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alexira [117]
3 years ago
13

Simplify 31/2 + 42/4

Mathematics
2 answers:
Vladimir79 [104]3 years ago
4 0

\frac{31}{2}+ \frac{42}{4}

Make the denominators the same in order to add them together

\frac{2}{2} (\frac{31}{2}) +  \frac{42}{4} = \frac{62}{4}+ \frac{42}{4} =\frac{104}{4} = 26

kykrilka [37]3 years ago
3 0
The answer is 26. (Change denominators
You might be interested in
City A had a population of 10000 in the year 1990. City A’s population grows at a constant rate of 3% per year. City B has a pop
Georgia [21]

Answer:

City A and city B will have equal population 25years after 1990

Step-by-step explanation:

Given

Let

t \to years after 1990

A_t \to population function of city A

B_t \to population function of city B

<u>City A</u>

A_0 = 10000 ---- initial population (1990)

r_A =3\% --- rate

<u>City B</u>

B_{10} = \frac{1}{2} * A_{10} ----- t = 10 in 2000

A_{20} = B_{20} * (1 + 20\%) ---- t = 20 in 2010

Required

When they will have the same population

Both functions follow exponential function.

So, we have:

A_t = A_0 * (1 + r_A)^t

B_t = B_0 * (1 + r_B)^t

Calculate the population of city A in 2000 (t = 10)

A_t = A_0 * (1 + r_A)^t

A_{10} = 10000 * (1 + 3\%)^{10}

A_{10} = 10000 * (1 + 0.03)^{10}

A_{10} = 10000 * (1.03)^{10}

A_{10} = 13439.16

Calculate the population of city A in 2010 (t = 20)

A_t = A_0 * (1 + r_A)^t

A_{20} = 10000 * (1 + 3\%)^{20}

A_{20} = 10000 * (1 + 0.03)^{20}

A_{20} = 10000 * (1.03)^{20}

A_{20} = 18061.11

From the question, we have:

B_{10} = \frac{1}{2} * A_{10}  and  A_{20} = B_{20} * (1 + 20\%)

B_{10} = \frac{1}{2} * A_{10}

B_{10} = \frac{1}{2} * 13439.16

B_{10} = 6719.58

A_{20} = B_{20} * (1 + 20\%)

18061.11 = B_{20} * (1 + 20\%)

18061.11 = B_{20} * (1 + 0.20)

18061.11 = B_{20} * (1.20)

Solve for B20

B_{20} = \frac{18061.11}{1.20}

B_{20} = 15050.93

B_{10} = 6719.58 and B_{20} = 15050.93 can be used to determine the function of city B

B_t = B_0 * (1 + r_B)^t

For: B_{10} = 6719.58

We have:

B_{10} = B_0 * (1 + r_B)^{10}

B_0 * (1 + r_B)^{10} = 6719.58

For: B_{20} = 15050.93

We have:

B_{20} = B_0 * (1 + r_B)^{20}

B_0 * (1 + r_B)^{20} = 15050.93

Divide B_0 * (1 + r_B)^{20} = 15050.93 by B_0 * (1 + r_B)^{10} = 6719.58

\frac{B_0 * (1 + r_B)^{20}}{B_0 * (1 + r_B)^{10}} = \frac{15050.93}{6719.58}

\frac{(1 + r_B)^{20}}{(1 + r_B)^{10}} = 2.2399

Apply law of indices

(1 + r_B)^{20-10} = 2.2399

(1 + r_B)^{10} = 2.2399 --- (1)

Take 10th root of both sides

1 + r_B = \sqrt[10]{2.2399}

1 + r_B = 1.08

Subtract 1 from both sides

r_B = 0.08

To calculate B_0, we have:

B_0 * (1 + r_B)^{10} = 6719.58

Recall that: (1 + r_B)^{10} = 2.2399

So:

B_0 * 2.2399 = 6719.58

B_0  = \frac{6719.58}{2.2399}

B_0  = 3000

Hence:

B_t = B_0 * (1 + r_B)^t

B_t = 3000 * (1 + 0.08)^t

B_t = 3000 * (1.08)^t

The question requires that we solve for t when:

A_t = B_t

Where:

A_t = A_0 * (1 + r_A)^t

A_t = 10000 * (1 + 3\%)^t

A_t = 10000 * (1 + 0.03)^t

A_t = 10000 * (1.03)^t

and

B_t = 3000 * (1.08)^t

A_t = B_t becomes

10000 * (1.03)^t = 3000 * (1.08)^t

Divide both sides by 10000

(1.03)^t = 0.3 * (1.08)^t

Divide both sides by (1.08)^t

(\frac{1.03}{1.08})^t = 0.3

(0.9537)^t = 0.3

Take natural logarithm of both sides

\ln(0.9537)^t = \ln(0.3)

Rewrite as:

t\cdot\ln(0.9537) = \ln(0.3)

Solve for t

t = \frac{\ln(0.3)}{ln(0.9537)}

t = 25.397

Approximate

t = 25

7 0
3 years ago
The sales tax in your city is 8.8%, and an item costs $55 dollars before tax. How much would you pay for that item?
IRISSAK [1]

Answer:

The answer is $ 59.84

Step-by-step explanation:

Ok, I know this is not one of the options, but hear me out:

To find the sales tax for that item, you need to multiply the dollar amount by the sales tax (in percent):

$55 * 8.8% = $4.84

So the sales tax is $4.84.  However, the question asks "How much would you pay for that item?", not what the sales tax is.  So I would solve this problem by adding the sales tax to the dollar amount of the item:

$55 + $4.84 = $ 59.84

If you are able to write or type your answer, I would type $ 59.84. If you can only select one of the given values, then I would suggest going with             A: $ 4.84 just because its the only number that is actually relevant at all to the problem.

7 0
3 years ago
Read 2 more answers
A Fair coin is tossed and a marble is chosen from the bag whose contents are shown below. what is the probability of the coin La
Vera_Pavlovna [14]

Answer:

P(Coin landing heads and blue marble is randomly selected) = 3/20.

Step-by-step explanation:

In this question, two events simultaneously take place. First, all the probabilities have to be identified. It is mentioned that the coin is a fair coin, therefore the probabilities of all the outcomes associated with the coin tossing will be equal. Therefore:

P(Coin landing heads) = 1/2.

P(Coin landing tails) = 1/2.

There are a total of 3 blue + 4 green + 3 red = 10 marbles in the bag. Therefore:

P(Selected marble is blue) = 3/10.

P(Selected marble is green) = 4/10.

P(Selected marble is red) = 3/10.

Assuming that both the events are independent, the probabilities of both the events can safely be multiplied. Therefore:

P(Coin landing heads and blue marble is randomly selected) = 1/2 * 3*10 = 3/20.

Therefore, the answer is 3/20!!!

3 0
3 years ago
Read 2 more answers
How long will it take bernando to make the trip if he drives at 80 miles per hour?
brilliants [131]
How long is the trip?
7 0
3 years ago
A thunderstorm cloud holds about 6,200,000,000 raindrops. Which of the following shows this number in scientific notation? Answe
maksim [4K]

Answer:

the answer is G

which is 6.2*10 to the 9th power.

Step-by-step explanation:

In scientific notation you must leave one digit to the place value of ones

so that one digit is 6

So ue come up with 6.2 when ue eliminate all other zeros and end the decimal point between 6 and 2 and that way you have 6.2*10 to the 9th power

6 0
3 years ago
Read 2 more answers
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