A doctor prescribe 125 miligrams of a therapeutic drug that decays by about 10% each hour. Write an exponentia lmodel representing the amount A in milligrams of the drug remainng in the patient's system after t hours.
Answer:
[tex]C(t)=125\cdot 0.9^t[/tex]
Step-by-step explanation:
Exponential Decay Function
The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential decaying function is expressed as:
[tex]C(t)=C_o\cdot(1-r)^t[/tex]
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
The doctor prescribed 125 milligrams of a therapeutic drug. It decays by 10% each hour. The initial value is Co=125 and the decay rate is r=0.1 per hour. Substituting into the function:
[tex]C(t)=125\cdot(1-0.1)^t[/tex]
Operating:
[tex]\mathbf{C(t)=125\cdot 0.9^t}[/tex]
Where t is expressed in hours.
PLEASE HELP NOW!!!!!
Which expression is equivalent to 3^2 • 3^-5
3²×3^-5
Multiply the terms with the same base by adding their exponents
3²-5
Calculate the differences
3^-³
Express with a positive exponent using a ^-n =1/n
a
1/3³
Write the exponentiation as a multiplication
3×3×3
Multiply the numbers
27
Answer is 1/27
Nora makes $3000 a month. If she spends 10% of that on clothes each month, how much does she spend on clothes?
Answer:
$300
Step-by-step explanation:
10% converted into a decimal is 0.10.
To find 10% of 3,000, you would multiply them.
3,000 times 0.10 is 300.
Therefore, Nora spends $300 a month on clothes.
PLEASE GOD I NEED THIS NOW
ΔDEF ≅ΔDFG by the postulate________
a. ASA
b. SSS
c. SAS
d. SSA
Answer:
b. SSS
Step-by-step explanation:
The diagram provided shows that:
DE is congruent to DG,
EF is congruent to FG, and
DF is congruent to DF
Thus, all three sides of ∆DEF is congruent to all corresponding sides of ∆DFG. Therefore, by the Side-Side-Side Congruence Theorem, ΔDEF ≅ΔDFG.
Which statement correctly compares the slopes of the two functions? OA Function fhas a slope of which makes it steeper than function g. O B. Function g has a slope of , which makes it steeper than function f. Function ghas a slope of 2, which makes it steeper than function f. O c. OD Function f has a slope of 3, which makes it steeper than function g
Answer:
B. Function g has slope 3 which makes it steeper
Step-by-step explanation:
Answer:
its B 100% but on plato its C
Step-by-step explanation:
The height of an object thrown straight up from a height 5 feet above the ground is given by the equation h(t) =-16t^2 +42t +5, where is the time in seconds after the object is thrown. Find the average speed of the object from 1.5 to 2.25 seconds.
Answer:
The average speed of the object is 18.67 ft/s.
Step-by-step explanation:
Given;
height function, f(t) = -16t² + 42t + 5
The average speed is given by ;
[tex]v = \frac{dx}{dt} \\\\h(t) = -16t^2+42t+5\\\\h(1.5)= -16(1.5)^2 + 42(1.5)+5 = 32 \ ft\\\\[/tex]
from 1.5 s to 2.25 s = 0.75 s,
[tex]h(0.75)= -16(0.75)^2 + 42(0.75)+5 = 27.5 \ ft[/tex]
[tex]h(2.25)= 27.5 +(-16(2.25)^2 + 42(2.25)+5) \\\\h(2.25) = 27.5 + 18.5 = 46 \ ft[/tex]
The average speed is given by ;
[tex]v = \frac{h(2.25) - h(1.5)}{2.25-1.5}\\\\v = \frac{46-32}{0.75}\\\\v = 18.67 \ ft/s[/tex]
Therefore, the average speed of the object is 18.67 ft/s.
Simplify: 5x - 12y + 8x + 2x² + 4x²
Answer:
Your answer is: [tex]6x^2-12y+13x[/tex]
Simplify the expression.
Step-by-step explanation:
Hope this helped : )
A supermarket sells orange juice in three sizes. The 32 fl oz container costs $1.99,the 64 fl oz container costs $3.69, and the 96 fl oz container costs $5.85. Which size orange juice has the lowest price per fluid ounce? Explain!
Answer:
64 fl oz
Step-by-step explanation:
To find the best price you take the cost and divide it by the number of fluid ounces ($1.99/32). For the 32 oz it costs .062, for the 64 oz it costs .057, and for the 96 oz it costs .060 (these are all approximate number btw). Therefore, since 64 oz has the lowest number it has the lowest price per fluid oz.
Help !! (x + 2y = 6.)
Answer:
what do you exactly want me to do? rewrite the equation or solve it?
