Basically degrees of freedom are related to sample size (n-1). If the df increases, it also stands that the sample size is increasing; the graph of the t-distribution will have skinnier tails, pushing the critical value towards the mean.
Answer:
k = 10
Step-by-step explanation:
f(x) has been moved up 10 units to get g(x). So, k = 10
Answer:
24) x = 9.2
25) x = 30.8
Step-by-step explanation:
Given
See attachment for triangles
Solving (24)
To solve for x, we make use of cosine formula
i.e.
cos(40) = adjacent ÷ hypotenuse
So, we have:
cos(40) = x ÷ 12
Multiply both sides by 12
12 cos(40) = x
12 * 0.7660 = x
x = 9.2
Solving (25)
To solve for x, we make use of sine formula
i.e.
sin(25) = opposite ÷ hypotenuse
So, we have:
sin(25) = 13 ÷ x
Multiply both sides by
x sin(25) = 13
Divide by sin(25)
x = 13 ÷ sin(25)
Using a calculator
x = 30.8
Answer:
y=3/2x+11/2
Step-by-step explanation:
Hello! Sorry I just saw this
Anyways, let's continue
first, we need to find the equation of the line with the one that is (-2,-4) and (2,2)
first, we need to find the slope
the equation for slope is y2-y1/x2-x1
so let's label the points
x1=-2
y1=-4
x2=2
y2=2
now plug it in
2-(-4)/2-(-2)=6/4=3/2
now, let's turn it into a line
the point-slope form is y-y1=m(x-x1) (m=slope)
now, plug it in
y-(-4)=3/2(x-(-2))
simplify to
y+4=3/2(x+2)
turn into y=mx+b format
y+4=3/2x+3
subtract 4 on both sides
y=3/2x-1
Now for the line that is parallel.
Parallel lines have the same slopes, so you automatically know that the new line will be y=3/2x+b
To make sure (-3,1) is a solution to the point, put 1 as y and -3 as x
1=3/2(-3)+b
1=-9/2+b
add 9/2 on both sides
b=11/2 or 5.5
now, put it into the equation
y=3/2x+11/2
Hope this helps!
Answer:
x = 18
m = 21.2
p = 31.8
Step-by-step explanation:
The ratio of the left-side length to the bottom-side length is the same for both triangles:
x/11.2 = (x +27)/28
28x = 11.2(x +27) = 11.2x +302.4 . . . . . multiply by 11.2·28
16.8x = 302.4 . . . . . . . subtract 11.2x
x = 18 . . . . . . . . . . . . divide by 16.8
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The length of m can be found using the Pythagorean theorem. The sum of the squares of the legs is the square of the hypotenuse.
x^2 +11.2^2 = m^2
m = √(324 +125.44) = √449.44 = 21.2
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The length of p can also be found using the Pythagorean theorem. We prefer the proportion ...
p/27 = m/x
p = 27(21.2/18) = 31.8
The lengths of the unknown sides in the figure are ...
x = 18
m = 21.2
p = 31.8
