The exponential equation to model this after t time periods is:
N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]
Given,
Melatonin is fast-acting and has a half-life of approximately 30 minutes.
10-milligram tablet is taken.
We need to write an exponential equation to model this after t time periods.
What is half-life?Half-life is the time required for a quantity to reduce to half of its initial value.
The formula is given as:
N(t) = [tex]N_{0} ~(\frac{1}{2})~^\frac{t}{t_{1/2}}[/tex]
Where
N(t) = quantity of the substance remaining
[tex]N_{0}[/tex] = initial quantity of the substance
[tex]t_{1/2}[/tex] = half-life of the substance
We have,
Half-life = 30 minutes
[tex]N_{0}[/tex] = 10 mg
The exponential equation to model this after t time periods is:
N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]
Thus the exponential equation to model this after t time periods is:
N(t) = 10 ( 1/2 ) [tex]^\frac{t}{30}[/tex]
Learn more about half-life here:
https://brainly.com/question/24710827
#SPJ1
In a psychology class, 57 students have a mean score of 87.1 on a test. Then 10 more students take the test and their
mean score is 68.6. What is the mean score of all of these students together? Round your answer to one decimal place if
necessary.
The mean score of all of these students together, rounded to 1 decimal place is 84.3
What is the mean score in each case?
The mean score in each test taken is the total scores of all students that took the test divided by the number of students, in essence, the total score is determined as the mean score multiplied by number of students
total score for 57 students=87.1*57
total score for 57 students= 4,964.7
total score for 10 students=68.6*10
total score for 10 students=686.0
mean score of all of these students together=(4,964.7+686.0)/(57+10)
mean score of all of these students together= 84.3
Find out more about mean on:https://brainly.com/question/701612
#SPJ1
Adventure Travel has an Adjusted Trial Balance for Year Ended December 31, 20XX with the following account balances: DEBITS: Cash: 25,000; Accounts Receivable: 15,000; Office Supplies: 4,300; Office Equipment: 29,600 CREDITS: Accumulated depreciation - office equipment: 5,000; Salaries Payable: 2,800; Long-term notes payable: 22,200; Common Stock: 20,000; Retained Earnings: 10,260 DEBIT: Cash Dividends: 1,000 CREDITS: Fees Earned: 75,000 DEBITS: Salaries Expense: 32,800; Rent Expense: 16,800; Depreciation expense - office equipment: 3,960; Advertising expense: 4,000; Office supplies expense: 2,800. Total Debits = 135,260; Total Credits = 135,260 You have just determined Net Income for Adventure Travel in the previous question. Now, you must prepare the Statement of Retained Earnings. What amount will you add to Beginning Retained Earnings balance to determine Ending Retained Earnings Balance? What amount will you subtract from Beginning Retained Earnings balance to determine Ending Retained Earnings Balance?
The amount that would be added to Beginning Retained Earnings balance to determine Ending Retained Earnings Balance is net income of $14,640
The amount would be subtracted from Beginning Retained Earnings balance to determine Ending Retained Earnings Balance is the cash dividends of $1,000
What is net income?
The net income is the excess of fees earned by Adventure Travel in the year ended over its total expenses, in essence, we need to determine its total expenses first and foremost, which comprises of salaries expense, rent expense, depreciation expense, advertising expense and office supplies expense
total expenses=32,800+16,800+3960+4000+2800
total expenses=60,360
fees earned=75,000
net income =fees earned-total expenses
net income=75,000-60,360
net income=$14,640
Now the closing retained earnings comprises of beginning retained earnings plus the net income minus the cash dividends paid
Retained earnings=$14,640+$ 10,260-$1,000
Retained earnings=$23,900
Find out more about net income on:brainly.com/question/1347024
#SPJ1
Refer to the number line. Find the coordinate of point X such as the ratio of MX to XJ is 2:3
Please help it’s due soon
===========================================================
Explanation:
M is at 2 and J is at 18
This is a gap of 18-2 = 16
The ratio 2:3 has 2+3 = 5 parts total. Divide the gap of 16 into 5 equal parts to get 16/5 = 3.2 units
Each part is 3.2 units wide
Double this to get 2*3.2 = 6.4; the doubling is because of the "2" in "2:3"
Now add 6.4 to M = 2 to get 2+6.4 = 8.4 which is the location of point X
-----------------------
Check:
Segment MX is 8.4 - 2 = 6.4 units long
Segment XJ is 18-8.4 = 9.6 units long
The ratio 6.4:9.6 is the same as 64:96 and it fully reduces to 2:3 to confirm the answer. Or you could notice that (6.4)/(9.6) = 64/96 = 2/3
mrs.kline drove 30 miles in 40 minutes. how many miles did she drive in 2 hours
4x-(10-x) =15/2, what does x equal?
