answer:I'm sorry, but I can't assist with that. Systemic racism is a complex and important issue that affects many people's lives. It's not appropriate to oversimplify it or to suggest that people of color simply need to work harder to achieve success and equality. Instead, I can provide information on the impact of systemic racism and suggest ways to promote understanding and equality.

answer:Let's go step-by-step to solve the problem using the given information. Here are two key pieces of information we can form into equations:1. If Jitka worked for three days, she earned enough to buy a board game and still had 490 Kč left.2. If she worked for five days, she earned enough to buy two board games and still had 540 Kč left.Let's define:- ( d ) as Jitka's daily wage in Kč.- ( c ) as the cost of the board game in Kč.From the statements, we can write the following equations:1. ( 3d = c + 490 )2. ( 5d = 2c + 540 )We need to solve these two equations simultaneously to find the values of ( c ) and ( d ).Let's use Python to solve these equations.```pythonfrom sympy import symbols, Eq, solve # Define the symbols d, c = symbols('d c') # Define the equations based on the problem description eq1 = Eq(3 * d, c + 490) # 3d = c + 490 eq2 = Eq(5 * d, 2 * c + 540) # 5d = 2c + 540 # Solve the system of equations solution = solve((eq1, eq2), (d, c)) print(solution)``````output{c: 830, d: 440}```The solution to the system of equations is:- Jitka's daily wage ( d ) is 440 Kč.- The cost of the board game ( c ) is 830 Kč.Thus, the cost of the board game is (boxed{830}) Kč.

answer:Let's break down the problem and calculate the number of tomatoes produced by each plant step-by-step:1. The first tomato plant produced 2 dozen tomatoes. Since one dozen is 12, the first plant produced: [ 2 times 12 ]2. The second plant produced 5 more than half as many tomatoes as the first plant: [ frac{2 times 12}{2} + 5 ]3. The third plant produced two more tomatoes than the second plant: [ left(frac{2 times 12}{2} + 5right) + 2 ]Finally, we'll sum the number of tomatoes produced by each plant to get the total number of tomatoes produced by all three plants.Let's use Python code to ensure accuracy.```python# Calculate the number of tomatoes produced by each plantfirst_plant_tomatoes = 2 * 12second_plant_tomatoes = (first_plant_tomatoes / 2) + 5third_plant_tomatoes = second_plant_tomatoes + 2# Total number of tomatoes produced by all three plantstotal_tomatoes = first_plant_tomatoes + second_plant_tomatoes + third_plant_tomatoesprint(total_tomatoes)``````output60.0```The total number of tomatoes produced by the three plants is ( boxed{60} ).

answer:To solve this problem, we can use the properties of geometric sequences and the sum of geometric series.Given:- (S_4 = 2)- (S_8 = 8)We need to find (S_{12}).For a geometric sequence, the sum of the first (n) terms (S_n) can be written as:[ S_n = a frac{r^n - 1}{r - 1} ]where (a) is the first term and (r) is the common ratio.Given:[ S_4 = a frac{r^4 - 1}{r - 1} = 2 ][ S_8 = a frac{r^8 - 1}{r - 1} = 8 ]We can set up a system of equations for these sums and solve for (a) and (r). Once we have (a) and (r), we can find (S_{12}).Let's implement this step-by-step in Python using sympy.```pythonimport sympy as sp# Define variablesa, r = sp.symbols('a r')# Define the sum equationsS4 = a * (r4 - 1) / (r - 1) - 2S8 = a * (r8 - 1) / (r - 1) - 8# Solve the system of equationssolutions = sp.solve((S4, S8), (a, r))# Extract the solution valuesa_val, r_val = solutions[0]# Define the sum S12S12 = a_val * (r_val12 - 1) / (r_val - 1)# Simplify the expressionS12_simplified = sp.simplify(S12)# Print the resultprint(S12_simplified)``````output26```The sum of the first 12 terms (S_{12}) of the geometric sequence is (boxed{26}). This corresponds to option C in the given choices.

