The sum of two numbers is twenty-five. One number is five less than the other.
Answers
Answer: x=15, y=10
*Note: x and y are only variables used to solve this problem, but know that the two numbers are 15 and 10.
Step-by-step explanation:
For this problem, we can use system of equations. Let's use x for one number and y for the other.
First Equation:
x+y=25
We get this equation because it states that the sum of the two numbers is 25.
Second Equation:
y=x-5
We get this equation because it says one number (y) is 5 less than the other (x).
Since we have two equations, we can use substitution method to solve.
[distribute 1 to (x-5)]
[combine like terms]
[add both sides by 5]
[divide both sides by 2]
Now that we have x, we can plug it into any of the equations to find y.
[plug in x=15]
[subtract both sides by 15]
Finally, we have our answer, x=15 and y=10.
Answer:25,-5
Step-by-step explanation:
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The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. The manufacturer replaces free all motors that fail while under guarantee. If she is willing to replace only 3% of the motors that fail, how long a guarantee should be offered? Assume that the lifetime of a motor follows a normal distribution.
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Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor's bid x is a is a random variable that is uniformly distributed between $10,000 and $15,000.a. Suppose you bid $12,000. What is the probability that your bid will be accepted? (please show calculations)b. Suppose you bid $14,000. What is the probability that your bid will be accepted? (please show calculations)c. What amount should you bid to maximize the probability that you get the property? (please show calculations)d. Suppose you know someone who is willing to pay you $16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not?
Answers
Let t hours be the time the second car is driving untill it overtakes the first car. The nfirst car is hours on the road.
If the lead car is going 60 mph, then for the hours it will go the distance
If the second place car is going 70 mph, then for the hours it will go the distance
These distances are equal, then
Answer: 9 hours
Answers
Answer:
There is a 3.7% probability that they both will like it.
Step-by-step explanation:
We can solve this problem using the Bayes rule derivation from conditional probability.
Bayes rule:
What is the probability of B, given that A?
In this problem, we have that:
is the probability that Ralph likes the movie, given that Melissa likes. The problem states that this is 10%. So
is the probability that Melissa likes the movie. The problem states that
.
If they randomly select a movie from a video store, what is the probability that they both will like it?
This is .
There is a 3.7% probability that they both will like it.
Answers
Answer: about 500
Step-by-step explanation:
Answer:
Step-by-step explanation:
800 meters
Answers
Answer:
about 20
Step-by-step explanation:
The vehicle must decline in value by $25,635 -10,000 = $15,635. At the rate of $3000 per year, it will take ...
15,635/3,000 ≈ 5.21167
In 5.2 years, she will be about 20 years old.
Answers
Answer:
A(t) = 300 -260e^(-t/50)
Step-by-step explanation:
The rate of change of A(t) is ...
A'(t) = 6 -6/300·A(t)
Rewriting, we have ...
A'(t) +(1/50)A(t) = 6
This has solution ...
A(t) = p + qe^-(t/50)
We need to find the values of p and q. Using the differential equation, we ahve ...
A'(t) = -q/50e^-(t/50) = 6 - (p +qe^-(t/50))/50
0 = 6 -p/50
p = 300
From the initial condition, ...
A(0) = 300 +q = 40
q = -260
So, the complete solution is ...
A(t) = 300 -260e^(-t/50)
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The salt in the tank increases in exponentially decaying fashion from 40 grams to 300 grams with a time constant of 50 minutes.
The number of grams of salt in the tank at any time t is 40 grams. The inflow and outflow of brine do not affect the amount of salt in the tank because the solution is well-mixed, and the salt concentration remains constant.
To solve this problem, we need to set up a differential equation that describes the rate of change of salt in the tank over time. Let A(t) represent the number of grams of salt in the tank at time t.
Let's break down the components affecting the rate of change of salt in the tank:
Salt inflow rate: The brine is being pumped into the tank at a constant rate of 6 liters per minute, and it contains 1 gram of salt per liter. So, the rate of salt inflow is 6 grams per minute.
Salt outflow rate: The solution in the tank is being pumped out at the same rate of 6 liters per minute, which means the rate of salt outflow is also 6 grams per minute.
Mixing of the solution: Since the tank is well-mixed, the concentration of salt remains uniform throughout the tank.
Now, let's set up the differential equation for A(t):
dA/dt = Rate of salt inflow - Rate of salt outflow
dA/dt = 6 grams/min - 6 grams/min
dA/dt = 0
The above equation shows that the rate of change of salt in the tank is constant and equal to zero. This means the number of grams of salt in the tank remains constant over time.
Now, let's find the constant value of A(t) using the initial condition where the tank initially contains 40 grams of salt.
When t = 0, A(0) = 40 grams
Since the rate of change is zero, A(t) will be the same as the initial amount of salt in the tank at any time t:
A(t) = 40 grams
So, the number of grams of salt in the tank at any time t is 40 grams. The inflow and outflow of brine do not affect the amount of salt in the tank because the solution is well-mixed, and the salt concentration remains constant.
To know more about differential equation:
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Answers
So, vertical stretching of F(x) by a factor of 7 will be equal to 7 F(x).
Thus,
G(x) = 7 F(x)
G(x) = 7x²
So, option C gives the correct answer