Answer:
About 0.6548 grams will be remaining.
Step-by-step explanation:
We can write an exponential function to model the situation. The standard exponential function is:
[tex]f(t)=a(r)^t[/tex]
The original sample contained 510 grams. So, a = 510.
Each half-life, the amount decreases by half. So, r = 1/2.
For t, since one half-life occurs every 38 days, we can substitute t/38 for t, where t is the time in days.
Therefore, our function is:
[tex]\displaystyle f(t)=510\Big(\frac{1}{2}\Big)^{t/38}[/tex]
One year has 365 days.
Therefore, the amount remaining after one year will be:
[tex]\displaystyle f(365)=510\Big(\frac{1}{2}\Big)^{365/38}\approx0.6548[/tex]
About 0.6548 grams will be remaining.
Alternatively, we can use the standard exponential growth/decay function modeled by:
[tex]f(t)=Ce^{kt}[/tex]
The starting sample is 510. So, C = 510.
After one half-life (38 days), the remaining amount will be 255. Therefore:
[tex]255=510e^{38k}[/tex]
Solving for k:
[tex]\displaystyle \frac{1}{2}=e^{38k}\Rightarrow k=\frac{1}{38}\ln\Big(\frac{1}{2}\Big)[/tex]
Thus, our function is:
[tex]f(t)=510e^{t\ln(.5)/38}[/tex]
Then after one year or 365 days, the amount remaining will be about:
[tex]f(365)=510e^{365\ln(.5)/38}\approx 0.6548[/tex]
Juan bought a laptop for $650 and a power adapter for $59. If the sales tax rate is 6%,
what was the total tax that Juan paid?
Answer:
$42.54
Step-by-step explanation:
total spent- 709
6/100*709= 42.54
if my answe helps please mark as brainliest.
What is the volume of the pyramid?
Answer: 484
Step-by-step explanation:
12x11x11=1,452
1,452/3=484
Hakeem left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Hakeem is xx minutes after he left his house, until he got back home.
Answer:
where is the pic of the graph?
The two trapezoids below are similar. What is the length of EF?
Answer:
x/24 = 7.5/30
30x = 180
________
30
x= 6
The length of EF in given trapezoid is 6 cm
What is trapezoids ?Trapezoids are quadrilaterals that have two parallel sides and two non-parallel sides. It is also called a Trapezium. A trapezoid is a four-sided closed shape.
a pair of opposite sides are parallel.
diagonals of trapezium bisect each other.
sum of all four angles of trapezium is = 360°
it has four unequal sides.
diagonals are congruent.
opposite side of an isosceles trapezium are congruent.
According to the question
Trapezoids ABCD and EFGH are similar,
Hence, corresponding sides ratio are equal
Thus, AB/EF = DC/HG
24/x = 30/7.5
30x = 180
x = 180/30
x= 6
Hence, The length of EF is 6 cm
To learn more about trapezoids from here
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Use distributive property to write an equivalent expression. Use paper and pencil to
work the problems out, and then check your answers once you have submitted the
practice. (Answers will be in the bubbled comments after the problem.)
A. 6 Gn+2)
B.p(4p +9)
C. 5r (r + 4
Answer:
A) 6Gn + 12 (or 6n+12, if that’s what you meant)
B) 4p²+9p
C) 5r²+20r
Step-by-step explanation:
A. If you meant 6(n+2)...
Multiply 6 by n and also 6 by 2:
6n + 12
B. Multiply p by 4p and also p by 9
4p²+9p
C. Multiply 5r by r and also 5r by 4
5r²+20r
Hope this helped!
which algebraic expression represents the word expression "three times the square of a number, n, subtracted from 54. ANSWER ASAP
What is 1102 using the polynomial identity (a+b)2=a2+2ab+b2 ?
Drag and drop the correct responses into the boxes.
Let the smaller value a = Response area and the larger value b = Response area. Then a2+2ab+b2 is Response area. This can be simplified to Response area. So, 1102 is equal to Response area.
Answer:
"Let the smaller value a = 10 and the larger value b = 100. Than a^2 + 2ab + b^2 is 10^2 + 2 * 10 * 100 + 100^2. This can be simplified to 12100. So, 110^2 is equal to 12100."
Hope this helped!
The smaller value is 10
The larger value is 100
So the square of 110 should be 12100
Calculation of the value:Since here we assume the smaller value be 10
So, the larger value be 100
Now
[tex]a^2 + 2ab + b^2 = 10^2 + 2 \times 10 \times 100 + 100^2.[/tex]
This can be simplified to 12100.
So, [tex]110^2[/tex] is equal to 12100.
Learn more about value here: https://brainly.com/question/17022004
In ARST, the measure of T=90°, ST = 7.7 feet, and RS = 9.7 feet. Find the measure
of R to the nearest degree.
9.7
7.7
X
T
R
Answer:
Submit Answer
Answer: 53
Step-by-step explanation:
Answer:
53
Step-by-step explanation:
Hey I'm Chloe, Can You Help Me Thank you :)
y varies proportionally with x. When x = 2, y = 18.
What is the constant of proportionality for this relationship?
Answer:
y = 9x
Step-by-step explanation:
Simplify 2x + 1 -x + 2.
Answer:
x+3
Step-by-step explanation:
Hope you have a good day, Loves!
Also if I'm right can you let me know please?
Also Also if I am right can I please have Brainliest??
(How in the hecc are three people answering this?)
Carter is going to invest $210 and leave it in an account for 5 years. Assuming the interest is compounded annually, what interest rate, to the nearest tenth of a percent, would be required in order for Carter to end up with $250?
Answer:360
Step-by-step explanation:g-g5
The rate of interest will be 0.35.
