Sidneys made $38 more than 3 times Casey’s weekly salary. If x represents Casey’s weekly salary , write an expression for sidney
1 answer:
y=3x+38 is the expression for Sidney's weekly salary.
Step-by-step explanation:
Given,
Casey's weekly salary = x
Let,
y be the weekly salary of Sidney's.
According to given statement;
Sidney makes $38 more than 3 times Casey's weekly salary.
Sidney's weekly salary = 3 times Casey's weekly salary + $38
y=3x+38 is the expression for Sidney's weekly salary.
Keywords: variable, addition
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Area of pool edge = Area of big rectangle - Area of the pool
Area of pool edge = Area of the pool = 40 × 60 = 2400 ft²
2400 = Area of big rectangle - 2400
Area of big rectangle = 2400 + 2400
Area of big rectangle = 4800
Length × width = 4800
From the diagram, we need the length to be [x + x] more than the length of the pool, where x is the distance from the pool edge to the patio edge.
We also need the width of the big rectangle to be [[x + x] more than the width of the pool.
Length = 60 + 2x
Width = 40 + 2x
Length × Width = [60+2x] × [40+2x]
4800 = 2400 + 120x + 80x + 4x²
0 = 4x² + 200x - 2400
0 = 4[x² + 50x - 600]
0 = x² + 50x - 600
0 = [x - 60] [x + 10]
x - 60 = 0 OR x + 10 = 0
x = 60 OR x = -10
We can only use the positive value of x since the context is length
Hence, x = 60
Area of pool edge = Area of the pool = 40 × 60 = 2400 ft²
2400 = Area of big rectangle - 2400
Area of big rectangle = 2400 + 2400
Area of big rectangle = 4800
Length × width = 4800
From the diagram, we need the length to be [x + x] more than the length of the pool, where x is the distance from the pool edge to the patio edge.
We also need the width of the big rectangle to be [[x + x] more than the width of the pool.
Length = 60 + 2x
Width = 40 + 2x
Length × Width = [60+2x] × [40+2x]
4800 = 2400 + 120x + 80x + 4x²
0 = 4x² + 200x - 2400
0 = 4[x² + 50x - 600]
0 = x² + 50x - 600
0 = [x - 60] [x + 10]
x - 60 = 0 OR x + 10 = 0
x = 60 OR x = -10
We can only use the positive value of x since the context is length
Hence, x = 60
Answer:
52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem:
Normal probability distribution:
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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct
This probability is the pvalue of Z when X = 30393 + 339 = 30732 subtracted by the pvalue of Z when X = 30393 - 339 = 30054. So
X = 30732
By the Central Limit Theorem
has a pvalue of 0.7642.
X = 30054
has a pvalue of 0.2358
0.7642 - 0.2358 = 0.5284
52.84% probability that the sample mean would differ from the population mean by less than 339 miles in a sample of 37 tires if the manager is correct