A scientist has a sample of the radioactive isotope bismuth-212. The isotope decays exponentially as shown in the table. Time (seconds) Mass (grams) 10 26.8 20 23.9 30 21.3 40 19.0 50 16.9 60 15.1 Which equation best represents the curve of best fit for this set of data? A. f(x) = 29 • 0.989x B. f(x) = 27 • 1.011x C. f(x) = 30 • 0.989x D. f(x) = 28 • 0.234x

Answers

Answer 1

Answer:

f(x) = 30 • 0.989x

Step-by-step explanation:

Given the data :

10 26.8

20 23.9

30 21.3

40 19

50 16.9

60 15.1

Using technology, the exponential model equation obtained by plotting the data is :

y = 30.068(0.989)^x

Based on the general exponential formula :

y = ab^x

y = predicted value

Initial value, a = 30.068

Rate = b = 0.989

The most appropriate model equation from the options given is :

f(x) = 30 • 0.989^x


Related Questions

Question
Solve the inequality b – 27 > 3 and write the solution in interval notation, using improper fractions if necessary.

Answers

Answer:

(30, ∞)

Step-by-step explanation:

b – 27 > 3

Add 27 to both sides

b > 30

In interval notation

(30, ∞)

Answer:

(30,∞ )

Step-by-step explanation:

b> 27+3

b> 30

After ordering the data set, what is the next step in drawing a box plot that shows the distribution of the amounts spent? 1. Make a dot plot for comparing. 2. Find the five boundary values. 3. Write a title for the box plot. 4. Plot and connect the end points.

Answers

Answer:

2. Find the five boundary values

Step-by-step explanation:

When drawing a dot, the steps are;

i) The data set (the list of numbers to be presented in the dot plot) are arranged in increasing order from left to right, with thee lowest value on the left and the highest value located at the right of the list

ii) The five boundary values are listed as follows;

The Minimum and Maximum Values

1) The minimum value is the lowest number in the list, which is the first number from the left

2) The maximum value is the final number on the right of the list

3) The Median, Q₂

The median number is the number which divides the data arranged in increasing number, into two equal parts

The First Quartile and Third Quartile

The numbers are divided from the median, such that the Lower half is to the left of the Median, and the Upper half is to the right of median

4) The First Quartile, Q₁ = The median of the Lower half

5) The Third Quartile, Q₂ = The median of the Upper half

iii) The box plot is then drawn with the five boundary values found above

Mr. K needs to hire an electrician. The electrician charges $82 for making a house call and an additional $55.00 per hour of labor. If Mr. K only budgeted $300 for the electrical repair, write, solve, and graph an inequality that shows the maximum amount of hours of labor Mr. K can afford to hire the electrician.

Answers

Answer:

[tex] \displaystyle4 \: \text{hours}[/tex]

Step-by-step explanation:

we are given that,

The electrician charges $82 for making a house call an additional $55.00 per hour of laborMr. K only budgeted $300 for the electrical repair

let the hours be h

from the first condition we obtain:

[tex] \displaystyle 82[/tex]

from the second condition we ge:

[tex] \displaystyle 82+ 55h[/tex]

from the final condition we acquire:

[tex] \displaystyle 82 + 55h \leqslant 300[/tex]

to figure out the hour we have to solve the equation to do so

cancel 82 from both sides:

[tex] \displaystyle 55h \leqslant 215[/tex]

divide both sides by 55:

[tex] \displaystyle h \leqslant 3.9636 \dots[/tex]

since 3.96.... is very close to 4 he can maximum afford 4 hours of labor

[tex] \displaystyle h = 4[/tex]

refer the attachment

Help plz..And No links!! I repeat No links!!

Answers

Answer:

5 more wheelbarrows

Step-by-step explanation:

10-5

The incomplete Venn diagram below shows the number of students in a class of 28 who play football and tennis. U F x T U = {all students in the class} F = {students who play football} T= {students who play tennis} Additional information about the class is that 12 students play tennis 15 students play football 8 students play ncither football nor tennis r students play BOTH football and tennis. (1) Complete the Venn diagram above to represent the information, showing the number of students in EACH subset. (3 marks) Calculate the value of x. ​

Answers

Answer:

28=12+15+8+x

28=35+x

35-28=x

x=7

Can you guys help me

Answers

(1,3) if you look at the graph, both inequality’s graphed overlap at (1,3) we only see green in (1,1)

Deliana thinks she needs to solve 5 ÷ 6. Do you agree with her? Explain why or why not.

