Which ratio is equivalent to the given ratio?
2 answers:
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Given:
- There are two savings accounts - account A has $150 and account B has $300 to begin with.
- Malorie deposits $16 in account A and $12 in account B every month.
To Find:
The number of months where the balance of both is equal and the balance itself.
Solution:
In 37.5 months, the account balances in both accounts will be equal.
This balance will be equal to $750 in both account A and B.
Calculation:
Let x be the number of months where both the accounts have equal balance.
So, at the end of x months, 16x is the amount of money that will be added to account A (since $16 is added every month).
And the total amount at the end of x months will therefore be $(150+16x)
Similarly, at the end of x months, 12x is the amount of money that will be added to account B (since $12 will be added every month).
And the total amount at the end of x months will therefore be $(300+12x)
By our assumption, x is the number of months it will take for both the accont balances will be equal. Therefore, we have the equation
Therefore, in 37.5 months, the account balances in both accounts will be equal.
This balance will be equal to i.e. $750 will be the balance in both account A and B.
a (i) The number of standard size is 288 eggs
a (ii) The number of medium size is 1,476 eggs
a (iii) The number of large size is 36 eggs
b (i) The expected profit made from selling the standard size is Gh¢43.2
b (ii) The expected profit made from selling the medium size is Gh¢516.6
b (iii) The expected profit made from selling the large size is Gh¢16.2
The given parameters:
the mean of the distribution, m = 0.06 kg
standard deviation (std) of the distribution, d = 0.009 kg
number of the samples, n = 1800 eggs
(i) Find the position of "less than 0.052 kg (standard size)":
- 1 standard deviation below the mean = m - d
- m - d = 0.06 kg - 0.009 kg = 0.051 kg
(<em>the </em><em>standard size</em><em> is 1 standard deviation below the mean</em>)
- less than 1 standard deviation below the mean in a normal distribution is equal to 16% of the data samples
- Number of standard size = 0.16 x 1800 = 288 eggs
(ii) Find the position of "Between 0.052 kg and 0.075kg (medium size)":
- 0.052 kg is 1 standard deviation below the mean
- 2 standard deviation above the mean = m + 2d
- m + 2d = 0.06 + 2(0.009) = 0.078 kg
(<em>the </em><em>medium size</em><em> is between 1 std below the mean and 2 std above the mean</em>)
- Between 1 std below the mean and 2 std above the mean in a normal distribution = (68 + 14)% = 82%
- Number of medium size = 0.82 x 1800 = 1,476 eggs
(iii) Find the position of "Greater than 0.075 kg (large size)":
- 0.078 kg is 2 standard deviation below the mean
- greater than 2 std above the mean in a normal distribution = 2 % of the data samples
- Number of large size = 0.02 x 1800 = 36 eggs
<u>Check:</u> <em>288 eggs + 1476 eggs + 36 eggs = 1,800 eggs</em>
(b) the cost of production of an egg = Gh¢0.45
the selling price of the standard size = Gh¢0.60
the selling price of the medium size = Gh¢0.80
the selling price of the large size = Gh¢0.95
(i) The expected profit made from selling the standard size:
Profit = total revenue - cost of production
Profit = 288(0.6) - 288(0.45) = Gh¢43.2
(ii) The expected profit made from selling the medium size:
Profit = total revenue - cost of production
Profit = 1476(0.8) - 1476(0.45) = Gh¢516.6
(iii) The expected profit made from selling the large size:
Profit = total revenue - cost of production
Profit = 36(0.9) - 36(0.45) = Gh¢16.2
Learn more here: brainly.com/question/22520030
