you can't do that. there isn't enough detail. we don't know how much each item costs
Part
How much time, in minutes, do water tank A and water tank B have to be drained in order for them to have the same amount of water?
Answer: In 20 minutes, tanks A and B will each have 120 gallons remaining in them.
Step-by-step explanation:
The equation, the amount at which they will be equal, represents the given starting amounts minus the gal/min times the unknown time in minutes, m.
220 - 5m = 180 - 3m Subtract 180 from both sides; add 5m to both sides.
220-180 -5m +5m = 180-180 +5m - 3m Combine like terms
40 = 2m Divide both sides by 2
20 = m
Check: Substitute 20 for m in the equation
220 - 5(20) = 180 - 3(20)
220 - 100 = 180 -60
120 = 120 True!
Answer: The required equation of the ellipse in standard form is
Step-by-step explanation: We are given to find the equation of an ellipse in standard form with the vertical major axis of length 10 units and minor axis of length 8 units.
Since the major axis is vertical, so it will lie on the Y-axis. Let the standard form of the ellipse be given by
where the length of major axis is 2a units and length of minor axis is 2b units.
According to the given information, we have
and
Substituting the values of a and b in equation (i), we get
Thus, the required equation of the ellipse in standard form is
Answer:
The calculated value of test statistic is z=2.48.
This has a P-value of P=0.00657.
If we state the null hypothesis at a significance level of , we would reject this null hypothesis as .
Step-by-step explanation:
We have in this problem, a hypothesis test of proportions.
The test statistic for this is the z-value, and is calculated like that:
Where the term 0.5/N is the correction for continuity and is negative in the cases that p>π.
p: proportion of the sample; π: proportion of the population; σ: standard deviation of the population.
The standard deviation of the population has to be calculated as:
The proportion of the sample (p) is .
Then, the test statistic z is
The P-value of this statistic is P(z>2.48)=0.00657
If we state the null hypothesis at a significance level of , we would reject this null hypothesis as .
Answer:
Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.
Step-by-step explanation:
Given that, the volume of cylindrical can with out top is 25 cm³.
Consider the height of the can be h and radius be r.
The volume of the can is V=
According to the problem,
The surface area of the base of the can is =
The metal for the bottom will cost $2.00 per cm²
The metal cost for the base is =$(2.00× )
The lateral surface area of the can is =
The metal for the side will cost $1.25 per cm²
The metal cost for the base is =$(1.25× )
Total cost of metal is C= 2.00 +
Putting
Differentiating with respect to r
Again differentiating with respect to r
To find the minimize cost, we set C'=0
⇒r=1.71
Now,
When r=1.71 cm, the metal cost will be minimum.
Therefore,
⇒h=2.72 cm
Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.
An expression is defined as a set of numbers, variables, and mathematical operations. The value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of the expression −b²−2bx²−x will be,
−b² − 2bx² − x
= − b² − 2b(-2)² − (-2)
= − b² − 8b + 4
Hence, the value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.
Learn more about Expression:
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Answer:
(a) The probability that a household views television between 3 and 9 hours a day is 0.5864.
(b) The viewing hours in the top 2% is 13.49 hours.
(c) The probability that a household views television more than 5 hours a day is 0.9099.
Step-by-step explanation:
Let X = daily viewing time of of television hours per household.
The mean daily viewing time is, μ = 8.35 hours.
The standard deviation of daily viewing time is, σ = 2.5 hours.
The random variable X is Normally distributed.
To compute the probability of a Normal random variable, first we need to compute the raw scores (X) to z-scores (Z).
(a)
Compute the probability that a household views television between 3 and 9 hours a day as follows:
Thus, the probability that a household views television between 3 and 9 hours a day is 0.5864.
(b)
Let the viewing hours in the top 2% be denoted by x.
Then,
P (X > x) = 0.02
⇒ P (X < x) = 1 - 0.02
P (X < x) = 0.98
⇒ P (Z < z) = 0.98
The value of z for the above probability is:
z = 2.054
*Use a z-table for the value.
Compute the value of x as follows:
Thus, the viewing hours in the top 2% is 13.49 hours.
(c)
Compute the probability that a household views television more than 5 hours a day as follows:
Thus, the probability that a household views television more than 5 hours a day is 0.9099.