A lab currently has 70 mg of radioactive material that decays at 3.5% per year. Federal regulation for the substance says that the material must be safely stored until it reaches its half-life, at which time the material can be disposed.
How many years will the lab have to safely
store the material before disposal?
Answer:
The lab will have to wait 19.45 yers to safely store the material before disposal.
Step-by-step explanation:
Exponential equation for substance decay:
A exponential equation for the amount of a substance after t years is given by:
[tex]A(t) = A(0)(1-r)^{t}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Decays at 3.5% per year.
This means that [tex]r = 0.035[/tex]
So
[tex]A(t) = A(0)(1-r)^{t}[/tex]
[tex]A(t) = A(0)(0.965)^{t}[/tex]
How many years will the lab have to safely store the material before disposal?
It needs to reach half-life, that is, t for which A(t) = 0.5A(0). So
[tex]A(t) = A(0)(0.965)^{t}[/tex]
[tex]0.5A(0) = A(0)(0.965)^{t}[/tex]
[tex](0.965)^t = 0.5[/tex]
[tex]\log{(0.965)^t} = \log{0.5}[/tex]
[tex]t\log{0.965} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.965}}[/tex]
[tex]t = 19.45[/tex]
The lab will have to wait 19.45 yers to safely store the material before disposal.
Subtract the polynomials:
(1 Point)
f(x) = 10x4 + 2x² +1; 8 (x) = 3x4 + 3x + 11
O f (x) – 8(x) = 7x4 + 2x2 – 3x – 10
O f(x) – 8 (x) = 7x4 + 2x2 – 3x + 12
O f (x) – 8(x) = 7x4 + 2x2 + 3x + 12
O f(x) – 8(x) = 7x4 + 2x2 + 3x - 10
Answer: thats the answer
Step-by-step explanation:
Make a triangle with 36 unit area and 9 unit base
I cannot necessarily "make" a triangle, but I do know that the dimensions or measurements of the triangle would be:
area = 36 units
base = 9 units
height = 8 units
What does "Uninsured Motorist Bodily Injury" typically cover
Answer:
Uninsured motorist bodily injury, or UMBI, pays for medical bills, pain and suffering, lost wages if you can't work after an accident and funeral expenses after a crash with an at-fault driver who doesn't have car insurance. It may also cover you if you're hit as a pedestrian or while riding your bike.
Step-by-step explanation:
how do I solve "k−26.5=99.1"
Answer: =125.6
Step-by-step explanation:
Add 26.5 to both sides of the equation
Simplify
Real answer not a scam
Answer:
Area = 240 cm²
Step-by-step explanation:
Area of the shape = area of rectangle + area of triangle
= L*W + ½*bh
L = 18 m
W = 10 m
b = 10 m
h = 30 - 18 = 12 m
Plug in the values
Area of the shape = 18*10 + ½*10*12
= 180 + 60
= 240 cm²
how many roots does y= x^5- 4x^2+ 3x
A.3
B.4
C.5
D.6
(x^2 is the power to)
Answer: 4
Step-by-step explanation:
We can write the equation as
[tex]x(x-1)^{2}(x^{2}+2x+3)=0\\\\x=0, 1, -1 \pm i\sqrt{2}[/tex]
Therefore, there are 4 distinct roots.
please help me please i really need help please
Answer:
c i took the test and got that one right
Step-by-step explanation:
A cell phone plan charges $19.90 a month, plus $0.05 per text message
Create & solve an inequality that represents the number of texts, t, that can be
sent while still keeping the monthly bill under $25?
Answer:
[tex]19.9+0.05t<25[/tex]
Less than 102 text messages.
