Answer:
9.54 cm
Step-by-step explanation:
In triangle ABD, AD is the hypotenuse (longest side)
We know that according to Pythagoras theorem,
a^2+b^2=c^2
In the figure, c (10cm) and a (5cm) is given. So,
(5)^2 + b^2 = 100
25+b^2 = 100
b^2 = 75
So b is √75 = 8.66
Therefore BD is 8.66 cm
Now even BDC is a triangle
In it, the hypotenuse is missing but we know the value of other sides
so, in Pythagorean theorem,
a=4 (CD)
b=8.66 (BD)
c=x
Therefore,
(4)^2 + (8.66)^2 = x^2
16+74.99= x^2
x^2 = 90.99
x= 9.54 cm
Hope this helps!
Answer:
18.14% probability that you would get at least 12 questions correct.
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:

What is the probability that you would get at least 12 questions correct?
This is 1 subtracted by the pvalue of Z when X = 12. So



has a pvalue of 0.8186.
So there is a 1-0.8186 = 0.1814 = 18.14% probability that you would get at least 12 questions correct.
The quotient will be less that 34 because 78 divided by 34 is 2