Answer:
24 ft cubed
Step-by-step explanation:
The volume of a rectangular prism is denoted by the formula: , where
is the length, w is the width, and h is the height.
Looking at the diagram, we can see that the length is 2 ft (so = 2), the width is 4 ft (so w = 4), and the height is 3 ft (so h = 3). Now, we can just plug in these values to find V, the volume:
Thus, the answer is 24 ft cubed.
Hope this helps!
Answer:
Step-by-step explanation:
You know how subtraction is the <em>opposite of addition </em>and division is the <em>opposite of multiplication</em>? A logarithm is the <em>opposite of an exponent</em>. You know how you can rewrite the equation 3 + 2 = 5 as 5 - 3 = 2, or the equation 3 × 2 = 6 as 6 ÷ 3 = 2? This is really useful when one of those numbers on the left is unknown. 3 + _ = 8 can be rewritten as 8 - 3 = _, 4 × _ = 12 can be rewritten as 12 ÷ 4 = _. We get all our knowns on one side and our unknown by itself on the other, and the rest is computation.
We know that ; as a logarithm, the <em>exponent</em> gets moved to its own side of the equation, and we write the equation like this:
, which you read as "the logarithm base 3 of 9 is 2." You could also read it as "the power you need to raise 3 to to get 9 is 2."
One historical quirk: because we use the decimal system, it's assumed that an expression like uses <em>base 10</em>, and you'd interpret it as "What power do I raise 10 to to get 1000?"
The expression means "the power you need to raise 10 to to get 100 is x," or, rearranging: "10 to the x is equal to 100," which in symbols is
.
(If we wanted to, we could also solve this: , so
)
Answer:
Probability that a Niffler can hold more than 32 pounds of shiny objects in their pouch is 0.1515.
Step-by-step explanation:
We are given that the amount a Niffler can hold in their pouch is approximately normally distributed with a mean of 25 pounds of shiny objects and a standard deviation of 6.8 pounds.
Let X = <u><em>amount a Niffler can hold in their pouch</em></u>
So, X ~ Normal()
The z score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = population mean = 25 pounds
= standard deviation = 6.8 pounds
Now, the probability that a Niffler can hold more than 32 pounds of shiny objects in their pouch is given by = P(X > 32 pounds)
P(X > 32 pounds) = P( >
) = P(Z > 1.03) = 1 - P(Z
1.03)
= 1 - 0.8485 = 0.1515
<em>The above probability is calculated by looking at the value of x = 1.03 in the z table which has an area of 0.8485.</em>
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Hence, the probability that a Niffler can hold more than 32 pounds of shiny objects in their pouch is 0.1515.