11. which of the following expressions is equivalent to $(3x^{-2})^{3}$?\n a. $9x^{-6}$\n b. $9x^{6}$\n c…

11. which of the following expressions is equivalent to $(3x^{-2})^{3}$?\n a. $9x^{-6}$\n b. $9x^{6}$\n c. $27x^{-4}$\n d. $27x^{-6}$\n12. a rectangle has a width of 7 cm and a length of 9 cm. what is its perimeter?\n a. 16 cm\n b. 32 cm\n c. 48 cm\n d. 62 cm\n13. a rectangular lot is three yards wide and four yards long. what is the area of the lot in square feet?\n a. $4\\text{ ft}^2$\n b. $12\\text{ ft}^2$\n c. $36\\text{ ft}^2$\n d. $108\\text{ ft}^2$\n14. what is the midpoint of the points $(-20,8)$ and $(5,3)$?\n a. $(5.5,7.5)$\n b. $(7.5,5.5)$\n c. $(5.5, - 7.5)$\n d. $(-7.5,5.5)$\n15. if 5 people buy 3 pens each and 3 people buy 7 pencils each, what is the ratio of the total number of pens to the total number of pencils?\n a. $5:7$\n b. $3:7$\n c. $5:3$\n d. $1:1$\nelectronics information\n1. which of the following is true regarding current and voltage?\n a. current is potential energy.\n b. voltage is kinetic energy.\n c. current is the buildup of charge.\n d. voltage is the potential energy difference between two charged terminals.\n2. what is the voltage across a 3 ω resistor if the ammeter reads 4 a?\n a. 0.75 v\n b. 7 v\n c. 12 v\n d. 1.33 v\n3. which of the following demonstrates the correct associations between the components of ohm’s law and their units of measure?\n a. current (amps); voltage (ohms)\n b. resistance (ohms); voltage (ohms)\n c. current (ohms); voltage (volts)\n d. resistance (amps); current (volts)

11. which of the following expressions is equivalent to $(3x^{-2})^{3}$?\n a. $9x^{-6}$\n b. $9x^{6}$\n c. $27x^{-4}$\n d. $27x^{-6}$\n12. a rectangle has a width of 7 cm and a length of 9 cm. what is its perimeter?\n a. 16 cm\n b. 32 cm\n c. 48 cm\n d. 62 cm\n13. a rectangular lot is three yards wide and four yards long. what is the area of the lot in square feet?\n a. $4\\text{ ft}^2$\n b. $12\\text{ ft}^2$\n c. $36\\text{ ft}^2$\n d. $108\\text{ ft}^2$\n14. what is the midpoint of the points $(-20,8)$ and $(5,3)$?\n a. $(5.5,7.5)$\n b. $(7.5,5.5)$\n c. $(5.5, - 7.5)$\n d. $(-7.5,5.5)$\n15. if 5 people buy 3 pens each and 3 people buy 7 pencils each, what is the ratio of the total number of pens to the total number of pencils?\n a. $5:7$\n b. $3:7$\n c. $5:3$\n d. $1:1$\nelectronics information\n1. which of the following is true regarding current and voltage?\n a. current is potential energy.\n b. voltage is kinetic energy.\n c. current is the buildup of charge.\n d. voltage is the potential energy difference between two charged terminals.\n2. what is the voltage across a 3 ω resistor if the ammeter reads 4 a?\n a. 0.75 v\n b. 7 v\n c. 12 v\n d. 1.33 v\n3. which of the following demonstrates the correct associations between the components of ohm’s law and their units of measure?\n a. current (amps); voltage (ohms)\n b. resistance (ohms); voltage (ohms)\n c. current (ohms); voltage (volts)\n d. resistance (amps); current (volts)

Answer

Question 11

Explanation:

Step1: Apply power - of - a - product rule

$(3x^{-2})^3=3^3\times(x^{-2})^3$

Step2: Calculate powers

$3^3 = 27$ and $(x^{-2})^3=x^{-2\times3}=x^{-6}$ So, $(3x^{-2})^3 = 27x^{-6}$

Answer:

d. $27x^{-6}$

Question 12

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is length and $w$ is width.

Step2: Substitute values

Given $l = 9$ cm and $w = 7$ cm, then $P=2(9 + 7)=2\times16 = 32$ cm

Answer:

b. $32$ cm

Question 13

Explanation:

Step1: Convert yards to feet

Since 1 yard = 3 feet, the width $w=3$ yards $=3\times3 = 9$ feet and the length $l = 4$ yards $=4\times3=12$ feet.

Step2: Calculate area

The area formula of a rectangle is $A=l\times w$, so $A = 12\times9=108$ square - feet

Answer:

d. $108$ ft²

Question 14

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Substitute values

Here $x_1=-20,y_1 = 8,x_2 = 5,y_2 = 3$. Then $\frac{-20 + 5}{2}=\frac{-15}{2}=-7.5$ and $\frac{8+3}{2}=\frac{11}{2}=5.5$

Answer:

d. $(-7.5,5.5)$

Question 15

Explanation:

Step1: Calculate total number of pens

5 people buy 3 pens each, so the total number of pens is $5\times3 = 15$.

Step2: Calculate total number of pencils

3 people buy 7 pencils each, so the total number of pencils is $3\times7 = 21$.

Step3: Find the ratio

The ratio of the total number of pens to the total number of pencils is $\frac{15}{21}=\frac{5}{7}=5:7$

Answer:

a. $5:7$

Electronics Information Question 1

Brief Explanations:

Voltage is defined as the potential energy difference between two charged terminals. Current is the flow of electric charge, not the buildup of charge. Potential energy is related to voltage, not current, and voltage is not kinetic energy.

Answer:

d. Voltage is the potential energy difference between two charged terminals.

Electronics Information Question 2

Explanation:

Step1: Recall Ohm's law

Ohm's law is $V = IR$, where $V$ is voltage, $I$ is current, and $R$ is resistance.

Step2: Substitute values

Given $R = 3\Omega$ and $I = 4A$, then $V=4\times3=12$ V

Answer:

c. $12$ V

Electronics Information Question 3

Brief Explanations:

In Ohm's law $V = IR$, the unit of current is Amps (A), the unit of voltage is Volts (V), and the unit of resistance is Ohms ($\Omega$).

Answer:

None of the above options are correct. The correct associations are Current (Amps); Voltage (Volts); Resistance (Ohms)