A company opened in 1998 and turned a profit its first year. The company's revenues increased annually thereafter. Which of the
following functions could model this situation where x represents the number of years in operation, and f(x) represents the
company's annual revenue [in millions]?

Question:

a. College GPA

b. Richter Scale

c. Acidity/Alkalinity

d. Compound Interest

e. Amortization Schedule

Answer:

The correct two options are;

b. Richter Scale

c. Acidity/Alkalinity

Step-by-step explanation:

Here we have

b. The Richter Scale, given by the following relation;

[tex]M = log(\frac{I}{I_0} )[/tex]

M = Earth quake magnitude

I = Earthquake intensity

I₀ = Earthquake intensity of magnitude 0

Comparing two Earthquakes, A and B, we have

[tex]M_A - M_B = log(\frac{I_A}{I_B} )[/tex]

c. Acidity/Alkalinity are determined by the pH of the solution, which is the negative logarithm of the hydrogen ion concentration

pH = -log₁₀ [H⁺].

Answer:

2.64575131106 2.6457513110645905905016157536392604257102591830824501803683344592010688232302

83627760392886474543610615064578338497463095743529888627214784427390555880107722

71715072972832389229968959486508726070097805420372382802371594110034193911600157

85255963059457410351523968027164073737990740415815199044034743194536713997305970

05051399692237545616097119027378154991633288287704000657570674651963497752083793

81811461309087647378659562433057994798128163230705483650107715617946361191553454

53647749482059309049484983403398900210478616673327950369392462257170537164925787

54832290732492671346980298949908037748251109227895568897919808814834090831685251

33535829539172211770714414974576907081989444441458972284741400303502353203719487

07382629318519364090832280596462783761021959794197089096354695861341181793067816

21360849101677835321255633463490021898146042255929503669562418692737327715022087

52309966469813203212818945478568020950635962446628550076190504139350447437123488

52233277362510045059621080672334698120004300514490251206257311759115423194459672

60497833404344683725636178255048160879406205511486397833055016369470076387773745

19511658095220474202064982102444056001996590904100285534069110102261166807200774

83070332613842826296809502470794656496344336830519708820348050486447262317930876

95722489377521119788376007845603903658809421599292501057753682356001720074065236

92473209967419778002535708540617794442886681589731184938101638162073015642647016

29841099690071341323798188477647769954391111945967670336972452475367740100245826

51593077528163005479339717508017899520565284447796194304512502890432970610508746

04492966897542257133380633247034508888234275409806214511439553803393190705392738

14520604335238180389333294731479058055670704161068722878104529957696633035133295

04704245502510500789645502552271857923370921821991843932537781386785650143790894

13002099040860186605228131329821735251716419633617853080179022873400337109527257

36428650922035916343820273976336550966714177816292894279884853951076819102168116

99677176780863793410667897509217050421558644370687652934899322442240273649792906

66842070305782257110537944215790013280304078494579431518120466309284152592404683

65282802722458530778415894238973955590959563491357495109757674781975590533726939

36521431268222909570986506137179452721677198255442288046052307455488310813325041

49932783468182066583447383366862454456169497251774270254688591746231942309355060

38899235355634465872922507362228284298215287903623847595555861643755472027361518

00826144981691174794610631845652307625691344410868551999982851633960745717970829

72776495645142655658205126240305961633868338746134237463526431296594527010213721

72174899143552932049575097114259427207988929665230498875939525378121455723193310

30690840194942118708515205734116214105775416917245804962369512932926647583857193

34312550616097509003957512063487575979549295499224726634074018815634940531052960

4465875564620943Step-by-step explanation:

Answer:

y = 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) has the same graph of y = 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) ⇒ 3rd answer

Step-by-step explanation:

Let us revise the rules of the trigonometric compound angles

cos(x + y) = cos x cos y - sin x sin y

sin(x + y) = sin x cos y + cos x sin y

Let us solve the problem using the rules above

y = 2 cos (x + [tex]\frac{\pi }{4}[/tex] )

∵ 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) = 2[cos x cos [tex]\frac{\pi }{4}[/tex]  - sin x sin [tex]\frac{\pi }{4}[/tex] ]

∵ cos [tex]\frac{\pi }{4}[/tex]  = [tex]\frac{\sqrt{2}}{2}[/tex]  and sin [tex]\frac{\pi }{4}[/tex]  = [tex]\frac{\sqrt{2}}{2}[/tex]  

