Answer:
The base is 6.69 and the height is 6.02 (these are rounded to the nearest hundredth)
Step-by-step explanation:
soh-cah-toa
cos 42 = adjacent/9
adjacent = cos 42 x 9
adjacent = 6.69
sin 42 = opposite/9
opposite = sin 42 x 9
opposite = 6.02
a, b, c - sides of a triangle
Therefore:
a + b > c
a + c > b
b + c > a
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We have a = AB, b = 140mi, c = 100mi.
(1) a + b > c
AB + 140 > 100 <em>subtract 140 from both sides</em>
AB > -40 → AB > 0
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(2) a + c > b
AB + 100 > 140 <em>subtract 100 from both sides</em>
AB > 40
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(3) b + c > a → a < b + c
AB < 140 + 100
AB < 240
<h3>Answer: 40 < AB < 240</h3>
-5.8 < 2.9, so -5.8 is colder than 2.9
The "explanation" for the problem has a typo in it. There are 11 possible ice cream/yogurt flavors to choose from, regardless of whether any are low-fat, so the total number of ways of choosing any 2 from the selection is
In particular we want to count the number of ways of picking 1 ice cream and 1 yogurt flavor from the low-fat variety. There are 6 total choices that are not low-fat of which we choose 0, 3 choices of low-fat ice cream of which we choose 1, and 2 choices of low-fat yogurt of which we also choose 1. In terms of the binomial coefficient, this is
So the probability of getting such a combination is
.
Answer:
(a) The probability distribution is valid.
(b) The histogram is attached below.
(c) The mean is 33.47.
Step-by-step explanation:
(a)
A probability distribution is valid if:
- P (X = x) ≥ 0 for all values of <em>x</em>.
- ∑ P (X = x) = 1
From the probability distribution table it can be seen that the probability for all <em>x</em> is greater than 0.
Compute the sum of all probabilities as follow:
Thus, the probability distribution is valid.
(b)
The histogram is attached below.
(c)
The formula of mean of a discrete probability distribution is:
Compute the mean as follows:
Thus, the mean is 33.47.