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sertanlavr [38]
3 years ago
15

The median of a set of three numbers is x. there at least three numbers in the set. Write an algebraic expression, in terms of x

, to represent the median of the new set of numbers obtained by
a. adding 1/8 to every number in the set

b. subtracting 9 1/4 from every number in the set

c. multiplying -5.8 to every number in the set and then adding 3 to the resulting numbers

d. dividing every number in the set by 0.5 and then subtracting 1 from the resulting numbers

e. adding 7.2 to the greatest number in the set

f. subtracting 4.2 from the least number in the set
Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
5 0
<span>The median of a set of three numbers is x. there at least three numbers in the set. Write an algebraic expression, in terms of x, to represent the median of the new set of numbers obtained by
a] </span><span>adding 1/8 to every number in the set
Let the numbers be w,x,y
adding 1/8 to the number we get:
(w+1/8),(x+1/8),(y+1/8)
the new median will be:
(x+1/8)

</span><span>b. subtracting 9 1/4 from every number in the set
Given our data set is w,x,y
adding 9 1/4 to each number we get:
(w+9 1/4),(x+9 1/4), (y+9 1/4)
thus the new median is:
(x+9 1/4)

c]</span><span>multiplying -5.8 to every number in the set and then adding 3 to the resulting numbers
Multiplying each number by -5.8 we get:
(-5.8w),(-5.8x),(-5.8y)
adding 3 to these numbers we get:
(-5.8w+3),(-5.8x+3),(-5.8y+3)
thus the new median is:
(-5.8x+3)

d]</span><span>dividing every number in the set by 0.5 and then subtracting 1 from the resulting numbers
dividing each number in our set by 0.5 we get:
(w/0.5),(x/0.5),(y/0.5)
this will give us:
(2w),(2x),(2y)
then subtracting 1 from the above we get:
(2w-1),(2x-1),(2y-1)
thus the median will be:
(2x-1)

</span><span>e. adding 7.2 to the greatest number in the set
from our set:
w.x.y
the greatest number is y, then adding 7.2 to the greatest numbers gives us:
y+7.2
thus new series is:
w,x,y+7.2
thus the median is:
x
</span>Conclusion
The median doesn't change<span>

</span><span>f. subtracting 4.2 from the least number in the set
</span>from our set w,x,y; subtracting 4.2 from the least number gives us:
w-4.2
the new set is:
w-4.2, x, y
thus the new median is x
Conclusion
The median doesn't change
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If IQ scores are normally distributed with a mean of 100 and a standard deviation of 5, what is the probability that a person se
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Answer:

2.28% probability that a person selected at random will have an IQ of 110 or higher

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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:

\mu = 100, \sigma = 5

What is the probability that a person selected at random will have an IQ of 110 or higher?

This is 1 subtracted by the pvalue of Z when X = 110. So

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2.28% probability that a person selected at random will have an IQ of 110 or higher

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A line passes through the point (1, - 6) and has a slope of 8. Write an equation in slope-intercept form for this line.
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Answer:

\boxed {\boxed {\sf y=8x-14}}

Step-by-step explanation:

We are asked to find the equation of a line in slope-intercept form. We are given a point and a slope, so we can use the point-slope formula.

y-y_1= m(x-x_1)

In this formula, m is the slope and (x₁, y₁) is the point the line passes through. The slope of the line is 8 and it passes through the point (1, -6). Therefore,

  • m= 8
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Substitute these values into the formula.

y- (-6) = 8(x-1)

Remember that 2 back to back subtraction signs are the same as an addition sign.

y+6=8(x-1)

The line must be in slope-intercept form or y=mx+b (m is the slope and b is the y-intercept. We must isolate the variable y on one side of the equation. First, distribute on the right side of the equation. Multiply each term inside the parentheses by 8.

y+6 = (8*x) + (8*-1)

y+6= (8x)+ (-8)

y+6=8x-8

6 is being added to y. The inverse operation of addition is subtraction, so we subtract 6 from both sides of the equation.

y+6-6=8x-8-6

y=8x-8-6

y= 8x-14

The equation of the line in slope-intercept form is <u>y=8x-14</u>. The slope is 8 and the y-intercept is -14.

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I used an online calculator to help me graph each of the functions.

The correct answer is option D

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