Write the equation the line that has a slope of 2 and a y-intercept (0,-9) then graph.

Answer:

(a)   x follows a poisson distribution with parameter λ = 8 / hour

(b)   P( X = 5 ) = 0.09160

      P( X ≥ 5 ) = 0.9004

(c)   the expected value  of the number of nonconforming parts produced during a 120-min period = 16 nonconforming parts per 120 minutes

The standard deviation = 4

(d)   P(X ≥ 20) = 0.5297

      P( X ≤  10) = 0.0108

Step-by-step explanation:

Suppose nonconforming parts are produced with a rate = 8 / hour (i.e. on average, 8 nonconforming parts will be made during a production period of one hour).

(a)  If x denotes the number of nonconforming parts made during one hour, then : x follows a poisson distribution with parameter λ = 8 / hour

(b)

What is the probability that exactly 5 nonconforming parts are produced during a 1-hour period? What is the probability that at least 5 nonconforming parts are produced during a 1-hour period?

the probability that exactly 5 nonconforming parts are produced during a 1-hour period can  be computed as:

P( X = 5 ) = [tex]e^{- \lambda } \lambda^x /x![/tex]

P( X = 5 ) = [tex]e^{- 8 }(8)^5 /5![/tex]

P( X = 5 ) = 0.09160

the probability that at least 5 nonconforming parts are produced during a 1-hour period

P( X ≥ 5 ) = 1 -  P( X ≤ 4)

[tex]P( X \geq 5 ) = 1 - \sum \limits ^4_{x=0} e^{-\lambda} \lambda ^x/x![/tex]

[tex]P( X \geq 5 ) = 1 - (e^{-8} 8 ^4/4! + e^{-8} 8 ^3/3! + e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )[/tex]

[tex]P( X \geq 5 ) = 1 - 0.0996[/tex]

P( X ≥ 5 ) = 0.9004

c)  What are the expected value and standard deviation of the number of nonconforming parts produced during a 120-min period?

the expected value  of the number of nonconforming parts produced during a 120-min period [tex]\lambda = 8 \times \dfrac {120}{60}[/tex]

= 16 nonconforming parts per 120 minutes

The standard deviation = [tex]\lambda^{1/2}[/tex]

The standard deviation = [tex](16)^{1/2}[/tex]

The standard deviation = 4

(d) What is the probability that at least 20 nonconforming parts produced during a 2.5-hour period? That at most 10 nonconforming parts produced during this period?

During a 2.5 - hour period , the expected value = 8 × 2.5 = 20

As such, the probability  that at least 20  nonconforming parts produced during a 2.5-hour period is:

P(X ≥ 20) = 1 - P(X ≤ 19)

[tex]P( X \geq 20 ) = 1 - \sum \limits ^{19}_{x=0} e^{-\lambda} \lambda ^x/x![/tex]

[tex]P( X \geq 20 ) = 1 - (e^{-8} 8 ^{19}/19! + e^{-8} 8 ^{18}/{18}! + e^{-8} 8 ^{17}/17!+...+e^{-8} 8 ^2/2! +e^{-8} 8 ^1/1! + e^{-8} 8 ^0/0! )[/tex]

P(X ≥ 20) = 1 -  0.4703

P(X ≥ 20) = 0.5297

Probability that at most  10 nonconforming parts produced during this period is:

P( X ≤  10) = [tex]\sum \limits ^{10}_{x=0} e^{-\lambda} \lambda ^x/x![/tex]

[tex]P( X \leq 10) = e^{8} 8 ^{10}/{10}! + e^{8} 8 ^{9}/{9}! + e^{8} 8 ^{8}/{8}! + ...+ e^{8} 8 ^{2}/{2}!+ e^{8} 8 ^{1}/{1}! + e^{8} 8 ^{0}/{0}![/tex]

P( X ≤  10) = 0.0108

Following are the calculation to the given points:

For point a)

With parameter, x follows the poisson distribution is [tex]\lambda=\frac{8}{hour}[/tex]

For point b)

The probability that exactly 5 nonconforming parts are generated in a one-hour period.

[tex]\to P(X=5)=e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0916[/tex]

There is a good chance that at least 5 nonconforming parts exist.

