Question

in 2009, usain bolt, a sprinter from jamaica, set the world record in the 100-meter dash with a time of 9.58 seconds. his approximate speed, in kilometers per hour, can be found using which conversion?(1) $\frac{9.58 \text{sec}}{100 \text{m}} cdot \frac{1000 \text{m}}{1 \text{km}} cdot \frac{1 \text{min}}{60 \text{sec}} cdot \frac{1 \text{hr}}{60 \text{min}}$(2) $\frac{100 \text{m}}{9.58 \text{sec}} cdot \frac{60 \text{sec}}{1 \text{min}} cdot \frac{1000 \text{m}}{1 \text{km}} cdot \frac{60 \text{min}}{1 \text{hr}}$(3) $\frac{100 \text{m}}{9.58 \text{sec}} cdot \frac{1 \text{km}}{1000 \text{m}} cdot \frac{1 \text{min}}{60 \text{sec}} cdot \frac{1 \text{hr}}{60 \text{min}}$(4) $\frac{100 \text{m}}{9.58 \text{sec}} cdot \frac{60 \text{sec}}{1 \text{min}} cdot \frac{1 \text{km}}{1000 \text{m}} cdot \frac{60 \text{min}}{1 \text{hr}}$the method of substitution was used to solve the system of equations below:$4x - 7y = 7$$x - y = -1$which equation is a correct first step when using this method?(1) $x = y - 1$(2) $y = x - 1$(3) $3x - 6y = 8$(4) $5x - 8y = 6$when $6x^3 - 2x + 8$ is subtracted from $5x^3 + 3x - 4$, the result is(1) $x^3 - 5x + 12$(2) $x^3 + x + 4$(3) $-x^3 + 5x - 12$(4) $-x^3 + x + 4$given $f(x) = x^2$, which function will shift $f(x)$ to the left 3 units?(1) $g(x) = x^2 + 3$(2) $h(x) = x^2 - 3$(3) $f(x) = (x - 3)^2$(4) $k(x) = (x + 3)^2$paul recorded the number of minutes he read each day, from monday through friday. his results are shown in the table:| day | number of minutes read ||-----|------------------------|| 1 | 12 || 2 | 16 || 3 | 19 || 4 | 27 || 5 | 29 |what is the correlation coefficient, to the nearest thousandth, and strength of the linear model of these data?(1) 0.984 and strong(2) 0.968 and strong(3) 0.984 and weak(4) 0.968 and weak

Explanation:

First Question: Unit Conversion

Step1: Set base speed value

$\frac{100\ \text{m}}{9.58\ \text{sec}}$

Step2: Convert sec to min

Multiply by $\frac{60\ \text{sec}}{1\ \text{min}}$

Step3: Convert m to km

Multiply by $\frac{1\ \text{km}}{1000\ \text{m}}$

Step4: Convert min to hr

Multiply by $\frac{60\ \text{min}}{1\ \text{hr}}$

Step1: Rearrange second equation

Solve $x - y = -1$ for $x$ or $y$.
$x = y - 1$

Step1: Write subtraction expression

$(5x^3 + 3x - 4) - (6x^3 - 2x + 8)$

Step2: Distribute negative sign

$5x^3 + 3x - 4 - 6x^3 + 2x - 8$

Step3: Combine like terms

$(5x^3-6x^3)+(3x+2x)+(-4-8) = -x^3 + 5x - 12$

Answer:

(4) $\frac{100\ \text{m}}{9.58\ \text{sec}} \cdot \frac{60\ \text{sec}}{1\ \text{min}} \cdot \frac{1\ \text{km}}{1000\ \text{m}} \cdot \frac{60\ \text{min}}{1\ \text{hr}}$

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Second Question: Substitution Method