All categories

2 years ago

The function n(d)=4⋅3d−1 represents the number of people who receive a newspaper on day d of a delivery schedule.

Mathematics

2 answers:

Aleks04 [339]2 years ago

3 0

The answer is 'The number of people receiving a paper on a given day is 3 times what it was the previous day.'

loris [4]2 years ago

3 0

The relation between number of people who receive a newspaper on day d of a delivery schedule is given by:

n(d) = 4.3 d - 1

On first day , i.e d =1

n = 4 × 3 -1

= 12 -1

= 11

For, d =2

n(d) = 4 × 3 × 2 -1

= 24 -1

= 23

for , d=3

n(d) = 4 × 3 × 3 - 1

= 36 -1

= 35

When , d = 4

n(4)= 4 × 3 × 4 - 1

= 48-1

= 47

n(5) = 4×3×5 -1

= 60 -1

= 59

As you can see the pattern ,the number of people who receives newspaper starting from day = 1,2,3,4,5,6,7.... is 11,23,35,47,59,71,83,.......

As the given sequence is Airthmetic progression , having , a = 11

d = 23 -11= 12,

$a_{n}$ = 11 +12 × (n-1)

= 11 + 12 n - 12

= 12 n - 1

= 4 × 3 × d - 1 →→n is replaced by d

You might be interested in

Pluto's distance P(t)P(t)P, left parenthesis, t, right parenthesis (in billions of kilometers) from the sun as a function of tim

Xelga [282]

Answer: P(t) = 1.25.sin( $\frac{\pi}{3}$ .t) + 5.65

Step-by-step explanation: A motion repeating itself in a fixed time period is a periodic motion and can be modeled by the functions:

y = A.sin(B.t - C) + D or y = Acos(B.t - C) + D

where:

A is amplitude A=|A|

B is related to the period by: T = $\frac{2.\pi}{B}$

C is the phase shift or horizontal shift: $\frac{C}{B}$

D is the vertical shift

In this question, the motion of Pluto is modeled by a sine function and doesn't have phase shift, C = 0.

Amplitude:

a = $\frac{largest - smallest}{2}$

At t=0, Pluto is the farthest from the sun, a distance 6.9 billions km away. At t=66, it is closest to the star, P(66) = 4.4 billions km. Then:

a = $\frac{6.9-4.4}{2}$

a = 1.25

b

A time period for Pluto is T=66 years:

66 = $\frac{2.\pi}{b}$

b = $\frac{\pi}{33}$

Vertical Shift

It can be calculated as:

d = $\frac{largest+smallest}{2}$

d = $\frac{6.9+4.4}{2}$

d = 5.65

Knowing a, b and d, substitute in the equivalent positions and find P(t).

P(t) = a.sin(b.t) + d

P(t) = 1.25.sin( $\frac{\pi}{3}$ .t) + 5.65

The Pluto's distance from the sun as a function of time is

P(t) = 1.25.sin( $\frac{\pi}{3}$ .t) + 5.65

8 0

2 years ago

A zookeeper is monitoring the population of birds. The flock needs to have exactly three times more females than males to thrive

KIM [24]

Answer:

The constraints are

$0 < x\leq 20$ and $0 < y\leq 60$

Step-by-step explanation:

Let

x ----> represent the number of male birds

y ----> represent the number of female birds

we know that

The flock needs to have exactly three times more females than males to thrive

$y=3x$ ----> equation A

The zoo only has room for a maximum of 20 male birds

$0 < x\leq 20$ ----> inequality B

we know that

The maximum number of male birds is 20

For x=20

substitute in the equation A

$y=3(20)=60$

The maximum number of female birds is 60

$0 < y\leq 60$ ----> inequality C

therefore

The constraints are

$0 < x\leq 20$ and $0 < y\leq 60$

4 0

2 years ago

Roger is building a storage shed with wood blocks that are in the shape of cubic prisms. Can he build a shed that is twice as hi

Fynjy0 [20]

Given that Roger is building a storage shed with wood blocks that are in the shape of cubic prisms.

cube is basicallye a box which is made of squares. That is all the sides (lenght, width and height) are equal.

Now we have to determine, Can he build a shed that is twice as high as it is wide.

that means if width is 1 then height should be twice which is 2.

yes that is possible if we put one cubical prism over another cubical prism. then height of shed due to two prism will be twice than the width.

Hence correct choice should be "A. Yes. For every block of width, he could build two blocks high."

3 0

2 years ago

Read 2 more answers

A rectangular storage container with an open top is to have a volume of 10m3. Thelength of its base is twice the width. Material

frutty [35]

Answer:

$163.54

Step-by-step explanation:

Volume of rectangular container = 10m^3

Length = 2(width)

Material for the base cost $10 per square meter

Material for the side cost $6 per square meter

Volume = L*B*H

L= 2W

V = (2W).W. H

10 = 2W^2.H

H = 10 /2W^2

H = 5/W^2

Let C(w) = cost function

C(w) = 10(L.W) + 6(2.L.H + 2.W.H)

= 10(2W.W) + 6(2.2W.H + 2.W.H)

= 10(2W^2) + 6(4W.H + 2.W.H)

= 10(2W^2) + 6(4W*5/W^2 + 2.W*5/W^2)

= 20W^2 + 6(20/W + 10/W)

= 20W^2 + 6((10+20)/W)

= 20W^2 + 6(30/W)

C(w) = 20W^2 + 180/W

To find the minimum value, differentiate C with respect to w

C'(w) = 40W - 180/W^2

Put C'(w) = 0

0 = 40W - 180/W^2

40W = 180/W^2

40W^3 = 180

W^3 = 180/40

W^3 = 4.5

W = cube rt(4.5)

W = 1.65m

C = 20(1.65)^2 + 180/1.65

C = 54.45 + 109.09

C= $163.54

Minimum cost = $163.54

6 0

2 years ago

Below is the number of pages in each of the six books that Pedro read this summer. \begin{aligned} &584, 201, 255, \\ &4

Sergio039 [100]

Answer:

Here is the representation of a histogram. This represents in a continuous distribution the probability frequency of the books that Pedro had read in the summer.

Know that the probability frequency is:

$f=100*\frac{dataX}{total data}$

6 0

2 years ago