Question 1

Given two vectors  and vector  ,that also lies in the xy plane,have the property A = B but  .The vector  is
A)  .
B)  .
C)  .
D)All are correct.

Accepted Answer

The answer of Given two vectors  and vector ...

Question 2

The speed limit on your street is 35 mi/hr.What is this speed in m/s?
A)16 m/s
B)22 m/s
C)56 m/s
D)78 m/s

Accepted Answer

To convert miles per hour (mi/hr) to meters per second (m/s), use the conversion factor: 1 mi/hr = 0.44704 m/s. Therefore, 35 mi/hr = 35 * 0.44704 m/s ≈ 15.6464 m/s, which rounds to approximately 16 m/s.

Question 3

The sides of a rectangle are measured to have lengths 0.234 cm and 12.78 cm.Find the area of the rectangle using the correct number of significant figures. A)2.99052 cm² B)2.9905 cm² C)2.991 cm² D)2.990 cm² E)2.99 cm²

Accepted Answer

The area of the rectangle is calculated by multiplying the lengths of its sides: 0.234 cm * 12.78 cm = 2.99052 cm². However, the answer must be reported with the correct number of significant figures, which is determined by the measurement with the least number of significant figures. Since 0.234 has three significant figures, the area should also be reported with three significant figures, making it 2.99 cm².

Question 4

A string with a length of 13.1 m is tightly tied between two trees.The second tree is some distance east and north of the first tree.If the second tree is 9.8 m east of the first tree,how far north of the first tree is the second tree?
A)3.3 m
B)6.6 m
C)8.7 m
D)11.5 m
E)22.9 m

Accepted Answer

We can use the Pythagorean Theorem to solve this problem. Let x be the distance north of the first tree to the second tree.
Then we have:
(9.8)^2 + x^2 = (13.1)^2
Simplifying this equation, we get:
x^2 = (13.1)^2 - (9.8)^2
x^2 = 171.21
x = √171.21 ≈ 13.1 m
Therefore, the second tree is 8.7 meters north of the first tree.

Question 5

The width of the nail of you thumb is approximately equal to which of the following units:
A)1 $\mu$m.
B)1 mm.
C)1 cm.
D)1 m.
E)1 km.

Accepted Answer

The width of the nail of your thumb is approximately equal to 1 cm. This is a common informal reference used for estimating small lengths.

Question 6

The fraction of a kilogram in a milligram is A)10^-6. B)10^-4. C)10^-3. D)10^-2.

Accepted Answer

1 kilogram = 1,000,000 milligrams Therefore, the fraction can be calculated as: 1 kg / 1,000,000 mg = 10^-6 Which in scientific notation is equivalent to 10^-6.

Question 7

What is the sum of the lengths of all the edges of a cube whose volume is 3.97 m³? A)4.53 m B)9.50 m C)12.67 m D)19.00 m

Accepted Answer

The volume of a cube is given by $ V = s^3 $, where $ s $ is the side length. Solving $ s^3 = 3.97 $ gives $ s \approx 1.58 $ m. A cube has 12 edges, so the total length of all edges is $ 12 \times 1.58 \approx 19.00 $ m.

Question 8

Vector  has length 15.2 m and is directed along the x-axis.Vector  has length 23.0 m and is directed along the y-axis.Vector  has length 6.3 m and is directed along the -y axis.What is the length of the vector  ?
A)18.4 m
B)22.4 m
C)24.7 m
D)28.3 m
E)33.0 m

Accepted Answer

The answer of Vector  has length 15.2 m and...

Question 9

The fraction of a square kilometer in a square millimeter is A)10^-12. B)10^-9. C)10^-3. D)10^-6.

Accepted Answer

A square kilometer is 10^6 square meters, and a square meter is 10^6 square millimeters, so a square kilometer is 10^12 square millimeters.

Question 10

The fraction of a cubic kilometer in a cubic millimeter is A)10^-12. B)10^-6. C)10^-9. D)10^-18.

