A truck driver drove 49 miles in 1 1/3 hours. What is the average speed, in miles per hour, or this trip?

There are 22 rows of seats on a concert hall: 23 seats are in the 1st row, 27 seats on the 2nd row, 31 seats on the 3rd row, and

JulijaS [17]

We can model this situation with an arithmetic series.
we have to find the number of all the seats, so we need to sum up the number of seats in all of the 22 rows.

1st row: 23
2nd row: 27
3rd row: 31
Notice how we are adding 4 each time.

So we have an arithmetic series with a first term of 23 and a common difference of 4.

We need to find the total number of seats. To do this, we use the formula for the sum of an arithmetic series (first n terms):

Sₙ = (n/2)(t₁ + tₙ)

where n is the term numbers, t₁ is the first term, tₙ is the nth term

We want to sum up to 22 terms, so we need to find the 22nd term

Formula for general term of an arithmetic sequence:

tₙ = t₁ + (n-1)d,

where t1 is the first term, n is the term number, d is the common difference. Since first term is 23 and common difference is 4, the general term for this situation is

tₙ = 23 + (n-1)(4)

The 22nd term, which is the 22nd row, is

t₂₂ = 23 + (22-1)(4) = 107

There are 107 seats in the 22nd row.

So we use the sum formula to find the total number of seats:

S₂₂ = (22/2)(23 + 107) = 1430 seats

Total of 1430 seats.
If all the seats are taken, then the total sale profit is

1430 * $29.99 = $42885.70

4 0

3 years ago

What is the solution to the equation 41+5 -3- 7+5?

AleksandrR [38]

Answer:

no solution

Step-by-step explanation:

it's just 41

4 0

3 years ago

Read 2 more answers

Melissa buys 2 1/2 pounds of salmon and 1 1/4 pounds of swordfish. She pays a total of $31.25, and the swordfish cost $.20 per p

julsineya [31]

Answer:

The combined cost of 1 pound of salmon and 1 pound of swordfish is $16.66

Step-by-step explanation:

Let us assume the cost of 1 pound salmon = $ m

So the cost of 1 pound of 1 pound swordfish cat = $ ( m - 0.20)

Now, the Amount of salmon purchased = 2 1/2 pounds

$2\frac{1}{2} = 2 + \frac{1}{2} = 2 + 0.5 = 2.5$

So, the amount of salmon purchased = 2.5 pounds

Cost of buying 2.5 pounds = 2.5 x ( 1 pound cost)

= 2.5 ( m) = $ 2.5 m ...... (1)

Also, the Amount of swordfish purchased = 1 1/4 pounds

$1\frac{1}{4} = 1 + \frac{1}{4} = 1 + 0.25 = 1.25$

So, the amount of swordfish purchased = 1.25 pounds

Cost of buying 1.25 pounds = 1.25 x ( 1 pound cost of swordfish)

= 1.25 ( m - 0.20) = $ 1.25 m - 0.25 .... (2)

Now, the combined cost paid = $ 31.25

⇒Cost of buying (2.5 pounds salmon + 1.25 pounds swordfish) = $ 31.25

or, 2.5 m + 1.25 m - 0.25 = 31.35 (from (1) and (2))

or, 3.75 m = 31.60

or, m = 31.60/3.75 = 8.43

⇒ m = $8.43

So, the cost of 1 pound salmon = m = $8.43

and the cost of 1 pound swordfish = m - 0.20 = $8.43 - 0.20 = $ 8.23

Hence, the combined cost 1 pound of salmon and 1 pound of swordfish = $8.43 + $ 8.23 = $ 16.66

6 0

3 years ago

15. The dollar amount y that remains to be repaid on a loan x months after the loan is issued is represented by y=-1000x + 8000.

irina [24]

Answer:

1) $8000

2) $1000

3) 8 months, since y represents our remaining amount to be paid, we set it equal to 0, to see when $0 need to be paid. Solving for x (months), we can it to be 8.

Step-by-step explanation:

We have the equation y = -1000x + 8000 which follows the linear equation:

y = mx + b, where m is our slope and b is our y-intercept

1) The initial balance can be found with our constant "b" which in this case is 8000. You can also plot the function of y and you will find that 8000 is the intercept when x = 0, aka the start

2) We can calculate the rate of change for when the loan is repaid by looking at the slope "m", in this case it is 1000. It subtracts 1000 each month, meaning $1000 is being payed and taken out of the bank account

3) To find how many months it will take for the loan to be repaid, let's solve for x when y = 0.

0 = -1000x + 8000

-8000 = -1000x

8 = x

It will take 8 months. Why? Since y represents our remaining amount to be paid, we set it = 0, to see when $0 need to be paid. Solving for x (months), we can it to be 8.

5 0

3 years ago

Using the problem below, solve and explain how you got the solution to the system of equation.

Paul [167]

Answer:

(5, -3)

y= -3

x= 5

Step-by-step explanation:

-x-2y=1

x+y=2

solve the equation

-x-2y=1

x=2-y

substitute the value of x into an equation

-(2-y)-2y=1

remove parenthesis

-2-y-2y=1

subtract y to 2y

-2-y=1

add 2 from both sides

-y=3

divide both sides by -y

y= -3

substitute the value of y into an equation

x=2-(-3)

remove parenthesis

x=2+3

add 2 to 3

x=5

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(5,-3)

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7 0

3 years ago