Dr. Banner monitored the decay of a new type of recyclable material he developed for his
gamma radiation study. He noted that the decay of the material could be modeled by the
function f(x) = 100(0.98). What is the rate of decay of Dr. Banner's material?
Answers
Answer:
The rate of decay is: [tex]2\%[/tex]
Step-by-step explanation:
Exponential functions are modeled by:
[tex]f(x) = a(b)^x[/tex]
Where [tex]a[/tex] is the y-intercept and b is the growth or decay constant. If [tex]b[/tex] is less than one, the function decays. If [tex]b[/tex] is greater than 1, the function grows.
To calculate the percentage, subtract [tex]b[/tex] from 1:
[tex]\% = 1 - b\\\% = 1 - 0.98\\\% = 0.02[/tex]
Multiply the result by 100 to get the percentage.
[tex]0.02 * 100 = 2\%[/tex]
Related Questions
Thomas drive from junction 2 to junction 3 on a road . The distance between the junctions is 12 miles and it takes 15 minutes. Hanna also drove from junction 2 to junction 3 on the road. She drove at an average speed of 50 mph . Who has the faster speed. Explain
Answers
Answer:
Hanna
Step-by-step explanation:
In order to find out how fast Thomas has drove as compared to Hanma we have to compare the speed of each other,
Speed of Hanna = 50mph (as given in ur question)
Speed of Thomas
Since the unit of time of the distance traveled by Thomas is not same as that of Hanna we have to convert the minutes into hour,
Distance traveled = 12miles
Time taken = 15minutes
Speed = 12miles/15mim
Converting minutes into hours we have to multiply by a number whose product will be 60 and that will 4
that is 15 times 4 is 60. But to make the ratio equal
we have to multiply the distance too by 4.
= 12*4/15*4
=48 miles/60minutes
=48miles/1hour
=48mph
Comparing both speeds
Speed of Hanna compared to Speed of Thomas,
50mph > 48mph
Hence, Hanna has the faster speed.
Moses is creating a large cube sculpture for a city park. He first makes a smaller cube to use as a rough model of his sculpture. The edge lengths of the model are each 25 in. The edge lengths of the sculpture will be 3 times the model's edge lengths. How many times as large is the volume of the sculpture than the volume of the model? Show your work.
Answers
From the calculations, the volume of the sculpture is 27 times the volume of the model.
Volume of a cubeThe volume of a cube is obtained using the formula;
Volume = l^3
Where l is the length of each edge. We should note that the lengths of all the edges in a cube are equal.
Hence,
volume of the model = (25)^3 = 15625 in^3
volume of the sculpture = (3 * 25)^3 = 421875 in^3
Ratio of the volume of the sculpture to the volume of the model = 421875 in^3/15625 in^3
= 27:1
Hence, the volume of the sculpture is 27 times the volume of the model.
Learn more about volume: https://brainly.com/question/12908738
What is the probability for blue or yellow (be sure to simplify)?
Answers
Answer:
Step-by-step explanation:
No of red marbles=n(A)=3.Total no of marbles=n(s)=3+2+5=10.Probability,p(A)=n(A)/n(s)
4.1: Angle Articulation
Triangle A'B'C' is a dilation of triangle ABC using center P and scale factor 2.
1. What do you think is true about the angles in A' B'C' compared to the angles in ABC?
2. Use the tools available to figure out if what you thought was true is definitely true for
these triangles.
3. Do you think it would be true for angles in any dilation?
Answers
1.) The measure of each angle of ABC is equal to the corresponding angle of A'B'C' , the measures of this angle is preserved when you rotate the triangle.
2.) It was clear that triangle A'B'C' is dilated form ABC, meaning the angles will be the same.
3.) The rules for dilation only change the length of the triangle not the angles.
Kiran is going to see a movie and is taking his 3 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $4. 50 each. How much total money would Kiran have to pay for his family if he were to buy 4 snacks for everybody to share? How much would Kiran have to pay if he bought xx snacks for everybody to share?
I will give brainlist plsssss I need helppp
Answers
Answer: I only have the first answer sorry. The 1st answer is $13.50
Step-by-step explanation:
I multiplied $4.50 by the 3 kids and got $13.50 for the snacks.
Using the table, if there are 5 flowers, how many petals are there?
A) 11
B) 6
C) 30
D) 25
Answers
Answer:
i think is 25
Step-by-step explanation:
you dont have no diagram but i think it 5x5=25
Please help me! I need to figure it out
Answers
[tex]Q_3-Q_1=Q_i[/tex]Answer:
The answer is 10. Frank has done more than Marquis by10.
Step-by-step explanation:
From the internet, the interquartile is Q_3-Q_1=Q_inter
From Marquis his Q_3 = 40 and Q_1 = 20
[tex]Q_3-Q_1=Q_i[/tex]
40-20=20
From Frank his Q_3 = 40 and Q_1 = 10
[tex]Q_3-Q_1=Q_i[/tex]
40-10=30
Frank's interquartile is 30 and Marquis interquartile is 20.
