Solve this equation. Enter your answer in the box. 75 – 3.5y – 4y = 4y + 6
2 answers:
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When you think of the situation as a whole, you may notice that the lines in the problem actually form a triangle. First, the man driving 10 miles east forms a bottom leg of the triangle 10 units long. When he drives the 2 miles north, he adds another leg of 2 units length. When the place of work is connected to the starting position through a line, a third and final line is drawn which creates the triangle.
So, how can we find the direct distance from his place of work to his home? We can use the Pythagorean Theorem (, where
and
are the lengths of the legs of the triangle and
is the length of the hypotenuse). We know that the lengths of the legs are 10 and 2, which we can use in the formula, as shown below:
Now, we can solve this equation for :
The distance would be √104 miles, or approximately 10.2 miles.
Answer:
Step-by-step explanation:
Let x be the number of days you want to rent
The flat rate for car rental is $35 a day
As for insurance, $10 for 3 days or fewer, and $5 per day if more than 3 days that is
Combine this with the flat rental rate $35 a day and we have
Answer:
0.62% probability that a random sample of 16 bulbs will have an average life of less than 775 hours.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
Normal probability distribution.
Problems of normally distributed samples can be 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:
Find the probability that a random sample of 16 bulbs will have an average life of less than 775 hours.
This probability is the pvalue of Z when . So
has a pvalue of 0.0062. So there is a 0.62% probability that a random sample of 16 bulbs will have an average life of less than 775 hours.