ : $\mu$ $\leq$ 41

Alternate Hypothesis, $H_A$ : $\mu$ > 41

(b) The value of z test statistics is 1.08.

(c) We conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.

Step-by-step explanation:

We are given that in a random sample of 40 such periods from Spanish colonial times, the sample mean is x¯ = 47.0. Previous studies of sunspot activity during this period indicate that σ = 35.

It is thought that for thousands of years, the mean number of sunspots per 4-week period was about µ = 41.

Let $\mu$ = mean sunspot activity during the Spanish colonial period.

(a) Null Hypothesis, $H_0$ : $\mu$ $\leq$ 41 {means that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41}

Alternate Hypothesis, $H_A$ : $\mu$ > 41 {means that the mean sunspot activity during the Spanish colonial period was higher than 41}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean = 47

σ = population standard deviation = 35

n = sample of periods from Spanish colonial times = 40

So, the test statistics = $\frac{47-41}{\frac{35}{\sqrt{40} } }$

= 1.08

(b) The value of z test statistics is 1.08.

(c) Now, the P-value of the test statistics is given by;

P-value = P(Z > 1.08) = 1 - P(Z < 1.08)

= 1 - 0.8599 = 0.1401

Since, the P-value of the test statistics is higher than the level of significance as 0.1401 > 0.05, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean sunspot activity during the Spanish colonial period was lesser than or equal to 41.

8 0

3 years ago

The box plots below show attendance at a local movie theater and high school basketball games:

cricket20 [7]

The standard deviation is a better measure of spread for movies than it is for basketball games.

A box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

As, Movies is more centric to mean and not skewed on a particular side whereas basketball games is not centric to mean but is skewed right then left.

Now, Standard deviation just measures the deviation or spread with respect to mean of collected data.

So, In the movies the data is more collected. Thus standard deviation is best suited for movie data.

Now, interquartile range. IQR relies on if the data is skewed.

So, in the basketball data the standard deviation will not give the information.

Hence, the standard deviation is a better measure of spread for movies than it is for basketball games.

Learn more about this concept here:

brainly.com/question/17157714

#SPJ1

5 0

2 years ago