Answer:
The half-life of this radioactive substance is of 8.6 months.
Step-by-step explanation:
Exponential decay of an amount:
The equation that models an amount after t units of time, subject to exponential decay, 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.
A radioactive substance decays to 30% of its original mass in 15 months.
This means that [tex]A(15) = 0.3A(0)[/tex]. We use this to find 1 - r.
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]0.3A(0) = A(0)(1-r)^{15}[/tex]
[tex](1-r)^{15} = 0.3[/tex]
[tex]\sqrt[15]{(1-r)^{15}} = \sqrt[15]{0.3}[/tex]
[tex]1 - r = (0.3)^{\frac{1}{15}}[/tex]
[tex]1 - r = 0.9229[/tex]
So
[tex]A(t) = A(0)(0.9229)^t[/tex]
Determine the half-life of this radioactive substance to the nearest tenth.
This is t for which A(t) = 0.5A(0). So
[tex]A(t) = A(0)(0.9229)^t[/tex]
[tex]0.5A(0) = A(0)(0.9229)^t[/tex]
[tex](0.9229)^t = 0.5[/tex]
[tex]\log{(0.9229)^t} = \log{0.5}[/tex]
[tex]t\log{0.9229} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.9229}}[/tex]
[tex]t = 8.6[/tex]
The half-life of this radioactive substance is of 8.6 months.
Tessellations
Determine whether the given figure tessellates the plane.
a. yes
b. no
Please select the best answer from the choices provided
Answer:
A. Yes
Step-by-step explanation:
I calculated it logically
Yes the given figure with triangular tessellates the plane.
All triangles tessellate.
The picture works because all three corners (A, B, and C) of the triangle come together to make a 180° angle - a straight line.
This property of triangles will be the foundation of our study of polygon tessellations, so we state it here: The sum of angles of any triangle is 180°.
Yes, the given figure tessellates the plane.
Hence, Yes the given figure tessellates the plane.
To learn more on triangles click:
https://brainly.com/question/2773823
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Randy wants to save $21 to buy a basketball he saved $7 each week which array represents the number of weeks randy needs to save $21
Answer:
he will have to save $7 for 3 weeks to get $21
Step-by-step explanation:
The length of a rectangle is 10 more than the width. If the
area is 24 square inches, what are the dimensions?
Answer:
Dimensions : L = 12 inches, Width = 2 inches
Step-by-step explanation:
Let width be w
Let length be w + 10
Area = length x width
24 = w x (w + 10)
[tex]24 = w^2 + 10w\\\\w^2 + 10w - 24 = 0\\\\w^2 +12w -2w -24 = 0\\\\w(w+12) -2(w+12) = 0\\(w-2)(w+12)=0 \\w = 2 , -12[/tex]
Since width is a side of a rectangle , it cannot be negative. so w = 2 inches .
Therefore , length = w + 10 = 12inches
Which expressions are equivalent to -3(t - 7 + 5t + 8)?
Answer: It's B, C, F Hope it helps!
Step-by-step explanation: -3(t-7+5t+8) collect like terms -3(6t+1)
which would give you -18t-3
It C to because 1. expand by distributing terms -(18t+9)+6
2. Remove parentheses -18t-9+6
3. Collect like terms -18t+(-9+6) simplify and it would give you -18t+3 it also F because I collect like terms (-3t-15t)+(21-24) and you simplify and that would give you -18t-3 as well can you make me brainliest bye!
A is 150m 2 miles long Directional signs are posted along the trail every 1/3 mile. How many signs are posted along the trail?
Can someone help me with this work ???
Answer:
bottom left
Step-by-step explanation:
Estimate the solution to the following system of equations by graphing. 3x + 5y = 14
6x - 4y = 9
Step-by-step explanation:
hope helps u
have a nice day
the parabola y=-x^2+12x-11 has an axis of symmetry of x=6. which of the following represents its range?
1) y>-11
2)y<25
3)y<6
4)y>10
(all of the ">/<" are underlined ones)
Answer: 1) y>-11
Step-by-step explanation:
Numerical expressions for add 12 to 8 then multiply by 5
Answer:
5(8+12)
Step-by-step explanation:
Solve the quadratic equation graphically using at least two different approaches. When necessary, give your solutions to the nearest hundredth.
x squared + 12 x + 11 = 0
a.
x = -11 or x = -1
c.
x = 10 or x = -3
b.
x = 1 or x = 6
d.
x =0 or x = -6
Please select the best answer from the choices provided
A
B
C
D
Answer:
answer a
a.
x = -11 or x = -1
HELP HELPP PLEASEEEE!
Answer:
Step-by-step explanation:
volume of pyramid with square base=a^2(h/3)
84=a^2*7/3
84*3/7=a^2
252/7=a^2
36=a^2
[tex]\sqrt{36[/tex]=a
6=a
therefore length=6
helppppppppppppppppppppppppppppppppppppppppp
Answer:
character
Step-by-step explanation:
I think Character because character is basically position and who you're playing as
Which answer choice below best describes the number (22 + 6)
Answer:
You FAILED to include any choices.
Step-by-step explanation:
If someone helps me with all of them i will mark them as brainliest
Answer:
Step-by-step explanation:
1. (a) 24 X 3/4= 18 multiplication
you have to multiply to get a smaller answer since you are using a fraction.
2. (a) 24 / (-3/4)= -32 division
you have to divide to get a bigger number than started since you are using a fraction
3. (A) 12-15= -3 subtraction
when you subtract a bigger number than the first number you end up normally with a negative number
4. (a) 12 -(-15) subtraction
when you subtract with a negative number you distribute so the two negatives cancel out and it become an addition sign. (if you look at it the two negatives and the parenthesis looks like an addition sign (+)
5. (A) -18 / (-3/4) =24 division
when you divide two negative values you will always get a positive answer. And again dividing a fraction will get you a bigger answer.
