A rectangular box has a volume of 108 cubic feet. How many cubic yards are in the volume of this box?

Zaid has a peculiar pair of four-sided dice. When he rolls the dice, the probability of any particular outcome is proportional t

AnnZ [12381]

Answer: a) $\bold{\dfrac{3}{16}}$ b) $\bold{\dfrac{1}{36}}$

Step-by-step explanation:

a) To achieve an even total, there are 3 possible combinations:

1) Even, Even, Even, Even $\dfrac{3\times 3\times 3\times 3}{6^4} \quad = \dfrac{3^4}{6^4}\quad =\dfrac{1}{16}$

2) Even, Even, Odd, Odd $\dfrac{3\times 3\times 3\times 3}{6^4} \quad = \dfrac{3^4}{6^4}\quad =\dfrac{1}{16}$

3) Odd, Odd, Odd, Odd $\dfrac{3\times 3\times 3\times 3}{6^4} \quad = \dfrac{3^4}{6^4}\quad =\dfrac{1}{16}$

Order is irrelevant

Summing these yields your final result: $\dfrac{1}{16}+\dfrac{1}{16}+\dfrac{1}{16}\quad =\large\boxed{\dfrac{3}{16}}$

b) If one die shows a 2 and another a 3, while the remaining two can show any digits, there’s only one way to get a 2, one way for a 3, and six potential numbers for each of the other two dice.

$\dfrac{1\times 1\times 6\times 6}{6^4}\quad =\dfrac{1}{6^2}\quad =\large\boxed{\dfrac{1}{36}}$

3 0

3 months ago

Ruben has two congruent wooden dowels. He cuts one dowel in two in order to have three pieces to make a triangle. Explain why, d

Inessa [12570]

Let's apply the Pythagorean theorem to determine whether a triangle could be formed.

Assuming we have two wooden dowels each measuring 8 inches, we can break one dowel in half, resulting in two pieces of 4 inches each.

Now we have three wooden dowels with lengths of 4 inches, 4 inches, and 8 inches.

According to the Pythagorean theorem:

a² + b² = c²
4² + 4² = 8²
16 + 16 = 64
34 ≠ 64

To form a triangle, the length of the cut wooden dowel needs to exceed that of the uncut dowel.

I also visually attempted this exercise on paper, cutting according to the assumed dimensions. No triangle can be constructed with these pieces.

4 0

3 months ago

Read 2 more answers

What is the monthly finance charge if the average daily balance is $15, the daily periodic rate is 0.06%, and the number of days

Leona [12618]

Given

The daily average balance is $15.

The daily periodic interest rate = 0.06%.

The cycle consists of 30 days.

Calculate the monthly finance charge.

To justify:

Let’s denote the monthly finance fee as x.

According to the details provided:

The average daily balance = $15.

The daily periodic rate = 0.06%,

First, we convert 0.06% to decimal:

$=\frac{0.06}{100}$

= 0.0006.

Daily finance charge = 0.0006 multiplied by 15.

= 0.009.

The number of days in the cycle totals 30.

Now, calculating the monthly finance charge:

The equation becomes:

x = 15 × 0.0006 × 30.

x = 0.009× 30.

x = $0.27.

Thus, the monthly finance charge amounts to $0.27.

Thus proved.

4 0

2 months ago

John has two jobs. For daytime work at a jewelry store he is paid

babunello [11817]

The probability that John's monthly commission from the jewelry store lies between $9,000 and $11,000 is 38.3%. Step-by-step explanation: In a Normal Distribution, which is a continuous probability distribution symmetric around the mean, we analyze the probability of John's commission falling in the specified range. The z-scores for the values in question correspond to 0.50 and -0.50, leading to probabilities of approximately 0.6915 and 0.3085 respectively. Consequently, the computed probability that John's commission is between $9,000 and $11,000 is 38.3%.

4 0

2 months ago