Answer: The maximum number of tickets of each kind that can be given away without exceeding $300 is 10 tickets of each kind. Explanation: This problem involves setting up and solving a system of inequalities based on the given constraints: the total cost and the minimum number of tickets of each type. The key concepts involved are linear inequalities, systems of inequalities, and graphical solution methods for linear programming problems. Steps: Define variables: Let $ x $ = number of $10 tickets Let $ y $ = number of $20 tickets Write the constraints: Cost constraint: Total cost cannot exceed $300: \[ 10x + 20y \leq 300 \] Minimum tickets constraint: At least 2 tickets of each kind: \[ x \geq 2 \] \[ y \geq 2 \] Simplify the cost inequality: Divide the entire inequality by 10: \[ x + 2y \leq 30 \] Graphical interpretation: Plot the line $ x + 2y = 30 $ on the coordinate plane. The feasible region is the area below or on this line, and to the right of the lines $ x=2 $ and $ y=2 $. Find the maximum number of tickets: Since the goal is to find the maximum number of tickets of each kind without exceeding $300, and considering the constraints $ x \geq 2 $, $ y \geq 2 $, the maximum occurs at the corner point of the feasible region. Determine the corner points: When $ y=2 $: \[ x + 2(2) = 30 \Rightarrow x + 4 = 30 \Rightarrow x=26 \] Check if $ x \geq 2 $: yes, so point $(26, 2)$. When $ x=2 $: \[ 2 + 2y = 30 \Rightarrow 2y=28 \Rightarrow y=14 \] Check if $ y \geq 2 $: yes, so point $(2, 14)$. Intersection with axes (if applicable): $ x=0 $: \[ 0 + 2y \leq 30 \Rightarrow y \leq 15 \] But $ x \geq 2 $, so ignore $ x=0 $. $ y=0 $: \[ x + 0 \leq 30 \Rightarrow x \leq 30 \] But $ y \geq 2 $, so ignore $ y=0 $. Determine the maximum total tickets: At point $(26, 2)$: total tickets = $ 26 + 2 = 28 $. At point $(2, 14)$: total tickets = $ 2 + 14 = 16 $. The maximum total tickets are at $(26, 2)$, with 28 tickets. Summary: The maximum number of tickets of each kind that can be given away without exceeding $300 is **26 tickets of $10 and 2 tickets of $20**. The total number of tickets given away in this case is 28. Note: The question asks for how many of each kind can be given away, so the answer is 26 tickets of $10 and 2 tickets of $20.

Write the name of the period that has the digits 913.

Answer: Thousands Explanation: In the context of place value in the decimal number system, each group of three digits is referred to as a "period." The periods are named from right to left as units, thousands, millions, etc. The digits 913 fall in the thousands period. Steps: Identify the Place Value System: The decimal system is organized in groups of three digits, each called a period. Determine the Period Name: The first period from the right is the units (or ones) period. The second period is the thousands period. The third period is the millions period, and so on. Locate the Digits 913: Since 913 is typically placed in the second group from the right in a larger number, it belongs to the thousands period. Thus, the name of the period that has the digits 913 is the thousands period.

32. Based on the measurements shown on △ABC, AB must be: A. less than 7 ft B. between 7 and 10 ft C. between 10 and 17 ft D. greater than 17 ft A 47° B 68° C 7 ft 10 ft

Answer: B. between 7 and 10 ft Explanation: To find the length of $ AB $ in $\triangle ABC$, we can use the Law of Cosines. This theorem relates the lengths of the sides of a triangle to the cosine of one of its angles. Given the sides $ AC = 10 $ ft, $ BC = 7 $ ft, and angle $ C = 68^\circ $, we can find $ AB $. Steps: Law of Cosines Formula: \[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \] where $ c $ is the side opposite angle $ C $. Substitute the Known Values: \[ AB^2 = 10^2 + 7^2 - 2 \cdot 10 \cdot 7 \cdot \cos(68^\circ) \] Calculate: \[ AB^2 = 100 + 49 - 140 \cdot \cos(68^\circ) \] Find $\cos(68^\circ)$: \[ \cos(68^\circ) \approx 0.3746 \] Continue Calculation: \[ AB^2 = 149 - 140 \cdot 0.3746 \] \[ AB^2 = 149 - 52.444 \] \[ AB^2 = 96.556 \] Solve for $ AB $: \[ AB = \sqrt{96.556} \approx 9.82 \text{ ft} \] Since $ AB \approx 9.82 $ ft, it falls between 7 and 10 ft. Thus, the correct answer is B. between 7 and 10 ft.

How does 2025 minus 1943 work?

Answer: 82 Explanation: To find the difference between 2025 and 1943, you subtract the smaller number from the larger number: \[ 2025 - 1943 = 82 \] This calculation shows that 2025 is 82 years after 1943.

• The circle graph above gives the distribution of salad dressing chosen by customers at a restaurant. If approximately 200 customers order each day at the restaurant. Which of the following is closest to the difference per day between the number who choose Italian dressing and the number who choose vinaigrette dressing? Blue cheese 20% French 5% Italian 45% Vinaigrette 30%

Answer: 30 Explanation: To find the difference between the number of customers choosing Italian dressing and those choosing vinaigrette, we need to calculate the number of customers for each dressing type based on the percentages given in the circle graph. Then, subtract the number of vinaigrette customers from the number of Italian dressing customers. Steps: Identify the percentages: Italian dressing: 45% Vinaigrette dressing: 30% Calculate the number of customers for each dressing: Total customers per day = 200 Italian dressing customers = $ 200 \times \frac{45}{100} = 90 $ Vinaigrette dressing customers = $ 200 \times \frac{30}{100} = 60 $ Find the difference: Difference = Italian dressing customers - Vinaigrette dressing customers Difference = $ 90 - 60 = 30 $ Thus, the difference per day between the number who choose Italian dressing and the number who choose vinaigrette dressing is 30.

