To find the population at the end of 1991, we need to calculate the population year by year, applying the given percentage changes sequentially. We start with the initial population in 1988 and then adjust it for the increase or decrease in each subsequent year.
The population in 1988 was 50,000.
\[ \text{P}_{1988} = 50,000 \]In 1989, the population increased by 25%.
\[ \text{Increase} = 25\% \text{ of } 50,000 = \frac{25}{100} \times 50,000 = 12,500 \] \[ \text{P}_{1989} = \text{P}_{1988} + \text{Increase} = 50,000 + 12,500 = 62,500 \]In 1990, the population decreased by 30% from the 1989 population.
\[ \text{Decrease} = 30\% \text{ of } 62,500 = \frac{30}{100} \times 62,500 = 18,750 \] \[ \text{P}_{1990} = \text{P}_{1989} - \text{Decrease} = 62,500 - 18,750 = 43,750 \]In 1991, there was an increase of 40% from the 1990 population.
\[ \text{Increase} = 40\% \text{ of } 43,750 = \frac{40}{100} \times 43,750 = 17,500 \] \[ \text{P}_{1991} = \text{P}_{1990} + \text{Increase} = 43,750 + 17,500 = 61,250 \]B) 61,250 is the population at the end of 1991, as calculated by applying the percentage changes sequentially.
If we add 1 to the numerator and subtract 1 from the denominator of a given fraction, it becomes 1. It becomes \( \frac{2}{3} \) if 1 is added to the denominator of the given fraction while the numerator is left unchanged. The positive difference of numerator and denominator of the fraction is:
The question asks which action is responsible for the survival of species over time. This relates to fundamental concepts in evolutionary biology, particularly natural selection.
B) Variation โ Variation refers to the differences among individuals within a species. These variations are the raw material upon which natural selection acts. When environmental conditions change, some individuals with specific variations might be better suited to survive and reproduce than others. This differential survival and reproduction lead to the adaptation of the species over time, ensuring its long-term survival. Without variation, a species would be unable to adapt to new challenges and would likely face extinction.
The problem asks us to identify the number of symbols in a given series that satisfy two conditions: they must be immediately preceded by a symbol AND immediately followed by a symbol. We need to scan the series from left to right and check each symbol against these conditions.
B) One
The symbol '@' is immediately preceded by '&' (a symbol) and immediately followed by '£' (a symbol). Therefore, there is exactly one such symbol.
To find the average score of the entire class, we need to calculate the total score of all students and then divide it by the total number of students. The total score can be found by summing the total scores of the two groups of students.
The total score of a group is the average score multiplied by the number of students in that group.
\[ \text{Total Score (Group 1)} = \text{Number of students (Group 1)} \times \text{Average score (Group 1)} \]\[ \text{Total Score (Group 1)} = 12 \times 80 = 960 \]The average score of the class is the total score of the class divided by the total number of students in the class.
\[ \text{Average Score (Class)} = \frac{\text{Total Score (Class)}}{\text{Total Number of Students}} \]\[ \text{Average Score (Class)} = \frac{2310}{30} = 77 \]D) 77 is the correct average score for the entire class.
To find the sum of all prime numbers between 60 and 90, we first need to identify all prime numbers in this range. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. We will list all numbers between 60 and 90 and then eliminate composite numbers to find the primes. Finally, we will sum these prime numbers.
The sum of all prime numbers between 60 and 90 is 523.
Correct Option: B) 523
This problem involves a dishonest dealer who claims to sell goods at cost price but uses a false weight to gain profit. We can solve this by understanding the relationship between the actual weight delivered, the professed weight, and the percentage gain. The gain percentage is calculated based on the difference between the actual quantity the customer pays for and the quantity they actually receive.
Let the cost price of 1 gm of goods be \(C\). The dealer professes to sell at cost price, meaning he charges the customer for the weight he claims to sell, at cost price \(C\).
Let the false weight used for 100 gm be \(x\) gm. This means the dealer actually gives \(x\) gm of goods to the customer, but charges for 100 gm.
The cost to the dealer for \(x\) gm of goods is \(x \times C\).
The selling price for the dealer (what he charges the customer) is for 100 gm at cost price, which is \(100 \times C\).
The profit made by the dealer is the difference between the selling price and the cost price:
\[ \text{Profit} = (100 \times C) - (x \times C) = (100 - x)C \]The profit percentage is calculated on the actual cost to the dealer, which is the cost of the goods he actually gives away (\(x \times C\)).
\[ \text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost to Dealer}} \times 100\% \]\[ 25\% = \frac{(100 - x)C}{xC} \times 100\% \]Now, we can solve for \(x\):
\[ \frac{25}{100} = \frac{100 - x}{x} \]\[ \frac{1}{4} = \frac{100 - x}{x} \]\[ x = 4(100 - x) \]\[ x = 400 - 4x \]\[ x + 4x = 400 \]\[ 5x = 400 \]\[ x = \frac{400}{5} \]\[ x = 80 \]So, for 100 gm, the dealer uses a weight of 80 gm.
D) 80 gm โ The calculation shows that to achieve a 25% gain by using a false weight while professing to sell at cost price, the dealer must use an 80 gm weight for every 100 gm he claims to sell.
This problem involves substituting given mathematical operators for letters and then evaluating the expression using the order of operations (BODMAS/PEMDAS).
Given: A means +, B means โ, C means ร, D means รท
Original expression: \(14 \text{ B } 5 \text{ C } 5 \text{ A } 30 \text{ D } 2 = ?\)
Substituting the operators, we get:
\[ 14 - 5 \times 5 + 30 \div 2 = ? \]First, perform Division:
\[ 14 - 5 \times 5 + 15 \]Combine \(14 + 15\):
\[ 29 - 25 \]B) The result of the expression is 4.
To find the value of an algebraic expression at a specific value of the variable, substitute the given value into the expression and simplify using the order of operations (PEMDAS/BODMAS).
Thus, the value of the expression \(x^2 - 5\) at \(x = -1\) is \(-4\).
D) -4 is the correct answer, as calculated by substituting \(x = -1\) into the expression \(x^2 - 5\).