1. After constructing the function according to the question, Q(t) = [tex]35e^{\frac{-ln2}{20}t}[/tex].
2. It will take 50 hours for the amount of Diazepam left in the body to reach 7 mg.
What is a function?
Exactly one element of Y is assigned to each element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function of the domain and codomain, respectively. Examples include f(x) = x/2 ("f of x equals x split by 2") ("f of x equals x divided by 2") Every input "x" has a single output "x/2," which makes it a function: • f(2) = 1.
Solution explained:
According to the question,
Q(t) = [tex]Pe^{rt}[/tex]
The half-life of Diazepam is 20 hours = t
Q(0) = p = 35 { the initial value}
Q(20) = [tex]35e^{20r} = \frac{1}{2} X 35[/tex]
= [tex]e^{20r} = \frac{1}{2}[/tex]
= [tex]20r = -ln2[/tex]
= [tex]r = \frac{-ln2}{20}[/tex]
Therefore, Q(t) = [tex]35e^{\frac{-ln2}{20}t}[/tex]
Now, Let
Q(t) = 7
[tex]35e^{\frac{-ln2}{20}t}[/tex] = 7
[tex]e^{\frac{-ln2}{20}t} = \frac{1}{5}[/tex]
[tex]{\frac{-ln2}{20}t} = -ln5[/tex]
After calculating,
t = 50 (hours)
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Rewrite the function by completing the square. h ( x ) = x 2 + 3 x − 18 h(x)=x 2 +3x−18
The quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2 - 20.25.
We are given a quadratic function:
h (x) = x^2 + 3x − 18
We need to rewrite the function by completing the square.
We can see the coefficient of x is 3.
So, we will add and subtract the square of half that.
So, find the square of half of 3, we will get;
(3 / 2)^2 = 9 / 4 = 2.25
add and subtract the square of half of 3 from the given function, we will get;
h(x) = x^2 +3x + -18 2.25 -2.25
arrange the expression, we will get;
h(x) = (x^2 +3x +2.25) -18 -2.25
write the expression in parentheses as a square, and simplify the constant, we will get;
h(x) = (x + 1.5)^2 - 20.25
So, the square function is written as h(x) = (x + 1.5)^2 - 20.25.
Thus, the quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2 - 20.25.
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In outer space, the distant an object travels varies directly with the amount of time it travels. If an asteroid travels 3000 miles in 6 hours, how far could the asteroid travel in 9 hours?
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
3000 miles = 6 hours
4500 miles = 9 hours
The distance asteroid travel in 9 hours is 4500 miles
What is a unit rate?Unit rate is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
3000 miles = 6 hours
Divide both sides by 6.
500 miles = 1 hour
Multiply 9 on both sides.
9 x 500 miles = 9 hours
9 hours = 4500 miles
Thus,
The distance asteroid travel in 9 hours is 4500 miles
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Write an equation for the nth term of the arithmetic sequence
The equation for the nth term of the arithmetic sequence is [tex]a_{n}[/tex] = 25 - 4n
The nth term of the arithmetic sequence:An arithmetic sequence or arithmetic progression is a series of numbers with a common difference. For example 1, 2, 3, 4... is an Arithmetic sequence with a common difference 1. In an Arithmetic sequence, the difference between every two consecutive terms will be equal.
The formula for the nth term of a sequence is given below
=> [tex]a_{n}[/tex] = a + (n-1)d
where a is the first term and d is a common difference.
Here we have
21, 17, 13 ... is the arithmetic sequence
Where first term a = 21
and common difference d = term2 - term1 = 17 - 21 = - 4
As we know the nth term of AP, [tex]a_{n}[/tex] = a + (n-1)d
=> [tex]a_{n}[/tex] = 21 + (n-1)(-4)
=> [tex]a_{n}[/tex] = 21 - 4n + 4
=> [tex]a_{n}[/tex] = 25 - 4n
Therefore,
The equation for the nth term of the arithmetic sequence is [tex]a_{n}[/tex] = 25 - 4n
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If your car gets 35 miles per gallon, how much does it cost to drive 420 miles when gasoline costs $2.50 per gallon?
The cost is $
(Simplify your answer. Round to the nearest cent as needed.)
Answer: 30$
Step-by-step explanation:
first you divide 420 by 35 and you get 12 times 2.50$ equals 30$
what is the quotient of -0.75 0.4 please help
The quotient of -0.75 /0.4 is approximately -1.88.
What is the quotient?
