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denis23 [38]
3 years ago
13

What is 8.4 x 10^12/4.2 x 10^6

Mathematics
1 answer:
Deffense [45]3 years ago
7 0

Answer:

2 × 10^{6}

Step-by-step explanation:

Using the rule of exponents

\frac{a^{m} }{a^{n} } ⇔ a^{(m-n)}

Split the fraction into a product, that is

= \frac{8.4}{4.2} × \frac{10^{12} }{10^{6} }

= 2 × 10^{(12-6)}

= 2 × 10^{6}

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The percentage of obese children aged 12-19 years in the United States is approximatelyP(t) = 0.04t + 4.6 if 0 ≤ t &lt; 10−0.010
Art [367]

Answer:

4.8% of of obese children aged 12-19 at the beginning of 1975.

9.15% of obese children aged 12-19 at the beggining of 1986

13.94% of obese children aged 12-19 at the beggining of 1995

Step-by-step explanation:

The percentage of obese children aged 12-19 years in the United States is given by the following piecewise function:

P(t) = \left \{ {{0.04t + 4.6, 0 \leq t < 10}\atop {-0.01005t^{2} + 0.945t - 3.4, 10 \leq t < 30}} \right.

In which t is measured in years.

What was the percentage of obese children aged 12-19 at the beginning of 1975?

This is the value of P when t = 5, so P(5).

For P(5), we apply the first definition of the piecewise function.

P(5) = 0.04(5) + 4.6 = 0.2 + 4.6 = 4.8

At the beginning of 1986?

The value of P when t = 16, so P(16).

For P(16), we apply the second definition of the piecewise function.

P(16) = -0.01005(16)^{2} + 0.945(16) - 3.4 = 9.15

At the beginning of 1995?

The value of P when t = 25, so P(25).]

For P(25), we apply the second definition of the piecewise function.

P(16) = -0.01005(25)^{2} + 0.945(25) - 3.4 = 13.94

6 0
3 years ago
A triangle in the xy-coordinate plane is formed by the points (3, 5), (− 1, 5) , and (3,− 6) . What is the perimeter and area of
kati45 [8]

Answer:

Therefore, the perimeter of the triangle is 26.7 units and the area is 22 square units.

Step-by-step explanation:

Given the vertices of a triangle as: A(3, 5), B(− 1, 5), and C(3,− 6)

Since A and B are on the same y-coordinate, we have that:

AB = 3-(-1)=4 Units

Since A and C are on the same x-coordinate, we have that:

AC=5-(-6)=11 Units

Next, we determine the distance BC using the distance formula.

Given: B(− 1, 5), and C(3,− 6)

BC=\sqrt{(3-(-1))^2+(-6-5)^2}\\= \sqrt{(4)^2+(-11)^2}=\sqrt{137}$ Units

Therefore:

Perimeter of the Triangle

= 4+11+\sqrt{137}\\ =15+\sqrt{137}$ Units\\=26.7 Units

On plotting the triangle, it forms a right triangle such that the:

Base = 4 Units

Height = 11 Units

Therefore:

Area of a triangle =\dfrac12 *Base*Height

Therefore:

Area of the Triangle = 0.5 X 4 X 11

=22 Square Units.

Therefore, the perimeter of the triangle is 26.7 units and the area is 22 square units.

5 0
3 years ago
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