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3 years ago

10

8. find the simplified form of the expression. give your answer in scientific notation. (3 x 10^6) (8 x 10^-4) a) 1.1 x 10^3 b)

2.4 x 10^3 c) 1.1 x 10^-23 d) 2.4 x 10^-23

1 answer:

andrew-mc [135]3 years ago

5 0

(3 x 10^6)(8 x 10^-4) = (3 x 8) x 10^(6 - 4) = 24 x 10^2 = 2.4 x 10^3

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3 years ago

You drive 150 miles in 3 hours before stopping for 30 minutes to have lunch and gas. After lunch you travel 100 miles in an hou

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2 years ago

A certain pickup truck gets 20mpg in the city and 28 mpg on the highway. If the driver drives 270 mi on 11 gal of gas, determine

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95 city and 175 highway miles.

Step-by-step explanation:

The driver gets 20 mpg in city, and 28 mpg on the highway.

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This equotion accounts for how many gallons were driven.

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3 years ago

Which expression is equivalent to *picture attached*

DiKsa [7]

Answer:

The correct option is;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$

Step-by-step explanation:

The given expression is presented as follows;

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )$

Which can be expanded into the following form;

$\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n$

From which we have;

$\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}$

$\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}$

Therefore, substituting the value of n = 50 we have;

$\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}$

$\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}$

Which gives;

$4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}$

$3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}$

$\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}$

Therefore, we have;

$4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )$ .

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2 years ago