This refers to the value you get after division operation has been carried out.
given in the question:
-0.75/0.4 = -1.875
≈ -1.88
Recall, according to the sign rule in mathematics:
Any negative number divided by a positive number gives a negative value.
hence the quotient of -0.75/0.4= -1.875
≈ -1.88
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Kathy invested $3000 at a rate of 7% for 4 years and 6 months. Find the amount she got back.
The amount that Kathy got back after 4 years and 6 months is $3945 .
In the question ,
it is given that ,
the amount invested by Kathy(P) = $3000
the rate at which the amount is invested (r) = 7% per annum
time for which the amount is invested (t) = 4 years and 6 month = 4.5 years
the simple interest calculated by
Simple Interest = ( 3000 × 7 × 4.5)/100
= 94500/100
= 945
So , the interest is $945 .
So , the amount that Kathy get = Principle + Interest
= 3000 + 945
= 3945
Therefore , amount that Kathy got back after 4 years and 6 months is $3945 .
The given question is incomplete , the complete question is
Kathy invested $3000 at a rate of 7% simple interest for 4 years and 6 months. Find the amount she got back.
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Find the exact value of the given expression.
cos(2tan^-1(24/7))
un ciclista recorre 300 metros por minuto. ¿cuantos kilómetros recorre en una hora?
Answer:
El ciclista recorre en una hora:
18 kilómetros.
Step-by-step explanation:
1 hora = 60 minutos
1 minuto = 1/60 = 0.01667 horas
1 kilómetro = 1000 metros
300 metros = 300/1000 = 0.3 kilómetros
Entonces:
300 metros por minuto = 300metros/minuto
300 metros / minuto = 0.3kilómetros / 0.01667 horas
= 0.3/0.01667
= 18 kilómetros/hora
El ciclista recorre 18 kilómetros cada hora
what is the sum of the first 80
Consecutive odd numbers?
Find the slope (2, -7) and (5, -4)
the slope is 1 because 3/3
Answer:
1
Step-by-step explanation:
When two points are given;
Slope =y2-y1/x2-x1= -4-(-7)/5-2
= -4+7/3
= 3/3
=1
7. In 2009, the national average price for milk was $3.11
and in 2011 it rose again to $3.57 per gallon.
Was the percent increase in cost greater from 2009
your answer.
The percentage increase in cost greater from 2009 is 14.79%
The average price of milk in 2009 = $3.11
The average of price of milk in 2011 = $3.57
The increase in price = The average of price of milk in 2011 - The average price of milk in 2009
Substitute the values in the equation
The increase in price = 3.57 - 3.11
= $0.46
The percentage increase = The increase in price / The average price of milk in 2009 × 100
Substitute the values in the equation
The percentage increase = ( 0.46 / 3.11 )×100
= 14.79%
Hence, the percentage increase in cost greater from 2009 is 14.79%
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PLS HELP ASAPPPP URGENT
Answer: 4 + (2*3)^2
Step-by-step explanation:
The growth of the world's population can be described by the equation A=Age, where time t is measure in years, A, is the population of the world at t=0, r is the annual growth rate, and A is the population at time t. Assume that r= 3% per year. How long will it take a
population of 8 billion to increase to 9 billion.
_ years, round to the nearest whole number
It will take 37.5 years.
From the question, we have
A_0 = 8 billion
A = 9 billion.
r= 3% per year
A = A_0*e^rt
9 = 8*e^3t/100
9/8 = e^3t/100
Taking log_e both sides,
log_e 9/8 = log_e e^3t/100
9/8 = 3t/100
t = (9*100)/(8*3)
t = 37.5 years
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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A die is rolled. Find the probability of the given event.
(a) The number showing is a 6;
The probability is :
(b) The number showing is an even number;
The probability is :
(c) The number showing is greater than 1;
The probability is :
4
find m
a. 14
b. 39
c. 51
d. 90
I WILL USE SUM OF INTERIOR ANGLES OF A TRIANGLE TO GET x
[tex](2x + 11) + (4x - 5) + 90 = 180 \\ 2x + 4x + 11 - 5 + 90 = 180 \\ 6x + 96 = 180 \\ 6x = 180 - 96 \\ 6x = 84 \\ \frac{6x}{6} = \frac{84}{6} \\ x = 14[/tex]
THE ANSWER IS OPTION a
X=14°
Need an answer quick please
The required amount in the savings account=$2704.05
What is simple interest?
