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3 years ago

Item 3

Mathematics

1 answer:

Paraphin [41]3 years ago

5 0

Answer:

The unit rate in ml per kg is 1.75 ml per kg.

Step-by-step explanation:

The amount of medicine, in milliliters, that a veterinarian prescribes is proportional to the weight, in kilograms, of a dog as shown on the graph.

In the graph x-axis labeled weight in kg and y-axis labeled the amount of medicine in ml. The points (0,0) and (8,14) are on the graph.

Hence, the slope of the graph represents the unit rate in ml per kg.

Now, the slope of a straight line passing through the points ( $x_{1},y_{1}$ ) and ( $x_{2},y_{2}$ ) is given by $[\frac{y_{2} - y_{1}}{x_{2} - x_{1}}]$ .

Therefore, the slope of the graph will be $\frac{14 - 0}{8 - 0} = \frac{7}{4} = 1.75$ and the unit rate in ml per kg is 1.75 ml per kg. (Answer)

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Which table represents the graph of a logarithmic function in the form y=log3x when b>1?

alex41 [277]

Answer:

The satisfied table of the given function $y = log_{b} (x)$

x 1/8 1/4 1/2 1 2

y -3 -2 -1 0 1

Step-by-step explanation:

Explanation :-

Given logarithmic function $y = log_{b} (x)$ if b >1

Given first table

put x = $\frac{1}{8}$ given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{8} )$

$y = log_{2} (2^{-3} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-3} ) = -3 log_{2} (2) = -3 (1) = -3$

y = -3

ii)

put x = $\frac{1}{4}$ given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{4} )$

$y = log_{2} (2^{-2} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-2} ) = -2 log_{2} (2) = -2 (1) = -2$

y = -2

iii)

put x = $\frac{1}{2}$ given b > 1 so we can choose b = 2

$y = log_{2} (\frac{1}{2} )$

$y = log_{2} (2^{-1} )$

we will apply logarithmic formula

log x ⁿ = n log (x)

$y = log_{2} (2^{-1} ) = -1 log_{2} (2) = - (1) = -1$

y = -1

iv)

put x = 1 given b > 1 so we can choose b = 2

$y = log_{2} (1 )$ = 0

y = 0

v)

put x = $2$ given b > 1 so we can choose b = 2

$y = log_{2} (2 )$

y = 1

Final answer:-

The satisfied table of the given function

x 1/8 1/4 1/2 1 2

y -3 -2 -1 0 1

8 0

3 years ago

Read 2 more answers

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Alex_Xolod [135]

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Range: y≤2 (notice the closed dot on the right and the arrow on the left)

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3 0

3 years ago

What is the volume of the prism 16cm 12 cm 8cm

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3 years ago

A countrys population in 1995 was 173 million in 1997 it was 178 million estamate the population in 2005 using the expontial gro

9966 [12]

Answer: the population in 2005 is

199393207

Step-by-step explanation:

The formula for exponential growth which is expressed as

A = P(1 + r/n)^ nt

Where

A represents the population after t years.

n represents the periodic interval at which growth is recorded.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 173 million

A = 178 million

t = 1997 - 1995 = 2 years

n = 1

Therefore

178 × 10^6 = 173 × 10^6(1 + r/1)^2 × 1

178 × 10^6/173 × 10^6 = (1 + r)^2

1.0289 = (1 + r)^2

Taking square root of both sides, it becomes

√1.0289 = √(1 + r)^2

1 + r = 1.0143

r = 1.0143 - 1 = 0.0143

Therefore, in 2005,

t = 2005 - 1995 = 10

A = 173 × 10^6(1 + 0.0143)^10

A = 173 × 10^6(1.0143)^10

A = 199393207

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3 years ago

A line passes through the points (5, –7.5) and has a y-intercept of 10.

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Answer:y=0.5x+10

Step-by-step explanation:

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