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3 years ago

2=(1+r/100n)^nt

Mathematics

1 answer:

klasskru [66]3 years ago

5 0

Answer:

a) Log ( 2 ) = 4t Log ( 83/80 )

b) 4.7 years

Step-by-step explanation:

Attached below is the detailed solution

a) exponential statement in log form for an investment at 15% quarterly

Log ( 2 ) = 4t Log ( 83/80 )

n = 4 , r = 15

b) using change to base to find double time in yr

Double time in yr

t = Log ( 2 ) / 4log ( 83/80 )

= 4.7 years

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The slope-intercept form of a line:

$y=mx+b$

m - slope

b - y-intercept

Convert 2x + 3y = -6 to the slope-intercet form:

$2x+3y=-6$ subtract 2x from both sides

$3y=-2x-6$ divide both sides by 3

$y=-\dfrac{2}{3}x-2$

Let $k:y=m_1x+b_1$ and $l:y=m_2x+b_2$

$l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

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Therefore

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$y=\dfrac{3}{2}x+b$

Put the coordinates of the point (0, 0) to the equation:

$0=\dfrac{3}{2}(0)+b$

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Answer: $\boxed{y=\dfrac{3}{2}x}$

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3 years ago

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Step-by-step explanation:

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3 years ago

(1 point) Two six-sided dice are rolled (one red one and one green one). Some possibilities are (Red

anygoal [31]

Complete question:

Two six-sided dice are rolled (one red one and one green one). Some possibilities are (Red= 1, Green=5) or (Red=2, Green=2) etc.

a)How many total possibilities are there?

For the rest of the questions, we will assume that the dice are fair and that all the possibilities in (a) are equally likely.

b)What is the probability that the sum on the two dice comes out to be 11?

c)What is the probability that the sum on the two dice comes out to be 7?

d)What is the probability that the numbers on the two dice are equal?

Answer:

Kindly check explanation

Step-by-step explanation:

Total probabilities :

Total possible outcomes on each dice = 6

Total probabilities = 6² = 36

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Total required outcome = 2

Total possible outcomes = 36

Probability = required outcome / Total possible outcomes

P(sum on both dice = 11) = 2 / 36 = 1/18

c)What is the probability that the sum on the two dice comes out to be 7?

Required outcome = 6

Possible outcomes = 36

P(obtaining a sum of 7) = 6/36 = 1/6

d)What is the probability that the numbers on the two dice are equal

= required outcome / possible outcomes

Required outcome = 1,1 ; 2,2; 3,3; 4,4 ; 5,5 ; 6,6

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3 years ago

HELP ASAP. Please solve. 2 plus or minus the square root of negative 36 over 2

AVprozaik [17]

Answer:

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3 years ago

A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t

11Alexandr11 [23.1K]

Answer:

Question 1: $dm/dt=0.2m$

Question 2: $m=Ae^{(0.2t)}$

Question 3: $m=10e^{(0.2t)}$

Question 4: $m=10g$

Explanation:

Question 1: Write down the differential equation the mass of the bacteria, m, satisfies: m′= .2m

a) By definition: $m'=dm/dt$

b) Given: $rate=0.2m$

c) By substitution: $dm/dt=0.2m$

Question 2: Find the general solution of this equation. Use A as a constant of integration.

a) Separate variables

$dm/m=0.2dt$

b) Integrate

$\int dm/m=\int 0.2dt$

$ln(m)=0.2t+C$

c) Antilogarithm

$m=e^{0.2t+C}$

$m=e^{0.2t}\cdot e^C$

$e^C=A\\\\m=Ae^{(0.2t)}$

Question 3. Which particular solution matches the additional information?

Use the measured rate of 4 grams per hour after 3 hours

$t=3hours,dm/dt=4g/h$

First, find the mass at t = 3 hours

$dm/dt=0.2m\\\\4=0.2m\\\\m=4/0.2\\\\m=20g$

Now substitute in the general solution of the differential equation, to find A:

$m=Ae^{(0.2t)}\\\\20=Ae^{(0.2\times 3)}\\\\A=20/e^{(0.6)}\\\\A=10.976$

Round A to 1 significant figure:

A = 10.

Particular solution:

$m=10e^{(0.2t)}$

Question 4. What was the mass of the bacteria at time =0?

Substitute t = 0 in the equation of the particular solution:

$m=10e^{0}\\\\m=10g$

3 0

3 years ago