We claim that the average weight of our "product" is 50 pounds, with a standard deviation of 2 pounds. We take a sample of 50 units, with a mean of 49.95 pounds and a standard deviation of 1.9999 pounds. What is a 95% prediction interval for the mean weight of the NEXT unit of production from our process? Use Z for ease of calculation.

Answer:

The range would decrease by 2

Step-by-step explanation:

The range is the difference between the highest number and the lowest number.

8 is the highest number and 1 is the lowest number here, so to find the range we would subtract 1 from 8.   8-1=7

But since 8 is being replaced by 6, we would subtract 1 from that instead.

6-1=5

The range decreased from 7 to 5, so it decreased by 2.

Hope that helps :)

Answer:

Step-by-step explanation:

Correlation describes how strongly pairs of given variablé are related. In this case, a detailed analysis that was carried out shows that the number of days missed by employees explains 60% of the variation in salary increases and also impressed upon this fact that employees who missed more days of work during the year received smaller raises than those who missed fewer days.

From the analysis, we can draw a conclusion that there is a correction between days missed and variation in salary increase and that this type of correction is a negative correlation where an increase in the number of days missed will lead to a decrease in the raises awarded to each employee.

Answer:26 2/3 feet

Step-by-step explanation:40/30 = 4/3

(26 2/3) / 20= 4/3

Answer:

1). [tex]P'(t) = (-9025t).e^{-0.05(53+0.95t^2)}[/tex]

2). (-435.36) dollars per week

Step-by-step explanation:

Weekly price decay of the product is represented by the function,

P(x) = [tex]95000.e^{-0.05x}[/tex]

And the price of the product changes over the period of 't' weeks is represented by,

x(t) = [tex]53+0.95t^2[/tex]

Function representing the rate of change in the profit with respect to the time will be represented by,

1). P'(t) = [tex]\frac{dP}{dx}.\frac{dx}{dt}[/tex]

Since, P(x) = [tex]95000.e^{-0.05x}[/tex]

P'(x) = [tex]95000\times (-0.05).e^{-0.05x}[/tex]

       = [tex](-4750).e^{-0.05x}[/tex]

Since, x(t) = 53 + 0.95t²

x'(t) = 1.9t

[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05x}\times (1.9t)[/tex]

By substituting x = 53 + 0.95t²

[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05(53+0.95t^2)}\times (1.9t)[/tex]

   P'(t) = [tex](-9025t).e^{-0.05(53+0.95t^2)}[/tex]

2). For t = 7 weeks,

P'(7) = [tex](-9025\times 7).e^{-0.05(53+0.95(7)^2)}[/tex]

       = [tex](-63175).e^{-4.9775}[/tex]

       = (-63175)(0.006891)

       = (-435.356) dollars per week

       ≈ (-435.36) dollars per week

Answer:

495.6 Euros

Step-by-step explanation:

If 1 pound equals 1.77 euros we can set up a proportion that;

[tex] \frac{1 pound}{1.77 euros} [/tex]

This proportion would be equal to the new amount;

[tex] \frac{280 pounds}{x euros} [/tex]

This means that

[tex] \frac{1 pound}{1.77 euros} = \frac{280 pounds}{ x euros} [/tex]

So;

[tex]280 pounds*1.77 euros / 1 pound[/tex]

Pounds cancel out; and so you have

[tex]280 * 1.77 euros[/tex]

giving you as performed on a calculator;

495.6 euros.

Hope this helps

Answer:

495.6 euros.

Step-by-step explanation:

For each pound we get 1.77 euros so:

it  is 280 * 1.77

= 495.6 euros.

Answer:

[tex]f(n) = 3f(n - 1) + 2f(n - 2)[/tex], if [tex]n \geq 2[/tex].

[tex]f(0) := 1[/tex],  [tex]f(1) := 3[/tex]

Step-by-step explanation:

Let [tex]f(n)[/tex] be the number of different tiling of [tex]1 \times n[/tex] floor. We can divide all possible tiling of floor [tex]1 \times n[/tex] into five not overlapping groups by color of last cell in the row (Blue, Red, Green, Orange, White).

The number of tiling [tex]1\times n[/tex] floor such that last cell in row is Blue is exactly f(n - 1) because we can throw away last [tex]1\times 1[/tex] tile and cover the rest [tex]1\times (n - 1)[/tex] cells in f(n - 1) ways. Similarly for Red and Green.

The number of tiling [tex]1\times n[/tex] floor such that last cell in row is Orange is exactly f(n - 2) because we can throw away last [tex]1\times 2[/tex] tile and cover the rest [tex]1\times (n - 2)[/tex] cells in f(n - 2) ways. Similarly for White.