Accepted Answer

A cubic kilometer is 10^9 meters cubed, and a cubic millimeter is 10^-9 meters cubed. Therefore, the fraction is 10^-18.

Question 11

A driver from Canada enters the U.S.The posted speed limit is 45 mph.What is this posted speed limit in km/h?
A)31
B)45
C)53
D)67
E)72

Accepted Answer

The answer of A driver from Canada enters the U.S.The...

Question 12

The solution of (3.75 * 10^-9)- (6.21 *10^-10)in scientific notation is A)1.92 * 10^-9. B)3.13 * 10^-9. C)4.83 * 10^-10. D)3.74 * 10^-9.

Accepted Answer

The answer of The solution of (3.75 * 10^-9)- (6.21...

Question 13

27500 people live in the Duchy of Grand Fenwick,which has a land area of a square 5.8 km on each side.How many people live there per square km?
A)820
B)817
C)810
D)809

Accepted Answer

The area of the Duchy is 5.8 km * 5.8 km = 33.64 square km. The population density is 27500 people / 33.64 square km = 817.16, which rounds to 820 people per square km.

Question 14

A gardener wants to build a circular fence around his vegetable garden.If he has 100 feet (1 ft = 0.3048 m)of wire,what is the maximum area covered? A)0.0000739 km² B)0.002342 km² C)23.4 km² D)75.2 km² E)81.99 km²

Accepted Answer

The circumference of the circle is 100 feet, which is approximately 30.48 meters. Using the formula for the circumference of a circle, C = 2πr, we can find the radius r. Then, using the formula for the area of a circle, A = πr², we calculate the area in square meters and convert it to square kilometers. The correct answer is approximately 0.0000739 km².

Question 15

The vector = (A_x ,A_y)= ( +7.07 m,+7.07 m)and the vector = (B_x ,B_y)= ( +5.00 m,+8.66 m).What is the magnitude of the angle between the vectors and ? A)15S1U1P1$\circ$S1S1P0 B)30S1U1P1$\circ$S1S1P0 C)45S1U1P1$\circ$S1S1P0 D)60S1U1P1$\circ$S1S1P0 E)75S1U1P1$\circ$S1S1P0

Accepted Answer

The answer of The vector = (A_x ,A_y)= (...

Question 16

A bicycle tire is inflated to a pressure of 93 psi.What is a pressure of 93 psi in the SI unit pascals (Pa)? A)6.4 * 10¹ Pa B)1.6 * 10² Pa C)1.6 * 10⁴ Pa D)3.2 * 10⁴ Pa E)6.4 * 10⁵ Pa

Accepted Answer

1 psi is approximately equal to 6894.76 Pa. Therefore, 93 psi is approximately 93 * 6894.76 Pa, which equals about 640,217 Pa or 6.4 * 10^5 Pa.

Question 17

What is the ratio of the Earth's density to that of Venus? Their radii are 6378 km and 6051 km,and their masses 5.97 *10²⁴ kg and 4.87 * 10²⁴ kg,respectively. A)0.96 B)1.05 C)1.16 D)1.44

Accepted Answer

The density of a planet can be calculated using the formula $\rho = \frac{M}{\frac{4}{3}\pi r^3}$, where $M$ is the mass and $r$ is the radius of the planet. For Earth, $\rho_{Earth} = \frac{5.97 \times 10^{24}}{\frac{4}{3}\pi (6378 \times 10^3)^3}$ and for Venus, $\rho_{Venus} = \frac{4.87 \times 10^{24}}{\frac{4}{3}\pi (6051 \times 10^3)^3}$. Calculating these densities and then taking the ratio $\frac{\rho_{Earth}}{\rho_{Venus}}$ gives approximately 1.05.

Question 18

Kobe Bryant of the LAL (LA Lakers)is 6'6" tall.His height in meters is
A)6.2 m.
B)3.5 m.
C)2.9 m.
D)1.98 m.

