Answer:
Ending Amount = beginning amount / 2^n where "n" is the number of half-lives or elapsed time / half-life
For this problem "n" = 25 / 11 = 2.2727272727
Ending Amount = 60 grams / 2^2.2727272
Ending Amount = 60 / 4.832357534
Ending Amount = 12.4162998242 grams
Source: www.1728.org/halflife.htm
Step-by-step explanation:
A radionuclide is a nuclide with excessive nuclear energy, which makes it unstable. The element would remain after 25 years, to the nearest whole number is 2 grams.
What is a radioactive isotope?A radionuclide is a nuclide with excessive nuclear energy, which makes it unstable. This surplus energy can be discharged as gamma radiation from the nucleus, transferred to one of its electrons and released as a conversion electron, or used to generate and produce a new particle from the nucleus.
Given the life of radioactive material is stated by the formula,
[tex]N_t = N_o e^{-\lambda t}[/tex]
Now, given the half-life of the comes in 11 years, therefore, the rate of decay will be,
[tex]N_t = N_o e^{-\lambda t}\\\\\dfrac{N_t}{ N_o }=e^{-\lambda t}\\\\0.5 = e^{-\lambda \times 11}\\\\\dfrac{ln(0.5)}{11}=\lambda[/tex]
λ = 0.14631
Given the initial mass is 60 grams, therefore, the amount that will be remaining after 25 years will be,
[tex]N_{25} = 60 \times e^{(-0.14631\times 25)}\\\\N = 1.5474\rm\ grams \approx 2\ grams[/tex]
Hence, the element would remain after 25 years, to the nearest whole number is 2 grams.
Learn more about Radioactive Isotopes:
https://brainly.com/question/1907960
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Find the measurement indicated in each parallelogram.
1)
с
40°
D
E
Answer:
D=40
C=140
E=140
Step-by-step explanation:
opposite angles are congruent in parallelograms, so D is equal to 40. Also, the interior angles of any quadrilateral always equal 360, and because there are only 2 angles left that we don't know what they equal, if we add 40 to 40, which equals 80, and then subtract 80 from 360, we get 280, which we then divide by 2, to get 140 for C and E.
Can someone help me? I’ll reward points + brainalist (btw only need help with number 13)
13/5 as mixed number add and subtract
Answer:
2 and 3/5
Step-by-step explanation:
5 can go into 13 twice and u have 3 left over which equals 2 and 3/5
hope this helps
1) Una bicicleta circula en línea recta a una
velocidad de 15km/h durante 45 minutos. ¿Qué
distancia recorre?
Answer:
the distance covered is 11.25 km
Step-by-step explanation:
Given that
The speed of the bicycle is 15 km/h
And, the time taken of the bicycle is 45 minutes
We need to determine the distance covered
As we know that
Speed = Distance ÷ Time
So, distance = Speed × time
= 15 km /h × 0.75 hours
= 11.25 km
The 0.75 hours come from
= 45 minutes ÷ 60 minutes
= 0.75 hours
Hence, the distance covered is 11.25 km
You are baking a casserole. The recipe calls for of a cup of beans to
make 5 servings. How many cups of beans would you need to make 25
servings?
Answer: 5 cups of beans
Step-by-step explanation:
25/5=5
OR
5•5=25
math work geometry help please
Answer:
(C)
Step-by-step explanation:
please click the heart and rate excellent and brainleist to ❤☺️☻♨️♨️☻☺️❤
2) Triangle ABC is an isosceles triangle with
Answer:
that makes no sense.
Step-by-step explanation:
What is the least common multiple of 41 and 50?
PLEASE HELP ME!!!!!!!