Step-by-step explanation:
Answer:
x=−2y+6
y=−12x+3
Step-by-step explanation:
Let's solve for x.
x+2y=6
Step 1: Add -2y to both sides.
x+2y+−2y=6+−2y
x=−2y+6
Let's solve for y.
x+2y=6
Step 1: Add -x to both sides.
x+2y+−x=6+−x
2y=−x+6
Step 2: Divide both sides by 2.
2y/2=−x+6/2
y=−12x+3
In the United States, which level of government has the highest authority?
STATE
COUNTY
CITY
NATIONAL
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = 3e−x, y = 3, x = 4; about y = 6
Answer:
I've been working on with the area of the region in my calc II class, and now have to deal with the volume.
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y=749√2,y=0,x=2,x=3
Step-by-step explanation:
Omar has 2 3/4 cups of dough to make dumplings.if he uses 3/16 cup of dough for each dumpling, how many whole dumplings can Omar make.
1st Answer:
2 3/4 cups of dough divided by the amount used for each dumpling 3/16
would be
11/4/3/16=
=44/3
=14 2/3
which would be about 14 whole dumplings!
Avery needs a total of $12.75 in quarters at
the local laundromat. She has already saved
$3.25. Which equation and solution process
can be used to determine q, the number of
additional quarters Avery needs to wash her
laundry?
A) 12.75 = 5 + 3.25
Sub
tract 3.25 from both sides and multiply
the difference by 25.
B)3.25 -0.259 = 12.75
Subtract 3.25 from both sides and divide
the difference by -0.25.
I
C)12.75 = 0.259 + 3.25
Subtract 3.25 from both sides and divide
the difference by 0.25.
D) 259 + 3.25 = 12.75.
Subtract 3.25 from both sides and divide
the difference by 25.
Answer:
C
Step-by-step explanation:
12.75=3.25+0.25q
9.50=0.25q
38=q.
Question 5 (6 points)
Mrs. Phillips is grading the semester exams for her Advanced Algebra course. She wants a visual representation of how the grades are spread
throughout the class. It would also be helpful to know where the upper 25% of grades are located. Below is the box and whisker plot she
designed
Answer:
The median is close to 90, but there is most likely one student and up to 25 % of the class who did poorly on an exam that otherwise looks pretty easy
Step-by-step explanation:
Hope this helps you!
~ Isimpfortnpu
f(x) = 4x – 9 Find f(6) elauating functions
Answer:
f(6)=15
Step-by-step explanation:
Just put 6 in place of x in the equation and solve[tex]f(x)=4x-9\\f(6)=4(6)-9\\f(6)=24-9\\f(6)=15[/tex]Two sides of a triangle measure 8 and 13. what represents x, the possible length in inches of the remaining side
Answer:
the possible number would be 159 in
Step-by-step explanation:
For what value of k does kx + 7y = 10 have a slope of 3?
Answer:
k = -21
Step-by-step explanation:
Slope y-intercept form : y = mx +c
kx + 7y = 10
7y = -kx + 10
y = [tex]\frac{-k}{7}x+\frac{10}{7}[/tex]
[tex]\frac{-k}{7}=3\\\\ -k = 3*7\\\\ -k = 21\\\\ k = -21[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
_________________________________
Hint :
[tex]slope = The \: \: coefficient \: \: of \: \: x \: \: in \: \: the \: \: slope-intercept \: \: form \\ [/tex]
_________________________________
Thus we need to find the slope-intercept form of the line which must be like this :
[tex]y = ax + b[/tex]
Let's do it...[tex]7y + kx = 10[/tex]
Subtract sides kx
[tex]7y + kx - kx = 10 - kx[/tex]
[tex]7y = 10 - kx[/tex]
[tex] 7y = - kx + 10[/tex]
Divide sides by 7
[tex] \frac{7y}{7} = \frac{ - kx + 10}{7} \\ [/tex]
[tex]y = \frac{ - kx}{7} + \frac{10}{7} \\ [/tex]
[tex]y = - \frac{k}{7} x + \frac{10}{7} \\ [/tex]
This is the slope-intercept form .
[tex]The \: \: coefficient \: \: of \: \: x = - \frac{k}{7} \\ [/tex]
The slope is 3 ,
Thus :
[tex] - \frac{k}{7} = 3 \\ [/tex]
Multiply sides by 7
[tex]7 \times ( - \frac{k}{7}) = 7 \times 3 \\ [/tex]
[tex] - k = 21[/tex]
Multiply sides by - 1
[tex] ( - 1) \times ( - k) = ( - 1) \times (21)[/tex]
[tex]k = - 21[/tex]
And we're done....
