there will be approximately 61 grams of the radioactive rhodium remaining after 120 seconds.
What are exponential growth and decay?A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay. Over time, exponential functions monitor constant growth. Examples from the actual world include radioactive decay, compound interest, and bacterial proliferation.
Given, You have 976 grams of a radioactive kind of rhodium.
The formula for the amount of a substance remaining after a certain amount of time given its half-life is:
N = N₀ *[tex](1/2)^{t / t_{1/2} }[/tex]
where:
N₀ is the initial amount of the substance
N is the amount of the substance remaining after time t
t₁/₂ is the half-life of the substance
In this problem, N₀ = 976 grams, t = 120 seconds, and t₁/₂ = 30 seconds. We can plug these values into the formula and solve for N:
N = 976 * (1/2)⁽¹²⁰/³⁰⁾
N = 976 * (1/2)⁴
N = 976 * 0.0625
N ≈ 61
Therefore, after 120 seconds, there will be approximately 61 grams of the radioactive rhodium remaining.
Learn more about exponential growth and decay here:
https://brainly.com/question/17161065
#SPJ1
The work of a student to solve the equation 3(3x − 4) = 8 + 2x + 5 is shown below: Step 1. 3(3x − 4) = 8 + 2x + 5 Step 2. 6x − 7 = 13 + 2x Step 3. 6x − 2x = 13 + 7 Step 4. 4x = 20 Step 5. x = 5 In which step did the student first make an error and what is the correct step? (1 point) Step 2, 9x − 12 = 13 + 2x Step 2, 9x − 4 = 2(6 + x + 3) Step 3, 6x + 2x = 13 + 7 Step 3, 6x − 2x = 13 − 7
Answer:
(a) Step 2. 9x -12 = 13 +2x
Step-by-step explanation:
The distributive property says a factor outside parentheses multiplies each term inside parentheses. It is an error to do addition of the factor, or to miss multiplying a term.
In Step 2 of this "solution", the factor of 3 is erroneously added to each coefficent inside parentheses. It should be multiplied.
Correct Step 2: 9x -12 = 13 +2x
__
The rest of the solution should be ...
Step 3: 9x -2x = 13 +12
Step 4: 7x = 25
Step 5: x = 25/7
___
Check
3(3(25/7) -4) = 8 + 2(25/7) +5
3((75 -28)/7) = 13 +50/7
141/7 = 141/7 . . . . . answer checks OK
URGENT
What will five 100's do to a grade of 92%? How many points will it bring my grades up by?
Answer:
See below ~
Step-by-step explanation:
Given
Mean = 92%Solving
Add 5 points of 100% and divide by 6 (total entries)92 + 5(100) / 6592/698.67%Solution
Five 100s will bring up the 92% up by 6.67% to 98.67%Point A is located at (-2, -3). After it is transformed, point A' is located at (-2, 3).
How was the point transformed?
It was reflected in the y-axis
it was rotated 180°
it was rotated 90 around the origin
it was reflected in the x-axis
Answer:
D.Step-by-step explanation:
All the other answers are wrong.
The points are reflected across the x-axis.
Here is why:
Point A is at (-2, -3)Point A' is located at (-2, 3)If you move across the x-axis in this form, you will see that they are reflected.Correct choice is D.
4.1: Angle Articulation
Triangle A'B'C' is a dilation of triangle ABC using center P and scale factor 2.
1. What do you think is true about the angles in A' B'C' compared to the angles in ABC?
2. Use the tools available to figure out if what you thought was true is definitely true for
these triangles.
3. Do you think it would be true for angles in any dilation?
1.) The measure of each angle of ABC is equal to the corresponding angle of A'B'C' , the measures of this angle is preserved when you rotate the triangle.
2.) It was clear that triangle A'B'C' is dilated form ABC, meaning the angles will be the same.
3.) The rules for dilation only change the length of the triangle not the angles.
Moses is creating a large cube sculpture for a city park. He first makes a smaller cube to use as a rough model of his sculpture. The edge lengths of the model are each 25 in. The edge lengths of the sculpture will be 3 times the model's edge lengths. How many times as large is the volume of the sculpture than the volume of the model? Show your work.
From the calculations, the volume of the sculpture is 27 times the volume of the model.
Volume of a cubeThe volume of a cube is obtained using the formula;
Volume = l^3
Where l is the length of each edge. We should note that the lengths of all the edges in a cube are equal.
Hence,
volume of the model = (25)^3 = 15625 in^3
volume of the sculpture = (3 * 25)^3 = 421875 in^3
Ratio of the volume of the sculpture to the volume of the model = 421875 in^3/15625 in^3
= 27:1
Hence, the volume of the sculpture is 27 times the volume of the model.
Learn more about volume: https://brainly.com/question/12908738
A number cube is rolled 450 times and the
results recorded as follows: There were
75 ones, 80 twos, 69 threes, 78 fours,
77 fives, and 71 sixes. What is the
experimental probability of rolling a two or a
three?
[A] 0.33 [B] 0.57 [C] 0.43 [D] 0.67
Answer:
A.) 0.33
Step-by-step explanation:
The courier travelled 508 km in 8h. b) At this rate, how long will it take the courier to travel 889 km?