Math Question from Image

Answer: Yes, Diego's statement is correct. The answer is $ \frac{6}{5} $ or $ 1 \frac{1}{5} $. Explanation: To find how many groups of $ \frac{5}{6} $ are in 1, we need to divide 1 by $ \frac{5}{6} $. This involves the concept of dividing fractions, which is done by multiplying by the reciprocal. Steps: Set up the division problem: \[ 1 \div \frac{5}{6} \] Convert the division to multiplication by the reciprocal: \[ 1 \times \frac{6}{5} \] Perform the multiplication: \[ 1 \times \frac{6}{5} = \frac{6}{5} \] Convert the improper fraction to a mixed number: \[ \frac{6}{5} = 1 \frac{1}{5} \] Thus, there are $ \frac{6}{5} $ or $ 1 \frac{1}{5} $ groups of $ \frac{5}{6} $ in 1.

Answer: The maximum number of tickets of each kind that can be given away without exceeding $300 is 10 tickets of each kind. Explanation: This problem involves setting up and solving a system of inequalities based on the given constraints: the total cost and the minimum number of tickets of each type. The key concepts involved are linear inequalities, systems of inequalities, and graphical solution methods for linear programming problems. Steps: Define variables: Let $ x $ = number of $10 tickets Let $ y $ = number of $20 tickets Write the constraints: Cost constraint: Total cost cannot exceed $300: \[ 10x + 20y \leq 300 \] Minimum tickets constraint: At least 2 tickets of each kind: \[ x \geq 2 \] \[ y \geq 2 \] Simplify the cost inequality: Divide the entire inequality by 10: \[ x + 2y \leq 30 \] Graphical interpretation: Plot the line $ x + 2y = 30 $ on the coordinate plane. The feasible region is the area below or on this line, and to the right of the lines $ x=2 $ and $ y=2 $. Find the maximum number of tickets: Since the goal is to find the maximum number of tickets of each kind without exceeding $300, and considering the constraints $ x \geq 2 $, $ y \geq 2 $, the maximum occurs at the corner point of the feasible region. Determine the corner points: When $ y=2 $: \[ x + 2(2) = 30 \Rightarrow x + 4 = 30 \Rightarrow x=26 \] Check if $ x \geq 2 $: yes, so point $(26, 2)$. When $ x=2 $: \[ 2 + 2y = 30 \Rightarrow 2y=28 \Rightarrow y=14 \] Check if $ y \geq 2 $: yes, so point $(2, 14)$. Intersection with axes (if applicable): $ x=0 $: \[ 0 + 2y \leq 30 \Rightarrow y \leq 15 \] But $ x \geq 2 $, so ignore $ x=0 $. $ y=0 $: \[ x + 0 \leq 30 \Rightarrow x \leq 30 \] But $ y \geq 2 $, so ignore $ y=0 $. Determine the maximum total tickets: At point $(26, 2)$: total tickets = $ 26 + 2 = 28 $. At point $(2, 14)$: total tickets = $ 2 + 14 = 16 $. The maximum total tickets are at $(26, 2)$, with 28 tickets. Summary: The maximum number of tickets of each kind that can be given away without exceeding $300 is **26 tickets of $10 and 2 tickets of $20**. The total number of tickets given away in this case is 28. Note: The question asks for how many of each kind can be given away, so the answer is 26 tickets of $10 and 2 tickets of $20.

Solved: A Radio Station Is Giving Away Tickets To A Play. They Plan To Give Away Tickets To Seats That Cost $10 Or $20. They Plan To Give Away At Least 20 Tickets, And The Total Cost Of All The Tickets Can Be No More Than $300. Make A Graph Showing How Many Tickets Of Each Kind Can Be Given Away.

i-Ready Analyzing Word Choice: Connotations — Quiz — Level H demanding the remaining four candidates stay silent. “Good, let’s continue. I choose rock.” The Proctor held a fist out in front of him to represent a rock. It was a trick then, Persephone thought. Because the Proctor chose his object before the students could select theirs, he had destroyed his own odds of winning. Next, the Proctor approached Calista and asked, “What is your choice?” Calista extended a flat hand signifying paper, knowing it smothered rock. The Proctor moved on to Ezekiel, who hesitated and then extended paper as well. Would they both be approved as Deciders? Persephone knew it couldn’t be that easy because nothing in her twelve years at the Academy had been that easy. Eleni, to Persephone’s left, obviously agreed, for on her turn she thrust two fingers forward to represent scissors, an immediate loss by the traditional rules of the game. Eleni must be thinking the wisest choice was to accept defeat by letting the Proctor’s rock crush her scissors—but how could intentionally losing be the right answer? Complete the sentences to describe what happens in this part of the story. The Proctor has changed ___ the game by showing his hand first. He chooses rock. Calista and Ezekiel both show paper, which ___ rock. Next, Eleni’s hand shows scissors, which means she has ___ the game on purpose. Persephone ___ all of her classmates’ choices.

A radio station is giving away tickets to a play. They plan to give away tickets to seats that cost $10 or $20. They plan to give away at least 20 tickets, and the total cost of all the tickets can be no more than $300. Make a graph showing how many tickets of each kind can be given away.