Calculating the interest on a loan using simple interest is quick and simple. Simple interest is calculated by dividing the principle by the daily interest rate and the number of days between installments.
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest.
P=2700, r=0.3%=0.003, t= 0.5 year
A= P(1+rt)
= 2700(1+ 0.003*0.5)
= 2700(1+ 0.0015)
= 2700(1.0015)
= 2704.05
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Which expression is equivalent to 6^-6 x 6^6
Answer:
Step-by-step explanation:
x^-3 * x^-3
can anyone help me with these please and thank you ?
Membership costs for belonging to a gym for a certain number of months are shown in the table below.
Answer:
y = 35.5x - 10
Step-by-step explanation:
If we graph the function with the help of the given table,
Since, there is a common difference in each term of 'cost of gym membership'
d = 61 - 25.5 = 35.5
d = 96.5 - 61 = 35.5
Graph will represent a linear function.
Let the equation of the line is,
y - y' = m(x - x')
where (x', y') is a point lying on the graph and 'm' is the slope.
Two points lying on the graph are (1, 25.5) and (2, 61).
Slope of the line =
=
= 35.5
Equation of the line passing through (1, 25.5) having slope 'm' = 35.5
y - 25.5 = 35.5(x - 1)
y = 35.5x - 35.5 + 25.5
y = 35.5x - 10
Here x = duration of membership
y = membership price
Therefore, equation representing Fit Zoom's membership price equation will be,
y = 35.5x - 10
Kirsty makes orange-strawberry punch. The table shows how many parts orange juice and strawberry juice to make one batch.
Orange-Strawberry Punch
Parts Orange Juice
4
Parts Strawberry Juice
5
Kirsty decides to increase the strawberry juice by one part. What is the new ratio of strawberry juice to orange juice?
For every 4 parts orange juice there are 4 parts strawberry juice.
For every 5 parts orange juice there are 4 parts strawberry juice.
For every 4 parts orange juice there are 6 parts strawberry juice.
For every 5 parts orange juice there are 6 parts strawberry juice.
Answer:
2nd one, hope this helps
Step-by-step explanation:
Answer:
It is C.
Step-by-step explanation:
Do not listen to top answer
I got it right on unit test review ….
Complete the calculation to convert
18
pounds
(lbs)
to grams
(g)
given that
1
lb.
=
453.92
grams.
The conversion of 19 pounds to grams is 8170.74 grams.
How to calculate the value?From the information illustrated, it should be noted that it was illustrated that 1 pound = 453.93 grams.
In this case, in order to fund the value of 18 pounds, we will have to multiply 18 by 453.93 grams.
This will be calculated as:
18lb = 18 × 453.93 grams.
= 8170.74 grams
The value is 8170.74 grams.
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Put these numbers in order from least to greatest
By writing the fractions as decimals, we will see that the numbers ordered from least to greatest are:
-5, 2/16, 23/40
How to order the numbers?The 3 numbers given are:
-5
23/40
2/16
The numbers should be ordered as they appear on a number line (from left to right)
The smaller number is, obviously, the negative one, so the thing that we need to check now is what of the two fractions is smaller.
To do so, we can write them as decimals:
23/40 = 0.575
2/16 = 0.125
So the smaller one is 2/16 and then comes 23/40
Then the numbers ordered from smaller to larger are:
-5, 2/16, 23/40
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brainliest if you answer :) thanksss
AC is congruent to SU
- Given the table below write an explicit
equation .
n
1
2
3
4
5
f(n)
5
58
13
20
29
The explicit equation for the table is,
f(n) = n² + 4
Given, the values of an explicit function,
Let the function be,
f(n) = an² + bn + c
f(1) = a(1)² + b(1) + c
5 = a + b + c
f(2) = a(2)² + b(2) + c
8 = 4a + 2b + c
f(3) = a(3)² + b(3) + c
13 = 9a + 3b + c
On subtracting the equations, we get
5 = 5a + b
3 = 3a + b
Again, on subtracting we get
2 = 2a
a = 1
On putting the values we get,
b = 0.
a + b + c = 5
1 + 0 + c = 5
c = 4
Hence, the explicit equation for the table is,
f(n) = n² + 4
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Which of the following are solutions to the inequality 2y+3<7? Mark all that are solutions.
[_] 2
[_] 0
[_] -1
[_] 1
y<2 is the solution to the inequality
What is Linear Inequality?
The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.