Step-by-step explanation:
Monthly charge of cell phone = $19.90
Cost of one text message = $0.05
Let number of text messages be [tex]t[/tex]
The monthly bill should be less than $25. So,
[tex]19.9+0.05t<25[/tex]
The required inequality is [tex]19.9+0.05t<25[/tex]
[tex]19.9+0.05t<25\\\Rightarrow 0.05t<25-19.9\\\Rightarrow t<\dfrac{5.1}{0.05}\\\Rightarrow t<102[/tex]
So, the number of text messages that can be sent while keeping the bill under $25 is less than 102.
Write each percentage as a fraction in simplest form.
1. 50% 2. 99% 3. 15%
4. 200%
Answer:
1. 1/2
2. 99/100
3. 3/20
4. 2
Dionne can fold 175 packing boxes in 50 minutes.
Elias can fold 120 packing boxes in 40 minutes.
Use unit rates to find how much time it will take each person to fold 210 packing boxes.
Drag the numbers to explain and show your answer. Numbers may be used once or not at all.
370803.54.550604
Dionne can fold
boxes in 1 minute and Elias can fold
boxes in 1 minute.
Dionne will fold 210 boxes in
minutes and Elias will fold 210 boxes in
minutes.
REFER THE ATTACHMENT ABOVE ☝☝☝☝
Answer:
[tex] \frac{176}{50m} = \frac{3.5}{1} [/tex]
RESULT
Use ratio and proportion.
Let x be the time it takes Dionne to fold 210 packing boxes:
[tex] \frac{175}{50} = \frac{210}{x} \\ \\ cross \: multiply \\ \\ \\ 175x = 50(210) \\ \\ x = \frac{50(210)}{175} \\ \\ x = \frac{50(210)}{175} \\ \\ x = 60[/tex]
So, it will take Dionne 60 minutes to fold 210 packing boxes.
Let y be the time it takes Elias to fold 210 packing boxes:
[tex] \frac{120}{40} = \frac{210}{x} \\ \\ cross \: multiply \\ \\ \\ 120x = 40(210) \\ \\ x = \frac{40(210)}{120} \\ \\ \\ x = 70[/tex]
So, it will take Elias 70 minutes to fold 210 packing boxes.
HELP PLSSSS I BEG UUUU PLSSS
Answer: Thursday
Step-by-step explanation:
I hope this helps
Answer: Thursday
Step-by-step explanation:
It's Thursday because any number below 0 is a negative number but, as Thursday is 3° above 0, it is positive.
Hope this helps :)
Two apples and six plums provide 300 calories. Three apples and five plums provide
350 calories. How many calories are provided by five apples and eight plum?
Answer:
4,596
Step-by-step explanation:
Select the correct answer. The hiking club is getting new T-shirts and will vote to choose the design. Marianna and Chloe are each designing a T-shirt using a computer program. Marianna’s design features an image of the mountains, with the peaks and valleys modeled by function m, where x is the horizontal distance, in inches, from the left edge of the design. Chloe’s design also features an image of the mountains, with the peaks and valleys modeled by function c, where x is the horizontal distance, in inches, from the left edge of the design. Which T-shirt design has the lowest valley floor over the first 6 inches of the design? Both designs have valley floors at the same height over the first 6 inches of the design. Marianna’s design doesn’t have a valley floor over the first 6 inches of the design. Chloe’s design has the lowest valley floor over the first 6 inches of the design. Marianna’s design has the lowest valley floor over the first 6 inches of the design.
Answer:
Step-by-step explanation:
What are the choices
Answer:
mariannas design has the lowest valley floor over the first 6 inches of the design
Step-by-step explanation:
correct.
a patients dose of medication increased from 100mg to 150mg. What is the percent increase in medication?
Answer:
The answer is 50% increase. Hope this helped!
Step-by-step explanation:
Write an equation in slope-intercept form for the line with slope -3/2 and y -intercept 2 .
Answer:
Y= -3/2x + 2
If the y-intercept was negative it would be y= -3/2-2
what is the answer of
reciprocal of 1/7
Answer:
7/1
Step-by-step explanation:
A reciprocal means you flip the numerator and the denominator (the top number and the bottom number) so In this case the reciprocal for 1/7 s 7/1.
