A closed container has 3.06 ⋅ 1023 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10−24 grams. Which of the following shows and explains the approximate total mass, in grams, of all the atoms of the gas in the container? (1 point)
0.47 grams, because (3.06 + 1.67) ⋅ (1023 ⋅ 10−24) = 4.73 ⋅ 10−1
0.51 grams, because (3.06 ⋅ 1.67) ⋅(1023 ⋅ 10-24) = 5.1102 ⋅ 10-1
4.73 grams, because (3.06 + 1.67) ⋅ (1023 ⋅ 10−24) = 4.73
5.11 grams, because (3.06 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 5.1102
The correct answer is 5.11 grams, because (3.06 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 5.1102 ⋅ 10-1.
To find the total mass of all the atoms of the gas in the container, we need to multiply the number of atoms by the weight of each atom. The number of atoms is 3.06 ⋅ 1023 and the weight of each atom is 1.67 ⋅ 10−24 grams.
The calculation would be (3.06 ⋅ 1.67) ⋅ (1023 ⋅ 10−24), which simplifies to (5.1102) ⋅ (10-1). Therefore, the approximate total mass is 5.11 grams.
Multiply (1.2 ⋅ 1028) ⋅ (3 ⋅ 10−19). Express the answer in scientific notation. (1 point)
3.6 ⋅ 109
3.6 ⋅ 1010
36 ⋅ 109
36 ⋅ 1010
The correct answer is 3.6 ⋅ 109.
To multiply these numbers, we multiply the coefficients and add the exponents. The coefficient multiplication is 1.2 ⋅ 3 = 3.6. The exponent addition is 28 + (-19) = 9.
Therefore, the answer is 3.6 ⋅ 109 in scientific notation.
The distance of planet Mercury from the Sun is approximately 5.8 ⋅ 107 kilometers, and the distance of Earth from the Sun is 1.5 ⋅ 108 kilometers. About how many more kilometers is the distance of Earth from the Sun than the distance of Mercury from the Sun? (1 point)
4.3 ⋅ 107 kilometers
9.2 ⋅ 107 kilometers
9.2 ⋅ 108 kilometers
5.7 ⋅ 109 kilometers
To find the difference in distance between Earth and Mercury from the Sun, we subtract the distance of Mercury from the distance of Earth.
1.5 ⋅ 108 kilometers - 5.8 ⋅ 107 kilometers
In order to subtract these numbers, they need to have the same exponent. We can rewrite 5.8 ⋅ 107 kilometers as 58 ⋅ 106 kilometers.
1.5 ⋅ 108 kilometers - 58 ⋅ 106 kilometers = 1.5 ⋅ 108 kilometers - 0.58 ⋅ 108 kilometers
Simplifying, we have:
(1.5 - 0.58) ⋅ 108 kilometers = 0.92 ⋅ 108 kilometers
Therefore, the distance of Earth from the Sun is approximately 9.2 ⋅ 107 kilometers more than the distance of Mercury from the Sun.
Triangle ABC is transformed to triangle A′ B′ C′, as shown below:
A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair 3, 0, B at ordered pair 4, negative 2, C at ordered pair 1, negative 3. A triangle A prime B prime C prime has A prime at ordered pair negative 3, 0, B prime at ordered pair negative 4, negative 2, C prime at ordered pair negative1, negative 3.
Which equation shows the correct relationship between the measures of the angles of the two triangles? (1 point)
The measure of angle ABC = The measure of angle B prime C prime A prime
The measure of angle ABC = The measure of angle C prime A prime B
The measure of angle BCA = The measure of angle C prime A prime B prime
The measure of angle BCA = The measure of angle B prime C prime A prime
The correct equation that shows the relationship between the measures of the angles of the two triangles is:
The measure of angle BCA = The measure of angle B prime C prime A prime.
The angles are corresponding angles in the two triangles, so they are equal to each other.
Angle ABC is formed by segments AB and BC on the following coordinate grid:
A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A line segment AB is shown with A as ordered pair 1, negative 1 and B as ordered pair 5, negative 4. Another line segment BC is shown with C as ordered pair 1, negative 4.
Angle ABC is rotated 90 degrees counterclockwise about the origin to form angle A′B′C′. Which statement shows the measure of angle A′B′C′? (1 point)
m∠ A′B′C′ = 90 degrees
m∠ A′B′C′ = m∠ABC
m∠ A′B′C′ = 180 degrees
m∠ A′B′C′ = 2 ⋅ m∠ABC
The correct statement showing the measure of angle A′B′C′ is:
m∠ A′B′C′ = m∠ABC.
When a figure is rotated counterclockwise by 90 degrees about the origin, the measure of the angles remain the same. Therefore, the measure of angle A′B′C′ is equal to the measure of angle ABC.
Polygons ABCD and A′B′C′D′ are shown on the following coordinate grid:
What set of transformations is performed on ABCD to form A′B′C′D′? (1 point)
A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A polygon ABCD is shown with vertex A on ordered pair 2, negative 2, vertex B on ordered pair 4, negative 2, vertex C on ordered pair 1, negative 3 and vertex D on ordered pair 5, negative 3. A polygon A prime B prime C prime D prime is shown with vertex A prime on ordered pair 1, 2 , vertex B prime on ordered pair 1, 4, vertex C prime on ordered 2, 1 and vertex D prime on ordered pair 2, 5.
A 90 degrees counterclockwise rotation about the origin followed by a translation 1 unit to the left
A translation 1 unit to the left, followed by a 90 degrees counterclockwise rotation about the origin
A 270 degrees counterclockwise rotation about the origin followed by a translation 1 unit to the left
A translation 1 unit to the left followed by a 270 degrees counterclockwise rotation about the origin