Equations of Exponential Functions

Given the following equations of an exponential function
R = 10.5(0.535)t
determine the decay rate.

a. 0.535%
b. 10.5%
c. 50%
d. 46.5%

Please select the best answer from the choices provided

You can get 3/8 from 13/8 by subtraction. The solution is 10 / 8

In order to get 3/8 from 13/8 we would have to carry out a subtraction of fractions.

That is we would have: 13/8 - 3/8

take the lcm of the denominator

[tex]\frac{13 - 3}{8}[/tex]

= 10 / 8

Hence when we take 3 / 8 from 13 / 8, the solution that we would have would be from subtraction. This is 10 / 8

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Answer:

<1=62

<2=83

<3=35 this is the answer of this question

Answer:

yeah it's true

Step-by-step explanation:

............THANKS.........

Answer:

14.1 inches

Step-by-step explanation:

The formula to be used to find the arc length is Ф = s(arc length) / r(radius)

First we rearrange the formula to find the arc length which would be s = Ф * r

This formula only works in radians so the first step is converting 135° to radians so we would do 135° * π radians/180° which would give us 3π/4

We would then multiply 3π/4 * 6 and get 18π/4,  plugging that value into a calculator returns us a value of ≈ 14.137

We then round to the nearest tenth and get an answer of 14.1 inches for the arc length of the circle below

Answer:

pi  3.1415926535897932384626433832795

Answer:

75 : 225

Step-by-step explanation:

[tex]\frac{\frac{1}{4} }{\frac{3}{4} } :\frac{75}{y}[/tex]

0.25 × y = 0.75 × 75

0.25y = 56.25

0.25y ÷ 0.25 = 56.25 ÷ 0.25

y = 225

Answer:

Years = {log(total) -log(Principal)} ÷ log(1 + rate)

Years = [log (200,000) -log (20,000)] / log (1.09)

Years = [5.3010299957 -4.3010299957] /  0.037426497941

Years = 1 / 0.037426497941

Years = 26.7190374471

*************************************************

Finding Doubling Time : (We'll calculate $100 becoming $200)

Years = {log(total) -log(Principal)} ÷ log(1 + rate)

Years = log (200) -log (100) / log(1.09)

Years =  (2.3010299957 -2) / 0.037426497941

Years = .3010299957 / 0.037426497941

Years 8.0432317278

It takes 8.0432317278 years for money to double at 9% per year.

Source:

http://www.1728.org/compint2.htm

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

You have to divide both numerators then the denominater.

So, it would look like:  160 over 90 x 100 over 290

160x100=16   90x290=25     16/25

Answer:

550 lattes he sold this week

Step-by-step explanation:

$275÷$0.50= 550

On solving the provided question, we can say that - by doing the fraction we have 3/12 = 1/4

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

balloons is 12

blew up is  1/3

friend blew up is  5

1/3*12 = 4

4+5 = 9

3/12 = 1/4

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Answer:

D

Step-by-step explanation:

i did a test with the same question

The representative sample of the population displayed by the dot plot is: dot plot D.

The representative sample of a population can be described as a subset of a particular population which displays or exhibit similar characteristics of the larger population group.

From the image given, the dot plot that reflects the characteristics of the dot plot of the population is the dot plot in option D.

Dot plot D is a representative sample.

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Answer:

1. A

2. C

Step-by-step explanation:

Answer: Choice A

angle GAF = angle TAE is the lie (aka false statement)

========================================================

Explanation:

Let's go through each answer choice to see which is true or which is false.

-----------------------------

Choice A

The markers for angles GAF and TAE are different. Both would need to have a single angle marker, or a double angle marker. The differing markers indicates the angles aren't the same.

Also, note that angle TAG isn't a 180 degree angle, or that point G isn't on line TA. We need this to be the the case, so that two vertical angles form. However, such a thing doesn't happen.

So that's why angles TAE and GAF aren't the same measure.

Choice A is the answer. You can stop here if you wanted.

-------------------------------

Choice B

Let

x = measure of angle TAE

y = measure of angle TAH

z = measure of angle HAF

We can see that x+y+z = 180, since angle EAF is a straight angle. The diagram gives y = 90 and z = 50, so,

x+y+z = 180

x+90+50 = 180

x+140 = 180

x = 180-140

x = 40

Angle TAE is 40 degrees. It adds with angle FAH to get 40+50 = 90, showing that the two angles are indeed complementary.

Choice B is a true statement, so we can rule it out.

-------------------------------

Choice C

Angle TAF is composed of angles TAH and HAF

Adding the two angles gets us 90+50 = 140, which is larger than 90.

Therefore angle TAF is obtuse.

Choice C is a true statement, and it can be ruled out as well.

Technically you could have stopped at choice A once you found the lie, but I figured to show why choices B and C could be ruled out.

Answer:

2019

Step-by-step explanation:

2010: 450,000

2011: (5% of 450,000) + 450,000 = 472,500

2012: (5% of 472,500) + 472,500 = 496,125

2013: (5% of 496,125) + 496,125 = 520,931.25

2014: (5% of 520,931.25) + 520,931.25 = 546,977.8125

2015: (5% of 546,977.8125) + 546,977.8125 = 574,326.703125

2015: (5% of 574,326.703125) + 574,326.703125 = 603,043.038281

2016: (5% of 603,043.038281) + 603,043.038281 = 633,195.190195

2017: (5% of 633,195.190195) + 633,195.190195 = 664,854.949705

2018: (5% of 664,854.949705) + 664,854.949705 = 698,097.69719

2019: (5% of 698,097.69719) + 698,097.69719 = 733,002.582049

Basically, take five percent of the population of the year and add it to the population of the previous year. This is the long way of doing it, but you get the population count for each year.

