A 15-g sample of radioactive iodine decays in such a way that the mass remaining after t days is given by
m(t) = 15e−0.073t,
where
m(t)
is measured in grams. After how many days is there only 5 g remaining?
15 days
Step-by-step explanation:
The half-life equation is given as
[tex]m(t) = m(0)e^{-0.073t}[/tex] (1)
where m(0) is the initial mass of radioactive iodine at t = 0. To solve for the time t, let's put the exponential part on the left-hand side:
[tex]e^{-0.073t} = \dfrac{m(t)}{m(0)}[/tex]
Taking the natural logarithm of both sides to get
[tex]\ln{e^{-0.073t}} = \ln\left[\dfrac{m(t)}{m(0)}\right][/tex] (2)
Recall the following properties of logarithms:
[tex]\ln{A}^b = b\ln{A}[/tex]
[tex]\ln{e} = 1[/tex]
We can rewrite Eqn(2) as
[tex]-0.073t = \ln\left[\dfrac{m(t)}{m(0)}\right][/tex]
Solving for t, we get
[tex]t = -\dfrac{1}{0.073}\ln\left[\dfrac{m(t)}{m(0)}\right][/tex]
Since m(0) = 15 gm and m(t) = 5 gm, then the amount of time that elapses to reduce the mass down to 5 gm is
[tex]t = -\dfrac{1}{0.073}\ln\left(\dfrac{5\:\text{g}}{15\:\text{g}}\right)[/tex]
[tex]\:\:\:\:\:= 15\:\text{days}[/tex]
i need help on this math problem
Answer:
I can't see the problem I am blind but still very hard to see it's not quite clear
How do you find the answer for 30=6x+20
Answer:
5/4Step-by-step explanation:
How do you find the answer for 30=6x+20?
solve for x30 = 6x + 20
10 = 6x
x = 10/6
semplify5/4
------------------ check
30 = 6 * 10/6 + 20
30 = 10 + 20
30 = 30
the answer is good
A triangle has an angle that measures 60°. The other two angles are in a ratio of 3:5. What are the measures of those two angles?
Answer:
180
Step-by-step explanation:
all 3 angles of all triangles sum to 180
if one angle = 60, the other two angles sum to 120
a 3:5 ratio means one angle is 3/8 of 120 and the other is 5/8 of 120
3/8 times 120 = 3(120)/8 = 3(15)= 45 degrees
5/8 times 120 = 5(120)/8 = 5(15) = 75 degrees
45+75 = 120
120+60 = 180 degrees = sum of all 3 angles
in case you need an explanation and can I be get brainlest?
6.2 Margin of error and the confidence interval. A study of stress on the campus of your university using the College Undergraduate Stress Scale (CUSS) reported an average stress level of 1123 (a higher score indicating more stress) with a margin of error of 43 for 95% confidence. The study was based on a random sample of 400 undergraduates. a. Give the 95% confidence interval. b. If you wanted 99% confidence for the same study, would your margin of error be greater than, equal to, or less than 43
Using confidence interval concepts, it is found that:
a. The 95% confidence interval is (1080, 1166).
b. The margin of error would be greater than 43.
Item a:
The interval is the sample mean plus/minus the margin of error, hence:
[tex]1123 - 43 = 1080[/tex]
[tex]1123 + 43 = 1166[/tex]
The 95% confidence interval is (1080, 1166).
Item b:
The margin of error is direct proportional to the critical value.The higher the confidence level, the higher the critical value, and thus, the higher the margin of error.Hence: The margin of error would be greater than 43.
A similar problem is given at https://brainly.com/question/25675821
A garden table and a bench cost $907 combined. The garden table costs $43 less than the bench. What is the cost of the
bench?
907 - 43 = 864 / 2 = 432: 907 - 432 = 475
The garden table costs $432.
The bench costs $475.
475 + 432 = 907
I hope this helps! :)
An unopened bag of gummy bears weighs 2 1/3 ounces. Drayven has 3/4 of a bag of gummy bears and Akila has 2/3 of a bag. Who has more? If they put their bags together, would they have more than one bag? Explain your answer.
Answer:
Drayven has more
Step-by-step explanation:
If you look at the fractions through a drawing you would see that my claim is correct.
Review:
Match each decimal with its equivalent simplified fraction.
NOTE: Simplified fractions may be in the improper fraction format.
0.25
[Choose]
0.14
[Choose ]
1.4
[Choose ]
0.4
[Choose ]
0.375
[Choose ]
Answer:
0.25-1/4
0.14-7/50
1.4-7/5
0.4-2/5
0.375-3/8
-3/5 divided by 5
full steps
Answer:
-3/25
Step-by-step explanation:
[- 3 / 5 ] / 5
- 3
5
-------
5
1
-------------------
- 3 x 1 = -3
5 x 5 = 25
-------------------
-3 / 25
A recipe calls for 2 cups of sugar for each 5 cups of flour. How many cups of sugar needed for 15 cups of flour?
Answer:
6 cups of sugar
Step-by-step explanation:
2/5=x/15
x=6
Substitution method
-3x + 3y = 4
-x + y = 3
A population of bacteria is initially 2,000. After three hours the population is 1,000.
Assuming this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours. Write your answer in the form f(t)=a(b)t. Report numbers as fractions when necessary, or if using decimals, round to four decimal places.
The population starts at 2000, so a=2000.
We also know that the population in 3 hours is 1000, so we can setup the equation:
2000 b^3 = 1000
This gets us:
b^3 = 1/2
And taking the cube root of both sides gives us:
b ≈ 0.7937005259841
Rounding that to 4 places, we have:
f(t) = 2000 (0.7937)^t
What is the value of x in the solution to this system of equations?
y = x + 1
y = 5x + 13
Step-by-step explanation:
y=x+1
y=5x+13
=13x/1
=5x/x
A.CED.A Garnetta owned 2400 shares of Metropolitan Corporation at a price of $45.50. The stock split 4-for-3. How was Garnetta financially affected by the split
Garnetta will have 3,200 shares worth $ 34,125 each.
Given that Garnetta owned 2400 shares of Metropolitan Corporation at a price of $ 45.50, and the stock split 4-for-3, to determine how Garnetta was financially affected by the split the following calculation must be performed:
3 = 2400 4 = X 4 x 2400/3 = X 9600/3 = X 3200 = X (2400 x 45.50) / 3200 = X 109200/3200 = X 34.125 = X
Therefore, Garnetta will have 3,200 shares worth $ 34,125 each.
Learn more in https://brainly.com/question/13981349
Which inequality is graphed below?
A- y<1/4x-1
B- y>1/4x-1
C- y<_ 1/4x-1
D- y>_ 1/4x-1
Step-by-step explanation:
It is represented by ,
=> y ≥ 1/4x -1
¿De qué número es 60 el 80%?
Answer:
48
Step-by-step explanation:
someone please help me on this anyone pls no link :(
9514 1404 393
Answer:
The correct answer is marked. (8·3)
Step-by-step explanation:
The order of operations requires that you start with by evaluating expressions in parentheses. Within parentheses, the order of operations applies, so you need to do multiplication before addition.
In this expression, the multiplication operation inside the parentheses is performed first. That is, you first compute 8·3.
_____
Additional comment
After that, you do the subtraction, to get ...
11 ÷ (-12) +2⁴
Then the exponential term is evaluated, and you have ...
11 ÷ (-12) +16
The division will result in a fraction, making it ...
(-11/12) +16
And, finally, the addition gives you ...
15 1/12
Kaleb is ordering food for his siblings. Each burger costs $4 and each order of fries cost $2 each. Kaleb wants to spend at most $20. Let x represent burgers and y represent fries. a. Write a linear inequality to find the number of burgers and fries Kaleb can buy.
Answer:
4x + 2y ≤ 20
Step-by-step explanation:
x = burger
y = fries
a. 4x + 2y ≤ 20 at most means ≤
-6 10/9 divided by 6/5
Answer:
-160/27
Step-by-step explanation:
Someone pls help me with these worksheets.
(Please answer properly, if u don't know, just ignore it)
Answer:
i wrote answer of the question 1 to 4 but i don't know the answer to 5
Answer: 1) (3,0) 2) (4,2) 3) (5,1) not sure about 4 and 5
1) (3,7/2) 2) (1,-4) 3) (-3,2) im bad at word problems, sorry.
Step-by-step explanation: all i can say without sounding confusing is divide on both sides!! <3
What is 11 divided by 1/4
7. Jairaj has 20 50-cent and 10-cent coins altogether. He has a total of $6.80 How many 50-cent coins does he have?
Answer:
He will have 8 50-cent coins
Step-by-step explanation:
Let x = the number of 10-cent coins
Let y = the number of 50-cent coins
x + y = 20 y = 20 - x
[Set up an equation] .10x + .50y = 6.80
[Multiply both sides by 100] 10x + 50y = 680
[Plug-in] 10x + 50(20 - x) = 680
[Multiply] 10x + 1,000 - 50x = 680
[Combine like terms & subtract 1,000 from both sides] -40x = -320
[Divide both sides by -40] x = 8 coins
Have a nice day! - hopefully this is correct, I got a bit turned around for a bit lol
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
What is the average rate of change of the functionf (x) = 20(1/4)^xfrom x = 1 to x = 2?
