If there initially 12 grams of the substance, 5.35 grams will remain after 3 hours
The initial amount, a = 12 grams
The amount after 2 hours, y = 7 grams
Time taken, x = 2 hours
First, let us calculate the decay constant, b
The formula for the final value of an exponential decay is:
[tex]y=a(1-b)^x[/tex]
Substitute y = 12, a = 7, and x = 2 into the equation to solve for b
[tex]7=12(1-b)^2\\\\\frac{7}{12} = (1-b)^2\\\\0.583=(1-b)^2\\\\\sqrt{0.583} = 1 - b\\\\0.764=1-b\\\\b=1-0.764\\\\b=0.236[/tex]
The decay constant, b = 0.236
After 3 hours:
Substitute x = 3, a = 12, and b = 0.236 to solve for y
[tex]y=a(1-b)^x\\\\y=12(1-0.236)^3\\\\y = 5.35[/tex]
Therefore, 5.35 grams will remain after 3 hours
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Veronica has two offers for a $65,000 student loan. The first loan has a 6.3% interest rate for 15 years, and the second loan has a 4.8% interest rate for 20 years. Both loans have interest compounded every month. Veronica is interested in finding the loan that minimizes the amount of interest that she will pay over the life of the loan. Which loan has a lower amount of interest paid?
The second option has a lower amount of interest paid.
In order to determine the loan option that minimizes loan payment, the future value of both loan options has to be determined.
FV = P (1 + r)^nm
FV = Future value
P = Present value
R = interest rate
m = number of compounding
N = number of years
First loan option
65000( 1 + 0.063/12)^300 = 312,707.21
Second loan option
65000( 1 + 0.048/12)^240 = 169,435.51
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Find the surface area of the following cylinder. Round your answer to the nearest square centimeter.
Answer:
V=2(pi)(r)(h)+2(pi)(r^2)
v=2(pi)(10/2)(0.8)+2(pi)(10/2)^2
TSA=159.512
TSA=160
Step-by-step explanation:
According to Josh's checkbook register, he had a transaction for less than -608 dollars on Monday. Which of the following best describes this transaction?
A.
Josh received less than 608 dollars on Monday.
B.
Josh received more than 608 dollars on Monday.
C.
Josh spent less than 608 dollars on Monday.
D.
Josh spent more than 608 dollars on Monday.
Answer:
A option A is the write answer
Please look the image attached
Answer:
I think it is c
Step-by-step explanation:
I might be wrong wait for a second answer if it is the same then I think I am right
answer fully please //////////
Answer:
yes,the distributive property can be rewrite as i have given below:
(8×8)-(8×4)
f(x) = 9x ^ 2 - 3 then what is f(3) ? Work must be shown for this problem or no credit will be earned.
Answer:
f ( 3 ) = 81
Step-by-step explanation:
→ Substitute in x = 3
9 × 3² - 3
→ Simplify
9 × 9 - 3
→ Simplify again
78
solve for x and y then find the measure of each angle
Step-by-step explanation:
∵ MP is a straight line.
∴ ∠MNQ + ∠PNQ = 180°
[tex](3y + 8)° + (3y + 22)° = 180° \\ 3y + 8 + 3y + 22 = 180 \\ 6y + 30 = 180 \\ 6y = 150 \\ y = 25[/tex]
∵ MP is a straight line.
∴ ∠MNR + ∠PNR = 180°
[tex](2x + 5)° + (3x - 55)° = 180° \\ 2x + 5 + 3x - 55 = 180 \\ 5x - 50 = 180 \\ 5x = 230 \\ x = 46[/tex]
Solve
-x + 4 = x + 6
Answer:
-1
Step-by-step explanation:
1. subtract 4 from both sides
-x = x+2
2. subtract x from both sides
-2x = 2
3. divide both sides by 2
simplify
x= -1
Hope this helps :)
write down five million four thousand three hundread in standard form
the answer is 5,004,300
You invest AED 5000 in a saving account that earns 4% interest each year. If you do not use the account for a year, how much money will you have in your account after a year?
Answer:
5200 AED or 1404 USD
Step-by-step explanation:
You have 5000 in your account. If your money grows 4% each year, it's basically like multiplying by 1.04.