Answer:

ffyftxrrxrrxcvcmuvcyztzxvujgyh

Step-by-step explanation:

✋☝☝✊✋❤❤❤

Answer:

A

Step-by-step explanation:

Hi I don't usually upload pictures but I was too lazy to type so I did it on paper. I had to get the numbers in the parenthesis out so I multiplied the + by everything in the parenthesis following the negative and positive multiplication rules. Then, I combined and subtracted like terms.

Hope this helps !!

-Ketifa

Answer:

y=2x+2

Step-by-step explanation:

you have to substitute x and y in the given equations and which one works

for y=x+3 , 4=1+3 true , 6=2+3 false

for y=3x+1, 4=3*1+3 false

for y=2x+2, 4= 2*1+2 true, 6= 2*2+2 true, 8= 2*3+2 true, 10=2*4+2 true

for y=4x, 4=4*1 true, 6= 4*2 false

The nearest integer that is a solution, gotten through graphing of the quadratic function x² + 2x - 2 = 5, is x = -4

Quadratic equations when plotted on a graph follows a parabolic path.

To plot the functions there will be table of values that is used in making the graph. The table of values is solved as follows

x² + 2x - 2 = 5 rearranging the equation will result to x² + 2x - 7 = 0

For x = -20,  y = (-20)² + 2 * -20 - 7 = 353

For x = 0,  y = (0)² + 2 * 0 - 7 = -7

For x = 20,  y = (20)² + 2 * 20 - 7 = 433

x      y

-20  353

0      -7

20    433

The graph is plotted and attached. From the graph the solution is

x = -3.828, to the nearest integer = -4

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Sales Tax = $3.00

The total amount paid by the group was $48.15

The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:

Sales tax = $37.50 * 8% = $3.00

The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:

Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15

So the total amount paid by the group was $48.15.

Answer:

add the 3 and 4

Step-by-step explanation:

Answer:

Infinity (∞)

Step-by-step explanation:

Graph the function and observe that the function P(t) increases without bound as x increases.

Answer:

(a) [tex]\sigma = 7.04[/tex]

(b) [tex]\sigma = 14.1[/tex]

(c) The population standard deviation is multiplied by k

Step-by-step explanation:

Given

[tex]Dataset: 12, 7, 18, 23, 24, 27[/tex]

Solving (a): The population standard deviation

Start by calculating the mean

[tex]\mu = \frac{\sum x}{n}[/tex]

[tex]\mu = \frac{12+7+18+23+24+27}{6}[/tex]

[tex]\mu = \frac{111}{6}[/tex]

[tex]\mu = 18.5[/tex]

The population standard deviation is:

[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]

This gives:

[tex]\sigma = \sqrt{\frac{(12-18.5)^2 + (7 - 18.5)^2 + (18-18.5)^2 + (23-18.5)^2 + (24 - 18.5)^2 + (27 - 18.5)^2}{6}}[/tex]

[tex]\sigma = \sqrt{\frac{297.5}{6}}[/tex]

[tex]\sigma = \sqrt{49.5833}[/tex]

[tex]\sigma = 7.04[/tex]

Solving (b): Double the dataset and calculate the new population standard deviation

The new dataset is:

[tex]Dataset: 24, 14, 36, 46, 48, 54[/tex]

Start by calculating the mean

[tex]\mu = \frac{\sum x}{n}[/tex]

[tex]\mu = \frac{24+ 14+ 36+ 46+ 48+ 54}{6}[/tex]

[tex]\mu = \frac{222}{6}[/tex]

[tex]\mu = 37[/tex]

The population standard deviation is:

[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]

This gives:

[tex]\sigma = \sqrt{\frac{(24-37)^2 +(14-37)^2 +(36-37)^2 +(46-37)^2 +(48-37)^2 +(54-37)^2}{6}}[/tex]

[tex]\sigma = \sqrt{\frac{1190}{6}}[/tex]

[tex]\sigma = \sqrt{198.33}[/tex]

[tex]\sigma = 14.1[/tex]

Solving (c): What happens when the dataset is multiplied by k

In (a), we have:

[tex]\sigma = 7.04[/tex]

In (b), when the dataset is doubled,

[tex]\sigma = 14.1[/tex]

This implies that when the dataset is multiplied by k, the population standard deviation will be multiplied by the same factor:

i.e.

[tex]New \sigma = k * \sigma[/tex]

The number of hours does each group member work on the project is 4 hours. Therefore, the correct answer is option B.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is x+45/4=4x.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

4x-x=45/4

3x=45/4

x=15/4

x=3.75

x≈4 hours

Therefore, option B is the correct answer.

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Here we go...

= 2x² - y² = 17

= 2x² = 17 + y²

= x² = 17 + y²/2

= x = √17+y²/2

= x + 2y = 1

= x = 1 - 2y

___________________

Sry,if i misunderstood the question.. do let me know in the comment section

Answer:

160 in³

Step-by-step explanation:

Volume of rectangular pyramid, V = (Length * width * height) / 3

Length = 10 in ; width = 8 in ; height = 6 in

V = (10 * 8 * 6) / 3

V = 160 in³

Answer:

yes it is

Step-by-step explanation:

Answer:

40.5 m²

Step-by-step explanation:

Area of the shaded = area of the square - area of the triangle

Area of square = s²

s = 9 m

Area of square = 9² = 81 m²

Area of triangle = ½*b*h

b = 9 m

h = 9 m

Area of triangle = ½*9*9 = 40.5 m²

Area of the shaded = 81 - 40.5 = 40.5 m²

Answer:

35

Step-by-step explanation: