What is 2 to the 4 times 2 to the -7

Find the area of the region between two concentric circular paths. If the radii of the circular paths are 210 m. and 490 m. resp

taurus [48]

Given :

The radii of the circular paths are 210 m. and 490 m.

To Find :

The area of the region between two concentric circular paths.

Solution :

Area of the outer circle :

$\: \qquad \dashrightarrow \sf{{ \pi \: \times {(490)}^{2} {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ \dfrac{22}{7} \times \:490 \times 490 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ \dfrac{22}{ \cancel{7}} \times \cancel{490} \times 490 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ {22} \times 70 \times 490 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \bf{{ \ 754600 \: {m}^{2}}}$

⠀

Area of the inner circle :

$\: \qquad \dashrightarrow \sf{{ \pi \: \times {(210)}^{2} {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ \dfrac{22}{7} \times \:210 \times 210 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ \dfrac{22}{ \cancel{7}} \times \cancel{210} \times 210 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \sf{{ \ {22} \times 30 \times 210 \: {m}^{2}}}$

$\: \qquad \dashrightarrow \bf{{ \ 138600 \: {m}^{2}}}$

⠀

Therefore,

Area of the region inside the circular paths :

$\: \qquad \dashrightarrow \sf{{ \ (754600 - 138600 ) \: {m}^{2}}}$

$\: \qquad \dashrightarrow \bf{{ \ 616000 \: {m}^{2}}}$

6 0

2 years ago

A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population

NikAS [45]

Answer:

<u>The probability that the average weight of the boxes will exceed 94 pounds is 43.25%</u>

Step-by-step explanation:

1. Let's review the information provided to answer the question correctly:

Mean of the population of box weights = 90 pounds

Standard deviation of the population of box weights = 24 pounds

Sample size = 36 boxes

2. What is the probability that the average weight of the boxes will exceed 94 lb?

For answering this question, we will use the z-scores table.

For using the correct z-score, we should use the correct standard deviation. In this case, we have that:

94 - 90 = 4 pounds above the mean.

4 pounds are 4/24 of the standard deviation,

therefore, simplifying:

4/24 = 1/6 = 0.1666......and we'll round to 0.17

z-score is 0.17 because 4 pounds is 1/6 of the standard deviation (24).

The probability of a z-score is 0.5675, but in this case we're asked by a weight over 94 pounds, not under 94 pounds, thus:

1 - 0.5675 = 0.4325

<u>The probability that the average weight of the boxes will exceed 94 pounds is 43.25%</u>

8 0

2 years ago

The diagram shows the dimensions of a teepee. Find the volume of the building to the nearest cubic unit. Use 3.14 for pi.

LekaFEV [45]

The volume of a cone uses the following formula:

$V = \pi r^{2} \frac{h}{3}$

Our diameter is 20 feet, so divide this by 2 to find the radius:

$20 \div 2 = 10$

We now have all of our values need to fill in the formula. Plug in these values:

$\pi = 3.14, r = 10, h = 17$

$3.14 * 10^{2} * \frac{17}{3}$

$3.14 * 100 * 5.67$

$314 * 5.67 = 1780.38$

The volume of the cone is 1780 cubic feet.

7 0

3 years ago

Simplify the expression (6x^3 divided by 3x^4)^2

Evgesh-ka [11]

(6x^3/3x^4)^2 = (2/x)^2 = 4/x^2

3 0

3 years ago

Read 2 more answers

What is the constant of proportionality in the equation y = 2x?

kow [346]

Answer: 2 because of the constant proportionality

Step-by-step explanation: hope this helps!

7 0

2 years ago