take for the tub to overflow if both the faucet and drain were open at the
same time?
Answer:
20
Step-by-step explanation:
Knowing that it is a 30-gallon bathtub.
And it fills at a rate of 3 gallons per minute.
But also drains 1.5 gallons per minute.
So this is for the first minute.
3 - 1.5 = 1.5
So there will be 1.5 gallons of water in the tub after the first minute.
Now do,
30 ÷ 1.5 = 20
It will take 20 full minutes for the bathtub to fill up.
b. Keep the base the same and then add the exponents.
c. Multiply the bases and then subtract the exponents.
d. Keep the base the same and then subtract the exponents.
Answer:
The correct option is d. To simplify the given expression we should keep the base the same and then subtract the exponents.
Step-by-step explanation:
The given expression is
In the above expression we have common base 3 but the exponents are different.
According to the rule of exponent, if the numerator and denominator have same base and different exponent, then the base remains the same and the exponent of denominator subtracted from exponent of numerator.
Use this rule in the given expression.
Therefore the correct option is d.
Answer:
d or Keep the base the same and then subtract the exponents.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Simplify in steps considering the hierarchy of operations:
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Answer:
t = 2.9272 > 1.708 at 25 degrees of freedom
null hypothesis is rejected
The council decides that it will increase the transportation budget if the amount of waiting time for drivers is not exceeds 18 minutes
Step-by-step explanation:
Step (i):-
A sample of 26 main roads results in a mean waiting time of 21.1 minutes with a sample standard deviation of 5.4 minutes.
Given sample size 'n' = 26
The mean of the sample 'x⁻ = 21.1 min
Standard deviation of the sample 'S' = 5.4 min
The Population mean 'μ' = 18min
Step(ii):-
Null hypothesis: H₀ : The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 18 minutes.
'μ' > 18min
Alternative hypothesis :H₁:
'μ' <18min
Level of significance : ∝=0.05
Degrees of freedom γ = n-1 = 26-1 =25
The test statistic
t = 2.9272
Step(iii):-
The tabulated value t = 1.708 at 25 degrees of freedom
t = 2.9272 > 1.708 at 25 degrees of freedom
Null hypothesis is rejected at 5% significance level of significance
Conclusion:-
The council decides that it will increase the transportation budget if the amount of waiting time for drivers is not exceeds 18 minutes
if g is a quadratic function with a positive leading coefficient and a vertex at (0,3), which statement is true?
А.
The function fintersects the x-axis at two points, and the function g never intersects the x-axis.
B
The function fintersects the x-axis at two points, and the function g intersects the x-axis at only one point.
c.
Both of the functions fand g intersect the x-axis at only one point.
D
Both of the functions fand g intersect the x-axis at exactly two points.
Answer: А.
The function f intersects the x-axis at two points, and the function g never intersects the x-axis.
Step-by-step explanation:
In the graph we can see f(x), first let's do some analysis of the graph.
First, f(x) is a quadratic equation: f(x) = a*x^2 + b*x + c.
The arms of the graph go up, so the leading coefficient of f(x) is positive.
The vertex of f(x) is near (-0.5, -2)
The roots are at x = -2 and x = 1. (intersects the x-axis at two points)
Now, we know that:
g(x) has a positive leading coefficient, and a vertex at (0, 3)
As the leading coefficient is positive, the arms go up, and the minimum value will be the value at the vertex, so the minimum value of g(x) is 3, when x = 0.
As the minimum value of y is 3, we can see that the graph never goes to the negative y-axis, so it never intersects the x-axis.
so:
f(x) intersects the x-axis at two points
g(x) does not intersect the x-axis.
The correct option is A.
Answer:
The answer is A.) The function f intersects the x-axis at two points, and the function g never intersects the x-axis.
Step-by-step explanation:
I took the test and got it right.