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3 years ago

Which equation, when solved, results in a different value of x than the other three?

Mathematics

2 answers:

aev [14]3 years ago

8 0

Solve each one to find that D is the answer

mart [117]3 years ago

3 0

Answer: The correct equation is (D) $8.3-0.6x=11.3.$

Step-by-step explanation: We are to select the equation that results in a different value of 'x' than the other three equations.

Let us solve the equations one by one.

(A). We have

$8.3=-0.6x+11.3\\\\\Rightarrow -0.6x=8.3-11.3\\\\\Rightarrow -0.6x=-3\\\\\Rightarrow x=\dfrac{3}{0.6}\\\\\Rightarrow x=5.$

(B) We have

$11.3=8.3+0.6x\\\\\Rightarrow 0.6x=11.3-8.3\\\\\Rightarrow 0.6x=3\\\\\Rightarrow x=\dfrac{3}{0.6}\\\\\Rightarrow x=5.$

(C) We have

$11.3-0.6x=8.3\\\\\Rightarrow 0.6x=11.3-8.3\\\\\Rightarrow 0.6x=3\\\\\Rightarrow x=\dfrac{3}{0.6}\\\\\Rightarrow x=5.$

(D) We have

$8.3-0.6x=11.3\\\\\Rightarrow -0.6x=11.3-8.3\\\\\Rightarrow -0.6x=3\\\\\Rightarrow x=-\dfrac{3}{0.6}\\\\\Rightarrow x=-5.$

Therefore, we see that the solution of the first three equations is x = 5 and the solution of the last equation is x = - 5.

Thus, the equation (D) results in a different value of 'x' when solved.Option (D) is correct.

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3 years ago

During the 7th examination of the Offspring cohort in the Framingham Heart Study, there were 1219 participants being treated for

AlexFokin [52]

Answer:

95% confidence interval for the proportion of the population which are on treatment is [0.3293 , 0.3607].

Step-by-step explanation:

We are given that during the 7th examination of the Offspring cohort in the Framing ham Heart Study, there were 1219 participants being treated for hypertension and 2,313 who were not on treatment.

The sample proportion is : $\hat p$ = x/n = 1219/3532 = 0.345

Firstly, the pivotal quantity for 95% confidence interval for the proportion of the population 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 = 0.345

n = sample of participants = 3532

p = population proportion

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

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

= [ $0.345-1.96 \times {\sqrt{\frac{0.345(1-0.345)}{3532} } }$ , $0.345+1.96 \times {\sqrt{\frac{0.345(1-0.345)}{3532} } }$ ]

= [0.3293 , 0.3607]

Hence, 95% confidence interval for the proportion of the population which are on treatment is [0.3293 , 0.3607].

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