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:
The angle x is 32 degrees.
Step-by-step explanation:
As the angles make supplementary angle then
148+x=180
x=180-148
=32 degrees
Hence Prooved!
Answer:
Option B
Step-by-step explanation:
Option A
a² - b² = (a+ b)(a - b)
It's a polynomial identity.
Option B
a³ + b³ = (a - b)(a² - ab + b²)
It's not a polynomial identity.
Because the identity is,
a³ + b³ = (a + b)(a² - ab + b²)
Option C
a³ - b³ = (a - b)(a² + ab + b²)
It's a polynomial identity.
Option D
(a²+ b²)(c² + d²) = (ac - bd)² + (ad + bc)²
= a²c² - 2abcd + b²d² + a²d² + b²c² + 2abcd
= a²c² + b²c² + b²d² + a²d²
= c²(a² + b²) + d²(a² + b²)
= (a²+ b²)(c² + d²)
Therefore, it's a polynomial identity.
Option B will be the answer.
