El 1 de noviembre de 2005, la señora Rodgers invirtió $ 10,000 en un certificado de depósito a 10 años que pagaba interés a la t

V = x³ - 6x²y + 12xy² - 8y³

V = (x - 2y)³

   = (x - 2y)(x - 2y)(x - 2y) ( start by expanding the first pair of factors )

   = (x² - 4xy + 4y²)(x - 2y) ( multiply the terms from the first group with those in the second )

   = x³ - 4x²y + 4xy² - 2x²y + 8xy² - 8y³ ( combine similar terms )

  = x³ - 6x²y + 12xy² - 8y³

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.

Answer:

$786

Step-by-step explanation:

50, 60, 72

calculate the variance between the earnings from the first and second hours to obtain 10.

determine the difference between the second and third hours, resulting in 12.

it becomes clear that these differences are consistently increasing in even numbers starting from 10, such as 10, 12, 14, 16, 18, 20, 22, 24, 26, 28....etc

to compute the total income over the 24 hours, continue adding the next even number until the 24th hour

the total will be $786.