Answers

Answer:

5 is small 6 is bigger

Step-by-step explanation:

because 6 is bigger and 5 is small than divide

what is the value of x.

Answers

Answer: x=45

(3x-9)+30+24=180
3x-9+54=180
3x+45=180
-45 -45
3x=135
x=45

Explanation: All interior angles of a triangle add up to 180°. Add all interior angles and set it up equal to 180°. Then solve for x.

Which of the following is a solution set to the equation x^2-10x+16=0

Answers

Answer:

x=2. or. x=8

Step-by-step explanation:

x^2-10x+16=0. s=-10

x^2-8x-2x+16=0. p=16

x(x-8)-2(x-8)=0. [-8,-2]

(x-2)(x-8)

x=2. or. x=8

Roberto has $20 to buy baseballs for his little league team. Each baseball costs $6. How many baseballs Conan he buy?

Answers

Answer:

3

Step-by-step explanation:


Assuming the trend that exists in the data set below applies to all students, how long should Trevor study if
he want to get at least a 75% on the test?

Answers

Answer:

He should study for at least 88 minutes

Step-by-step explanation:

The missing parameters are:

[tex]y = 0.36805x + 42.6864[/tex] --- equation of trend

[tex]y \to grade[/tex]

[tex]x \to time[/tex]

Required

x when [tex]y = 75[/tex]

[tex]y = 0.36805x + 42.6864[/tex] becomes

[tex]75 = 0.36805x + 42.6864[/tex]

Collect like terms

[tex]0.36805x = 75 - 42.6864[/tex]

[tex]0.36805x = 32.3136[/tex]

Solve for x

[tex]x = \frac{32.3136}{0.36805}[/tex]

[tex]x = 87.80[/tex]

[tex]x \approx 88[/tex]

Helppppppppppp meeeeeeeeeee

Answers

Answer:

the value of x°= 20°

explanation is in the picture attached below

hope it is helpful to you

Question and choices are in the photo please explain the answer

Answers

Step-by-step explanation:

but sorry i can't get the answer of (2x-1) =3 (x+5) because the answer of this came -16

Sympathetic Division function ​

Answers

This initiates the fight or flight response

lmk if this helped :)

Can please someone help me

Answers

Answer:

1. $40

2. 10 computers

3. 300 miles

Step-by-step explanation:

1. Time between 12:00 and 2:00 is 2 hours, the difference in the money is $10, so the money earned per hour is $5. 5:00 is 3 hours from 2:00, so 25+5*3 is 40, or $40.

2. Time between 1:00 and 3:00 is 2 hours, and the difference in the numbers of computers fixed is 2, so the number of computers fixed per hour is 1. 6:00 is 3 hours from 3:00, so 7+3*1 is 10, or 10 computers.

3. Time between 6:00 and 9:00 is 3 hours and the difference in the distance is 150 miles, so the miles traveled per hour is 50. 12:00 is 3 hours from 9:00, so 150+50*3 is 300, or 300 miles.

Answer this equation

1 . Y/-7 = -7

Answers

Step-by-step explanation:

Y/-7= -7

Cross multiple

-7× -7 =Y

49 =Y

Answer:

y = 49

Step-by-step explanation:

y ÷ - 7 = - 7

y ÷ - 7 × - 7 = - 7 × - 7

y = 49

the graphs of f(x) =-2x and g(x)=(1/2)^z are shown

Answers

Answer:

f(x)-3x+5 and g(x)=4+5 is it true ?Step-by-step explanation:

the number of calls received by an office on Monday morning between 8:00am and 9:30 am has a mean of 3.Calculate the probability of getting no more than 3 calls between eight and nine in the morning.

Answers

Answer:

Step-bLet X be the number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM.

In mathematical terms,  

X

P

o

i

s

s

o

n

(

2

)

.

The PMF of the random variable X is given as,

P

(

X

=

x

)

=

e

2

×

2

x

x

!

f

o

r

x

=

0

,

1

,

2

,

.

.

.

.

.

=

0

E

l

s

e

w

h

e

r

e

The probability of getting no more than 3 calls between eight and nine in the morning is obtained by the following way,

P

(

X

3

)

=

P

(

X

=

0

)

+

P

(

X

=

1

)

+

P

(

X

=

2

)

+

P

(

X

=

3

)

=

e

2

×

2

0

0

!

