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Please someone help I need this loads of points will be reported if you do weird answers

Options:

A. [1,10]        B. [10,20]      C. [15,25]     D. [1,30]

Answer:

A. [1,10]

Step-by-step explanation:

Given

[tex]N(t) = 100e^{-0.023t}[/tex]

Required

Interval with the fastest rate of decay

The rate of change over [a,b] is calculated as:

[tex]Rate = \frac{N(b) - N(a)}{b - a}[/tex]

So, we have:

A. [1,10]        

[tex]Rate = \frac{N(10)-N(1)}{10 - 1}[/tex]

[tex]Rate = \frac{N(10)-N(1)}{9}[/tex]

Calculate N(10) and N(1)

[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]

[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]

So:

[tex]Rate = \frac{79.45-97.73}{9} = \frac{-18.28}{9} = -2.03[/tex]

B. [10,20]      

[tex]Rate = \frac{N(20)-N(10)}{20 - 10}[/tex]

[tex]Rate = \frac{N(20)-N(10)}{10}[/tex]

Calculate N(20) and N(10)

[tex]N(20) = 100e^{-0.023*20} = 100e^{-0.46} = 63.13[/tex]

[tex]N(10) = 100e^{-0.023*10} = 100e^{-0.23} = 79.45[/tex]

So:

[tex]Rate = \frac{63.13 - 79.45}{10} = \frac{-16.32}{10} = -1.632[/tex]

C. [15,25]    

[tex]Rate = \frac{N(25)-N(15)}{25 - 15}[/tex]

[tex]Rate = \frac{N(25)-N(15)}{20}[/tex]

Calculate N(25) and N(15)

[tex]N(25) = 100e^{-0.023*25} = 100e^{-0.575} = 56.27[/tex]

[tex]N(15) = 100e^{-0.023*15} = 100e^{-0.345} = 70.82[/tex]

So:

[tex]Rate = \frac{56.27 - 70.82}{10} = \frac{-14.55}{10} = -1.455[/tex]

D. [1,30]

[tex]Rate = \frac{N(30)-N(1)}{30 - 1}[/tex]

[tex]Rate = \frac{N(30)-N(1)}{29}[/tex]

Calculate N(30) and N(1)

[tex]N(30) = 100e^{-0.023*30} = 100e^{-0.69} = 50.16[/tex]

[tex]N(1) = 100e^{-0.023*1} = 100e^{-0.023} = 97.73[/tex]

So:

[tex]Rate = \frac{50.16 - 97.73}{29} = \frac{-47.57}{29} = -1.64[/tex]

By comparing the values of the calculated rates,

-2.03 is the smallest, in other words; the fastest rate

Hence, the interval [1,10] has the fastest rate of decay

The required average rate of change is the fastest on [tex][1,10][/tex].

The formula for the average rate of change on the interval [tex][a,b][/tex]  is,

[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{b-a}[/tex]

Now, applying the given function into the above function is,

Now, [tex]a=1,b=10[/tex] then,

[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{10-1} =-2.03[/tex]

Now, [tex]a=10,b=20[/tex] then,

[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{20-10} =-1.6325[/tex]

Now, [tex]a=15,b=25[/tex] then,

[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{25-15} =-1.455[/tex]

Now, [tex]a=1,b=30[/tex] then,

[tex]\frac{100e^{-0.023b}-100e^{-0.023b}}{30-1} =-1.64[/tex]

So the average rate of change is fastest on [tex][1,10][/tex]

Learn more about the topic of the average rate of change:

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Answer:

1/2

Step-by-step explanation:

total of the pockets

= 8

the probability

= 4/8

= 1/2

Answer:

Answer:

12

Step-by-step explanation:

a coin has two possibilities: Head and Tales

a die has six possibilities: 1, 2, 3, 4, 5, 6

2x6=12

Answer:

D) all are true

I think it's helps you

Answer:

Step-by-step explanation:

Since this is a 2 variable equation system we will find the values of x & y by equaization.

x-5=-7x+11

x+7x=11+5

8x=16

x=16/8

x=2

Please mark brainliest.

nvm there is the right answer

Answer:

The length is 23 inches and the width is 6 inches.

Step-by-step explanation:

The perimeter for a rectangular shape is represented as:

P = 2L + 2W, where L represents length and W represents width

We can represent the length as:

L = 3W + 5

Substituting this into the perimeter function, we get:

P = 2 (3W + 5) + 2W

Substituting 58 for P, we get:

58 = 2 (3W + 5) + 2W

58 = 6W + 10 + 2W

58 = 8W + 10

58 - 10 = 8W + 10 - 10

48 = 8W

48 / 8 = 8W / 8

6 = W

With 6 being the established value for the width, we can substitute this back into the equation for length:

L = 3W + 5

L = 3(6) + 5

L = 18 + 5

L = 23

To check our work, we can substitute both the width and length into the perimeter equation:

P = 2L + 2W

58 = 2(23) + 2(6)

58 = 46 + 12

58 = 58

Therefore, length is 23 inches and the width is 6 inches.