Differences between the both of them.
30-20=10
Point A is located at (-2, -3). After it is transformed, point A' is located at (-2, 3).
How was the point transformed?
It was reflected in the y-axis
it was rotated 180°
it was rotated 90 around the origin
it was reflected in the x-axis
Answers
Answer:
D.Step-by-step explanation:
All the other answers are wrong.
The points are reflected across the x-axis.
Here is why:
Point A is at (-2, -3)Point A' is located at (-2, 3)If you move across the x-axis in this form, you will see that they are reflected.Correct choice is D.
I need to know the of the blue line
Answers
Step-by-step explanation:
if i pick (3,4) and (6,10)
the formula for gradient is difference in y divided by difference in x . therefore
10-4 divided by 6 - 3 equals to 6 divided by 3 = 2
the gradient is 2
URGENT
What will five 100's do to a grade of 92%? How many points will it bring my grades up by?
Answers
Answer:
See below ~
Step-by-step explanation:
Given
Mean = 92%Solving
Add 5 points of 100% and divide by 6 (total entries)92 + 5(100) / 6592/698.67%Solution
Five 100s will bring up the 92% up by 6.67% to 98.67%Help will name Brainliest
Answers
Answer:
x = 5
Step-by-step explanation:
using the sine or cosine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 10 ( divide both sides by 2 )
x = 5
Subtract.
3x−5x−4−x2+12x−17x2−16
Answers
Step-by-step explanation:
3x - 5x - 4 - x^2 + 12x - 17x^2 - 16
= -2x - 20 - 18x^2 + 12x
= 10x - 20 - 18x^2
Hope it helpz~ uh..
Factor the expression 25x² - 36.
O A. (5x²-6)(5x² + 6)
B. (5x-6)²
O C. The expression is already fully factored.
OD. (5x-6)(5x + 6)
Answers
One number is 1 less than three times another number. if the product of the two numbers is 102, find the number
Answers
Answer:
25.25
Step-by-step explanation:
3y-1 (y) = 102
4y-1 = 102
4y = 101
y = 25.25
Which expression is equivalent to 10x2y 25x2? 5x2(2y 5) 5x2y(5 20y) 10xy(x 15y) 10x2(y 25)
Answers
GCF is the highest value that can divide an expression. The equivalent expression to 10x^2y + 25x^2 is 5x^2 (2y + 5)
Factoring polynomial expressionsGCF is the highest value that can divide an expression. Given the expression below
10x^2y + 25x^2
Find the factor of each
10x^2y = 5 * 2 * x^2 * y
25x^2 = 5 * 5 * x^2
Since 5x^2 is common to both factors, hence
10x^2y + 25x^2 = 5x^2 (2y + 5)
The equivalent expression to 10x^2y + 25x^2 is 5x^2 (2y + 5)
Learn more on factoring here: https://brainly.com/question/24734894
A right triangle has one leg that is 12 units long and a hypotenuse that is 15 units long. Find the length of the other leg.
Answers
Answer:
9
Step-by-step explanation:
let's assume ;
12=a
15=c
?=b
so;
a2+b2=c2
(12)2+b2=(15)2
144+b2=225
b2=225-144
b2=81 (square root both sides)
You'll get
b=9
NB; 2 is used as squared
Answer:
ITS 9
Step-by-step explanation:
Trust me i just finished the quiz (credit to dude on top)
What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest
form.
1/1/2 1/1/2 2ft
Answers
Answer:
[tex]\text{the volume of the prism =} \ 4\frac{1}{2} \ ft^3[/tex]
Step-by-step explanation:
Formula _____________________
the volume of a prism = base × height
================================
[tex]\text{base\ =} \ 2\times 1\frac{1}{2} =2\times \left( 1+\frac{1}{2} \right) =2\times \left( \frac{3}{2} \right) =3[/tex]
[tex]\text{the volume of the prism =} \ 3\times \left( 1\frac{1}{2} \right) =3\times \left( \frac{3}{2} \right) =\frac{9}{2} =4\frac{1}{2}[/tex]
Bobby spent $12 at the football game Friday night. He spent $2 on nachos, $5 on drinks, $3 on popcorn, and $2 on candy. What percentage of Bobby's expenses do the nachos and candy represent?
Answers
Answer:
33.3%
Step-by-step explanation:
$2 on nachos and $2 on candy will get you $4 spent on them both.
You then have a fraction (4/12)which is 1/3.
1/3=33.3%
Explanation: he spent 4$ on nachos and candy, over a total of 24. The fraction turns into 1/5 which as a percentage is 20%
The area of a computer screen is 108 in with a side length of 12. What is the area of a tv screen similar to the computer screen with a side length of 20 in?
Answers
Answer:180in squared
Step-by-step explanation:
108 divided by 12 is 9, so 20*9= 180
look how he has proved that
infinity is equal to 0
how please help me please please please please
Answers
Answer:
false
Step-by-step explanation:
as a guy who studied calculus, a lot of things were done that are just mathematically incorrect. for instance,
infinity - infinity is not 0.
