Every hour, a research assistant removes half the mass of a bacteria culture originally weighing 4,800 micrograms to observe under a microscope. The research assistant will stop this process once the mass is equal to 300 micrograms.

Which equation represents this situation, and after how many hours will the research assistant stop removing half the mass of the bacteria culture?

Answers

Answer 1

Answer:

Step-by-step explanation:

4,800 mcg × 0.5^t = 300 mcg

0.5^t = 1/16 = (1/2)⁴

t = 4

Answer 2

Answer:

[tex]4,800\left(\frac{1}{2}\right)^{t} \, = \, 300; \ 3 \ \text{hours}[/tex]

Step-by-step explanation:

Every hour, the research assistant is removing half the mass from the original 4,800 micrograms of the bacteria culture. So, the mass remaining after t hours can be represented by an exponential expression, a(b)t, where a is the initial mass of the bacteria culture and b is the base of the exponent that represents the decay factor. Since half of the mass of bacteria is being removed every hour, half of the mass remains. So, b = [tex]\frac{1}{2}[/tex]. The exponential expression for this situation is [tex]4,800\left(\frac{1}{2}\right)^{t}[/tex].

The research assistant will stop removing half the mass from the original bacteria culture after the original bacteria culture has a mass of 300 micrograms. Hence, set the expression for the mass remaining after t hours equal to 300.

[tex]4,800\left(\frac{1}{2}\right)^{t} \, = \, 300[/tex]

In order to solve this equation for t, the base needs to be isolated. Divide both sides of the inequality by 4,800.

[tex]\begin{array}{rclC40C40} 4,800\left(\frac{1}{2}\right)^{t} &=& 300\\ \left(\frac{1}{2}\right)^{t} &=& \frac{1}{16} \end{array}[/tex]

Next, rewrite the base of [tex]\frac{1}{16}[/tex] as a power of [tex]\frac{1}{2}[/tex]. Then, set the exponents equal to each other to solve for t.

[tex]\begin{array}{rclC40C40C30} \left(\frac{1}{2}\right)^{t} &=& \frac{1}{16} \\ \left(\frac{1}{2}\right)^{t} &=& \left(\frac{1}{2}\right)^{4} \\ t &=& 4 \end{array}[/tex]

So, after 4 hours the research assistant will stop removing half the mass of the bacteria culture.


Related Questions

This year, John played in 10 baseball games. In these games he had hit the ball 2,3,1,1,3,2,4,6,2, and x times. The mean is 3 hits per game. Find the missing value

Answers

Answer:

x = 3

Step-by-step explanation:

The mean is the average so set up an equation that adds up all the points and divides them by the total, set equal to 3, and solve for x

(2+3+1+1+3+2+4+6+2+x)/10 = 3

(24 + x)/10 = 3

24 + x = 30

x = 6

To check if this is correct, add up all the numbers and divide by 10.

2+3+1+1+3+2+4+6+2+6 = 30/10 = 3

Answer:

Step-by-step explanation:

To solve this problem, we need to use the formula for calculating the mean or average of a set of data, which is:mean = sum of all values / number of valuesLet's first find the mean of John's hits in the 10 games he played this year:mean = (2+3+0+1+3+2+4+0+2+3) / 10 = 2.0So, John's mean hits per game in the 10 games he played this year is 2.0.To increase his mean by 0.5 in the first 10 games he plays next year, John needs to achieve a mean of 2.5 hits per game. Let's call the total number of hits John needs to achieve this mean "x".To find "x", we can use the formula for calculating the mean again:2.5 = (total number of hits in the next 10 games + total number of hits in the previous 10 games) / 20Multiplying both sides by 20, we get:total number of hits in the next 10 games + total number of hits in the previous 10 games = 50Substituting the total number of hits in the previous 10 games with the sum of all hits John had in those games, we get:total number of hits in the next 10 games + (2+3+0+1+3+2+4+0+2+3) = 50Simplifying this equation, we get:total number of hits in the next 10 games = 50 - 20 = 30Therefore, John needs to achieve a total of 30 hits in the first 10 games he plays next year to increase his mean hits per game by 0.5. So, the answer is (3) 20.

what is the answer to -1x3+4

Answers

Answer:

Your answer is 1, look below please

Step-by-step explanation:

ASSUMING that the x is a variable your equation is -1x=3+4 which would be...

