Answer:
10,088 pounds
Step-by-step explanation:
Provided data
103 bushels of apples
102 bushels of grapes
101 bushels of oranges
With the respective weight per bushel:
Apples = 32 pounds
Grapes = 25 pounds
Oranges = 42 pounds
The total weight can be calculated by summing the products of each type:
Total Weight: 103(32) + 102(25) + 101(42) = 10,088 pounds
Given:
Triangle ABC is rotated 90 degrees counterclockwise and then translated vertically by 3 units to form triangle A'B'C'.
To determine:
The transformation rule necessary to map each point (x,y) on Triangle ABC to its equivalent point on Triangle A'B'C'.
Solution:
For a figure that undergoes a 90-degree counterclockwise rotation, the transformation will be defined as:
To translate a figure upward by 3 units, the appropriate transformation will be applied afterwards.
Hence, when triangle ABC experiences a rotation of 90 degrees counterclockwise followed by a translation of 3 units upward to create triangle A'B'C', the transformation rule will be established accordingly.
Laura sold 32 boxes, Kelly sold 17, and Tia sold 34 boxes. Step-by-step explanation: Let Laura's boxes be represented by L. Kelly sold L - 15, and Tia sold 2(L - 15). Therefore, the equation L + (L - 15) + 2(L - 15) = 83 can be solved as follows: 4L - 45 = 83, giving us 4L = 128, hence L = 32. Subsequently, Laura sold 32 boxes, Kelly sold 17 (which is 32 - 15), and Tia sold 34 (totaling twice Kelly's sales). The overall total is 32 + 17 + 34 = 83.
Answer: 0.31
Step-by-step explanation:
Let A signifies the event of the Tampa Bay Buccaneers scoring a touchdown on their initial drive while B signifies the occurrence of their defense achieving 3 or more sacks during the game.
Given: P(A)=0.14 P(B) = 0.31 P(A or B)=0.14
Formula: P(A and B)= P(A) + P(B) - P(A or B)
Now, we calculate the probability of both scoring a touchdown on the initial drive and achieving 3 or more sacks in the game as follows:-
P(A and B)= 0.14 + 0.31 - 0.14=0.31
Therefore, the required probability is: 0.31
1. Selected Case B. 2. 9 cm³. 3. 20 cm. 4. 4.5 m³. Explanation: In question 1, we need to fit a drum with a volume of 14,000 cm³. The volume of a cylinder can be calculated via the formula πr²h. For Case A, with r = 100 mm (10 cm) and h = 300 mm (30 cm), the total volume is approximately 9424.78 cm³, insufficient for the given drum. Case B, with r = 200 mm (20 cm) and h = 30 cm, gives a volume of approximately 37699.11 cm³. Case C with r = 32 cm and h = 250 mm (25 cm) results in a volume of about 80424.77 cm³. The smallest volume among Cases B and C is Case B at 37699.11 cm³, thus it is the correct choice. For question 2, the dimensions of the speaker are Length = 45 cm = 0.45 m, Width = 0.4 m, Height = 50 cm = 0.5 m, leading to a volume of 0.09 m³ or 9 cm³. Question 3 involves a speaker with a volume of 30,000 cm³ with Length = 30 cm = 0.45 m and Height = 500 mm = 50 cm, requiring to find its Width: 30,000 = 30 × W × 50, hence W = 20 cm. For question 4, with dimensions of Base = 2 m, Length = 3 m, Height =1.5 m, the volume of the prism is calculated as 4.5 m³.
