Asa received scores of 72, 97, and 82 on her last three math tests. she needs a mean test score of 82 to qualify for the math te

Answer:

7040

Step-by-step explanation:

C= 2000

B = 20/100 x 2000 = 400 + 2000 = 2400

A= 10/100 x 2400 = 240+2400= 2640

2000 + 2400 + 2640 = 7040

Answer:

(1) The necessary proportion of spirit to varnish stands at 1:3.

(2) A total of 80 ml of mineral spirit is required.

(3) The ratio of the heights to the widths of the tapestries is 3:2.

Step-by-step explanation:

(1) To achieve a mixture containing 25% mineral spirit, the blend consists of 25% spirit and 75% varnish.

Therefore,

Consequently, the proportion of spirit to varnish is 1:3.

(2) Using 240ml of varnish indicates this is 75% of the entire solution, which means the ratio of varnish to the total solution is 3:4.

Let the total solution quantity be .

Thus, .

⇒

⇒

⇒

⇒

This means the total solution amounts to 320 ml.

Now, calculating Spirit = Total solution - Varnish

⇒Spirit = 320ml-240ml

⇒Spirit = 80ml

Therefore, when using 240 ml of varnish, you will require 80 ml of mineral spirit.

(3) The dimensions of Robison's tapestries are uniform at 1.5m in length and 1m in width. Initially, to obtain whole numbers, we multiply these dimensions by 10.

Thus, the dimensions become 15m long and 10m wide.

Now, the proportion of Height to Width is 15:10

⇒

⇒

Thus, the proportion of the heights of the tapestries to their widths is 3:2.

1,107 cc The scanning consists of 10 intervals: [0,1.5), [1.5,3), [3,4.5), [4.5,6), [6,7.5), [7.5,9), [9,10.5), [10.5,12), [12,13.5), [13.5,15) To estimate the volume using the Midpoint Rule, n should be set to 10. Given that we will use n=5, we will split the range [0,15] into five intervals of lengths 3 each: [0,3], [3,6], [6,9], [9,12], [12,15] and calculate their midpoints: 1.5, 4.5, 7.5, 10.5, and 13.5. Next, we will determine the volume V from the five cylinders, where each has a height h=3 and the base area A corresponds to the calculated midpoints' intervals: Cylinder 1 Midpoint=1.5, corresponding to the 2nd interval A = 18, V= height * area of the base = 18*3 = 54 cc Cylinder 2 Midpoint=4.5, corresponding to the 4th interval A = 78, V= height * area of the base = 78*3 = 234 cc Cylinder 3 Midpoint=7.5, corresponding to the 6th interval A = 106, V= height * area of the base = 106*3 = 318 cc Cylinder 4 Midpoint=10.5, corresponding to the 8th interval A = 129, V= height * area of the base = 129*3 = 387 cc Cylinder 5 Midpoint=13.5, corresponding to the 10th interval A = 38, V= height * area of the base = 38*3 = 114 cc Thus, the estimated volume is 54 + 234 + 318 + 387 + 114 = 1,107