5000 * 1.04 = 5200
If the question is asking in USD, the conversion rate from AED to USD is
AED * 0.27 = USD
We can substitute
5200 AED* 0.27 = 1404 USD.
ill mark brainliest thanks
Answer:
first one
Step-by-step explanation:
nos
5. In the diagram above, zero represents the location of Martin Luther King Middle School Point K represents the
library, which is located to the east of the middle school. In words, create a real-world situation that could
represent point L, and describe its location in relation to 0 and point K.
Answer:
1/12
Step-by-step explanation:
A shipment of 8 computers contains 3 with defects. Find the probability that a sample of size 2, drawn from the 8, will not contain a defective computer.
What is the probability that a sample of 2 of the 8 computers will not contain a defective computer?
(Type an integer or a simplified fraction.)
Answer:
5/28
Step-by-step explanation:
First of all, probability is defined as the number of ways a certain event can happen divided by the total ways of an event happening. In this scenario, we are asked to find the number of non-defective computers divided by the total ways that a sample of two can be chosen.
The number of ways to choose 2 computers from 8 can be written as [tex]8\choose2[/tex], which is equal to [tex]\frac{8\cdot7}{2}[/tex], which is 28. Now, there are 3 defective computers, for a total of 5 non-defective computers, so the probability is 5/28.
Solve the inequality
-5/7 - 6/7z < -2/7
[tex]-\cfrac{5}{7}-\cfrac{6}{7}z~~ < ~~-\cfrac{2}{7}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{7}}{-5-6z~~ < ~~-2} \\\\\\ \stackrel{\textit{dividing by a negative value}}{-6z~<~3\implies z ~\stackrel{\stackrel{notice}{\downarrow }}{>}~\cfrac{3}{-6}}\implies \boxed{z~>-\cfrac{1}{2}}[/tex]
A hotel reservation number consist of 4 digits, followed by 1 letters, followed by 3 digits. How many different reservation numbers are possible?
Answer:
24000000
(might not be correct)
Step-by-step explanation:
might not be right but ill try:
ten digits: 10
4times:10x10x10x10=10000
times a letter:24 letters= 10000x24=240000
time three digits: 10x10x10=100x240000=24000000
The total number of combination for the repeating and not repeating cases are 260000000 and 604800 respectively.
What is permutation and combination?Permutation and combination are the ways of counting.
Permutation implies selection of objects regardless of arrangement while Combination implies the selection when arrangement is important.
Given that,
The hotel reservation number contains 4 digits, 1 letter and then 3 digits.
Now, there are two possible cases for the given problem as follows,
Case 1 : The digits are repeating.
Then the total number of combinations for digits varying from 0 to 9 and 26 letters will be,
10 × 10 × 10 × 10 × 26 × 10 × 10 × 10
= 260000000
Case 2 : The digits are not repeating.
Then, for seven digits out of 10 the number of combinations are ¹⁰P₇.
And, for 26 letters it is ²⁶P₁.
Thus the total number of combinations are ¹⁰P₇ × ⁶P₁ which is equal to,
10 × 9 × 8 × 7 × 6 × 5 × 4 × 26
= 604800
Hence, the different number of combinations for the reservation number for the two cases are 260000000 and 604800 respectively.
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a 25 -ft ladder rests against the side of a house. the distance between the top of the lader and the ground is 17 ft more than the distance between the base od the ladder and the bottom of the house. find both distances.
Answer:
Step-by-step explanation:
x² + (x + 17)² = 25²
x² + x² + 34x + 289 = 625
2x² + 34x - 336 = 0
x² + 17x - 168 = 0
x = (-17 ±√(17² - 4(1)(-168))) / (2(1))
x = 7 or - 24 the negative distance makes no sense, but if we plug our good answer of 7 ft in for the base length, the height comes out to be + 24 ft
base = 7 ft
height = 24 ft
One integer is 2 less than another. The sum of their squares is 34. Find the integers.
