Here are the answers to your questions:
Question 1:
The ratio of white keys to black keys is given as 5 white keys for every 2 black keys. Therefore, the ratio of white keys to black keys is 5:2.
(none of the options provided are correct)
Question 2:
The data described is bimodal with two modes (14 and 16) indicating that many students participated in activities. The best answer is:
The data is bimodal with an approximate range of 20. This means that the most frequent number of activities was either 14 or 16, which might mean that the activities vary in each school.
Question 3:
To find the amount needed for 7 servings based on the previous servings:
From the recipe:
- For 5 servings: 15 cups of sauce → 3 cups of sauce per serving
- For 7 servings: \(3 \times 7 = 21\) cups of sauce
- Oregano for 5 servings: 2.5 tsp → \(2.5 / 5 = 0.5\) tsp per serving → for 7 servings: \(0.5 \times 7 = 3.5\) tsp of oregano
The recipe will need 21 cups of sauce and 3.5 teaspoons of oregano for 7 servings.
Question 4:
Surface area of a rectangular prism = \(2lw + 2lh + 2wh\)
Where l = 4.5 cm, w = 6 cm, h = 5 cm:
\(= 2(4.5 \cdot 6) + 2(4.5 \cdot 5) + 2(6 \cdot 5) = 54 + 45 + 60 = 159\) cm²
The surface area of the prism is 159 cm².
Question 5:
To find the mean:
Sum = \(77 + 84 + 45 + 54 + 33 + 37 + 60 + 43 + 69 + 73 + 65 + 49 = 490\)
Mean = \(490 / 12 ≈ 40.83\) (please double-check calculations)
However, based on listed options: mean is about 57.4. This represents average students that left early.
(The average seems to be inaccurate based on my calculations, please recalculate for confirmation.)
Question 6:
The statistical question that can result in numerical data is:
How many students at your school ride horses?
Question 7:
To estimate papers graded in 60 minutes:
From the table, if he grades 20 papers in 50 minutes, the rate is \(20 / 50 = 0.4\) papers per minute.
In 60 minutes, he will grade \(0.4 \times 60 = 24\) papers.
So, in 60 minutes, he will grade 24 papers.
Question 8:
Calculate rates:
Rita: \(1505 / 7 ≈ 215\) words per minute
Joy: \(1110 / 5 = 222\) words per minute
Thus, Rita read at the faster rate because 222 words per minute > 215 words per minute.
Question 9:
Adding a teacher's age of 45 will either keep or reduce the mean based on the distribution. If mean age before was 45 then:
The mean would remain the same around \(43-45\), option: The value of the mean would remain the same at about 44.
Question 10:
Calculating perimeter:
Length = \(9 - (-12) = 21\) feet
Width = \(15 - (-9) = 24\) feet
Perimeter = \(2(l + w) = 2(21 + 24) = 90\) feet.
So, the perimeter is 90 feet.
Question 11:
Range = \(54 - 14 = 40\)
IQR = \(49 - 26 = 23\)
The range is 40, and the IQR is 23, so:
The range is 40, and the IQR is 23.
Question 12:
The percentage equivalent to \(11/50\):
\( (11/50) \times 100 = 22% \)
Thus, the answer is 22%.
Question 13:
Point B is described as (3, 1) since it is three units right and one unit up from the origin.
So the answer is (3, 1).
Question 14:
The distance formula for points \((x_1, y_1)\) and \((x_2, y_2)\) on a vertical line can be calculated as \(|y_2 - y_1| = |22 - (-10)| = 32\) units.
So, the distance is 32 units.
Question 15:
Volume of rectangular prism = \(length \cdot width \cdot height\) = \(30 \cdot 22 \cdot 20.8 = 12480\) in³.
Please check thy calculations, but it seems you missed options in regards to unit conversions.
Max water that the rectangular container will hold is 12,480 in³.
Please ensure to double-check the calculations provided, especially averages, as they can depend on accuracy.