Solution :
Let y = amount of caffeine at a given time in body.
n = number of hours
So [tex]$\frac{dy}{dn}= - \ Y$[/tex]
[tex]$\Rightarrow \frac{dY}{Y}=- 0.01 \ dn[/tex]
ln Y = -0.01 n + C
At n = 0, Y = 130 mg
ln 130 = -0.01 x 0 + C
C = ln 130
[tex]$ \ln \frac{Y}{130} =- 0.01 \ n$[/tex]
[tex]$Y = 130 \ e^{-0.01n}$[/tex]
When Y = 65
[tex]$65 = 130 \ e^{-0.01 n }$[/tex]
[tex]$\frac{65}{130}=e^{-0.01n}$[/tex]
[tex]$\ln \frac{1}{2} = -0.01 \ n$[/tex]
n = 69.315 hours
At n = 24 hours
[tex]$Y = 130 \ e^{-0.01 \times 24}$[/tex]
Y = 102.26 mg
A salesperson at a jewelry store earns 3% commission each week. Last week, Heidi sold $750
worth of jewelry. How much did she make in commission? How much did the jewelry store make
from her sales?
Heidi earned $ in commission.
3. Sam and Tim each have savings accounts. Every month they each put in some of their
earnings from mowing lawns. Use the tables to find the y-value of the solution to the
system shown.
х
1
2
3
4
f(x)
80
110
140
170
х
1
2
3
4
g(x)
100
120
140
160
Answer:
[tex]y = 30x +50[/tex] --- Sam
[tex]y = 20x +80[/tex] --- Tim
Step-by-step explanation:
Given
Sam Tim
х --- f(x) --------------- g(x)
1 --- 80 --------------- 100
2 --- 110 --------------- 120
3 --- 140 --------------- 140
4 --- 170 -------------- 160
Required
Determine the y value
y value implies the equation of the table
Calculating the equation of Sam
First, we need to take any corresponding values of x and y
[tex](x_1,y_1) = (1,80)[/tex]
[tex](x_2,y_2) = (4,170)[/tex]
Next, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{170 - 80}{4 - 1}[/tex]
[tex]m = \frac{90}{3}[/tex]
[tex]m = 30[/tex]
Next, we calculate the line equation using:
[tex]y - y_1=m(x-x_1)[/tex]
[tex]y - 80 = 30(x - 1)[/tex]
[tex]y - 80 = 30x - 30[/tex]
Make y the subject
[tex]y = 30x - 30 + 80[/tex]
[tex]y = 30x +50[/tex]
Calculating the equation of Tim
First, we need to take any corresponding values of x and y
[tex](x_1,y_1) = (1,100)[/tex]
[tex](x_2,y_2) = (4,160)[/tex]
Next, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{160 - 100}{4 - 1}[/tex]
[tex]m = \frac{60}{3}[/tex]
[tex]m = 20[/tex]
Next, we calculate the line equation using:
[tex]y - y_1=m(x-x_1)[/tex]
[tex]y - 100 = 20(x - 1)[/tex]
[tex]y - 100 = 20x - 20[/tex]
Make y the subject
[tex]y = 20x - 20+100[/tex]
[tex]y = 20x +80[/tex]
Solve for x.
(9x – 16)+(3x + 11)+(7x – 5)=180
Answer:
10
Step-by-step explanation:
See the picture attached.
What’s 4/5 divided by 3
Answer:
[tex]\frac{4}{15}[/tex]
Step-by-step explanation:
remember when dividing with fractions, you are multiplying by the reciprocal.
this means
[tex]\frac{4}{5} \div3=\frac{4}{5}*\frac{1}{3}=\frac{4}{15}[/tex]
Answer:
the answer is 0.26 it was originally 0.26666666666 which is repetition so I lowered it down to .26
What integer represents a 5-point loss added to a 2–point gain?
Answer:
-3
Step-by-step explanation:
5 point loss is -5,
2 point gain is (+)2.
If it's added, the expression will be -5 + 2.
-5 + 2 is -3.
-3 is an integer, because integers are whole numbers and their opposites.
If this helped, please mark it brainliest.. unless there is a better answer. Thanks.