So we get recurrent relation:

[tex]f(n) = 3f(n - 1) + 2f(n - 2)[/tex], if [tex]n \geq 2[/tex].

Now we should define the initial conditions.

[tex]f(0) := 1[/tex] because there is only one empty tiling.

[tex]f(1) := 3[/tex] because we can place Blue, Red or Green tile.

This completely define our recurent sequence because the depth of reccurence is 2.

Focus on Gamble B only. Multiply each winnings with their corresponding probabilities.

5100*0.50 = 2550

200*0.25 = 50

0*0.25 = 0

Add up those results: 2550+50+0 = 2600

The expected value of gamble B is $2600

Answer:

[tex]x=8[/tex]

[tex]y=24[/tex]

Step-by-step explanation:

3x+2y=72

If y=3x, we plug it into our equation and get:

3x+2×3x=72

3x+6x=72

9x=72

Divide both sides by 9

x=8

Answer:

x = 8

Step-by-step explanation:

3x + 2y = 72

Put y as (3x), and solve for x.

3x + 2(3x) = 72

Multiply 2(3x).

3x + 6x = 72

Add like terms 3x and 6x.

9x = 72

Divide 9 into both sides and isolate x.

x = 72/9

x = 8

The value of x is 8.

Answer:

[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]

And if we solve for a we got

[tex]a=14.4 +1.64*1.1=16.204[/tex]

The 95th percentile of the hip breadth of adult men is 16.2 inches.

Step-by-step explanation:

Let X the random variable that represent the hips breadths of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(14.4,1.1)[/tex]  

Where [tex]\mu=14.4[/tex] and [tex]\sigma=1.1[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.05[/tex]   (a)

[tex]P(X<a)=0.95[/tex]   (b)

We can find a quantile in the normal standard distribution who accumulates 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64

Using this value we can set up the following equation:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.95[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.95[/tex]

And we have:

[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]

And if we solve for a we got

[tex]a=14.4 +1.64*1.1=16.204[/tex]

The 95th percentile of the hip breadth of adult men is 16.2 inches.

Answer:

X<3

Step-by-step explanation:

4x-7 <5

4x < 5+7

4x < 12

X < 12/4

X < 3

Hope this helps..

Good Luck!

Answer:

24024 are the total number of ways of choosing 4 campsites out of 14.

Step-by-step explanation:

We are given that there are a total of 14 campsite out of which 4 campsites are to be chosen.

It is a simple example of selection problem.

Number of ways to choose the first campsite = 14

Now, one campsite is chosen, 13 campsites are left.

Therefore,

Number of ways to choose the second campsite = 13

Now, one more campsite is chosen, 12 campsites are left.

Therefore,

Number of ways to choose the third campsite = 12

Now, one more campsite is chosen, 11 campsites are left.

Therefore,

Number of ways to choose the fourth campsite = 11

So, total number of ways for choosing 4 campsites out of 14:

14 [tex]\times[/tex] 13 [tex]\times[/tex] 12 [tex]\times[/tex] 11 = 24024

Hence, answer is 24024.

Answer:

6 times.

Step-by-step explanation:

There is a 1/9 chance you pick the orange one. If you pick 54 times, you can expect to pick the orange marble 6 times.

Answer:

12.04

Step-by-step explanation:

Because the questions are true and false, that is, there are only two answer options, therefore, you have a success probability = 1/2 = 0.5

The standard deviation can be calculated as follows:

Standard Deviation = (n*p* (1-p)] ^ (1/2)

replacing we have:

SD = (290 * (1-0.5)] ^ (1/2) = 12.04

That is, the standard deviation is 12.04

Answer:

B. The intervals are centered around the sample mean GPA.

D. 95% of the intervals will contain the population mean in the long run.

Step-by-step explanation:

Confidence interval:

Depends on two things: The sample mean and the margin of error.

Lower end: Sample mean - margin of error

Upper end: Sample mean + margin of error

This means that the intervals are centered around the sample mean.

x% level:

x% of the intervals will contain the population mean in the long run.

So the true statements are:

B. The intervals are centered around the sample mean GPA.

D. 95% of the intervals will contain the population mean in the long run.

Answer:

All rhombi are parallelograms.

All squares are rhombi.

No trapezoid is a rectangle.

