The perimeter of a square field is 64 m. If the field is surrounded by a running path of width 3.5 m, find the area of the path. How to solve​

Answer:

a. [tex]\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c[/tex]

b. [tex]x(t) = 6\frac{2}{3} \cdot c \cdot t[/tex]

c. [tex]c = \dfrac{3}{8} \ g/L[/tex]

Step-by-step explanation:

a. The volume of water initially in the fish tank = 15 liters

The volume of brine added per minute = 5 liters per minute

The rate at which the mixture is drained = 5 liters per minute

The amount of salt in the fish tank after t minutes = x

Where the volume of water with x grams of salt = 15 liters

dx =  (5·c - 5·c/3)×dt = 20/3·c = [tex]6\frac{2}{3} \cdot c \cdot dt[/tex]

[tex]\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c[/tex]

b. The amount of salt, x after t minutes is given by the relation

[tex]\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c[/tex]

[tex]dx = 6\frac{2}{3} \cdot c \cdot dt[/tex]

[tex]x(t) = \int\limits \, dx = \int\limits \left ( 6\frac{2}{3} \cdot c \right) \cdot dt[/tex]

[tex]x(t) = 6\frac{2}{3} \cdot c \cdot t[/tex]

c. Given that in 10 minutes, the amount of salt in the tank = 25 grams, and the volume is 15 liters, we have;

[tex]x(10) = 25 \ grams(15 \ in \ liters) = 6\frac{2}{3} \times c \times 10[/tex]

[tex]6\frac{2}{3} \times c =\dfrac{25 \ grams }{10}[/tex]

[tex]c =\dfrac{25 \ g/L }{10 \times 6\frac{2}{3} } = \dfrac{25 \ g/L}{10 \times \dfrac{20}{3} } =\dfrac{3}{200} \times 25 \ g/L= \dfrac{75}{200} \ g/L = \dfrac{3}{8} \ g/L[/tex]

[tex]c = \dfrac{3}{8} \ g/L[/tex]

y-intercept is where the line on your graph crosses through the y-axis

Answer:

Step-by-step explanation:

Answer:

4/9

Step-by-step explanation:

you know how many marbles there are in the bag so you add the number which is 9 so this shkws it will be something out of 9 since that is the total so now there are 4 blue marbles so you will just have to 4/9 I think thats how I would go on doing it.

Answer:

Step-by-step explanation:

The perimeter of ABCD is 30cm

The Sum of the perimeter of three rectangles at the corner is 20cm.

following the variables as the same as you assigned

large rectangle: u by v

rectangle center A: 2a by 2b

rectangle center B: 2c by 2d

rectangle center D: 2e by 2f

2 equations (from the givens):

2u+2v=30

2(a + b + c + d + e + f )= 20

now to find the length

a+b+a/2+b/2+(v-b/2-d/2)+c/2+d+c+d/2+(u-c/2)+(v-f/2)+e/2+f+e+f/2+(u-e/2-a/2)

which is (a+b+c+d+e+f)+u+v+u+v = 10+30=40

Answer:

1.5 pints.

Step-by-step explanation:

Solution,

Given,

1 cup = 8 oz.

2 cup = 1 pint.

So,

24 oz = 1 cup / 8 = 3 cup.

Then,

We have,

3 cup = 1 pint / 2 cups = 1.5 pints.

Answer:

(x - 36) is the measure of the angle A  

Step-by-step explanation:

Answer: Expanded Notation to Numeric Form with Decim. Convert each problem to numeric notation. Ex) 4x 10+9+(2*70) +(6x/100). Answers. 49.26. 1) 7 * 100+ 2 ...

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

In order to figure out which of the 4 is a function, you must perform the vertical line test for each. No vertical line should intersect the graph of the relation at more than one point. D is the only one that doesnt hit two points when performing the vertical line test.

Since there are unique outputs for every point of x-axis so it represents a fucntion. Hence option D is correct.

Use the concept of fucntion is defined as:

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Since we know that in a fucntion,

For each element of the domain, there is only one output.

Therefore,

For Figure A:

There are two outputs for each value of the positive x-axis.

This is not a function.

For Figure B:

There are outputs for x = 3,

Hence this is also not a fucntion.

For Figure C:

For a circle, there are always two puts,

Hence, This is also not a fucntion.
Figure D:

W can see that for each value of x-axis, there is a unique output,

Hence this is a function. So option D is correct.

To learn more about the function visit:

https://brainly.com/question/8892191

#SPJ6

Answer:

A, D and F

Step-by-step explanation:

3√6 = √3^2*6

3√6 = √54

Applicable answers

A. √54 = √27*2 = √27 * √2

D. 3√6 = √54

F. √54 = √9*6 = √9 * √6

Answer:

B.

