The length of a ribbon is 3/4 meter. sun yi needs pieces measuring 1/3 meter for an art project. what is the greatest number of pieces measuring 1/3 meter that can be cut from the ribbon? how much ribbon will be left after sun yi cuts the ribbon explain your reasoning

3/4 of a meter in decimal form is 0.75m

1/3 of a meter in decimal form is 0.33m

 Only two whole pieces measuring 0.33 can be cut from the ribbon since

0.33 + 0.33 = 0.66 (which is 0.09 less than 0.75) 

therefore any other piece will measure  0.75 - 0.66 = 0.09

For simplicity we can multiply by 100 to convert meters to cm, so

0.75 * 100 = 75cm,  0.33 * 100 = 33cm,  0.66 * 100 = 66 cm,  0.09  * 100 = 9cm.

So  two ribbons each 33cm long, totaling 66cm ,can be cut from the 75cm ribbon and only 9cm of the ribbon will be left.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places