Since 2009 the number of smartphones shipped from manufacturers to stores around the world has increased exponentially. The growth from 2009 through 2015 can be modeled using the function G (t) = 174 . 1.67^t where t is the number of years singe 2009 and G (t) is measured in millions of smartphones.

Use this information and your knowledge of exponential and logistic growth to explore the mathematical concepts in the questions below.

Since 2009 The Number Of Smartphones Shipped From Manufacturers To Stores Around The World Has Increased

Answers

Answer 1

The y-intercept indicates that 174 million smartphones were shipped to stores in 2009. This implies that after two years, in 2011, smartphone manufacturers shipped 500 million smartphones to stores worldwide.

Since 2009 the number of smartphones shipped from manufacturers to stores around the world has increased exponentially.

What is the exponential function?

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

The growth from 2009 through 2015 can be modeled using the function G(t) = 174 * 1.67^t where t is the number of years since 2009 and G(t) is measured in millions of smartphones.

The required graph of the exponential function G(t) has been attached below

Now, finding the y-intercept

G(t) = 174· 1.67^t...(i)

Substitute the value of t = 0 in the above function,

G(t) = 174* 1.67⁰

G(t) = 174(1)

G(t) = 174

The meaning of the y-intercept is that 174 million smartphones are being shipped to stores in years 2009.

Substitute the value of G(t) =500 in the exponential function(i),

500 = 174 * 1.67^t

500/174 = 1.67^t

2.8735 = 1.67^t

In(2.8735 ) = t In (1.67)

t = In (2.8735 ) / In (1.67

t = 2.05827 ≈ 2

Hence, This means after 2 years i.e. in 2011, smartphone manufacturers were shipping 500 million smartphones to stores around the world.

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Since 2009 The Number Of Smartphones Shipped From Manufacturers To Stores Around The World Has Increased

Related Questions

isabel drove 335 miles in 5 hours at the same rate how any miles would she drive in 8 hours

Answers

Isabel Drive 67 miles every hour
335/5=67
Therefore, if she was to drive eight hours she would drive 536 miles
Answer=536 miles

5. Find the volumes of the following sugar containers. Round to
Domino 1 decimal place.
SUGAR
a. Domino granulated sugar in canister: radius-1.56 inches;
height-6.93 inches
in³
b. Domino sugar cubes in box: length-15.5 cm; width-8.6 cm;
height-3.8 cm.
Domino
SUGAR CUBES
cm³

Answers

The volume of the canister is 36.7 in³. The volume of box is 482.6 cm³

To find the volume of a canister, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

In this case, the canister has a radius of 1.56 inches and a height of 6.93 inches,

volume of canister = π × (1.56 inches)² × 6.93 inches

volume of canister = 36.7 in³

To find the volume of a box, we can use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

In this case, the box has a length of 15.5 cm, a width of 8.6 cm, and a height of 3.8 cm

volume of box = 15.5 cm × 8.6 cm × 3.8 cm

volume of box = 482.6 cm³

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Find X and RDB



X= ______
RDB=______

Answers

Using the secant-secant theorem,

[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ m\angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]

The measure of the angle ∠RDB will be 45°.

What is the angle of the chord?

In geometry, a chord of a circle is a straight line segment whose endpoints both lie on the circle. A diameter of a circle is the longest chord, and it passes through the centre of the circle.

Calculate the value of x as below,

( 13x + 7 - 60 ) / 2 = 5x - 10

13x - 53 = 10x - 20

3x - 53 = -20

3x = 33

x = 11

The measure of the angle ∠RDB is,

∠RDB = 5x - 10

∠RDB = ( 5 x 11 ) - 10

∠RDB = 45°

Therefore, the value of an angle ∠RDB will be 45°.

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What is an equation of the line that passes through the points (4, 4) and (8, 5)?