What is compound interest?
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Compound interest formula[tex]CI = P(1+\frac{r}{n}) ^{nt} -P[/tex]
and, the Amount is given by
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
Where,
A is amount
P is principal
r is rate of interest
n is number of times interest is compounded per year
t is time
According to the given question
Principal, P = $210
Amount, A = $250
Time, t = 5 years
n = 1
Therefore, the interest rate is given by
Amount = [tex]P(1+\frac{r}{n}) ^{nt}[/tex]
⇒[tex]250 = 210(1+\frac{r}{1}) ^{5}[/tex]
⇒[tex]\frac{250}{210} =(1+r)^{5}[/tex]
⇒[tex]1.19 = (1+r)^{5}[/tex]
⇒[tex]\sqrt[5]{1.19} = 1+r\\[/tex]
⇒ 1.035 = 1 + r
⇒ r = 1.035 - 1
⇒ r = 0.35
Hence, the interest rate is o.35.
Learn more about compound interest here:
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7x + 4 = 25, then x is equal to
a) 29/ 7 b) 100/7 c) 2 d/ 3
Answer:
d) 3
Step-by-step explanation:
7x+4=25
7x=21
X=3
Answer: D. 3
Step-by-step explanation:
Given
7x+4=25
Subtract 4 on both sides
7x+4-4=25-4
7x=21
Divide 7 on both sides
7x/7=21/7
x=3
Hope this helps!! :)
Please let me know if you have any questions
8x8x8=_______=_______
Answer:
8*8*8= 8^3= 512
Step-by-step explanation:
Answer:
8x8x8= 8^3 = 512
Step-by-step explanation:
Hope this helps
help plzz WILL MARK BRAINLIST
Answer:
224
Step-by-step explanation:
Given
f(x) = 4x² - 4x
f(-7) = 4 * (-7)² - 4 * (-7)
= 196 + 28
= 224
Hope it will help :)
Sarah is planning for a children's party. She wants to provide each child with a party bag containing 3 items, a whistle, a ball and a tube of sweets. Whistles are sold in packs of 5, balls in packs of 3 and sweets in packs of 6, she doesn't want any single items left over, even if it means she has too many party bags. What are the minimum party bags she can make and how many packs of each item does she need to buy?
In this problem, a, b, c, and d are nonzoro integers.If a/b is added to x, the sum is c/d Which statement
can be used to prove that x must be a rational number?
Functions:Question 5
What is the y-intercept of the line whose equation is shown below?
y = - 3.3 +7
Select one:
3
-3
4
7
Solve for q.
7(q + 7) = 5q + 59
Answer:
5.
Step-by-step explanation:
7(q + 7) = 5q + 59
7q + 49 = 5q + 59
7q - 5q = 59 - 49
2q = 10
q = 5.
What is the area of the composite figure?
7 yds;
12 yds.
18 yds.
Pls help pls thank you
Answer:
2 1/2 pounds
Step-by-step explanation:
Solve for x.
(x + 10)°
(4x - 35)°
Answer:
x = 15
Step-by-step explanation:
x+10=4x−35
x+10−4x=4x−35−4x
−3x+10−10=−35−10
−3x=−45
x = 15
- 6(x + 2) = 30
- 6(x + 2) = 30
- 6x + (- 12) = 30
The solution is -
Answer:
-7
Step-by-step explanation:
A rectangle has length 6 cm and width 4 cm. Give the length and width of another rectangle with the same area but a different perimeter.
Answer:
length could be 8 cm and width would be 3 cm and that would have a perimiter of 24 cm also
3^-7
Simplify please.
Answer:
0.000457 what I got
Step-by-step explanation:
7. Look at this figure
There are different shapes in the figure (Do not count the
trapezoid itself)
b2
9:24 AM
2/9/2029
Answer:
thx for the 32 points
Step-by-step explanation:
Is a bucket used to carry water more likely to have a capacity of a pint or a gallon
Answer:
well it depends on the size of the bucket but some buckets may be a gallon but then some are bigger id-k if this makes sense im srry
Step-by-step explanation:
what is the domain of the relation
Answer:d I believe
Step-by-step explanation:
Riko is ordering a submarine sandwich for 6 people. Each person will eat the same size section of the sandwich. The section size should be at least 4 inches. What is the length of the smallest sandwich Riko should order?
Answer: 24 inches.
Step-by-step explanation:
If each section length is 4 inches, then that means that each person will need to eat a sandwich section that is at least 4 inches.
There are 6 people, which means that each person will eat 4 inches of a sandwich.
To calculate the length of the sandwich Riko should order, we should mutliply 6 by 4, because there are 6 people and each person will be eating 4 inches of a sandwich.
6 x 4 = 24.
In conclusion, the smallest sandwich Riko should order is a sandwich that is 24 inches long.
(Quick Note: This is also the smallest sandwich Riko could order, because the text states that each person eats at least 4 inches.)
Find the least common multiple of the set of numbers
8,9
The least common multiple of 8 and 9 is____?
Answer:
72
Step-by-step explanation:
plz mark brainliest :D
Divide. 0.996 ÷ 0.12
Answer:
8.3
Step-by-step explanation:
Answer:
- 0.996 - Percentage increase =
- 0.996 - (12% × - 0.996) =
- 0.996 - 12% × - 0.996 =
(1 - 12%) × - 0.996 =
(100% - 12%) × - 0.996 =
88% × - 0.996 =
88 ÷ 100 × - 0.996 =
88 × - 0.996 ÷ 100 =
- 87.648 ÷ 100 =
- 0.87648 ≈
- 0.88
Step-by-step explanation:
pls brainlsit