About 92 days are taken for 90 % of the material to decay.
The mass of radioisotopes ([tex]m[/tex]), measured in milligrams, decreases exponentially in time ([tex]t[/tex]), measured in days. The model that represents such decrease is described below:
[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex] (1)
Where:
[tex]m_{o}[/tex] - Initial mass, in milligrams.[tex]m(t)[/tex] - Current mass, in milligrams.[tex]\tau[/tex] - Time constant, in days.In addition, the time constant is defined in terms of half-life ([tex]t_{1/2}[/tex]), in days:
[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex] (2)
If we know that [tex]m_{o} = 85\,mg[/tex], [tex]t_{1/2} = 27.7\,d[/tex] and [tex]m(t) = 8.5\,mg[/tex], then the time required for decaying is:
[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex]
[tex]\tau = \frac{27.7\,d}{\ln 2}[/tex]
[tex]\tau \approx 39.963\,d[/tex]
[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]
[tex]t = -(39.963\,d)\cdot \ln \frac{8.5\,mg}{85\,mg}[/tex]
[tex]t\approx 92.018\,d[/tex]
About 92 days are taken for 90 % of the material to decay.
We kindly invite to check this question on half-life: https://brainly.com/question/24710827
Find the exact length of the third side.
10
8
Answer: 6
Step-by-step explanation:
The typical way to solve this problem is with the Pythagorean Theorem, which states that a^2 + b^2 = c^2, where a and b are the legs of the right triangle, and c is the hypotenuse. Unfortunately, due to a lack of a diagram, I am forced to infer.
Because the most famous Pythagorean triplet is 3, 4, 5, and 8 and 10 are multiples of the latter two terms, I can infer that the final side length is 6.
Hope it helps :) and if it is wrong, please let me know, and repost another question with the provided diagram.
Diane has $12 to spend on a mixture of green and red grapes. What equation can she use to graph a line showing the different amounts of green and red grapes she can buy for $12. Green grapes cost $3/lb and red grapes cost $2/lb.
Answer:
y ≥ [tex]\frac{3}{2}[/tex]x + 6
Step-by-step explanation:
12 ≥ 3x + 2y
Money available ≥ cost of green grapes + cost of red grapes
To turn this into slope-intercept form,
12 ≥ 3x + 2y
2y ≥ -3x + 12
y ≥ [tex]\frac{3}{2}[/tex]x + 6
Graphed - see attached
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Betty is 3 times as old as Mike. In 5 years, she will be twice as old. How old are they now?
Answer:
Betty is 15.
Mike is 5.
Step-by-step explanation:
We can let Betty's age be b and Mike's age be m.
Since Betty's age is 3 times of Mike, then
[tex]b=3m[/tex]
In 5 years, the age of Betty and Mike would be [tex]b+5[/tex] and [tex]m+5[/tex] respectively.
Since Betty is 2 times as old as Mike then, then [tex]b+5=2(m+5)[/tex].
We know that [tex]b=3m[/tex], so we can substitute that:
[tex]3m+5=2(m+5)[/tex]
Expand:
[tex]3m+5=2m+10[/tex]
Subtract 5 from both sides:
[tex]3m+5-5=2m+10-5[/tex]
[tex]3m=2m+5[/tex]
Subtract 2m from both sides:
[tex]3m-2m=2m+5-2m[/tex]
[tex]m=5[/tex].
Mike is 5 years old.
Since Betty is 3 times as old as Mike, Betty's age is [tex]5*3=15[/tex]
Write the expression 83⋅83⋅83⋅83⋅83⋅83 as a power.Enter your answer by filling in the boxes.$$
Answer:
It's (8/3) 6 I took the test and that was the answer. Your Welcome!!!!!!!!!!!!!
