Answer:
k = 10
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
∠ZYM is an exterior angle and
∠YZX and ∠ZXY are the 2 opposite interior angles, hence
4k + 5 + 6k + 10 = 115
10k + 15 = 115 ( subtract 15 from both sides )
10k = 100 ( divide both sides by 10 )
k = 10
<h3>
Answer: Choice A</h3>
2 models divided into 100 parts. Left: 68 are shaded gray. Right: 68 are shaded gray.
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Explanation:
Consider the problem of 0.68 of 1, in other words 0.68*1 or simply 0.68
The number 0.68 is 68/100 or 68 over 100. We can have a 10 by 10 grid of tiny squares. Shade in 68 of them to represent 0.68 aka 68 hundredths.
So you'd have 6 full rows shaded (to account for 0.60 so far) and then an additional 8 squares in the seventh row (adding on 0.08 to get 0.60+0.08 = 0.68)
All of this is for one square. Double this process and you'd get 0.68*2 to represent the value 1.36
In total, 2*68 = 136 squares are shaded out of 2*100 = 200 squares total.
A) maximum mean weight of passengers = <span>load limit ÷ number of passengers
</span><span>
maximum mean weight of passengers = 3750 </span>÷ 25 = <span>150lb
</span>B) First, find the z-score:
z = (value - mean) / stdev
= (150 - 199) / 41
= -1.20
We need to find P(z > -1.20) = 1 - P(z < -1.20)
Now, look at a standard normal table to find <span>P(z < -1.20) = 0.11507, therefore:
</span>P(z > -1.20) = 1 - <span>0.11507 = 0.8849
Hence, <span>the probability that the mean weight of 25 randomly selected skiers exceeds 150lb is about 88.5%</span> </span>
C) With only 20 passengers, the new maximum mean weight of passengers = 3750 ÷ 20 = <span>187.5lb
Let's repeat the steps of point B)
z = (187.5 - 199) / 41
= -0.29
P(z > -0.29) = 1 - P(z < -0.29) = 1 - 0.3859 = 0.6141
</span>Hence, <span>the probability that the mean weight of 20 randomly selected skiers exceeds 187.5lb is about 61.4%
D) The mean weight of skiers is 199lb, therefore:
number</span> of passengers = <span>load limit ÷ <span>mean weight of passengers
= 3750 </span></span><span>÷ 199
= 18.8
The new capacity of 20 skiers is safer than 25 skiers, but we cannot consider it safe enough, since the maximum capacity should be of 18 skiers.</span>
Answer:
No
Step-by-step explanation:
15+ 4 1/2 + 6 3/4 = 26 1/4 in. and that is just 3 3/4 in. less 2 1/2 feet/ 30 in.
Answer:
Step-by-step explanation:
because you are finding the total they both had in September, you add. 12 + 9 = 21
