The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that only two of the setups can be done on a particular day, and the two computers to be set up are randomly selected from the six (implying 15 equally likely outcomes; if the computers are numbered 1, 2, . . . , 6, then one outcome consists of computers 1 and 2, another consists of computers 1 and 3, and so on).

Required:
a. What is the probability that both selected setups are for laptop computers?
b. What is the probability that both selected setups are desktop machines?
c. What is the probability that at least one selected setup is for a desktop computer?
d. What is the probability that at least on computer of each type is chosen for setup?

Answer:

9

Step-by-step explanation:

If we substitute the variables for the numbers, the equation looks like this:

8+2(5)-9

Because 2s was multiplying 2 by s in the original equation, we can do that step first!

8+2(5)-9

8+10-9

Personally, I think it's a lot easier to subtract 9 from 10 first, but you can solve this part in any order.

8+10-9

8+1

This is the last part; we just have to add 8 and 1 now!

8+1=9

Hope this helps!!! Have a wonderful day C:

Answer:

When you spend $45 or more, you get 3 free songs.

You already spent $15.

Then, if we define m as the amount that you need to spend in order to get the 3 free songs, the minimum value of m will be such that you spend exactly $45 in total.

$15 + m = $45.

But if you spend more than $45 you also get the songs, so the inequality that represents this situation is:

$15 + m ≥ $45.

2)Solving the equation for m we have:

m ≥ $45 - $15 = $30

m ≥ $30.

So the minimum amount that you can spend in order to get the songs is when the equality is true, this means that:

m = $30 is the minimum that you must spend if you want the 3 free songs.

Answer:

FOR QUESTION 5

1. Angle 1 congruent to angle 4; given

2. Angle 1 supplementary  to angle 2; assumed from diagram

3. Angle 4 supplementary  to angle 3; assumed from diagram

4. Angle 2 congruent to angle 3; angles supplementary to congruent angles are congruent

5. Angle 3 congruent to angle 5; verticla angles are congruent

6. Angle 2 congruent to angle 5; substitution

FOR QUESTION 6

1. Angle 2 congruent to angle 3; given

2. Angle 2 congruent to angle 1; vertical angles are congruent

3. Angle 3 congruent to angle 4; vertical angles are congruent

4. Angle 1 congruent to angle four; substituiton (see statement #1)

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

the opposite of -6.5 is 6.5.

The absolute value of |-6.5| is 6.5.

Hope this helps.

Answer:

185

Step-by-step explanation:

222/6=37

5*37=185

Answer:

a) True. The differential equation is [tex]\frac{dT}{dt}+0.0004\cdot T = 0.06[/tex], where [tex]T[/tex] is measured in Celsius.

b) The temperature of the object after 200 second inside the microwave is approximately 34.611 ºC.

Step-by-step explanation:

a) The object is heated up by convection and radiation, from First Law of Thermodynamics we get that energy interactions on the object are represented by:

[tex]-\dot Q_{out} + \dot W_{in} = \frac{dU_{sys}}{dt}[/tex] (Eq. 1)

Where:

[tex]\dot Q_{in}[/tex] - Heat transfer rate to the object, measured in watts.

[tex]\dot W_{in}[/tex] - Electric power given by the microwave owen, measured in watts.

[tex]U_{sys}[/tex] - Internal energy of the object, measured in watts.

Then, we expand the expression by means of definition from Heat Transfer and Thermodynamics:

[tex]-h_{c}\cdot A_{s}\cdot (T-T_{\infty})+\dot W_{in} = m\cdot c\cdot \frac{dT}{dt}[/tex]

Where:

[tex]h_{c}[/tex] - Heat transfer coefficient, measured in watts per square meter-Celsius.

[tex]A_{s}[/tex] - Surface area of the object, measured in square meters.

[tex]T[/tex] - Temperature of the object, measured in Celsius.

[tex]T_{\infty}[/tex] - Internal temperature of the microwave oven, measured in Celsius.

[tex]m[/tex] - Mass of the object, measured in kilograms.

[tex]c[/tex] - Specific heat of the object, measured in joules per kilogram-Celsius.

