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seropon [69]
3 years ago
5

Wilma and Betty are playing a number game. Wilma tells Betty, "I'm thinking of a number between 1 and 10. If I take the number a

nd add 4 to it and then multiply that by 3, I get 30." What number is Wilma thinking of?
Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
8 0
Just work this problem out backwards. First write out an equation.
(x+4)•3=30

Now solve :

(x+4)•3=30

3x+12=30
-12   -12

3x=18
/3   /3

x=6

Your answer is 6!

Hoped I helped!
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Let X denote the life of a semiconductor laser (in hours) with the following probabilities: P(X ≤ 5000) = 0.05 and P(X > 7000
Anna [14]

Answer:

a) P [ x ≤ 7000] is 0.55

b) P [ x > 5000 ] = 0.95

c)  P [ 5000 < x ≤ 7000 ] = 0,5

Step-by-step explanation:

a)  P [ x > 7000 ]  =  0.45   straightforward    P [ x ≤ 7000] is 0.55

The whole spectrum of probabilities is 1 which in this particular case is divided in two parts having 7000 as a limit, then we subtact 1 - 0.45

b) P [ x ≤ 5000]  = 0.05   again we get P [ x > 5000] taking 1-0.05 to get

P [ x > 5000 ] = 0.95

c) P [ 5000 < x ≤ 7000 ]

Under Normal curve distribution the probability of  x ≤ 7000 includes values   smallers  ( to the left of 5000) so we subtract from 0.55 - 0.05 = 0.50

c) P [ 5000 < x ≤ 7000 ] = 0,5

6 0
3 years ago
I need help with three problems!!!!!
Marrrta [24]
I hope this helps you

7 0
3 years ago
Find w and y, will give brainliest for the correct answer
Alex Ar [27]

Answer: w=12, y=6√3

Step-by-step explanation:

Looking at the figure, we can split the triangle into 2 separate triangles. One on the left and one on the left. The triangle on the right is a 30-60-90 triangle. For this triangle, the hypotenuse is 2x in length. This is directly opposite of the right angle. The leg opposite to 30° is x in length. The leg opposite 60° is x√3 in length. Once you know the length of one side, you can plug in x to find the length of the other legs.

In this case, w and y are located on the same 30-60-90 triangle. Normally we would focus on that triangle to find our values, but in this instance, we don't have any values. We have to use the left triangle to find the leg that both triangles share.

The left triangle is a 45-45-90 triangle. For this triangle, the legs opposite of 45° is x in length. The hypotenuse is x√2. Since we know the hypotenuse, we can use it to find x.

x√2=8

x=8/√2

x=5.7 or 6       [Let's use 6 so that it is easier to work with a whole number]

Now that we know x, we can find w and y. Going back to the right triangle, we know the hypotenuse is 2x. We plug in 6 to find the length.

w=2x

w=2(6)

w=12

We know the leg opposite of 60° is x√3. We can plug in x.

y=6√3

7 0
3 years ago
​A cable company has a one time installation fee and then a monthly charge to use their service. The total cost of modeled by th
SpyIntel [72]

Answer:

130=monthly charge

119=one time installation fee

Step-by-step explanation:

119 is the y-intercept and in problems like these, it is always the one time fee. 130 is the monthly payment because it has an x, which could account for the number of months. For example , say six months passed, you could multiply 130 * 6 to get the monthly fee for six months. I hope that makes sense!

6 0
2 years ago
Suppose a tank contains 400 gallons of salt water. If pure water flows into the tank at the rate of 7 gallons per minute and the
Strike441 [17]

Answer:

Step-by-step explanation:

This is a differential equation problem most easily solved with an exponential decay equation of the form

y=Ce^{kt}. We know that the initial amount of salt in the tank is 28 pounds, so

C = 28. Now we just need to find k.

The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is \frac{dy}{dt}. Thus, the change in the concentration of salt is found in

\frac{dy}{dt}= inflow of salt - outflow of salt

Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:

3(\frac{y}{400})

Therefore,

\frac{dy}{dt}=0-3(\frac{y}{400}) or just

\frac{dy}{dt}=-\frac{3y}{400} and in terms of time,

-\frac{3t}{400}

Thus, our equation is

y=28e^{-\frac{3t}{400} and filling in 16 for the number of minutes in t:

y = 24.834 pounds of salt

6 0
3 years ago
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