Answer:
14 hours
Step-by-step explanation:
Finding the rate of travel
Distance covered / Time taken508 kilometers / 8 hours63.5 kilometers per hourTime taken to cover 889 km
Distance / Rate of Travel889 kilometers / 63.5 kilometers per hour14 hoursJodi sorted shapes into two groups based on the types of angles they
appear to have, as shown below.
Both shapes in group A and group B are inscribed in a circle
Shapes present in group A and group BIn group A and group B, we have different shapes present in them.
In group A, we have two shapes that are inscribed in a circle.
In group B, what both shapes have in common is that they're inscribed in a circle.
The shape below belong to a rectangle.
Both shapes have a common factor which are
They are both inscribed in a circleLearn more on shapes here;
https://brainly.com/question/25965491
Which expression is equivalent to 10x2y 25x2? 5x2(2y 5) 5x2y(5 20y) 10xy(x 15y) 10x2(y 25)
GCF is the highest value that can divide an expression. The equivalent expression to 10x^2y + 25x^2 is 5x^2 (2y + 5)
Factoring polynomial expressionsGCF is the highest value that can divide an expression. Given the expression below
10x^2y + 25x^2
Find the factor of each
10x^2y = 5 * 2 * x^2 * y
25x^2 = 5 * 5 * x^2
Since 5x^2 is common to both factors, hence
10x^2y + 25x^2 = 5x^2 (2y + 5)
The equivalent expression to 10x^2y + 25x^2 is 5x^2 (2y + 5)
Learn more on factoring here: https://brainly.com/question/24734894
Help will name Brainliest
Answer:
x = 5
Step-by-step explanation:
using the sine or cosine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 10 ( divide both sides by 2 )
x = 5
Please help I'll give Brainliest and Thanks. its also due in 15 minutes.
Simplify: -1║2/3 - 4║ ÷ 5/6
║means an absolute value line.
A. -4
B. -25/9
C. 25/9
D. 4
Answer:
A or -4
Step-by-step explanation:
simplify to -1 || -10/3 || × 6/5
-1 × 10/3 × 6/5
-1 × 2 × 2
What is the volume of the prism?
Enter your answer in the box as a mixed number in simplest
form.
1/1/2 1/1/2 2ft
Answer:
[tex]\text{the volume of the prism =} \ 4\frac{1}{2} \ ft^3[/tex]
Step-by-step explanation:
Formula _____________________
the volume of a prism = base × height
================================
[tex]\text{base\ =} \ 2\times 1\frac{1}{2} =2\times \left( 1+\frac{1}{2} \right) =2\times \left( \frac{3}{2} \right) =3[/tex]
[tex]\text{the volume of the prism =} \ 3\times \left( 1\frac{1}{2} \right) =3\times \left( \frac{3}{2} \right) =\frac{9}{2} =4\frac{1}{2}[/tex]
Allison and Amir are working on a school project together. Allison will do 3/4 of the research, and Amir will do the rest. Amir can do 1/8 of the research in an hour. How long will it take amir to complete his research
Answer: 2hours
Step-by-step explanation:
Allison does 3/4 and Amir does 1/4
Amir can do 1/8 in 1hr, how long will it take to complete ¼ work
1/4 ÷ 1/8 =2
Using the table, if there are 5 flowers, how many petals are there?
A) 11
B) 6
C) 30
D) 25
Answer:
i think is 25
Step-by-step explanation:
you dont have no diagram but i think it 5x5=25
Daddy spends 50% of his salary on rent, 1/4 of the remainder on groceries and keeps the rest. If he keeps $4800, how much is his salary
Answer:
$19,200
Step-by-step explanation:
Daddy spent 3/4 of his salary on things.
This means that you can multiply 4,800*4 to find the salary as 4,800 is 1/4 of the total salary.
4,800*4=19,200
Thomas drive from junction 2 to junction 3 on a road . The distance between the junctions is 12 miles and it takes 15 minutes. Hanna also drove from junction 2 to junction 3 on the road. She drove at an average speed of 50 mph . Who has the faster speed. Explain
Answer:
Hanna
Step-by-step explanation:
In order to find out how fast Thomas has drove as compared to Hanma we have to compare the speed of each other,
Speed of Hanna = 50mph (as given in ur question)
Speed of Thomas
Since the unit of time of the distance traveled by Thomas is not same as that of Hanna we have to convert the minutes into hour,
Distance traveled = 12miles
Time taken = 15minutes
Speed = 12miles/15mim
Converting minutes into hours we have to multiply by a number whose product will be 60 and that will 4
that is 15 times 4 is 60. But to make the ratio equal
we have to multiply the distance too by 4.
= 12*4/15*4
=48 miles/60minutes
=48miles/1hour
=48mph
Comparing both speeds
Speed of Hanna compared to Speed of Thomas,
50mph > 48mph
Hence, Hanna has the faster speed.
