Answer:
0.13% of students have scored less than 45 points
Step-by-step explanation:
Problems of normally distributed samples can be 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:
About what percent of students have scored less than 45 points?
This is the pvalue of Z when X = 45. So
has a pvalue of 0.0013
0.13% of students have scored less than 45 points
y = x^2 + 5x -3
y-x =2
Replace y in the second equation with the first one:
x^2 + 5x -3 - x = 2
Simplify by combining like terms:
x^2 + 4x -3 = 2
Subtract 2 from both sides:
x^2 + 4x -5 = 0
Fctor the polynomial:
(x-1) (x+5) = 0
Solve for both X's:
x = 1 and x = -5
Now replace x in the second equation with both value and solve for y:
y -1 =2, y = 3
y - -5 =2, y +5 = 2, y = -3
Now combine the sets of answers:
(1,3) and (-5,-3)
The rule of the function g (x) will be;
⇒ g (x) = - x + 3
What is mean by Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
g (x) is the indicated transformation of f (x).
The rule of f (x) is,
f (x) = - x + 5 ; horizontally translation 2 units left.
Now,
The rule of f (x) is,
f (x) = - x + 5 ; horizontally translation 2 units left.
Since, g (x) is the indicated transformation of f (x).
So, g (x) = f (x + 2)
Hence, We get;
g (x) = - (x + 2) + 5
= - x - 2 + 5
= - x + 3
Thus, The rule of the function g (x) will be;
⇒ g (x) = - x + 3
Learn more about the transformation visit:
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1) Factor out common terms in the first two terms, then in the last two terms
{x}^{3}(x+2)-2(x+2)
2) Factor out the common term x+2
(x+2)({x}^{3}-2)
Done!
Answer: 120
Step-by-step explanation:
3+2=5
Let x be the amount of money to be shared
Paul’s share which is (3/5)x is 60+ Quinn’s share which is (2/5)x
Therefore
(3/5)x= (2/5)x + 60
(3/5)x - (2/5)x= 60
(x/5)=60
Cross multiply
x= 60*5=300
It means that Quinn’s share is (2/5)(300)= 120
