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3 years ago

What is x and what's m<M?

Mathematics

1 answer:

sweet [91]3 years ago

5 0

Use the property that angles sum up to 360 degrees.

Also use property that <M = <R and <A = <P.

That gives the following equation:

m<R + m<A + m<M + m<P = 360

6x+5 + 9x+25 + 6x+5 + 9x+25 = 360

30x + 60 = 360

x = 10

Answer:

x = 10

m<M = 6x+5 = 65 degrees

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The orthocenter is outside the triangle if it's an obtuse triangle.

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2 years ago

Read 2 more answers

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].

6 0

3 years ago

I need working out and answers for the following:

LenaWriter [7]

A. 4x - 3 = 2x + 7
4x - 2x = 7 + 3
2x = 10
x = 5

B. 2x + 6 = 7x - 14
2x - 7x = - 14 - 6
-5x = -20
x = 4

C. 2( x + 3) = x - 4
2x + 6 = x - 4
2x - x = -4 - 6
x = -10

D.4 ( 5x - 2) = 2( 9x + 3)
20x - 8 = 18x + 6
20x - 18x = 6 + 8
2x = 14
x = 7

E.4x - 1/2 = x - 7
4x - x = -7 + 1/2
3x = (-14 + 1)/2
3x = -13/2
x = -13/6

F. 3x + 2 = 2x + 13/3
3x - 2x = 13/3 - 2
x = (13 - 6)/3
x = 7/3

Hope This Helps You!

4 0

3 years ago