Sally is selling two types of seashells by the seashore. She is selling large and small shells. She sells small shells for 2 dol
1 answer:
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Answer:
Range of F(x) = (-∞ ,72).
Step-by-step explanation:
Range of the function F(x) means the set of values which are taken by the function along its domain.
F(x) = 72 -
Since coefficient of is negative on the right side ,
Maximum value of F(x) will come at x = 0.
Which is, F(0) = 72.
Now, as x increases , F(x) decreases , when x will reach infinity ,
F(x) will be reaching negative of infinity .
Thus, F(x) is ranging from -∞ to 72 .
Range of F(x) = (-∞ ,72).
The equation of a parabola with a directrix at y = -3 and a focus at (5 , 3) is y = one twelfth (x - 5)² ⇒ 1st answer
Step-by-step explanation:
The form of the equation of the parabola is (x - h)² = 4p(y - k), where
- The vertex of the parabola is (h , k)
- The focus is (h , k + p)
- The directrix is at y = k - p
∵ The focus of the parabola is at (5 , 3)
- Compare it with the 2nd rule above
∴ h = 5
∴ k + p = 3 ⇒ (1)
∵ The directrix is at y = -3
- By using the 3rd rule above
∴ k - p = -3 ⇒ (2)
Solve the system of equations to find k and p
Add equations (1) and (2) to eliminate p
∴ 2k = 0
- Divide both sides by 2
∴ k = 0
- Substitute the value of k in equation (1) to find p
∵ 0 + p = 3
∴ p = 3
Substitute the values of h , k , and p in the form of the equation above
∵ (x - 5)² = 4(3)(y - 0)
∴ (x - 5)² = 12 y
- Divide both sides by 12
∴ (x - 5)² = y
- Switch the two sides
∴ y = (x - 5)²
The equation of a parabola with a directrix at y = -3 and a focus at (5 , 3) is y = (x - 5)²
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Answer:
Comparing the p value with a significance level for example we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't say that the population mean for the athletes is significantly lower than the population mean for non athletes.
Step-by-step explanation:
Data given and notation
represent the mean for athletes
represent the mean for non athletes
represent the sample standard deviation for athletes
represent the sample standard deviation for non athletes
sample size for the group 2
sample size for the group 2
Significance level provided
t would represent the statistic (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to check if the population mean for athletes is lower than the population mean for non athletes, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We don't have the population standard deviation's, we can apply a t test to compare means, 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 whether the means of two groups are equal to each other.
With the info given we can replace in formula (1) like this:
P value
We need to find first the degrees of freedom given by:
Since is a one left tailed test the p value would be:
Comparing the p value with a significance level for example we see that
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't say that the population mean for the athletes is significantly lower than the population mean for non athletes.