Brandon’s family is having pizza for dinner tonight. Before knowing he would have to share with the rest of his family, Brandon cut a piece for himself as shown by the diagram. Both of his parents, his sister, and his two brothers will now equally share the remaining pizza. What is the approximate area each one receives?

Given:

The geometric sequence is

[tex]4, -12, 36,...[/tex]

To find:

The sum of first 8 terms of the given geometric sequence.

Solution:

We have,

[tex]4, -12, 36,...[/tex]

Here, the first term is 4 and the common ratio is

[tex]r=\dfrac{-12}{4}[/tex]

[tex]r=-3[/tex]

The sum of first n terms of a geometric sequence is

[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]

Where, a is the first term and r is the common ratio.

Putting n=8, a=4 and r=-3, we get

[tex]S_8=\dfrac{4((-3)^8-1)}{-3-1}[/tex]

[tex]S_8=\dfrac{4(6561-1)}{-4}[/tex]

[tex]S_8=-6560[/tex]

Therefore, the sum of first 8 terms is -6560.

Answer:

Option (1)  ;   y = 7x

Step-by-step explanation:

(1) reads y = 7x, a line with slope 7, therefore the rate of change in this is 7

(2) says that y increases 12 units every time that x increases 4 Then the rate of change is: (increase in y / increase in x = 12/4 =3

(3) shows a table from which we can see that an increase of y in 8 corresponds to an increase of x in 2:  rate of change = (8 - 0) , (2 - 0) = 4

(4) shos a line with slope (rate of change) given by:  (12 - 0) / (2 - 0) = 12/2 = 6

Therefore, the greatest rate of change is shown by the first expression  

y = 7 x

Answer:

Step-by-step explanation:

d=20t+1/3, b=30t

20t+1/3=30t

10t=1/3

t=1/30 hr

t=(1/30)60=2 min

Chu gf fr uvv V dhh gg jb cub

Answer:

the lines are neither

Step-by-step explanation:

Answer:

He can buy 10 cds

Step-by-step explanation:

125-30=95

95 divided by 9 = 10.5555555556

Answer:

t=3

Step-by-step explanation:

Answer:

15/2

Step-by-step explanation:

5/1 * 3/2 = 15/2

Answer:

(x,y) becomes (-y,x) so (3,2) would become (-2,3)

Answer:

Your answer is "H"

Step-by-step explanation:

The answer is the answer is H

Answer:

b and d

Step-by-step explanation:

Answer: 36.56

Step-by-step explanation:

Answer: It would be  2 1/2 liters

Step-by-step explanation:

There can be 2 and a half litres of water will be filled in 1 bottle.

What is division?

Division is breaking a number up into an equal number of parts.

Given that,  3 litres of water can fill 1 ⅕ bottles,

Since, there are 3 litres in 6/5 bottles

so, 1 litre = 6/5×3 = 2 ¹/₂

Hence, There can be 2 and a half litres of water will be filled in 1 bottle.

For more references on division, click;

https://brainly.com/question/21416852

#SPJ2

Answer:

253cm²

Step-by-step explanation:

Area of the trapezoid = 1/2(b1+b2)*h

Given

h = 22cm

b1 = 10.5cm

b2 = 12.5cm

Substitute

Area of the trapezoid = 1/2(10.5+12.5)*22

Area of the trapezoid = 1/2(23)*22

Area of the trapezoid =11*23

Area of the trapezoid = 253cm²

Hence the area of the trapezoid is 253cm²

Answer:

Number of moles Aluminium sulfide

1 mole of sulfide contains 150 g

Therefore; 16.2/150  

              = 0.108 moles  

The mole ratio of Al2S3 : Al(OH)3 is 1:2

Therefore; moles of Aluminium hydroxide will be;

 = (0.108 × 2)

 = 0.216 moles  

But, 1 mole of  Al(OH)3 contains 77 g

Therefore, the mass of aluminium hydroxide is

  0.216 moles × 77

=  16.632 g

Step-by-step explanation:

Answer:

There's no concern that water will dilute the digestive juices or interfere with digestion. In fact, drinking water during or after a meal actually aids digestion. Water is essential for good health. Water and other liquids help break down food so that your body can absorb the nutrients.

Answer:

chewing on it or by ice

Step-by-step explanation:

Answer:

1,280in cubes

Step-by-step explanation:

For one box it would be 4 x 4 x 4=64. Then for 20 boxes it would be 64 x 20= 1,280 cubic inches.