- Substitute them in the right hand side

∴ 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) = 2[ [tex]\frac{\sqrt{2}}{2}[/tex] cos x  -  [tex]\frac{\sqrt{2}}{2}[/tex] sin x]

- Multiply the bracket in the right hand side by 2

∴ 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) = [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x

∴ y = [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x

Now let us find the function which give the same right hand side of the function above

y = 2 sin (x + [tex]\frac{3\pi }{4}[/tex] )

∵ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) = 2[sin x cos [tex]\frac{3\pi }{4}[/tex]  + cos x sin [tex]\frac{3\pi }{4}[/tex] ]

∵ sin [tex]\frac{3\pi }{4}[/tex]  = [tex]\frac{\sqrt{2}}{2}[/tex]  and cos [tex]\frac{3\pi }{4}[/tex]  = [tex]-\frac{\sqrt{2}}{2}[/tex]  

- Substitute them in the right hand side

∴ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) = 2[ [tex]-\frac{\sqrt{2}}{2}[/tex] sin x  + [tex]\frac{\sqrt{2}}{2}[/tex] cos x]

- Multiply the bracket in the right hand side by 2

∴ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) =  [tex]-\sqrt{2}[/tex] sin x  + [tex]\sqrt{2}[/tex] cos x

- Switch the two terms of the right hand side

∴ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) =  [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x  

∴ y =  [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x

- The same with right hand side of the function above

∴ y = 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) has the same graph of y = 2 cos (x + [tex]\frac{\pi }{4}[/tex] )

Answer:

y=2sin(x+3pi/4)

Step-by-step explanation:

Answer C

Answer:It would be A. $19x + $160 < $635

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

12x6x5 is 360. The volume formula is V=L*W*H

Answer:

B=62, a=3.7, C=7.9

Step-by-step explanation:

Answer:

[tex]28.8\%[/tex].

Step-by-step explanation:

We have been given that prices  increase  at  a  monthly  rate  of  2.4%. We are asked to find the percentage at which prices will increase in a year.

We know that 1 year equals 12 months.

To find the increase in one year, we will multiply monthly increase rate by 12 as:

[tex]\text{Yearly increase rate}=12\times 2.4\%[/tex]

[tex]\text{Yearly increase rate}=28.8\%[/tex]

Therefore, the prices will increase at a rate of [tex]28.8\%[/tex] in a year.

Answer:

C) x=-2 x=-5

Step-by-step explanation:

When you look at the X-axis you can see that is crosses at the points (-5,0) and (-2,0)

Answer:

The zeros are x=-2 and x=-5.

Answer:

2044 cups

Step-by-step explanation:

In a quart, there are 4 cups:

1 quart = 4 cups

In 512 quarts, there will be:

4 * 512 cups = 2048 cups

If only 4 cups remained after watering, then the number of cups used to water the plants is:

2048 - 4 = 2044 cups

7-18

18 cups is correct cuz 5/12 in quarts well in the 1st place 4 cups go into a quart then u gatta figure out 4x4=16 and then the 12 at 5/12 add them cuz u got 2 and im pretty sure ull get 7-18

HOPE IT HELPED :D :D

Answer:

The answer is for sure x = 9

Answer:

x=9

Step-by-step explanation:

Given:

Given that we need to determine the value 0.15 of $2 dollars.

Value:

Let us determine the value of 0.15 of $2 dollars.

Value of 0.15 of $2 dollars can be determined by multiplying 0.15 by 2.

Thus, we have;

[tex]0.15 \times 2[/tex]

Multiplying the values, we get;

[tex]0.3[/tex]

Thus, the value of 0.15 of $2 dollars is 0.3 dollars.

Answer:

$0.30

Step-by-step explanation:

0.15 of $2

of is multiplication

0.15 × 2

0.3

Answer:

see below

Step-by-step explanation:

exponent to log: [tex]a^b[/tex] = c ---> logₐc = b

ie. question 6

log ₁₀(3x+1) = 2 -----> [tex]10^{2} = 3x+1[/tex]

that will get you through questions 1 to 3, 5 to 6, and 8

in question 4, all you have to do is know that 2^2 = 4 and 2^3 = 8, by setting the bases equal, you can manipulate the exponents to get 2x+8 = 3x-3

for questions 7 and 9,

remember that:

logₐc + logₐd = logₐ(cd)

logₐc - logₐd = logₐ([tex]\frac{c}{d}[/tex])

remember change of base is [tex]log_{a} b = \frac{log_xb}{log_xa}[/tex], this will be useful if you need your calculator since calculators only have base 10 and maybe if your calculator is good enough natural base e

Answer:

16/25 or 0.64 or 64%

Step-by-step explanation:

Please kindly check the attached file for explanation

Answer: The probability of picking a green block or red block is 0.64 (or 64%)

Step-by-step explanation: The total number of blocks can be derived as;

31 (R) + 49(G) + 24(Y) + 21(P) = 125

With 125 blocks in total, there are 125 possibilities and the possibility of picking any of the four colors shall be be determined as a fraction of the entire possible outcomes.

