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3 years ago

Interquartile range for 16,23,25,27,29,33,35,40,43

Mathematics

1 answer:

grin007 [14]3 years ago

7 0

Answer:

the interquartile range is 13.5

minimum 16

maximum 43

medium 29

lower Q1 24

upper Q3 37.5 or 38

Range 27

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Ezpress 3x + 11/x² + 6x + 9<br>as partial fractions,

andreev551 [17]

Answer:

$\frac{3}{x + 3} + \frac{2}{(x+3)^2}$

Step-by-step explanation:

Given

$\frac{3x + 11}{x^2 +6x + 9}$

Required

Express as partial fraction

$\frac{3x + 11}{x^2 +6x + 9}$

Expand the numerator

$\frac{3x + 11}{x^2 +3x +3x+ 9}$

Factorize

$\frac{3x + 11}{x(x +3) +3(x+ 3)}$

Factor out x + 3

$\frac{3x + 11}{(x +3)(x+ 3)}$

$\frac{3x + 11}{(x +3)^2}$

As a partial fraction, we have:

$\frac{3x + 11}{(x +3)^2} = \frac{A}{x + 3} + \frac{B}{(x+3)^2}$

Take LCM

$\frac{3x + 11}{(x +3)^2} = \frac{A(x+3) + B}{(x + 3)^2}$

Cancel out (x + 3)^2 on both sides

$3x + 11 = A(x+3) + B$

Open bracket

$3x + 11 = Ax+3A + B$

By comparison, we have:

$Ax = 3x$ ===> $A = 3$

$3A + B = 11$

Substitute 3 for A

$3*3 + B = 11$

$9 + B = 11$

Solve for B

$B = 11-9$

$B =2$

Substitute: $A = 3$ and $B =2$ in

$\frac{3x + 11}{(x +3)^2} = \frac{A}{x + 3} + \frac{B}{(x+3)^2}$

$\frac{3x + 11}{(x +3)^2} = \frac{3}{x + 3} + \frac{2}{(x+3)^2}$

Hence, the partial fraction is:

$\frac{3}{x + 3} + \frac{2}{(x+3)^2}$

7 0

3 years ago

Exponential Function:

antoniya [11.8K]

Answer:

See below

Step-by-step explanation:

<h3>Given</h3>

Initial population at 8:00 AM
3000000
Growth rate = 10% = 1.1 times per 20 min

<h3>Solution</h3>

<u>1. Table</u>

<em>Note. I am not sure what are the last 3 rows. Just added next 3 terms.</em>

8:00 ≡ G(0) ≡ 3000000 ≡ 3000000
8:20 ≡ G(1) ≡ 3000000 *1.1 ≡ 3300000
8:40 ≡ G(2) ≡ 3000000 *1.1^2 ≡ 3630000
9:00 ≡ G(3) ≡ 3000000 *1.1^3 ≡ 3993000
9:20 ≡ G(4) ≡ 3000000 *1.1^4 ≡ 4392300

<u>2. Population at 10:00</u>

Time passed since 8:00 is 2 hours = 2*3*20 min = 6* 20 min
Population = 3000000*1.1^6 = 5314683

<u>3. Function to reflect the population growth</u>

G(x) = 3000000*1.1^x
G(x) - is dependent variable, population of bacteria
x - is independent variable, time increment of 20 min

<u>4. Population after 5 hours</u>

5 hours = 5*3*20 min = 15*20 min
G(15) = 3000000*1.1^15 ≈ 12531745

3 0

3 years ago

Read 2 more answers

Which equation represents the line that passes

viktelen [127]

Answer:

1) y=3x+1

Step-by-step explanation:

passes through the points

(-1.-2) and (3, 10)

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3 years ago

What is the domain of y = csc(x)?

Stells [14]

Answer:

csc

Step-by-step explanation:

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3 years ago

BRAINLIEST to whoever gets it right

STatiana [176]

The scale factor applied to the model is 8000. 8000 times one equals 8000

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3 years ago