Answer:
Quadratic Formula
so
x = -5
and
x = 0.5
Step-by-step explanation:
Whenever you see a problem in this form, which you will see a lot of, you can try to factor it or use the "least squares" method or what have you, but those won't always work, unfortunately.
Fortunately, the quadratic formula will never fail you with quadratic expressions.
This is the Quadratic Formula
a is the the number on the variable with the exponent ^2
b is the number on the variable with no exponent
c is the third number
a and b cannot be equal to 0; c can be
Since we're looking for a number with an equation that has a square root in it, we're going to get two answers. These two answers come from the radical being separately added AND subtracted from the radical. It's basically two problems.
Plugging in our numbers to this equation gives us x values of -5 and 0.5. This will always work with polynomials with factors of ^2 in them.
If you have a TI-84 calculator or newer, there's a tool on it that will factor polynomials like this one for you just by giving it the numbers.
Well first of all you got to show your answer.
4x²-5=3x+4
4x²-3x-9=0
x=(3±√((-3)²-4*4*-9))/2*4
x=3±√(9+144) /8
x=(3±√153) /8
x=⅜±√153/8
Number of people that chose salad = 81
Percentage of people that chose salad over meat dish = 27%
Let us assume the number of people on the survey = x
Then
27% * x = 81
(27/100) * x = 81
27x = 81 * 100
27x = 8100
x = 8100/27
= 300
So a total of 300 people participated in the survey.I hope the procedure is clear enough for you to understand. Based on this method you can always solve similar types of problems without requiring any kind of help from outside.
Answer:
The actual SAT-M score marking the 98th percentile is 735.
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:
Find the actual SAT-M score marking the 98th percentile
This is X when Z has a pvalue of 0.98. So it is X when Z = 2.054. So