The probability of picking a green ball when picked at random is given as;

P(Green) = Number of required outcomes ÷ Number of all possible outcomes

P(Green) = 49/125

(Note that there are 49 green blocks and a total of 125 blocks of all four colors)

Also the probability of picking a red ball when picked at random is given as;

P(Red) = Number of required outcomes ÷ Number of all possible outcomes

P(Red) = 31/125

The probability of picking a green block or a red block is given as P(green or red)

P(Green or Red) = 49/125 + 31/125

P(Green or Red) = 80/125

P(Green or Red) = 16/25

P(Green or Red) = 0.64

Therefore the probability of picking a green or red block at random is 0.64 or 64%

Answer:

375

Step-by-step explanation:

713 - 37 = 676

676 divided by 2 = 338

That would be the washer but we need to add the 37 again for the dryer

338 + 37 = 375

The magnitude of the first duckling's displacement is 13 units, and for the second duckling it is approximately 15.3 units. The second duckling wandered 2.3 units farther than the first.

The student is asking about the displacements of two ducklings from their nest and how much farther one wandered than the other. To compare the displacements of the two ducklings, we calculate the magnitudes of their displacements using the Pythagorean theorem.

For the first duckling's displacement, with coordinates (12,5), the magnitude is
sqrt(122 + 52) = sqrt(144 + 25) = sqrt(169) = 13 units.

For the second duckling's displacement, with coordinates (13,-8), the magnitude is
sqrt(132 + (-8)2) = sqrt(169 + 64) = sqrt(233) = approximately 15.3 units.

The second duckling wandered farther by the difference in magnitudes, which is 15.3 units - 13 units = 2.3 units. Therefore, the second duckling wandered 2.3 units farther than the first duckling.

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Answer:

331.25

Step-by-step explanation:

First you want to find how much each class cost. So first you want to divide $198.75 by 15 and you will get 13.25. Once you do that you will multiply              13.25 by 25 to get 331.25. Your welcome.

To find y:

[tex]3y-14=180[/tex]

[tex]3y=194[/tex]

[tex]y=64.7[/tex]

To find z:

[tex]180 - 64.7 = z[/tex]

[tex]z = 115.3[/tex]

Answer:

what is the question

Step-by-step explanation:

Answer:

Step-by-step explanation:

We would section the bread into a cuboid at the bottom and a semi cylinder at the top.

Considering the bottom, the formula for determining the volume of a cuboid is expressed as

Volume = length × width × height

Therefore,

Volume = 20 × 11 × 6 = 1320 cm³

Considering the semi cylinder,

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder

h represents the height of the cylinder.

π = 3.14

Looking at the diagram,

Height = 20 cm

Diameter = 11 cm

Radius = diameter/2 = 11/2 = 5.5 cm

Since it is a semi cylinder, then

Volume = 1/2 × 3.14 × 5.5² × 20 = 949.85 cm³

Therefore, volume of this loaf of bread is

1320 + 949.85 = 2269.85 cm³

Answer: 11%

Step-by-step explanation: What I did is i added 21 8 and 2 together and subtracted them by the amount of students which is 28. Then with that number/ 3 I divided by 28 which gave me the percentage .10714. I then rounded and ended with 11%. Im pretty sure this is the right answer if anyone thinks they know im wrong please say

Answer:

THE CORRECT ANSWER IS 3/28

Step-by-step explanation:

Answer:

If you plug it all in you will get x=2 x=-3

Step-by-step explanation:

The quadratic formula is

-b+/-[tex]\sqrt[/tex]-b^2-4ac all over 2(a)

your equation 2x^2+2x-12

you can label it

a=1      b=2               c=-12

If you plug it all in and solve you will get x=2 x=-3

The values of x would be 2 and 3 which are determined by using the quadratic formula to solve the given quadratic function.

The quadratic function is defined as a function containing the highest power of a variable is two.

