PLEASE HELP
1 answer:
F(x) = x³ - 18x² + 107x - 210
X - Intercept: f(x) = x³ - 18x² + 107x - 210
0 = x³ - 18x³ + 107x - 210
0 = x³ - 7x² - 11x² + 77x + 30x - 210
0 = x²(x) - x²(7) - 11x(x) + 11x(7) + 30(x) - 30(7)
0 = x²(x - 7) - 11x(x - 7) + 30(x - 7)
0 = (x² - 11x + 30)(x - 7)
0 = (x² - 6x - 5x + 30)(x - 7)
0 = (x(x) - x(6) - 5(x) + 5(6))(x - 7)
0 = (x(x - 6) - 5(x - 6))(x - 7)
0 = (x - 5)(x - 6)(x - 7)
0 = x - 5 or 0 = x - 6 or 0 = x - 7
+ 5 + 5 + 6 + 6 + 7 + 7
5 = x or 6 = x or 7 = x
Solution Set: {5, 6, 7}
Y - Intercept: f(x) = x³ - 18x² + 107x - 210
f(x) = (0)³ - 18(0)² + 108(0) - 210)
f(x) = 0 - 18(0) + 0 - 210
f(x) = 0 - 0 - 210
f(x) = 0 - 210
f(x) = -210
Shape of the Graph: Odd Degree Polynomials With a Positive Leading Coefficient
X - Intercept: f(x) = x³ - 18x² + 107x - 210
0 = x³ - 18x³ + 107x - 210
0 = x³ - 7x² - 11x² + 77x + 30x - 210
0 = x²(x) - x²(7) - 11x(x) + 11x(7) + 30(x) - 30(7)
0 = x²(x - 7) - 11x(x - 7) + 30(x - 7)
0 = (x² - 11x + 30)(x - 7)
0 = (x² - 6x - 5x + 30)(x - 7)
0 = (x(x) - x(6) - 5(x) + 5(6))(x - 7)
0 = (x(x - 6) - 5(x - 6))(x - 7)
0 = (x - 5)(x - 6)(x - 7)
0 = x - 5 or 0 = x - 6 or 0 = x - 7
+ 5 + 5 + 6 + 6 + 7 + 7
5 = x or 6 = x or 7 = x
Solution Set: {5, 6, 7}
Y - Intercept: f(x) = x³ - 18x² + 107x - 210
f(x) = (0)³ - 18(0)² + 108(0) - 210)
f(x) = 0 - 18(0) + 0 - 210
f(x) = 0 - 0 - 210
f(x) = 0 - 210
f(x) = -210
Shape of the Graph: Odd Degree Polynomials With a Positive Leading Coefficient
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Answer:
See below.
Step-by-step explanation:
Recall that the x-intercept is basically: (x,0).
In other words, we just need to substitute y with 0 in order to find the x-intercept.
Thus, we will have:
Looks like you did most of it.
The next step would be setting them equal to 105, like the problem suggests.
Then we can plug back in to find the numbers.
The three numbers are .
Hope this helps.
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Answer:
The 95% confidence interval of the proportion of all adults that have high blood pressure is 0.17059 < < 0.314695
Step-by-step explanation:
The confidence interval for a proportion is given by the following formula;
Where:
x = 33
n = 136
= x/n = 33/136 = 0.243
z value for 95% confidence is 1.96
Plugging in the values, we have;
Which gives;
0.17059 < < 0.314695
Hence the 95% confidence interval of the proportion of all adults that have high blood pressure = 0.17059 < < 0.314695
From the above we have;
23.2 < x < 42.798
Since we are dealing with people, we round down as follows;
23 < x < 42.