The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour period, one defective circuit board was found. (a) Find the probability that it was produced during the first hour of operation during that period. (Round your answer to four decimal places.) (b) Find the probability that it was produced during the last hour of operation during that period. (Round your answer to four decimal places.) (c) Given that no defective circuit boards were produced during the first five hours of operation, find the probability that the defective board was manufactured during the sixth hour. (Round your answer to four decimal places.)

Explanation:

Because we have a midsegment, this means that it is half as long as the side it's parallel to. You can think of "mid" as "middle" and that could lead to "halfway" to remember to take half.

So z = 14/2 = 7

Answer:

(0,0) is the x and y intercept of the function

Step-by-step explanation:

The parabola touches the x and y axis at 0

The x intercept is (0,0) and the y intercept is (0,0)

Answer:

(0, 0) is the x and y intercepts

Step-by-step explanation:

intercepts are where the curve of the equation contacts an axis

The equation is y = x²

Answer:

PW, BW,  GW, PY,  BY, GY

Step-by-step explanation:

We need to determine the sample space

pink(P), blue (B), and green (G) cards,   (W) and yellow (Y) envelopes

Each color card can match with each color envelope

Start with the white envelopes and each color card

and then the yellow envelopes with each color card

PW   BW  GW

PY  BY   GY

Answer:

Step-by-step explanation:

triangol BCD = triangle BDA

so

3x - 1 = 34 - 2x

5x = 35

x = 35 : 5

Answer:

x = 7

Step-by-step explanation:

BD is an angle bisector , so

∠ ABD = ∠ DBC , that is

3x - 1 = 34 - 2x ( add 2x to both sides )

5x - 1 = 34 ( add 1 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Answer:

(-8/7 ; 5/7)

Step-by-step explanation:

5t + 1/2s = 3 - - - (1)

3t - 6s = 9 - - - - - (2)

Multiply (1) by 12 and (2) by 1

Add the result to eliminate s

60t + 6s = 36

3t - 6s = 9

____________

63t = 45

t = 45 / 63

t = 5/7

Put t = 5/7 in either (1) or (2) to obtain the value of s

3(5/7) - 6s = 9

15/7 - 6s = 9

-6s = 9 - 15/7

-6s = (63 - 15)/7

-6s = 48/7

s = 48/7 * - 1/6

s = - 8/7

Answer:

False

True

True

Step-by-step explanation:

Angle 1 cannot be equal to angle 4. Even by just viewing one can see that they can't be equal.

Angle 1 and 2 when combined give a 90 degree angle going from a to c.

Angle 3 and 4 form a 180 degree angle.

HOPE THIS HELPED

volume= a^2 * h

area= a^2+4ah

take the second equation, solve for h

4ah=1100-a^2

h=1100/4a -1/4 a now put that expression in volume equation for h.

YOu now have a volume expression as function of a.

take the derivative, set to zero, solve for a. Then put that value back into the volume equation, solve for Volume.

Cited from jiskha

9514 1404 393

Answer:

  400 mL/h

Step-by-step explanation:

The required rate is ...

  (100 mL)/(1/4 h) = 100×(4/1) mL/h = 400 mL/h

Answer:

probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)

=194/285 or 0.6807.

Step-by-step explanation:

The sample space of all possible choices of three integers from the set {1,2,…..,20} has C(20,3) = (20×19×18)/3! elements.

The complement of the event space E consists of all possible choices of three integers from the complement of the set of all the multiples of 3 in the above set because the product of the chosen integers is a multiple of 3 if and only if at least one of them is a multiple of 3. Hence we have to choose three elements from the set {1,2,4,5,7,8,10,11,13,14,16,17,19,20} which has 14 elements.

Hence

|E'| = C(14,3)

= 14×13×12/3!.

Therefore probability P(E')

= |E'|/|S|

= (14×13×12)/(20×19×18)

= (14×13×2)/(20×19×3)

=(7×13)/(5×19×3)

= 91/285.

Therefore the required probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)=194/285 or 0.6807.

Answer:

rectangle

Step-by-step explanation:

Perimeter of 20 feet

rectangle (square is technically a rectangle):

sides 5 and 5

5*5 = 25ft²

Circle:

20/(2π) = 3.18309...

3.1809...²π = 31.831ft²

Max area of rectangle (i.e. square) has a smaller area than a circle.

Answer:

$80

Step-by-step explanation:

To find the largest price, assume that all 20 copies of the workbook will have 400 pages.

Since the company charges 1 cent per page, this means each workbook will cost 400 cents. This is equivalent to 4 dollars.

