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DENIUS [597]
3 years ago
11

Which statement is true ? Help plzzzz

Mathematics
1 answer:
Zarrin [17]3 years ago
7 0

Answer:

Correct choice is B

Step-by-step explanation:

The quadratic function g(x) has equation g(x)=ax^2+bx+c. Find values of a, b and c:

g(0)=2=a\cdot 0^2+b\cdot 0+c\Rightarrow c=2.

g(2)=3=a\cdot 2^2+b\cdot 2++2\Rightarrow 4a+2b=1.

g(4)=2=a\cdot 4^2+b\cdot 4+2\Rightarrow 16a+4b=0.

From the last equation b=-4a and 4a-8a=1,\\ \\a=-\dfrac{1}{4},\\ \\b=1.

The equation of the quadratic function g(x) is

g(x)=-\dfrac{1}{4}x^2+x+2. This quadratic function determines the parabola with vertex at point (3,2). Thus,

1. The maximal value of f(x) is 4 at x=2.

2. The maximal value of g(x) is 3 at x=2.

Thus, the maximal value of f(x) is greater than the maximal value of g(x). So option B is correct.

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3 years ago
A random sample of 4000 college students yielded 2250 who are in favor of banning Hawaiian shirts. Estimate the true proportion
Andreas93 [3]

Answer: (0.5496, 0.5754)

Step-by-step explanation:

The confidence interval for population proportion (p) is given by :-

\hat{p}\pm z*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}  , where \hat{p}= Sample proportion , n= sample size , z*= Critical z-value.

Let p be the  proportion of all college students who are in favor of banning Hawaiian shirt.

Given, A random sample of 4000 college students yielded 2250 who are in favor of banning Hawaiian shirts.

i.e. n=4000

\hat{p}=\dfrac{2250}{4000}=0.5625

z-value for 90% confidence level is 1.645

Now , 90% confidence interval for p would be :

0.5625\pm (1.645)(\sqrt{\dfrac{0.5625(1-0.5625)}{4000}})

=0.5625\pm (1.645)(\sqrt{0.0000615234375})\\\\=0.5625\pm (1.645)(0.00784368774876)\\\\\approx0.5625\pm0.0129\\\\=(0.5625-0.0129, \ 0.5625+0.0129)\\\\=(0.5496,\ 0.5754)

Hence, the required 90% interval = (0.5496, 0.5754)

6 0
3 years ago
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