Answer:

The solutions of the equation in the interval [0,2π )

                    ={  [tex]\frac{\pi }{3}[/tex] }

General solution    θ = 2 nπ +α

                                θ =   [tex]2n\pi + \frac{\pi }{3}[/tex]

Step-by-step explanation:

Step(i):-

Given equation

                      cos x + sin x tan x = 2

               ⇒      [tex]cos x + sin x \frac{sin x}{cos x} = 2[/tex]

    On simplification , we get

              ⇒     [tex]\frac{sin^{2} x+ cos^2x}{cos x} = 2[/tex]

we know that trigonometry formula

[tex]sin^{2} x+ cos^2 x = 1[/tex]

now we get

             [tex]\frac{1}{cos x} = 2[/tex]

⇒         [tex]cos x = \frac{1}{2}[/tex]

⇒         cos x = cos 60°

Step(ii):-

General solution of cosθ = cosα

General solution    θ = 2 nπ +α

                               θ = 2 nπ +60°

                                θ =   [tex]2n\pi + \frac{\pi }{3}[/tex]

put n = 0 ⇒ θ = 60°

Put n =1 ⇒  θ = 360°+60°= 420°

.....and so on

The solutions of the equation in the interval  =[tex]\frac{\pi }{3}[/tex]

Final answer:-

The solutions of the equation in the interval [0,2π )

                    ={  [tex]\frac{\pi }{3}[/tex] }

General solution    θ = 2 nπ +α

                                θ =   [tex]2n\pi + \frac{\pi }{3}[/tex]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is:

X: height of seaweed.

X~N(μ;σ²)

μ= 10 cm

σ= 2 cm

You have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

P(X≤x)= 0.30

P(X≥x)= 0.70

Using the standard normal distribution you have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then using the formula Z= (X-μ)/σ translate the Z value to the corresponding X value.

P(Z≤z)= 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

z= -0.52

Now you have to clear the value of X:

Z= (X-μ)/σ

Z*σ= X-μ

X= (Z*σ)+μ

X= (-0.52*2)+10= 8.96

The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm

I hope this helps!

Answer:-0.53 and 9.72

Step-by-step explanation:

Answer:

Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = $ 1,264,000

Total start-up amount required, according to the details provided in the question = $1,264,000

Step-by-step explanation:

- Hay 1000 m² de espacio de almacén para construir a $ 42 por m². Dinero total requerido = 1000 × 42 = $ 42,000.

- Hay 6000 m² de espacio de acceso pavimentado para construir a $ 32 por m². Dinero total requerido = 6000 × 32 = $ 192,000.

- Compra de servidores de última generación para revisar los autobuses antes de comenzar sus recorridos. Costo total = $ 630,000.

- Se necesita comprar equipo especial para revisar los neumáticos. Costo = $ 400,000.

Monto total de inicio requerido, de acuerdo con los detalles proporcionados en la pregunta = 42000 + 192000 + 630000 + 400000 = $ 1,264,000

¡¡¡Espero que esto ayude!!!

English Translation

- There is 1000 m² of warehouse space to construct at $42 per m². Total required money = 1000 × 42 = $42,000

- There is 6000 m² of paved access space to construct at $32 per m². Total money required = 6000 × 32 = $192,000

- Purchase of state-of-the-art servers to check the buses before starting their tours. Total Cost = $630,000

- Purchase of special equipment is needed to check the tires. Cost = $400,000

Total start-up amount required, according to the details provided in the question = 42000 + 192000 + 630000 + 400000 = $1,264,000

Hope this Helps!!!

Answer:

The GDP gap is 9 % when there is 4.5 % unemployment.

Step-by-step explanation:

The statement shows a reverse relationship, where an increase in unemployment is following by decrease in potential GDP and can be translated into the following rate:

[tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex]

The GDP gap at a given increase in unemployment can be estimated by the following expression:

[tex]\frac{g}{u} = r[/tex]

[tex]g = r\cdot u[/tex]

Where:

[tex]r[/tex] - GDP gap-unemployment increase rate, dimensionless.

[tex]u[/tex] - Increase in unemployment rate, measured in percentage.

[tex]g[/tex] - GDP gap, measured in percentage.

If [tex]r = \frac{2\,\% \,GDP}{1\,\% unemp.}[/tex] and [tex]u = 4.5\,\%\,unemp.[/tex], the GDP gap is:

[tex]g = \left(\frac{2\,\%\,GDP}{1\,\%\,unemp.} \right)\cdot (4.5\,\%\,unemp.)[/tex]

[tex]g = 9\,\%\,GDP[/tex]

The GDP gap is 9 % when there is 4.5 % unemployment.

Answer: h = 9

Step-by-step explanation: A system of linear equations is consistent when it has at least one solution.

