Answer:
Step-by-step explanation:
Suppose you have to use right-triangle trigonometry to find the apothem of a regular polygon. Which is greater, the apothem or t
1 answer:
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Answer:
- zeros: x = -3, -1, +2.
- end behavior: as x approaches -∞, f(x) approaches -∞.
Step-by-step explanation:
I like to use a graphing calculator for finding the zeros of higher order polynomials. The attachment shows them to be at x = -3, -1, +2.
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The zeros can also be found by trial and error, trying the choices offered by the rational root theorem: ±1, ±2, ±3, ±6. It is easiest to try ±1. Doing so shows that -1 is a root, and the residual quadratic is ...
x² +x -6
which factors as (x -2)(x +3), so telling you the remaining roots are -3 and +2.
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For any odd-degree polynomial with a positive leading coefficient, the sign of the function will match the sign of x when the magnitude of x gets large. Thus as x approaches negative infinity, so does f(x).
Answer:
1a) p-hat=0.38
1b) P=0.08
1c) The null hypothesis is not rejected
2a) p-hat=0.64
2b) P=0.0027
2c) The null hypothesis is rejected
3a) p-hat=0.55
3b) P=0.153
3c) The null hypothesis is not rejected
Step-by-step explanation:
(1) H0: p = 0.3 vs Ha: p ≠ 0.3. In their survey, they had a count of 38 using a sample size n=100.
1a) The p-hat is p-hat=38/100=0.38.
1b) The standard deviation is
The sample size is n=100.
The z-value is:
As it is a two-sided test, the p-value considers both tails of the distribution.
The p-value for this |z|=1.74 is P=0.08.
1c) The null hypothesis is not rejected.
(2) H0: p = 0.7 vs Ha: p ≠ 0.7. In their survey, they had a count of 320 using a sample size n=500.
2a) The p-hat is p-hat=320/500=0.64.
2b) The standard deviation is
The sample size is n=500.
The z-value is:
As it is a two-sided test, the p-value considers both tails of the distribution.
The p-value for this |z|=3 is P=0.0027.
2c) The null hypothesis is rejected.
(3) H0: p = 0.6 vs Ha: p < 0.6. In their survey, they had a count of 110 using a sample size n=200.
2a) The p-hat is p-hat=110/200=0.55.
2b) The standard deviation is
The sample size is n=200.
The z-value is:
As it is a two-sided test, the p-value considers both tails of the distribution.
The p-value for this |z|=1.43 is P=0.153.
2c) The null hypothesis is not rejected.