[tex]\to P(X\geq 5) =1-P(X\leq 4)[/tex]

                 [tex]=1 -\sum_{x=0}^{4} \ e^{-\lambda } \frac{\lambda ^{x}}{x!} \\\\=1-0.0996\\\\=0.9004[/tex]

For point c)

Expected value for 120-minute period [tex]\lambda=8\times \frac{120}{60} =16[/tex] 120 minutes of nonconforming sections

[tex]\to \sigma ==(\lambda)^{\frac{1}{2} =(16)^{\frac{1}{2}} =4[/tex]

For point d)

Expected value for 2.5 hours

[tex]\to \lambda =8\times 2.5=20[/tex]

As a result, there is a good chance that at least 20 nonconforming items were manufactured.

[tex]\to P(X\geq 20)=1-P(X\leq 19)[/tex]

                   [tex]=1-\sum_{x=0}^{19}\ e^{-\lambda }\frac{\lambda^{x}}{x!}\\\\=1-0.4703\\\\=0.5297[/tex]

There is a chance that no more than 10 nonconforming parts were created.

[tex]\to P(X\leq 10)=\sum_{x=0}^{10}e^{-\lambda }\frac{\lambda ^{x}}{x!} =0.0108[/tex]

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Answer:

a. True

Step-by-step explanation:

This is because, since the sample mean equals the population means, the distribution of the sample means about the sample size would also be the distribution of the sample size distributed about the population mean.

This usually results in a normally distributed population for a sample size greater than 30.

So, if the sample size is greater than 30, the population mean and sample mean would have the same value and distribution.

Answer:

406.4

Step-by-step explanation:

When rounding you only look at the number you're rounding and the one before it. In this case it would be the 4 and 3 after the decimal since we're rounding to the nearest cent. If the numbers before the one you're rounding are 0-4 then you leave the number the same. If the numbers are between 5-9 then you add one to the number. Since the number before 4 is between 0-4 you leave it as 4. But if it was between 5-9 then you'd change the 4 to 5.

Answer:

y = 4/3x +4

Step-by-step explanation:

Answer:327412000

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

First we distribute

2x-4=6

isolate x

2x=10

divide both sides by 2

x=5

(plz give brianliest ty)

Answer:

X=5

Step-by-step explanation:

2x+(-4)=6

2x=6+4

2x=10

X=10/2

X=5

add 6 plus 33 then do x+1 then you divide

Step-by-step explanation:

Answer:

67

Step-by-step explanation:

Answer:

[tex]\Huge \boxed{-2.3, \ \frac{-1}{3} , \ \sqrt{3} , \ \sqrt{7} , \ 5.1}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

We will convert the values into decimals for simplicity.

[tex]\sqrt{7} = 2.64575131106...[/tex]

[tex]-2.3=-2.3[/tex]

[tex]\sqrt{3} = 1.73205080757...[/tex]

[tex]5.1=5.1[/tex]

[tex]\displaystyle \frac{-1}{3} =-0.333333333...[/tex]

Arranging from least to greatest:

[tex]\displaystyle -2.3, \ \frac{-1}{3} , \ \sqrt{3} , \ \sqrt{7} , \ 5.1[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

Line Segment

Step-by-step explanation:

Because the start on a line and end on a line.

Answer:

line segment

Step-by-step explanation:

Answer:

as we know, the integral of [tex]x^{n}[/tex] is [tex]\frac{x^{n+1} }{n+1}[/tex]

so, the integral of x.[tex]2^{x}[/tex] will be found as follows:

here, we will use a trick called 'integration by parts'

let x = u and [tex]2^{x}[/tex] = v

∫uv dx = u∫v dx - ∫[(du/dx)* ∫v dx] dx

∫x.[tex]2^{x}[/tex] dx = x∫[tex]2^{x}[/tex] - ∫[(dx/dx) * ∫[tex]2^{x}[/tex] dx ] dx

∫x.[tex]2^{x}[/tex] dx = x*[tex]\frac{2^{x+ 1}}{x+ 1}[/tex] - 1 * [tex]\frac{2^{x + 1} }{x + 1}[/tex]

= [tex]\frac{2^{x} }{x + 1}[/tex]( x - 1 )

Answer:

is it acceleration or velocity?

Step-by-step explanation:

Answer:

Hi

Step-by-step explanation:

Hi

Answer:

Length is 28. Width is 8.

Step-by-step explanation:

The perimeter of a rectangle is given by the following formula:

[tex]P=2l+2w[/tex]

We know that the length is 4 inches less than 4 times the width. Therefore:

[tex]l=4w-4[/tex]

Substitute this for l. Let's also substitute 72 for P. Therefore:

[tex]72=2(4w-4)+2w[/tex]

Distribute:

[tex]72=8w-8+2w[/tex]

Combine like terms:

[tex]72=10w-8[/tex]

Add 8 to both sides:

[tex]80=10w[/tex]

Divide both sides by 10:

[tex]w=8[/tex]

Therefore, the width is 8.