Answer:
2050
Step-by-step explanation:
PLEASE HELP ME ALSO SOLVE THIS
Answer:
hiii
Step-by-step explanation:
hiii
I need assistance on what to do
Answer:
156.9
Step-by-step explanation:
∠x=4(∠y)
Angles in a triangle add to 180:
∠x+∠y+90=180
4(∠y)+∠y=90
5(∠y)=90
∠y=18
The left side of the parallelogram is opposite ∠y, which we know, and we know the adjacent (marked as 57) so we can use tan:
tanA=opposite/adjacent
tan18=(side)/57
side=18.5204226853
Similarly, we can find the base of the shape using cos:
cosA=adjacent/hypotenuse
cos18=57/(base)
base=59.9333467816
Perimeter = 2(side)+2(base)
=2(18.5204226853)+2(59.9333467816)
=37.0408453706+119.866693563
=156.907538934
≈156.9
PLEASE PLEASE HELP ME OUT!! CURRENTLY REALLY STRUGGLING AND TRYING TO PASS THIS SCHOOL YEAR, WILL GIVE BRAINLIEST!
Answer:
3. X = (-4, -5), Y = (0, -3), Z = (-1, -7)
4. Refer back to my explanation.
5. a. Refer back to my explanation.
5. b. 28 units^2; please solve for the other rectangle.
5. c. No, because translation means moving the figure, not changing the shape or size.
Step-by-step explanation:
Warning in advance: the picture is very blurry when looking at the numbers on the graph so I have tried my best to decipher them.
3.
First, write down the ordered pairs for X, Y, and Z.
X = (-1, 4)
Y = (3, 6)
Z = (2, 2)
Note that horizontal movement (moving left or right) affects only the x coordinate. If you are moving to the left, you will subtract from the x coordinate. If you are moving to the right, you will add to the x coordinate.
Vertical movement (moving up or down) affects only the y coordinate. If you are moving up, you will add to the y coordinate. If you are moving down, you will subtract from the y coordinate.
Apply this concept to the ordered pairs:
Moving left = subtraction from x coordinate
Moving down = subtraction from y coordinate
X2 = (-1 - 3, 4 - 9) = (-4, -5)
Y2 = (3 - 3, 6 - 9) = (0, -3)
Z2 = (2 - 3, 2 - 9) = (-1, -7)
Your new image should have X at (-4, -5), Y at (0, -3), and Z at (-1, -7).
4.
After reading the concepts and seeing my explanation and demonstration, please try number 4 on your own. If you have any questions, feel free to ask me for help.
5. a.
The same goes for this problem since it is the same concept.
5. b.
To find the area of a rectangle, use the equation length × width, also known as l × w. In order to figure out what the length and width are equal to, count the units on the graph. JK is 7 units wide. Since this is a rectangle, ML will be the same width, 7 units. KL is 4 units long so JM will also be 4 units long. Now that we know the number of units, we can plug the numbers into the formula:
4 units × 7 units = 28 units^2
The question asks to solve for the area of each rectangle so please try the same for the rectangle you create from problem 5. a.
5. c.
The area of a figure will not change after translation because translation does not affect the figure's size or shape. If the figure is only moved, then no part of its area is changed so no, the area of a figure will not change.
a lorry is travelling at 13.5m/s along a stretch of road
Answer:
Proved
Step-by-step explanation:
This question is incomplete. The complete details are:
[tex]v = 13.5m/s[/tex] --- speed of the lorry
[tex]v_2 =50km/h[/tex] --- speed limit on the road
Required
Prove that the lorry is within the speed limit
To do this, we simply convert the speed of the lorry to km/h.
So, we have:
[tex]v = 13.5m/s[/tex]
[tex]1m = 0.001km[/tex]
and
[tex]1s = \frac{1}{3600}h[/tex]
So, the expression becomes:
[tex]v = \frac{13.5 * 0.001km}{1/3600h}[/tex]
[tex]v = \frac{0.0135km}{1/3600h}[/tex]
Rewrite as:
[tex]v = 0.0135km/h * 3600[/tex]
[tex]v = 48.6km/h[/tex]
48.6km/h is less than 50km/h (the speed limit).
Hence, the lorry is within the speed limit.
A population of 65 foxes in a wildlife preserve triples in size every 12 years. The function y = 65.3*, where x is the number of 12-year periods, models the population growth. How
many foxes will there be after 36 years?
After 36 years there will be foxes. (Type a whole number.)