Work out the value of x
Answer:
Step-by-step explanation:
Add 87° + 63° = 150°
then set up this equation:
x + 150° = 180°
x + 150° = 180°
- 150° = -150°
x = 30°
When you add 87 + 63 + 30
it should give you 180° if it doesnt equal 180° then recheck your work.
This screenshot should help you
Stay Safe GL!
What is the probability for blue or yellow (be sure to simplify)?
Answer:
Step-by-step explanation:
No of red marbles=n(A)=3.Total no of marbles=n(s)=3+2+5=10.Probability,p(A)=n(A)/n(s)
Please help me! I need to figure it out
[tex]Q_3-Q_1=Q_i[/tex]Answer:
The answer is 10. Frank has done more than Marquis by10.
Step-by-step explanation:
From the internet, the interquartile is Q_3-Q_1=Q_inter
From Marquis his Q_3 = 40 and Q_1 = 20
[tex]Q_3-Q_1=Q_i[/tex]
40-20=20
From Frank his Q_3 = 40 and Q_1 = 10
[tex]Q_3-Q_1=Q_i[/tex]
40-10=30
Frank's interquartile is 30 and Marquis interquartile is 20.
Differences between the both of them.
30-20=10
The area of a computer screen is 108 in with a side length of 12. What is the area of a tv screen similar to the computer screen with a side length of 20 in?
Answer:180in squared
Step-by-step explanation:
108 divided by 12 is 9, so 20*9= 180
what is the LCM of 24 and 54?
Answer: 216
Step-by-step explanation:
The LCM of 24 and 54 is 216. To find the least common multiple of 24 and 54, we need to find the multiples of 24 and 54 (multiples of 24 = 24, 48, 72, 96 . . . . 216; multiples of 54 = 54, 108, 162, 216) and choose the smallest multiple that is exactly divisible by 24 and 54, i.e., 216.
Answer: 216
Step-by-step explanation: The LCM of 24 and 54 is 216. To find the least common multiple of 24 and 54, You need to find the multiples of 24 and 54.
I need to know the of the blue line
Step-by-step explanation:
if i pick (3,4) and (6,10)
the formula for gradient is difference in y divided by difference in x . therefore
10-4 divided by 6 - 3 equals to 6 divided by 3 = 2
the gradient is 2
Help!! Algebra 1 math equation
Answer:
6
Step-by-step explanation:
The answer is 6. You're looking for the rate of change in the number of DVD's. from 9,15,21,27, each time you add 6, so +6 is your constant variation.
In a rhombus ABCD, m∠A = 31°. Point O is a point of intersection of diagonals. Find the measures of the angles of triangle ΔBOC.
m
SHOW PROPER WORK
Kiran is going to see a movie and is taking his 3 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $4. 50 each. How much total money would Kiran have to pay for his family if he were to buy 4 snacks for everybody to share? How much would Kiran have to pay if he bought xx snacks for everybody to share?
I will give brainlist plsssss I need helppp
Answer: I only have the first answer sorry. The 1st answer is $13.50
Step-by-step explanation:
I multiplied $4.50 by the 3 kids and got $13.50 for the snacks.
Nina’s garden is 4 1/5 meters long and 3/10 meter wide. What is the area of Nina’s garden
Answer:
12.6
Step-by-step explanation:
1/5 = .2
3/10 = .3
4.2 x .3 = 12.6
You a roll a 6-sided die two times.
What is the probability of rolling a number greater than 4 and then rolling a 5?
Answer:
[tex]\frac{1}{18}[/tex]
Step-by-step explanation:
First, let’ find the probability of rolling a number greater than a 4The scorers that satisfy this are 5 & 6This is a [tex]\frac{1}{3}[/tex] chance of getting a 5 or a 6AND means × when it comes to probabilityChance of rolling a 5 is [tex]\frac{1}{6}[/tex]Multipy the two fractions together[tex]\frac{1}{3}\times\frac{1}{6}=\frac{1}{18}[/tex]how many groups of 7 does it take to make 7 tens
Answer:
It takes 10 groups of 7 to make 7 tens
Step-by-step explanation:
I’m smart
For a project, Carlos must provide one cut-out paper model of each type of triangle: acute, right, and obtuse. He sketches each triangle on graph paper before making the models.
On a coordinate plane, 3 triangles are shown. One triangle has points (3, 3), (3, 6), (6, 3). Another triangle has points (5, 7), (4, 10), (7, 8). Another triangle has points (7, 1), (7, 6), and (9, 4).
What is the total area of the three triangles?
12.5 square units
13 square units
13.5 square units
14 square units
Answer:
Its 12.5 squares eric deleted my answer!
Step-by-step explanation:
Answer: B. 13
Step-by-step explanation: On Edge!!!!
Which expression is equivalent to -3x+9?
A.-3(x+9)
B.-3(x-3)
C.-3(x+12)
D.3(-x-3)
Explanation:
Use the distributive property to pull out the -3
When going in reverse like this, we divide each term by -3
-3x/(-3) = x
9/(-3) = -3
So -3x+9 = -3(x-3)
We can verify this by multiplying the -3 outside with each term inside
-3 times x = -3x
-3 times -3 = 9
This shows how -3(x-3) turns into -3x+9 again.