Grandma Betty's recipe makes 6 cupcakes and uses frac{1}{3} of a cup of sugar.How many cups of sugar will it take to make 2 frac{1}{2} dozen cupcakes?a. 1frac{1}{2} cupsb. frac{2}{3} cupc. frac{3}{5} cupd. frac{1}{9} cup

Solve. 5x + 3y = 15 for y when x = 0.

When 142 is added to a number, the result is 64 more than 3 times the number. Find the number.

Please, solve for the values of x for each of the following exponential equations and inequalities.
(a) ${\displaystyle 8^{2-x}=2}$
(b) ${\displaystyle {\left(\frac{1}{2}\right)}^x<\left(\frac{1}{8}\right)}$
(c) ${\displaystyle 5^x={25}^{x-2}}$
(d) ${\displaystyle 3^{x+2}\ge 27}$
(e) ${\displaystyle 4^{3x}=8^{x-1}}$

Suppose a,$b\in Z$. If a∣b, then ${\displaystyle a^2\mid b^2.}$
If x is an odd integer, then $x^3$ is odd.
If a is an odd integer, then $a^2+3a+5$ is odd.

Consider the statement: "Mary wants to (spend, at least spend, at most spend) 20 minutes a day exercising". Depending on which word you chose in parenthesis you end up with a different expression.
Write the expression for each of the word choices and label.

Given an acceleration vector,initial velocity ${\displaystyle ⟨u_0,v_0⟩}$ ,and initial position ${\displaystyle ⟨x_0,y_0⟩}$,find the velocity and position vectors for ${\displaystyle t\ge 0}$
${\displaystyle a\left(t\right)=⟨0,1⟩,⟨u_0,v_0⟩=⟨2,3⟩,⟨x_0,y_0⟩=⟨0,0⟩}$

Show that an exponential model fits the data. Then write a recursive rule that models the data. $$\text{Misplaced hline}$$