The half-life of a certain radioactive material is 37 days. An initial amount of the material has
a mass of 477 kg. Write an exponential function that models the decay of this material. Find
how much radioactive material remains after 6 days. Round your answer to the nearest
thousandth.
Answer is option B that ends with 426.288 kg.
The exponential function that models the decay of this material is [tex]477(\frac{1}{2})^{(\frac{t}{37} )}[/tex] and the quantity of substance remains is 426.28 grams
What is Half life?Half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.
What is Radioactive material?Radionuclides (or radioactive materials) are a class of chemicals where the nucleus of the atom is unstable
Given,
Half life of a certain radioactive material = 37 days
Initial amount of the material = 477 grams
Quantity of substance remains N(t) = [tex]N_{0}(\frac{1}{2})^{(\frac{t}{half-life} )}[/tex]
Substitute the value in the equation N(t) =[tex]477(\frac{1}{2})^{(\frac{t}{37} )}[/tex]
[tex]477(\frac{1}{2})^{(\frac{t}{37} )}[/tex] is the exponential function that models the decay of this material.
Quantity of substance remains after 6 days = [tex]477(\frac{1}{2})^{(\frac{6}{37} )}[/tex] = 426.28 grams
Hence, the exponential function that models the decay of this material is [tex]477(\frac{1}{2})^{(\frac{t}{37} )}[/tex] and Quantity of substance remains is 426.28 grams
Learn more about Half life and Radioactive material here
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help plz question is in the photo
Answer:
A. Trinomial
Step-by-step explanation:
It says it's a polynomial and that based on the number of terms. So right then you can cancel out cubic and quadratic because they aren't polynomials. Also:
Cubic is just a variable with the exponent of 3. Examples:
[tex]x^3,y^3,z^3[/tex]
Binomial is a polynomial with 2 terms. Examples:
[tex]5x+3; 6x+2; x+7[/tex]
A quadratic has a division sign.
Answer this there is a pic
Answer:
A
Step-by-step explanation:
1:2.5 because 2/2=1 and 5/2=2.5
find the output, y, when the input, x, is -5.
Answer:
y = -2
Step-by-step explanation:
When x = -5
Go to the blue line
y = -2
Answer:
There are 2 questions with the same question but with a different graph.
This graphs answer is -2.
But the other graph that people are confused about is 7.
Step-by-step explanation:
Hope this helps! :)
Which of the points (s, t) is inside the shaded region of the set of inequalities shown below?
s<24 - 0.66t
s>12 - t
s< 30 - t
s>0
t>0
O A. (1,8)
O B. (-9,21)
O C. (9,4)
O D. (30, 10)
Answer:
Only point C. (9,4)
Step-by-step explanation:
To check if the points are inside the region of the inequalities, we just need to use the values of the point in each inequation, and if the point satisfy all inequations, the point is inside the region.
point A = (1,8): s = 1 and t = 8
first inequation: s<24 - 0.66t
1 < 24 - 0.66*8
1 < 18.72 (true)
second inequation: s>12 - t
1 > 12 - 8
1 > 4 (false)
So point A is not inside the region.
point B = (-9,21): s = -9 and t = 21
As we can see from the fourth inequation, the s value needs to be greater than 0, and point B has s negative, so point B is not inside the region.
point C = (9,4): s = 9 and t = 4
first inequation: s<24 - 0.66t
9 < 24 - 0.66*4
9 < 21.36 (true)
second inequation: s>12 - t
9 > 12 - 4
9 > 8 (true)
third inequation: s< 30 - t
9 < 30 - 4
9 < 26 (true)
fourth inequation: s>0
9 > 0 (true)
fifth inequation: t>0
4 > 0 (true)
As all conditions are true, point C is inside the region.
point D = (30,10): s = 30 and t = 10
first inequation: s<24 - 0.66t
30 < 24 - 0.66*10
30 < 17.4 (false)
So point D is not inside the region.
Answer:9,4
Step-by-step explanation:
add or subtract (7x^2-x-2)-(-6x^3+3)
Answer:
[tex] \tt{}6x ^{3} + {7x}^{2} - x - 5[/tex]
Step-by-step explanation:
[tex] \tt{}(7 {x}^{2} - x - 2) - ( - 6 {x}^{3} + 3)[/tex]
[tex] \tt{}7 {x}^{2} - x - 2 + 6x^{3} - 3[/tex]
[tex] \tt{} {7x}^{2} - x - 5 + 6x ^{3} [/tex]
[tex] \tt{}6x ^{3} + {7x}^{2} - x - 5[/tex]
Answer:
[tex]6 {x}^{3} + 7 {x}^{2} - x - 5[/tex]
Step-by-step explanation:
[tex](7 {x}^{2} - x - 2) - ( - 6 {x}^{3} + 3)[/tex]
➡️ [tex]7 {x}^{2} - 2 - ( - {6}^{3} + 3)[/tex]
➡️ [tex]7 {x}^{2} - x - 2 + 6 {x}^{3} - 3[/tex]
-2 - 3-(2 + 3)-5➡️ [tex]7 {x}^{2} - x - 5 + 6 {x}^{3} [/tex]
➡️ [tex]6 {x}^{3} + 7 {x}^{2} - x - 5[/tex] ✅
Which answer choice shows the number fifty-four and four hundredths written in standard form? A. 54,400 B. 54.04 C. 54.004 D. 54.0004
Answer:
c
Step-by-step explanation:
HELP will mark brainliest
Answer:
x=55 degrees
Step-by-step explanation:
Angle X + 125 degrees is 180 degrees. 180 minus 125 is 55.