A bag contains seven red marbles and three blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. Find the probability that both the first and second marbles are red.
Answer:
Step-by-step explanation:
A bag contains 8 red marbles, 3 blue marbles and 7 green marbles.
Total = 18 marbles.
Probability of drawing three red marbles = probability of drawing one red without replacement + probab of drawing another without reeplacement + probab of drawing a third without replacement.
Probability of drawing three red marbles = 8/18 + 7/17 + 6/16 = 0.4444 + 0.4118 + 0.3750 = 1.2312.
Which problem can be solved using the equation below?
Answer:
Mr. peter puts 24 students into groups of 8. How many groups are there?
Step-by-step explanation:
Whenever the word "groups" is used, it typically means to divide. Because we see the word "groups", it would be reasonable to assume that you will be dividing something.
Can Some One Help Me. Plz
Answer:
$16,000
Step-by-step explanation:
This is because 5 is the thousand place and the hundredth place is more than 5 so, it rounds up (to 16000)
Feel free to mark this as brainliest :D
Answer:
16,000
Step-by-step explanation:
15,827
8 is greater than 4 so you round up
5 turns to 6 and everything to the right turns to 0
So the answer is 16,000
Can anyone do this two question for me it’s test just have 15 minutes please do quick god bless you
The probability of tails of a weighted coin is 0.58. The number of tails is noted each of the 25 times the coin is tossed. If this procedure is repeated 150 times, what type of distribution is simulated
Answer:
It is a sampling distribution of the sample proportion for which n = 150 and p = 0.58
Step-by-step explanation:
Given -
Probability of tails of a weighted coin = 0.58
Number of tail is noted each 25 times
Repetition of procedure = 150 times
mean = p = 0.58
SD = Sqrt {p(1-p)/n}
Substituting the given values, we get -
SD = Sqrt {0.58(1 – 0.58)/150}
= 0.04029
It is a sampling distribution of the sample proportion for which n = 150 and p = 0.58
Answer:
The options are not given so these are the options:
- A binomial distribution with n = 25 and p = 0.58
- A binomial distribution with n = 2 and p = 0.58
- A sampling distribution of the sample proportion with n = 25 and p = 0.58
- A sampling distribution of the sample proportion with n = 150 and p = 0.58
- There is not enough information to determine the distribution.
Step-by-step explanation:
The answer is - A binomial distribution with n = 25 and p = 0.58.
I got it right on my test.
Good luck!
Find the
area of the parallelogram.
The area of this parallelogram is:
10 unit²
Answer:
10 units
Step-by-step explanation:
2x5
Marcus bought a booklet of tickets to use at the amusement park. He used 50% of the tickets on rides, 1/3 of the tickets on video games, and the rest of the tickets in the batting cage. Marcus says he used 10% of the tickets in the batting cage. Do you agree? Explain.
Answer:
No, i dont agree as 1/3 in percentage is 33%
33+50=88
100-88=12
Meaning that he used 12% of the tickets in the batting cage.
What is its equation in slope-intercept form ?
Answer:
Candice
Step-by-step explanation:
Borrows 15,200 for 10 months at an annual rate of 4.55%. What is the interest owed after 10 months
the answer in the photo check it
los trabajadores de una mina se encuentran a 20 metros bajo tierra .Si excavan 3 metros desde alli suben otros 8 metros para coger una caretilla a que altura estaba la carretilla
Answer:
carretilla
Step-by-step explanation:
la carretilla se encontraba a unos 18 metros de altura
HELP ME PLEASE I DONT KNOW WHAT THIS IS!!!!!
Answer:
A
Step-by-step explanation:
MArk me brainliest! pls :)
HELP ME PLEASE! 20 POINTS!
Answer:
1 no answer=1/100
2 no answer=1/100
3 no answer=100
Step-by-step explanation:
Write the length of the radius if the diameter is 6 centimeters
Answer:
3 centimeters
Step-by-step explanation:
The diameter is 2 times the radius, meaning 6/2 is 3.
Answer:
3cm (This is because diameter is double the radius)
If 3/4 of an inch on a map is equal to 45 miles , what does 1 inch represent?
Answer:
60 miles
Step-by-step explanation:
if 45 = 3/4
divide 45 by 3 = 15
15 * 4 = 60
Use the picture to answer the questions.
What is the value of x in the figure?
Answer: b
Step-by-step explanation:
10 + 50=60
60+30=90
You are correct the answer is B
a) Work out (8 x 10*) * (2 x 10-)
Give your answer in standard form.
b) Work out (6 x 10?) + (3 x 10°)
Give your answer in standard form.
Answer:
A. 16 × 10¯⁷
B. 2 × 10⁷
Step-by-step explanation:
A. 8×10¯³ × 2×10¯⁴
Recall:
Mᵃ × Mᵇ = Mᵃ⁺ᵇ
Thus,
(8×10¯³) × (2×10¯⁴) = (8×2) × 10¯³ ⁺ ¯⁴
= 16 × 10¯³¯⁴
= 16 × 10¯⁷
Therefore,
(8×10¯³) × (2×10¯⁴) = 16 × 10¯⁷
B. (6×10²) ÷ (3×10¯⁵)
Recall:
Mᵃ ÷ Mᵇ = Mᵃ¯ᵇ
Thus,
(6×10²) ÷ (3×10¯⁵) = (6/3) × 10² ¯ ¯⁵
= 2 × 10²⁺⁵
= 2 × 10⁷
Therefore,
(6×10²) ÷ (3×10¯⁵) = 2 × 10⁷