Answers

Answer:

y=0.25x+3

Step-by-step explanation:

use desmos graphing calculator and put the coordinates into a table

A carpenter states that it will take 21.5 hours
to build the deck. If the carpenter charges
$24.00 per hour, how much will the carpenter
be paid?
F
$45.50
G
$129.00
H
$504.00
J $516.00

Answers

Answer:

The carpenter will be paid $516.00

Step-by-step explanation:

1. Multiply

(Since the carpenter is being paid per hour, and the pay is $24.00, and the time it takes to work is 21.5, we can set up this equation):

21.5 x 24.00 = $516.00

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Kathryn invests $1000 in one account and $2200 in an account paying 3 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest?

Answers

She invested $1000 at 2% and 2200 at 5% simple interest.

What is simple interest?

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, P₁ = 1000, P₂ = 2200, assuming r₁ = x% and r₂ = (x + 3)% and the sum of simple interest obtained from both these investments is $130.

(1000×x×1)/100 + {(2200×(x + 3)×1}/100 = 130.

10x + 22x + 66 = 130.

32x = 64.

x = 2.

So, the rate of interest is 2% and 5%.

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Solve using order of operations
16÷2×6-3

Answers

8 • 6 - 3
48 - 3
=46
(NOTE) Recall what the "Order of Operations" includes.____________PEMDASParenthesis: ( )Exponents: ^2Multiplication: ×, *Division: /, ÷Addition: +Subtraction: -____________

The Order of Operations, also referred to as PEMDAS, is the rule that defines the sequence in which an expression with multiply operations can be solved.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In this scenario, we are dividing, multiplying, adding, and subtracting numbers. This being laid out, lets begin.

1. Multiply and divide (left to right).

[tex]16[/tex] ÷ [tex]2 * 6 = 48[/tex]

[tex]=48-3[/tex]

2. Add and subtract (left to right).

[tex]48-3=45[/tex]

Hence, our final solution after using the order of operations would be [tex]45[/tex].

Hope this helps!


A triangular banner for the basketball championship hangs in the gym. It has an area of 48 square feet. What is the length of the base and height (in ft), if the base is two-thirds of the height?

Answers

From the area of a triangle, the height of the triangle is 12ft

Area of Triangle

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, which is given by

A = 1/2 b * h

A = Area of triangleb = baseh = height

In the given question, the base is two-thirds of the height.

b = 2/3h

Let's substitute the values into the formula

A = 1/2 * 2/3h * h

A = 2/6 * h²

A = 1/3h²

48 = 1/3h²

h² = 48 * 3

h = √144

h = 12ft

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Given L(-6, -7) and M(3, 6), what is the length of LM to the nearest tenth?
LM

Answers

Answer:

LM ≈ 15.8

Step-by-step explanation:

calculate the length d using the distance formula

d = [tex]}\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = L (- 6, - 7 ) and (x₂, y₂ ) = M (3, 6 )

LM = [tex]\sqrt{(3-(-6))^2+(6-(-7))^2}[/tex]

    = [tex]\sqrt{(3+6)^2+(6+7)^2}[/tex]

   = [tex]\sqrt{9^2+13^2}[/tex]

   = [tex]\sqrt{81+169}[/tex]

  = [tex]\sqrt{250}[/tex]

  ≈  15.8 ( to the nearest tenth )

Which of the following is a requirement for employees who must wear PPE?

Answers

The option that's a requirement for employees who must wear PPE is C. Participate in PPE training.

What is a personal protective equipment?

Personal protective equipment (PPE) is clothing that is comfortable to wear in order to reduce the risk of hazards at work that cause serious illnesses and injuries.

Personal protective equipment (PPE) will be divided into the following categories for this purpose: eye and face protection, hand protection, body protection, respiratory protection, and hearing protection.

Personal protective equipment (PPE) should be used when all other measures to control exposure are ineffective. It only protects the wearer while they are wearing it. PPE offers no protection if it fails.

All personal protective equipment should be designed and built safely, and it should be kept clean and reliable. It should be comfortable for workers to use. Personal protective equipment that does not fit properly can mean the difference between being safe and being dangerously exposed. Employers must provide personal protective equipment to their employees and ensure its proper use when engineering, work practices, and administrative controls are not feasible or provide adequate protection

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Complete question

Which of the following is a requirement for employees who must wear PPE?

a. Speak to the. project manager.

b. Get necessary clothes.