After some algebraic handling, we get this non-homogeneous first order differential equation:

[tex]\frac{dT}{dt} = -\frac{h_{c}\cdot A_{s}}{m\cdot c} \cdot (T-T_{\infty}) + \frac{\dot W_{in}}{m\cdot c}[/tex]

[tex]\frac{dT}{dt}+\frac{h_{c}\cdot A_{s}}{m\cdot c}\cdot T =\frac{h_{c}\cdot A_{s}}{m\cdot c}\cdot T_{\infty}+\frac{\dot W_{in}}{m\cdot c}[/tex] (Ec. 2)

If we know that [tex]h_{c} = 40\,\frac{W}{m^{2}\cdot ^{\circ}C}[/tex], [tex]A_{s} = 0.01\,m^{2}[/tex], [tex]m = 1\,kg[/tex], [tex]c = 1000\,\frac{J}{kg\cdot ^{\circ}C}[/tex], [tex]T_{\infty} = 25\,^{\circ}C[/tex] and [tex]\dot W_{in} = 50\,W[/tex], the differential equation is:

[tex]\frac{dT}{dt}+0.0004\cdot T = 0.06[/tex]

b) The solution of this differential equation is:

[tex]T(t) = T_{o}\cdot e^{-0.0004\cdot t}+ \frac{0.06}{0.0004}\cdot (1-e^{-0.0004\cdot t})[/tex]

Where [tex]T_{o}[/tex] is the initial temperature of the object, measured in Celsius.

[tex]T(t) = T_{o}\cdot e^{-0.0004\cdot t}+150\cdot (1-e^{-0.0004\cdot t})[/tex]

[tex]T(t) = 150+(T_{o}-150)\cdot e^{-0.0004\cdot t}[/tex]

Where [tex]t[/tex] is the time, measured in seconds.

If we know that [tex]T_{o} = 25\,^{\circ}C[/tex], then:

[tex]T(t) = 150-125\cdot e^{-0.0004\cdot t}[/tex] (Ec. 3)

For [tex]t = 200\,s[/tex], we get that temperature of the object is:

[tex]T(200) = 150-125\cdot e^{-0.0004\times 200}[/tex]

[tex]T(200) \approx 34.611\,^{\circ}C[/tex]

The temperature of the object after 200 second inside the microwave is approximately 34.611 ºC.

Answer:

1) variables

2)26

3)8x+2y+2

4)38

Answer:

253 units

Step-by-step explanation:

-253 is 253 units behind 0.

Answer:

CT=37

Step-by-step explanation:

5x-3 = 2x+21

-2x

3x-3 = 21

+3

3x = 24

÷3

× = 8

5(8) - 3 = 37

2(8) +21 =37

Answer:

a = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]\frac{2a}{3} -\frac{1}{6} =\frac{1}{3}[/tex]

[tex]\frac{4a}{6}-\frac{1}{6} =\frac{2}{6}[/tex]

(now you can multiply the whole equation by 6 to remove the fractions

4a - 1 = 2

4a = 2+1

4a = 3

a = [tex]\frac{3}{4}[/tex]

Answer:

a=3/4

Step-by-step explanation:

Answer:

they're both acute im 100% sure

Step-by-step explanation:

Answer:

let monday be a = 800 (nearest 100)

let tuesday be b = 700 (nearest 100)

a+b = 800 + 700 = 1500

a+b = 1500

Answer:

2/9

Step-by-step explanation:

Any fraction in the form 0.n repeated is in the form n/9

Answer:

|(15,055) is the number of pages in a book with

15,055 words.

Step-by-step explanation:

becuz the no of pages is a function to the words ..

Answer:

41.4$

Step-by-step explanation:

10% of 230 is 23$

23/5=4.6

4.6$=2%

18.4$=8%

23+18.4$

41.4$

Answer:

41.4

Step-by-step explanation:

Hope this helped

Answer:

1 minute

Step-by-step explanation:

141/47=3. then 3*20=60 which is equal to one minute

Answer:

1y157

Step-by-step explanation:

Answer:

27÷3 =9

Step-by-step explanation:

27 divided by 3 is 9

Answer: 3 * 9 = 27,    27 / 3= 9,  27/9 = 3

Step-by-step explanation:

3 being multiplied by 9 will give you 27.