Answer:

230.2128. Im pretty sure

Step-by-step explanation:

Answer:

27%

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

i don't know

Answer:

0.1373 = 13.73% probability that the lines are occupied for exactly 5 calls

Step-by-step explanation:

For each call, there are only two possible outcomes. Either the lines are occupied, or they are not. The events that the lines are occupied on successive calls are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The phone lines to an airline reservation system are occupied 61% of the time.

This means that [tex]p = 0.61[/tex]

If 11 calls are placed, what is the probability that the lines are occupied for exactly 5 calls

This is P(X = 5) when n = 11. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{11,5}.(0.61)^{5}.(0.39)^{6} = 0.1373[/tex]

0.1373 = 13.73% probability that the lines are occupied for exactly 5 calls

Answer:

[tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]

General Formulas and Concepts:

Alg I

Terms/CoefficientsFactorExponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]

Pre-Calc

[Right Triangle Only] Pythagorean Theorem: a² + b² = c²

a is a legb is a legc is hypotenuse

Trigonometric Ratio: [tex]\displaystyle sec(\theta) = \frac{1}{cos(\theta)}[/tex]

Trigonometric Identity: [tex]\displaystyle tan^2\theta + 1 = sec^2\theta[/tex]

TI: [tex]\displaystyle sin(2x) = 2sin(x)cos(x)[/tex]

TI: [tex]\displaystyle cos^2(\theta) = \frac{cos(2x) + 1}{2}[/tex]

Calc

Integration Rule [Reverse Power Rule]:                                                                [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

IP [Addition/Subtraction]:                                                             [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

U-Substitution

U-Trig Substitution: x² + a² → x = atanθ

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \int {\frac{dx}{(81x^2 + 4)^2}}[/tex]

Step 2: Identify Sub Variables Pt.1

Rewrite integral [factor expression]:

[tex]\displaystyle \int {\frac{dx}{[(9x)^2 + 4]^2}}[/tex]

Identify u-trig sub:

[tex]\displaystyle x = atan\theta\\9x = 2tan\theta \rightarrow x = \frac{2}{9}tan\theta\\dx = \frac{2}{9}sec^2\theta d\theta[/tex]

Later, back-sub θ (integrate w/ respect to x):

[tex]\displaystyle tan\theta = \frac{9x}{2} \rightarrow \theta = arctan(\frac{9x}{2})[/tex]

Step 3: Integrate Pt.1

[Int] Sub u-trig variables:                                                                                 [tex]\displaystyle \int {\frac{\frac{2}{9}sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]:                                                                           [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Evaluate exponents:                                                                                [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4tan^2\theta + 4]^2}} \ d\theta[/tex][Int] Factor:                                                                                                      [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4(tan^2\theta + 1)]^2}} \ d\theta[/tex][Int] Rewrite [TI]:                                                                                              [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4sec^2\theta]^2}} \ d\theta[/tex][Int] Evaluate exponents:                                                                                [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{16sec^4\theta} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]:                                                                          [tex]\displaystyle \frac{1}{72} \int {\frac{sec^2\theta}{sec^4\theta} \ d\theta[/tex][Int] Divide [ER - D]:                                                                                         [tex]\displaystyle \frac{1}{72} \int {\frac{1}{sec^2\theta} \ d\theta[/tex][Int] Rewrite [TR]:                                                                                            [tex]\displaystyle \frac{1}{72} \int {cos^2\theta} \ d\theta[/tex][Int] Rewrite [TI]:                                                                                              [tex]\displaystyle \frac{1}{72} \int {\frac{cos(2\theta) + 1}{2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]:                                                                          [tex]\displaystyle \frac{1}{144} \int {cos(2\theta) + 1} \ d\theta[/tex][Int] Rewrite [Int Prop - A/S]:                                                                          [tex]\displaystyle \frac{1}{144} [\int {cos(2\theta) \ d\theta + \int {1} \ d\theta][/tex]  