Answer:
585 foxes
Step-by-step explanation:
36/12 = 3
That means there are 3 fifteen-year periods in 36 years.
So after 3 fifteen-year periods, there will be 65 × 3³ foxes
That is 75(27) foxes
585 foxes
Please help name brainliest
To honor veterans, Carl has planned a Walking for Vets Program. He has mapped out a 1000 mile path and plans to walk 12 hours per day. If Carl exercises regularly, which is the best approximation of how long the walk will take?
Answer:
20 days
Step-by-step explanation:
y=x^2-10x-5
what’s (x,y)
Answer:
(5, -30)
Step-by-step explanation:
PLEASE HELP! 50 POINTS PLUS BRAINLIEST TO THE MOST EXPLAINED ANSWER (PLEASE SHOW THE PROCESS)
Chauncey is building a storage bench for his son’s playroom. The storage bench will fit into the corner and against two walls to form a triangle. Chauncey wants to buy a triangular shaped cover for the bench.
Formula for Area of Triangle:
A = ½ x b x h
(the photo is below)
If the base of the storage bench is 2 ½ ft. and the height along one side of the wall is 4 ½ ft. What is the area of the triangular cover?
Answer:
2.5 times 4.5 times .5 = 5.625 ft squared
Step-by-step explanation:
Lets look at our Formula
.5 times base of triangle (b) times height of triangle (h)
Based on the photo, the height is 4.5 feet and the base is 2.5 feet.
4.5 times 2.5 times .5 (the 1/2 in the formula) = 5.625 ft squared.
Remember that it is 1/2 times the base and height, b/c triangle is half of square. Ft squared because ft times ft equals ft squared
Plumbing A school custodian discovered a leak in a water pipe. The custodian
1,664 fluid Ounces of water had leaked out. How many gallons of water is this? Use the conversion
1 gallon
factor
128 fluid Ounces
1,664 fluid ounces = gallons
Answer:
13 gallons of water
Step-by-step explanation:
Identify the angles (Interior vs Exterior)
Please help! I will give you a heart !
find a20 of a geometric sequence of the first few terms of the sequence given by -1/2;1/4;-1/8;1/16
Answer:
[tex]a_{20} = 1/1048576[/tex]
Step-by-step explanation:
Given
[tex]Sequence: -1/2;1/4;-1/8;1/16[/tex]
Required
Determine [tex]a_{20[/tex]
Since it is a geometric sequence, first we need to calculate the common ratio (r)
[tex]r = \frac{a_2}{a_1}[/tex]
From the sequence:
[tex]a_2 = 1/4[/tex]
[tex]a_1 = -1/2[/tex]
[tex]a_1[/tex] is the same as [tex]a[/tex]
So:
[tex]r = \frac{a_2}{a_1}[/tex]
[tex]r = \frac{1/4}{-1/2}[/tex]
[tex]r = -1/2[/tex]
[tex]a_{20[/tex] is then calculated as:
[tex]a_n = ar^{n-1}[/tex]
Where
[tex]n = 20[/tex]
[tex]a_{20} = ar^{20-1}[/tex]
[tex]a_{20} = ar^{19}[/tex]
[tex]a_{20} = (-1/2) * (-1/2)^{19}[/tex]
Apply law of indices
[tex]a_{20} = (-1/2)^{1+19}[/tex]
[tex]a_{20} = (-1/2)^{20}[/tex]
Evaluate the exponent
[tex]a_{20} = 1/1048576[/tex]
The radius of the cylindrical construction pipe is 2.5ft, if the pipe is 25ft long, what is the volume? Use the value 3.14 for pi, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer
Answer:
Step-by-step explanation:
r = 2.5 ft
h = 25 ft
Volume of cylindrical pipe = πr²h
= 3.14 * 2.5* 2.5 * 25
= 490.625 {as tenth place value is ≥ 5, add 1 to the whole number}
= 491 cubic feet
The digit 2 in which number represents a value of 2 thousandths?
Answer:
0.002
Step-by-step explanation:
2 thousandths is in the thousandths place, which is 3 digits to the right of the decimal point. Hope this helped!
plz help im timed!!!