-1x=7, then divide by -1 which gives us -7

I used a calculator and it said it the answer is 1

I’m stuck please help me

Answers

Answer:

7

Step-by-step explanation:

→ First find the hypotenuse of length 2 and 3

√2² + 3² = √13

→ Use it to find the length of d

√6² + (√13)² = 7

Margo is planning a vacation. Assume that they have 2 possible destinations: beach or mountains. There are 2 vacation areas in the beach destination with 5 available condos for 1 of the areas, and 4 available condos for the other areas. There are 3 mountain destinations with 1 available condo for 2 of the areas, and 3 available condos for the other areas. A trip plan involves the selection of a destination, area, and a condo. First, draw out the tree diagram representing making these choices below:

Required:
a. How many outcomes are there in the sample space?
b. Write out the event "Margo picks a beach destination" in set notation.

Answers

Answer:

There are 14 outcomes in the sample space.

x= { x/x ∈ b, where b≠0 }

Step-by-step explanation:

The tree diagram is as follows

                                                                                                   Sample Space

Margo→→→→Beach (b)→→→→→→→1 destination→→→→→→→5 condos              5

     ║                   ║→→→→→→→→→→2 destination→→→→→→→→→4 condos       4

     ║

     ║

     ║→→→→→Mountain (m) →→→→→→→→1 destination→→→→→→ 1condo         1

                                    ║→→→→→→→→→→2 destination→→→→→ 1condo         1

                                     ║→→→→→→→→→→ 3destination→→→→→ 3 condos     3

Part a:

There are 14 outcomes in the sample space .

5+4+1+1+3= 14

Part b:

Margo picks a beach destination in set notation is

x= { x/x ∈ b, where b≠0 }

x such that x belongs to b ( beach destination) and b is not equal to zero.


Which fraction is in simplest form?
17
51

19
30

21
24

21
35

Answers

19/30 is already in simplest formed
I think it’s 19/30 !!!!!!


You use a 40% off coupon followed by a 30% off coupon. is that
this is the same as a 70% off coupon. Explain

Answers

Answer:

Yes since 40+30=70 so it would be the same

Step-by-step explanation:

Can you please help me thanks

Answers

Answer:

34.1x

Step-by-step explanation:

Each hour adds 34.1 more earnings. 4 x 34.1 = 136.4. 16 x 34.1 = 545.6 and so on and so forth.

Answer:

The cost per hour is 34.1

Step-by-step explanation:

136.40/4=34.1

545.60/16=34.1

716.10/21=34.1

the proportional is 34.1 in the earnings and time in an hour.


An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession
and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 9.
Event B: The sun is divisible by 3.
Round your answers to two decimal places.
I need the answers fast

Answers

Answer:

A=11.1%

B=33.33%

Step-by-step explanation:

A.First Die        Second die

6                          5

5                          6

6                          4

4                          6

4/36=1/9=.11=11.1 %

12/36=0.3333=33.333 percent

Which expression is a factor of
g(x) = 36x2 + 23x - 3

Answers

I believe it is 3......

Determine whether each of the properties described applies to volumetric or graduated glassware.

a. Used for applications in which great accuracy is needed __________
b. Capable of measuring a range of volumes of liquid _________
c. Designed to measure one specific volume of liquid _________

Answers

Answer:

a. volumetric glassware

b. Graduated glassware

c. volumetric glassware

Step-by-step explanation:

The graduated glassware and the volumetric glassware is the factory  calibrated used to deliver such as the graduated cylinders and pipettes and it contains the volumetric flask of a known amount of the liquid.

A volumetric glassware is a type of the laboratory flask and a graduated glassware is mostly of the cylinder shape and is also known as the measuring cylinder.

