Given :
The percent of concentration of a certain drug in the bloodstream x hours after the drug is administered is given by [tex]K(x) = \dfrac{5x}{x^2+9}[/tex].
To Find :
Find the time at which the concentration is a maximum. b. Find the maximum concentration.
Solution :
For maximum value of x, K'(x) = 0.
[tex]K'(x) = \dfrac{5(x^2+9)- 5x(2x)}{(x^2+9)^2}=0\\\\5x^2+45-10x^2=0\\\\5x^2 = 45\\\\x = \pm 3[/tex]
Since, time cannot be negative, so ignoring x = -3 .
Putting value of x = 3, we get, K(3) = 15/( 9 + 9) = 5/6
Therefore, maximum value drug in bloodstream is 5/6 at time x = 3 units.
Hence, this is the required solution.
HELP FAST !!!
Find the solution of the system of equations.
-8x + 7y = -2
- 8x + 8y = 8
-56x + 49y= -14
- 56x + 56y=64
105y=50
y=0.48
-8x+7(0.48)=-2
-8x+3.36=-2
-8x=-5.36
x=0.67
Answer:
(x, y) = (9, 10)
Step-by-step explanation:
-8x + 7y = -2...... (1)
- 8x + 8y = 8......(2)
Multiplying on both sides of the equations (1) & (2) by 8 and 7 respectively, we find:
-64x + 56y = - 16...(3)
-56x + 56y = 56.....(4)
Subtracting equation (4) from equation (3), we find:
-64x + 56y = - 16
-56x + 56y = 56
+ - -
_____________
- 8x = - 72
x = - 72/-8
x = 9
Substituting x = 9 in equation (1), we find:
-8(9) +7y = - 2
-72 +7y = - 2
7y = 72 - 2
7y = 70
y = 70/7
y = 10
(x, y) = (9, 10)
Carli and Angela share a cell phone plan and split the bill each month. Last month, their total bill was $109. Carli went over her data limit on her phone, so her share of the bill was $15 more than Angela's to account for the overage charge. Which system of equations represents this situation?
A. c+a=15
c=a+109
B. c+a=109
c=a+15
C. c+a=109
a=c+15
D. c-a=15
c=a+109
Answer:
C
Step-by-step explanation:
plz help me I dont want to fail
Answer:
ksjnfkjabfjkbfkjbdkjfbjdbjbdsjvbsdhbcjhdbvhsdjv
Step-by-step explanation:
sorry I really need points-
2.Larry's car travels 230 miles on 10 gallons of fuel. What is the ratio of miles to
gallons for Larry's car?
A 10 Miles to 1 Gallon
B 10 Gallons to 1 Mile
<
23 Miles to 1 Gallon
D 23 Gallons to 1 Mile
Answer:
D
Step-by-step explanation:
If he travels 230 miles on 10gallons of fuel, then he will travel 23 miles on 1 gallon of fuel. So it is 230 gallons to one mile.
Gina says that for all real numbers a and b, ab=ba. is this statement true or false? If false, give a counterexample
Answer:
True
Step-by-step explanation:
The communative property states that the order in addition and multiplication dosen't matter.
PLEASE HELP ME WITH ME MATH In a survey of 3500 people who owned a certain type of car, 1750 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
50%
Step-by-step explanation:
3500 divided by 1750 is 2 which is equal to 50%
Multiply 1 4/5 * 1 ???
Answer:
9/5 or 1 4/5
Step-by-step explanation:
You’re welcome :)
Answer:
your answer will come to be 1.8
Stephanie ate 12 of the 40 chips in a bag. What percentage of the chips did Stephanie eat?
Answer:
30%
Step-by-step explanation:
Answer:30%
Step-by-step explanation:
What is the equation of the line that passes through the point (-5,-7)and has a slope of 2/5
Answer:
6.33333 is the answer <3
2/3x = -36
Possible answers
+24
-24
+54
-54
Answer:
-54
Step-by-step explanation:
2/3x=-36
3*2/3=3(-26)
2x=-108
2x/2= -108/2
x=-54
Find in slope standard form 3х – 5y = 10
Answer:-5y=-3x+10
Divide all by -5
Y= 3/5x+10/-5
Negative divide by negative is positive--3/-5= 3/5
Slope is 3/5 y intercept is -2
Step-by-step explanation:
A high school has 28 players on the football team. The summary of the players' weights is given in the box plot. Approximately, what is the percentage of players weighing greater than or equal to 242 pounds?
Answer:
25%
Step-by-step explanation:
Looking at the attached diagram, we can see that the box plot is divided into 3 sections,
Q1 = First Quartile (1/4 the players) = 25%
Q2 = Second Quartile (2/4 = 1/2 of the players) = 50%
Q3 = Third Quartile (3/4 of the players) = 75%
From the attached diagram, the weight of 242 pounds is on the Third Quartile, this means , 75% of the players weigh 242 pounds and below
The percentage of players weighing greater than or equal to 242 pounds is calculated as: 100 - 75%
= 25%
The percentage of players weighing greater than or equal to 242 pounds is 25 %.
Quartile of Data ;From the attached diagram, we can see that the box plot is divided into 3 sections.[tex]Q_{1}[/tex] = First Quartile , which represent [tex]\frac{1}{4}[/tex] part of the player. That is 25%[tex]Q_{2} =[/tex] Second Quartile ,which represent 1/2 of the players= 50%[tex]Q_{3}=[/tex]Third Quartile , which represent 3/4 of the players = 75%From the attached diagram, the weight of 242 pounds is comes on the Third Quartile.
