A bag contains 3 red Skittles, 4 yellow Skittles, 6 green Skittles, 5 red jelly beans, 8 yellow jelly beans, and 7 green jellybeans. a) Give an example of a mutually exclusive event.

Answers

Answer 1

Answer: a shop contains 3 red shelves, 4 yellow shelves, 6 green shelves, 5 red chairs, 8 yellow chairs, and 7 green chairs.

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A house cost $120,000 when it was purchased. The value of the house increases by 10% each year. Find the rate of growth each month.

Answers

FIRST MODEL:

Well the model for the value of the house is:

$V={ \left( \frac { 11 }{ 10 } \right) }^( t )\cdot 120000$

V = Value

t = Years passed {t≥0}

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When t=0, V=120000

When t=1, V=132000

When t=2, V=145200

etc... etc...

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Now, this model is actually curved so there is no constant rate of growth each month. We can only calculate what the rate of growth is at a particular time. If we want to find out the rate of growth at a particular time, we must differentiate the formula (model) above.

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$V={ \left( \frac { 11 }{ 10 } \right) }^( t )\cdot 120000\n \n \ln { V=\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^( t )\cdot 120000 \right) } }$

$\n \n \ln { V=\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^( t ) \right) } } +\ln { \left( 120000 \right) } \n \n \ln { V=t\ln { \left( \frac { 11 }{ 10 } \right) } } +\ln { \left( 120000 \right) }$

$\n \n \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\ln { \left( \frac { 11 }{ 10 } \right) } \n \n V\cdot \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\ln { \left( \frac { 11 }{ 10 } \right) } \cdot V$

$\n \n \therefore \quad \frac { dV }{ dt } =\ln { \left( \frac { 11 }{ 10 } \right) } \cdot { \left( \frac { 11 }{ 10 } \right) }^( t )\cdot 120000$

Plug any value of (t) that is greater than 0 into the formula above to find out how quickly the investment is growing. If you want to find out how quickly the investment was growing after 1 month had passed, transform t into 1/12.

The rate of growth is being measured in years, not months. So when t=1/12, the rate of growth turns out to be 11528.42 per annum.

SECOND MODEL (What you are ultimately looking for):

$V={ \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000$

V = Value of house

t = months that have gone by {t≥0}

Formula above differentiated:

$V={ \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000\n \n \ln { V } =\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000 \right) }$

$\n \n \ln { V=\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } } \right) } } +\ln { \left( 120000 \right) }$

$\n \n \ln { V=\frac { t }{ 12 } } \ln { \left( \frac { 11 }{ 10 } \right) } +\ln { \left( 120000 \right) }$

$\n \n \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\frac { 1 }{ 12 } \ln { \left( \frac { 11 }{ 10 } \right) }$

$\n \n V\cdot \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\frac { 1 }{ 12 } \ln { \left( \frac { 11 }{ 10 } \right) } \cdot V$

$\n \n \therefore \quad \frac { dV }{ dt } =\frac { 1 }{ 12 } \ln { \left( \frac { 11 }{ 10 } \right) } \cdot { \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000$

When t=1, dV/dt = 960.70 (2dp)

dV/dt in this case will measure the rate of growth monthly. As more money is accumulated, this rate of growth will rise. The rate of growth is constantly increasing as the graph of V is actually a curve. You can only find out the rate at which the house value is growing monthly at a particular time.

How much farther is earth form the sun than it is from Venus?

Answers

Answer:

Earth is 1.1 x 10^8 km farther from the Sun than it is from Venus

Step-by-step explanation:

Frazer is training for a cycle race. In the first week he cycles 195 miles

Answers

Answer: Hope it helps...

Step-by-step explanation: mark as an brainliest... if so

F(-14) if f(x) = 2x - 3

Answers

Answer:

The correct answer is -31.

Step-by-step explanation:

f(-14) means that x=-14. You have to replace x with -14. Then, you multiply -14 by 2. That is -28. Next you subtract 3 from -28. That gives you -31.

Four different sets of objects contain 2, 5, 6, and 7 objects, respectively. How many unique combinations can be formed by picking one object from each set?

Answers

The correct answer for the question that is being presented above is this one: "A. 960."Four different sets of objects contain 2, 5, 6, and 7 objects, respectively.

= 2 * 5 * 6 * 7
= 960

Here are the following choices:
A. 960
B. 141
C. 23
D. 529

Answer: 420

Step-by-step explanation:

2*5*6*7 = 420

Ten people are entered in a race. If there are no ties, in how many ways can the first three places come out?A. 1440

B. 720

C. 30

D. 132

Answers

B) 720 different possibilities

Answer: (720) is the right answer

Step-by-step explanation:

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