He added up his transactions incorrectly.

Answer:

it is 11 i believe if not sry delete my answer

Step-by-step explanation:

If the ambient temperature is 0 then the damage index would be 14. Then the correct option is D.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

Sven investigates the amount of damage to the head gaskets on the trucks in his fleet and the damage index depends on the ambient temperature.

He develops the equation y = –23x + 14 to model the relationship.

where y be the damage index and x be the temperature.

At zero temperature, the damage index will be

y = –23 (0) + 14

y = 14

The damage index is 14.

More about the linear system link is given below.

https://brainly.com/question/20379472

Answer:

215 in³

Step-by-step explanation:

This is just for math problems.

The 1970 Dodge Challenger could have engines ranging from 225 cubic inches to 440 cubic inches.

What is the difference in displacement between the smallest and largest engines?

Now it's a math problem.

440 - 225 = 215

Answer: 215 in³

$10.50

14÷4= 3.5 so, 3.5 x 3 = 10.50

Answer:

The Answer is D

Step-by-step explanation:

Answer:

20 is 12 1/2

21 is 11 1/5

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

5, 5, 6, 7, 7, 7

7 appears the most

Answer:

The mode is 7

Step-by-step explanation:

Add all of these numbers and divide it by 8 to get 7

Answer:13.04

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Since 3 symbols represent 18 books, half of the symbol is 3. 18+3=21

Vic's cookies having a ratio of flour to butter of 250/170 contains less

butter than Imani's cookies, 750/630, what Vic will think is therefore;

(A) Imani's cookies have too much butter

The quantity of flour per 170 grams of butter in Vic's cookies = 250 grams

The amount of flour Imani uses for every 630 grams of butter = 750 grams

Required:

What Vic will think about the amount of butter in Imani's cookies

Solution;

[tex]Ratio \ of \ butter \ per \ gram \ of \ flour \ in \ Vic's \ cookies = \dfrac{170 \, g}{250 \, g} = \dfrac{17}{25} = \mathbf{0.68}[/tex]

[tex]Ratio \ of \ butter \ per \ gram \ of \ flour \ in \ Imani's\ cookies = \dfrac{630\, g}{750\, g} = \dfrac{17}{25} = \mathbf{0.84}[/tex]

Imani's cookies contains more cookies than Vic's cookies, what Vic will

think of the amount of butter in Imani's cookies is therefore;

(A) Imani's cookies have too much butter

Learn more about fractions here:

https://brainly.com/question/24378782

Answer:

Step-by-step explanation:

the answer is A ^^

Answer:

The data is:

Number of nickels = 246

Number of dimes = 312

Number of quarters = 204.

Now, in your group there are N people.

Dividing the coins into N people, you find that each one received the same amount of each type of coin. Then the quotient between each number of coins and N must be a whole number.

Now, you can see that the 3 numbers are even, so we know that N must be even.

For example, if N = 2, we could divide the 3 numbers of coins and get an integer in each case, but this is worded as "You and some friends" so N must be larger than 2.

Try with the next even integer:

N = 4.

nickels: 246/4 = 61.5

61.5 is not an integer: Then N can not be 4.

The next even number is N = 6.

nickels: 246/6 = 41

dimes: 312/6 = 52

quarters: 204/6 = 34

In each case we have integers, this means that 6 divides the 3 numbers of coins, so each person can receive the same amount of coins.

The we can conclude with:

There are 6 persons in the group.

Each person gets 41 nickels, 52 dimes and 34 quarters.

Step-by-step explanation:

Take the average of the two points that are on each side of the shapes.

--> to find the circle's number, 1+0/2 = 0.5

triangle = 3+2/2 = 2.5

star = 4+3/2 = 3.5

Answer:

ED = 12

HOPE THIS HELP YOU , FOR ANY QUESTION PLEASE ASK ME .

31 < 31,5 < 32

31,5 is between 31 and 32

Answer:

It's between 5 and 6.

Step-by-step explanation:

I took the test and got it right. The explanation they give is that the number lies between the square roots of two perfect squares, 25, and 36, so it is between 5 and 6.

Answer:

1.2 × 10^6 hours

Step-by-step explanation:

Given the following :

equation relating the distance traveled in miles, d, to the number of hours flying, t ;

t=1500d

How long will it take the airplane to travel 800 miles

Here, d = 800 miles

Hence,

t = 1500(800) = 1,200,000 hours

t = 1.2 × 10^6 hours