y = x - 4
y = x² - 4x
Substitute the first equation into the second equation:
y = x² - 4x
x - 4 = x² - 4x [since y = x - 4, you can substitute (x - 4) for y] Add 4 on both sides
x = x² - 4x + 4 Subtract x on both sides to get the equation equal to 0
0 = x² - 5x + 4 Now you need to factor the equation. Find the factors of 4 that add or subtract to -5
Factors of 4: 1, 2, 4 [1 × 4, 2 × 2]
1 and 4 add up to 5
So instead of -5x:
0 = x² - 5x + 4
You can replace it with:
0 = x² - 1x - 4x + 4 [the sum of -1x and -4x is -5x] Now factor the equation separately. Factor out x from (x² - 1x), and factor out -4 from (-4x + 4)
0 = x(x - 1) - 4(x - 1) Factor out (x - 1)
0 = (x - 1)(x - 4) Now set (x-1) and (x-4) equal to 0
x - 1 = 0
x = 1
x - 4 = 0
x = 4
x = 4, x = 1 Now that you found x, plug it into one of the equations(does not matter which equation) to find y
y = x - 4
y = 4 - 4
y = 0 (4, 0)
y = x - 4
y = 1 - 4
y = -3 (1, -3)
Answer:
If we compare the p value and a significance level given for example we see that so we can conclude that we can reject the null hypothesis, and the the actual true mean is significantly different from 100.
Step-by-step explanation:
Data given and notation
represent the mean of seventh-grade girls in Midwest school district
represent the standard deviation for the sample
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
Calculate the P-value
First we need to calculate the degrees of freedom given by:
Since is a two tailed test the p value would be:
Conclusion
If we compare the p value and a significance level given for example we see that so we can conclude that we can reject the null hypothesis, and the the actual true mean is significantly different from 100.
The value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10. Option C
<h3>How to determine the value</h3>
It is important to note that for line TV to be parallel to line QS, the sides of the triangle must be divided equally.
Thus, we have
RT/TQ = RV/VS
RT = x + 10
TQ = x - 3
RV = x + 10
VS = x
Substitute the value
Cross multiply
(x+ 4) × x = (x + 10) × (x-3)
x² + 4x = x² -3x + 10x -30
Divide through by x²
4x = -3x + 10x - 30
Collect like terms
4x + 3x - 10x = - 30
-3x = -30
x = -30/ -3
x = 10
Thus, the value of 'x' that would make Line segment T V is parallel to Line segment Q S is 10 Option C
Learn more about triangles here:
https://brainly.in/question/1399334
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I think the answer is A.
So, when you are first given a set of data, order the numbers from least to greatest:
3, 4, 4, 5, 5, 5, 6, 6, 6, 8, 8, 8, 8, 9, 10, 10
Now we have to find the median...
3, 4, 4, 5, 5, 5, 6, (6, 6) 8, 8, 8, 8, 9, 10, 10
There is an even amount, so we have to add the 2 numbers in the middle and then divide by 2 to get the median. 6 + 6 = 12 /2 = 6
6 is the median. Now we have to find our minimum, maximum, and quartiles.
(3, 4, 4, (5, 5), 5, 6, 6) (6, 8, 8, (8, 8), 9, 10, 10)
Min= 3 , 1st quartile = 5, 2nd Quartile ( Median ) = 6 , 3rd Quartile = 8, Maximum = 10.
So you would plot the dots and connect the lines and make the box!
Hope this helps!