Answer:
x = 33
<C = 81
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+ 2x+ 2x+15 = 180
Combine like terms
5x+15 = 180
Subtract 15 from each side
5x +15-15 =180-15
5x = 165
Divide by 5
5x/5 =165/5
x = 33
<C = 2x+15 = 2(33)+15 = 66+15 = 81
know your algebras and practice on expansion and factorisation
So,
If we visualize it, we can see a 3 x 3 square, with each unit representing 2 in.
If we do simple multiplication, we can figure out that each side is 6 in. long.
Fourfold of 6 in. reveals the perimeter: 24 in.
Answer:
Mean = 78.2
Standard deviation = 5.8
Step-by-step explanation:
Mathematically z-score;
= (x-mean)/SD
From the question;
12% of test scores were above 85
Thus;
P( x > 85) = 12%
P(x > 85) = 0.12
Now let’s get the z-score that has a probability of 0.12
This can be obtained from the standard normal distribution table and it is = 1.175
Thus;
1.175 = (85 - mean)/SD
let’s call the mean a and the SD b
1.175 = (85-a)/b
1.175b = 85 - a
a = 85 - 1.175b ••••••••(i)
Secondly 8% of scores were below 70
Let’s find the z-score corresponding to this proportion;
We use the standard normal distribution table as usual;
P( x < 70) = 0.08
z-score = -1.405
Thus;
-1.405 =( 70-a)/b
-1.405b = 70-a
a = 70 + 1.405b ••••••(ii)
Equate the two a
70 + 1.405b = 85 - 1.175b
85 -70 = 1.405b + 1.175b
15 = 2.58b
b = 15/2.58
b = 5.81
a = 70 + 1.405b
a = 70 + 1.405(5.81)
a = 78.16
So mean = 78.2 and Standard deviation is 5.8
Answer:
Step-by-step explanation:
The probability that the man gets x out of 20 correct follows a Binomial distribution, so the probability is calculated as:
Where n is the number of identical experiments and p is the probability of success. In this case n is 20.
Additionally, if he has no ESP the probability that he predict correctly is 0.5, because he is only guessing.
Then, the probability that he gets x out of 20 correct is equal to:
Therefore the probability that he would have done at least 17 out of 20 well if he had no ESP is:
Where:
So, 
is equal to:
