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melamori03 [73]
3 years ago
5

Amy works for 36 hours per week for 10 weeks during the summer, making $\$3000$. If she works for 30 weeks during the school yea

r at the same rate of pay and needs to make another $\$3000$, how many hours per week must she work?
Mathematics
1 answer:
Zinaida [17]3 years ago
6 0

Answer:

12 hours per week

Step-by-step explanation:

1. Find how many hours she worked to make $3,000 (36x10=360 hours)

2. divide 360 hours by 30 weeks

she would need to work 12 hours per week to make $3,000

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In a particular game, a fair die is tossed. If the number of spots showing is either four or five, you win $1. If the number of
TiliK225 [7]

Answer:

The probability that you win at least $1 both times is 0.25 = 25%.

Step-by-step explanation:

For each game, there are only two possible outcomes. Either you win at least $1, or you do not. Games are independent. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Probability of winning at least $1 on a single game:

The die has 6 sides.

If it lands on 4, 5 or 6(either of the three sides), you win at least $1. So

p = \frac{1}{2} = 0.5

You are going to play the game twice.

This means that n = 2

The probability that you win at least $1 both times is

This is P(X = 2).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{2,2}.(0.5)^{2}.(0.5)^{2} = 0.25

The probability that you win at least $1 both times is 0.25 = 25%.

4 0
3 years ago
A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int
Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}

By expanding the previous equation:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0

Since there is no accumulation within the tank, expression is simplified to this:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}, where c(0) = 0 \frac{pounds}{gallon}.

\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}

The solution of this equation is:

c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})

The salt concentration after 8 minutes is:

c(8) = 0.166 \frac{pounds}{gallon}

The instantaneous amount of salt in the tank is:

m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds

3 0
3 years ago
Identify the constant term in this expression 28m + 4n - 12m +3 =
kodGreya [7K]

Step-by-step explanation:

28m+4n-12m+3

28m-12m+4n+3

16m+4n+3

8 0
2 years ago
A scientist needs to make 2 liters of saline solution (salt water), in which the salt
gulaghasi [49]

Answer:

1.60 L of 10% solution

0.40 L of 35% solution

Step-by-step explanation:

If x = amount of 10% saline solution, and y = amount of 35% saline solution, then:

x + y = 2

0.10x + 0.35y = 0.15(2)

Solve with substitution:

0.10x + 0.35(2 − x) = 0.15(2)

0.10x + 0.70 − 0.35x = 0.30

0.40 = 0.25x

x = 1.60

y = 0.40

5 0
3 years ago
A robot can complete 3 tasks in 2/5 hour. Each task takes the same amount of time. a. How long does it take the robot to complet
Elena L [17]
It takes 8 minutes
The robot can complete 7.5 tasks in an hour
3 0
3 years ago
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