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Vlada [557]
2 years ago
11

If two fair dice (with faces numbered 1,2,3,4,5,6) are tossed together, what is the probability that the total score will be a p

erfect cube?
Mathematics
1 answer:
grin007 [14]2 years ago
6 0

Answer:

\frac{5}{36}

Step-by-step explanation:

There are 6^2=36 non-distinct sums that can be achieved when rolling two fair sided dice.

The smallest of these sums is 1+1=2 and the largest of these sums is 6+6=12. Within this range, there exists only one perfect cube, 2^3=8.

Count how many ways we can achieve a sum of 8 with two dice:

\begin{cases}2+6=8,\\6+2=8,\\3+5=8, \\5+3=8,\\4+4=8\end{cases}\\\\\implies \text{5 ways}

Thus the probability the total score (sum) will be a perfect cube when rolling two fair six-sided dice is equal to \boxed{5/36}

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In the past, the population proportion of consumers preferring orange juice with no pulp was equation. To test if this populatio
geniusboy [140]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

a) For the null hypothesis,

P = 0.45

For the alternative hypothesis,

P ≠ 0.45

b) For the decision rule, we would reject H0 if 0.1 > p value and accepth H0 if 0.1 < p value

Considering the population proportion, probability of success, p = 0.45

q = probability of failure = 1 - p

q = 1 - 0.45 = 0.55

Considering the sample,

Sample proportion, p = x/n

Where

x = number of success = 52

n = number of samples = 120

p = 52/120 = 0.43

c) We would determine the test statistic which is the z score

z = (p - P)/√pq/n

z = (0.43 - 0.45)/√(0.45 × 0.55)/120 = - 0.44

Recall, population proportion, P = 0.45

The difference between sample proportion and population proportion(P - p) is 0.45 - 0.43 = 0.02

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.45 - 0.02 = 0.43

the p for the right tail is 0.45 + 0.02 = 0.47

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area below the test z score in the left tail 0.3336

We would double this area to include the area in the right tail of z = 0.44 Thus

p = 0.3336 × 2 = 0.67

d) Since alpha, 0.1 < than the p value, 0.67, then we would fail to reject the null hypothesis. Therefore, at a 1% level of significance, we do not have enough evidence to reject the​ null hypothesis

4 0
3 years ago
Please help,
Bess [88]

It is A bc (4)=7(1)-3

5 0
3 years ago
4 1/2 cups converted to fluid ounces
Dmitry_Shevchenko [17]

Answer:

4.5 cup to oz is 36 FLUID OUNCES

6 0
3 years ago
Rewrite the equation by completing the square. 4 x^2 +20 x +25 = 0
Sav [38]

Answer:

x=-5/2

Step-by-step explanation:

4 x^2 +20 x +25 = 0

x^2+5x=-25/4

(b/2)^2=(5/2)^2

x^2+5x+25/4=0

(x+5/2)^2=0

x=-5/2

(Hope this helps)

6 0
3 years ago
Match the missing term with the perfect square trinomial 9X^2+?+25<br> 49<br> 6x<br> 36<br> 30x
Igoryamba
9x^2+t+25=(ax+b)^2

9x^2+t+25=a^2*x^2+2abx+b^2 so

a^2=9 so a=3

b^2=25 so b=5 then

t=2ab using a and b from above

t=2*3*5=30

So the missing term is 30x
4 0
3 years ago
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