In the context,

a). The volumetric glassware is used in the applications where much accuracy is needed to perform the experiment.

b). Graduated glassware is used for measuring a wide range of volume of the liquid used in the laboratory,

c). The volumetric glassware is used to measure one specific amount of the volume of the liquid to be used.

Pls help I’ll brainlest ASAP pls

Answers

Answer:

128

explanation:

cross multiply whereby 8*-112

it gives u -896 which u divide by -7 to get value of m as 128

hope it helps

4. Which of the following is a pair of vertical angles?
Angles 1 and 4
Angles 1 and 3
Angles 1 and 2
Angles 1 and 8

Answers

Answer:

Angles 1 and 8 because they are vertically aline

Answer:

Angles 1 and 8

Step-by-step explanation:

i took the test

A study shows that unemployment has not impacted white-collar and blue-collar workers equally (Newsweek, April 20, 2009). According to the Bureau of Labor Statistics report, while the national unemployment rate is 8.5%, it is only 4.3% for those with a college degree. It is fair to assume that 27% of people in the labor force are college educated. You have just heard that another worker in a large firm has been laid off. What is the probability that the worker is college educated

Answers

Answer:

0.137

Step-by-step explanation:

The computation is shown below:

Educated = 0.27

And, unemployed to educated is 0.043

Now probability of educated and unemployed is

= 0.043 × 0.27

= 0.1161

So, the educated would be

= 0.01161 ÷ 0.085

= 0.137

1. The ratio of 2h to 30min is
A. 1:15
B. 4:1
C. none of these​

Answers

Answer:

B. 4:1

Step-by-step explanation:

Since its 2 hours:30 minutes, in hours that is 2:1/2. So then if you want it in whole numbers you just multiply 2:1/2× 2 which would be 4:1.

The circumference of the earth is approx. 40,000 km.

a) What is the diameter of the earth?

b) Calculate the volume of the soil​

Answers

I believe the answer you are look for is A

Thirty security personnel need to be hired. They will work one week on and one week off for 20 hours per week. If they are paid $15/hour, what is the security labor cost for a four-week month?

Answers

Answer:

$18,000

Step-by-step explanation:

Step 1.

Figure out how much it costs to hire one security personal for a month

2×20×15

=600

$600 per person per month

Step 2.

Multiply that number by the no. of people needed to be hired

600×30

=18000

∴ The security labor cost for a four-week month is $18,000

Can someone help me, please????

Answers

Answer: -12

Step-by-step explanation:

if you'd like to convert a Fahrenheit temperature to an approximate Celsius temperature: Start with the temperature in Fahrenheit

Answer:

-12 degrees

Step-by-step explanation:

Fahrenheit and Celsius

10 degree fahrenheit

What is the celsius?

____________________

Take a look at the picture with the information provided, we see that f is the vertical line while c is the horizontal line. Since we are looking for 10 degree fahrenheit, let's find it on the vertical line. If we look at the red line, when it goes across 10 fahrenheit, the approximate part that it hits celsius is -12 degrees.

Which statements are correct based on the graph? Select all that apply.
BCDE is rotated 90° to form JKLM.
PQRS is rotated 90° to form JKLM.
BCDE is rotated 180° to form JKLM.
JKLM is rotated 180° to form BCDE.
PQRS is rotated 180° to form BCDE.

Answers

Answer:

2,3,4

Step-by-step explanation:

hope this helps=D

Answer:

B,C,D

Step-by-step explanation:

Vie
What is the y-intercept of the line with the equation y = 4x+ 2?
a-2
C. 2
b 4
d.
NIN
Please select the best answer from the choices provided
A
D
Mark this and retum
Save and Exit
Next

Answers

Answer:

c. 2

Step-by-step explanation:

the Y- intercept is 2 because it says +2

A triangle has sides with lengths of 7 yards, 8 yards, and 9 yards. Is it a
right triangle?

Answers

Answer:

No, it is not a right triangle.

Step-by-step explanation:

A right triangle will follow the Pythagorean Theorem: a² + b² = c²

c is the hypotenuse, or the longest side. In this case, it is 9.

