When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of a radioactive isotope initially and after 2 hours. What are the amounts left after 1 hour, 3 hours, and 4 hours?
Answers
Answer:
Hour elapsed 0 1 2 3 4
Grams 1986 1032.7 537 279.2 145.2
Explanation:
To find the amount left after 1 hour, 3 hours, and 4 hours, we need to find the common ratio.
Since we know the initial amount and the amount left after 2 hours, the ratio of these quantities is the square of the common ratio, so
r² = 537/1986
r² = 0.2704
r = √0.2704
r = 0.52
Then, the amount left after 1 hour is the initial amount multiplied by the common ratio, so
For 1 hour
Amount left = 1986(0.52) = 1032.7 grams
In the same way, the amount left after 3 and 4 hours is
For 3 hours
Amount left = 537(0.52) = 279.2 grams
For 4 hours
Amount left = 279.2(0.52) = 145.2 grams
Therefore, the complete table is
Hour elapsed 0 1 2 3 4
Grams 1986 1032.7 537 279.2 145.2
Related Questions
Let g be a group with normal subgroups m and n. furthermore, assume n is a subste of m. use the first isomorphic theorem to prove that (g/n)/(m/n) is isomorphic to g/m.
Answers
The proof of (g/n)/(g/m) isomorphic to g/m from the first isomorphism theorem is as shown below.
Let a group g with normal subgroups m and n. Furthermore, n is a subset of m.
Proof: We have to prove (g/n)/(m/n) ≅ g/m (1)
g/m and g/n are valid because m and n are normal in g. As normality satisfies the intermediate subgroup condition, n is normal in m. because normality is image-closed m/n is a normal subgroup in g/n. Under the quotient map by n, the normal subgroup m of g is sent to a normal subgroup m/n of g/n. Thus the L.H.S of the statement to prove makes sense.
To describe the isomorphism from the left side to the right side
φ: g/n \to g/m
ψ(gn) = gm
So, a coset of n is taken by the map and it gives the corresponding coset of m. This is well-defined, because if h∈ n, thus h∈ m, hence (gh)m = g(hm) = gm.
The map is a homomorphism. So we observe that it maps the identity element to the identity element, keeps group multiplication preserved, and also preserves the inverse map.
Also, the map is surjective because any coset gm is present as the image of gn under ψ.
Lastly, we need to find the kernel of the map which is given by the set of gn such that gm = m. This is those cosets of n that are in m, and this is the same as the coset space m/n. Thus the kernel of the map is exactly g/m. Thus, the surjective homomorphism ψ: g/n → g/m has kernel m/n. And now by the first isomorphism theorem
(g/n)/(m/n)≅g/m where ≅ shows isomorphism
another problem to prove whether f is an isomorphism:
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For the function Rx) = +2, which of these could be a value of Ax) when x isclose to 2? A. 0.01B. 2C. -0.01D. 10,000
Answers
The given function F(x) is,
[tex]F(x)=\frac{1}{x-2}[/tex]Take the limit of the function when x ix close to 2.
[tex]Lt_{x\rightarrow2}\frac{1}{x-2}=\infty[/tex]Hence, the function diverges.
Look at photo down below for question
Answers
The coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0)
What is translation of graph?Function translation takes a function (and its graph) and, by adding and subtraction, moves the graph around the plane without changing its shape.
Given is a triangle coordinate on x - y plane.
The rule (x, y) → (- x, - y) represents the rotation of a figure by 180 °.
Now, initially the coordinates of the triangle are -
(-2, 2) , (-3, 8) , (-7, 0)
After transforming the graph by the rotation of 180°, the new coordinates will be -
(2, - 2) , (3, -8) , (7, 0)
Plot the coordinates on the graph and you will get the rotated image.
Therefore, the coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0).
