Answer:
4(x + 8) is equivalent to 4x + 32, 4x + 8(4),
2(2x + 16)
Step-by-step explanation:
4(x + 8)
4 × x + 4 × 8
4x + 32
Thus, 4(x + 8) is equivalent to 4x + 32, 4x + 8(4),
2(2x + 16)
-TheUnknownScientist
The function N(t) = 100e^−0.023t models the number of grams in a sample of cesium-137 that remain after t years. On which interval is the sample's average rate of decay the fastest?
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:
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Brandon just bought a new coffee table. The length of the coffee table is 5 more than 3 times the width. If the perimeter of the coffee table top is 58 inches, what is the length and width of the coffee table?
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.
5x-4<4(1+x) what is the answer and how do you do it
Answer:
Step-by-step explanation:
5x-4<4(1+x)
5x-4<4+4x
5x-4x<4+4
x<8
Charles inherited $500,000 from his grandfather. He decides to invest the money into a fund that has 4% annual interest. If the interest is compounded continuously, what is the total amount that is compounded annually?
Answer:
this is answer$10,000$1o,5oo ok
Sally has a car that accelerates at 5 m/s^2. If the car has a mass of 1000 kg, how much force does the car produce?
F=______
m=______
a=______
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
Select the correct answer.
What is the range of the function graphed below?
A. -∞ < y < -2
B. -∞ < y < ∞
C. -∞ < y < 2
D. -2 < y < ∞
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.
What is the range of a function?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.
Learn more about graph of a function here
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Which point is located at -8.65?
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:
Student A starts with $100 in the bank and makes $5 a day. Student B starts with $50 and makes $7 a day. Assuming the students save their money, when will they have the same amount of money ?
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.
The American antelope (pronghorn) and the wildebeest are among the fastest mammals on the planet,
particularly at running long distances. The maximum recorded speed for the antelope is 88.5 km/h, which it
can sustain for nearly one kilometer.
On the other hand, the distance, d, in kilometers that the wildebeest can run in t hours is given by the equation
d=80.5t
Assuming both animals are running at constant speeds, which animal can run faster?
Choose 1 answer:
The American antelope
B
The wildebeest
They can run at the same speed.
Answer:
The Wildebeest
Step-by-step explanation:
I’m guessing
Answer:
Correct answer is a
Step-by-step explanation:
If a coin and a is die is rolled at same time how many outcomes are possible? Please help me
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
Make “a” the subject of the following formula
y + az = z
Giving brainliest show work pls ! Ty
Answer:
1/2
Step-by-step explanation:
total of the pockets
= 8
the probability
= 4/8
= 1/2
Three students, Brayden, Adrian, and Aubrey, line up one behind the other. How many different ways can they stand in line?
Please help me please please
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:
Write the equation of the line shown in the graph below
Can someone please help both of these
Answer:
4x/3-2
-x/2 +5
this are the answers
Can you please help me
nvm there is the right answer
Find an expression for the area of the rectangle. Write your answer in standard form.
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.
OMG PLEASE HELP YOUR BOY OUT I NEED TO GET THIS ONE RIGHT TO PASS THE TEST!!!
Which of the following rational functions is graphed below?
A. F(x) = (x - 1)/((x + 2) ^ 2)
B. F(x) = (x + 1)/((x + 3)(x - 2))
C. F(x) = (x - 1)/(x(x - 3))
D. F(x) = (x - 1)/(x(x + 2)) O
Answer:
The Answer is C
What speed would a plane average on a trip
of 4000 miles that took 6 hours?
(A) 150.0 miles per hour
(B) 666.6 miles per hour
(C) 366.6 miles per hour
(D) 1500.0 miles per hour
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
Enter the equation of the circle with the given center and radius.
Center: (9, 0)
radius: √5
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
y= x - 5
y=-7x + 11
Cherry
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.
There are two bags containing only purple and yellow marbles. Bag A has yellow marbles and purple marbles. Bag B has yellow marbles and purple marbles. A marble is randomly chosen from each bag. List these events from least likely to most likely. Event : choosing a purple marble from Bag B. Event : choosing a yellow or purple marble from Bag A. Event : choosing a red marble from Bag B. Event : choosing a yellow marble from Bag A.
Work out the size of angle A.
A
11 cm
9 cm
38°
B
С
what’s the area besties?
Answer:
36
Step-by-step explanation:
2(4.5*3)=13.5
2(3+7.5)=22.5
13.5+22.5=36
can guys help me please
Answer:
there is 243.84 cm in 8 feet
round to the nearest hundredths =3266.53
Please anwser this question.
Answer:
step by step is kid cause it sounds cool
Step-by-step explanation:
so therefore the answer is kid
What is the answer to the problem 4x + 6x
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!
Which of the following is/are correct in the case of free fall motion?
(I) Free fall is a linear motion.
(II) Free fall is a uniformly accelerated motion.
(III) Free fall is a motion under gravity alone.
A) I and II
B) I only
C) II only
D) I, II, and III
Answer:
D) all are true
I think it's helps you
Greg rented a truck for one day. There was a base fee of $15.95, and there was an additional charge of 85 cents for each mile driven Grey had to pay $159.57
when he returned the truck For how many miles dhe drive the truck
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
The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores are shown below. Find the mean score.
506 635 345 344 633
344 359 536 470 482
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