The number of nails of a given length is normally distributed with a mean length of 5 in and a standard deviation of 0.03 find t
1 answer:
Answer:
19 nails
Step-by-step explanation:
Let's first determine the z-score by using the formula:
Where x=5.03, μ=5, σ=0.03 and so:
We can now use a z-score table to determine that 1.00 is synonymous with 0.8413 meaning 84.13%. This means that 84.13% of the nails are less than or equal to 5.03 inches long. Therefore, since we know 100% = 1 in decimals we can determine that the length greater than 5.03 inches is 1-0.8413=0.1587. This means that 15.87% of the 120 nails are greater than 5.03 inches long.
Finally, we can determine how many nails are greater than 5.03 by determining what is 15.87% of 120 which is:
And so 19 out of the 120 nails are greater than 5.03 inches long.
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Answer:
c is greater than or equal to -1.
Step-by-step explanation:
Subtract 3 from both sides, divide by 5.
I have attached the work to your problem below.
I hope this helps.
To answer this question, we need to recall that: "the diagonals of a rectangle bisect each other"
Thus, if we assign the point of intersection of the two diagonals in the rectangle as point O, we can say that the triangle OQR is an "isosceles triangle". Note that this is because the lengths OR and OQ are equal since we know that: "the diagonals of a rectangle bisect each other". See the below diagram for clarity.
Now, we have to recall that:
- the base angles of any isosceles triangle are equal. This is a fact, and this means that the angles
- also the sum of all the angles in any triangle is 180 degrees
Now, considering the isosceles triangle OQR, we have that:
Now, since the figure already shows that angle Now, since we have established that the base angles
we can now solve the above equation for m<2 as follows:
Therefore, the correct answer is: option D