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How much would $500 invested at 6% interest compounded monthly be worth after 5 years? Round your answer to the nearest cent. A.$669.11B.$674.43C.$886.41D.$512.63
Answers
Solution:
Given that;
[tex]\begin{gathered} Principal=P=\text{ \$500} \\ rate=r=\frac{6}{100}=0.06 \\ time=t=\text{ 5 years} \end{gathered}[/tex]To find the amount in 5 years, we will apply the compound interest formula below
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ Since,\text{ it is compounded montly, n = 12} \end{gathered}[/tex]Substitute the values of the variables into the formula above
[tex]\begin{gathered} A=500(1+\frac{0.06}{12})^{(5\times12)}=500\left(1+\frac{0.06}{12}\right)^{60}=674.42507 \\ A=\text{ \$}674.43\text{ \lparen nearest cent\rparen} \end{gathered}[/tex]Hence, the answer is B
Identify pairs of lines which look perpendicular in the diagram. There are more than one answers.
Answers
Answer:
Angles gh, fh, and jh are perpendicular :)
Step-by-step explanation:
perpendicular is when line touch and they make a 90* angle and the three angles that i have listed all touch and make 90*
You have read 4 of the books shown. Which choice shows 2 ways of writing the fraction of these books that you read?
Answers
Using proportions, two ways of writing the fraction of these books that you read is:
4/12 and 1/3.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations, especially multiplication or division.
One example of application of proportions is for relative frequencies, as a relative frequency is given by the number of successes in the sample divided by the sample size.
In the context of this problem, it is found that:
The number of successes on the sample is of 4, as you have read 4 books.The sample size is of 12, as there is a total of 12 books.Hence the relative frequency is:
4/12.
12 is divisible by 4, hence the fraction can be simplified as follows:
1/3.
Missing informationThe number of books is missing, and is of 12. (researching the problem on a search engine).
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if 6x-1=29, what is the value of x2+x
Answers
We are given
[tex]6x-1=29[/tex]Therefore the value of x can be gotten by simplifying the above equation
[tex]\begin{gathered} 6x=29+1 \\ 6x=30 \\ x=\frac{30}{6} \\ x=5 \end{gathered}[/tex]Given that x is 5, we can proceed to find the value of the expression.
[tex]\begin{gathered} x^2+x \\ \Rightarrow(5)^2+5 \\ \Rightarrow25+5 \\ \Rightarrow30 \end{gathered}[/tex]This implies that
[tex]x^2+2\Rightarrow30[/tex]The figure is not drawn to scale. m
Answers
For the given function
The sum of all angles = 360°
So,
[tex]\begin{gathered} y+x+125+90=360 \\ m\angle x=27 \\ So,\text{ } \\ y+27+125+90=360 \\ y+242=360 \\ y=360-242=118 \end{gathered}[/tex]So, the difference between x and y will be:
[tex]y-x=118-27=91[/tex]So, the answer will be:
∠x is 91° smaller than ∠y
PLEASE HELP!!
Points A(-1, 2) and B(5,8) are the endpoints of AB. What are the coordinates of point C on AB such that AC is 2/3 the length of AB
Answers
The coordinates of the point C on the line AB such that AC is 2/3 the length of AB is (3,6) .
In the question ,
it is given that
the coordinates of the end points of A and B is A(-1,2) and B(5,8) .
also AC = 2/3(AB)
So , AC/AB = 2/3
and given that point C is on the line AB , hence AC+CB=AC
2+CB=3
So , CB=1
hence AC/CB = 2/1
so , the point C divides the line AB in the ration 2:1 .
and we have the coordinates of end points ,
that is x₁[tex]=[/tex] -1 , y₁=2 and x₂=5 , y₂ = 8 and the ratio m=2 and n=1 .
Substituting the above values in the section formula ,
which states that the coordinate of point C will be
((m*x₂+n*x₁)/(m+n) , (m*y₂+n*y₁)/(m+n))
= ((2*5+1*(-1))/(2+1) , (2*8+1*2)/(2+1))
= ((10-1)/3 , (16+2)/3)
= (9/3 , 18/3)
= (3,6)
Therefore , The coordinates of the point C on AB such that AC is 2/3 the length of AB is (3,6) .
