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Lera25 [3.4K]
3 years ago
11

City A's population of 1115000 is decreasing at a rate of 15000 per year. City B's population of 698000 is increasing at a rate

of 45000 per year. In how many years will the populations be equal? Form the equation and round the answer to the nearest whole number.
Mathematics
1 answer:
vredina [299]3 years ago
7 0

Answer:

7 years

Step-by-step explanation:

Let x  be number of years the populations be equal

City A's population of 1115000 is decreasing at a rate of 15000 per year.

The population is decreasing at a constant rate so we use equation

y= mx + b

where m is the slope(rate), b is the initial population

m= -15000 (decreasing) , b= 1115000

y= -15000 x + 1115000

City B's population of 698000 is increasing at a rate of 45000 per year.

m= 45000 (increasing) , b= 698000

y= 45000 x + 698000

Now we set the equations equal and solve for x

45000 x + 698000 = -15000 x + 1115000

Add 15000 on both sides

60000 x + 698000 = 1115000

Subtract 689000 on both sides

60000 x = 417000

Divide by 60000 on both sides

x= 6.95

So after 7 years the population will be equal.

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(a) Attached to this response.

(b)

<em>(i)</em> <em>0 cups = 0.275</em>

<em>(ii) 4 cups = 0.125</em>

<em>(iii) 8 cups = 0.025</em>

<em />

<em />

Step-by-step explanation:

(a) The frequency and relative frequency table has been attached to this response.

i. The first column, labelled x, is the number of cups of coffee consumed per day.

ii. The second column, labelled f, is the number of people that consumed x cups of coffee per day. It is found by counting the number of occurrences (i.e frequency) of the numbers of the first column, x, in the given data.

For example, 0 in first column appears 11 times in the given data. Also, 5 in the first column appears 4 times in the given data.

iii. The third column, labelled r, is the relative relative frequency of the number of cups of coffee. It is calculated by dividing the frequency of the cups of coffee by the total number of people that consumed it. As shown on the table, it is calculated by dividing the each of the values on the second column by the sum of the values on that same column (second column).

For example, the relative frequency of 2 cups of coffee is given by:

r = 7  ÷ 40 = 0.175

Also, the relative frequency of 4 cups of coffee is given by;

r = 5 ÷ 40 = 0.125

(b) The probability (Pₓ) that a randomly selected person consumed x cups of coffee is given by;

Pₓ = frequency of x ÷ total frequency

This is also the relative frequency of x

Therefore,

<em>(i) The probability (P₀) that a randomly selected person consumed 0 cups of coffee is given by;</em>

the relative frequency of 0<em> = 0.275</em>

<em></em>

<em>(ii) The probability (P₄) that a randomly selected person consumed 4 cups of coffee is given by;</em>

the relative frequency of 4<em> = 0.125</em>

<em>(iii) The probability (P₈) that a randomly selected person consumed 8 cups of coffee is given by;</em>

the relative frequency of 8<em> = 0.025</em>

<em></em>

<em></em>

<em></em>

Download docx
5 0
3 years ago
X to the 2 power -6 when X = -14
riadik2000 [5.3K]
-14x-14 = 196 then subtract -6 from 196 because they'll cancel each other out. the answer is 190.
8 0
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