Answer:
Its 83 the power of 6. Also Please choose my anwer as brainliest
Find the area! Explain all thinking!! Thank you! <3
Answer:
80
Step-by-step explanation:
you can divide the shape into a square and a rectangle, the square being the 7 by 10 area. by that logic, you can find the area of that portion to be 70. now you have the cut off rectangle to find, and you know one side is 2. to find the other side, you have to subtract 7 from 12 because by doing that you get the value of just that portion of the side. by doing that you get 5. going from there, you can multiply 2 by 5 to get 10 for the area of the rectangle. now you have to add 70 and 10, and you get 80!
hope this helped :D
Alr guys I need a refreser on long division because my little sister needs help with it (Help :') )
Answer:
116 remainder 1
116 1/3
116.333
Step-by-step explanation:
Answer:
116 with a remainder of 1
Step-by-step explanation:
Picture below shows step by step work
Hopefully this helps!
Brainliest please?
Triangle BDC is an isosceles triangle. Triangle ACE is a right-angled triangle.
Show that triangle ABC is an equilateral triangle.
IM FAILLING PLZ HELPPPPP MEEEE
Answer: (x+ 13, y+13)
Step-by-step explanation:
Selena and Demi run a gift delivery business. Selena charges a delivery fee that is $18, and she also charges $6 per gift delivered. Demi charges $16, and she also charges $8 per gift delivered. How many gifts have to be delivered before they charge the same amount?
Answer:
1 gift
Step-by-step explanation:
Cost per gift + delivered cost
Selena $6x + $18
Demi $8x + $16
$8x + $16 = $6x + $18
$2x - $16 = $18
$2x = $18 - $16
$2x = $2
x = 1
which temperature values would an interpolation be limited to? less than 3 between 3 and 60 between 20 and 80 greater than 55
Answer:
B. between 3 and 60
Step-by-step explanation:
Answer: B.
Step-by-step explanation: On Edge! :)
The temperature at 6 am was −3°C. By lunch time the temperature had risen by 5°C. What was the temperature at lunch time?
Answer:
2°C
Step-by-step explanation:
just add 5 to -3
-3+5=2
so ur answer is 2
Using the formula find the slope of a line with these two points (2,10) and (5,15).
Answer:
1.66667
Step-by-step explanation:
using online slope calculater
A whole number has a 2 in the tens place. If the 2 were moved from the tens place to the thousands place, how many times greater would the value of the 2 be?
The value of the 2 would be ____ times greater
Answer:
10?
Step-by-step explanation:
it is either 10x or 100x :)) can i get brainliest? hope ur having a good day btw :DD
The place value of 2 will be 100 times greater than before.
What is place value?Place value is a numerical value that every digit in a number has based on its position.
For example; in a number 2398, the place value of 3 is 300, as it is placed at hundredth place.
Given that, A whole number has a 2 in the tens place. If the 2 were moved from the tens place to the thousands place,
At tens place, the value of a number will multiplied by 10 as it is at tenth place,
At tens place = 20
Similarly,
At thousand place, the value of a number will multiplied by 100 as it is at thousand place,
At thousand place = 2000
2000 / 20 = 100
Hence, the value of 2 will be 100 times greater than before.
For more references on place value, click;
https://brainly.com/question/27734142
#SPJ2
What is the period of the trigonometric function f(t) = 3sin(t/2)?
A) 2Pie
B) 3pie
C) 4pie
D) pie/2
How do you solve for x?
2(x - 3)^2 - 32 = 0
[tex] \: \: \: \: \: \: \: \: [/tex]
[tex]x = - 1 \\ x = \: 7[/tex]
Step-by-step explanation:
[tex]2(x - 3 {)}^{2} - 32 = 0[/tex]
divide both sides[tex](x - 3 {)}^{2} - 16 = 0[/tex]
use a²- b² =(a - b ) (a + b) to factor the expression[tex](x - 3 - 4) \times (x - 3 + 4) = 0[/tex]
calculate the difference and the sum[tex](x - 7) \times (x + 1) = 0[/tex]
when the product of factors equals 0 ,at least one factor is 0[tex]x - 7 = 0 \\ x + 1 = 0[/tex]
solve the equation for x[tex]x = 7 \\ x + 1 = 0[/tex]
the equation has 2 solutions[tex]x = - 1 \\ x = 7[/tex]
hope it helps[tex] \: \: \: \: \: \: \: [/tex]
Sam is 4 years younger than Linda. The sum of their ages is 28. Find both Sam and Linda’s age and show your work.
