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3 years ago

If f(x)=5x^2-3 and g(x)=x^2-4x-8, find (f-g)(x)

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

7 0

Answer:

4x^2 + 4x + 3.

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 5x^2 - 3 - (x^2 - 4x - 6)

= 5x^2 - 3 - x^2 + 4x + 6

= 4x^2 + 4x + 3.

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g In a certain rural county, a public health researcher spoke with 111 residents 65-years or older, and 28 of them had obtained

Marat540 [252]

Answer:

95% confidence interval for the percent of the 65-plus population that were getting the flu shot is [0.169 , 0.331].

Step-by-step explanation:

We are given that in a certain rural county, a public health researcher spoke with 111 residents 65-years or older, and 28 of them had obtained a flu shot.

Firstly, the Pivotal quantity for 95% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of residents 65-years or older who had obtained a flu shot = $\frac{28}{111}$ = 0.25

n = sample of residents 65-years or older = 111

p = population proportion of residents who were getting the flu shot

Here for constructing 95% confidence interval we have used One-sample z test for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.25-1.96 \times {\sqrt{\frac{0.25(1-0.25)}{111} } }$ , $0.25+1.96 \times {\sqrt{\frac{0.25(1-0.25)}{111} } }$ ]

= [0.169 , 0.331]

Therefore, 95% confidence interval for the percent of the 65-plus population that were getting the flu shot is [0.169 , 0.331].

7 0

3 years ago

What is 1/4 subtract 1 and 1/2 A. 1/2 B. 1/8 C. 3/4 D. 3/8

Lelu [443]

Answer:

-1 1/4

Step-by-step explanation:

1/4 - (1 1/2)

Get a common denominator

1/4 - 1 2/4

Take the larger number and subtract the smaller number and take the sign of the larger

1 2/4 - 1/4 = 1 1/4

The sign of the larger was negative

-1 1/4

3 0

3 years ago

Complete the general form of the equation of a sinusoidal function having an amplitude of 4, a period of π , and a phase shift t

alex41 [277]

Answer:

4 sin (2x - 4).

Step-by-step explanation:

The amplitude of sin x = 1 so our curve with amplitude 4 will have 4 sin x as part of the general form. To alter the period from 2pi to pi we multiply the x by 2, giving 4 sin 2x, Finally to get a phase shift of 2 to the right, we replace the x by x - 2.

Our formula is 4 sin (2(x - 2))

= 4 sin (2x - 4).

8 0

3 years ago

How do you 3rd root a number

zepelin [54]

Ex: 7^3=(7×7×7) --- 7×7=49×7=343

7 0

3 years ago

If she can skip 300 feet in 20 seconds how far could she skip per second

elena55 [62]

300/20 = 15

she can skip 15 feet per second

hope this helps