Benton has an extension ladder than can only be used at a length of 10 feet, 15 feet, or 20 feet. He places the base of the ladd
er 6 feet from the wall and needs the top of the ladder to reach 8 feet.
Which ladder length would Benton need to use to reach this height on the wall?
A. 10 feet
B. 15 feet
C. None of these ladder lengths would reach this height.
Which ladder length would Benton need to use to reach this height on the wall?
A. 10 feet
B. 15 feet
C. None of these ladder lengths would reach this height.
1 answer:
A. 10 feet.
Think of it like this:
The wall is upright, it's 90° and it's 8 feet high. The distance from the bottom of the ladder to the bottom of the wall (along the ground, which is perpendicular to the wall) is 6 feet. When Benton places the base of the ladder 6 feet away from the wall and the top is resting at the top of the wall, it looks like a triangle, right?
Using pythagoras (this rule about right-angled triangles and stuff), we can already see that the two sides when simplified are 3:4. Because the 'triangle' is a right-angled triangle, the other side HAS to be 5 to complete the ratio. We just multiply it by 2 to get the correct ratio and that's your answer!
Think of it like this:
The wall is upright, it's 90° and it's 8 feet high. The distance from the bottom of the ladder to the bottom of the wall (along the ground, which is perpendicular to the wall) is 6 feet. When Benton places the base of the ladder 6 feet away from the wall and the top is resting at the top of the wall, it looks like a triangle, right?
Using pythagoras (this rule about right-angled triangles and stuff), we can already see that the two sides when simplified are 3:4. Because the 'triangle' is a right-angled triangle, the other side HAS to be 5 to complete the ratio. We just multiply it by 2 to get the correct ratio and that's your answer!
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Answer:
The bulbs should be replaced each 1060.5 days.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
How often should the bulbs be replaced so that no more than 1% burn out between replacement periods?
This is the first percentile, that is, the value of X when Z has a pvalue of 0.01. So X when Z = -2.325.
The bulbs should be replaced each 1060.5 days.