Answer:
So -3
Step-by-step explanation:
PLEASEE HELP ITS DUE TODAY
Answer:
43.44 for the first one
16 cats from the second one
496 for the third one
Step-by-step explanation:
Answer:
a. 43.44
b. 16
c. 496
Step-by-step explanation:
a. (14.48) x 3= 43.44
b. 25% of 64= 16
c. 31 x 16= 496
the area of square field is 5184 square meter find the area rectangular Field whose perimeter is equal to the perimeter of square field and whose length is twice of its breadth
Answer:1296 if I’m not wrong please
Step-by-step explanation:
Step-by-step explanation:
Appropriate Question :
The area of square field is 5184m². Find the area of the rectangular field whose perimeter is equal to the perimeter of square field and whose length is twice of its breadth.[tex] \frak{\red{Given}} \begin{cases} & \sf {Area\ of\ the\ square\ field\ is\ 5184m^2.} \\ & \sf {Perimeter\ of\ rectangular\ field\ is\ equal\ to\ perimeter\ of\ square\ field.} \\ & \sf {Length\ of\ the\ rectangular\ field\ is\ twice\ to\ the\ breadth\ of\ the\ square\ field.} \end{cases}[/tex]
Need to find : We have to find the area of the rectangular field.
We are given the area of the square field, that is 5184m². So firstly, let us find out the side of the square field.Let the side of the square field be a.
SidE :-
a² = 5184m²a = √5184ma = 2 × 2 × 2 × 9a = 72m∴ Hence, the side of the square field is 72m. Now, let's find out the perimeter of square.
⠀⠀⠀⠀⠀━━━━━━━─━━━━━━━
[tex] \red \bigstar \sf{\underline{Finding\ perimeter\ of\ square:-}} [/tex]
[tex] \sf \dashrightarrow {Perimeter\ of\ square\ =\ 4a} \\ \\ \sf \dashrightarrow {4 \times 72} \\ \\ \dashrightarrow {\underline{\boxed{\purple{\frak{288m}}}}} [/tex]
∴ Hence, the perimeter of the square field is 288m. Now, let us find out the length and breadth of the rectangular field.
⠀⠀⠀⠀⠀━━━━━━━─━━━━━━━
Since, it is given that perimeter of the rectangular field is equal to the perimeter of square field. Also, the length of the rectangular field is twice the breadth of the square field.[tex] \sf : \implies {Perimeter\ of\ rectangle\ =\ Perimeter\ of\ square} \\ \\ \sf : \implies {2(l\ +\ b)\ =\ 288} \\ \\ \sf : \implies {2(2b\ +\ b)\ =\ 288} \\ \\ \sf : \implies {4b\ +\ 2b\ =\ 288} \\ \\ \sf : \implies {6b\ =\ 288} \\ \\ \sf : \implies {b\ =\ \dfrac{\cancel{288}}{\cancel{6}}} \\ \\ : \implies {\underline{\boxed{\purple{\frak{b\ =\ 48m}}}}} [/tex]
∴ Hence, breadth of the rectangular field is 48m. Now, let's find out the length of the rectangular field.
LengtH :-
2(48)2 × 4896m∴ Hence, the length of the rectangular field is 96m. Now, let's find out the area of the rectangular field.
⠀⠀⠀⠀⠀━━━━━━━─━━━━━━━
[tex] \red \bigstar \sf{\underline{Finding\ area\ of\ the\ rectangular\ field:-}} [/tex]
[tex] \sf : \implies {Area\ of\ rectangle\ =\ l \times b} \\ \\ \sf : \implies {Area\ of\ rectangle\ =\ 96 \times 48} \\ \\ : \implies {\underbrace{\boxed{\pink{\frak{Area\ of\ rectangle\ =\ 4608m^2}}}}_{\sf \blue{\tiny{Area\ of\ the\ field}}}} [/tex]
∴ Hence, area of the rectangular field is 4608m².
Find the slope of the line (-4,4) (-3,-2)
Suppose that 45% of all babies in a particluar hospital are boys. If 8 babies born in the hospital are randomly selected, what is the probability that fewer than 3 of them are boys?
Answer:
3
Step-by-step explanation:
Find the inverse: f(x) = -3 -4/3 x
Answer:
3+4/3x
Step-by-step explanation:
ASAP please help me I need this quick
The question and answers are in the picture
Answer:
4 + 4 + 4 = 12
Step-by-step explanation:
Perimeter (P) = a + b + c (a, b, c being all the sides, which are all equal to 4)
What is - 9 + 3 = I know its -6 but how
Answer:
You count something
Step-by-step explanation:
If you imagine 9 slots that are empty and you fill 3 of them then there is 6 empty slots so -6
CAN SOMEONE PLEASE ANSWER THIS QUESTION ASAP!!
Add -4 + (-15).
-11
19
-19
11
Step-by-step explanation:
-4+(-15)
=(-19)
I think it helps you
Would like to help me with my math homework?
Math homework is on College for Readiness
Answer:
Well, I might answer some questions, but maybe not since its collage work ( guessing from the name of it) and i'm only in 6th grade, but I HAVE answered collage questions before on here and got them correct.. (The upcoming and this sentence is pre-written and copy and pasted in every brainly question or comment I write or answer.) If this answer helped you please consider giving it brainliest.
