All categories

3 years ago

In the picture thank you

Mathematics

2 answers:

jonny [76]3 years ago

7 0

Answer:

1100 adults and 1400 students

Step-by-step explanation:

Let S = students and A = adults.

We have two conditions.

(1) 5S + 10A = 18 000

(2) S + A = 2500 Subtract A from each side

(3) S = 2500 – A Substitute (3) into (1)

5(2500 – A) + 10A = 18 000 Remove parentheses

12 500 – 5A + 10 A = 18 000 Combine like terms

12 500 + 5A = 18 000 Subtract 12 500 from each side

5A = 5500 Divide each side by 6

(4) A = 1100 Substitute (4) into (2)

S + 1100 = 2500 Subtract 1100 from each side

S = 1400

There were 1100 adults and 1400 students.

Check:

5 × 1400 + 10 × 1100 = 18 000 1400 + 1100 = 2500

7 000 + 11 000 = 18 000 2500 = 2500

1 8 000 = 18 000

dmitriy555 [2]3 years ago

5 0

Answer:

The correct answer is b) 1100 adults and 1400 students.

Step-by-step explanation:

To find this, set up a system of equations in which x is the number of students who attend and y is the number of adults who attend.

First start by creating an equation for money made.

5x + 10y = 18,000

Now write an equation for the amount that attend.

x + y = 2,500

Now multiply the bottom equation by -5 and add the equations together.

-5x - 5y = -12,500

5x + 10y = 18,000

5y = 5,500

y = 1,100

Since this is the number of adults, we can plug into an original equation to find the number of students.

x + y = 2,500

x + 1,100 = 2,500

x = 1,400

You might be interested in

Create and solve a system of equations and solve for x and y.

Helga [31]

Answer:

Step-by-step explanation: x+4-5=y

8 0

2 years ago

Which of the following expressions is equal to 1 divided by 16

faust18 [17]

Answer: 21

Step-by-step explanation:

8 0

3 years ago

A litre bottle of KERPOW washing up liquid costs £1.95.

Alex_Xolod [135]

Answer:

500 washes

Step-by-step explanation:

Number of washes

Total volume / Volume used each time
5 L / 10 mL

But remember : 1 L = 1000 mL

5000 mL / 10 mL
500 washes

4 0

2 years ago

Can someone explain to me how integers work?

ollegr [7]

What are Integers?

The integers (from the Latin integer, which means with untouched integrity, whole, entire) are the set of numbers consisting of the natural numbers including 0 (0, 1, 2, 3, ...) and their negatives (0, −1, −2, −3, ...). They are numbers that can be written without a fractional or decimal component, and fall within the set {... −2, −1, 0, 1, 2, ...}. For example, 65, 7, and −756 are integers; 1.6 and 1½ are not integers. In other terms, integers are the numbers one can count with items such as apples or fingers, and their negatives, including 0.

6 0

3 years ago

A 500500-gallon tank initially contains 200200 gallons of brine containing 100100 pounds of dissolved salt. brine containing 11

mixer [17]

Let $A(t)$ denote the amount of salt in the tank at time $t$ . We're given that the tank initially holds $A(0)=100$ lbs of salt.

The rate at which salt flows in and out of the tank is given by the relation

$\dfrac{\mathrm dA}{\mathrm dt}=\underbrace{\dfrac{11\text{ lb}}{1\text{ gal}}\times\dfrac{44\text{ gal}}{1\text{ min}}}_{\text{rate in}}-\underbrace{\dfrac{A(t)}{200+(44-11)t}\times\dfrac{11\text{ gal}}{1\text{ min}}}_{\text{rate out}}$
$\implies A'(t)+\dfrac{11}{200+33t}A(t)=484$

Find the integrating factor:

$\mu(t)=\exp\left(\displaystyle\int\frac{11}{200+33t}\,\mathrm dt\right)=(200+33t)^{1/3}$

Distribute $\mu(t)$ along both sides of the ODE:

$(200+33t)^{1/3}A'(t)+11(200+33t)^{-2/3}A(t)=484(200+33t)^{-1/3}$
$\bigg((200+33t)^{1/3}A(t)\bigg)'=484(200+33t)^{-1/3}$
$A(t)=484\displaystyle\int(200+33t)^{-1/3}\,\mathrm dt$
$A(t)=22(200+33t)^{2/3}+C$

Since $A(0)=100$ , we get

$100=22(200)^{2/3}+C\implies C\approx-652.39$

so that the particular solution for $A(t)$ is

$A(t)=22(200+33t)^{2/3}-652.39$

The tank becomes full when the volume of solution in the tank at time $t$ is the same as the total volume of the tank:

$200+(44-11)t=500\implies 33t=300\implies t\approx9.09$

at which point the amount of salt in the solution would be

$A(9.09)\approx733.47\text{ lb}$

4 0

3 years ago