The solution is (x, y) = (5, 16). My "work" is to make use of a graphing calculator.
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You can subtract the second equation from the first. This gives
... 0 = 3x -15
Then, divide by 3 and add 5.
... 0 = x - 5
... 5 = x
Substitute this value into either equation to find y.
... y = 2x +6
... y = 2·5 +6
... y = 16
The strategy to subtract the second equation from the first is based on the observation that both equations give expressions for y, and the x-coefficient in the first equation is the larger of the two x-coefficients. Thus, the subtraction we chose will eliminate y and give an x-term with a positive coefficient.
Answer:
16 cm
Step-by-step explanation:
We have to first find the radius of the circle.
The area of a sector is given as:
where α = central angle of the sector = 120°
r = radius of the circle
Therefore:
The diameter of a circle is twice its radius, therefore:
D = 2 * 8 = 16 cm
The diameter of the circle is 16 cm
Answer:
n = 20
Step-by-step explanation:
Cross multiplication would result in:
16 * n = 8 * 40
16n = 320
n = 320 / 16
n = 20
Therefore <u>the value of "n" in this proportion is 20.</u>
Hope this helps!
Answer:
Null hypothesis:
Alternative hypothesis:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so then we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.
Step-by-step explanation:
1) Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
2) State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean pressure is lower than the specificated value 7.3, the system of hypothesis are :
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-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".
3) Calculate the statistic
We can replace in formula (1) the info given like this:
4) P-value
Since is a one-side lower test the p value would given by:
5) Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean pressure for the automobile engines is not significantly less than 7.3 at 1% of significance.