Answer:
Step-by-step explanation:
Since the number of pages that this new toner can print is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = the number of pages.
µ = mean
σ = standard deviation
From the information given,
µ = 2300 pages
σ = 150 pages
1)
the probability that this toner can print more than 2100 pages is expressed as
P(x > 2100) = 1 - P(x ≤ 2100)
For x = 2100,
z = (2100 - 2300)/150 = - 1.33
Looking at the normal distribution table, the probability corresponding to the z score is 0.092
P(x > 2100) = 1 - 0.092 = 0.908
2) P(x < 2200)
z = (x - µ)/σ/√n
n = 10
z = (2200 - 2300)/150/√10
z = - 100/47.43 = - 2.12
Looking at the normal distribution table, the probability corresponding to the z score is 0.017
P(x < 2200) = 0.017
3) for underperforming toners, the z score corresponding to the probability value of 3%(0.03) is
- 1.88
Therefore,
- 1.88 = (x - 2300)/150
150 × - 1.88 = x - 2300
- 288 = x - 2300
x = - 288 + 2300
x = 2018
The threshold should be
x < 2018 pages
Answer:
3:4
Step-by-step explanation:
there are 6 boys for every 8 girls, so the initial ratio is 6:8. however, this can be simplified by finding a number both 6 and 8 are evenly divisible by. In this case, you can divide the ratio by 2. 6/2 = 3 and 8/2 = 4, which is why the simplified form is 3:4
I'm not sure if this is the easiest way of doing this, but it surely work.
Let the base of the triangle be AB, and let CH be the height. Just for reference, we have
Moreover, let CH=y and BC=z
Now, AHC, CHB and ABC are all right triangles. If we write the pythagorean theorem for each of them, we have the following system
If we solve the first two equations for y squared, we have
And we can deduce
So that the third equation becomes
(we can't accept the negative root because negative lengths make no sense)
The answer to the first part is 172 plants per row with a remainder of 3 plants
The answer to the second part is, Martin knows that 7 goes into 700 100 times, 7 goes into 490 70 times, and 7 goes into 17 twice with a remainder of 3. He then adds 100 70 and 2 together to get 172 with a remainder of 3.
Answer:
No
Step-by-step explanation:
In order for three sides to make a triangle, if any two sides are added together, their sum should be greater than the third side:
=><u> 5 + 7 = 12 < 13 (DOES NOT check off the rule)</u>
=> 7 + 13 = 20 > 5 (Checks off the rule)
=> 5 + 13 = 18 > 7 (Checks off the rule)
As shown, even though 2 of the statements check off the rule the third one does not, this means that the sides don't make a triangle.
Hope this helps!