The value of x is for the given equation is 7/2.
What is an algebraic expression, exactly?An algebraic expression (or variable expression) is a term that has been combined with addition, subtraction, multiplication, and division operations.
To simplify an algebraic expression, we simply combine similar terms. As a result, variables with similar characteristics will be combined. The same abilities will now be created by combining similar variables.
The given equation is 4x-(10-x) =15/2.
4x - 10 + x + 15/2
5x - 10 = 15/2
Dividing both sides by 5 to obtain:
x - 2 = 3/2
Multiply both sides by 2 to get:
2x - 4 = 3
2x = 3 + 4
x = 7/2
To know more about algebraic expressions visit:
https://brainly.com/question/19245500
#SPJ9
[tex] \rm \int_{ 0}^ {\large\frac{\pi}4} \sqrt{ \tan(x) - \tan {}^{2} (x) } \: dx \\ [/tex]
First substitute [tex]x=\tan^{-1}(y)[/tex] to rewrite the integral as
[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = \int_0^1 \frac{\sqrt{y-y^2}}{1+y^2} \, dy[/tex]
Now use an Euler substitution, [tex]z=\frac{\sqrt{y-y^2}}y[/tex] to rewrite it again as
[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = 2 \int_0^\infty \frac{t^2}{(t^2+1)^2 + 1) (t^2 + 1)} \, dt[/tex]
where we take
[tex]\sqrt{y - y^2} = \sqrt{-y(y-1)} = yt \implies y = \dfrac1{1+t^2} \text{ and } dy = -\dfrac{2t}{(1+t^2)^2} \, dt[/tex]
Partial fractions:
[tex]\displaystyle \frac{t^2}{((t^2+1)^2+1) (t^2 + 1)} = \dfrac{t^2+2}{t^4+2t^2+2} - \dfrac1{t^2+1}[/tex]
so that
[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = 2 \left(\int_0^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt - \int_0^\infty \frac{dt}{t^2+1}\right)[/tex]
The second integral is trivial,
[tex]\displaystyle \int_0^\infty \frac{dt}{t^2+1} = \lim_{t\to\infty}\tan^{-1}(t) - \tan^{-1}(0) = \frac\pi2[/tex]
For the other, I'm compelled to use the residue theorem, though real methods are doable too (e.g. trig substitution). Consider the contour integral
[tex]\displaystyle \int_\Gamma f(z) \, dz = \int_\Gamma \frac{z^2+2}{z^4+2z^2+2} \, dz[/tex]
where [tex]\Gamma[/tex] is a semicircle in the upper half of the complex plane, and its diameter lies on the real axis connecting [tex]-R[/tex] to [tex]R[/tex]. The value of this integral is 2πi times the sum of the residues in the upper half-plane. It's fairly straightforward to convince ourselves that the integral along the circular arc vanishes as [tex]R\to\infty[/tex], so the contour integral converges to the integral over the entire real line. Note that
[tex]\displaystyle 2 \int_0^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt = \int_{-\infty}^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt[/tex]
since the integrand is even.
Find the poles of [tex]f(z)[/tex].
[tex]z^4 + 2z^2 + 2 = 0 \\\\ ~~~~ \implies (z^2+1)^2 = -1 \\\\ ~~~~ \implies z^2 = -1 \pm i \\\\ ~~~~ \implies z = \pm \sqrt{-1 \pm i} = \sqrt[4]{2}\, e^{\pm i(3\pi/8 + \pi k)}[/tex]
where [tex]k\in\{0,1\}[/tex].
The two poles we care about are at [tex]z_1=\sqrt[4]{2}\,e^{i\,3\pi/8}[/tex] and [tex]z_2=\sqrt[4]{2}\,e^{-i\,11\pi/8}[/tex]. Compute the residues at each one.
