I need help with this please

Complete Question

In a sample of 80 light bulbs, the mean lifetime was 1217 hours with a standard deviation of 52 hours. a. Find the 95% confidence interval for the mean lifetime of this type of bulb. Justify the reason you chose the distribution used to construct the confidence interval. b. How many light bulbs must be sampled so that a 95% confidence interval will specify the mean lifetime to within [tex]\pm 8 \ hours[/tex]?

Answer:

a

    [tex]1206 <  \mu <  1228 [/tex]

The reason why a normal distribution was chosen is because the sample size is large enough that is  [tex]n > 30[/tex]  

b

   [tex]n =162 [/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n  =  80  

    The sample mean is  [tex]\= x = 1217[/tex]

     The standard deviation is  [tex]\sigma = 52[/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the normal distribution table the critical value  of   is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }[/tex]

=>    [tex]E = 1.96  *  \frac{ 52}{\sqrt{80} }[/tex]

=>    [tex]E = 11.395 [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x -E <  \mu <  \=x  +E[/tex]

=>   [tex]1217  -11.395 <  \mu <  1217  + 11.395[/tex]

=>   [tex]1206 <  \mu <  1228 [/tex]

Generally the sample size is mathematically represented as  

   [tex]n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2[/tex]

Here  E =  8

=>   [tex]n = [\frac{1.96  * 52 }{8} ] ^2[/tex]

=>   [tex]n =162 [/tex]

Which year group is this question from?

9514 1404 393

Answer:

  q = 58

Step-by-step explanation:

If the variation is inverse, when p is multiplied by 1/2, q will be multiplied by the inverse (reciprocal) of 1/2, which is 2/1 = 2.

When p = (1/2)(28), q = (2)(29) = 59

  q = 58

Answer:

0.23

Step-by-step explanation:

A formula I like to use to find the answer to these types of questions is

[tex]\frac{828}{3600} =\frac{x}{100}[/tex]

first, multiply 828×100=82,800

now divide 82800÷3600=23

so your answer is 23%=[tex]\frac{23}{100}[/tex]=0.23

Answer:

The solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].

Step-by-step explanation:

This second-order differential equation is homogeneous and linear of the form:

[tex]y'' + p\cdot y' +q\cdot y = 0[/tex] (1)

Where:

[tex]p[/tex] - First-order constant coefficient, dimensionless.

[tex]q[/tex] - Zero-order constant coefficient, dimensionless.

Whose characteristic polynomial is:

[tex]\lambda^{2}+p\cdot \lambda + q = 0[/tex] (2)

Where [tex]\lambda[/tex] contains the roots associated with the solution of the differential equation.

If we know that [tex]p = 6[/tex] and [tex]q = 9[/tex], the roots of the characteristic equation are, respectively:

[tex]\lambda^{2}+6\cdot \lambda + 9 = 0[/tex]

[tex](\lambda +3)\cdot (\lambda + 3) = 0[/tex]

Which means that [tex]\lambda_{1} = \lambda_{2} = 3[/tex] and the solution of the differential equation is of the form:

[tex]y(x) = e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)[/tex] (3)

Where [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are integration constants.

The first derivative of the equation above is:

[tex]y'(x) = 3\cdot e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)+c_{2}\cdot e^{3\cdot x}[/tex] (4)

Now, if we get that [tex]y(0) = 0[/tex] and [tex]y'(0) = 1[/tex], then the system of equations to the solved is:

[tex]c_{1} = 0[/tex] (3b)

[tex]c_{1}+c_{2} = 1[/tex] (4b)

The solution of this system is: [tex]c_{1} = 0[/tex], [tex]c_{2} = 1[/tex]. Therefore, the solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].

Answer:

Answers are below :)

Step-by-step explanation:

Q1- Divide both sides by 2

       x +12 = 20/2

Simplify 20/2 to 10

x + 12 =10

Subtract 12 from  both sides

x = 10 - 12

Simplify 10 - 12 to -2

x = -2

Q2. Add 2 to both sides

-4x = 10 + 2

Simplify 10 + 2 to 12

-4x=12

Divide both sides by -4

x = -12/4

Simplify 12/4 to 3

x = -3

Answer:

1. x=-2

2. X=-3

Step-by-step explanation:

1. 2(X+12)

  2x+24=20

  2x= -4

  x= -2

2. -4x-2=10

   -4x=12

   x=-3

Answer:

The answer is D.