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
If you begin a problem with a one digit integer , multiply the number by 4 add 7 divide by 3 subtract 5 and answer of 0 what is the beginning integer ?
Answer: imma figure this out
Step-by-step explanation:
Answer:
Answer: imma figure this out
Step-by-step explanation:
What is the slope of the line represented by the equation 3x + 4y
12?
Answer:
Are you looking for coordinates or a equation?
Step-by-step explanation:
Answer:
y=-3/4x+3
Step-by-step explanation:
3x+4y=12
-3. -3
4y=-3x+12 (I put the 3x first just so that it is already in slope intercept form)
4y/4=-3x/4+12/4
y=-3/4x+3
please answer asap idk how
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the ratio and proportion.
here, we clearly notice, that,
4 cups have 2 ounces each, that is
=> 4×2 = 8 ounces
also, 1 cup with 3 ounces,
=> 1×3 = 3 ounces,
adding both we get as,
8+3 = 11 ounces,
the total is 11 ounces.
For what value of x is angle ABC isosceles?
Kareem is a software salesman. His base salary is $2200, and he makes an additional $60 for every copy of Math is Fun he sells.
Let P represent his total pay (in dollars), and let N represent the number of copies of Math is Fun he sells. Write an equation relating P to N. Then use this
equation to find his total pay if he sells 26 copies of Math is Fun.
Answer:
Step-by-step explanation:
a. p=2200+60n
b. p=2200+60(26)
p=2200 plus 1560
p=3760
The equation that should be related P to N should be considered as the 2200+60n.
And, the total pay when he sells 26 copies of Math is Fun should be 3760.
Calculation of the equation & the total pay:Since
His base salary is $2200, and he makes an additional $60 for every copy of Math is Fun he sells.
Here P means the total pay
So, here the equation be p=2200+60n
Now the total pay be
p=2200+60(26)
= 2,200 + 1,560
= 3,760
hence, The equation that should be related P to N should be considered as the 2200+60n.
And, the total pay when he sells 26 copies of Math is Fun should be 3760.
Learn more about an equation here: https://brainly.com/question/15844891
Problem Solving Method
Problem to solve
Alexis had 98 trading cards last Saturday.
(o
She gave a dozen to her little brother but her big brother gave her a pair.
Alexis traded 9 more cards for 4 new ones that were more valuable.
She then traded another half dozen for 1 that she had been hoping to find.
Alexis wants to get a card album for her birthday so she can organize all her cards.
Yesterday she was running home with all of her cards in her bag. She dropped two of her
cards along the way because the bag was not zipped.
How many cards did she have when she got home?
What is the first thing that you would do to solve this problem?
Caluina Stan
Answer:
76 cards
Step-by-step explanation:
First you would take 96-12 to get 84. Then, take 84+ 2-9 to get 79. Then take 79 +4-6 to get 77.then take 77+1-2 to get 76 cards.
Select the statements that is SOMETIMES TRUE.
a. A parallelogram has congruent diagonals.
b. A rhombus is a parallelogram.
c. A parallelogram is a square.
d. A rectangle is a square.
Answer:
A and B
Step-by-step explanation:
Here, we want to select the statements that are sometimes true
The correct answers are that;
1. A parallelogram has congruent diagonals
This is in the case of a rectangle
Whenever we have the diagonals of a parallelogram equal, then what we have is a rhombus
b. A rhombus is a parallelogram
In this case, we have that a rhombus is a kind of parallelogram with all four sides equal and the diagonal meet at 90 degrees
Please help!! Quadrilaterals and other polygons
yes or no
if yes pls tell me what the unit rate is
I WILL MARK U BRAINLIEST
(attachment)
Answer:
Yes, and the unit rate is 1:48
Step-by-step explanation:
If you start by dividing 204 by 4.25, you will see you get an answer of 48. Now if you move on to the next row, and divide 252 by 5.25, you also get 48. If you do the same with the last two rows, you get 48 for both. This shows that the unit rate is 1:48.
PLEASE HELP. The graph below represents which system of inequalities?
Simplify
23 + 4.8
Plz help
Answer:
40
Step-by-step explanation:
plz mark B R A I N L I E S T
Answer:
the answer is 40.. the second one
Step-by-step explanation:
PEMDAS
Exponents first
2^3 = 2*2*2 = 8
Next up, Multiplication 4*8=32
Last but not least, addition
Add 32+8
and your final answer is 40!
Help for a cookie!:D
Answer:
0.305
0.097
Step-by-step explanation:
…..………....
The gardening store sells clay flower pots, which hold 8 liters of dirt, and ceramic flower pots, which hold 5 liters. Trevor bought 4 flower pots, which will hold a total of 26 liters of dirt. How many of each type of flower pot did he buy?