The difference of two numbers is 3. their sum is 13. find the numbers. creater the system and solve
1 answer:
Hey there :)
Let us translate the words into mathematics!
The difference of 2 numbers is 3
x - y = 3
The sum of 2 numbers is 13
x + y = 13
(eq. 1) x - y = 3
(eq.2) x + y = 13
eq. 1 + eq.2 ⇒ x - y = 3
+ x + y = 13 ( -y and +y cancels out )
2x = 16
x = 8
We have the value of x, simply substitute it in either of the formulae to find y
x - y = 3 , 8 - y = 3 , 8 - 3 = y , 5 = y
x + y = 13 , 13 - 8 = y , 5 = y
x = 8 , y = 5
Let us translate the words into mathematics!
The difference of 2 numbers is 3
x - y = 3
The sum of 2 numbers is 13
x + y = 13
(eq. 1) x - y = 3
(eq.2) x + y = 13
eq. 1 + eq.2 ⇒ x - y = 3
+ x + y = 13 ( -y and +y cancels out )
2x = 16
x = 8
We have the value of x, simply substitute it in either of the formulae to find y
x - y = 3 , 8 - y = 3 , 8 - 3 = y , 5 = y
x + y = 13 , 13 - 8 = y , 5 = y
x = 8 , y = 5
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Answer:
464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
It assumes the scores are normally distributed with a mean score of 75 and a standard deviation of 15.
This means that
How many students will score between 48 and 75?
First we find the proportion, which is the pvalue of Z when X = 75 subtracted by the pvalue of Z when X = 48. So
X = 75
has a p-value of 0.5
X = 48
has a p-value of 0.0359
1 - 0.0359 = 0.4641
Out of 1000:
0.4641*1000 = 464
464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.