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3 years ago

8

Rebecca ran 21 miles in 5 hours. If she ran at a constant speed, how many miles did she run in 2 hours? 8.4 miles 42 miles 4.2 m

iles 1.2 miles

1 answer:

Sholpan [36]3 years ago

6 0

Answer: 8.4 miles

Step-by-step explanation:

d = rt

Solve for her rate

21 = 5r

r = 21/5

r = 4.2

Solve for if the time is 2 hours and rate (solved previously) is 4.2

d = 4.2*2

d = 8.4

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3 years ago

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Can somebody prove this mathmatical induction?

Flauer [41]

Answer:

See explanation

Step-by-step explanation:

1 step:

n=1, then

$\sum \limits_{j=1}^1 2^j=2^1=2\\ \\2(2^1-1)=2(2-1)=2\cdot 1=2$

So, for j=1 this statement is true

2 step:

Assume that for n=k the following statement is true

$\sum \limits_{j=1}^k2^j=2(2^k-1)$

3 step:

Check for n=k+1 whether the statement

$\sum \limits_{j=1}^{k+1}2^j=2(2^{k+1}-1)$

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Start with the left side:

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}\ \ (\ast)$

According to the 2nd step,

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Substitute it into the $\ast$

$\sum \limits _{j=1}^{k+1}2^j=\sum \limits _{j=1}^k2^j+2^{k+1}=2(2^k-1)+2^{k+1}=2^{k+1}-2+2^{k+1}=2\cdot 2^{k+1}-2=2^{k+2}-2=2(2^{k+1}-1)$

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4 0

3 years ago

You are recreating a scale drawing at a different scale. The original scale is 1 cm : 8 m. The new scale is 1 cm : 2 m. In the o

densk [106]

Answer:

The segment should be 36 centimeters long

Step-by-step explanation:

Let us use the ratio method to solve the question

∵ The original scale is 1 cm : 8 m

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→ cm : m

→ 1 : 8

→ 9 : x

→ By using the cross multiplication

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∴ The actual length of the segment is 72 m

∵ The new scale is 1 cm : 2 m

∵ The actual length of the segment is 72 m

→ By using the ratio method

→ cm : m

→ 1 : 2

→ y : 72

→ By using the cross multiplication

∵ y × 2 = 1 × 72

∴ 2y = 72

→ Divide both sides by 2 to find y

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∴ The drawing length of the segment is 36 cm in the new scale

∴ The segment should be 36 centimeters long

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3 years ago

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poizon [28]

Answer:

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2 years ago

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Answer:

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I hope this helps! Please mark as brainliest! :D Good Luck! :)

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3 years ago