Find the total cost by multiplying this by 20:

20(4)

= 80

So, the largest price to print 20 copies is $80

Markdown is the difference (at sale) between the price an item is placed at for retail sale, and the actual price the item is sold

The correct option is; B. GHC 50.00

The reason for choosing option B is as follows;

The known parameters

The percentage by which damaged items are marked down = 25% to 40%

The percentage markdown offered by the newspaper coupon = 10%

The original marked price of the item = GHC 100

Strategy:

Apply the damaged items and coupon markdown percentages to the original marked price of GHC100 sum the results to find the total markdown

Solution:

Markdown due to damage:

Given that the item is damaged, to have the lowest price, we apply the largest markdown of 40%;

40% is removed from the price to which the item marked down due to damage, as follows;

The markdown due to damage = 40/100 × GHC 100 = GHC 40

Markdown due to Coupon Holder:

The markdown the coupon holder is to get = 10% off the retail price

Given that the damage is not mentioned in the newspaper, we have;

∴ The markdown the coupon holder is to get = 10/100 × GHC 100 = GHC 10

Total markdown:

The total markdown is therefore equal to GHC 40 + GHC 10 = GHC 50

The Lowest Price of A Damaged Items marked GHC100:

The lowest price of the item = Original price - Maximum markdown

The lowest price of the item = GHC 100 - GHC 50 = GHC 50

Learn more about markdown and markup concepts here;

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Answers:

First bottle's unit cost = 27 cents per oz

Second bottle's unit cost = 27 cents per oz

Both have the same unit cost.

----------------------------------------

Work Shown:

unit cost = price/(number of ounces)

1st bottle unit cost = (1.35)/(5) = 0.27 dollars per oz = 27 cents per oz

2nd bottle unit cost = (2.16)/(8) = 0.27 dollars per oz = 27 cents per oz

Both lead to the same unit cost. Therefore, you can pick either option and it doesn't matter.

the trip to the airport was 6.25 miles.

We have to find LCM

3 | 45,75,63

3 | 15,25,21

5 | 5,25,7

5 | 1,5,7

7 | 1,1,7

LCM=3×3×5×5×7=1575

The least common denominator for the group of denominators using the method of prime numbers is 1575.

LCM stands for Least Common Multiple. It is a method to find the smallest common multiple between any two or more numbers.  A factor is one of the numbers that multiplies by a whole number to get that number.

For the given situation,

The numbers are 45, 75, 63​

Prime factors of 45 = [tex]3,3,5[/tex]

Prime factors of 75 = [tex]3,5,5[/tex]

Prime factors of 63 = [tex]3,3,7[/tex]

Then the LCM can be found by, first take the common factors then multiple the remaining factors as,

⇒ [tex](3)(3)(5)(5)(7)[/tex]

⇒ [tex]1575[/tex]

Hence we can conclude that the least common denominator for the group of denominators using the method of prime numbers is 1575.

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Answer:

y=2/3x+1

Step-by-step explanation:

9514 1404 393

Answer:

  perimeter ≈ 12.4 units

Step-by-step explanation:

The side adjacent to the angle is given. The relationships useful for the other two sides are ...

  Tan = Opposite/Adjacent

  Cos = Adjacent/Hypotenuse

From these, we have ...

  opposite = 5·tan(22°) ≈ 2.02

  hypotenuse = 5/cos(22°) ≈ 5.39

Then the perimeter is ...

  P = a + b + c = 2.02 + 5 + 5.39 = 12.41

The perimeter of ∆ABC is about 12.4 units.

Step-by-step explanation:

[tex]re(i(x + yi) = - im(x + yi) \\ re(xi - y) = - im(x + yi) \\ - y = - (y) \\ - y = - y \\ proved \: is \: correct[/tex]

Answer:

The answer is "[tex]\frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]".

Step-by-step explanation:

Given:

[tex]y = e^{{\color{\red}5}\sqrt{x}}[/tex]

let

[tex]\to t= 5\sqrt{x}\\\\\frac{dt}{dx}= 5 \frac{1}{2\sqrt{x}}\\\\\frac{dt}{dx}= \frac{5}{2\sqrt{x}}\\\\[/tex]

and

[tex]\to y=e^t\\\\\to \frac{dy}{dt}=e^t\\[/tex]

[tex]\to \frac{dy}{dt}=e^{5\sqrt{x} }\\[/tex]

So,

[tex]\to \frac{dy}{dx}= \frac{dy}{dt} \times \frac{dt}{dx}[/tex]

         [tex]=e^{5\sqrt{x} }\times \frac{5}{2\sqrt{x}}\\\\= \frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]