The length is 4 less than 4 times the width. Thus: "

[tex]l=4(8)-4[/tex]

Multiply:

[tex]l=32-4[/tex]

Subtract:

[tex]l=28[/tex]

Therefore, the length is 28 and the width is 8.

And we're done!

Answer:

- 1/2

Step-by-step explanation:

(-4/5) × (- 5/8)

- 4/5 × - 5/8

First we mulitply across

The top and the bottom.

- 20 / 40

because -4 × -5 = +20

and -5 × -8 = +40

Now we simplify the fraction

- 20 / 40

= - 2 /4

= - 1/2

Because we have to simplify it and so I divided it by 10 first.

-20 ÷ 10 = -2 and -40 ÷ 10 = -4

Then I simplified it again by dividing it by 2.

-2 ÷ 2 = -1 and -4 ÷ 2 = -2

So finally we have:

-1/2

And we cannot simplify that anymore so that is the answer.

Hope that helped!

Answer:

1/2

Step-by-step explanation:

since negative * negative= positive we multiply the top and bottom to get. 20/40 which simplifies

Answer:

123.76

Step-by-step explanation:

a negative times a negative is a positive

22.1 times 5.6 is 123.76

Answer:

2598960 ways

Step-by-step explanation:

Given

Standard Deck = 52

Five-card hands

Required

Determine the number of ways

To solve this question, we make use of combination formula

[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]

Where n = 52 and r = 5

[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex] becomes

[tex]^{52}C_5 = \frac{52!}{(52-5)!5!}[/tex]

[tex]^{52}C_5 = \frac{52!}{47!5!}[/tex]

[tex]^{52}C_5 = \frac{52 * 51 * 50 * 49 * 48 * 47!}{47! * 5 * 4 * 3 * 2 * 1}[/tex]

[tex]^{52}C_5 = \frac{52 * 51 * 50 * 49 * 48}{5 * 4 * 3 * 2 * 1}[/tex]

[tex]^{52}C_5 = \frac{311875200}{120}[/tex]

[tex]^{52}C_5 = 2598960[/tex]

Hence, there are 2598960 ways

Answer:

-12

Step-by-step explanation:

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{e = - 4}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{6(3 - e) = 42}[/tex]

Distribute 6 through the parentheses

⇒[tex] \sf{18 - 6e = 42}[/tex]

Move 18 to right hand side and change it's sign

⇒[tex] \sf{ - 6e = 42 - 18}[/tex]

Subtract 18 from 42

⇒[tex] \sf{ - 6e = 24}[/tex]

Divide both sides of the equation by -6

⇒[tex] \sf{ \frac{ - 6e}{ - 6} = \frac{24}{ - 6} }[/tex]

Calculate

⇒[tex] \sf{e = - 4}[/tex]

Hope I helped!

Best regards!!

Answer: 32/3

Step-by-step explanation:

To find the area of the region between the curves, you first want to find the interval of both curves. You can do that by setting both curves equal to each other.

[tex]-\frac{1}{2}x^2+2=\frac{1}{2} x^2-2[/tex]                   [subtract both sides by 2]

[tex]-\frac{1}{2}x^2= \frac{1}{2} x^2-4[/tex]                         [subtract both sides by [tex]\frac{1}{2} x^2[/tex]]

[tex]-x^2=-4\\x=2,-2[/tex]        

Now that we know the interval, we set this into an integral and subtract the top curve by the bottom curve. *Note: I can't type in -2 into the interval, therefore only a "-" will be displayed.

[tex]\int\limits^2_- {|-\frac{1}{2}x^2+2-(\frac{1}{2}x^2-2) | } \, dx[/tex]                     [distribute -1]

[tex]\int\limits^2_-{|-\frac{1}{2}x^2+2-\frac{1}{2}x^2+2 |} \, dx[/tex]                       [combine like terms]

[tex]\int\limits^2_- {|-x^2+4|} \, dx[/tex]                                          [solve integral]

[tex]\frac{32}{3}[/tex]

The area between the curves is 32/3. This was also the reason why we had the absolute values because area can never be negative.

