Y=x+5 y=-2x-4 use substitution

When a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the environmen

gtnhenbr [62]

Answer:

(a) The point estimate of the proportion of the population who would answer yes is 0.295.

(b) The margin of error for a 95% confidence interval is 0.0259.

(c) 95% confidence interval for population proportion is [0.2691 , 0.3209].

Step-by-step explanation:

We are given that a survey asked subjects whether they would be willing to accept cuts in their standard of living to protect the environment, 352 of 1195 subjects said yes.

Let $\hat p$ = sample proportion of subjects who said yes.

(a) The point estimate of the proportion of the population who would answer yes = $\hat p$ = $\frac{X}{n}$

So, $\hat p = \frac{352}{1195}$ = 0.295

(b) Margin of error is given by = $Z_(_\frac{\alpha}{2}_) \times \text{Standard of Error}$

where, $\alpha$ = level of significance = 1 - 0.95 = 5%

At 5% level of significance, z table gives critical value of 1.96 for two-sided interval.

Standard of error = $\sqrt{\frac{\hat p(1-\hat p)}{n} }$ = $\sqrt{\frac{0.295(1-0.295)}{1195} }$ = 0.0132

So, Margin of error for 95% confidence interval = $1.96 \times 0.0132$

= 0.0259

(c) 95% confidence interval for population proportion is given by =

Point estimate $\pm$ Margin of error

⇒ 0.295 $\pm$ 0.0259

⇒ [0.295 - 0.0259 , 0.295 + 0.0259]

⇒ [0.2691 , 0.3209]

So, 95% confidence interval = [0.2691 , 0.3209]

The numbers in this interval represent that we are 95% confident that the population proportion will lie between 0.2691 and 0.3209.

(d) Assumptions needed for constructing a confidence interval are;

The data must be sampled randomly.
Sample values must be independent of each other.
Data must follow normal distribution.

8 0

3 years ago

Geometry help , only answer if your sure please. The question is in the attached

GuDViN [60]

Your answer would be D, The translation doesn't change the size or shape. Just location.

Hope this helped.

5 0

3 years ago

La suma de dos números es 135 y su diferencia 37, hallar los dos números

ExtremeBDS [4]

Answer- 86 and 49

Step-by-step explanation: 86+49=135

86-49=37

8 0

4 years ago

. A painter mixes two and a half pints of yellow paint with 4 pints of red paint to make a certain shade of orange paint. How ma

spin [16.1K]

Answer:

6

Step-by-step explanation:

A painter mixes 2 1/2 pints (2.5 pints) of yellow paint with 4 pints of red paint to make a certain shade of orange paint. The ratio of yellow paint to red paint is 2.5:4. In order to find the pints of yellow paint needed to be mixed with 10 pints of red paint, we will use conversion fractions.

10 red pints × (2.5 yellow pints/ 4 red pints) ≈ 6 pints (we round off to 1 significant figure)

5 0

3 years ago

I WILL GIVE BRAINLIST IF ALL ANSWERED CORRECTLY

pentagon [3]

Answer:

The length of the track is approximately 51.7 ft

The track has three sides of the square and the distance round a half of a complete circle

Step-by-step explanation:

The given track shape and measurements are;

The shape on the left side of the track = Square

The shape on the right side of the track = Half circle

The area of the square on the the left side of the track = 128 square feet

Therefore, from the area, A, of a square of side length, s, which is s × s, and letting the side length of the square = s, we have;

Area of the square portion of the track = s × s = s² = 128 ft²

Therefore, s = √(128 ft²) = 8·√(2) ft.

Whereby the side length of the square is bounded by the diameter of the half circle, we have;

Length of the diameter of the half circle = s = 8·√(2) ft.

The length of the perimeter of the half circle = π·D/2 = π × 8·√(2)/2 = π × 4·√(2) ≈ 17.77 ft.

The perimeter of the track, which is the length of the track is made up of the three sides of the square opposite to the half circle and the circumference of the half circle.

Therefore;

The length of the track = 3 × 8·√(2) ft + π × 4·√(2) ft. = 4·√2×(π+6) ≈ 51.7 ft

The length of the track ≈ 51.7 ft

Which gives;

The track has three sides of the square and the distance round a half of a complete circle.

4 0

3 years ago