Santiago tried to evaluate an expression step by step. (4⋅109)⋅0.00003=(4⋅109)⋅(3⋅10−5)Ste p 1=(4⋅3)⋅(109⋅10−5)Step 2=12⋅1014Step 3\qquad\begin{aligned} &(4 \cdot 10^9) \cdot 0.00003 \\ =&(4 \cdot 10^9) \cdot (3\cdot10^{-5})&\green{\text{St ep } 1} \\ =&(4\cdot3)\cdot(10^9\cdot10^{- 5})&\blue{\text{Step } 2} \\ =&12 \cdot10^{14}&\purple{\text{Step } 3} \end{aligned}===(4⋅109)⋅0.00003(4⋅1 09)⋅(3⋅10−5)(4⋅3)⋅(109⋅10−5)12⋅1014 Step 1Step 2Step 3 Find Santiago's mistake. Choose 1 Choose 1 (Choice A) A Step 1\green{\text{Step }1}Step 1start color #28ae7b, start text, S, t, e, p, space, end text, 1, end color #28ae7b (Choice B) B Step 2\blue{\text{Step }2}Step 2start color #6495ed, start text, S, t, e, p, space, end text, 2, end color #6495ed (Choice C) C Step 3\purple{\text{Step }3}Step 3start color #9d38bd, start text, S, t, e, p, space, end text, 3, end color #9d38bd (Choice D) D Santiago did not make a mistake.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.