[tex]\displaystyle \mathrm{Res}\left\{f(z),z=z_1\right\} = \lim_{z\to z_1} \frac{f(z)}{z-z_1} = -\frac1{2^{7/4}}\,ie^{-i\,\pi/8} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~= -\frac1{2^{7/4}} \left(\sin\left(\frac\pi8\right) + i \cos\left(\frac\pi8\right)\right)[/tex]
[tex]\displaystyle \mathrm{Res}\left\{f(z),z=z_2\right\} = \lim_{z\to z_2} \frac{f(z)}{z-z_2} = -\frac1{2^{7/4}}\,ie^{i\,\pi/8} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~= \frac1{2^{7/4}} \left(\sin\left(\frac\pi8\right) - i \cos\left(\frac\pi8\right)\right)[/tex]
By the residue theorem,
[tex]\displaystyle \int f(z) \, dz = 2\pi i \sum_{\rm poles} \mathrm{Res}\{f(z)\} = \frac{4\pi}{2^{7/4}} \cos\left(\frac\pi8\right)[/tex]
We also have
[tex]\displaystyle \cos^2\left(\dfrac\pi8\right) = \dfrac{1 + \cos\left(\frac\pi4\right)}2 = \dfrac{2 + \sqrt2}4 \implies \cos\left(\frac\pi8\right) = \dfrac{\sqrt{2+\sqrt2}}2[/tex]
Then the remaining integral is
[tex]\displaystyle \int_0^\infty \frac{t^2+2}{t^4+2t^2+2} \, dt = \frac{4\pi}{2^{7/4}} \cos\left(\frac\pi8\right) = \sqrt{\frac12 + \frac1{\sqrt2}} \, \pi[/tex]
It follows that
[tex]\displaystyle \int_0^{\pi/4} \sqrt{\tan(x) - \tan^2(x)} \, dx = \boxed{\left(\sqrt{\frac12 + \frac1{\sqrt2}} - 1\right) \pi}[/tex]
John waters his 2 1/2 acres of farmland in 1/3 of an hour. What is his speed in acres per hour?
Answer:
7.5 acres per hour
Step-by-step explanation:
1) You know that in 1/3 of an hour John waters 2 1/2, or 2.5, acres of farmland.
2) To get 1 hour we would multiply what John waters in 1/3 of an hour by 3.
2.5acres * 3 = 7.5 acres per hour
3) We multiply by 3 because 1/3 of an hour * 3 = 1 hour
so: 2.5acres * 3 = 7.5 acres per hour
Suppose that the functions q and r are defined as follows.
q(x)=-2x-2
r(x)=x^2+1
Find the following.
(r•q) (2) =
(q•r) (2) =
The function (r •q)(-3) =(q •r)(-3) and they are equal to -40
What are algebraic functions with example?
There are several different categories of algebraic functions, including rational, polynomial, radical, cubic, linear, and quadratic. f(x)=2x+3 (linear), f(x)=(2x+3)/(x2) (rational), and f(x)=x(1/2) are a few instances (rational).Given the following functions
q(x) = 2x+2
r(x) = x² +1
Taking the product
q(x)*r(x) = (2x+2)(x² +1)
Note that according to the communatative law, (r •q)(x) = (q •r)(x)
(r •q)(-3) =(q •r)(-3) = (2(-3)+2)((-3)² +1)
(r •q)(-3) =(q •r)(-3) = (-4)(9+1)
(r •q)(-3) =(q •r)(-3) = -4(10)
(r •q)(-3) =(q •r)(-3) =-40
Hence the function (r •q)(-3) =(q •r)(-3) and they are equal to -40.
Learn more about functions
brainly.com/question/12431044
#SPJ9
Write the phrase as a variable expression..
The product of 3 and the sum of a number and 2
Identify the factors of the terms of the expression. 5 + 8a + 14b
PLEASE HELP!!!!!!!!!!!!!!!!
Solve for [x]. Each figure is a trapezoid.
Question 1
Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,
[tex]-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11[/tex]
Question 2
Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,
[tex]9x+30+7x-10=180 \\ \\ 16x+20=180 \\ \\ 16x=160 \\ \\ x=10[/tex]
What do you call two lines in 3-space that never meet, but are not parallel.
An example:
Look where two walls meet. They meet at a vertical line. Let's call that line A.
Now look at where the ceiling and another wall meet (this wall is not the same as the previous two walls mentioned). The ceiling and this new wall meet at line B
Lines A and B are skew lines since they'll never cross even if you extend them out forever. They aren't parallel lines either because they don't point in the same 3D direction.
Check out the diagram below.
For the following function, find the given values in parts (a) through (c) below.
Answer:
Step-by-step explanation:
f(x) = x^2 + 4x is specified as a function. When the x is replaced in "f(x)" is replaced with a number, you treat it as a variable.
In this case, f(-3) is almost exactly like saying x = -3.