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What’s the answer pls
Answers
If I'm not mistaken, the answer is 43.17
there are 100 coins and someone flips them and doesn't tell us the results. i can ask one yes/no question. after the answer i will start guessing the coin flip results. for each correct guess i get 1 dollar and for each wrong guess i lose 1 dollar. what is the best strategy to play this game and what is the maximum expected value of the return.
Answers
The answer is not 1 so it is not that simple that you can divide it into 2 equal size subsets and ask whether the final sequence is in there. From what I got through his hints, it should be related to Central Limit theorem.
Given that,
One hundred coins are flipped, but the outcome is kept a secret. I am able to pose one yes/no query. I'll begin speculating on the outcomes of the coin toss following the response. I receive $1 for each accurate guess, and I lose $1 for each unreliable guess.
To find:
What is the most effective gaming approach and what is the highest possible return on investment
By Central Limit Theorem,
It is not straightforward to divide the response into two subsets of equal size and then check to see if the final sequence is present because the answer is not 1. His indications led me to believe that it should be connected to the Central Limit theorem.
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the average number of miles driven on a full tank of gas for a hyundai veracruz before its low fuel light comes on is 320. assume this mileage follows the normal distribution with a standard deviation of 30 miles. what is the probability that, before the low fuel light comes on, the car will travel
Answers
The probability that, before the low fuel light comes on the car will travel is 0.2576
Given,
The average number of miles driven on a full tank of gas before its low fuel light comes on is ( μ )= 320
It follows the standard deviation of ( δ ) = 30
For the normal distribution,
P(X < x) = P( Z < x - μ / δ)
a)
P( X < 330) = P( Z < 330 - 320 / 30)
= P( Z < 0.3333)
= 0.6306
b)
P( X > 308) = P( Z > 308 - 320 / 30)
= P( Z > -0.4)
= P( Z < 0.4)
= 0.6554
c)
P( 305 < X < 325) = P( X < 325) - P( X < 305)
= P( Z < 325 - 320 / 30) - P( Z < 305 - 320 / 30)
= P( Z < 0.1667) - P( Z < -0.5)
= 0.5662 - ( 1 - 0.6915)
= 0.2576
d) P(X = 340) = 0
Since X is a continuous random variable (For normal distribution).
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I need help!
Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
Answers
Using the information of the factors f ( x ) are
( x + 1 ) ⇒ f ( -1 )( x - 4 ) ⇒ f ( 4 )( 2x - 3 ) ⇒ f ( 3/2 )What is a function in math?The term function as used n math refers to a relation consisting of variables. the variables are of two major types which include
The dependent variableThe independent variableThe given function is substituted in the several equations given but the equations that yielded the desirable result of f ( x ) = 0 are:
option 4option 5option 6Therefore they are the correct choice
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What is the slope that passes through these points?
(0, -4) and (-5, -5)
Answers
Answer: m=1/5
Step-by-step explanation:
Safiya travels at an average speed of 40 mph for 30 miles.
Without stopping, Safiya then travels 50 miles in 1.5 hours.
Find her average speed for the entire journey to 2 dp.
Pls help
Answers
Average speed is 35.56 mph.
Calculating average speed involves dividing the whole distance travelled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time. Average speed refers to the average speed during the course of a journey.
We have to find the average speed of the whole journey.
First we have to find total distance for whole journey and then total time for whole journey.
Total distance for whole journey = 30 miles + 50 miles = 80 miles
Time for 30 miles = distance/speed = 30/40 = 3/4 hrs = 0.75 hrs
Total time = 1.5 + 0.75 hrs = 2.25 hrs
Average speed = total distance/ total time
= 80/2.25
= 35.56 mph.
The average speed is 35.56 mph.
