8) benjamin wrapped a box in shipping paper to mail to his grandfather. 18 in. 24 in. 20 in. find the total…

8)

Explanation:

Step1: Recall surface - area formula for rectangular prism

The formula for the surface area of a rectangular prism is $SA = 2(lw+lh + wh)$, where $l$ is the length, $w$ is the width, and $h$ is the height. Here, $l = 24$ in, $w = 18$ in, and $h = 20$ in.

Step2: Calculate $lw$, $lh$, and $wh$

$lw=24\times18 = 432$ in², $lh = 24\times20=480$ in², $wh=18\times20 = 360$ in².

Step3: Calculate the surface area

$SA=2(432 + 480+360)=2\times1272 = 2544$ in².

Answer:

$2544$ in²

9)

Explanation:

Step1: Recall volume formula for cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius and $h$ is the height. Given $r = 4.2$ m and $h = 8$ m.

Step2: Calculate $r^{2}$

$r^{2}=(4.2)^{2}=17.64$ m².

Step3: Calculate the volume

$V=\frac{1}{3}\times\pi\times17.64\times8=\frac{1}{3}\times\pi\times141.12\approx\frac{1}{3}\times3.14\times141.12 = 147.7056$ m³.

Answer:

$147.7056$ m³

10)

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A=P(1 +\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $P = 3000$, $r=0.028$, $n = 1$ (assuming annual compounding), and $t=\frac{60}{12}=5$ years.

Step2: Substitute values into the formula

$A = 3000(1+\frac{0.028}{1})^{1\times5}=3000\times(1.028)^{5}$.

Step3: Calculate $(1.028)^{5}$

$(1.028)^{5}=1.028\times1.028\times1.028\times1.028\times1.028\approx1.1487$.

Step4: Calculate $A$

$A = 3000\times1.1487=3446.1$.

Answer:

$$3446.1$

11)

Explanation:

Step1: Add $12x$ to both sides

$-12x - 7+12x=-3x + 92+12x$, which simplifies to $-7 = 9x+92$.

Step2: Subtract 92 from both sides

$-7-92=9x+92 - 92$, so $-99 = 9x$.

Step3: Solve for $x$

$x=\frac{-99}{9}=-11$.

Answer:

$x=-11$