Answer:
Sam = 6 years
Linda = 22 years
Step-by-step explanation:
this is best solved by using an algebraic equation
let Sam's age be x
let Linda's age be 4x
now that we defines our variables let's make an algebraic equation
the sum of their ages is 28 so
4x + x = 28
combine like terms
5x = 28
find for x
x = 28÷ 5 = 5.6 (don't approximate yet let's take the raw age)
Sam is 5.6 years
Linda is 4 years older so we multiply Sam's age by 4
4 × 5.6 = 22.4
Linda is 22.4 years
now let's round our answers to the nearest whole
5.6 ~ 6 years
22.4 ~ 22 years
let's double check and add our answers now
22 + 6 = 28
the answer is correct
The ratio of dogs to cats is 25:75. How many cats are there if there are 75 dogs?
Answer:
225
Step-by-step explanation:
25:75=75:?
25*3 is 75, so 75*3 is ?
75*3 is 225
Hope this helps!
Let me know if it does
Answer: 225 cats
Step-by-step explanation:
25 dogs x 3: 75 cats x 3
75 dogs: 225 cats
2x+5+2x+3x in One sloution, and no solution.
- BRAINLIEST answerer
Order the following fractions from least to greatest
Answer:
1/8, 2/9, 3/7, 5/8, 4/5
Step-by-step explanation:
mark brainlist
Answer: he is right I don't want to still his win
Step-by-step explanation:
mark him brainiest
Please lmk, thank you.
Answer:
True
Step-by-step explanation: I gotchu friend
HELP PLS!!!!!!
How many oranges can you make by just using 3 straight cuts? (a) 3 (b) 6 (c) 7 (d) 8
Answer:
D will be the answer
Step-by-step explanation:
You could cut the orange into four pieces by using 2 straight cuts/making an x on the orange. Then you could flip the orange onto the side/middle and cut again to make 8 pieces.
Hope this works for you!
can someone PLEASE tell me the answer to this?
Show your work and explain please :D
Answer:
6ft: 25.667ft / 7ft: 22ft
Step-by-step explanation:
Since the question shows 7ft but the diagram shows 6ft I will show how to do both
FOR 6FT
Justin's height remained the same at 5'6" (or 5.5ft) and the distance between him and the mirror was 6ft
Now if we assume the triangles are congruent to each other, then set sides A and C equal to each other and solve for x
6/28 = 5.5/x
6x = 154
x = 25.667ft
FOR 7FT
Same process as before, replace 6 with 7
7/28 = 5.5/x
7x = 154
x = 22ft
Jean and Jericho who are playing in the school grounds decided to sit on a
seesaw. Jean, who is heavier, tends to raise Jericho on the other end of the seesaw.
They tried to position themselves in order to balance the weight of each other.
Questions: Underline the correct answer.
1. This situation illustrates (direct, inverse) variation.
2. The two quantities that must vary in this situation are (weight and
distance from the center, height and weight).
3. The heavier the kid, the (closer, farther) he/she should be at the
center to balance the seesaw?
4. When Jean moves farther from the center, Jericho tends to go (up,
down).
5. If Jericho moves closer to the center, Jean tends to go (up, down).
We want to see underline the correct part in each statement.
1) This situation illustrates (direct, inverse) variation.2) The two quantities that must vary in this situation are (weight and distance from the center, height and weight).3) The heavier the kid, the (closer, farther) he/she should be at the center to balance the seesaw?4) When Jean moves farther from the center, Jericho tends to go (up, down).5) If Jericho moves closer to the center, Jean tends to go (up, down).So, Jean and Jericho are playing on a seesaw.
