9514 1404 393
Answer:
B
Step-by-step explanation:
If you remove the variables and the equal signs from the equations and put brackets around what is left, you have the matrix that represents the equations:
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<em>Additional comment</em>
You need to be sure the variables are in the same order in both equations, as they are here. If there are equations with missing variables, you need to use a zero (0) coefficient in the missing variable's location.
Answer:
a. 0.93 b. 0.06 c. 0.05
Step-by-step explanation:
Probability is commonly known as the chance of success of a particular event. The probability of failure of the event can also be estimated.
(a) Probability of not having type 2 defect is:
= 1 - 0.07 = 0.93
(b) Probability of having type 1 and 2 defects is:
(c) probability pf having both type 1 and type 2 defects but not type 3 defect is:
Answer:
The rate of change or slope m = -50
Step-by-step explanation:
The slope-intercept form of the line equation
where
Given that there is $500 in Holly's bank account.
Thus, the y-intercept b = 500
It is stated that she takes out $50 from her account each month but doesn't put money back in.
It means the rate of change or slope is decreasing.
Thus, the rate of change or slope m = -50
<u>EXTRA BONUS!</u>
We can also determine the line equation by substituting m = -50 and b = 500 in the slope-intercept form
y = -50x + 500
Here:
The slope m = -50
The y-intercept = 500
Answer: About 72 feet
The more accurate value is roughly 71.7260397 feet (however, this value isn't fully exact either).
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Explanation:
Check out the diagram below. It's effectively the same diagram your teacher provided, but I've added points M and N. I've left out any unnecessary lines.
We're told that "(the length of cable from) E to the ground is 35 feet", so this is the red portion of cable that I've marked this as NE = 35, ie segment NE is 35 feet long. We're also told that NF = 40 feet, which is also shown in red.
The blue portions are chords of the circle. We're given one chord as LE = 80 ft, while the other chord JF is what we want to find out.
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What we need to find is the radius of this circle. Right away, it's not clear what the radius is; however, we can use the chord LE = 80 to help find it.
It turns out that the chord length c is connected to the radius r and central angle theta like so:
c = 2*r*sin(0.5*theta)
where theta must be in radian mode. The central angle subtends the arc that forms the chord in question.
If we started at point L, and counted the number of spaces to get to E while going clockwise, then we can see that there are 5 spaces
Those five spaces could be written as
Or you could mark it as such on the diagram for a visual reference. Overall, the circle has been cut into 12 equal slices. So going from L to E, going clockwise, will have us take up 5/12 of the full circle.
There are 2pi radians in a full circle, meaning the central angle LME is (5/12)*2pi = 5pi/6 radians.
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Plug theta = 5pi/6 and c = 80 into the formula mentioned. Isolate the radius.
c = 2*r*sin(0.5*theta)
80 = 2*r*sin(0.5*5pi/6)
80 = 2*r*sin(5pi/12)
80 = 2*r*0.9659258
80 = 2*0.9659258*r
80 = 1.9318516r
1.9318516r = 80
r = 80/1.931 8516
r = 41.4110483
The radius is approximate. The radius is in feet. Make sure your calculator is in radian mode.
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Now that we know the radius, we can determine how long chord JF is.
The central angle for chord JF is angle JMF
If we start at J and go to F, along the shorter path, then we've gone 4 spaces. This is 4/12 = 1/3 of the full circle. So the radian measure of angle JMF is (1/3)*2pi = 2pi/3 radians.
So,
c = 2*r*sin(0.5*theta)
c = 2*41.4110483*sin(0.5*2pi/3)
c = 71.7260397
Chord JF is roughly 71.7260397 feet long.
When rounding to the nearest foot, that's about 72 feet.
In quadrant II, will be negative. So