That means a and b are 7 and 8.

Now let's plug in the values to see if they simplify correctly.

(7)² + (8)² = (9)²

Simplify the exponents.

49 + 64 = 81

Add the left side.

113 = 81

The above expression is not true; therefore, this triangle is not a right triangle.

If x is a positive integer, and x = 3y = 6z, what is the value of x + y in terms of z?


F. 3z

G. 5z

H. 8z

J. [tex]\frac{25}{3} z[/tex]

K. [tex]\frac{31}{3}z[/tex]

Answers

5z is the correct answer for the question

Admission to the circus costs $4 plus $0.50 per ride. Ella spent $17.50 at the circus.

Answers

Answer:

Ella went on 27 rides.

Step-by-step explanation:

$17.50 - $4 = $13.50

A liter of water contains about 3.35 * 10 ^ 25 molecules. A certain river discharges about 2.4 * 10 ^ 7 of water every second. About how many molecules does the river discharge every minute?

Answers

Answer: 3.6791719e+46

Step-by-step explanation :

3.35 * 10 = 33.5 ^25

molecules per litre = 33.5 ^ 25

2.4 * 10 = 24 ^ 7 = 4,586,471,424  ( we'll assume this is ml as the question doesn't specify ) so thats 4,586,471,424ml discharged every second which is 4,586,471 litres per second. 4,586,471 * 60 seconds in a minute = 275,188,260 litres discharged every minute.

molecules per litre is 33.5 ^ 25 and litres discharged per minute is 275,188,260  

so the answer would be : 275,188,260  *  33.5 ^ 25 = 3.6791719e+46 (in other words a big number)

Check yourself ^

In which type of economic system, does the government handle decisions related to the production of goods and services?
A.
command
B.
market-driven
C.
mixed
D.
market

Answers

Answer:

D Market

Step-by-step explanation:

the production determines how the goods and services are destributed and applied so the goods can flow all based off of the market

Answer:

Step-by-step explanation:

The answer is 'command'.

Plz help mee
A. 49.75
B.74.75
C.156
D.1196

Answers

Answer:

B: 74.75

Step-by-step explanation:

If four roommates (I don't know how to spell it) want to divide the prize of a computer which costs 299 is the same as: 299/3 which gives you 74.75

el 2% que fraccion representa​

Answers

2/100 or 1/50 :p la respuesta

Match the term to its definition
Brainlessly and 25 points
Definitions on picture
•wages
•stock
•gross domestic product
•credit
•standard of living
•stock
•market crash
•interest
•great depression
•consumer
•surplus

Answers

Chicken nsnsnsndbd bhzhx

The distance from the origin to the point (-6, 8) is

Answers

Answer:

10

Step-by-step explanation:

[tex]\sqrt{(-6-0)^2+(8-0)^2} =10.[/tex]

I don't understand exponents well best answer gets brainly ​

Answers

Answer:

i think its 125

Step-by-step explanation:

since 5^7 = 78,125 and 5^4 = 625

then it would be 78,125

                           ----------  = 125

                             625

sorry if im wrong ;-;

Forty percent of all high school graduate work during the summer to earn money for college tuition for the upcoming fall term. Assuming a binomial distribution, if 6 graduates are selected at random, what is the probability that at least 2 graduates have a summer job

Answers

Answer:

0.7667 = 76.67% probability that at least 2 graduates have a summer job

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Forty percent of all high school graduate work during the summer to earn money for college tuition for the upcoming fall term.

This means that [tex]p = 0.4[/tex]

6 graduates.

This means that [tex]n = 6[/tex]

What is the probability that at least 2 graduates have a summer job

This is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.4)^{0}.(0.6)^{6} = 0.0467[/tex]

[tex]P(X = 1) = C_{6,1}.(0.4)^{1}.(0.6)^{5} = 0.1866[/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0467 + 0.1866 = 0.2333[/tex]

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.2333 = 0.7667[/tex]

0.7667 = 76.67% probability that at least 2 graduates have a summer job

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