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3 years ago

11

a motorcycle dealer paid a certain price for a motorcycle and marked it up by 1/5 of the price he paid. Later, he sold it for $1

4,000. What was the original price?

1 answer:

katovenus [111]3 years ago

5 0

Okay so $14,000 is the equivalent of 6/5ths
so divide $14,000 by 6= $2333.3r

you need 5/5
so $2333.3r x 5 = $11666.67
this is the original price

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A culture started with 3000 bacteria. After 4 hours, it grew to 3,600 bacteria. Predict how many bacteria will be present after

Vlad [161]

Hello Shannonrodrigue. You can solve this by setting up an exponential growth equation.

$A = A_ob^t$
$3600 = 3000b^4$

Now we solve for b
$3600 = 3000b^4$
$\frac{3600}{3000} = \frac{3000b^{4}}{3000}$
$\frac{6}{5} = b^4$
$\sqrt[4]{\frac{6}{5}} = \sqrt[4]{b^4}$
$\sqrt[4]{\frac{6}{5}} = b$

Now that we have found b, we can use the equation $A = 3000b^t$ to predict how many bacteria will be present after 10 hours.
$b = \sqrt[4]{\frac{6}{5}}$
t = 10
$A = 3000b^t$
$A = 3000\sqrt[4]{\frac{6}{5}}^{10} = 4732.3228 = 4732$

Answer = 4732

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3 years ago

Please someone help me to prove this.

morpeh [17]

Answer: see proof below

<u>Step-by-step explanation:</u>

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

<u />

<u>Proof LHS → RHS</u>

LHS: 2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]

Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]

Distribute: cos²2A + 2cos2A·sin2A + sin²2A

Pythagorean Identity: 1 + 2cos2A·sin2A

Double Angle: 1 + sin4A

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3 years ago

An item is regularly priced at $83. It is now priced at a discount of 55% off the regular price.

mart [117]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Please answer this by solving it

mr Goodwill [35]

Answer:

5 5/6

Step-by-step explanation:

Change them into improper fractions. Multiply the denominator by the whole number and then add the numerator. Put that number over the denominator.

2 X 3 = 6 3 X 2 = 6

6 + 1 = 7 6 + 1 = 7

7/3 7/2

New expression: 7/3 + 7/2

Find a common denominator. Both denominators can go into 6.

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Change this back into a mixed number by dividing.

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3 years ago