It will take approximately 286.8 years for half of the initial amount (900 grams) to decay.
To find the time it takes for half of the initial amount to decay, we need to find the value of t when D(t) is half of the initial amount (900 grams).
Half of the initial amount = 900 grams / 2 = 450 grams
Now, set D(t) equal to 450 and solve for t:
[tex]450 = 900 * e^{-0.002415 * t}[/tex]
Divide both sides by 900:
[tex]e^{-0.002415 * t} = 0.5[/tex]
To find t, take the natural logarithm (ln) of both sides:
[tex]ln(e^{-0.002415 * t}) = ln(0.5)[/tex]
Now, use the property that [tex]ln(e^x) = x:[/tex]
-0.002415 * t = ln(0.5)
Now, solve for t:
t = ln(0.5) / -0.002415
Using a calculator, we get:
t ≈ 286.8 years
So, it will take approximately 286.8 years for half of the initial amount (900 grams) to decay.
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(1 point) consider the function f(t)=⎧⎩⎨⎪⎪⎪⎪0,−5,−6,6,t<00≤t<11≤t<7t≥7;f(t)={0,t<0−5,0≤t<1−6,1≤t<76,t≥7; 1. write the function in terms of unit step function
Final answer:
The function f(t) can be represented in terms of the unit step function as f(t) = -5u(t) - u(t-1) + 6u(t-7), with each term turning on at specific breakpoints.
Explanation:
To write the function f(t) in terms of the unit step function, you can think of f(t) as a piecewise function that changes values at various breakpoints. The unit step function, denoted as u(t), is defined to be 0 when t < 0 and 1 when t ≥ 0. For the given function f(t), we can write it using the unit step function as follows:
f(t) = -5u(t) -u(t-1) + 6u(t-7)
This representation uses the properties of the unit step function to 'turn on' different function values at specified points. Each term corresponds to a segment of the piecewise function, with the coefficients representing the value of f(t) within each segment.
In a fraternity with 37 members, 18 take mathematics, 5 take both mathematics and art history, and 8 take neither mathematics nor art history. How many take art history but not mathematics?
Answer:
Fraternity of 32 members with 8 taking neither math or physics
Of the 24, 5 took both. 24 - 5 = 19 taking one. 18 taking just Math.
Just 1 took only Physics.
Step-by-step explanation:
how many factors are in the expression x(1+y)^z
a. 3
b.2
c.0
d.1
There are two factors: ( x ) and (1+y). So option (b) is correct.
To find the factors in the expression ( x(1+y)^z ), we break it down into its components.
1. ( x ) - This is a factor because it's multiplied by the rest of the expression.
2. (1+y) - This is also a factor because it's part of the expression being raised to the power of \( z \).
3. ( z ) - The exponent does not affect the number of factors, as it's simply the power to which the expression is raised.
So, there are two factors: ( x ) and (1+y).
Detailed calculation:
( x ) is multiplied by the entire expression, so it's a factor.
(1+y) is a factor because it's part of the expression.
( z ) is an exponent and doesn't count as a separate factor.
Thus, the answer is (b) 2.
What is the least possible sum of 24
Over a 12 hour period from 8 pm to 8 am the tempeture fell a steady rate 8°F to 16°F if the temperature fell at the same rate every hour what was the temperature at 4 am
A certain recipe calls for 2 3/4 cups of sugar.if the recipe is to be doubled, how much sugar should be used
A condo in Culver City, California, listed for $1.4 million with 20% down and financing at 5% for 30 years. What's the monthly payment?
Answer:
Step-by-step explanation:
$6,014.40
Lucy is thinking of a number.The number is greater than two hundred twenty- five. her number is less than 2 hundred 2 tens 7 ones. what is lucy's number?
on monday your bank account was balanced -$12.58 because you didn't realize this, you wrote a check for -$30.72 for groceries what is the new balance in your checking account?
The new balance after I bought groceries worth of 30.72 dollars is -43.3 dollars.
What are he types of sign distributions?Sign distributions are of four types they are:- negative distributed to negative results in positive and positive distributed positive results to positive. Negative distributed to positive or vice versa results in negative.
According to the given question on Monday I had -12.58 dollars.
I bought some groceries worth -30.72 dollars which will also be deducted from my bank account.
∴ The final balance I have is ( -12.58 - 30.72) dollars which is,
= -43.3 dollars.
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Which group of 3 cards would allow Carlos to win with 21 points?
A. 6 of clubs, 7 of spades, 8 of diamonds
B. Ace of hearts, Ace of diamonds, 10 of hearts
C. Jack of clubs, 7 of clubs, 4 of spades
D. 8 of clubs, 9 of hearts, 9 of spades
:what does this problem solve as
1/2(4x−5)+52=10
What is the quotient of d-2 / d4-6d3+d+17=
A. d3− 4d2 + 9d + 35 B. d3− 8d2 + 17d –17 C. d3− 8d2 + 16d − 31 R 79 D. d3– 4d2– 8d –15 R–13
Answer:
Step-by-step explanation:
hey can the other person get brainliest. thanks
At a pet store, Davina counted 12 parrots out of 20 birds. What is an equivalent ratio of parrots to birds in the pet store?
The shortest side of a right triangle measures 11m. The lengths of the other two sides are consecutive integers. Find the lengths of the other two sides.
(40 points + Brainliest for right answer).