We have been given that quadratic function as

2x² + 2x - 12

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a = 2, b = 2 and c = -12

Using the quadratic formula to solve the above quadratic function

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute the values of  a = 2, b = 2 and c = -12 in the quadratic formula,

[tex]x = \dfrac{-2\pm\sqrt{2^2-4\times2\times-12}}{2\times2}[/tex]

[tex]x = \dfrac{-2\pm\sqrt{4+96}}{4}[/tex]

[tex]x = \dfrac{-2\pm\sqrt{100}}{4}[/tex]

[tex]x = \dfrac{-2\pm10}{4}[/tex]

x = (-2+10)/4 and x = (-2-10)/4

x = (8)/4 and x = (12)/4

x = 2 and x = 3

Therefore, the values of x would be 2 and 3 which are determined by using the quadratic formula to solve the given quadratic function.

Learn more about quadratic function here:

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A tangent line intersecting with a radius always creates a  right angle.

A tangent line intersects with a circle at only one point.

This point is referred to as the point of tangency.

When a radius is drawn to intersect with the tangent line at the point of tangency, then the angle at that point of intersection is a right angle i.e. the measure of the angle is 90 degrees.

This is so because both lines (i.e. the radius and the tangent line) are perpendicular lines.

Hence, the text that completes the statement is right angle.

Read more about tangent lines at:

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Answer:

4

Step-by-step explanation:

(x+8)(8) = (10+6)(6) -->

8x + 64 = 60 + 36 -->

8x = 32 -->

x = 4

Answer:

66 in total. 44 boys and 22 girls

Step-by-step explanation:

you have to multiply 22 by 2 because there is twice as many (half of two is one) boys than there is girls.

Answer:

66

Step-by-step explanation:

There is a 2:1 ratio of boys to girls, and there are 22 more boys than girls. We can assume that 2/3 of the class are boys while 1/3 of the class is girls.

The difference between the two is 1/3. This can be found by taking away the smaller of the two from the larger, in this case it's 2/3 - 1/3. Removing the third, it's 2-1 which can be done by multiplying the two fractions by three. If we add the third back by dividing by three, we get 1/3.

This means that 22 people must be equivalent to 1/3 the total class' population. If x/3 = 22, then 22 * 3 must be x.

22 * 3 = 66, so there must be 66 students in the class.

Answer:

Mark types the fastest rate of words per minute at 75 words per minute

Step-by-step explanation:

In this question, we want to know which of the three typists has the fastest typing rate.

To calculate this, what we need to do is to divide the total number of words they can type by the number of minutes taken to type those words.

For Natasha, we have; 2600 words / 40 minutes = 65 words per minute

For Henry, we have 4900 words/70 minutes = 70 words per minute

For Mark, we have 3750 words/50 minutes = 75 words per minute

We can see that Mark with 75 words per minute has the fastest typing rate

Under the elimination method, we normalized the systems of equations, resulting in the equation: 0=1. Since this is not possible, the system has no solutions.

To determine the number of solutions for the system of equations, we can use the method of substitution or elimination. Let's use elimination:

Because 0 does not equal 1, we can conclude that the system of equations has no solutions.

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Answer: The 18 pint bucket.

Step-by-step explanation: If you convert all of the units to gallons, you will find that the 7 quart bucket contains 1.75 gallons and the 18 pint bucket contains 2.25 gallons. Since 2.25 is the greatest amount, the 18 pint bucket contains the most water.

Answer:

13 cups of the 80% chlorine solution + 7 cups of the 60% chlorine solution

Step-by-step explanation:

The pool company recommendation is 20 cups of 73% chlorine to treat their pool

Concentration of chlorine solution in stock = 80% and 60%

Therefore to make 20 cups of 73% solution, we require;

X cups of the 80% chlorine solution and

Y cups of the 60% chlorine solution

That gives 0.8·X + 06·Y = 0.73 × 20

X + Y = 20

Solving gives X = 13 cups

and Y = 7 cups

Therefore to  make the optimal solution, 13 cups of the 80% chlorine solution should be mixed with 7 cups of the 60% chlorine solution.

Answer: 9.16 feet

Step-by-step explanation:

Hi, to answer this question, since we have formed a right triangle (see attachment) we have to apply the Pythagorean theorem:

a2 +b2 = c2

Where c is the hypotenuse of a right rectangle (the longest side) and a and b are the lengths of the other 2 sides.

In this case the hypotenuse us the ladder.

So, replacing with the values:

4^2 + b ^2 = 10^2

16 + b^2 = 100

b^2 = 100-16

b^2 = 84

b = √84

b= 9.16 feet

Answer:

It has grown by 1406.50%

Step-by-step explanation:

Take 3234956 and divide it by 2300 and you get your percentage from population then to now

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