Answer:
40 degrees
Step-by-step explanation:
x and 40 (degrees) are "vertical angles" and are thus equal. So x = 40 degrees.
You first have to find the slope using the slope formula. That looks like this with our values:
. So the slope is -1/8. Use one of the points to first write the equation in y = mx + b form. We have an x and a y to use from one of the points and we also have the slope we just found. Filling in accordingly to solve for b gives us
and
. Adding 5/8 to both sides and getting a common denominator gives us that
. Writing our slope-intercept form we have
. Standard form for a line is Ax + By = C...no fractions allowed. So let's get rid of that 8 by multiplying each term by 8 to get 8y = -x - 11. Add x to both sides to get it into the correct form: x + 8y = -11
Answer:
The true statements are:
B. Interquartile ranges are not significantly impacted by outliers
C. Lower and upper quartiles are needed to find the interquartile range
E. The data values should be listed in order before trying to find the interquartile range
Step-by-step explanation:
The interquartile range is the difference between the first and third quartiles
Steps to find the interquartile range:
- Put the numbers in order
- Find the median Place parentheses around the numbers before and after the median
- Find Q1 and Q3 which are the medians of the data before and after the median of all data
- Subtract Q1 from Q3 to find the interquartile range
The interquartile range is not sensitive to outliers
Now let us find the true statements
A. Subtract the lowest and highest values to find the interquartile range ⇒ NOT true (<em>because the interquartial range is the difference between the lower and upper quartiles</em>)
B. Interquartile ranges are not significantly impacted by outliers ⇒ True <em>(because it does not depends on the smallest and largest data)</em>
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C. Lower and upper quartiles are needed to find the interquartile range ⇒ True <em>(because IQR = Q3 - Q2)</em>
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D. A small interquartile range means the data is spread far away from the median ⇒ NOT true (<em>because a small interquartile means data is not spread far away from the median</em>)
E. The data values should be listed in order before trying to find the interquartile range ⇒ True <em>(because we can find the interquartial range by finding the values of the upper and lower quartiles)</em>
So, parallel lines have the same slope, therefore a parallel line to 2x+12, will have the same slope as that one, so which is it?
so, we're really looking for the equation of a line whose slope is 2, and runs through -1,1.
![\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -1}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 2 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-1=2[x-(-1)] \\\\\\ y-1=2(x+1)\implies y-1=2x+2\implies y=2x+3](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%5C%5C%0A%25%20%20%20%28a%2Cb%29%0A%26%28%7B%7B%20-1%7D%7D%5Cquad%20%2C%26%7B%7B%201%7D%7D%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0A%25%20slope%20%20%3D%20m%0Aslope%20%3D%20%7B%7B%20m%7D%7D%3D%20%5Ccfrac%7Brise%7D%7Brun%7D%20%5Cimplies%202%0A%5C%5C%5C%5C%5C%5C%0A%25%20point-slope%20intercept%0A%5Cstackrel%7B%5Ctextit%7Bpoint-slope%20form%7D%7D%7By-%7B%7B%20y_1%7D%7D%3D%7B%7B%20m%7D%7D%28x-%7B%7B%20x_1%7D%7D%29%7D%5Cimplies%20y-1%3D2%5Bx-%28-1%29%5D%0A%5C%5C%5C%5C%5C%5C%0Ay-1%3D2%28x%2B1%29%5Cimplies%20y-1%3D2x%2B2%5Cimplies%20y%3D2x%2B3)
Answer: the term number is 38
Step-by-step explanation:
Let the number of the term be x
The value of the xth term = 488
In an arithmetic sequence, the terms differ by a common difference, d. This means that the difference between two consecutive terms, d is constant.
The formula for the nth term is
Tn = a + (n-1)d
Where
Tn = the nth term of the arithmetic sequence
a = the first term of the arithmetic sequence.
d = common difference.
From the information given,
a = 7
d = 13
We are looking for the xth term.
Tx = 488 = 7 + (x-1)13
488 = 7 + 13x - 13
Collecting like terms on the left hand side and right hand side of the equation,
13x = 488 -7 + 13
13x = 494
x = 38
The value of the 38th term is 488.
