Determine whether the following statement is true or false. If false, give a counterexample. If true, give an example.
1 answer:
You might be interested in
Answer:
C.
Step-by-step explanation:
Domain is only affected if certain values can make the result something that either doesn't make sense or is an error. In your situation, it wants you to find the domain of f/g, which is a fraction. The only rule we have for fractions regarding domain is that we simply can't divide by zero, to find the domain for any fraction with variables in the denominator, what I do is take the denominator, set it equal to 0, and solve for x.
So, if we're taking f/g, we have:
4x - 3 makes up our denominator, the bottom part of the fraction. So
4x - 3 = 0
4x = 3
x = 3/4
So the denominator is equal to zero when x is equal to 3/4. This would produce an error in any calculator because you can't divide by zero. The domain here is all real numbers except for 3/4.
(For future problems, the only thing to look out for is if your numerator, the top part of the fraction, factors into something that cancels with the bottom. In that case, it wouldn't affect domain because you aren't actually dividing by anything. For example:
If we factor the top, we see that x^2 - 4 = (x - 2)(x + 2). In this case, we have (x - 2) in both the top and bottom of the fraction, so it cancels out, and from there nothing else is restricting our domain. It would be all real numbers in a case like that.)
Answer:
80 feet
Step-by-step explanation:
Given:
Initial speed of the car () = 40 ft/sec
Deceleration of the car () = -10 ft/sec²
Final speed of the car () = 0 ft/sec
Let the distance traveled by the car be 'x' at any time 't'. Let 'v' be the velocity at any time 't'.
Now, deceleration means rate of decrease of velocity.
So,
Negative sign means the velocity is decreasing with time.
Now, using chain rule of differentiation. Therefore,
Integrating both sides under the limit 40 to 0 for 'v' and 0 to 'x' for 'x'. This gives,
Therefore, the car travels a distance of 80 feet before stopping.
We have the mean, μ = 20 and the standard deviation, σ = 4
X ≈ N(20, 4²)
We want P(X<15)
Standardising gives
P(X<15) = P(Z<
)
P(X<15) = P(Z< -1.25) ⇒ When the value of the z-score is negative, we will read the value of z<1.25 on the z-table then subtract the answer from 1
P(X<15) = 1 - P(Z<1.25)
P(X<15) = 1 - 0.8944
P(X<15) = 0.1056
Hence, the probability that pizza takes less than 15 minutes to be delivered is 0.1056 = 10.56%
X ≈ N(20, 4²)
We want P(X<15)
Standardising gives
P(X<15) = P(Z<
P(X<15) = P(Z< -1.25) ⇒ When the value of the z-score is negative, we will read the value of z<1.25 on the z-table then subtract the answer from 1
P(X<15) = 1 - P(Z<1.25)
P(X<15) = 1 - 0.8944
P(X<15) = 0.1056
Hence, the probability that pizza takes less than 15 minutes to be delivered is 0.1056 = 10.56%