A tank contains 30 lb of salt dissolved in 300 gallons of water. a brine solution is pumped into the tank at a rate of 3 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 3 gal/min. determine a(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by cin(t) = 2 + sin(t/4) lb/gal.

Answer:

6280

Step-by-step explanation:

It's 6280

Final answer:

The average speed of the train Megan is traveling on is 40 miles per hour. It's obtained by dividing the total distance of 80 miles by the total time of 2 hours.

Explanation:

To find the average speed of the train that Megan is riding, which covers 80 miles in 2 hours, we will use the formula for average speed, which is total distance divided by total time. The train travels 40 miles one way and 40 miles back, totaling 80 miles.

Here is the step-by-step calculation:

Calculate the total distance the train travels: 40 miles one way + 40 miles back = 80 miles.

Calculate the total time of the journey: 2 hours.

Divide the total distance by the total time to find the average speed: 80 miles / 2 hours = 40 miles per hour.

This means the average speed of the train is 40 miles per hour.

To calculate Caleb's monthly car payments, use the loan amortization formula that deals with compound interest, not simple interest. Input the loan amount of $6,900, the monthly interest rate (annual rate of 5.4% divided by 12), and the total number of payments (5 years times 12 payments per year) into the formula to find the monthly payment.

Caleb's car loan scenario comes under financial mathematics, specifically, it deals with loan amortization using the concept of compound interest. Since the car loan spans multiple years, compound interest is the accurate model to use, not simple interest. As opposed to simple interest which only accrues on the original amount or principal, compound interest accrues on the principal and all interest previously added.

The formula to calculate the monthly payment, P, on a loan is given by, where PV represents t

he present value or the amount of loan, which is $6,900 in this case; r is the monthly interest rate which can be calculated as annual interest rate divided by 12, translating to 0.054/12 in this case; and n is the total number of payments (i.e., 5 years of payments with 12 payments per year, hence, 5*12).

To calculate the monthly payment, plug these values into the formula which should give you the monthly payment amount that Caleb needs to pay for his car loan.

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Answer:

The median of the data set is 14.

Answer:

1.68 kilo grams are required for 14 people.

Step-by-step explanation:

First of all the answer is required in kilo grams and the data given is in grams.

Lets convert the given value to kilo grams;

480 grams = 0.48 kilo grams

If 0.48 kilo grams are required to cater 4 people then how many kilo grams are required to cater 14 people?

⇒[tex]\frac{0.48}{4} *14[/tex] kilo grams

1.68 kilo grams.

The length of the hypotenuse of the triangle is √58 cm (Option D).

To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's label the sides of the triangle:

Side a = 7 cm (one of the legs)

Side b = 3 cm (the other leg)

Side c = ? (the hypotenuse)

The Pythagorean theorem is:

[tex]c^2 = a^2 + b^2[/tex]

Substitute the given values:

[tex]c^2 = 7^2 + 3^2\\\\c^2 = 49 + 9\\\\c^2 = 58[/tex]

Now, we can find the square root of both sides to solve for c:

c = √58 cm

So, the length of the hypotenuse of the triangle is √58 cm.

The correct answer is: D. √58 cm

To know more about hypotenuse, refer here:

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Final answer:

The question pertains to creating five-digit numbers using the digits 0, 1, 2, and 3, with the restriction that the digit 0 cannot be used as the first digit. We consider the choices for each digit, leading to a total of 768 different combinations.

Explanation:

The student is asking about forming five-digit numbers with a set of digits 0, 1, 2, 3. To create five-digit numbers with these digits, we need to consider that each digit position can be one of these four digits. The fact that 0 is included as one of the possible digits is significant because it means 0 cannot be used as the first digit in a five-digit number as that would create a four-digit number.

Since there are restrictions on the use of 0 in the first position, the first position can only be filled with digits 1, 2, or 3, providing us with three choices for the first digit. The remaining four positions can be filled by any of the four digits (0, 1, 2, 3) without restriction. Thus, for each of the remaining four positions, we have four choices.

To calculate the total number of different five-digit numbers that can be formed, we would multiply the number of choices for each position, which yields 3 choices for the first digit and 4 choices for each of the remaining four digits. Therefore, the formula becomes 3 * 4 * 4 * 4 * 4, which equals 768 different five-digit numbers.

There are 768 five-digit numbers that can be formed using the digits {0, 1, 2, 3}.

To find out how many five-digit numbers can be formed using the set of digits {0, 1, 2, 3}, we can use the concept of permutations.

Since we want to form a five-digit number, we have 5 positions to fill. For each position, we have 4 choices: 0, 1, 2, or 3.

However, since the number cannot start with 0, we have only 3 choices for the first digit.

After choosing the first digit, the remaining four positions can be filled with any of the digits {0, 1, 2, 3}.

So, the total number of five-digit numbers that can be formed using the given set of digits is:

3 (choices for the first digit) × 4 (choices for each of the remaining four digits) × 4 (choices for each of the remaining four digits) × 4 (choices for each of the remaining four digits) × 4 (choices for each of the remaining four digits)

This simplifies to:

3 × 4^4 = 3 × 256 = 768

Therefore, there are 768 five-digit numbers that can be formed using the digits {0, 1, 2, 3}.

Question

Suppose we want to form five-digit numbers using the set of digits {0, 1, 2, 3}. For example, 30133 and 22301 are such numbers, but 03731 is not. How many such numbers are possible? There are no five-digit numbers formed by using the digits {0, 1, 2, 3}.

Answer:

P(B) = 0.55 .

Step-by-step explanation:

We are given that  P(A or ​B) = 0.6 ​, P(A) = 0.4 ​, and​ P(A and ​B) = 0.35 .

As we know that;

     P(A or B) = P(A) + P(B) - P(A and B)

         0.6 = 0.4 + P(B) - 0.35

           P(B) = 0.35 + 0.6 - 0.4 = 0.55

Therefore, P(B) = 0.55 .

Answer:

All options are correct except Δx = 0.

So select: Δy = 0 Δy = n Δx = n Δy = -n  Δx = -n

Step-by-step explanation:

Δy can be positive, negative, or zero. The value of  Δx can be positive or negative but not zero. From Odyssey ware.

Based on the concept of the axis of symmetry, the equation of the axis of symmetry of the parabola is x = 2.

To find the equation of the axis of symmetry of a parabola given its x-intercepts, we can use the fact that the axis of symmetry is the vertical line that passes through the midpoint of the x-intercepts.

The midpoint formula is given by:

x-coordinate of midpoint = (x-intercept1 + x-intercept2) / 2

In this case, the x-intercepts are -3 and 7. Let's calculate the midpoint:

Midpoint = (-3 + 7) / 2

Midpoint = 4 / 2

Midpoint = 2

Therefore, the x-coordinate of the midpoint (and the equation of the axis of symmetry) is x = 2.

Hence, in this case, it is concluded that the equation of the axis of symmetry of the parabola is x = 2.

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