The matrix given is:

[tex]\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right][/tex]

Transform this matrix in a row-echelon form:

[tex]\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right][/tex]   [tex]R_{2} = 3R_{2}+R_{1}[/tex] [tex]\left[\begin{array}{ccc}-15&21&h\\0&0&-9+h\end{array}\right][/tex]

For this row-echelon form to have solutions:

-9 + h = 0

h = 9

For this system to be consistent: h = 9.

Answer:

a. 0.00783

b. 0.003876

Step-by-step explanation:

The computation is shown below;

a. The probability for the rivet to be defective is

Let us assume A is the event for seam failure and B would be event for rivets failure

Now

a) [tex]P[A] = 1 - P[B']^{30}[/tex]

[tex]0.21 = 1 - P[B']^{30}[/tex]

[tex]0.79 = P[B']^{30}[/tex]

[tex]P[B'] = 0.79^{\frac{1}{30}}[/tex]

P[B'] = 0.99217

P[B] = 1 - P[B']

= 0.00783

b) Now the Next one is

[tex]0.08 = 1 - P[B']^{25}[/tex]

[tex]0.89 =P[B']^{30}[/tex]

[tex]P[B'] = 0.89^{(\frac{1}{30})}[/tex]

= 0.99612

So,

P[B]  is

= 1 - P[B']

= 0.003876

We simply applied the above formula so that each one part could be calculated i.e the probabilities of the given question

Answer:

1. [tex]$ \mu = \$306,500 $[/tex]

2. [tex]\sigma = \$24,500[/tex]

3. [tex]n = 150[/tex]

4. [tex]$ \mu_{x}= \mu = \$306,500 $[/tex]

5. [tex]\sigma_x = \$ 2,000 \\\\[/tex]

Step-by-step explanation:

The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500.

From the above information, we know that,  

The population mean is

[tex]$ \mu = \$306,500 $[/tex]

The population standard deviation is

[tex]\sigma = \$24,500[/tex]

Suppose a random sample of 150 Americans is selected

[tex]n = 150[/tex]

Since the sample size is quite large then according to the central limit theorem, the sample mean is approximately normally distributed.

The sample mean would be the same as the population mean  that is

[tex]$ \mu_{x}= \mu = \$306,500 $[/tex]

The sample standard deviation is given by

[tex]\sigma_x = \frac{\sigma}{\sqrt{n} }[/tex]

Where [tex]\sigma[/tex] is the population standard deviation and n is the sample size.

[tex]\sigma_x = \frac{24,500}{\sqrt{150} } \\\\\sigma_x = \$ 2,000 \\\\[/tex]

Therefore, the required parameters are:

1. [tex]$ \mu = \$306,500 $[/tex]

2. [tex]\sigma = \$24,500[/tex]

3. [tex]n = 150[/tex]

4. [tex]$ \mu_{x}= \mu = \$306,500 $[/tex]

5. [tex]\sigma_x = \$ 2,000 \\\\[/tex]

Answer:

C. [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

You can use the formula to find the slope: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

(-1.5, 1.5) & (1.5, 0)

[tex]\frac{0-(-1.5)}{1.5-(-1.5)} =\\\\\frac{0+1.5}{1.5+1.5} =\\\\\frac{1.5}{3} =\\\\\frac{1}{2}[/tex]

The slope is [tex]\frac{1}{2}[/tex]

Answer:

2√21

Step-by-step explanation:

√81 is √4 times √21

Since √4 is a perfect square, √4 = 2

We are left with 2 times √21

2√21

Answer:

2√21

Step-by-step explanation:

√84

84 can be written as 4 × 21.

√(4 × 21)

Distribute the square root to both terms.

√4 × √21

4 is a perfect square.

2 × √21

Answer:

D. 32 sq. unit s

Step-by-step explanation:

4×18/2=32

Answer:

second side = s  first side = s +1  third side = s +2

39 feet = s + (s+1) + (s +2)

39 feet = 3s +3

36 feet = 3s

s = second side = 12 feet

first side = 13 feet

third side = 14 feet

Step-by-step explanation:

Answer:I believe that it is A but i am not fully sure

Step-by-step explanation:

Answer:

The nearest penny will be £9146.6

Step-by-step explanation:

A = P[1 + (r/n)]^(nt)

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

A = 8300 [ 1 + {1.4 / (7*100)}]^(7*7)

A = 8300 [ 1 + {0.002}]^(49)

A= 8300 [ 1.002 ]^(49)

A = 8300 [ 1.102 ]

A = £9146.6

What is Compound Interest (CI) ?

Compound Interest is all about adding interest to principal amount of loan , deposit .

Answer:

1.90.93

2.90.27

Step-by-step explanation:

Answer:

one above correct

Step-by-step explanation:

1st - 90.93

2nd-90.27