Step-by-step explanation:

hope that helps

Answer: B' (x-4,y)

Step-by-step explanation: A figure which is moved from one location to antoher, without changing its size, shape or orientation, is a figure that went through translation.

So, when a point is translated, it means it changed its position.

Point B has x- and y-coordinates: B(x,y)

Point B' after being translated 4 units left means:

(x,y) → (x-4,y)

In other words, translated point B has coordinates

B(x-4, y)

Because moving left is saying the point is moving towards the negative "side" of the x-axis.

Answer Choices:

A) (-6, -1)

B) (6, -1)

C) (-6, 1)

Answer:

3x ≤ - 6

Step-by-step explanation:

let the number be x.

three times of it would be 3x

since 3x is at most -6, 3x must be less than or equal to -6.

hence, 3x ≤ -6

however, your option seems to not have any sign that has equal to so perhaps the nearest answer would be 3x < -6

Answer: The answer would be -5w-1

Step-by-step explanation:

Answer:

xcgvb                     vgjbnnnnnnnnnn vbjn bvh

Step-by-step explanation:

Answer:

0.98778

Step-by-step explanation:

When we are given a random number rod samples, we solve using z score formula

z = (x-μ)/σ/√n, where

x is the raw score = 102.1 mL

μ is the population mean = 101.5 milliliters (mL)

σ is the population standard deviation = 1.6.

n = 36

z = 102.1 - 101.5/1.6/√36

z = 2.25

Probability value from Z-Table:

P(x<102.1) = 0.98778

Hence, If 36 bottles are randomly selected, find the probability that the mean content is less than 102.1 mL is 0.98778

Answer:

Down payment is when you are trying to by something that is expensive up front like a house or a car.  It is usually paid in cash or equivalent at the time of finalizing the transaction. A loan of some sort is then required to finance the remainder of the payment.

Step-by-step explanation:

Answer:

tesrdxtcfygvoubucewh cwcs wuehcbwch w

Step-by-step explanation:

w edch dwjbsxchwej chwxc

Answer:

your answer is 7

Step-by-step explanation:

i may be wrong but i think that is the correct answer oh and Have a good thanksgiving everyone

Answer:

13.3 and 28.2 years

Step-by-step explanation:

from Khan academy

Answer:

9 weeks

Step-by-step explanation:

Answer:

0.0544

Step-by-step explanation:

From the given information;

The population proportion of the voters that would support the ballot measures in region A = 0.46

The random sample n = 400 voters

The required probability can therefore be computed as follows:

[tex]P[p_1>0.5] = P \bigg [ \dfrac{p_1-P_1}{\sqrt{\dfrac{P_1(1-P_1)}{n_1}}}>\dfrac{0.5-0.46}{\sqrt{\dfrac{0.46(1-0.46)}{400}}} \bigg][/tex]

[tex]P[p_1>0.5] = P \bigg [ Z>\dfrac{0.04}{\sqrt{\dfrac{0.46(0.54)}{400}}} \bigg][/tex]

[tex]P[p_1>0.5] = P \bigg [ Z>\dfrac{0.04}{\sqrt{6.21\times 10^{-4}}} \bigg][/tex]

[tex]P[p_1>0.5] = P \bigg [ Z>1.605 \bigg][/tex]

[tex]P[p_1>0.5] = 1- P [ Z<1.605 ][/tex]

Using the Excel Function =NORMDIST(1.605)

[tex]P[p_1>0.5] = 1- 0.9456[/tex]

[tex]P[p_1>0.5] =0.0544[/tex]

Therefore, the required probability = 0.0544

Answer:

y = 10 + 5x

Step-by-step explanation:

The question seem incomplete as the question requirement is not stated.

However, I'll solve for the equation and also plot the graph that illustrates the equation.

From the question, we have the following.

Base Amount = 10

Additional = 5 (weekly)

Let y represents her savings at any given weeks and x represents the number of weeks

y is calculated using

y = Base Amount + Additional * weeks

y = 10 + 5 * x

y = 10 + 5x

Next, it to plot the graph.

Take x = 0

y = 10 + 5 * 0

y = 10 + 0

y = 10

Take x = 3

y = 10 + 5 * 3

y = 10 + 15

y = 25

So, the graph must pass through

(0,10) and (3,25)

See attachment for graph.