+

e

2

×

2

1

1

!

+

e

2

×

2

2

2

!

+

e

2

×

2

3

3

!

=

0

.13534

+

0

.27067

+

0

.27067

+

0

.18045

=

0

.85712

Hence the probability of getting no more than 3 calls between eight and nine in the morning is 0.85712.y-step explanation:

Mark is building a sandbox inside a play area. How much play area remains outside of the sandbox?

Answers

Answer:125

Step-by-step explanation:

Franklin races bikes. In his city, there are 44 lengths of race tracks. The chart shows the race tracks and each track's length in miles. Race Track Length in Miles A \frac{1}{4} 4 1 ​ B \frac{3}{2} 2 3 ​ C 1\frac{3}{4}1 4 3 ​ D \frac{4}{4} 4 4 ​ Frankin races 33 laps in the same lane. The total distance he races is more than 4\frac{1}{2}4 2 1 ​ miles. Which track does Franklin race on?

Answers

Answer:

51

Step-by-step explanation:

51 is elaginlent to 44 and 33 12 garde things

Find the gradient of the line segment between the points (-4,4) and (0,12).

Answers

gradient = 12-4 ÷0-(-4)=8÷4=2

Answer:

gradient = 2

Step-by-step explanation:

Calculate the gradient m using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 4) and (x₂, y₂ ) = (0, 12)

m = [tex]\frac{12-4}{0+4}[/tex] = [tex]\frac{8}{4}[/tex] = 2

factorise fully the expression 2d^2-7d

Answers

Answer:

d(2d-7)

Step-by-step explanation:

2d^2 -7d

take common

=d(2d-7)

Answer :

[tex] \large \boxed{ \rightarrow d(2d - 7)}[/tex]

Solution :

[tex] \rightarrow2d {}^{2} - 7d[/tex]

[tex] \rightarrow d(2d - 7)[/tex]

[tex] \mathfrak{hope \:it \: helps \: you.....}[/tex]

I don’t understand this equation. m= -3 and b = 3

Answers

can you please put the equation so i can answer it?

thank you!

Can you please put the equation so that we could answer it

MATH WIZZES, PLEASE HELP ME OUT HERE!! I NEED THIS PROBLEM DONE SOON, BECUASE IT'S DUE IN LIKE 2 MINUTES HELLPPPPPPP
The equations in this system were added to solve for y. What is the value of y?

x + 6 y = 10. -x + 3 y = -15. = 9 y = -5.

Answers

Answer:

y=-5/9

Step-by-step explanation:

it says 9y=-5

divide both sides by 9

y=-5/9

5/9 hope the answer helps

How do you find the perimeter of a rectangle with the dimensions

(x^2+2x-16) ft (length)
and (x+5) ft (width)

Answers

Answer:

(2x²+6x-22) ft

Step-by-step explanation:

l = (x²+2x-16) ft

and w = (x+5) ft

the Perimeter =

2(x²+2x-16) +2(x+5)

= 2x²+4x-32+2x+10

= 2x²+6x-22

find the positive square root of 0.00822649

Answers

Answer:

Step-by-step explanation: Although you did not specify, perhaps your were supposed to find some way to do this without a calculator. First ignore the decimals and think about 822649

900 * 900 = 810000 so the first digit of the square root is a 9

The last two numbers are 49 so the square root ends in a 7

Assume the square root is 9a7 where a is not known and expand

(907 + 10a)^2 = 822649 + other terms in a = 822649

a = 0, and we have found 822649 = 907 ^2

0.00822649 is obtained from 822649 by moving the decimal point 8 places

That tells us the square root is obtained from by moving 4 places

The answer is 0.0907......

Please help this is due today!!

Answers

Answer:

c is the answer

Step-by-step explanation:

Graphs really aren't my thing but I really feel like it is c

GOOD LUCK HOPEFULLY YOU GET A GOOD GRADE

Which equation(s) have -4 and 4 as solutions?
A. x2 = 8
B. x2 + 16 = 0
C. 2x2 = 32
D. -3x2 = -48
E. 6x2 + 56 = -40
F 27 - 5x2 = -53

Answers

C because...
2x^2 = 32 becomes...
2x^2 - 32 = 0 (FACTOR OUT THE 2!)
2(x^2 - 16) = 0 —> now we have a difference of squares
2 (x + 4) (x - 4) = 0
Our two solutions are 4 and -4.

