Answer:
4= 36 ÷ 9
Step-by-step explanation:
Answer:
- 20 taffy bags and 15 caramel candy bags
Step-by-step explanation:
<u>Given:</u>
- t = the number of taffy bags
- c = the number of caramel bags
- Number of taffy's are 5 more than caramel bags
- Taffy bags weigh 8 ounces and caramel bags weigh 16 ounces
- Total weight is 400 ounces
<u>Equations:</u>
- t = c + 5 (the difference in number of bags)
- 8t + 16c = 400 (the weight of the bags)
<u>Simplify the second equation by dividing all terms by 8:</u>
<u>Substitute t and solve for c:</u>
- c + 5 + 2c = 50
- 3c = 50 - 5
- 3c = 45
- c = 45/3
- c = 15
<u>Find the value of t:</u>
<u>Answer:</u>
- 20 taffy bags and 15 caramel candy bags
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>