OR

[tex]\to g(x) = 5\sqrt{x} \\\\\to f(x) = e^{(x)}\\\\[/tex]

Derivate:  

[tex]\to f''g' = \frac{e^{(5\sqrt{x})}5}{(2\sqrt{x})}[/tex]

Answer:

D

Step-by-step explanation:

x- coordinate = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]

y- coordinate = sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]

That is ( [tex]\frac{\sqrt{2} }{2}[/tex] , [tex]\frac{\sqrt{2} }{2}[/tex] ) → D

Answer:

H0 : correlation is equal to 0

H1 : correlation is not equal to 0 ;

Pvalue < α ;

There is sufficient evidence

r = 0.945 ;

Pvalue = 0.01524

Step-by-step explanation:

Given the data :

Lemon_Imports_(x) Crash_Fatality_Rate_(y)

230 15.8

264 15.6

359 15.5

482 15.3

531 14.9

Using technology :

The regression equation obtained is :

y = 16.3363-0.002455X

Where, slope = - 0.002455 ; Intercept = 16.3363

The Correlation Coefficient, r = 0.945

H0 : correlation is equal to 0

H1 : correlation is not equal to 0 ;

The test statistic, T:

T = r / √(1 - r²) / (n - 2)

n = 5 ;

T = 0.945 / √(1 - 0.945²) / (5 - 2)

T = 0.945 / 0.1888341

T = 5.00439

The Pvalue = 0.01524

Since Pvalue < α ; Reject the Null and conclude that there is sufficient evidence to support the claim.

Answer:

(2x – 1)2 = 9

4x-2=9

4x=9+2

4x=11

x=11/4

x=2.75

9514 1404 393

Answer:

  (11, -13)

Step-by-step explanation:

If midpoint M is halfway between A and B:

  M = (A +B)/2

Then B is ...

  B = 2M -A

  B = 2(4, -9) -(-3, -5) = (8+3, -18+5)

  B = (11, -13)

Answer:

Use the midpoint formula:

[tex]midpoint=(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})[/tex]

Substitute in the values:

[tex](4, -9)=(\frac{-3+x_{2}}{2} +\frac{-5+y_{2}}{2} )[/tex]

[tex]4=\frac{-3+x_{2}}{2} \\4(2)=-3+x_{2}\\8+3=x_{2}\\x_{2}=11[/tex]      [tex]-9=\frac{-5+y_{2}}{2} \\(-9)(2)=-5+y_{2}\\-18+5=y_{2}\\y_{2}=-13[/tex]

Therefore, Point B = (11, -13)

Answer: a

Step-by-step explanation:

the function is given, and it's value is where the object is ("how far to the right").

so as long as it rises (going more right), this will be apply.

in the screenshot I graphed the function. of course t is graphed as x and "along the x-axis" is graphed as y, but the pattern is the same anyways.

for the first 1.25 seconds the object goes to the left, and after that always to the right.

since we look at t to calculate x, t effectively takes the role of the important variable that is normally given to x. the calculation pattern are just the same. so let's find the lowest point of this function by calculating it out.

x(t) = 2t² – 5t – 18

x'(t) = 4t -5

x'(t) = 0

0 = 4t -5

5 = 4t

1.25 = t

plugging it into the second derivative

x''(t) = 4

x''(1.25) = 4

it's positive, so at t=1.25 there is a low point

(of course the second derivative is constant anyways.)

the object is traveling toward the right

the object is traveling toward the rightfor t > 1.25

The object is moving to the right, for t > 1.25, the object is moving in a rightward direction.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

An object travels along the x-axis so that its position after t seconds is given by:

x(t) = 2t² – 5t – 18

x'(t) = 4t - 5

x'(t) = 0

4t -5 = 0

t = 5/4 = 1.25 seconds

x''(t) = 4

x''(1.25) = 4

x''(1.25) > 0

At t = 1.25 the object travels at a low point.

Thus, the object is moving to the right, for t > 1.25, the object is moving in a rightward direction.

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x=3

Step-by-step explanation:

x+2=5

x=5-2

x=3

Answer:

[tex]y = 7 - 7x \\ y + 7x = 7 \\ 7x + y = 7[/tex]

Answer:

7x + y = 7

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = 7 - 7x ( add 7x to both sides )

7x + y = 7 ← in standard form

Answer:

0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 590 hours, standard deviation of 25 hours.

This means that [tex]\mu = 590, \sigma = 25[/tex]

Find the probability of a bulb lasting for at most 622 hours.

This is the p-value of Z when X = 622.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{622 - 590}{25}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997.

0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.