Illustrate an abstract mathematical concept with symbols and shapes. The scene should show two balances. On the left balance, depict a weight labeled '8' multiplied by a cube, symbolizing '10 to the power of 3'. On the right balance, a weight labeled '40 times', then an alphabetic block labeled 'a' being multiplied by a square, symbolizing '10 to the power of 2'. Make sure to imply equilibrium between both scales, whispering a sense of solving for 'a'. Remember -- no text, just symbols, weights, and balance scales.

For what value of a will 8×103 be 40 times larger than a×102?

ok i got the answers if you guys want them

2
1.15741 * 10^-5
27,000,000
8.9987 * 10^7
2.3 * 10^-8 ; 3.2 * 10^-10 ; 2.3 * 10^-10 ; 2.3 * 10^-12
4.39814 * 10^2 days
2.62 * 10^6
9.3
4.79 * 10^-3
1.9823 * 10^-3
6.08 * 10^12
1.2 * 10^4
4.3 * 10^3
3 * 10^-3
yw :)

To find the value of a, we can set up an equation using the given information.

We are given that 8×10^3 (8000) is 40 times larger than a×10^2 (100a). In other words, 8000 is equal to 40 times 100a.

We can write this equation as:

8000 = 40(100a)

Simplifying the equation, we get:

8000 = 4000a

Dividing both sides of the equation by 4000, we find:

a = 2

Therefore, for a value of 2, 8×10^3 (8000) will be 40 times larger than a×10^2 (200).

Janiya found that her playlist will play for 3.8×102 seconds, 6.3¯¯¯ ×105minutes, 1.05¯¯¯¯¯ ×104 hours, or 4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×102 days. Which answer uses the most appropriate units?(1 point)

Responses

3.8×107 seconds
3.8 times 10 superscript 7 baseline seconds

4.39814¯¯¯¯¯¯¯¯¯¯¯¯ ×102 days
4 point modifying above 39814 with bar times 10 squared days

1.05 ¯¯¯¯¯¯ ×104 hours
1 point modifying above 05 with bar times 10 superscript 4 baseline hours

6.3¯¯¯ ×105 minutes

To find the distance from Earth to the sun, we need to add the distance from Venus to the sun (67,000,000 miles) to the distance Earth is farther (2.6×10^7 miles).

Therefore, we can calculate the distance using the following equation:

Distance from Earth to the sun = Distance from Venus to the sun + Distance Earth is farther
Distance from Earth to the sun = 67,000,000 miles + 2.6×10^7 miles

Adding the values, we get:

Distance from Earth to the sun = 67,000,000 miles + 2.6×10^7 miles = 93,000,000 miles

Therefore, the distance from Earth to the sun is 9.3×10^7 miles, expressed in scientific notation to 1 decimal place.

To calculate how much heavier a grain of rice is than a strand of hair, we need to subtract the mass of the hair from the mass of the rice.

Grain of rice mass = 0.002 ounces

Strand of hair mass = 2.17×10^(-5) ounces

Subtracting the two masses:

0.002 ounces - 2.17×10^(-5) ounces = 0.0019823 ounces

To express the result in scientific notation, we need to write 0.0019823 as a number between 1 and 10, multiplied by a power of 10.

0.0019823 can be written as 1.9823×10^(-3).

Therefore, a grain of rice is approximately 1.9823×10^(-3) ounces heavier than a strand of hair.

To calculate how many miles light travels in a year, we need to multiply the speed of light (1.9×10^5 mi./sec) by the number of seconds in a year (3.2×10^7 seconds).

Using scientific notation, we proceed with the calculation:

(1.9×10^5 mi./sec) × (3.2×10^7 seconds) = 6.08×10^12 mi.

Therefore, light travels approximately 6.08×10^12 miles in a year.

To calculate how many meters the tectonic plate would move in 2×10^6 years, we need to multiply the average rate of movement (0.006 m/year) by the number of years (2×10^6 years).

Using scientific notation, we can perform the calculation:

(0.006 m/year) × (2×10^6 years) = 1.2×10^4 m

Therefore, the tectonic plate would move approximately 1.2×10^4 meters in 2×10^6 years.

r they right

idk

To convert the temperature of the sun's center from scientific notation to decimal notation, we need to multiply 2.7 by 10 raised to the power of 7.

Therefore, 2.7 × 10^7 can be written in decimal notation as 27,000,000.