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igomit [66]
2 years ago
11

At a school event, there were 96 girls. The ratio of the number of girls to the number of boys was 4 : 5. After some time, some

boys arrived and th ratio became 2 : 3. How many boys arrived?
Mathematics
1 answer:
TiliK225 [7]2 years ago
6 0
The girls are 4/9 of the total number of boys and girls, so the total number is 9×96/4=216 and there are 5/9×216=120 boys.
Let the extra number of boys be b, then the total becomes 216+b. We have 96 girls and 120+b boys.
The ratio 2/3=96/(120+b).
Cross multiplying: 2(120+b)=3×96=288.
240+2b=288, 2b=288-240=48, b=24.
So 24 boys arrived.
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9. Determine how long it takes for 80% of the material to decay.
Vilka [71]

Using an exponential function, it is found that it takes 18.6 days for 80% of the material to decay.

The amount of a substance after t days is modeled by:

A(t) = A(0)e^{-kt}

In which:

  • k is the decay rate, as a decimal.
  • A(0) is the initial amount.

The half-life is of 8 days, hence A(8) = 0.5A(0), and this is used to find k.

A(t) = A(0)e^{-kt}

0.5A(0) = A(0)e^{-8k}

e^{-8k} = 0.5

\ln{e^{-8k}} = \ln{0.5}

-8k = \ln{0.5}

k = -\frac{\ln{0.5}}{8}

k = 0.08664339757

Hence:

A(t) = A(0)e^{-0.08664339757t}

The time it takes for 80% of the material to decay it t for which A(t) = 0.2A(0), hence:

0.2A(0) = A(0)e^{-0.08664339757t}

e^{-0.08664339757t} = 0.2

\ln{e^{-0.08664339757t}} = \ln{0.2}

-0.08664339757t = \ln{0.2}

t = -\frac{\ln{0.2}}{0.08664339757}

t = 18.6

It takes 18.6 days for 80% of the material to decay.

To learn more about exponential functions, you can take a look at brainly.com/question/24906920

5 0
2 years ago
What is the slope of the line that passes through the points (-3, 6) and (1,2)
Nadya [2.5K]

Answer:

the slope is -1

m = -1

Step-by-step explanation:

y2 - y1     y

--------- = ----

x2 - x1     x

= y/x = m

2 - 6

-------

1 - - 3

= -4/4

m = -1

8 0
3 years ago
The quotient of y and 6 is 29 find the value of y
atroni [7]
Y÷6=29
y=29 x 6
y=174

Hope I can help u
7 0
2 years ago
Do you multiply area or add it
pogonyaev
It's the formula. Base times height.
For example: if 50 is the base and 10 is the height, just multiply them both.
50 x 10 = 500. And I don't think you add area-that's for finding the perimeter
5 0
3 years ago
When a trinomial is factored as (x + m)(x + n), what is the product of m and n?
liq [111]
I hope this is what you were looking for! x^2 + xn + xm + mn
6 0
3 years ago
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