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3 years ago

12

80% of salmon pass through a single dam unharmed. By what percent does the number of salmon decrease when passing through a sing

le dam?

2 answers:

aalyn [17]3 years ago

3 0

Answer:20%

Step-by-step explanation:

icang [17]3 years ago

3 0

Answer: 20%

Step-by-step explanation:

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A display case of hat pins are marked 5 for $3. If Patty has $21, how many hat pins can Patty get? (assume no other taxes and fe

Nonamiya [84]

Answer: 35

Explanation: If patty has $21, and $3 is the price for 5 hat pins, then: 21/3=7, so she can buy 7 packages which cost $3 and contain 5 pins, and because the question asked the number of pins, we will multiply 7 • 5 and that equals 35

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2 years ago

Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

<u>ANSWER</u>

${r}^{2} = 4 \cos2\theta$

<u>EXPLANATION</u>

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

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3 years ago

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3 years ago

Jessica picks tomatoes in her garden. She fills several bags. This line plot shows the weight of each bag.

Strike441 [17]

Answer:

3/4 lb

Step-by-step explanation:

Lightest: 3 3/4

Heaviest: 4 1/2 = 4 2/4

4 2/4 - 3 3/4 = 18/4 - 15/4 = 3/4

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3 years ago

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