What is the value of x in the equation 3/2(4x – 1) – 3x = 5/4

A survey asked whether respondents favored or opposed the death penalty for people convicted of murder. Software shows the resul

pav-90 [236]

Answer:

95% confidence interval for the proportion of the adults who were opposed to the death penalty is (0.668, 0.704).

Step-by-step explanation:

We are given that a survey asked whether respondents favored or opposed the death penalty for people convicted of murder. Software shows the results below, where X refers to the number of the respondents who were in favor.

X = 1,790

N = 2,610

$\hat p$ = Sample proportion = X/N = 0.6858

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 = 0.6858

n = sample of respondents = 2,610

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

= [ $0.6858-1.96 \times {\sqrt{\frac{0.6858(1-0.6858)}{2610} }$ , $0.6858+1.96 \times {\sqrt{\frac{0.6858(1-0.6858)}{2610} }$ ]

= [0.668 , 0.704]

Therefore, 95% confidence interval for the population proportion of the adults is (0.668, 0.704).

3 0

3 years ago

2x+1=3(y-1) 6(2y-1)=5x Find values of x and y

olchik [2.2K]

Answer:

x= -10/3

y= -8/9

Step-by-step explanation:

2x+1=3(y−1);6(2y−1)=5x

Rewrite equations:

2x+1=3y−3;12y−6=5x

Step: Solve2x+1=3y−3for x:

2x+1=3y−3

2x+1+−1=3y−3+−1(Add -1 to both sides)

2x=3y−4

2x2=3y−42(Divide both sides by 2)

x=32y−2

Step: Substitute32y−2forxin12y−6=5x:

12y−6=5x

12y−6=5(32y−2)

12y−6=152y−10(Simplify both sides of the equation)

12y−6+−152y=152y−10+−152y(Add (-15)/2y to both sides)

92y−6=−10

92y−6+6=−10+6(Add 6 to both sides)

92y=−4

92y92=−492(Divide both sides by 9/2)

y=−89

Step: Substitute−89foryinx=32y−2:

x=32y−2

x=32(−89)−2

x=−103(Simplify both sides of the equation)

4 0

3 years ago

Read 2 more answers

Math help!!!!! thanks!!!!!!!

astraxan [27]

PEMDAS
We start with exponents.
4 x 4 is 16
12 divided by 3 is 4
4 times 5 is 20
20-16 is 4
4 is the answer.

5 0

3 years ago

Read 2 more answers

Find the dinmeter of a cirele with a circumference, C, of 73 cm. Help will give brainlist if get correct answer

Masteriza [31]

Answer:

73/3.14=23.2484076433

Step-by-step explanation:

Divide the circumference by π, or 3.14 for an estimation.

And that's it; you have the circle's diameter

6 0

2 years ago

Read 2 more answers

Can you guys help me with this please???

almond37 [142]

Answer:

y=-25x+225

Step-by-step explanation:

The slope is -25 and I think the y-intercept is 225.

Hope this helps.

5 0

3 years ago

What is the value of x in the equation 3/2(4x – 1) – 3x = 5/4 – (x + 2)?