A laptop has a listed price of 715.95 before tax. If the sale tax rat is 9.25%, find the cost of the laptop with the sales tax included. Round your answer to the nearest cent, as necessary.
Find f. f '''(x) = cos(x), f(0) = 4, f '(0) = 2, f ''(0) = 6
sales price is 67.50 sales tax is 5% how much is the total amount paid
the temperature of a pot of water is shown. the temperature of the water changed -2.5 degree F per minute. What was the temperature after 20 minutes?
mrs. baker purchased a number of juice packs at a cost of $0.30 each and a loaf of bread that cost $1.19. the total cost of her purchases was 2.99. which equation would you use the determine how many juice packs mrs. baker purchased
Answer:
0.30j + 1.19 = 2.99
Step-by-step explanation: Hope this helps! :D
Silver is a white metal and is an excellent conductor of heat and electricity. The density of silver is 10.49 g/cm3. Silver does not react with water but it does react with nitric acid. Silver tarnishes when exposed to air or light. What is a physical property of silver?
density because everything else would fall under the category of chemical properties instead of physical properties and the other 3 properties would result in a chemical change while density would not
You are debating about whether to buy a new computer for $800.00 or a refurbished computer with the same equipment for $640.00. If you are paid $10.00/hour and your deductions are FICA (7.65%), federal tax withholding (12%), and state tax withholding (8%), how many hours do you have to work to pay for the new computer?
A) 111 hours
B) 89 hours
C) 98 hours
D) 87 hours
First calculate all the deduction
FICA = $10 per hour x 0.0765 = $0.77 per hr
Fed tax = $10 per hr x 0.12 = $1.2 per hr
State tax = $10 per hr x 0.08 = $0.8 per hr
Remaining pay = 10 – 0.77 – 1.2 – 0.8 = $7.23 per hour
Time required = $640 / $7.23 per hr
Time required = 89 hrs
After calculating deductions from the gross wage of $10.00, the net income per hour is $7.235. To buy the new computer for $800, we divide the cost by the net wage, resulting in approximately 110.58 hours. Therefore, the student would need to work about 111 hours to afford it.
To calculate the number of hours needed to work to pay for the new computer, we must first determine the net income per hour after all the deductions. With a gross wage of $10.00 per hour, the deductions would be:
FICA: 7.65% of $10.00 = $0.765Federal Tax: 12% of $10.00 = $1.20State Tax: 8% of $10.00 = $0.80This totals $2.765 in deductions per hour. Subtracting this from the gross wage gives a net income per hour:
$10.00 - $2.765 = $7.235.
To afford the new computer costing $800, we divide the cost of the computer by the net income per hour to find the total number of hours needed:
$800.00 / $7.235 ≈ 110.58 hours.
Since we cannot work a fraction of an hour, we will need to round up to the nearest whole number, which suggests that the student would need to work approximately 111 hours to afford the new computer.
Prove the identity csc^2xsec^2x=sec^2x+csc^2x
Which equation represents the linear function that is shown on the graph below?
ANSWERS:
y= 1/2x +4
y= 1/2x -2
y= 4x -2
y= -2x +4
The equation y = (1/2)x - 2.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
We have points from the graph (6,1) and (8,2).
The slope of the equation is;
m = (2-1) / (8-6)
m = 1/2
And the y-intercept;
We have the slope-intercept form of the equation,
y = mx + b
y = x/2 + b
To find the y-intercept, we substitute the point (6,1)
b = -2
Therefore, we have the equation of the linear function y = (1/2)x - 2.
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Please help me on 3 and 4 please thanks ❤️
Paul is riding his bike 48 miles to the beach. His average rate of speed is 13.8 miles per hour. Paul stopped for a snack after 3 hours. How many miles does he have to go after his snack? Round your answer to the nearest tenth if necessary.
13.8 miles per hour x 3 hours = 41.4 miles ( what he already rode)
48 - 41.4 = 6.6 more miles to go
Atif has a z score of 1.02 from a converted iq score. from a z table, the percentage between his score and the mean is 34.61%. what percent of people have iqs at or lower than atif's score?
About 19/20 of celery is water. What percent is this
Find equations for the horizontal and vertical tangent lines to the curves
50 POINTS!!!
Suzanne ran 3 3/4 miles in the morning and 4 1/2 miles in the afternoon. How many kilometers did she run altogether? Assume 1 mile = 1.6 kilometers.
Answer:- Total distance traveled by Suzanne in kilometers=13.2 kilometers.
Explanation:-
Distance traveled by Suzanne in the morning=[tex]3\frac{3}{4}\text{ miles}[/tex]
Distance traveled by Suzanne in the evening=[tex]4\frac{1}{2}\text{ miles}[/tex]
Total distance traveled by Suzanne=[tex][3\frac{3}{4}+4\frac{1}{2}\text{ miles}[/tex]
[tex]=\frac{15}{4}+\frac{9}{2}\text{ miles}[/tex]
[tex]=\frac{15+18}{4}\text{ miles}[/tex]
[tex]=\frac{33}{4}\text{ miles}[/tex]
[tex]=8.25\text{ miles}[/tex]
Total distance traveled by Suzanne in kilometers=[tex]8.25\times1.6\text{ kilometers}=13.2\text{ kilometers}[/tex]
Total distance traveled by Suzanne in kilometers[tex]=13.2\text{ kilometers}[/tex]