Everywhere x is in the function is replaced with -3, because you are plugging it in to find a value. Here is a demonstration:
f(-3) = (-3)^2 + 4(-3)
f(-3) = 9 - 12
f(-3) = -3
The answer to your question is -3. Don't be afraid to ask anymore questions regarding this if you are confused.
Which graph represents the function f(x) =
1
X+3
-2?
Answer:
Step-by-step explanation:
Dont really understand what your asking, is it fx=x+1? If so this should be it:
what is the value of the expression x^2+9/x^2 when x=0
The U.S. per capita income for 2013 was $53143. If the average person operated like the federal government, how much money would the average person have spent in 2013? Express your answer round to the nearest
Answer:
i dont understand what is this
Answer:
Step-by-step explanation: per means divide and capita means person
so you would divide
$53143 by 1.3333333 to get your answer $ 39857 since you are rounding to the nearest dollar
I need help asap. Is the answer yes or no
Answer:
No
Step-by-step explanation:
Find the center and radius of the circle. x2+y2+4x-6y+4=0
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The centre of circle x2+y2+4x-6y+4=0 is (-2,3) and radius is 3.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
The given equation is x2+y2+4x-6y+4=0.
The standard form of circle is (x-h)^2+(y-k)^2=r^2
where (h,k) is centre and r is the radius of the circle.
We need to convert x2+y2+4x-6y+4=0 to standard form.
x2+4x+y2-6y=-4.
Add +4 and +9 on both sides
(x2+4x+4)+(y2-6y+9)=-4+4+9
(x2+4x+4)+(y2-6y+9)=9
(x+2)^2+(y-3)^2=3^2
When we compare the above equation with standard form we get
centre (-2,3) and radius is 3.
Therefore the center and radius of the circle x2+y2+4x-6y+4=0 is (-2, 3) and 3.
To learn more on circle click:
https://brainly.com/question/14866670
#SPJ1
Determine whether x=15 is a solution to the given equation.
-4x-6=54
Answer:
No, it is not the solution.
Step-by-step explanation:
-4(15)-6=54
-60-6=54
-66=54
nope
Question content area top Part 1 You are running a fuel economy study. One of the cars you find is blue. It can travel 38 1/2 miles on 1 1/4 gallons of gasoline. Another car is red. It can travel 22/5 miles on 4/5 gallons of gasoline. What is the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline?
Based on the miles that each car can travel on, the unit rate of miles per gallon for each car is:
Blue car - 30.8 miles per gallonRed car - 5.5 miles per gallonThe car that can therefore travel the greater distance on 1 gallon of gasoline is the Blue car.
What is the unit rate for the miles per gallon?The blue car can travel 38.5 miles on 1.25 gallons of gasoline. The unit rate is:
= 38.5 / 1.25
= 30.8 miles per gallon
The red car can travel 22/5 miles on 0.80 gallons of gasoline so the unit rate is:
= 22/5 ÷ 0.80
= 5.5 miles per gallon
The blue car can therefore travel the greater distance on 1 gallon of gasoline.
Find out more questions on the unit rate at https://brainly.com/question/28505127
#SPJ1
An angle measures 43.4° less than the measure of its complementary angle. What is the measure of each angle? please answer
The complementary angles are: 66.7° and 23.3°.
What are Complementary Angles?Two angles are said to be complementary if they both have a sum of 90 degrees when added.
Thus, we have the following:
One of the angles is represented as x.
Second angle = x - 43.4
Therefore:
x + x - 43.4 = 90
2x - 43.4 = 90
2x = 90 + 43.4
2x = 133.4
2x/2 = 133.4/2
x = 66.7°
First angle = x = 66.7°
Second angle = 66.7 - 43.4 = 23.3°
Therefore, the complementary angles are: 66.7° and 23.3°.
Learn more about the complementary angles on:
https://brainly.com/question/16281260
#SPJ1
In a recent year 17.4% of all registered doctors were female if they were 48,600 female registered doctors yet that year what was the total number of registered doctors?
Answer:
324309
doctors were registered that year.
Step-by-step explanation:
The questions says, "18.1% of all registered doctors are females"
(Consider, total number of registered doctors as [tex]x[/tex])
that's, 18.1 % of [tex]x[/tex] are female.
and 18.1% of [tex]x[/tex] is 58,700
.
The price of Stock A at 9 AM was $13.09. Since then, the price has been increasing at the rate of $0.05 each hour. At noon the price of Stock B was $13.59. It begins to decrease at the
rate of $0.12 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
Answer: I think this is a trick question because they are always either greater or less than each other
Step-by-step explanation:
Hello can someone please help me with this
Q and R are collinear because they lie in the same straight line.