Please answer its fill in the blanks

the words are at the bottom

Answers

1 is f 2 is c 3 is a 4 is h and 5 is b

Answer:

1. Grassland

2. grass

3. Temperate grassland

4. prairies

5. steppe

6. tropical grassland

7. savanna

8. intermountain grassland

9. mixed prairie

10. tallgrass prairie

Step-by-step explanation:

Which of the following best describes the relationship between Angle a and angle b in the image below ( Choose all that apply)

Answers

You are correct in selecting "linear pairs" since they form a straight line.

The angles are also adjacent because they're next to each other like that. In fact, "linear pair" means "adjacent and supplementary".

The angles are not complementary because they don't add to 90 degrees. Instead, they add to 180 degrees so that's what makes them supplementary.

The angles are also not vertical angles. They would need to be opposite one another in an X configuration for this to happen. This means vertical angles cannot be adjacent, and vice versa.

2 Answers:  Choice B and Choice C

Angle a and angle b within the image are the linear pairs of angle within the image below.

What is the angle?

It is a direction from which an individual observe something.

How to determine relationship between angles?

From the figure we are able to find that angle a and angle b are the linear pair because these are formed when two lines intersect one another at one point. The angles are said to be linear if they're adjacent to every other after the intersection of the 2 lines. The sum of angles of a linear pair is often adequate to 180 degrees.

Hence the angle a and angle b are linear pairs.

Learn more about linear pairs at https://brainly.com/question/2065148

#SPJ2

Other Questions
You are the main speaker in a debate either to propose or oppos on a tittle children of literate parents performs well than that of illiterate parents 2. A data catalog identifies all of the following, except: a. Attribute data type b. Attribute range of values c. Attribute constraints d. Attribute value for Instructor ID The base salary of 500$ per week plus a commission of 10.5% of sales How does structure of a cell suggest it's function? Which words from "Work Without Hope" create the speaker's despairing tone? who was the first president of somalia Which words should not use in the closing of a formal email letter? A group of 42 monkeys meet in the forest for a swinging competition. The monkeys divide into teams with 8 monkeys on each team. They make as many teams as they can, but not every monkey is in a team. How many teams of monkeys will there be? Answer must be a whole number. How many monkeys remain without a team? Answer must be a whole number. Evaluate the expression 4q(q + 3w)^2 when q = 2 and w = 3 How does blood flowfrom a person's legback to the person'sheart?Blood flows back tothe heart_______. "Darcie wants to crochet a minimum of 333 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal." pls help lol Which of the following is NOT one of the factors complicating the techniques for addressing the fixed-position layout? A) The volume of materials needed is dynamic.B) At different stages of a project, different materials are needed; therefore, different items become critical as the project develops.C) Takt times at workstations are dynamic.D) There is limited space at virtually all sites.E) All of the above are complicating factors Suppose the dollar amount of the externality, per gallon of gasoline, is constant, regardless of how much gasoline is produced. Then the externality could be internalized if producers of gasoline were a. required to pay a tax of $0.45 per gallon of gasoline sold. b. provided a subsidy of $0.45 per gallon of gasoline sold. c. required to pay a tax of $0.30 per gallon of gasoline sold. d. provided a subsidy of $0.30 per gallon of gasoline sold. Which city is located in the North Central Hills region John's salary is $1250 a month plus a 5% commission on all his sales. What must the amount of his sales be to earn at least $1500 each month? also it's not $15,000 How does the underlined sentence contribute to the theme that culture can limit our thinking? It indicates that the aunts portrayal of right and wrong is inauthentic and unconvincing. It shows that children and adults have opposing perspectives on what goodness is. It characterizes the children as eager to accept any viewpoint that disagrees with their aunts. It satirizes the bachelors conception of goodness by comparing it to the one in the aunts story. Diet, temperature, oxygen levels and humidity) How do these environmental factors affect the genotype or phenotype in an animal? PLEASE HELP PLEASE HELP ME !!!! WILL GIVE BRAINLIEST TO WHOEVER ANSWERS CORRECTLY Select all the equationsrepresented by this tape diagram.A. 6 + 6 + 6 + 6 + 6 = ?B. 5 + 6 = ?C. ? = 6.5D. ? = 6.6.6.6.6E. ? = 5 = 6F.5 = ?= 6 How do you convert parts per million (ppm) to meters?