What is the volume of a cube that has a height of 10 inches
Answer:
1000 inches
Step-by-step explanation:
V= a3=103=1000in³
Answer:1,000in3
Step-by-step explanation:
V=LxWxH
V=10x10x10
V= 1,000
Name the first 10 perfect squares. Why are they perfect squares?"
Answer:
why a math problem
Step-by-step explanation:
math is hard
When there is no outlier is thebetter measure of center for a set of data
Median
Mode
Range
None of the above
Answer:
Median
Explanation:
The median is the middle number. This answer fits best with the question asked.
The mode is the number that occurs the most. This number doesn't really have a correlation to the middle of this data.
The range is just how many numbers the data spans across. It has no relation to the middle of the data.
Zayne has a bag filled with coins. The bag contains 7 quarters, 8 dimes, 3 nickels, and 9 pennies. He randomly chooses a coins from the bag. What is the probability that Zayne chooses a quarter or a nickel?
Answer:
Q=7/27 N=1/9 which is 10/27
Step-by-step explanation:
you add all the coins together
then if it is quarter then it is 7/27
if it is a nickel then it is 3/27 = 1/9
A triangle has a base of x 1/2 m and a height of x 3/4 m. if the area of the triangle is 16 m^2, what are the base and the height of the triangle
Answer:
base = 6.4m
height = 5m
Step-by-step explanation:
Given area = 16m^2
3/4 -1/2 = 1/4 into something x 0.25 its size then add
We see that 2.5 is 10 multiplied. not relevant unless doing algebra
We also see that 0.5 is 0.25 x 2 not relevant unless doing algebra
We start with 5
16/5 = 3.2
if 5 is the height then 3.2 x 2 must be the base.
As we half base to find area so we change this value and reverse the area 1/2 above. 3.2 x 2 = 6.4m base. and 5m height stays as it is.
If we did algebra
Then 1/2 = 0.5 = 4.5
3/4 = 0.75 = 3.75
and we would have to plug in 1 as x
3 as x to find one value as 5.5 (-1) = 4.5
We find 3.75 as 5 (-1 )- 1/4 = 3.75
3.75 x 4.5 = 16.875m^2
and is closest fit using 1/4, 1/2 and -1.
But 3.2 x 5 is a better multiplication as 3 1/5 and finds 16 exact.
solve for x
3(x+2)=5x-7
give your answer as an improper fraction
Answer:
13/2
Step-by-step explanation:
3x+6=5x-7
2x=13
13/2
Help please will give brainly! Clara’s friend Brian decides to find his median as well. Find the median and type it in the answer box. What does the median show us?
Answer:
The median is 88. The median shows that Brian gets on average 88% on his tests.
Step-by-step explanation:
If you put the numbers in order and get the average of the two middle number, it is 88.
Solve this equation 2/3x+ 5= 1
Answer:
x=-6
Step-by-step explanation:
2/3x+5=1
Subtract 5 from both sides:
2/3x=-4
Multiply both sides by 3:
2x=-12
Divide both sides by 2:
x=-6
Hope this helps!
Answer:
-6
Step-by-step explanation:
2/3x +5 = 1
-5 -5
2/3x = -4
2/3x/2/3 = -4/2/3
= -6
:3 if I helped, please mark as brainliest!
I need help with this please ASAP!!!
Answer:
B and c
Step-by-step explanation:
A monkey is swinging from a tree. On each swing, she travels along an arc that is
75%, percent as long as the previous swing's arc. The total length of the arcs from her first 4 swings is 175m.How long was the monkey's 1st swing?
Round your final answer to the nearest meter.
Answer:
Total length of the first swing=64 m
Step-by-step explanation:
The total length of all four swings can be expressed as; Total length of all 4 swings=Length of first swing+length of second swing+length of third swing+length of fourth swing
where;
Total length of all 4 swings=175 m
Length of first swing=x
Length of second swing=75% of length of first swing=(75/100)×x=0.75 x
Length of third swing=75% of length of second swing
Length of third swing=(75/100)×0.75 x=0.5625 x
Length of fourth swing=75% of length of third swing
Length of fourth swing=(75/100)×0.5625 x=0.421875 x
replacing;
Total length of all 4 swings
175=x+0.75 x+0.5625 x+0.421875 x
2.734375 x=175
x=175/2.734375
x=64
Total length of the first swing=x=64 m
The angular velocity of a fan blade is 6.2 radians per second.
Approximately how many revolutions does the fan blade make in 1.6 minutes?
Enter your answer, rounded to the nearest tenth of a revolution
Answer:
94.7 revolutions
Step-by-step explanation:
In the question above, we are given the following values for the fan
Angular velocity = 6.2 radians per seconds
Time = 1.6 minutes.
