Answer:
The length of KL is 409.2 foot
Step-by-step explanation:
Firstly, please check attachment for diagrammatic representation.
From the diagram, we can see that we are asked to calculate the value of the hypotenuse KL. Kindly note that the hypotenuse is the longest side of the right-angled triangle and it faces the angle 90 at all times.
Looking at what we have, we can see that we have adjacent and we are asked to calculate hypotenuse.
The trigonometric identity to use here is the Cosine
Cosine = length of adjacent/length of hypotenuse
cos 76 = 99/hypotenuse
hypotenuse = 99/cos76
hypotenuse = 99/0.24192
hypotenuse = 409.22 which is 409.2 to the nearest tenth of a foot
Answer:
a) 
b) 0.27778
Step-by-step explanation:
a)
There are 26 lowercase letters and 10 digits.
The character that must be a digit can be generated in 10 different ways and the others, in 26+10=36 different ways.
Since the password is 6 characters long, by the Fundamental Rule of Counting there are
10*36*36*36*36*36 = 604,661,760
In scientific notation this number can be expressed as
b)
By the <em>Fundamental Rule of Counting</em>, there would be
different combinations of 6 characters, but only the number computed in a) are valid combinations, so the probability of generating a valid password is
4d + 12 = 4(d + 3)
Basically, you just need to determine what 4d and 12 have in common. In this case, they both divide evenly by 4. Therefore 4 (d + 3) = 4d + 12 according to the distributive property.
Answer:
0.0111% probability that he answers at least 10 questions correctly
Step-by-step explanation:
For each question, there are only two outcomes. Either it is answered correctly, or it is not. The probability of a question being answered correctly is independent from other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
A multiple-choice examination has 15 questions, each with five answers, only one of which is correct.
This means that 
What is the probability that he answers at least 10 questions correctly?
0.0111% probability that he answers at least 10 questions correctly
Answer:
5/4
Step-by-step explanation:
5/6+5/12
or, {(5×2)+5}/12
or, 15/12 = 5/4