C. Participate in PPE training.

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Answers

Answer: 23.1, 13.35718336 years or 14 rounded

Step-by-step explanation:

[tex]Given:A= 23.1e^{0.0152t}[/tex]

when A = end amount, and t = years after 2000

Part A).

What was the population of the state in 2000. According to our function, this would be when t = 0

[tex]23.1e^{0.0152(0)}\\\\=23.1(1)\\\\=\boxed{23.1}[/tex]

Part B).

When will the population of the state reach 28.3 million?

This would be when A = 28.3

[tex]28.3=23.1e^{0.0152t}\\\\\frac{28.3}{23.1} =\frac{23.1e^{0.0152t}}{23.1} \\\\\frac{28.3}{23.1} =e^{0.0152t}\\\\ln^{\frac{28.3}{23.1} }=ln^{e^{0.0152t}}\\\\ln^{\frac{28.3}{23.1} }=0.0152t\\\\t=\frac{ln^{\frac{28.3}{23.1} }}{0.0152} \\\\\boxed{t=13.35718336 \ \ years}[/tex]

Select all of the verbal phrases which can be represented by the expression 25.75x + 10

Answers

Answer:

B: 25.75 times a number x, plus 10 | D: the product of 25.75 and x, plus 10

Step-by-step explanation:

B: 25.75 times "x" = 25.75x + 10

D: The product of 25.75 and x = 25.75x  + 10

Which statement best describes the functions represented in the graphs?
A.Both functions are continuous and linear.
B.Only function p is continuous and linear.
C.Both functions are discrete and exponential.
D.Only function a is discrete and exponential.

Answers

The statement that best describes the functions represented in the graphs is B. Only function p is continuous and linear.

What is a linear function?

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

How to know continuous function?

A function at a place can only be continuous if it is defined there, has a limit there, and its value at that point is equal to the value of the limit there.

The graph of function p is linear and continuous

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Find the sum of the arithmetic sequence 1, 3, 5, 7, … , 99.

Answers

The sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525

What is Sequence?

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given sequence is 1, 3, 5, 7, … , 99.

It is a arithmetic sequence, the difference between two consecutive terms will be same

d=3-1=2

first term a=1

l=last term =99

We need to find 99 is which term in the sequence

Aₙ = a + ( n - 1 ) d

99=1+(n-1)2

99=1+2n-2

99=2n-1

100=2n

Divide both sides by 2

50=n

Now we need to find the sum of 50 terms

Sₙ=n/2(l+d)

=50/2(99+2)

=25(101)

=2525

Hence, the sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525

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When Terri makes fruit salad she uses 4 oranges and 3 cups of grapes for every 2 bananas. If Terry uses five bananas how many oranges and how many cups of grapes will she use? Write and solve a proportion

Answers

Answer:

7.5 cups of grapes

Step-by-step explanation:

4o:3g:2b

With 5b, there's an increase in 2.5 from 2b. (divide 5b/2b)

Since the increase in all the other fruits is proportional by the same amount of 2.5.

This leaves you with 10o:7.5g:5b

Suppose a mutual fund has total assets of $25,500,000 and liabilities of $2,100,000. Currently there are 10,200,000 shares outstanding. Determine the net asset value of the fund? Round to the nearest cent. Show your work

Answers

The net asset value of the given mutual fund will be 2.29.

What is the arithmetic operator?

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Division = divide any two numbers or variables called division.

Multiplication = to multiply any two or more numbers or variables called multiplication.

As per the given,

Total assets = $25,500,000

Liabilities = $2,100,000

Total shares = 10,200,000

Net asset = (total assets - total liability)/total shares outstanding

Net assets = (25,500,000 - 2,100,000)/10,200,000

Net assets = 2.29

Hence "The net asset value of the given mutual fund will be 2.29".