Step 1
We would convert the time given to seconds
1 minute = 60 seconds
1.6 minutes = ?
We cross multiply
1.6 minutes × 60 seconds
= 96 seconds
Step 2
Number of revolutions made by the fan is calculated as :
Angular velocity(rad/s)
× time(seconds)
Number of revolutions = 6.2 radians per seconds × 96 seconds
=595.2 radians
Converting from radians to revolution
1 radian = 0.159155 revolutions
595.2 radians =
Cross multiply
= 595.2 radians × 0.159155 revolutions
= 94.729056 revolutions.
Approximately to the nearest tenth = 94.7 revolutions.
Therefore, the number of revolutions the fan blade makes in 1.6 minutes is 94.7 revolutions.
1.6 minutes is 1.6 x 60 = 96 seconds.
Its angular velocity is 6.2 radians per second: 6.2 radians/second x 96 seconds = 595.2 radians.
One revolution of the fan is one circumference of the fan, which is 2pi radians.
Dividing 595.2 radians by 2pi radians gives us an answer of 94.7 revolutions.
It took Darcy two days to drive from Orlando to Pittsburgh. She drove 595 miles on the first day and at least 1,020 miles in total. How many miles did she drive on the second day?
Answer:
Darcy drove 425 miles
Step-by-step explanation:
you find this out by doing the equation 1,020-595
please help
This spinner has 6 equal sections. what are the odds in simplest form against spinning blue or yellow?
A) 1:2
B) 2:3
C) 3:2
D) 2:1
Answer:
D
Step-by-step explanation:
hope this helps!!! good luck:)
Answer: its C 3:2
Step-by-step explanation: see how it has the word AGAINST that means the opposite of the word FAVOR if the Question was. . .
This spinner has 6 equal sections. what are the odds in simplest form FAVOR spinning blue or yellow? then the Answer would be B 2:3
but sense the Question is. . .
This spinner has 6 equal sections. what are the odds in simplest form AGAINST spinning blue or yellow?
your Answer is . . .
C) 3 : 2
Have a wonderful day :D
Ms. Sanders put $5,200 in a savings account that pays 4.2% simple interest. Each year she withdraws the interest and treats herself to a visit to a spa. How much can she spend each year?
Answer:
$218.40
Step-by-step explanation:
i=prt
i=(5200)(.042)(1)
Center (2,8) r=6 plz help
Answer:
(x-2)^2+(y-8)^2=36
Step-by-step explanation:
what is the radius of a circle with a volume of 12348 inches cubed
Answer:
14.34 in
Step-by-step explanation:
calculator website i'll link below
PlEAssE HeLPLL!!!!! LIKE REALLY HELP ME!!
Answer:
168745
Step-by-step explanation:
times them all together.
Answer:
16875 cm^3
Step-by-step explanation:
V = lwh
45 * 15 * 25 = 16875
A small TV that regularly sells for $89.00 is on sale at a 15% discount. What is the amount of discount?
Answer:
$13.35
Step-by-step explanation:
To find the amount of discount, multiply the discount rate by the usual price of the small TV.
discount rate * regular price
The discount rate is 15% and the regular price of the small TV is $89.00
15%*$89.00
15%*89
Convert 15% to a decimal by dividing 15 by 100, or moving the decimal place two spots to the left.
15/100=0.15
15.0-->1.5-->0.15
0.15*89
Multiply
13.35
The discount amount is $13.35
So the amount of discount is $13.35
Look at the attached picture
Hope it will help you
Good luck on your assignment
I need help. How do you get 12.4 as an answer with using these instruction below.
Answer:
There are many solutions.
Here is one of them:
1 x 4 / 10 + 14 - 2 = 12.4
Hope this helps!
:)
For 10 straight days Samantha measure the amount of food that her cat Dewey a recording the results
Answer:
is there like a table or something to help me with the question
Martha used 2/3
tablespoons of pepper to make 1/6
liters of gravy. If Martha's recipe is for 1 liter of gravy, how much pepper will she need to make double the recipe?
A) 2 tablespoons of pepper
B) 4 tablespoons of pepper
C) 8 tablespoons of pepper
D) 12 tablespoons of pepper
plz helppp
Answer:
8 tablespoons of pepper
Step-by-step explanation:
Therefore, double the recipe: 4 × 2 = 8 tablespoons of pepper
Find the volume of a pyramid with a square base, where the area of the base is 19.6\text{ cm}^219.6 cm 2 and the height of the pyramid is 12.7\text{ cm}12.7 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answer:
V = 83.0 cm^3
Step-by-step explanation:
To find the volume of the squared pyramid you use the following formula:
[tex]V=\frac{1}{3}Bh[/tex] ( 1 )
B: base of the pyramid = 19.6 cm^2
h: height of the pyramid = 12.7 cm
you replace the values of B and h in the equation ( 1 ):
[tex]V=\frac{1}{3}Bh=\frac{1}{3}(19.6cm^2)(12.7cm)\\\\V=82.97cm^3\approx 83.0cm^3[/tex]
hence, the volume of the pyramid is 83.0 cm^3
