How maby solutions does this have 8 + 2 (x - 6 ) = -2 +2x - 2
1 answer:
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Answer:
<em>She will be paid $1,350</em>
Step-by-step explanation:
<u>Linear Modeling</u>
Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.
The linear function can be expressed in the slope-intercept format:
y=mx+b, where m and b are constants.
The payments for a salesperson will be linearly modeled. There are two known points: When the sales were $16,000, the payment was $1,600. This makes the point (16,000;1,600).
We also know when the sales were $12,000, the payment was $1,400. The point is (12,000;1,400)
Let's use the points to find the values of m and b.
Using (16,000;1,600):
1,600=m*16,000+b
Using (12,000;1,400):
1,400=m*12,000+b
Subtracting both equations:
200=16,000m-12,000m
200=4,000m
Solving:
m=200/4,000=0.05
Using the first equation and the value of m:
1,600=0.05*16,000+b
1,600=800+b
Solving:
b=800
The equation is now complete:
y=0.05x+800
She sold $11,000 this month, so the payment is:
Y=550+800=1,350
She will be paid $1,350
Using the given information and what we know about linear equations, we will find the sketch below.
<h3>How to sketch a graph?</h3>Here we need to analyze each part separately.
In a coordinate axis where the y-axis represents distance and the x-axis represents time, we will have that:
First, we know that he rides for 30 minutes at a given speed, this will be represented with an increasing linear function.
Then he stops for 20 minutes, this is represented with a horizontal line.
Finally, he returns the motion, but slower than before, so the slope of this line will be smaller than the first one.
So for 0 to 30 we have an increasing linear equation, then for 30 to 50 we have a constant horizontal line, then for 50 to 80 we have another increasing linear equation
The sketch can be seen below.
If you want to learn more about linear equations, you can read:
Answer:
First of all, we need to determine the system of hypothesis, which must have a null and alternative hypothesis.
In all hypothesis proof procedure, we must work with the null one, rejecting it or accepting it. If we reject the null hypothesis, it will mean that our principal hypothesis is true.
According to the problem, the null hypothesis must be: ; because it says that 100 is the normal mean that is used.
The alternative hypothesis must be: ; because the question is asking if there's enough evidence to say that they children have a higher IQ than 100.
Then, we must calculate the P-value, which is the probability value that we are gonna use to accept or reject the null hypothesis. This P-value we can calculate it with the formula: ; where x is the sample mean, u is the hypothetical mean parameter, o is the sample deviation and n is the sample.
Extracting all values from the problem: x = 104.3; u = 100; o = 14 and n = 20.
Applying all values to the formula:
Then, this Z-value will give us the P-value by using the Z-table with the 0.05 level of significance. In table attached, we can see that the result is 0.9265. However, the P-value is 1 - 0.9265 = 0.735. We need to do this subtraction because, the result 0.9265 belong to the bigger area (as it's shown is the image in blue colour), and we need the smaller area, which belong to the 0.05 level of significance.
<em>In this problems, if the P-value is more than the level of significance, the null hypothesis is accepted. If the P-value is less than the level of significance the null hypothesis is rejected.</em>
Therefore, there is no enough evidence to say that the sample children have higher IQs, because the P-value is higher than the level of significance. (0.735>0.05).