Which model is 85% shaded?
Done
Answer:
I would need to see the models to answer this question.
Answer:
?
Step-by-step explanation:
You want to deposit 6% of $53,070.00 each year into an IRA(Individual Retirement Account). How much of your salary are you depositing in a year?
Question
How many solutions does the system of nonlinear equations graphed below
have?
Answer: Look at the number of points where the graphs intersect each other...the points where the graphs of the functions cross each other are the solutions to the system. Upon looking, you should see 4 points where the graphs intersect, so there are 4 solutions to the non-linear system of equations.
Jessica is having dinner at a restaurant with several friends. She receives her bill which is
$22. She has a coupon for a 5% discount. After the discount is applied there is a 9% sales tax.
What is Jessica's total bill?
$20
$22
$20.78
$22.78
Answer:
22.78
Step-by-step explanation:
22 x 0.05 = 1.1
22 - 1.1 = 20.9
20.9 x 0.09 = 1.881
20.9 + 1.881 = 22.781
4. He drove at Puerto Princesa City to Taytay at an average speed of 40 kph
How far did he travel?
The journey lasted for 5 hours and 15 minutes.
Kart bought a new motorcycle.
Problem
Solution
Step-by-step explanation:
Distance = Speed x Time
Given Distance = 40km/h or kph
Time = 5 hours 15 minutes
=
[tex]5 \frac{15}{60} \\ = 5 \frac{1}{4} \\ = 5.25hours [/tex]
Distance Travelled = 40 kph x 5.25 hours
= 210km
which ratio represents the probability of taking a red apple from a bag containing 8 red apples, 4 yellow apples, and 3 green apples?
Answer:
8:15
or 8/15
Step-by-step explanation:
8 out of 15
Answer:
8:15
Step-by-step explanation:
There are 8 red apples and total of 15 apples
The length of a rectangle is 5 less than twice the width, and the area of the rectangle is 52 ft^2. Find the dimensions of the rectangle.
9514 1404 393
Answer:
6.5 ft wide by 8 ft long
Step-by-step explanation:
We can let x represent the width of the rectangle. Then the length is ...
L = 2x -5
and the area is ...
A = LW = (2x -5)(x) = 52
2x² -5x -52 = 0 . . . . . put in standard form
(2x -13)(x +4) = 0 . . . . factor
x = 6.5, -4 . . . . . . . . . . values that make the factors zero
The length is then ...
L = A/W = 52/6.5 = 8
or
L = 2W -5 = 2(6.5) -5 = 13 -5 = 8
The rectangle is 6.5 feet wide and 8 feet long.
The American Psychological Associated conducted a survey in 2003 of psychologists to estimate the average incomes for psychologists based on their academic degree and years of experience. 36 psychologists responded who had a just received their masters degree in 2003. The average was $48,800 with a standard deviation of $16,800.
This question is incomplete, the complete question;
The American Psychological Associated conducted a survey in 2003 of psychologists to estimate the average incomes for psychologists based on their academic degree and years of experience. 36 psychologists responded who had a just received their masters degree in 2003. The average was $48,800 with a standard deviation of $16,800.
The 95% Confidence Interval is ($, $ )
Answer:
at 95%, confidence interval is ( $43312, $54288 )
Step-by-step explanation:
Given the data in the question;
sample size n = 36
mean x' = 48,800
standard deviation σ = 16,800
at 95% confidence level;
∝ = 1 - 95% = 1 - 0.95 = 0.05
∝/2 = 0.05 / 2 = 0.025
z critical value, [tex]Z_{\alpha/2[/tex] = 1.96
now, confidence interval for population mean is given by the formula
x' ± [tex]Z_{\alpha/2[/tex]( σ/√n )
so we substitute
⇒ 48800 ± 1.96( 16800/√36 )
⇒ 48800 ± 1.96( 2800 )
⇒ 48800 ± 5488
⇒ 48800 - 5488, 48800 + 5488
⇒ ( 43312, 54288 )
Therefore, at 95%, confidence interval is ( $43312, $54288 )