27 divided by 9 will give you 3.

27 divide by 3 will give you 9.

Answer:

Add 16.20+ 40+8

Step-by-step explanation: 16+20+40+8= 84

Answer:

A person pushing a swing will make the swing rotate about its pivot.

A worker applies a force to a spanner to rotate a nut.

A person removes a bottle's cork by pushing down the bottle opener's lever.

A force is applied to a door knob and the door swings open about its hinge.

Answer:

Step-by-step explanation:

2.6 ÷ 2 = 1.3

Answer:

P[ X < 2,4 ]  = 0,1587   or   15,87 %

Step-by-step explanation:

Normal Distribution  N ( 2,6 , 0,2 )

mean = μ₀ = 2,6 ft  and

standard dviation is

σ = 0,2 ft

Samle size 53    n  = 53

2,4 - 2,6 = 0,2

That means the difference between 2,4 and the mean of the sample ( 2,6) is equal to one standar deviation.  The empircal rule establishes that the interval [  μ₀ ± σ]  contans 68,3 % of all values, by symmetry

μ₀ - σ = 68,3/2

μ₀ - σ = 34,15

Then the half of the bell shape curve is 0,5 and  from 0,2 up to 0 ( the normalized μ₀ ) is 34,15 then dfference between

0,5 - 0,3415   =  0,1585  or   15,85% is the probability

Other procedure is:

P[ X < 2,4 ]  = [X  -  μ₀ ] / σ

P[ X < 2,4 ]  = 2,4 - 2,6 / 0,2

P[ X < 2,4 ]  = - 0,2/0,2

P[ X < 2,4 ]  = - 1

And fom z - table we find for z (score) = - 1

P[ X < 2,4 ]  = 0,1587

Answer:

0.0668

Step-by-step explanation:

z=x−μσ=2.3−2.60.2=−1.50

Using the normal distribution tables, we find that the area under the standard normal curve to the left of z=−1.50 is approximately 0.0668. Thus, the probability that an individual man’s step length is less than 2.3 feet is approximately 0.0668.

Answer:

3 1/5

Step-by-step explanation:

24/5 ÷ 3/2

24/5 x 2/3

48/15

16/5

3 1/5

Answer:

$7.38

Step-by-step explanation:

multiply 49.20 by 15 percent.

Answer:

With 98x50 its like there are 98 fiveties. In 97x 50 there are 97 fiveties. There is one more 50 in 98x50.

Step-by-step explanation:With 98x50 its like there are 98 fiveties. In 97x 50 there are 97 fiveties. There is one more 50 in 98x50.

Answer:

duno

Step-by-step explanation: duno

Answer:

A)

[tex]-39.6[/tex]

B)

[tex]4.5\text{ minutes}[/tex]

Step-by-step explanation:

We know that the scuba diver is exploring a reef 39.6 meters below the sea level.

Remember that sea level is always 0 meters in elevation.

We also know that the diver ascended to the surface at a rate of 8.8 meters per minute.

Part A)

Since sea level is the 0th meter, anything below this will be negative.

So, since the diver is 39.6 meters below sea level, we can express this as:

[tex]-39.6[/tex]

Part B)

We know that the diver ascends at a rate of 8.8 meters per minute.

The diver is currently at 39.6 meters.

Remember that the surface is the sea level. So, we want to find after how many minutes m does the diver reach the 0th meter.

So, we can write the following equation and solve for m:

[tex]-39.6+8.8m=0[/tex]

The -39.6 represents the diver's current altitude.

The 8.8m represents the diver's rate of ascending 8.8 meters per minute m. Notice that 8.8m is positive because we're ascending.

And the 0 represents the 0th meter or sea level or the surface.

So, solve for m. Add 39.6 to both sides:

[tex]8.8m=39.6[/tex]

Divide both sides by 8.8. So:

[tex]m=4.5[/tex]

So, it will take the diver 4 and a half minutes to reach the surface.

And we're done!