- •Trix•
( Yes I know my - •Trix• thingy is not my user but its what I would change it to if I could but I can't, please address me as Trix while commenting or talking to me here.)
Answer:
Grade?
Step-by-step explanation:
which of these is not a linear graph.
Answer:
D
Step-by-step explanation:
It isn't linear
Answer:
D)
Step-by-step explanation:
Linear graphs are straight they can be positive or negative but they do not have bending points in them.
I added a picture to help you
MCQ (100)
Q32. If tan(t) =13, then cot(-t) = ?
I NEED THIS ASAP I HAVE TROUBLE WITH IT PLEASEEEEEEEEEEE!!!!!!!!
WORTH 11 POINTS !!!!!!!!! IT IS ALL I HAVE SRRY BBY
SHOW ALL WORK FOR EXTRA POINTS PLSSSSSSS!!!!!!!
Judy earns $11.80 per hour working at a fast food restaurant . How much money
will she earn for 12.5 hours of work?
Answer:
$147.50
Step-by-step explanation:
all you have to do is multiply the two numbers together
Find the length of side x in simplest radical form with a rational denominator
Answer:
4
Step-by-step explanation:
that is what i think it is i am almost positive
HELP PLEASE NEED HELP ASAP!!
Work out the problem -5-8
-13
Answer:
since 5+8 is 13 and there's a '-' in the five than it's-13
If 6a=5b what are the following ratios?Please show your work
a+b/b
I give brainliest to first person.
Answer:
5b-5
Step-by-step explanation:
Replace a with a=5/6 * b
Cliff's Rentals rents out jet skis. The hourly charge is $50. Marcus rented a jet ski for 3 hours and paid $165.
Which equation can be used to determine the price, P, for h hours? Pls help me
Answer:
50h + 3 = 165P
Step-by-step explanation:
in a company, 40% of the workers are women. If 1380 woman work for the company, how many total workers are there?
Answer:
Step-by-step explanation:
The total number of workers is our unknown. If 40% of this unknown number are women and the number of women is 1380, then the equation looks like this:
(remember that the word "of" generally means to multiply)
(also remember that we have to use the decimal form of a percent in an equation)
.40(x) = 1380 then divide to get the number of total workers:
x = 3450
What does a cluster tell you about the data on a scatter plot?
Answer:
it all depends on where it is if it is in the middle you do not have enough information to determine if it is increasing or decreasing
Step-by-step explanation:
whats 13 divided by 8 as a mixed number
Answer:
the answer would be 13/8
13 divided by 8 can be written [tex]1\dfrac{5}{8}[/tex] as a mixed number.
The division is a mathematical operation that contains decoupling a quantity or number into equal proportions. It is the inverse operation of multiplication. In division, a number called the dividend is divided by another number called the divisor to get the quotient.
13 can be split as follows:
13 = 1 × 8 + 5.
It is evident that when 13 is divided by 8, it gives 1 as a quotient and the remainder is 5.
Thus, the fraction [tex]\frac{13}{8}[/tex] in the mixed form is [tex]1\dfrac{5}{8}[/tex].
Learn more about Division here:
https://brainly.com/question/2273245
#SPJ6
Ingrid collect 6 cans of food and 18 boxes of food for the food bank.Which describes the relationship between cans of food and boxes of food
Answer:
Ingrid collected 3 times as many boxes as she did cans
Step-by-step explanation:
kevin has a ratio of 2 wrong answers to 7 correct answers on his math test. If he got 6 questions ewrong then how many did he answr correctly
Answer:
21 questions
Step-by-step explanation:
Given
[tex]Wrong : Right = 2:7[/tex]
Required
Determine the number of correct answers if he answered 6 wrongly
The required ratio can be represented as:
[tex]Wrong : Right = 6 : X[/tex]
Where X represents number of right answers for 6 wrong answers.
Next, we equate both ratios:
[tex]6:X = 2:7[/tex]
Convert to fraction
[tex]\frac{6}{X} = \frac{2}{7}[/tex]
Cross Multiply
[tex]X * 2 = 6 * 7[/tex]
[tex]2X = 42[/tex]
Divide through by 2
[tex]X = 21[/tex]
Hence, he answered 21 correctly
Nick ivides 527 baseball cards evenly into 17 stacks. How many baseball cards are in each stack?
Answer:
31
Step-by-step explanation:
527 divided by 17
Evaluate
Please help
Answer:
27
Step-by-step explanation:
3x3x3=9; if you break it apart, 3x3= 9, then multiply that by the last 3, which will give you 27.
Hope that helped!