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siniylev [52]
3 years ago
5

Paula made this model to show the sum of two mixed numbers. Write the addition equation shown by the model and solve it.

Mathematics
1 answer:
kipiarov [429]3 years ago
5 0

Answer:

3\frac{2}{3} + 2\frac{2}{3} = 6\frac{1}{3}

Step-by-step explanation:

Given

See attachment for number line

Required

Determine the model

From the attachment, we can see that each partition is 1/3

The gray rectangle covers 11 partitions.

So:

Gray = 11 * \frac{1}{3}

Gray = \frac{11}{3}

Express as a mixed number

Gray = 3\frac{2}{3}

The black rectangle covers 8 partitions

So:

Black= 8 * \frac{1}{3}

Black= \frac{8}{3}

Express as a mixed number

Black= 2\frac{2}{3}

So, the model is:

Gray + Black = Total

Where Total is the point where the black rectangle stops

3\frac{2}{3} + 2\frac{2}{3} = 6\frac{1}{3}

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The population of a certain species of fish has a relative growth rate of 1.1% per year. It is estimated that the population in
Juliette [100K]

Answer:

(a) n(t) = P(0)*e^(0.010939940t)

(b) 12,674,681 (nearest unit)

(c) 14 years (nearest year)

Step-by-step explanation:

rate = 1.1% / year = 1.011

(a)

P(0) = 12,000,000  = population in 2010

In compound interest format, after t years

P(t) = P(0)* (1.011)^t

Given format = P(0)* e^(rt)

therefore

e^(rt) = 1.011^t       use law of exponents

(e^r)^t = 1.011^t

e^r = 1.011

r = log_e(1.011) = 0.010939940   (to 9 decimal places)

required formula is

n(t) = P(0)*e^(0.010939940t)

(b)

in 2015,

P(0)=12000000, n = 5 (years after 2010)

n(5) = 12000000*e^( 0.010939940 * 5 ) = 12,674,680.6 = 12,674,681 (nearest unit)

(c)

to reach 14 million, we equate

n(t) = 14,000,000

12,000,000 *e^(0.010939940*t) = 14,000,000

e^(0.010939940*t) = 14000000/12000000 = 7/6

take log on both sides

0.010939940*t = log(7/6)

t = log(7/6) / 0.010939940 = 14.091 years = 14 years to the nearest year.

See graph attached.  Y-axis is in millions, x-axis is in years.

4 0
3 years ago
Determine the total number of roots of each polynomial function using the factored form.
Tanzania [10]

Answer:

3 roots

Step-by-step explanation:

The roots of a function is the x intercepts.

x=-1

x=3

x=4

6 0
3 years ago
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During a sale, a shop offered a discount of 10% on the marked prices of all the items. What
Snowcat [4.5K]

Answer:

₹2835

Step-by-step explanation:

Working out discount of 10% of jeans at ₹1450:

10% of 1450 = 1450/10 = ₹145

the price would now be ₹1450 - ₹145 = ₹1305

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10% of 850 = 850/10 = ₹85

the price would now be ₹850 - ₹85 = ₹765

so the price of two shirts = ₹765 × 2 = ₹1530

the total the customer would have to pay:

₹1305 + ₹1530 = ₹2835

8 0
2 years ago
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∠A and \angle B∠B are supplementary angles. If m\angle A=(2x-16)^{\circ}∠A=(2x−16) ∘ and m\angle B=(5x+28)^{\circ}∠B=(5x+28) ∘ ,
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Answer:

The measure of angle A is 32

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A+B=180

2x-16+5x+28=180

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A=48-16

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3 years ago
Error and correct in
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IFKDIKDKSBWKANDBSKSLFBAKKENSS
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