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A company manufactures two types of electric hedge trimmers, one of which is cordless. The cord-type trimmer requires 2 hours to make, and the cordless model requires 10 hours. The company has only 1000 work hours to use in manufacturing each day, and the packaging department can package only 200 trimmers per day.
(a) Write the inequalities that describe the constraints on the number of each type of hedge trimmer produced. (Let x represent the number of cord-type models, and let y represent the number of cordless models.)

Answers

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

The inequalities that describe the constraints on the number of each type of hedge trimmer produced are:

x + y ≤ 200

2x + 10y ≤ 1000

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Total number of hours = 1000

Total number of trimmers = 200

Let x represent the number of cord-type models,

Let y represent the number of cordless models.

Now,

x + y ≤ 200

2x + 10y ≤ 1000

Thus,

The inequalities that describe the constraints on the number of each type of hedge trimmer produced are:

x + y ≤ 200

2x + 10y ≤ 1000

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Determine the domain of the rational function ƒ(a) = 3/a+5

Answers

Answer:

domain { a ∈ R , a ≠ - 5 }

Step-by-step explanation:

the denominator of f(a) cannot equal zero as this would make f(a) undefined. Equating the denominator to zero and solving gives the value that a cannot be.

a + 5 = 0 ( subtract 5 from both sides )

a = - 5 ← excluded value

domain { a ∈ R, a ≠ - 5 }

-4x+11y=-32
-9x+4y=11
elimination

Answers

Answer:

x = -3; y = -4

Step-by-step explanation:

We can start by eliminating x, which will give us y:

[tex]9(-4x +11y=-32)\\-4(-9x+4y=11)\\\\-36x+99y=-288\\36x-16y=-44\\\\83y=-332\\y=-4[/tex]

Now we can plug in -4 for y in the first equation to find x:

[tex]-4x+11(-4)=-32\\-4x-44=-32\\-4x=12\\x=-3[/tex]

Consider a political discussion group consisting of 9 ​Democrats, 9 ​Republicans, and 5 Independents. Suppose that two group members are randomly​ selected, in​ succession, to attend a political convention. Find the probability of selecting two Democrats.

Answers

Hence, the probability of selecting two Democrats is [tex]45[/tex].

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen.

The meaning of probability is basically the extent to which something is likely to happen.

Here given that,

Consider a political discussion group consisting of [tex]9[/tex] ​Democrats, [tex]9[/tex] ​Republicans, and [tex]5[/tex] Independents. Suppose that two group members are randomly​ selected, in​ succession, to attend a political convention.

Let us assume ,

The discussion of the democratic is [tex]x_1=9[/tex].

The discussion of the democratic is [tex]x_2=9[/tex].

The discussion of the democratic is [tex]x_3=5[/tex]

So, the total number of candidates are

[tex]x_t=x_1+x_+x_3\\\\=9+9+5\\\\=23[/tex]

Probability of independate candidate from the group of candidates is

[tex]P_1=\frac{x_3}{x_t}\\\\P_1=\frac{5}{23}\\\\[/tex]

As, the remaining number of candidates after the selectio of the independent candidate is

[tex]x_r=x_t-1\\\\x_r=23-1\\\\x_r=22[/tex]

Now, the remaining number of candidates from the group of total remaining candidates is

[tex]P_2=\frac{x_1}{x_r}\\\\P_2=\frac{9}{22}[/tex]

So, the probability of an independent Democrat using the probability is

[tex]P=P_1[/tex] × [tex]P_2[/tex]

[tex]P=\frac{5}{23}[/tex] ×[tex]\frac{9}{22}[/tex]

[tex]P=\frac{110(207)}{506}\\\\P=\frac{22770}{506}\\\\P=45[/tex]

Hence, the probability of selecting two Democrats is [tex]45[/tex].

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HELP ME OUT THANKS SO MUCH

Answers

r = 12
Hope this helps

Answer:

R would equal 12

Step-by-step explanation:

Chris bought a guitar for $77.00 and sold it for $126.28. What percent profit did Chris make on the guitar

Answers

Answer:

ten is the fight one

Step-by-step explanation:

True

Answer:

39%

Step-by-step explanation:

126.28 minus 77 is 49.28.

