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ExtremeBDS [4]
3 years ago
9

PASSCODE DECODER RING SHRI o If it takes 6 hours to bake 3 cakes, then at that rate, how many cakes could be baked in 12 hours?

If Ava makes $15 in 2 hours, what is her rate of pay? 3nt took 5 hours to mow 6 yards. At that rate, how many yards can be mowed in 20 hours? co malaya $ o 94 If 10 bags of ice cost $12, how much does 1 bag cost? 5 A car gets 30 miles per gallon of gas. At that rate, how many gallons would it take for the car to go 360 If you type 75 words in 3 minutes, at what rate do you type? RECORD PASSCODE Directions Complete the questions, match each answer on the decoder eing, med record the letter from that spot When complete, go back to The Nission page te access the posscode reader to check your answer and solve another part of the mystery​

Mathematics
1 answer:
fomenos3 years ago
8 0

The rate is a <em>fraction</em> that compares the values of <em>two quantities</em>. The <u>expected</u> answers to the questions are given below:

1. Given that <u>3</u> cakes takes <u>6</u> hours to bake, then:

1 cake = \frac{6}{3}

           = 2 hours

So that;

the <em>number </em>of cake to be baked in 12 hours = \frac{12 hours}{2 hours}

                                    = 6

The <em>number</em> of cake to be baked in <u>12</u> hours is 6.

2. Ava's rate of pay = \frac{15}{2}

                                 = $7.5 pr hour

Thus Ava's rate of pay is $7.5 per hour.

3. It took 5 hours to mow 6 yards. Thus;

To mow 1 yard = \frac{5}{6} hours

The <em>number</em> of yards to be mowed in 20 hours = 20 ÷ \frac{5}{6}

                                                = 20 x \frac{6}{5}

                                                = 24

The number of yards to be mowed in <em>20</em> hours is <u>24</u>.

4. Given that <u>10</u> bags of rice cost $12, then;

1 bag = \frac{12}{10}

         = 1.2

1 bag = $1.2

The cost of a bag of rice is $1.2.

5. Rate = 30 miles per gallon

The number of gallons required = \frac{360}{30}

                                        = 12

Thus 12 gallons would be required by the car to travel <u>360 miles</u>.

6. Rate = \frac{75}{3}

            = 25

Rate = 25 words per minute

The typing <em>speed</em> is 25 words per minute.

For more on rate, check: brainly.com/question/119866

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0.55199

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Let u= ln x and v=ln y. Write ln(x^3y^2) in terms of u and v.
amid [387]
<h2>Answer:</h2>

a. 3u + 2v

<h2>Step-by-step explanation:</h2>

To solve this problem, we need to apply some properties of logarithms. Properties are useful to simplify complicated expressions. Here we need to use a very useful property of logarithms called  <em>the logarithm of a product is the sum of the logarithms, </em>that is:

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From the function, it is then true that:

ln(x^{3}y^{2})=ln(x^{3})+ln(y^{2})

The other property we must use is Logarithm of a Power:

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Then:

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Since:

u=ln(x) \\ v=ln(y)

Then:

ln(x^{3}y^{2})=3u+2v

Finally, the correct option is:

a. 3u + 2v

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