A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength-training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength-training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week.Which statement describes when the plans are based on the same number of aerobic exercise sessions?

Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.

Answers

Answer 1

Answer: Let y be the number of strength-training exercises per week.
Let x be the number of aerobic exercises per week.
For the beginner plan:
15y + 20x = 90 ..........(1)
For the advanced plan:
20y + 30x = 130 ........(2)
Multiply both sides of (1) by 3 to get:
45y + 60x = 270 ........(3)
Multiply both sides of (2) by2 to get:
40y + 60x = 260 .......(4)
Subtracting (4) from (3) we get:
5y = 10
y = 2
Plugging in the value of 2 for y in equation and solving, we find x = 3.
Therefore the correct statement is:
"Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week."

Answer 2

Answer:

Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.

How to Solve Algebra Word Problems?

Let y be the number of strength-training exercises per week.

Let x be the number of aerobic exercises per week.

For the beginner plan, the equation would be gotten as;

15y + 20x = 90 ------(eq 1)

The equation to represent the advanced plan would be;

20y + 30x = 130 -------(eq 2)

Multiply both sides of eq 1 by 4 to get:

60y + 80x = 360 ------(eq 3)

Multiply both sides of eq 2 by 3 to get:

60y + 90x = 390 ------(eq 4)

Subtract eq(3) from eq(4) we get:

10x = 30

Thus; x = 3

Then; 15y + 20(3) = 90

15y = 30

y = 2

Thus, the correct statement is:

"Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week."

Read more about Algebra Word Problems at; brainly.com/question/4344214

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A machine does 1000 tasks in 4.3 x 10^-2 seconds. How much task will be done in 2 hours? Leave answer in scientific notation.

Answers

You need to find out how many times (4.3 x 10^-2 seconds) goes into 2 hours,
and however many times that is, the machine will do that many thousand tasks.
It's just a simple division problem.

2 hours = 7,200 seconds

(7.2 x 10^3 seconds) / (4.3 x 10^-2 seconds) = 1.674 418 605 x 10^5 times (rounded)

The machine completes 1.674 418 60 x 10^8 tasks, and it's working on
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Evaluate the expression x - 7. If x= 12.
19
6
17
5

Answers

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{5}}}}}$

Step-by-step explanation:

Given , value of x = 12

To find : Value of the given expression

Given expression = $\sf{x - 7 }$

plug the value of x

$\dashrightarrow{ \sf{ 12 - 7}}$

Subtract 7 from 12

$\dashrightarrow{ \sf{5}}$

Hope I helped!

Best regards! :D

a community hall is in the shape of a cuboid. the hall is 20m long, 15m wide and 4m high. the community hall needs re-decorating with new paint for the walls and ceiling, and new tiles on the floor. a 20l tin of paint covers 40 squared metres and costs £15. 1 squared metre floor tiles cost £3 each. work out the total cost of paint and tiles needed to decorate the community hall.

Answers

Answer:

the total cost of paint and tiles needed to decorate the community hall is £105 + £900 = £1005.

Step-by-step explanation:

Area of the walls:

- The community hall is shaped like a cuboid, so the walls are the four rectangular sides.

- The length and height of each wall are given as 20m and 4m, respectively.

- The total area of the walls is the sum of the areas of all four walls: 2 * (length * height + width * height).

- Substituting the given values, we have: 2 * (20m * 4m + 15m * 4m).

2. Area of the ceiling:

- The ceiling is also a rectangle, with the same length and width as the floor.

- The area of the ceiling is given by length * width: 20m * 15m.

3. Area of the floor:

- The area of the floor is the same as the area of the ceiling: 20m * 15m.

Now, let's calculate the areas:

1. Area of the walls:

- 2 * (20m * 4m + 15m * 4m) = 2 * (80m^2 + 60m^2) = 2 * 140m^2 = 280m^2.

2. Area of the ceiling:

- 20m * 15m = 300m^2.

3. Area of the floor:

- 20m * 15m = 300m^2.

Next, we can calculate the number of tins of paint and tiles needed and their costs:

- Number of tins of paint needed = Area of walls / Coverage per tin = 280m^2 / 40m^2/tin = 7 tins.

- Cost of paint = Number of tins * Cost per tin = 7 tins * £15/tin = £105.

- Number of tiles needed = Area of floor / Area per tile = 300m^2 / 1m^2/tile = 300 tiles.

- Cost of tiles = Number of tiles * Cost per tile = 300 tiles * £3/tile = £900.

Therefore, the total cost of paint and tiles needed to decorate the community hall is £105 + £900 = £1005.

yes, i am a student

The value of y varies directly with x, and y=5 , when x=10. Find y when x=24

Answers

Answer:

y=12

Step-by-step explanation:

5 is half of 10 so there for y is always half of x in this problem

When I was 2 years old, my sister was half of my age. Now Im 80 years old, how old is my sister?

Answers

Half of 2 = 1 so 1 year apart . That means

80-1 = 79 years

if u were 2 years old n your sister was half your age then her age must be 1
so her present age is 80-1=79(since she was just one year smaller than u)

What value represents the vertical translation from the graph of the parent function f(x) = x2 to the graph of the functiong(x) = (x + 5)2 + 3?