Step-by-step explanation:
the average rate of change of a function f(x) between two values of x is
(f(x2) - f(x1)) / (x2 - x1)
f(x) = 20× (1/4)^x
x1 = 1
x2 = 2
f(x2) = 20× (1/4)² = 20/16 = 5/4
f(x1) = 20× (1/4)¹ = 20/4 = 5
(5/4 - 5) / (2 - 1) = (5/4 - 20/4) / 1 = -15/4
the average rate of change is -15/4.
Convert
161 oz = ____ lb ______oz
Answer:
161oz = 10.0625 (then you round)
Step-by-step explanation:
Simplify the linear expression.
−2x+3(−5x+1)
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's simply the given expression ~
[tex] - 2x + 3( - 5x + 1)[/tex][tex] - 2x - 15x + 3[/tex][tex] - 17x + 3[/tex]emily ran 3 3/4 miles in 5 hours what unit rate for miles per hour did she run
Answer: The answer is 3
Step-by-step explanation:
:]
Pls sove brailest will be given
Answer: 6a3b3
Step-by-step explanation:
Reformatting the input:
Changes made to your input should not affect the solution:
(1): "0.6" was replaced by "(6/10)".
STEP 1:
Equation at the end of step 1
6
0-(((——•(a2))•b)•(0-(2•5ab2)))
10
STEP 2:
3
Simplify —
5
Equation at the end of step 2:
3
0 - (((— • a2) • b) • ( -2•5ab2))
5
STEP 3:
Equation at the end of step 3
3a2
0 - ((——— • b) • ( -2•5ab2))
5
STEP 4:
Multiplying exponential expressions :
4.1 a2 multiplied by a1 = a(2 + 1) = a3
Multiplying exponential expressions :
4.2 b1 multiplied by b2 = b(1 + 2) = b3
Canceling Out:
4.3 Canceling out 5 as it appears on both sides of the fraction line
Equation at the end of step 4:
0 - -6a3b3
STEP 5:
Final result :
6a3b3
Help help help help help help math sucks help
domain for f(x) = -0.25(x − 4) 2 − 6
Answer:
The domain will be (-8,8), {x|x E R}
Step-by-step explanation:
The -8,8 has to be sideways on the right. Thats the answer.
You spin each spinner once. You get $39 if you spin a 2 and a vowel. You get $26 if you spin a 2 and a consonant. You get $9 if you spin a 1 and a vowel. Everything else earns $0. What is the expected value of this game? Round your answer to the second decimal if necessary
The expected value of the game is the mean value of the game
The expected value of the game is $9
For the first spinner;
The probability to spin 2 is 1/4The probability to spin 1 is 3/4For the second spinner;
The probability to spin a vowel is 1/4The probability to spin a consonant is 3/4So, the probability of spinning a 2 and a vowel is:
[tex]\mathbf{P(2\ and\ vowel) = \frac 14 \times \frac 14 = \frac{1}{16}}[/tex]
The earning for spinning a 2 and a vowel is $39.
So, the expected earning is:
[tex]\mathbf{Expected = 39 \times \frac{1}{16} = 2.4375}[/tex]
So, the probability of spinning a 2 and a consonant is:
[tex]\mathbf{P(2\ and\ consonant) = \frac 14 \times \frac 34 = \frac{3}{16}}[/tex]
The earning for spinning a 2 and a consonant is $26.
So, the expected earning is:
[tex]\mathbf{Expected = 26 \times \frac{3}{16} = 4.875}[/tex]
So, the probability of spinning a 1 and a vowel is:
[tex]\mathbf{P(1\ and\ vowel) = \frac 34 \times \frac 14 = \frac{3}{16}}[/tex]
The earning for spinning a 1 and a vowel is $9.
So, the expected earning is:
[tex]\mathbf{Expected = 9 \times \frac{3}{16} = 1.6875}[/tex]
So, the expected value of the game is:
[tex]\mathbf{Game =2.4375+ 4.875 + 1.6875}[/tex]
[tex]\mathbf{Game =9}[/tex]
Hence, the expected value of the game is $9
Read more about expected values at:
https://brainly.com/question/13499496