Jean is heavier than Jericho.
Now, notice that a seesaw is a lever. So it "amplificates" the force that you apply in one end to lift the weight that is on the other end. Depending on the form of the lever and the weights, the force that you need to do changes.
If we define:
W₁ = Jean's weight.d₁ = Jean's distance to the center.W₂ = Jericho's weight.d₂ = Jericho's distance to the center.We must have:
W₁*d₁ = W₂*d₂
Then:
1) This situation illustrates (direct, inverse) variation.
d₁, the position of Jean, varies inversely with respect to Jean's weight.
2) The two quantities that must vary in this situation are (weight and
distance from the center, height and weight).
(by the equation above)
3) The heavier the kid, the (closer, farther) he/she should be at the
center to balance the seesaw?
By the given equation, we see that d₁ must be smaller than d₂.
And the last two are trivial:
4) When Jean moves farther from the center, Jericho tends to go (up,
down).
5) If Jericho moves closer to the center, Jean tends to go (up, down).
If you want to learn more, you can read:
https://brainly.com/question/18320907
9. Using a twenty sided number cube, what is the probability that you will roll an even number or
an odd prime number? The number 1 isn't an odd prime. Round to three decimals.
(1 point)
Answer:
0.85
Step-by-step explanation:
total samples cases = 20
chances that are even or odd prime are 17 chances
2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20
probability = 17/20
= 0.85
I NEED HELP please, take 50 points if you answer It and a 50/50 at a brainiest.
"The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00. Write a function to represent this scenario.
Which graph represents this wage increase for x < 12?"
-normally I'd just double-check this but. . . you get it.
Red dots are starting co-ordinates and whites are ending co-ordinates .
So the graph must have red dots at the start of line and not mandatory for at the end of line.
x<12It should not be at end
Check option B
x ends at first point .And also the interval is 2
so Option B is correct
The average rate of change of g(x) between x = 4 and x = 7 is Five-sixths. Which statement must be true?.
based on the information in the table is the cost of the pizza proportional to the number of toppings?
Wren recorded an outside temperature of –2°F at 8 a.m. When she checked the temperature again, it was 4°F at 12:00 p.m. If x represents the time and y represents the temperature in degrees Fahrenheit, what is the slope of the line through these two data points?
–1.5
–0.5
0.5
1.5
Answer:
1.5
1.5
Step-by-step explanation:
The steps are in the image above
The slope of the line through these two data points is 1.5.
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
x represents the time and y represents the temperature in degrees Fahrenheit.
temperature of –2°F at 8 a.m. Hence:
-2 = 8m + b (1)
it was 4°F at 12:00 p.m. Hence:
4 = 12m + b (2)
Solving equations 1 and 2 simultaneously gives:
m = 1.5, b = -14
The slope of the line through these two data points is 1.5.
Find out more on linear equation at: https://brainly.com/question/14323743
what is (x-2) (3x-4)=
a.3x² - 6x-8
b.3x² - 2x - 8
c.3x² + 10x + 8
d.3x² - 10x + 8
Answer:
D. 3x^2-10x+8
Step-by-step explanation:
[tex] \: \: \: \: \: [/tex]
D. 3x²- 10x + 8hope it helps
refer to the attachment
[tex] \: \: \: \: \: [/tex]
a tv was sold at 9% profit with cost price rs 18000 calculate the sale price of tv
Answer:
the sale price of tv is 1620
Step-by-step explanation:
9/100 because full percentage is from 100%
9/100 x 18000
cut 00 from 18000
we will cut it because 100 also have two 0 and 18000 we will cut two 0
next it will be = 9/1 x 180 one is nothing no so it will be
9 x180 answer = 620
plz mark me as brainliest