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 average rate of change :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:
https://brainly.com/question/20884505
Julio's family traveled 3 8 of the distance to his aunt's house on Saturday. They traveled 3 5 of the remaining distance on Sunday. What fraction of the total distance to his aunt's house was traveled on Sunday?
Answer: [tex]\dfrac{3}{8}[/tex]
Step-by-step explanation:
Given
Julio traveled [tex]\frac{3}{8}[/tex] of distance to his aunt's house on Saturday
they have traveled [tex]\frac{3}{5}[/tex] of the remaining distance on Sunday
suppose the total distance is [tex]x[/tex]
Distance traveled on Saturday
[tex]\dfrac{3x}{8}[/tex]
Remaining distance is
[tex]x-\dfrac{3x}{8}=\dfrac{5x}{8}[/tex]
Distance traveled on Sunday
[tex]\Rightarrow \dfrac{3}{5}\times \dfrac{5x}{8}=\dfrac{3x}{8}[/tex]
The fraction of distance traveled on Sunday is
[tex]\Rightarrow \dfrac{\frac{3x}{8}}{x}=\dfrac{3}{8}[/tex]
What is the equation of the line that passes through the point (5, -2) and has a
slope of -2/5
Answer:
y=-2/5x
Step-by-step explanation:
y-y1=m(x-x1)
y-(-2)=-2/5(x-5)
y+2=-2/5(x-5)
y=-2/5x+10/5-2
y=-2/5x+2-2
y=-2/5x
Which of the following is true?
Swing Company
A -1 > 3
B -26 > -14
C -20 < 0
D 9 < -7
Answer:
C..... I think it is a answer
How would you begin to plot the ordered pair ( 6,2)?
an expression that is equivalent to 60x+28y.
Answer:
Step-by-step explanation:
The trick here is to identify the greatest common factor of 60 and 28. 4 is such a factor. We can therefore rewrite 60x + 28y as
4(15x + 7)
There are other possible answers.
600x + 280y
------------------- is an example.
100
Simplify: (16-5)-9 x 1 A. 5 B. 2 C. 4 D. 3
Answer:
B it right...
Step-by-step explanation:
Answer: B 2
Step-by-step explanation:
16 - 5 = 11
11 - 9.1 = 2 option B
Find x. Round to the nearest tenth and only type the number for your
answer.
25
X
16
22
Answer:
10.7
Step-by-step explanation:
To find x we have to basically do pythagoream theorem twice. Both the traingles share the same long side. The find the long side of the top traingle do, [tex]a^{2} +16^{2} =25^{2}[/tex], and we find the long side to be [tex]\sqrt{369}[/tex]. Using this we now plug it into the pythagoream theorem for the bottom triangle. [tex]\sqrt{369} ^{2} +x^{2} =22^{2}[/tex], and doing this out we find that x=[tex]\sqrt{115}[/tex] or about 10.7.
A farmer plants the same amount every day, adding up to 134 acres at the end of the year. If the year is 12 over, how many acres has the farmer planted?
fAnswer:
1608 acres
Step-by-step explanation:
total acres planted in 12 years = acres planted per year x number of years
134 x 12 = 1608
Answer:
5/6
Step-by-step explanation:
1 2/3 x 1/2 = 5/6
Please answer correctly! I will mark you as Brainliest!
Answer:
56.5 in
Step-by-step explanation:
Answer:
56.5 in³
Step-by-step explanation:
I wrote out the work in the file below:
Find the shaded angle
Answer:
332°
Step-by-step explanation:
Given is an isosceles triangle,
Measures of base angles of an isosceles triangle are equal.
Therefore,
Measure of central angle
= 180° - ( 76° + 76°)
= 180° - 152°
= 28°
Measure of shaded angle
= 360° - 28°
= 332°
USING YOUR MATH
5. A circular swimming pool has a diameter of 22 feet. A cover that just fits over the top of the
pool would have an area that is closest to which of the following?
(1) 69 sq.ft
(3) 732 sq.ft
(2) 380 sq.ft
(4) 1,521 sq.ft
Answer:
[tex]area = \pi {r}^{2} \\ = \frac{22}{7} ( { \frac{22}{2} )}^{2} \\ = 380 \: sq \: feet[/tex]
What is the vertex for y= 4 (x-2)^2 +3
Please helpp ASAP
100 points extra and brainleist
Step-by-step explanation:
C and D are the correct objectives
Drag each label to the correct location on the tree diagram. Each label can be used more than once, but not all labels will be used.
Brandon is making party decorations by selecting one of two kinds of balloons—heart-shaped balloons or oval-shaped balloons. He puts them in one of three baskets—red, pink, or white. The sample space for the event of selecting a balloon and putting it in one of the baskets is represented in the tree diagram. Complete the sample space.
oval
red
white
pink
Answer:
He is 100% right
Step-by-step explanation:
Subtract one-third from 8 times b
i think the answer is 1/3 from 8x 6 =-46.7 i think
Simplify 3/8 squared
Answer:
9/64
Step-by-step explanation:
3 x 3 is 9 and 8 x 8 is 64 and this fraction cannot be simplified
In a quiz contest, Mary answers 90% of the questions correctly without any additional clues from the quiz coordinator. The randomly generated numbers below simulate this situation.
The numbers 0 to 8 represent questions answered correctly without additional clues, and the number 9 represents questions that needed additional clues.
