<h2>Firstly, we let for the number to be any number or letter.</h2>
- So let the number be (x)
Step-by-step explanation:
The above pictures shows working.
What is the final amount if 660 is increased by 1% followed by a further 1% increase? Give your answer rounded to 2 DP.
1 answer:
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Each of the 4 choices has been drawn step by step as follows:
the first transformation is drawn in light grey
the second transformation is drawn in dark grey
the third transformation is described as how it should be.
Choice I, picture I:
Rotate 180°, reflect over the x-axis, reflect over the line y=x
the last transformation should be : reflect with respect to the y-axis
Choice II, picture II:
Reflect over the x-axis, rotate 180°, reflect over the x-axis
the last transformation should be : reflect with respect to the y-axis
Choice III, picture III:
Rotate 180°, reflect over the y-axis, reflect over the line y=x
the last transformation should be : reflect with respect to the x-axis
Choice IV, picture IV:
Reflect over the y-axis, reflect over the x-axis, rotate 180°
the last transformation should be : rotate 180° CORRECT!
Answer: Reflect over the y-axis, reflect over the x-axis, rotate 180°
the first transformation is drawn in light grey
the second transformation is drawn in dark grey
the third transformation is described as how it should be.
Choice I, picture I:
Rotate 180°, reflect over the x-axis, reflect over the line y=x
the last transformation should be : reflect with respect to the y-axis
Choice II, picture II:
Reflect over the x-axis, rotate 180°, reflect over the x-axis
the last transformation should be : reflect with respect to the y-axis
Choice III, picture III:
Rotate 180°, reflect over the y-axis, reflect over the line y=x
the last transformation should be : reflect with respect to the x-axis
Choice IV, picture IV:
Reflect over the y-axis, reflect over the x-axis, rotate 180°
the last transformation should be : rotate 180° CORRECT!
Answer: Reflect over the y-axis, reflect over the x-axis, rotate 180°
Answer:
a) 68.26% probability that a student scores between 350 and 550
b) A score of 638(or higher).
c) The 60th percentile of test scores is 475.3.
d) The middle 30% of the test scores is between 411.5 and 488.5.
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:
a. What is the probability that a student scores between 350 and 550?
This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So
X = 550
has a pvalue of 0.8413
X = 350
has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
68.26% probability that a student scores between 350 and 550
b. If the upper 3% scholarship, what score must a student receive to get a scholarship?
100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88
A score of 638(or higher).
c. Find the 60th percentile of the test scores.
X when Z has a pvalue of 0.60. So it is X when Z = 0.253
The 60th percentile of test scores is 475.3.
d. Find the middle 30% of the test scores.
50 - (30/2) = 35th percentile
50 + (30/2) = 65th percentile.
35th percentile:
X when Z has a pvalue of 0.35. So X when Z = -0.385.
65th percentile:
X when Z has a pvalue of 0.35. So X when Z = 0.385.
The middle 30% of the test scores is between 411.5 and 488.5.