Adam is 4 years older than Tara. Five years ago the sum of their ages was 48. Use algebraic equations to represent the situation
1 answer:
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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.
Answer:
The translation statement is given by:
After the translation, the coordinates of vertex A is (-2,6).
Step-by-step explanation:
Given :
Vertices of a triangle ABC are:
A(−3, 4), B(4, −2), C(8, 3)
The triangle is translated 2 units up and 1 unit right.
To find the co-ordinates of point A after translation.
Translation rules.
For shift of units up, the translation is given as:
For shift of units right, the translation is given as:
So, it says the triangles is translated 2 units up and 1 unit right.
The translation statement is given by:
So, co-ordinates of point A after translation is given by :
After the translation, the coordinates of vertex A is (-2,6).