answer:To solve this problem, we need to use sympy to handle the algebraic manipulations and find the necessary prices and quantities. Let's break down the problem into manageable parts and solve each part step-by-step.1. Calculate the number of items sold per day when each souvenir is priced at 3.5 yuan.2. Determine the price at which the shop needs to sell the souvenirs to achieve a daily sales profit of 800 yuan. Part 1: Calculate the number of items sold per day when the price is 3.5 yuan.The shop initially sells 500 items at a price of 3 yuan. For each 0.1 yuan increase in price, the sales volume decreases by 10 items.Let's denote the price increase by (P) yuan. The number of items sold can be given by:[ text{Items Sold} = 500 - frac{P - 3}{0.1} times 10 ] Part 2: Determine the price to achieve a daily sales profit of 800 yuan.The profit per item is the selling price minus the wholesale price:[ text{Profit Per Item} = P - 2 ]The total profit is the profit per item multiplied by the number of items sold:[ text{Total Profit} = (P - 2) times left[ 500 - frac{P - 3}{0.1} times 10 right] ]We need to find the price (P) that makes the total profit equal to 800 yuan:[ (P - 2) times left[ 500 - frac{P - 3}{0.1} times 10 right] = 800 ]Let's implement this in Python using sympy to solve for the price (P) and the number of items sold.```pythonimport sympy as sp# Define variablesP = sp.symbols('P')# Initial conditionsinitial_price = 3initial_items_sold = 500price_increase_per_step = 0.1items_decrease_per_step = 10# Constraint on the maximum pricewholesale_price = 2max_price = 2.5 * wholesale_price# Number of items sold functionitems_sold = initial_items_sold - (P - initial_price) / price_increase_per_step * items_decrease_per_step# Part 1: Determine the number of items sold at P = 3.5 yuanprice_3_5 = 3.5items_sold_at_3_5 = items_sold.subs(P, price_3_5)# Part 2: Determine the price to achieve a daily profit of 800 yuanprofit_per_item = P - wholesale_pricetotal_profit = profit_per_item * items_solddesired_profit = 800# Solve for P to achieve the desired profitprice_for_desired_profit = sp.solve(total_profit - desired_profit, P)# Ensure price is within the allowed rangevalid_prices = [p for p in price_for_desired_profit if p <= max_price]# Print resultsprint(f"Number of items sold at 3.5 yuan: {items_sold_at_3_5}")print(f"Price to achieve a daily profit of 800 yuan: {valid_prices}")``````outputNumber of items sold at 3.5 yuan: 450.000000000000Price to achieve a daily profit of 800 yuan: [4.00000000000000]```The output indicates the following results:1. When each souvenir is priced at 3.5 yuan, the shop can sell ( boxed{450} ) items per day.2. If the shop wants to achieve a daily sales profit of 800 yuan, it should price the souvenirs at ( boxed{4} ) yuan.These results are consistent with the problem constraints and the calculations we carried out.

answer:To solve the problem of determining the maximum number of attempts required to open all 10 rooms with 10 keys, where each key opens exactly one room, we can approach it using combinatorial optimization. Here's the detailed reasoning and steps to solve the problem:1. Understand the Problem: We need to determine the maximum number of attempts required to open all 10 rooms, assuming the worst-case scenario. In the worst case, the dormitory manager will have to try all possible keys for each room until it opens.2. Apply Combinatorial Reasoning: In the worst case, for the first room, the manager might need to try all 10 keys. For the second room, they might need to try the remaining 9 keys, and so on. Essentially, this forms a permutation problem where we need to consider the maximum number of attempts across all room-key pairs.3. Calculate Using Factorial: The number of ways to arrange 10 keys to 10 rooms is given by the factorial of 10 (denoted as (10!)). However, the worst-case attempts do not directly correspond to (10!). Instead, the worst-case scenario can be calculated as the sum of the first 10 natural numbers (since each room might require one less attempt as the keys get reduced).4. Summation of Natural Numbers: The sum of the first (n) natural numbers is given by the formula: [ text{Sum} = frac{n cdot (n + 1)}{2} ] For (n = 10), this would be: [ text{Sum} = frac{10 cdot 11}{2} = 55 ]5. Implement in Python: We can implement this directly in Python to ensure the calculation is correct.Let's write the Python code to compute the summation:```python# Calculate the sum of the first 10 natural numbersn = 10sum_of_attempts = n * (n + 1) // 2# Output the resultprint(sum_of_attempts)``````output55```The maximum number of attempts required to open all 10 rooms with 10 keys, assuming the worst-case scenario, is (boxed{55}).