Step 4: Identify Sub Variables Pt.2

Determine u-sub for trig int:

u = 2θ

du = 2dθ

Step 5: Integrate Pt.2

[Ints] Rewrite [Int Prop - MC]:                                                                       [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {2cos(2\theta) \ d\theta + \int {1 \theta ^0} \ d\theta][/tex][Int] U-Sub:                                                                                                     [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {cos(u) \ du + \int {1 \theta ^0} \ d\theta][/tex][Ints] Integrate [Trig/Int Rule - RPR]:                                                             [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(u) + \theta + C][/tex][Expression] Back Sub:                                                                                 [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(2 \theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Rewrite [TI]:                                                                                           [tex]\displaystyle \frac{1}{144} [\frac{1}{2}(2sin(\theta)cos(\theta)) + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply:                                                                                                 [tex]\displaystyle \frac{1}{144} [sin(\theta)cos(\theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Back Sub:                                                                                             [tex]\displaystyle \frac{1}{144} [sin(arctan(\frac{9x}{2}))cos(arctan(\frac{9x}{2})) + arctan(\frac{9x}{2}) + C][/tex]

Step 6: Triangle

Find trig values:

[tex]\displaystyle tan\theta = \frac{9x}{2}[/tex]

[tex]\displaystyle \theta = arctan(\frac{9x}{2})[/tex]

tanθ = opposite / adjacent; solve hypotenuse of right triangle, determine trig ratios:

sinθ = opposite / hypotenuse

cosθ = adjacent / hypotenuse

Leg a = 2

Leg b = 9x

Leg c = ?

Sub variables [PT]:                                                                                         [tex]\displaystyle 2^2 + (9x)^2 = c^2[/tex]Evaluate exponents:                                                                                      [tex]\displaystyle 4 + 81x^2 = c^2[/tex][Equality Property] Square root both sides:                                                  [tex]\displaystyle \sqrt{4 + 81x^2} = c[/tex]Rewrite:                                                                                                           [tex]c = \sqrt{81x^2 + 4}[/tex]

Substitute into trig ratios:

[tex]\displaystyle sin\theta = \frac{9x}{\sqrt{81x^2 + 4}}[/tex]

[tex]\displaystyle cos\theta = \frac{2}{\sqrt{81x^2 + 4}}[/tex]

Step 7: Integrate Pt.3

[Exp] Sub variables [TR]:                                                                               [tex]\displaystyle \frac{1}{144} [\frac{9x}{\sqrt{81x^2 + 4}} \cdot \frac{2}{\sqrt{81x^2 + 4}} + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply:                                                                                                 [tex]\displaystyle \frac{1}{144} [\frac{18x}{81x^2 + 4} + arctan(\frac{9x}{2}) + C][/tex][Exp] Distribute:                                                                                             [tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]

Answer:

0.192 hour

Step-by-step explanation:

41$ / 8 = 0.192 hours = 11.703 minutes

Answer:

20 ft.

Step-by-step explanation:

You can solve this as a proportion:

[tex]\frac{1}{2} = \frac{10}{y}[/tex]

The y is equal to 20.

Hope it helps!

(3/4 km)/(1/4 hour) = (3 km)/hour

1 - 0.082 = 0.918
Multiply by 0.918

Answer:

2=72 4=148  6=222  10=370 15=555 16=592

sorry about the second part i didnt see it

Answer:

148, 3 , 740, 1110, 8.

Step-by-step explanation:

Miles: 148 + 740 + 1,110 = 1,998

Gallons: 2 + 4 + 3 + 10 + 15 + 8 = 42

9514 1404 393

Answer:

  14.9 cm

Step-by-step explanation:

To find c using the Law of Sines, you must know angle C. That is found from ...

  C = 180° -A -B = 180° -150° -12° = 18°

Then the law of sines tells you ...

  c/sin(C) = b/sin(B)

  c = b·sin(C)/sin(B) = (10 cm)·sin(18°)/sin(12°)

  c ≈ 14.9 cm

9514 1404 393

Answer:

  60 cm

Step-by-step explanation:

The model ship will be x feet long, where ...

  x/100 = 1/50

  x = 100/50 = 2

In meters, that is ...

  2(0.3 m) = 0.6 m

A meter is 100 cm, so the length in centimeters is ...

  (0.6)(100 cm) = 60 cm

Answer:

I took the test!!

Step-by-step explanation:

Pit this in your calculator exactly like this 4,000(1.05)^5 and you get the answer 5,105.12625. So round your answer to the nearest dollar, which is 5,105.

Answer:

C.

Step-by-step explanation:

The answer is C !!! :)