Evaluate the expression when x=10, y=−2, and z=−5. −x2+6z/y=

A survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 sen

tatyana61 [14]

Answer:

96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

Step-by-step explanation:

We are given that a survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 seniors, 55 was the average desired retirement age, with a standard deviation of 3.4 years.

Firstly, the Pivotal quantity for 96% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average desired retirement age = 55 years

$\sigma$ = sample standard deviation = 3.4 years

n = sample of seniors = 101

$\mu$ = true mean retirement age of all college students

Here for constructing 96% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 96% confidence interval for the population mean, $\mu$ is ;

P(-2.114 < $t_1_0_0$ < 2.114) = 0.96 {As the critical value of t at 100 degree

of freedom are -2.114 & 2.114 with P = 2%}

P(-2.114 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.114) = 0.96

P( $-2.114 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.114 \times {\frac{s}{\sqrt{n} } }$ ) = 0.96

P( $\bar X-2.114 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.114 \times {\frac{s}{\sqrt{n} } }$ ) = 0.96

96% confidence interval for $\mu$ = [ $\bar X-2.114 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.114 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $55-2.114 \times {\frac{3.4}{\sqrt{101} } }$ , $55+2.114 \times {\frac{3.4}{\sqrt{101} } }$ ]

= [54.30 , 55.70]

Therefore, 96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

7 0

3 years ago

Twenty years ago a small town in Texas had a population of 10,000. The population has increased 8% each year

yan [13]

Answer:

A

Step-by-step explanation:

8% = .08 in decimal form

10 000 ( 1 + .08)^10 =

8 0

2 years ago

Solve the system of equations by graphing. x+y=3 y=2x−15

Stella [2.4K]

Hey!

Hope this helps...

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

x + y = 3

x = 3 - y

y = 2x - 15

y = 2(3 - y) - 15

y = 6 - 2y - 15

y = -2y - 9

3y = -9

y = -3

y = 2x - 15

-3 = 2x - 15

-2x = -12

x = 6

So...

The answer is: (6, -3)

4 0

3 years ago

Read 2 more answers

A cone is filled to a height of 3 inches with a liquid. The liquid is then poured into an empty cylinder with the same height an

Tasya [4]

Answer: 1 inch

Volume of the cylinder = πr²h

Volume of the cone = 1/3πr²h

If the radius are the same for both the cone and the cylinder, then the liquid will reach 1/3 of its height in the cylinder compared to the cone.

Height = 1/3 x 3 inches
Height = 1 inch

----------------------------------------------------------------------------------------
Answer: The height of the cylinder will be 1 inch.
----------------------------------------------------------------------------------------

3 0

3 years ago

Joe is the proud owner of Joe's Old Time BBQ Pit. He sells two types of BBQ sauce - Hot N' Spicy and Mild Mannered. Each gallon

oksano4ka [1.4K]

Answer:

P=$254

Step-by-step explanation:

let Hot N' Spicy be x

and Mild Mannered be y

the objective function is

38x+35y=P

the constraints are

1. tomato sauce

2x+3y=18--------1

2. hot peppers

2x+y=10--------2

solving 1 and 2 we have

using substitution method

2x+y=10--------2

y=10-2x

put y=10-2x in eqn 1

2x+3(10-2x)=18

2x+30-6x=18

2x-6x=18-30

-4x=-12

x=12/4

x=3

put x=3 in eqn 2 we have

2(3)+y=10

6+y=10

y=10-6

y=4

He should make 3 gallons of Hot N' Spicy

and 4 gallons Mild Mannered

38(3)+35(4)=P

114+140=P

254=P

P=$254

5 0

3 years ago