Hope I could help!
HELP PLS!!!
120=x-523?
Answer:
-62760
Step-by-step explanation:
Negative nine times a
number equals -117.
!!!!please helppppppp
9514 1404 393
Answer:
13/18
Step-by-step explanation:
5 of the 18 students have a cat, so 13 of them do not.
The probability that a student in the group does not have a cat is 13/18.
PLEASE HELP ME KSDAKJDSAJDJKS
Answer: x = 16
Step-by-step explanation:
60x - 60 = 900
60x = 960
60x / 60 = 960 / 60
x = 16
Trapezoid ABCD has an area of 525 cm squared. If height AB = 21 cm and BC = 37 cm, what is the measure of AD?
Answer:
AD = 13
Step-by-step explanation:
Area of trapezoid ABCD
[tex] = \frac{1}{2} (AB + AD) \times AB \\ \\ 525= \frac{1}{2} (37+ AD) \times21\\ \\ 525 \times 2= (37+ AD) \times21 \\ \\ 1050 = 21 \times 37 + 21AD \\ \\ 1050 = 777+ 21AD \\ \\ 21AD = 1050 - 777 \\ \\ 21AD = 273 \\ \\ AD = \frac{273}{21} \\ \\ AD = 13[/tex]
PLEASE HELP
I will give brainliest to right answer
Answer:
I'm pretty sure it is D because they're not super close to the line they're more spread out but I'm not rly sure
Can someone help me? I’ll reward points + brainalist
Step-by-step explanation:
the question of your answer is d
Answer:
Step-by-step explanation:
12 points and brainliest pls and thank you ! (no unknown links or ill report u and ur whole acc)
Answer:
13
cuz one of those square part = to 90 degrease
so 77 degrease is already shown so minus 90-77
and u get 14
Answer:
x = 13°
Step-by-step explanation:
Angles 77° and BGE are vertical and thus equal angles. Angle x and BGE are complementary angles; thus, x + 77° = 90°. Solving this for x, we get:
x = 13°
find the distance between the two points
(1, 2), (-3, 5)
Answer:
13
Step-by-step explanation:
if you cannot find the awnser next time try mathaway it gives you the awnser and tells you an explanation.
help i cant do fractions
PLEASE HELP I WILL MARK BRAINLIST!!
14: [tex]\frac{1}{2} = \frac{8}{1}[/tex] [tex]\frac{x}{y} = \frac{56}{1}[/tex]
56/8 = 7 so multiply 1/2 by 7/1 to get the unidentified fraction "x/y"
1/2 · 7/1 = 7/2 or 3 1/2
15. [tex]\frac{2}{5} = \frac{x}{100}[/tex]
to get from 100 to 5, you would divide by 20, so to solve for x, multiply 2 by 20, to get a product of 40.
40/100 = 40% or D
16. [tex]\frac{3}{5} = \frac{12}{x}[/tex]
A
Can someone help me? I’ll reward points + brainalist
Answer:
B
Step-by-step explanation:
2 CDs - $9.98
5 CDs - [tex]\frac{5}{2}[/tex] × $9.98 = $24.95 (Option B)
Answer:
B.
Step-by-step explanation:
Cost of 2 CD = 9.98
cost of 1 CD = 9.98/2 =4.99
Cost of 5 CD = 4.99 × 5 = 24.95
Solve for x. Round to the nearest tenth.
15°
33
x
The length of x in the right triangle is 31.9 units.
How to solve the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the side of a right triangle can be found using trigonometric ratios as follows:
Hence,
cos 15° = adjacent / hypotenuse
adjacent side = x
hypotenuse side = 33 units
cos 15° = x / 33
cross multiply
x = 33 cos 15°
x = 33 × 0.96592582628
x = 31.8755522675
Therefore,
x = 31.9 units
learn more on right triangle here:https://brainly.com/question/20046799
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