According to the question
2y+3<7
subtracting 3 from both sides
we get,
2y<4
dividing both sides with 2
we get,
y<2
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The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 73% of
in the carbon-14 expected in living matter, when did the tree die?
The tree died about ] years ago.
Do not round until the final answer. Then round to the nearest whole number.)
Answer:
Time 2 540 years
Step-by-step explanation:
T = 5 600 yares - Half-life
73% - Carbon content
N = 0.73·N₀
Decay constant:
λ = ln 2 / T = 0.693 / 5600 ≈ 0.000124 (years)⁻¹
Law of radioactive decay:
N = N₀·e^(-λ·t)
0.73·N₀ = N₀·e^(-λ·t)
0.73 = e^(-λ·t)
ln (0.73) = -λ·t
t = ln (0.73) / (-λ) = ln (0.73) / (- 0.000124) ≈ 2 540 years
Which of the statements are true about the image?
Answer:
which image
Step-by-step explanation:
if you tell me I will answer the question
Answer:
image not found
you can send the image privately
What is the absolute value of -330?
Answer:
Why is | 330 | the absolute value of the number 330?
The absolute value of a number is how far away the number is from zero. The absolute value is ALWAYS positive.
What is the absolute value of -330?
The negative version of the number is also | 330 |
More Examples
Here are more examples of even and odd numbers in sequence:
Number 328 329 331 332
Absolute Value 328 329 331 332
you want to obtain a sample to estimate a population proportion. based on the previous evidence, you believe the population proportion is approximately 76%. you would like to be 95% confident that your estimate is within 4.5% of the true population proportion. how large of a sample size is required?
n=
A proportion is an equation in which two ratios are set equal to each other and the large sample size required is [tex]0.75[/tex].
What is population proportion?
A fraction is represented in the form of [tex]\frac{a}{b}[/tex], a while ratio [tex]a:b[/tex], then a proportion states that two ratios are equal. Here, [tex]a[/tex] and [tex]b[/tex] are any two integers.
Here, we are determining the minimum sample size for the determination of the population proportion. So, the general formula is of the form is:-
[tex]n=(\frac{z_\frac{x}{2}.x}{E})^{2}[/tex]
Here given values are:-
σ[tex]=76[/tex], population standard deviation
[tex]1-x=0.95\\[/tex], Confidence level
[tex]E=4.5[/tex], Error
Determining the critical value, we get
[tex]z_\frac{x}{2}\\P(z\leq z_\frac{x}{2})=1-\frac{x}{2}\\1-x=0.95\\x=1-0.95\\x=0.05\\\frac{x}{2}=\frac{0.5}{2}\\\frac{x}{2}=0.25\\1-\frac{x}{2}=1-0.25\\\\=0.75[/tex]
Hence, a large sample size is required is [tex]0.75[/tex].
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You are solving a measurement problem where the numbers 3.0471 x 10^9 and 2.4 x 10^-4 are divided. How many significant digits should the quotient have?
A. 2
B. 3
C. 4
D. 5
Answer:
5(d)
Step-by-step explanation:
(3.0471×10⁹)/2.4×10^-4
30471×10^9-4÷24×10^-4-1
30471×10⁵÷24×10^-5
(30471÷24)×10^5-(-5)
1269.625×10^5+5
1269.625×10¹⁰
1.269625×10^10-3
1.269625×10⁷
1.2696 to 5s.f
Suppose Tom borrows $4000 at an interest rate of 3% compounded each year.
Assume that no payments are made on the loan.
Follow the instructions below. Do not do any rounding.
(a) Find the amount owed at the end of 1 year.
(b) Find the amount owed at the end of 2 years.
The amount owed at the end of 1 year is $4120 and by the end of 2 years, $4243.60 when Tom borrows $4000 at an interest rate of 3% compounded each year.
What is compound interest?The interest you earn on interest is known as compound interest. Simple math can be used to demonstrate this: if you have $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will end up with $110.25 at the end of the second year. In order to calculate compound interest, multiply the principal of the original loan by the annual interest rate multiplied by the number of compound periods minus one.
Here,
principle amount=$4000
rate of interest=3%
For first year,
A=P(1+r/n)^(nt)
A=4000(1+3/12)^12*1
A=$4,120.00
For first year,
A=P(1+r/n)^(nt)
A=4120(1+3/12)^12*1
A=$4,243.60
When Tom borrows $4000 at an interest rate of 3% compounded annually, the total amount due at the end of one year is $4120, and at the end of two years, it is $4243.60.
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