The equation is y = 10 + 5x

Given that,

y = Base Amount + Additional ( weeks)

y = 10 + 5 (x)

y = 10 + 5x

learn more about the equation here: https://brainly.com/question/10821476

Answer:

we need explaining of this question

Answer: -22

Good Luck!

Answer:

65%

Step-by-step explanation:

Percentage = 1365/2100 *100

= 65%

Answer:

ŷ = 739.49X + 4876.43

y = 6755.98 - 388.24x + 125.30x²

y = 5428.98(1.09)^x

B.)

Linear:

ŷ = 739.49(9) + 4876.43

y = 11531.8

Year 2010 ; x = 10

y = 739.49(10) + 4876.43

y = 12271.3

Year 2011 ; x = 11

y = 739.49(11) + 4876.43

y = 13010.8

Quadratic :

Year 2009 ; x = 9

y = 6755.98 - 388.24(9) + 125.30(9^2)

y = 13411.1

Year 2010 ; x = 10

y = 6755.98 - 388.24(10) + 125.30(10^2)

y = 15403.6

Year 2011 ; x = 11

y = 6755.98 - 388.24(11) + 125.30(11^2)

y = 17646.6

Exponential:

Year 2009 ; x = 9

y = 5428.98(1.09)^9

y = 11791.2

Year 2010 ; x = 10

y = 5428.98(1.09)^10

y = 12852.4

Year 2011 ; x = 11

y = 5428.98(1.09)^11

y = 14009.1

Step-by-step explanation:

X :

1

2

3

4

5

6

7

8

Y:

6231

6574

7237

7211

7701

8581

10302

11796

Using the online linear regression calculator :

The linear trend :

ŷ = 739.49X + 4876.43

Where x = year

With 2006 representing 1 ; and so on

Slope = m = 739.49

Intercept (c) = 4876.43

y = predicted variable

The quadratic model:

General form:

y = A + Bx + Cx²

y = 6755.98 - 388.24x + 125.30x²

The exponential model:

y = AB^x

y = 5428.98(1.09)^x

B.) Next three years :

Year 2009 ; x = 9

Year 2010 ; x = 10

Year 2011 ; x = 11

Linear:

ŷ = 739.49(9) + 4876.43

y = 11531.8

Year 2010 ; x = 10

y = 739.49(10) + 4876.43

y = 12271.3

Year 2011 ; x = 11

y = 739.49(11) + 4876.43

y = 13010.8

Quadratic :

Year 2009 ; x = 9

y = 6755.98 - 388.24(9) + 125.30(9^2)

y = 13411.1

Year 2010 ; x = 10

y = 6755.98 - 388.24(10) + 125.30(10^2)

y = 15403.6

Year 2011 ; x = 11

y = 6755.98 - 388.24(11) + 125.30(11^2)

y = 17646.6

Exponential:

Year 2009 ; x = 9

y = 5428.98(1.09)^9

y = 11791.2

Year 2010 ; x = 10

y = 5428.98(1.09)^10

y = 12852.4

Year 2011 ; x = 11

y = 5428.98(1.09)^11

y = 14009.1

It is false that the expressions 4x − 2(5x − 1) and 6x + 2 are equivalent expressions

The expression is given as:

4x − 2(5x − 1)

Open the bracket

4x − 2(5x − 1) = 4x − 10x + 2

Evaluate the like terms

4x − 2(5x − 1) = − 6x + 2

− 6x + 2 and 6x + 2 are not equal expressions

Hence, 4x − 2(5x − 1) and 6x + 2 are not equivalent expressions

Read more about equivalent expressions at:

https://brainly.com/question/2972832

#SPJ2

Answer: D

Step-by-step explanation: Edge

Answer:

It is D i think.

Answer:

First multiply each brackets

90-60

30

Step-by-step explanation:

Answer:

9 x 3= 27 and 30 + 30=  60.. so 60- 27= 33, but if you want to do 27- 30.. it would be -33.

Step-by-step explanation:

Hope that answers your question!

Answer:

U = 71           L=60

Step-by-step explanation:

You subtract 180 from 109 to get the measure of U and then you add measure  U and E to get 120. Then, you subtract 180 from 120 to get measure L.

Answer:

(-3, -7)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)  

Step-by-step explanation:

Step 1: Define

Point-Slope Form:   y + 7 = 4/3(x + 3)

Step 2: Break function

Slope m = 4/3

Point (-3, -7)