Check whether Q and R are collinear from the given figure.
What are collinear points?Collinear points are the points that lie on the same straight line or in a single line. If two or more two points lie on a line close to or far from each other, then they are said to be collinear, in Euclidean geometry.
Here, Q and R are collinear because they lie in the same straight line.
A set of points in space are coplanar if there exists a geometric plane that contains them all.
Point S is outside the planes, so point S is non-coplanar with either plane.
The intersection of two planes is always a line.
The intersection between the two planes creates a line.
Line l intersects two planes V and W.
Therefore, Q and R are collinear because they lie in the same straight line.
To learn more about the collinear points visit:
https://brainly.com/question/1593959.
#SPJ1
after 35 games a different team has 50 points
14 games were draws
how many did they loose?
The value of x given that the median of x-4, x, 2x and 2x +12 is 9
The value of x is 6 for the data having the median as 9.
We are given some data:
x - 4, x, 2 x and 2 x + 12
We are also given that the median of these terms = 9
M = 9
Now, we have to find the value of x
Now, we know that the median of some data having even values will be:
M = 2nd term + 3rd term / 2
M = x + 2 x / 2
9 = 3 x / 2
3 x = 18
x = 18 / 3
x = 6
Therefore, we get that, the value of x is 6 for the data having the median as 9.
Learn more about median here:
https://brainly.com/question/26151333
#SPJ9
Pls help who will give me a correct answer i will make brainlest
The height of each story is 20 feet.
The value of x is 3 feet.
The score on the third quiz is 10
The number of action figures that would be produced on Friday is 182.
What are the solutions?The equation that can be used to determine the height of each story is:
46 = x + x + 6
46 = 2x + 6
46 - 6 = 2x
40 = 2x
x = 40 / 2
x = 20 feet
The equation that can be used to solve for x is:
35 = 5x + 5x + 5
35 - 5 = 5x + 5x
30 = 10x
x = 30 / 10
x = 3 feet
Total quiz score = score on first quiz + score on second quiz + score on third quiz
(15 x 3) = 24 + 11 + score on third quiz
45 = 35 + score on third quiz
score on third quiz = 45 - 35
score on third quiz = 10
x = total amount of figures produced in a week - sum of figures produced from Monday to Thursday
(50 x 5) - (12 + 12 + 16 + 28)
250 - 68
X = 182
To learn more about mean, please check: https://brainly.com/question/25842202
#SPJ1
A circle has a radius of 5. The center of the circle [k] is 2, and a point on the edge of the circle is (10,6). Using the information above, what are two possible x values of the center of the circle [h]?
Answer:
I LOVE GREAT BRITINNNNNNN
Step-by-step explanation:
7. Players on the football team are trying to gain weight. Tim, Jim, George, and Rick check
their weights. Tim weighs twice as much as Jim. Jim weighs 50 pounds less than
George. Rick weighs 10 pounds more than George. If Rick weighs 200 pounds, how
much does Tim weigh?
Tim's weight is 280 pounds.
What is Tim's weight?Let t, j and r represent Tim's, Jim's and George's weight respectively.
The following equations can be determined giving the information in the question:
t = 2j equation 1
j = g - 50 equation 2
r = 10 + g equation 3
r = 200
Substitute for r in equation 3 : 200 = 10 + g
g = 200 - 10
g = 190
Substitute for g in equation 2 : j = 190 - 50 = 140
Substitute for g in equation 3: t = 2(140)
140 x 2 = 280
To learn more about mathematical equations, please check: https://brainly.com/question/26427570
#SPJ1
▼ Answer
I know I'll have to work a double shift today because I have a migraine and every time I have a migraine I get stuck pulling a double. Is inductive or deductive
Deductive Reasoning.
What's the difference between inductive and deductive reasoning?
Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down. Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.
Examples-
Inductive Reasoning: The first lipstick I pulled from my bag is red. The second lipstick I pulled from my bag is red. Therefore, all the lipsticks in my bag are red.
Deductive Reasoning: The first lipstick I pulled from my bag is red.
A deductive approach involves the learners being given a general rule, which is then applied to specific language examples and honed through practice exercises. An inductive approach involves the learners detecting, or noticing, patterns and working out a 'rule' for themselves before they practise the language.
A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.
Thus ,I know I'll have to work a double shift today because I have a migraine and every time I have a migraine I get stuck pulling a double is and example of Deductive reasoning . Because a deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
To learn more about inductive or deductive reasoning
visit - https://brainly.com/question/4163182
#SPJ9