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When an integer is subtracted from 2 times the next consecutive odd integer, the
difference is 9. Find the value of the greater integer.
Answers
Answer:
7
Step-by-step explanation:
Let x be the "integer." We'll assume it is odd.
The next consecutive odd integer would be x+2.
(2(x+2) - x) =9 [When an integer is subtracted from 2 times the next consecutive odd integer the difference is 9]
(2(x+2) - x) =9
(2x+4) - x) =9
x+4 =9
x = 5
The greater integer is x+2 or 7
Check:
If 5 is subtracted from 2 times the next consecutive odd integer, 7, is the difference 9?
2*7 - 5 = 9?
14 - 5 = 9?
14 - 5 = 9? YES
this is a 45-45-90 triangle, what is the measure of x? rationalize the denominator
Answers
The value of x in the right triangle is 15√2.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees.
The sides of a right triangle can be named base on the angle position. This includes hypotenuse side, opposite side and adjacent side.
Therefore, the side x of the right triangle can be found using trigonometric ratios as follows:
cos 45 = adjacent / hypotenuse
cos 45° = x / 30
cross multiply
30 cos 45° = x
Therefore,
x = 30 × 1 / √2
x = 30 / √2 × √2 / √2
x = 30√2 / 2
x = 15√2
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Find the indicated part round your answer to the nearest degree
Answers
Solution
For this case we can do the following:
tan x = 35/30
And we can solve for x and we got:
[tex]x=\tan ^{-1}(\frac{35}{30})=49.39[/tex]And rounded to the nearest degree is:
49º
If ax-3=bx+5 then the solution for x in terms of a and b is
Answers
In this equation the solution for x in terms of a and b is 8.
What is equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
Sol- As per the question given that- ax-3= bx+5------(equation 1)
Let ax=3-----(equation 2)
And bx =5------(equation 3)
On adding equation(1)and (2) we get
(ax)+(bx)= 3+5
(ax)+(bx)=8
x(a+b)+y(a+b)=8
(x+y)+(a+b)=8
1×(a+b)=8
Thus
a+b=8
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Zack plans to attend the Carroll County Fair and is trying to decide what would be a better deal. He can pay $40 for unlimited rides, or he can pay $15 for admission plus $1 per ride. If Zack goes on a certain number of rides, the two options wind up costing him the same amount. How many rides is that?
Answers
Let
x -----> number of rides
y ----> the total cost
so
The linear equation that represents both situations are
y=40 -----> equation A
y=x+15 ----> equation B
equate both equations
40=x+15
solve for x
x=40-15
x=25
therefore
the number of rides is 25Can someone help me please with this !!!!!
Answers
Answer:
A. [tex]9n - 190 = 5n[/tex]
Step-by-step explanation:
Dora earning 5 dollars per song is represented by [tex]5n[/tex].
Gary earning 9 dollars a song but paying the $190 fee is represented by [tex]9n - 190[/tex] because the fee from the coffee shop is subtracted from his total earnings.
Pls help me. I'm struggling so bad
Answers
The formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .
in the question ,
it is given that the
formula to find , "gravitational force" between two objects is
[tex]F_{g}[/tex] = (G*M₁*M₂)/r²
to express the formula in terms of M₁ ,
we first multiply both the sides by r² ,
on multiplying , we get
[tex]F_{g}[/tex]*r² = G * M₁ * M₂
On dividing both sides by G ,
we get
( [tex]F_{g}[/tex]*r² ) /G = M₁ * M₂
we have to find the formula for M₁ ,
we divide both sides by M₂,
So , on dividing both sides by M₂ , we get
( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) = M₁
hence M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ )
Therefore , the formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .
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Write the equation of the line that passes through the given points.
1,2.5) and (0,-1.5)
Answers
Answer:
y = 4x - 1.5
Step-by-step explanation:
We need to find the slope (m) and the y-intercept (b), if we are writing this in the slop intercept form of a line.
y =mx + b
The slope is the change in y over the change in x.