Accepted Answer

To convert feet to meters, we need to multiply by 0.3048. Therefore, Kobe Bryant's height in meters is 6.6 x 0.3048 = 1.98m. The correct answer is D.

Question 19

A CD that is 0.75 mm thick has outer diameter of 128 mm and inner diameter of 15 mm.The volume of the CD is A)1920 mm³. B)5300 mm³. C)9520 mm³. D)38079 mm³.

Accepted Answer

The volume of the CD can be calculated by subtracting the volume of the hole in the center from the volume of the entire disc. The volume of the entire disc is the volume of a cylinder with height 0.75 mm and radius 64.5 mm (the average of the outer and inner radii):
V1 = πr^2h = π(64.5)^2(0.75) ≈ 9520 mm^3

The volume of the hole in the center is the volume of a cylinder with height 0.75 mm and radius 7.5 mm (the difference between the outer and inner radii):
V2 = πr^2h = π(7.5)^2(0.75) ≈ 133 mm^3

Therefore, the volume of the CD is:
V1 - V2 ≈ 9387 mm^3, which is closest to option C, 9520 mm^3.

Question 20

A right cylinder has a cross sectional area of 25.0 cm² and a height of 50.0 cm.What is the volume of the cylinder in SI units? A)0.000125 m³ B)0.00125 m³ C)0.0125 m³ D)0.125 m³ E)1.250 m³

Accepted Answer

The formula for the volume of a cylinder is V = A × h, where A is the cross-sectional area and h is the height.

Substituting the given values, we get:

V = (25.0 cm²) × (50.0 cm)

To convert to SI units, we need to convert cm² to m² and cm to m:

V = (25.0 × 10⁻⁴ m²) × (50.0 × 10⁻² m)

V = 1.250 × 10⁻³ m³

Therefore, the answer is B, 0.00125 m³.

Quiz 1: Overview

Given two vectors and vector ,that also lies in the xy plane,have the property A = B but .The vector is

The speed limit on your street is 35 mi/hr.What is this speed in m/s?

The sides of a rectangle are measured to have lengths 0.234 cm and 12.78 cm.Find the area of the rectangle using the correct number of significant figures.

A string with a length of 13.1 m is tightly tied between two trees.The second tree is some distance east and north of the first tree.If the second tree is 9.8 m east of the first tree,how far north of the first tree is the second tree?

The width of the nail of you thumb is approximately equal to which of the following units:

The fraction of a kilogram in a milligram is

What is the sum of the lengths of all the edges of a cube whose volume is 3.97 m³?

Vector has length 15.2 m and is directed along the x-axis.Vector has length 23.0 m and is directed along the y-axis.Vector has length 6.3 m and is directed along the -y axis.What is the length of the vector ?

The fraction of a square kilometer in a square millimeter is

The fraction of a cubic kilometer in a cubic millimeter is

A driver from Canada enters the U.S.The posted speed limit is 45 mph.What is this posted speed limit in km/h?

The solution of (3.75 * 10^-9) - (6.21 *10^-10) in scientific notation is

27500 people live in the Duchy of Grand Fenwick,which has a land area of a square 5.8 km on each side.How many people live there per square km?

A gardener wants to build a circular fence around his vegetable garden.If he has 100 feet (1 ft = 0.3048 m) of wire,what is the maximum area covered?

A bicycle tire is inflated to a pressure of 93 psi.What is a pressure of 93 psi in the SI unit pascals (Pa) ?

What is the ratio of the Earth's density to that of Venus? Their radii are 6378 km and 6051 km,and their masses 5.97 10²⁴ kg and 4.87 10²⁴ kg,respectively.

Kobe Bryant of the LAL (LA Lakers) is 6'6" tall.His height in meters is

A CD that is 0.75 mm thick has outer diameter of 128 mm and inner diameter of 15 mm.The volume of the CD is

A right cylinder has a cross sectional area of 25.0 cm² and a height of 50.0 cm.What is the volume of the cylinder in SI units?