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STALIN [3.7K]
3 years ago
9

A biologist studied the frequency of croaks for frogs from two different regions. From a random sample of 32 frogs located in th

e northern region, the mean number of croaks per hour was 21.3, and from a random sample of 38 frogs located in the southern region, the mean number of croaks per hour was 28.9. To estimate the difference in the mean number of croaks (southern minus northern), a 95 percent confidence interval was constructed from the samples. The interval was reported as (7.1, 8.1). Which of the following claims is supported by the interval?
A. All southern frogs croak more times per hour than do all northern frogs.
B. The northern frogs are likely to have a greater mean number of croaks per hour than the southern frogs.
C. The southern frogs are likely to have a greater mean number of croaks per hour than the northern frogs.
D. All frogs in the study have about the same number of croaks per hour.
E. The northern and southern frogs have the same mean number of croaks per hour.
Mathematics
1 answer:
ikadub [295]3 years ago
6 0

Answer:

C

Step-by-step explanation:

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Ryan created the two-way table below to describe his scoring in his soccer team’s wins and losses last season. Ryan’s Scoring in
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Answer: There is 40% of team's win that Ryan score a goal.

Step-by-step explanation:

Since we have given that

                              Team Won   Team lost

Ryan scored               6                   4

Did not score             9                   11

(by Ryan)

-------------------------------------------------------------------------

Total                          15                    15

Percentage of team's win that Ryan score a goal is given by

\dfrac{6}{15}\times 100\\\\=40\%

Hence, there is 40% of team's win that Ryan score a goal.

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HELP 40 POINTS
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Answer: the function g(x) has the smallest minimum y-value.


Explanation:


1) The function f(x) = 3x² + 12x + 16 is a parabola.


The vertex of the parabola is the minimum or maximum on the parabola.


If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.


The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.


When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).


Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.


Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).


Then the minimum value is 4 (when x = - 2).


2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>

The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.


When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2


Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

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