The range of the function defined as y = 5x is

A vat of milk has spilled on a tile floor. The milk flow can be expressed with the function r(t) = 4t, where t represents time i

Likurg_2 [28]

R(t) = 4t
A(r) = π(r^2)

a) A(t) = A[r(t)] = π[r(t)]^2 = π[4t]^2 = 16π(t^2)

b) t = 4,

A(4) = 16*3.14*(16)^2 = 12,861.44

3 0

3 years ago

The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increas

Mazyrski [523]

Answer:

The population in 40 years will be 1220.

Step-by-step explanation:

The population of a town grows at a rate proportional to the population present at time t.

This means that:

$P(t) = P(0)e^{rt}$

In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.

The initial population of 500 increases by 25% in 10 years.

This means that $P(0) = 500, P(10) = 1.25*500 = 625$

We apply this to the equation and find t.

$P(t) = P(0)e^{rt}$

$625 = 500e^{10r}$

$e^{10r} = \frac{625}{500}$

$e^{10r} = 1.25$

Applying ln to both sides

$\ln{e^{10r}} = \ln{1.25}$

$10r = \ln{1.25}$

$r = \frac{\ln{1.25}}{10}$

$r = 0.0223$

So

$P(t) = 500e^{0.0223t}$

What will be the population in 40 years

This is P(40).

$P(t) = 500e^{0.0223t}$

$P(40) = 500e^{0.0223*40} = 1220$

The population in 40 years will be 1220.

7 0

3 years ago

An elliptical track has a major axis that is 50 yards long and a minor axis that is 44 yards long. Find an equation for the trac

Luden [163]

Do It Have a Pictures

8 0

3 years ago

A sample of 11 students using a Ti-89 calculator averaged 31.5 items identified, with a standard deviation of 8.35. A sample of

lina2011 [118]

Answer:

We reject H₀, with CI = 90 % we can conclude that the mean numbers of times identified with Ti-84 does not exceed that of the Ti-89 by more than 1,80

Step-by-step explanation:

Ti-89 Calculator

Sample mean x = 31,5

Sample standard deviation s₂ = 8,35

Sample size n₂ = 11

Ti-84 Calculator

Sample mean y = 46,2

Sample standard deviation s₁ = 9,99

Sample size n₁ = 12

t(s) = ( y - x - d ) / √s₁²/n₁ + s₂²/n₂

t(s) = 12,9 / √(99,8/12) + (69,72/11)

t(s) = 12,9 / √8,32 + 6,34

t(s) = 12,9 / 3,83

t(s) = 3,37

Test Hypothesis

Null Hypothesis H₀ y - x > 1,80

Altenative Hypothesis Hₐ y - x ≤ 1,80

We have a t(s) = 3,37

We need to compare with t(c) critical value for

t(c) α; n₁ +n₂-2 df = 12 +11 -2 df = 21

If we choose CI = 95 % then α = 5 % α = 0,05

From t-student table

t(c) = 1,72

t(s) = 3,37

t(s) >t(c)

t(s) is in the rejection region therefore we accept Hₐ with CI = 95 %

8 0

2 years ago

a school cafeteria makes cheese sauce for macaroni using 15 cups of Swiss cheese and 17 cups of cheddar cheese Perry tries to ma

deff fn [24]

No, Perry is not using the correct ratio, because 15:17 is not equivalent to 5:7

15 divided by 3 is indeed 5 but divided 17 by 3 does not give you 7, nor a whole number.

I hope this helps.

3 0

3 years ago

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