49.28 divided by 126.28 is 0.39 and a bunch of other numbers but round it up and its 0.39. move the decimal to the right two places and youve got 39%

hope this helped!

Express cos L as a fraction in simplest terms.
15
39
K
36

Answers

The representation of cos L in simplest term is 5/13. It can be obatined by trigonometric ratios.

What are trigonometric ratio?

The ratio of sides of a right angled triangle is known ars trigonometric ratios. There are six trigonometric ratios. Which are as follows:

sin = P/H, cos = B/H, tan = P/B

cosec = H/P, sec = H/B, cot = B/P

Here, P is perpendicular, H is hypotaneous, and B is base. These ratios simplify the calculation.

SInce the angle is not specified hence, consider the given angle is L. Now, L is given angle hence, the base will be 15 and hypotenous will be 39.

Now, consider the trigonometric ratio of cos.

[tex]cosL=\frac{Base}{Hypotenuse}\\[/tex]

Subsitute 15 for base and 39 for hypotenuse in the above expression.

[tex]cosL=\frac{15}{39}\\=\frac{5}{13}[/tex]

Hence, the representation of cos L in simplest term is 5/13. It can be obatined by trigonometric ratios.

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Sydney owes her mother $5 and her brother owes her mother $7.Graph the integers that represents the amount they owe their mother as negative integer on a number line.How much more will her brother have to reap their than Sydney ?

Answers

Answer:

Sydney will have to pay -5, and her brother will have to pay -7. Her brother will have to pay $2 more than Sydney.

Step-by-step explanation:

select independent or not independent for each situation

Answers

Answer: the first one

Step-by-step explanation:

A function's graph is shown below.
If you would like to enlarge the graph or make numbers and letters easier to read, you may click on it to open it in a new window. You may then enlarge that window with your mouse. To further enlarge the image, use your browser's zoom capabilities. On a PC this is usually ctrl shift + (and zooming out is ctrl -). On an Apple computer this is usually apple shift + (and zooming out is apple -).
Use interval notation to answer the following questions.
The domain of this function is ?
The range of this function is ?

Answers

The domain and the range of the function are given as follows:

Domain: (-2,3].Range: [-8, 2).

How to obtain the domain and the range of the function?

The domain of a function is composed by the set that contains all possible values assumed by the input of the function.

On a graph, the input of the function is given by the values of x, hence the domain of the graphed function is given by the following interval:

(-2,3].

The meaning of the circles on the intervals is of:

Open circle: open interval.Closed circle: closed interval.

The range is composed by the set containing all the values assumed by the output of the function.

Hence, on the graph, the range is composed by the values of y of the function, which are given as follows:

[-8, 2).

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C. Solve the following;
1. Elisse has 20 meters of ribbon. How many 15 cm of ribbon can be cut from it?
2. Mr. JB has a rectangular lot that measures 550 meters by 0.75 km. What is the area of the land in square meter. He is selling the whole lot for 206, 250,000 pesos, how much is the price per square meter?
3. Drinking 8 glasses of water a day is good for your health. If each glass of water is equivalent to 148 mL, how many liters of water you need to consume everyday.
4. Your baby brother has a body temperature of 100°F. What is his body temperature in °C ? Does he has a normal body temperature?
5. Your mother asked you to buy 2.5kg of sugar. Each pack of sugar in the store weighs 250 grams. How many packs of sugar will you buy?
6. The 120 grams powdered milk make 12 cups of milk. How many kilograms of powdered milk can produce 60 cups of milk. How many liters is 60 cups of milk?
7. You have 8 modules to study in a day. Your teacher gave you this schedule for 5 days from Monday to Friday.

