What is the unit price for the cans of lemonade at each of the stores

For each of these lists of integers, provide a simple formula orrule that generates the terms of an integer sequence that begins

Anuta_ua [19.1K]

Answer:

b) next three terms of the sequence are 47, 51, 55

c) The next three terms are 1100, 1101, 1110

d) The next three items in the sequence are therefore, 8,8,8

f) The next three terms are 654729075, 13749310575, 316234143225

g) Therefore the next three items in the sequence are 0,0,0

Step-by-step explanation:

b)7, 11, 15, 19, 23, 27, 31, 35, 39, 43, ...

the common difference, d = $T_{2} - T_{1} = 11 - 7 = 4$

$a_{n} = a_{n-1} + 4$

43 + 4 = 47

47 + 4 = 51

51 + 4 = 55

next three terms of the sequence are 47, 51, 55

c) 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011,...

Each of these terms are binary numbers of 1,2,3,4........

The 1st next term is the 12th term = 1100₂

The second next term is the 13th term = 1101₂

The third next term is the 14th term = 1110₂

The next three terms are 1100, 1101, 1110

d) 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, ...

1 is repeated 1 time , 2 is repeated 3 times, 3 is repeated 5 times, 5 is repeated 7 times, the next number will sure be repeated 9 times( the repetition follows an odd number pattern)

To know the next number that will be repeated 9 times:

1+2 = 3

2+3 = 5

3 + 5 = 8

The pattern is that the previous summation adds to the preceding number

The next three items in the sequence are therefore, 8,8,8

f) 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425,...

The above sequence follows the pattern $a_{n} = a_{n-1} (2n -1)\\$

The next three terms are the 10th, 11th and 12th terms

a₁₀ = 34459425((2*10)-1)

a₁₀ = 654729075

a₁₁ = 654729075((2*11)-1)

a₁₁ = 13749310575

a₁₂ = 13749310575((2*12)-1)

a₁₂ = 316234143225

The next three terms are 654729075, 13749310575, 316234143225

g) 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1,...

The sequence changes between 1 and 0. 6 zeros are expected next

Therefore the next three items in the sequence are 0,0,0

8 0

2 years ago

Read 2 more answers

PLEASE HELP!!! Trapezoid ABCD was dilated to create trapezoid A'B'C'D'. Which statements are true about the trapezoids? Check al

hichkok12 [17]

Answer:

Option A , B and D are true.

The statement which are true:

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

Step-by-step explanation:

Given in figure trapezoid ABCD;

The coordinates of ABCD are:

A= (-4, 0)

B = (-2, 4)

C = (2,4)

D = (4, 0)

Since, trapezoid ABCD was dilated to create trapezoid A'B'C'D' as shown in figure;

The coordinates of A'B'C'D' are;

A' =(-2, 0)

B'=(-1, 2)

C' = (1, 2)

D' = (2, 0)

First calculate the length of AD

Using Distance formula for any two points i.e,

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Since, A = (-4, 0) and D = (4, 0)

then;

Length of AD = $\sqrt{(4-(-4))^2+(0-0)^2} = \sqrt{(4+4)^2} =\sqrt{64}=8$ units

Therefore, the length of side AD is, 8 units.

Similarly find the length of A'D'.

Where A' = (-2, 0) and D' =(2,0)

Using distance formula:

Length of A'D' = $\sqrt{(2-(-2))^2+(0-0)^2} =\sqrt{(2+2)^2}= \sqrt{4^2} = 4$

Therefore, the length of side A'D' is, 4 units.

Now, find the slope of CD and C'D'

where C =(2, 4) , D = (4, 0) , C' = (1, 2) and D' =(2,0)

using slope formula for any two points is given by:

$Slope = \frac{y_2-y_1}{x_2-x_1}$

$Slope of CD = \frac{0-4}{4-2} = \frac{-4}{2} = -2$

Similarly,

$Slope of C'D' = \frac{0-2}{2-1} = \frac{-4}{2} = -2$

Since, Sides CD and C'D' have same slope i.e, -2

Scale factor(k) states that every coordinate of the original figure has been multiplied by the scale factor.

If k > 1, then the image is an enlargement.

if 0<k< 1, then the image is a reduction.

If k = 1, then the figure and the image are congruent.

The rule for dilation with scale factor(k) is;

$(x, y) \rightarrow (kx , ky)$

To find the scale factor:

A = (-4, 0) and A' = (-2, 0)

$(-2, 0) \rightarrow (-4k , 0)$

On comparing we ghet;

-4k = -2

Divide -4 both sides we get;

$k = \frac{1}{2}$

∴ The Scale factor is, $k = \frac{1}{2}$

Since, k < 1 which implies the image is a reduction.

Therefore, the statements which are true regarding about trapezoids are;

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

6 0

2 years ago

At Webster High School, 1/5 of the students play a sport. Of the students who play a sport, 1/10 play football. What fraction of

suter [353]

Answer:

1/50

Step-by-step explanation:

1/5 times 1/10 is 1/50

:)

7 0

2 years ago

A baseball team plays in a stadium that holds 62000 spectators. With the ticket price at $11, the average attendance has been 27

sasho [114]

Answer:

$15.625

Step-by-step explanation:

Let the revenue collected be R and price per spectator be p then the number of spectators be N. Therefore

R=Np

Using equation of slope of y=mx +c where m is gradient and c is y-intercept

When p=$11, N=27000 and when p=$8, N=31000

The gradient, m will be

$m=\frac {31000-27000}{8-11}= -1333.33$

To get the y-intercept

N=-1333.33p+c

When spectator number n is 27000, the price p is $11

27000=-1333.33(11)+c hence we solve c

c=27000+(11*1333.33)= 41666.67

Therefore, the linear equation is

N=-1333.33p+ 41666.67

Substituting the linear equation into R=Np we obtain

R=p(-1333.33p+41666.67)

$R=-1333.33p^{2}+41666.67p$

To obtain maximum revenue, we differentiate the above with respect to price hence obtain

0=2*-1333.33p+41666.67

$p=-\frac {41666.67}{2(-1333.33)}= 15.625$

Therefore, the price that maximizes revenue is $15.625

4 0

2 years ago

X² +8x +15 ÷ x²+ 6x +5<br>

sineoko [7]

<h3>⚘Refer to the attachment!</h3>

7 0

2 years ago