Answer:
no se bro no se inglés así no se que bas a aaer
Step-by-step explanation:
pero puedes consultar por
pls help me i will give u thanks
Answer:
c) (6,5)
Step-by-step explanation:
The horizontal axis represents x values
The vertical axis represents y values
For BOTH Bruce and Felicia, graph a line to represent y, the area each person covered using x tiles.
The tiles that Bruce used were each 1/4 of a square foot in area. The table shows the area covered by Felicia’s tiles in terms of the number of tiles used.
Number of tiles Area covered
6 1
12 2
18 3
Bruce and Felicia want to know whose tiles cover the most area per tile.
If the area each person covered using x tiles. Bruce's tiles cover the most area per tile.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the tiles that Bruce used were each 1/4 of a square foot in the area and a table shows as,
Number of tiles(y) 6 12 18
Area covered (x) 1 2 3
Felicia tile's relationship between the number of tiles and the area covered is,
(1/6) =(12/2)=(18/3)
y=(1/6)x
The equation of a line to represent y, the area each person covered using x tiles for Bruce is,
y =(1/4)x.
Thus, if the area each person covered using x tiles. Bruce's tiles cover the most area per tile.
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help me with this please
hey I need someone to help me
Answer:
A and F
Step-by-step explanation:
You plug in each one and see which ever one gets 20.
What is a quartic function with only two real zeros at x = 7 and x = 13
A. y = (x - 10) ^ 5 - 81 OR y = x ^ 5 - 20x ^ 4 + 92x ^ 3 + 34x ^ 2 - 20x + 91
B. Y= (x - 10) ^ 4 - 81 OR y = x^4 - 20x +91
C. y = (x - 3) ^ 4 - 41 OR y = 2x ^ 4 - 21x ^ 3 + 52x ^ 2 - 17x + 609
D. y = (x+ 8)^4 + 71 OR y = x^4 - 3x^3 + 7x^2 - 5x + 13
Zeros be a and b
a=7b=13Function
[tex]\\ \sf\longmapsto y=x^2-(a+b)x+ab[/tex]
[tex]\\ \sf\longmapsto y=x^2-(7+13)x+(7)(13)[/tex]
[tex]\\ \sf\longmapsto y=x^2-20x+91[/tex]
Option B
Cinco múltiplos del 12
Answer:
60 Sana po makatulong pa brainlest please
y>= -5x + 8 what is m?
Answer:
The slope = -5
Step-by-step explanation:
y ≥ -5x + 8
Look at the problem as y = -5x + 8 and compare to the slope intercept form. The slope = -5
an expression for the area of a rectangular piece of sheet metal is X^2+8x+12.
An expression for the length of the same piece of sheet metal is x+6.
Determine an expression for the width.
[tex]\text{Area of rectangle} = \text{Length} \times \text{Width}\\\\\\\implies \text{Width} = \dfrac{\text{Area of reactangle}}{\text{Length}} = \dfrac{x^2 +8x +12}{x+6} = \dfrac{x^2 + 6x +2x +12}{x+6}\\\\\\\\ = \dfrac{x(x+6) +2(x+6)}{x+6}=\dfrac{(x+6)(x+2)}{x+6} = x+2[/tex]
Evaluate 11/6 - 2/8=
Answer:
19/12
Step-by-step explanation:
Hurry help plz
Solve for an angle in right triangles
[tex]\cos \angle B = \dfrac{2}{7}\\\\\implies \angle B = \cos^{-1} \left( \dfrac{2}{7} \right) = 1.28^{\circ}[/tex]
c¹⁰ ÷ c⁵ please help me asap thank you
Answer:
c^5
Step-by-step explanation:
All you have to do is take away the powers because of the law of indeces when dividing number with indices
Hope this helps :) im really bad at the explanations part :D
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PLEASE HELP!!!!
On a Saturday, a library checked out 117 books. If 36 of the books were fiction, what is the ratio
of non-fiction books to fiction books checked out?
Answer the following questions,
0
(a) What number is 95% of 80
0
(b) 85% of what is 51?
Answer:
95% of 80 is 76 and 85% of 60 is 51.
Step-by-step explanation:
Answer:
a. 76, b. 60.
Step-by-step explanation:
a) 80 * 0.95 = 76.
b) 0.85 x = 51
x = 51/0.85 = 60.