44 51 99 66 23
68 72 20 20 59
50 89 39 36 20
90 13 51 47 92
49 20 89 10 13
52 82 52 52 99
28 10 33 35 73
40 44 30 95 22
99 10 55 10 35
36 78 92 37 96
The estimated probability that it would take at least three questions for Mary to need additional clues is (_____)
The estimated probability that Mary needed additional clues to answer two consecutive questions is (_____)
To solve this problem, we should note that there are:
total questions = 100
questions answered correctly = 90
questions that needed additional clues = 10
1. The first question is to find the probability that in the third question, Mary would need additional clue. Therefore this implies that in the first and second questions, Mary would answer it correctly. Therefore:
Probability = (question 1 answered correctly) * (question 2 answered correctly) * (question 3 needed clue)
Probability = (90/100)*(89/99)*(10/98)
Probability = 0.08256 = 8.26%
2. The second question finds for the probability that two consecutive needs additional clue, therefore:
Probability = (question 1 needed clue) * (question 2 needed clue)
Probability = (10/100)*(9/99)
Probability = 9.1*10^-3 = 0.91%
Answer:
1. The estimated probability that it would take at least three questions for Mary to need additional clues is 0.24
2. The estimated probability that Mary needed additional clues to answer two consecutive questions is 0.06
Step-by-step explanation:
I just took the test! I hope this helps you! <3
Which speeds are equal to 1/2 mile per hour? Mark all that apply.
5/6 mile/5/12 hour
1/4 mile / 1/2 hour
1/10 hour / 1/5 mile
3/8 mile / 3/4 hour
2/3 hour / 1/3 mile
4/5 mile / 4/10 hour
/
answer :
3/8 mile / 3/4 hour
Help Me Please
The interior angles formed by the sides of a quadrilateral have measures that sum to 360°.
What is the value of x?
Answer:
x = 59
Step-by-step explanation:
combine all four angle measure expressions and set equal to 360°, then solve
x + x + 2x + 3 + 2x + 3 = 360
6x + 6 = 360
6x = 354
x = 59
A triangle has an area of 230.86 square inches. The height of the triangle is 23.8 inches. What is the length of the base of the triangle?
I'll give brainlist!! Pls help
Answer:
Length of the base of the triangle = 19.37 inch (Approx.)
Step-by-step explanation:
Given:
Area of given triangle = 230.56 square inches
Height of the triangle = 23.8 inches
Find:
Length of the base of the triangle
Computation:
Area of triangle = (1/2)(b)(h)
Area of given triangle = (1/2)(Length of the base of the triangle)(Height of the triangle)
230.56 = (1/2)(Length of the base of the triangle)(23.8)
461.12 = (Length of the base of the triangle)(23.8)
(Length of the base of the triangle)(23.8) = 461.12
Length of the base of the triangle = 19.37 inch (Approx.)
What is the horizontal asymptote of the function f (x)= x^2-25/2x^2 ?
Help pls I’ll give brainleist.
Answer:
Step-by-step explanation:
C and E look good Dani
help me find the cube of 1000
Answer:
10 X 10 X 10
Step-by-step explanation:
if thts what you talking aboyt
from the Deck of 52 cards is drawn at a random . what is the probability of a face card or ace ?
Step-by-step explanation:
Given that,
Total no. of cards = 52 (Total no. of outcomes)
There are 12 face cards. No of favorable outcomes = 12
P(E) = favorable outcome/total no of outcomes
So,
[tex]P(F)=\dfrac{12}{52}\\\\=\dfrac{3}{13}[/tex]
There is 4 ace in a deck of 52 cards.
[tex]P(A)=\dfrac{4}{52}\\\\=\dfrac{1}{13}[/tex]
Hence, this is the required solution.
Scores on a test are normally distributed with a mean of 200 and a standard deviation of 12. Find each probability
Complete question is;
Scores on a test are normally distributed with a mean of 200 and a standard deviation of 12. Find the probability that a randomly selected student scored less than 218.
Answer:
0.93
Step-by-step explanation:
We are given;
Mean; μ = 200
Standard deviation; σ = 12
Random value; x¯ = 218
Z-score formula is;
z = (x¯ - μ)/σ
z = (218 - 200)/12
z = 18/12
z = 1.5
From z-table, attached, probability = 0.93
The store has 6 blue notebooks, 11 red notebooks, 7 purple notebooks, 5 black notebooks, and 3 green notebooks. What is the probability that Melissa will buy a purple notebook?
7/25
7/32
3/16
11/32
Answer: 7/32
Step-by-step explanation:
Answer:
7/32
Step-by-step explanation:
i did the test and got it right
PLEASE HELP
consider the function f(x)=3x+10
Factor x^3 +5x^2- 24x
Step-by-step explanation:
(−3)(+8)
Nathan started out on a road trip with his friend Ryan. Nathan picked Ryan up at his house and they started out. Nathan kept track of the distance he was from his house, d, after h hours of driving in the chart below.
Hours
2
4
6
10
Distance
114
224
334
554
How fast were the boys traveling? Be sure to give the correct units. "Show your work."
Answer:
57 mph
Step-by-step explanation:
Half of 114=57.
HELP ME NOW PLS WBAHS
Answer:
8
Step-by-step explanation:
you would add 1+3+4
Answer: The answer is 12
Step-by-step explanation: 4 x 3 x 1 just multiply all the number together