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3 years ago

What is the volume of the rectangular pyramid?

Mathematics

1 answer:

Annette [7]3 years ago

5 0

Answer:

Step-by-step explanation:

The formula of a volume of a pyramid:

$V=\dfrac{1}{3}BH$

B - area of a base

H - height

In the base we have the rectangle 12ft × 6ft.

Therefore

$B=(12)(6)=72\ ft^2$

H = 15 ft

Substitute:

$V=\dfrac{1}{3}(72)(15)=\dfrac{(72)(15\!\!\!\!\!\diagup^5)}{3\!\!\!\!\diagup_1}=(72)(5)=360\ ft^3$

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Production times are evenly distributed between 8 and 15.8 minutes and production times are never outside of this interval. What

dezoksy [38]

Answer:

29.49% probability that a production time is between 9.7 and 12 minutes

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d, in which d is greater than c, is given by the following formula.

$P(c \leq X \leq d) = \frac{d - c}{b-a}$

Production times are evenly distributed between 8 and 15.8 minutes and production times are never outside of this interval.

This means that $a = 8, b = 15.8$

What is the probability that a production time is between 9.7 and 12 minutes?

$d = 12, c = 9.7$ .

$P(c \leq X \leq d) = \frac{d - c}{b-a}$

$P(9.7 \leq X \leq 12) = \frac{12 - 9.7}{15.8 - 8} = 0.2949$

29.49% probability that a production time is between 9.7 and 12 minutes

5 0

3 years ago

What is the value of x in the problem ?

Elis [28]

Answer:

The x angle is 112 degrees

Step-by-step explanation:

Step 1: Find the adjacent angle to 134

$134 + w = 180$

$w + 134 - 134 = 180 - 134$

$w = 46$

Step 2: Find the last angle inside the triangle

$46 + 22 + x = 180$

$68 + x = 180$

$x + 68 - 68 = 180 - 68$

$x = 112$

Answer: The x angle is 112 degrees

4 0

3 years ago

Consider rolling two fair dice one 3-sided the other 5-sided

Ne4ueva [31]

Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose

$1\leq x\leq 3,\quad 1\leq y \leq 5$

We have $P(X=x)=\frac{1}{3}$ and $P(Y=y)=\frac{1}{5}$ , because the dice are fair.

Now we use the assumption of independence to claim that

$P(X=x, Y=y) = P(X=x)\cdot P(Y=y) =\dfrac{1}{3}\cdot\dfrac{1}{5} = \dfrac{1}{15}$

Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:

2 in a unique way (1+1)
3 in two possible ways (1+2, 2+1)
4 in three possible ways
5 in three possible ways
6 in three possible ways
7 in two possible ways
8 in a unique way

This implies that the probabilities of the outcomes of $W=X+Y$ are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5