The point (5, -1) is solution of equation: y= 2x - 11
1 answer:
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Essentially, what we're looking at here are two alternate interior angles.
Wait. What? Alternate interior angles?
It sounds like some super fancy math jargon, but it's a fairly simple concept that I'll try my best to explain. First, let's look at lines L and M as two parallel lines, meaning that these two are lines with equal slopes, and will never intersect. See that line that goes in between the parallel lines L and M? That's called a transversal. It's basically a line that goes through two parallel lines.
Now we know that there's a transversal going through the parallel lines. So what? Well, there's a couple of special attributes to transversals. See the two angles, 7x-7 and 4x+14? As you can tell, these two angles alternate in the interior space between the transversal and the parallel lines.
Alternate interior angles are equal. There's a way to prove that they're equal, but I won't bore you with the specifics since that's not what the question's asking.
If the angles need to be equal for lines L and M to be parallel, we can make an equation that'll solve for x:
7x - 7 = 4x + 14
<u>Subtract 4x from both sides:</u>
7x - 4 x - 7 = 4x - 4x + 14
3x - 7 = 14
<u>Add 7 to both sides:</u>
3x - 7 + 7 = 14 + 7
3x = 21
<u>Divide both sides by 3 to completely isolate x:</u>
=
x = 7
And that's our answer! If you need me to explain anything any further, just ask!
- breezyツ
Answer:
(a) 1155.84
(b) 48.2%
(c) D
Step-by-step explanation:
The number of total responses is, <em>N</em> = 38,528.
(a)
It is provided that 3% answered with "a lot".
Compute the actual number of responses consisting of "a lot" as follows:
n (a lot) = N × P (a lot)
= 38528 × 0.03
= 1155.84
Thus, the actual number of responses consisting of "a lot" is 1155.84.
(b)
The number of responses consisting of "very little or none" is,
n (very little or none) = 18,566
Compute the percentage of responses consisted of "very little or none" as follows:
The percentage is: 0.482 × 100% = 48.2%.
Thus, the percentage of responses consisted of "very little or none" is 48.2%.
(c)
As the sample size increases the sample statistic value gets closer and closer to the actual population parameter value.
Thus, making the sample statistic an unbiased estimator of the population parameter.
And proving that the sample is a true representative of the population.
Thus, the correct option is (D).