Answers

Answer:

133, 412500, 500, 1.184, 37.8, 10, 0.6

Step-by-step explanation:

If we think about how many centimeters are in a meter, we know that

1m = 100cm

Using this, we can see that

20m = 2000cm

Now divide by 15:

2000 ÷ 15 ≈ 133

She can make roughly about 133 ribbons.

To solve the next question, we need to know how many kilometers are in a meter

1km = 0.001m

Let's covert 0.75 into m:

0.75 × 1000 = 750

Now solve for the area:

750 × 550 = 412500

The area of the rectangle is 412500

If he is selling the home for 206,250,000 pesos,

206,250,000 divided by 412500

206,250,000 ÷ 412500 = 500

The price per square meter is 500

If each glass is 148 milliliters, and we need to convert that into liters, we can use the equation:

1L = 1000mL

So converting 148 into liters,

148mL = 0.148L

Now, multiply by 8.

0.148 × 8 = 1.184L

We need to convert 100 Fahrenheit to Celsius.

100 F ≈ 37.8

This is definitely not a normal body temperature.

We can convert grams to kilograms using the equation:

1kg = 1000 g

Converting 2.5kg to g would look like this:

2.5kg = 2500g

250g × 10 = 2500g

We need to buy 10 packs of sugar.

If 120 grams of powdered milk can produce 60 cups of milk, and we need to figure out how many kg can produce the same amount, we use the equation:

1kg = 1000g

Converting 120g to kg would look like this:

120 ÷ 1000 = 0.120

Now, we need to figure out how many times 12 goes into 60.

12 × 5 = 60

Now we multiply 0.120 by 5

0.120 × 5 = 0.6

I hope this helps!

Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 17 centimeters and a height of 13 centimeters.

If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.

3,203 cm2
2,295 cm2
1,020 cm2
731 cm2

Answers

Answer:

283 cm^2

Step-by-step explanation:

hi your welcome

Answer:

Step-by-step explanation:

radius = r = 17

height = h = 13

First calculate the total surface area =

2πr (r + h)

2 (3.14) 17 (17 + 13)

2 (3.14) 17 (30)

6.28 (17)(30)

106.76 (30)

3202.80  cm²

Then subtract the area of the bottom base of the cake:

Base of the cake is the area of the round base

π r² = 3.14 (17)²

3.14 (289) = 907.46 cm²

Subtract area of base from total surface area:

I am rounding:

3203 - 908 = 2295 cm²

Second option or B

HELP PLEASE!
The answer choices are

A) 240

B) 270

C) 210

D) 120

Answers

If the rotation is clockwise the angle is 120°.

If the rotation is counterclockwise the angle is 240°

The correct options are A and D.

What is the angle of rotation that maps P to G?

We assume that the rotation is clockwise.

First, we can see that the rotation from P to F is just a rotation of 90°.

(point P as at 9 on a clock and point F is at 12 on a clock).

To go from point F to G, we need to move one of the sections defined by the dashed lines, and we know that each one of these measures 30°, then we need to add another 30° to the angle.

90° + 30° = 120°

Then the angle of rotation to map P to G is 120°.

The correct option is D.

Then if the rotation is counterclockwise, the rotation will be of 240°.

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Answers

The quadratic equation y = x² - 8 · x + 18 represents the parabola shown in the figure.

How to derive the quadratic equation behind the graph of the parabola

In this problem we find a representation of a parabola, which is described algebraically by quadratic equations, that is, polynomials of the form:

y = a · x² + b · x + c

Where a, b, c are the coefficients of the polynomial.

We can determine the value of the coefficients from the knowledge of three points set on Cartesian plane. First, select the points from Cartesian plane:

(x₁, y₁) = (0, 18), (x₂, y₂) = (4, 2), (x₃, y₃) = (7, 11)

Second, create a system of linear equations with three variables and three equations by replacing the variables x and y on the quadratic equation:

c = 18

16 · a + 4 · b + c = 2

49 · a + 7 · b + c = 11

Third, solve the system by numerical methods:

(a, b, c) = (1, - 8, 18)

Fourth, write the resulting quadratic equation:

y = x² - 8 · x + 18

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