A garden pond is 6 ft wide. The perimeter is 28 ft. What is the area
2 answers:
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X^2 + y^2 - x - 2*y = 0
To find both coordinates and radius we need to make this equation in circle form:
(x-a)^2 + (y-b)^2 = r^2
x^2 - 2*1/2*x + 1/4 - 1/4 + y^2 - 2*1*y + 1 - 1 = 0
Here we are adding and subtracting numbers in order to get square binomial.
(x - 1/2)^2 + (y-1)^2 = 5/4
coordinates of center are (1/2,1) and the radius is √
To find both coordinates and radius we need to make this equation in circle form:
(x-a)^2 + (y-b)^2 = r^2
x^2 - 2*1/2*x + 1/4 - 1/4 + y^2 - 2*1*y + 1 - 1 = 0
Here we are adding and subtracting numbers in order to get square binomial.
(x - 1/2)^2 + (y-1)^2 = 5/4
coordinates of center are (1/2,1) and the radius is √
Answer:
The actual SAT score is 2024.
The equivalent ACT score is 29.49.
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.
SAT score that is in the 95th percentile
Scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312, which means that
95th percentile is X when Z has a pvalue of 0.95, so X when Z = 1.645. The score is:
The actual SAT score is 2024.
Equivalent ACT score:
The equivalent ACT score is the 95th percentile of ACT scores.
Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1, which means that . So
The equivalent ACT score is 29.49.