The two points give us the y's ad x's
The y's are: -1.5 and 2.5
The x's are: 0 and 1
[tex]\frac{-1.5 - 2.5}{0-1}[/tex] = [tex]\frac{-4}{-1}[/tex] = 4 A negative divided by a negative is a positive.
We have the slope. The slope is the point (0,b). We are given that point.
(o, -1.5) The y-intercept is -1.5
y =mx + b
y = 4x - 1.5
-5< x < 5Graph the solution set on a number line
Answers
- 5 < x < 5
Number line:
What is the value of this expression
Answers
Plug in the values in the right positions. And simplify.
[tex] = \frac{1}{2} (12 \times \frac{1}{4} ) - \frac{1}{2} \\ = \frac{1}{2} (3) - \frac{1}{2} \\ = \frac{3}{2} - \frac{1}{2} \\ = \frac{2}{2} \\ = 1[/tex]
OPTION C IS THE ANSWER .
A and B are complementary angles. If mA = (2x +27)° and mB =
(2x-21), then find the measure of A.
Answers
Answer:
mA = 69 degrees
Step-by-step explanation:
A complementary angle has a measure of 90 degrees.
(2x + 27) + (2x - 21) = 90
Simplify
4x + 6 = 90
-6
4x = 84
/4
x = 21
mA: 2(21) + 27 = 69
Answer:
A = 69°
Step-by-step explanation:
Complementary angles sum 90°
A + B = 90°
(2x + 27) + (2x-21) = 90°
4x + 27 - 21 = 90°
4x + 6 = 90°
4x = 90 - 6
4x = 84°
x = 84°/4
x = 21
Then A:
A = 2x + 27
A = 2*21 + 27
A = 42 + 27
A = 69°
B = 2x - 21
B = 2(21) + 27
B = 42 - 21
B = 21°
Check:
69 + 21 = 90
Which of the following ordered pairs is either the x- or y-intercept of the function 3x + 2y = -6?
Answers
Answer:
x-intercept (-2,0)
y-intercept (0,-3)
Step-by-step explanation:
to find the x-intercept we set y=0
so 3x=-6
x=-2
to find the y-intercept we set x=0
so 2y=-6
y=-3
15 points for thiz one.
Answers
Answer:
(I) y=10-6x. (ii) y=x/-2 - 3
a student has taken 6 tests and received scores of 88, 73, 81, 80, 79, and 94. the seventh test is coming up and the student wants to know what score is needed on the seventh test to have a mean score of 83. determine the score the student needs. show your work.
Answers
Solution:
Let the score for the seventh test be represented below as
[tex]=x[/tex]The mean score t be attained after the sevent tests is
[tex]mean=83[/tex]The scores from the 6 tests are given below as
[tex]88,73,81,80,79,94[/tex]To figure out the seventh score, we will do the calculation below
[tex]\begin{gathered} mean=\frac{additionofthescores}{number\text{ of tests}} \\ 83=\frac{88+73+81+80+79+94+x}{7} \\ 83=\frac{495+x}{7} \\ cross\text{ multpily} \\ 83\times7=495+x \\ 495+x=581 \\ x=581-495 \\ x=86 \end{gathered}[/tex]Hence,
The final asnwer is
[tex]\Rightarrow86[/tex]how to graph y=2x+2 please help
Answers
The graph of the equation is attached to the solution.
We can graph the equation of the line by finding the x and y intercept of the line.
We know that the equation is in the slope intercept form.
Hence, we can write the y-intercept of the line as 2.
The coordinates of the point will be (0,2).
To find the x - intercept, we can put y = 0
0 = 2x + 2
-2 = 2x
x = -2/2 = -1
x = -1
The coordinates of the point will be (-1,0).
We can find another point on the line.
Let x = 1
y = 2(1) + 2
y = 2 + 2
y = 4
The coordinates of the point will be (1,4).
We can plot these points on the graph and get our graph.
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