Answer:

465.4

Step-by-step explanation:

mean=sum of all values/umber of vales

      =506+ 635 +345 +344+ 633 +344+359+ 536 +470+ 482 ​ /10

      =4654/10

   mean   =465.4

Answer:

C

Step-by-step explanation:

The range is all the (y) values the function could have. The function's left end approaches negative infinity, while the right end approaches the asymptote of the function, y = 2.

So, the range is -∞ < y < 2. The answer is C.

I hope this helps :]

The range of the function is option (C) -∞ < y < 2 is the correct answer.

The range is the set of possible output values, which are shown on the y-axis. The range of a function, f is the set of all values f(x) , such that x is in the domain of f. Graphically speaking, the range is the set of all y such that (x,y) is a point on the graph of f .

For the given situation,

The graph shows the function that is plotted on x-y axis.

The curve of the function tends from x-axis beyond infinity.

It bends at y = 2 and moves towards y-axis beyond infinity.

Hence we can conclude that the range of the function is option (C),        -∞ < y < 2 is the correct answer.

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Answer:

B. 8x² + 18x - 5

Step-by-step explanation:

(2x + 5)(4x - 1)

Use the distributive property to multiply 2x + 5 by 4x - 1.

8x² - 2x + 5(4x) + 5(-1)

8x² - 2x + 20x - 5

Combine 20x and -2x to get 18x.

8x² + 18x - 5

The expression for the area of the rectangle is 8x² + 18x - 5, which is B.

Answer:

10x lmboooo

Step-by-step explanation:

combine like terms

Answer:

10x.

Why? Well because 4 + 6 = 10. And since they both are x values the sum is 10x.

Step-by-step explanation:

Hope that this helps! :)

Have great rest of your day/night!

Answer:

No. They will not have the same amount of money.

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 3.875/100

r = 0.03875 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 10,000.00(1 + 0.03875/12)(12)(7.5)

A = 10,000.00(1 + 0.003229167)(90)

A = $13,366.37

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 3.875% per year compounded 12 times per year over 7.5 years is $13,366.37. Therefore, they cannnot save the same amount.

Answer:

You have to use the equation F=ma.

F: the force an object has (in this case the unknown)

M: the mass an object has (in this case 1000kg)

A: the acceleration an object has (in this case 5m/s^2)

when you plug in everything you should get F=5000N

Answer:

The answer is 5000 N (Newtons).

Explanation:

F=M*A

F=1000 kilograms * 5 m/s squared

F=5000 Newtons

Answer:

B) 666.6 miles per hour

Step-by-step explanation:

To solve this question, divide the 4000 miles with the 6 hours to get an answer in units of X miles per hour.

4000 miles/6 hours = 666.6 miles per hour

Answer:

this is answer$10,000$1o,5oo ok

Answer: point b

Step-by-step explanation:

eatch mark on the line is 0.1, b is right behind the 8.6 mark in the middle making it 8.65

Answer:

The answer is point b.

Step-by-step explanation:

Answer:

there is 243.84 cm in 8 feet

round to the nearest hundredths =3266.53

Answer:

36

Step-by-step explanation:

2(4.5*3)=13.5

2(3+7.5)=22.5

13.5+22.5=36

Answer: I think it’s 30 you can do it yourself by drawing a rectangle and then multiplying the Length times width

Step-by-step explanation:

Answer:

The Wildebeest

Step-by-step explanation:

I’m guessing

Answer:

Correct answer is a

Step-by-step explanation:

Answer:

(x - 9)² + y² = (√5)² = 5

Step-by-step explanation:

Start with the standard equation of a circle with center at (h, k) and radius r:

(x - h)^2 + (y - y)^2 = r^2

Now substitute 0 for k, 9 for h and √5 for r:

(x - 9)² + (y - 0)² = (√5)², which simplifies to:

(x - 9)² + y² = (√5)² = 5

Answer:

4x/3-2

-x/2 +5

this are the answers

Answer:

The Answer is C

Answer:

step by step is kid cause it sounds cool

Step-by-step explanation:

so therefore the answer is kid

Answer:

Step-by-step explanation:

5x-4<4(1+x)

5x-4<4+4x

5x-4x<4+4

x<8

Answer:

168.964706 miles

Step-by-step explanation:

Turn the info into a equation: 159.57 = .85x + 15.95

Solve for x (miles)

159.57 = .85x + 15.95

143.62 = .85x

x = 168.964706