Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute.a)What are the values of the mean and standard deviation after converting all pulse rates of women to z-scores using z=(x−μ)/σ?
b)The original pulse rates are measured with units of "beats per minute." What are the units of the corresponding z-scores?
Answers
Answer:
a) Mean=0 and Standard deviation=1
b) The z-scores have no units of measurement
Step-by-step explanation:
When we convert all the pulse rates of women to z-scores using the formula;
the mean is 0 and the standard deviation is 1.
The reason is that, the resulting distribution of z-scores forms a normal distribution which has a mean of 0 and a standard deviation of 1.
b) The z-scores are standardize scores and has no units of measurement. They give us how many standard deviations below or above the mean of the corresponding values.
Final answer:
Converting pulse rates into z-scores standardizes them into a standard normal distribution, yielding a mean of zero and a standard deviation of one. Z-scores are dimensionless and do not carry original physical units of measurement.
Explanation:
The question is asking about the properties of a z-score in the context of pulse rates of women. Here is the answer:
a) When converting to z-scores, regardless of the population parameters, the mean (μ) will always be 0 and standard deviation (σ) always 1. This conversion process is called standardization, which results in a standard normal distribution.
b) In the context of z-scores, the units are dimensionless. Because a z-score result is derived from a mathematical manipulation and not a direct measurement, it does not carry physical units like "beats per minute" in pulse rates. This characteristic enables us to make meaningful comparisons between different types of data.
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Elect the best answer for the question.1. What is the cube of 8? A. 512B. 64C. 2D. 24
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0.004045.
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A. 0
b. 0.5
c. 1
d. 50
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Answers
Answer:
For #9, the part of the expression that represents the quotient is the division problem in parenthesis. Specifically, "(45 ÷ 9)". I believe you only need the division symbol for this, though. Correct me if I'm wrong.
As for #10, the part of the expression representing the product of two factors is 5.2 being multiplied by the variable . This results in the the term
, with the coefficient being 5.2 and the variable being
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Answers
The Total number of hours required to repave the whole road is 36.
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
The Total length of the road that needs to be repaved = 3/5 miles
The Total length of the road which is repaved by the road crew per hour = 3/5 miles
The Total number of hours required to repave the whole road
= (Length of the road to be repaved)/(Length of the road repaved by the crew per hour)
= 3/4 divided by 1/48
= 3/4*48/1= 144/4
= 36
Hence, The Total number of hours required to repave the whole road is 36.
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Answer: 36 hours
Step-by-step explanation: Plz mark me brainlest
3/4 divided by 1/48
KCF
3/4*48/1= 144/4= 36
and the point P(-3,6) and then answer the following questions:
a. How would you find the line (B) that passes through point P and is perpendicular to line A? What is the equation of that line?
b. How would you find the length of the segment of line B from point P to line A?
c. How would you find the midpoint between point P and the intersection of line A and line B ?
Answers
Answer:
- y = -6/5x +12/5
- distance from P to A: (66√61)/61 ≈ 8.4504
- midpoint: (-18/61, 168/61) ≈ (-0.2951, 2.7541)
Step-by-step explanation:
a. The slope of the perpendicular line is the negative reciprocal of the slope of the given line, so is ...
m = -1/(5/6) = -6/5
Then the point-slope form of the desired line through (-3, 6) can be written as ...
y = m(x -h) +k . . . . . line with slope m through (h, k)
y = (-6/5)(x +3) +6
y = -6/5x +12/5 . . . equation of line B
__
b. The distance from point P to the intersection point (X) can be found from the formula for the distance from a point to a line.
When the line's equation is written in general form, ax+by+c=0, the distance from point (x, y) to the line is ...
d = |ax +by +c|/√(a² +b²)
The equation of line A can be written in general form as ...
y = 5/6x -5/2
6y = 5x -15
5x -6y -15 = 0
Then the distance from P to the line is ...
d = |5(-3) -6(6) -15|/√(5² +(-6)²) = 66/√61
The length of segment PX is (66√61)/61.
__
c. To find the midpoint, we need to know the point of intersection, X. We find that by solving the simultaneous equations ...
y = 5/6x -5/2
y = -6/5x +12/5
Equating y-values gives ...
5/6x -5/2 = -6/5x +12/5
Adding 6/5x +5/2 gives ...
x(5/6+6/5) = 12/5 +5/2
x(61/30) = 49/10
x = (49/10)(30/61) = 147/61
y = 5/6(147/61) -5/2 = -30/61
Then the point of intersection of the lines is X = (147/61, -30/61).
So, the midpoint of PX is ...
M = (P +X)/2
M = ((-3, 6) +(147/61, -30/61))/2
M = (-18/61, 168/61)
Final answer:
To find line B perpendicular to line A and pass through point P, calculate the negative reciprocal of line A's slope and use it in the line equation along with point P coordinates to find c. The segment length from point P to line A is calculated using the distance formula and involves finding the intersection point between lines A and B. The midpoint is calculated using the midpoint formula.
Explanation:
To answer this question, we need to understand that two lines are perpendicular if the product of their slopes is -1. Line A has a slope of 5/6. Therefore, the slope of line B, perpendicular to line A, is -6/5 (the negative reciprocal). The equation of a line is y = mx + c where m is the slope and c is the y-intercept. As line B passes through point P(-3,6), we can substitute these values into the line equation y = -6/5x + c to solve for c. This will give us the equation of line B.
To find the length of the segment from point P to Line A, we would first need to find the intersection point of Line A and B. Then use the distance formula, which is sqrt[(x2-x1)^2 + (y2-y1)^2].
The midpoint of two points, (x1,y1) and (x2,y2) is given by ((x1+x2)/2, (y1+y2)/2). This formula can be used to find the midpoint between point P and the intersection of line A and line B.
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