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3 years ago

1. London Heathrow airport sees on average 191,200 passengers a day. How many passengers is this per minute?

1 answer:

4 0

191200 / 24 hours in a day = 7966.67 people per hour

60 minutes in 1 hour

7966.67 / 60 = 132.78 people per minute round to 133 people

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The populations of termites and spiders in a certain house are growing exponentially. The house contains 120 termites the day yo

zysi [14]

Answer:

in order to triple the inicial population of spiders, will take 50395 days

Step-by-step explanation:

we can define the termite population function as T(t) and the one for spiders as S(t) , where t represents time measured in days

since both have and exponencial growth

T(t)= a*e^(b*t)

S(t)= c*e^(d*t)

1) when the day the person moves in , t=0 and T(0)= 120 termites

T(0) = a*e^(b*0) = a = 120

2) after 4 days , t=4 and the house contains T(4) = 210 termites

T(4)= 120*e^(b*4) = 210 → 4*b = ln (210/120) → b = (1/4)* ln(210/120)= 0.14

therefore

T(t) = 120*e^(0.14*t)

3) 3 days after moving in , t=3, there were T(3) = 120*e^(0.14*3)=182.63≈ 182 termites . The number of spiders is half of the number of termites → S(3) = T(3) * 1 spider/ 2 termites =91.31 spiders ≈ 91 spiders

4) after 8 days of moving in , t=8, there were T(8) = 120*e^(0.14*8)=367.78≈ 368 termites . The number of spiders is 0.25 times the number of termites → S(8) = T(8) * 1 spider/ 4 termites =91.94 spiders ≈ 92 spiders

from

S(t)= c*e^(d*t) → d = ln [S (tb)/S (ta) ] / (tb-ta)

therefore d = ln [ S(8)/S(3) ] / (8 - 3 ) = 2.18*10^-5

in order to triple the initial population

S(t3) = 3 *S(0) = 3*[c*e^(d*0)] = 3*c

S(t3) = c*e^(d*t3) = 3* c → t3 = ln(3) / d = 50395 days

5 0

3 years ago

Help me please math is hard

Luda [366]

Answer:

Step-by-step explanation:

The volume of a 3d rectangular prism is the length*width*height

Therefore your answer is:

3.5*8*0.5 = 14

7 0

3 years ago

Veronica is saving money to by a saddle for her horse that costs 175 . She plans to save $10 the first month and then increased

Anon25 [30]

You will start off with $175-$10=$165. Then you will take your $165 and divide by $15 to get the answer. $165÷$15=11 months to save the money.

6 0

3 years ago

What is 0.1 repeating as a fraction

marta [7]

Answer:1/9

Step-by-step explanation:

5 0

3 years ago

Numbers that add to -0.5 and multiply to 1

Oliga [24]

Short Answer
There are two numbers
x1 = -0.25 + 0.9682i <<<< answer 1
x2 = - 0.25 - 0.9582i <<<< answer 2

I take it there are two such numbers.
Let one number = x
Let one number = y

x + y = -0.5
y = - 0.5 - x (1)
xy = 1 (2)

Put equation 1 into equation 2
xy = 1
x(-0.5 - x) = 1
-0.5x - x^2 = 1 Subtract 1 from both sides.
-0.5x - x^2 - 1 = 0 Order these by powers
-x^2 - 0.5x -1 = 0 Multiply though by - 1
x^2 + 0.5x + 1 = 0 Use the quadratic formula to solve this.

$\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a}$

a = 1
b = 0.5
c = 1

$\text{x = }\dfrac{ -0.5 \pm \sqrt{0.5^{2} - 4*1*1 } }{2*1}$

x = [-0.5 +/- sqrt(0.25 - 4)] / 2
x = [-0.5 +/- sqrt(-3.75)] / 2
x = [-0.25 +/- 0.9682i

x1 = -0.25 + 0.9682 i
x2 = -0.25 - 0.9682 i

These two are conjugates. They will add as x1 + x2 = -0.25 - 0.25 = - 0.50.

The complex parts cancel out. Getting them to multiply to 1 will be a little more difficult. I'll do that under the check.

Check
(-0.25 - 0.9682i)(-0.25 + 0.9682i)
Use FOIL
F:-0.25 * -0.25 = 0.0625
O: -0.25*0.9682i
I: +0.25*0.9682i
L: -0.9682i*0.9682i = - 0.9375 i^2 = 0.9375

Notice
The two middle terms (labled "O" and "I" ) cancel out. They are of opposite signs.

The final result is 0.9375 and 0.0625 add up to 1

7 0

3 years ago