Answer:

x=0

Step-by-step explanation:

First, we distribute on both sides

6x+6-5x=8+2x-2

simplify

x+6=2x+6

subtract x from both sides

6=x+6

subtract 6 from both sides

x=0

(plz give brianliest ty)

Answer:

x = 0

Step-by-step explanation:

6 ( x + 1 ) -5x = 8 + 2 ( x - 1 ) (Distribute)

6x + 6 - 5x = 8 + 2x - 2 (Rearrange expression)

6x - 2x - 5x = 8 - 6 - 2 (Combine like terms)

-1x = 0 (Divide)

x = 0

Answer: Two-way frequency tables are especially important because they are often used to analyze survey results. Two-way frequency tables are also called contingency tables. Two-way frequency tables are a visual representation of the possible relationships between two sets of categorical data.

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

Each age bracket defines a domain of the function. The function value is constant for that domain. This function gives admission price (P) as a function of age (a).

  [tex]P(a)=\left\{\begin{array}{ccl}0&\text{for}&a\le5\\3&\text{for}&5<a\le18\\5&\text{for}&18<a<65\\4&\text{for}&a\ge65\end{array}\right.[/tex]

Answer:

37

Step-by-step explanation:

The calculation of size for a new television is shown below:-

With the help of Pythagoras theorem

[tex]h^2 = b^2 + p^2[/tex]

where

h indicates hypotenuse which is the diagonal length

b indicates the base which is the length of the horizontal side

p indicates perpendicular which is the TV length of the vertical side.

[tex]h^2 = \sqrt{b^2 + p^2}[/tex]

now, we will put the values into the above formula

[tex]= \sqrt{32^2 + 18^2} \\\\ = \sqrt{1024 + 324} \\\\ = \sqrt{1348}[/tex]

Which gives result

= 36.7

or

= 37

Answer:

A) 58

Step-by-step explanation:

Mean = Sum of all the data ÷  total number of data

         [tex]=\frac{52+70+88+15+65}{5}\\\\\\=\frac{290}{5}\\\\\\= 58[/tex]

Hey there! I'm happy to help!

The perimeter is the distance around a shape. Let's add up the lengths of our sides to ind it.

x+5x-2+7x-3

We combine all of the x values.

x+5x+7x=13x

And all of the constants.

-2-3=-5

Therefore, the perimeter is 13x-5.

Have a wonderful day! :D

Answer:

  all real numbers except x=2

Step-by-step explanation:

We assume you intend c(x) = 5/(x-2), rather than c(x) = (5/x) -2 as written.

__

The domain of c(x) is real numbers, excluding 2. Multiplying c(x) by d(x) doesn't change that.

The domain of (cd)(x) = c(x)×d(x) = 5(x+3)/(x-2) is "all real numbers except 2".

__

2 is excluded because c(x) is undefined for that value.

Answer:

Step-by-step explanation:

Ordered pair (0, 0) & (0.5, 2.5)  will fall on the line of graph

Step-by-step explanation:

Megan expects to save an average of 5 dollars per week from her babysitting earnings.

=> Saving Per  week  = 5 $

Saving in 0.5 Week = 0.5 * 5 = 2.5 $

hence ordered pair (0.5, 2.5)  will fall on the line of graph

Saving in 3 Week = 3 * 5 = 15 $

Hence (3, 18) will not fall on  line

Saving in 0 Week = 0.5 * 0 = 0 $

hence ordered pair (0, 0)  will fall on the line of graph

Saving in 4.5 Week = 4.5 * 5 = 22.5 $

Hence (4.5, 30) will not fall on  line

Ordered pair (0, 0) & (0.5, 2.5)  will fall on the line of graph

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

Megan expects to save an average of 5 dollars per week from her babysitting earnings.

=> Saving Per  week  = 5 $

Saving in 0.5 Week = 0.5 * 5 = 2.5 $

hence ordered pair (0.5, 2.5)  will fall on the line of graph

Saving in 3 Week = 3 * 5 = 15 $

Hence (3, 18) will not fall on  line

Saving in 0 Week = 0.5 * 0 = 0 $

hence ordered pair (0, 0)  will fall on the line of graph

Saving in 4.5 Week = 4.5 * 5 = 22.5 $

Hence (4.5, 30) will not fall on line

Hence, Ordered pair (0, 0) & (0.5, 2.5)  will fall on the line of graph.

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#SPJ2

To find the inverse, interchange the variables and solve for y. f−^1(x)=−3x/2−7/4

To find the inverse, interchange the variables and solve for  

f − 1 ( x ) = − 3 x 2 − 7 4

hope  this helped and I know this is the answer