MATHEMATICS MIDDLE SCHOOL

The price of a train ticket consists of an initial fee plus a constant fee per stop.The table compares the number of stops and the price of a ticket (in dollars).
Stops Price (dollars)
3 6.50
7 12.50
11 18.50
What is the initial fee?

Answers

Answer 1

Answer:

Answer:

Initial Fee is $2.

Step-by-step explanation:

Given:

Stops Price (dollars)

3 6.50

7 12.50

11 18.50

Also Given:

The price of a train ticket consists of an initial fee plus a constant fee per stop.

So let the Cost of initial fee be 'x'.

Also Let the Cost of Constant fee be 'y'.

Now Equation can framed as;

$Price (P) = x + (y* \textrm{Number of Stops})$

Now According to table;

Number of stops = 3

Price = 6.50

So equation can be framed as;

$x+3y =6.50 \ \ \ \ equation \ 1$

Also According to table;

Number of stops = 7

Price = 12.50

So equation can be framed as;

$x+7y =12.50 \ \ \ \ equation \ 2$

Now Subtracting equation 1 from equation 2 we get;

$(x+7y)-(x+3y) =12.50-6.50\n\nx+7y-x-3y=6\n\n4y =6\n\ny= (6)/(4)=\$1.5$

Substituting the value of y in equation 1 we get;

$x+3*1.5=6.50\n\nx+4.5=6.50\n\nx =6.50-4.5 = \$2$

Hence Initial Fee is $2.

Answer 2

Answer:

Final answer:

The initial fee of a train ticket, given a constant fee per stop, can be calculated by finding the constant fee per stop and subtracting the total of this fee for a given number of stops from the total price for those stops. By this calculation, the initial fee is $2.50.

Explanation:

To determine the initial fee that is related to the price of a train ticket, which consists of an initial fee plus a constant fee per stop, we should first calculate the cost per stop. We can do this by subtracting the price of a ticket for 3 stops from the price of a ticket for 7 stops. So, we get $12.50 - $6.50 = $6.00. We find the difference in the number of stops, which is 7 - 3 = 4 stops. Divide the total price difference by the difference in the number of stops to get the constant fee per each stop: $6.00 / 4 stops = $1.50 per stop. Now we know the constant fee for each stop, so we subtract that from the total price for 3 stops to find the initial fee: $6.50 - ($1.50 * 3) = $2.50. So, the initial fee is $2.50.

To find the initial fee, we need to determine the additional cost per stop. We can do this by using the formula y = mx + b, where y represents the price of the ticket, x represents the number of stops, m represents the constant fee per stop, and b represents the initial fee.

Using the given data, we can set up two equations using the points (3, 6.50) and (7, 12.50).

By subtracting these two equations, we can determine the value of b, which represents the initial fee. Thus, the initial fee is $3.

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Answers

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Step-by-step explanation:

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An element with Mass 630 grams decays by 18.8% per minute. How much of the element is remaining after 7 minutes, to the nearest 10th of a gram?

Answers

Answer:

146.6 grams

Step-by-step explanation:

We have been given an element with Mass 630 grams decays by 18.8% per minute.

We will use exponential decay function to solve our given problem.

$y=a\cdot (1-r)^x$ , where,

y = Final amount,

a = Initial amount,

r = Rate of decay in decimal form,

x = Time.

$18.8\%=(18.8)/(100)=0.188$

Substitute the given values:

$y=630\cdot (1-0.188)^7$

$y=630\cdot (0.812)^7$

$y=630\cdot 0.232751347$

$y=146.633349$

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Therefore, 146.6 grams of the element is remaining after 7 minutes.

$630 * {81.2}^(7)$
1.5

What is the area of the figure?

Answers

I have already answered it

We first divide the big shape into smaller shapes

We get a trapezium and a triangle

We add the areas of the trapezium and the triangle together to get the total area of the big shape
It would be:

Area = area of trapezium + Area of triangle
= $(1)/(2)$ × 5 (14 + 18) + $(1)/(2)$ × 12 × 18
= 80 + 48
= 128 mm²

I need help on 13-26 please

Answers

13. 10% of 40
= 40 × 0.10 = 4

14. 12% of 100
= 100 × .12 = 12

15. 99% of 60
= 60 × .99 = 59.4

16. 100% of 81
= 81 × 1 = 81

17. 45% of 360
= 360 × .45 = 162

18. 55% of 1,024
= 1024 × .55 = 563.2

19. 45 + n = 97
n = 97 - 45 = 52

20. n - 18 = 100
n = 100 + 18 = 118

21. n - 72 = 91
n = 91 + 72 = 163

22. n + 23 = 55
n = 55 - 23 = 32

23. 5 × t = 105
t = 105 ÷ 5 = 21

24. b ÷ 13 = 8
b = 8 × 13 = 104

25. k × 18 = 90
k = 90 ÷ 18 = 5

26. d ÷ 7 = 8
d = 8 × 7 = 56

Mr. Santos is carpeting his living room. The room measures 21 feet by 15 feet. The carpeting costs $9 per square foot. How much carpeting will he need (in square feet), and how much will it cost?