0÷0 is undefined. so you cant just equate it to ( 2 × infinity)
to sum up this proof is entirely false.
if you still have any doubts make sure to ask.
Answer:
Refer to the attachment .
_______
Hope it helps ⚜
Allison and Amir are working on a school project together. Allison will do 3/4 of the research, and Amir will do the rest. Amir can do 1/8 of the research in an hour. How long will it take amir to complete his research
Answers
Answer: 2hours
Step-by-step explanation:
Allison does 3/4 and Amir does 1/4
Amir can do 1/8 in 1hr, how long will it take to complete ¼ work
1/4 ÷ 1/8 =2
Which of the following is most likely the next step in the series?
:
⠀⠀⠀
OA.
OB.
O C.
OD.
Answers
The most likely next step in the series is 5 rows with 4 dots in each row and 4 columns.
Option C is the correct answer.
What is a series of patterns?A series of patterns is a sequence of recurring designs or motifs that follow a particular order or progression.
Patterns can be found in many different fields, such as mathematics, science, art, and literature.
We have,
From the series of patterns,
We see that,
In the first pattern, there are 3 rows with 2 dots in each row and 2 columns.
In the second pattern, there are 4 rows with 3 dots in each row and 3 columns.
This means,
In the third pattern, there must be 5 rows with 4 dots in each row and 4 columns.
Thus,
The most likely next step in the series is 5 rows with 4 dots in each row and 4 columns.
Learn more about series of patterns here:
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Please help I'll give Brainliest and Thanks. its also due in 15 minutes.
Simplify: -1║2/3 - 4║ ÷ 5/6
║means an absolute value line.
A. -4
B. -25/9
C. 25/9
D. 4
Answers
Answer:
A or -4
Step-by-step explanation:
simplify to -1 || -10/3 || × 6/5
-1 × 10/3 × 6/5
-1 × 2 × 2
Please help, I need this quickly. It's an easy trigonometric question.
Answers
OPTION D: None of these
[tex]\bold{EXPLANATIONS:}[/tex]
Answer:c x=13
Step-by-step explanation:
straight line =180
180-50=130
7x+3x=10x
130/10=13
So the answer is x=13
how many groups of 7 does it take to make 7 tens
Answers
Answer:
It takes 10 groups of 7 to make 7 tens
Step-by-step explanation:
I’m smart
8 cm 11 cm 14 cm volume
Answers
Answer:
410.7 cm^3
Step-by-step explanation:
volume = (l*w*h)/3
volume = (14*8*11)/3
volume = 410.667
The work of a student to solve the equation 3(3x − 4) = 8 + 2x + 5 is shown below: Step 1. 3(3x − 4) = 8 + 2x + 5 Step 2. 6x − 7 = 13 + 2x Step 3. 6x − 2x = 13 + 7 Step 4. 4x = 20 Step 5. x = 5 In which step did the student first make an error and what is the correct step? (1 point) Step 2, 9x − 12 = 13 + 2x Step 2, 9x − 4 = 2(6 + x + 3) Step 3, 6x + 2x = 13 + 7 Step 3, 6x − 2x = 13 − 7
Answers
Answer:
(a) Step 2. 9x -12 = 13 +2x
Step-by-step explanation:
The distributive property says a factor outside parentheses multiplies each term inside parentheses. It is an error to do addition of the factor, or to miss multiplying a term.
In Step 2 of this "solution", the factor of 3 is erroneously added to each coefficent inside parentheses. It should be multiplied.
Correct Step 2: 9x -12 = 13 +2x
__
The rest of the solution should be ...
Step 3: 9x -2x = 13 +12
Step 4: 7x = 25
Step 5: x = 25/7
___
Check
3(3(25/7) -4) = 8 + 2(25/7) +5
3((75 -28)/7) = 13 +50/7
141/7 = 141/7 . . . . . answer checks OK
What is the solution of the system? Solve using matrices. 25 points
x+2y=9
x+y=1
Answers
Answer:
x = -7 and y=8Step-by-step explanation:
solnusing by elimination method 1|x+2y=9 1| x+y=1 |x+2y=9 -|x+y=1 x-x+2y-y=9-1 0+y=8 y=8 1|x+2y=9 2|x+y=1 |x+2y=9 -|2x+2y=2x-2x+2y+2y=9-2-x=7divide -1 both side with the make value of xx=-7therefore x=-7 and y=8. this is my answerPlease help!! Will mark brainlyest.
Answers
Answer:
C. the X coordinates will increase by 2.Step-by-step explanation:
Here are the examples:
If a X coordinate moves 2 spaces to the left, then it will decrease.If a X coordinate moves 2 spaces to the right, then it will increase.In this case, a X coordinate will increase by 2.
Correct choice is C.
If 3 cups of sugar are used to make 12 cupcakes, how many cups of sugar are used to make 30 cupcakes
Answers
Answer:
7.5 cups of sugar
Step-by-step explanation:
3 cups /12 cupcakes * 30 cupcakes = 7.5 cups