Find all complex solutions of 3x^2+4x+5=0 please guide!

A simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week

Levart [38]

Answer:

99% confidence interval for the population proportion of employed individuals is [0.104 , 0.224].

Step-by-step explanation:

We are given that a simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week.

Of the 250 employed individuals surveyed, 41 responded that they did work at home at least once per week.

Firstly, the pivotal quantity for 99% 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 individuals who work at home at least once per week = $\frac{41}{250}$ = 0.164

n = sample of individuals surveyed = 250

<em>Here for constructing 99% confidence interval we have used One-sample z proportion statistics.</em>

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5%

level of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

P( $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

<em>99% confidence interval for p</em> = [ $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.164-2.5758 \times {\sqrt{\frac{0.164(1-0.164)}{250} } }$ , $0.164+2.5758 \times {\sqrt{\frac{0.164(1-0.164)}{250} } }$ ]

= [0.104 , 0.224]

Therefore, 99% confidence interval for the population proportion of employed individuals who work at home at least once per week is [0.104 , 0.224].

7 0

2 years ago

The equation of a circle is (x + 3)2 + (y – 5)2 = 81. Determine the coordinates of the center of the circle and the length of th

Nataly_w [17]

Answer:

The center of the circle is (-3 , 5) and the length of the radius is 9 units

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- The center-radius form of the circle equation is in the format

(x – h)² + (y – k)² = r², where the center is the point (h, k) and

the radius is r.

- This form of the equation is helpful, because you can easily find

the center and the radius.

* Now lets solve the problem

- The equation is (x + 3)² + (y - 5)² = 81

- By comparing the two equations

∵ (x – h)² + (y – k)² = r² and (x + 3)² + (y - 5)² = 81

# x - h = x + 3

∴ -h = 3 ⇒ divide both sides by -1

∴ h = -3

# y - k = y - 5

∴ k = 5

# h and k are the coordinates of the center of the circle

∴ The center of the circle is (-3 , 5)

# r² = 81 ⇒ take √ for both sides

∴ r = 9

∴ The length of the radius = 9 units

* The center of the circle is (-3 , 5) and the length of the radius is 9 units

3 0

3 years ago

Check the picture of the necessary information

denis-greek [22]

The probability would be out of 100,
in this case if it refers to the data from 2009 it would be 39:61

4 0

2 years ago

5

sashaice [31]

Answer:

An 8-pack of frozen waffles costs $6.91. What is the unit price, rounded to the nearest cent?

Step-by-step explanation:

it is jashdsdhkjasdhjsd

6 0

3 years ago

HELPPPPPP PLEASEEEEee 34 + 2 ⋅ 5 = ____. (Input whole numbers only.) (1 point)

yaroslaw [1]

The answer is 44
10+34

5 0

3 years ago