It means that 75% of the players weigh 242 pounds and below
Hence, The percentage of players weighing greater than or equal to 242 pounds is,
[tex]100-75=25[/tex]
Learn more about the Quartile here:
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A bakery made 9 cakes using 3 bags of flour. The bakery uses the same relationship between cakes made and the amount of flour used to make all of their cakes. Which table of values shows the relationship between the number of cakes the bakery makes to the number of bags of flours the bakery uses?
Answer:
c = 3b
Step-by-step explanation:
9 cakes proportional to 3 bags of flower
cake = k(bag)
c = kb
9 = k(3)
k = 3
c = 3b
you didn't send any table of values but this is the relationship between the cakes and flour, you can use it.
please mark brainliest if you like the answer
Brainliest...don’t need an explanation
Answer:
8
Step-by-step explanation:
if g(x) =x over 2 + 3 find g (4)
Answer: 2
Step-by-step explanation: 4/2=2
Also, what does the phrase "how much for 1" mean?
Answer:
It means your asking how much one of one type of thing is
Step-by-step explanation:
Find the opposite of each integer 0
Answer:
Thats not a full question.
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
find the missing side lengths. leave ur answers as radicals
Answer:
m = 34 ; n = 17√3
Step-by-step explanation:
m = 17 × 2 = 34
n² = 34² - 17² = 867 = 17² × 3 ⇒ n = 17√3
The graph shown below represents the relationship between the number of cookies and the cost of the cookies that a bakery sells. What is the unit rate and what does it represent? Y 13 12 10 9 ME Cost ($) B 12 14.06L 8 10 12 14 16 18 20 22 24
Answer:
[tex]Rate = \$0.5[/tex] per cookie
Every cookie is sold at $0.5
Step-by-step explanation:
See attachment for complete question
Required
Determine the unit rate
To solve this, we simply take any corresponding values of Cost of cookies and number of cookies
When
Cost = $2
Number = 4
[tex]Rate = Cost/Number[/tex]
[tex]Rate = \$2/4[/tex]
[tex]Rate = \$0.5[/tex] per cookie
Pick another corresponding values
When
Cost = $6
Number = 12
[tex]Rate = Cost/Number[/tex]
[tex]Rate = \$6/12[/tex]
[tex]Rate = \$0.5[/tex] per cookie
Hence, the unit rate is $0.5 per cookie
What it represents is that: Every cookie is sold at $0.5
Which statement about the planes is true?
bruh
why
what
?
osea si pero al a vez cuando pasa osea si parece pero no lo es pero lo es cuando puede ser
4^4÷4^7 as a fraction
Answer: multiply it by the bisector of the photosynthesis.
obviously
Step-by-step explanation:
Austin made 5 quarts of his special from-scratch cupcake mix. He was able to make 32 identical cupcakes using 3.5 quarts of his special mix. Austin would like to bake 20 more identical cupcakes to ice each cupcake in the likeness of a playing-card. Does he have enough left to create 20 additional cupcakes? Explain.
9514 1404 393
Answer:
no
Step-by-step explanation:
We can write a proportion to find how much mix is required to make 52 cupcakes.
quarts/cupcakes = 3.5/32 = x/52
Multiplying by 52, we find ...
x = 52(3.5/32) = 5.6875 . . . quarts needed for 52 cupcakes
This is more mix than Austin made. He does not have enough left for 20 more cupcakes.
Plz I need this ASAP
Answer:
12
Step-by-step explanation:
1/3( 4×3)+8
1/3(12)+8
4+8
12
Answer:
b
Step-by-step explanation:
How many numbers can be squared to get a value of 0?
Answer:
1
Step-by-step explanation:
0^2 equals 0 but 1 and -1 the numbers closest equal 1 so only one number can be squared to get 0
Name the theorem or postulate that lets you immediately conclude ∆ABD ≈ ∆CBD.
A. None of these
B.AAS
C.ASA
D.SAS
Answer:
The correct answer is B. AAS
Step-by-step explanation:
I took the test
hope this helps :)
SAS postulate is used to conclude that ∆ABD ≈ ∆CBD. Option D is correct.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
In the given triangle there are ACD, DB is the perpendicular bisector.
We need to prove ∆ABD ≈ ∆CBD.
In ∆ABD and ∆CBD
AB is congruent to BC by given diagram.
∠ABD ≅ ∠CBD both are 90 degrees.
BD ≅ BD both having common side.
∆ABD ≈ ∆CBD.
By SAS postulate.
Hence, the SAS postulate is used to conclude that ∆ABD ≈ ∆CBD.
To learn more on Triangles click:
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Zoey can tile 1 1/4 square yards in 1/3 hour. What is her unit rate?
In politics, marketing, etc. we often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).
In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 27% with a margin of error of 1.9%. Describe the conclusion about p using an absolute value inequality.
The answer field below uses the symbolic entry option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in and then =, the symbolic entry option will automatically convert that to ≥.
Be sure to use decimal numbers in your answer (such as using 0.40 for 40%).
Answer:
|0.251 < p < 0.289|
Step-by-step explanation:
Given that:
The proportion of people who like dark chocolate than milk chocolate in a made up poll is 27%
Margin of Error = 1.9%
The conclusion about the proportion p using absolute value inequality ;
Interval :
P ± margin of error
27% ± 1.9%
(27 - 1.9)% ; (27 + 1.9)%
25.1% ; 28.9%
0.251 ; 0.289
Hence,
|0.251 < p < 0.289|
What is the remainder after you divide 7*7*7... 124 times by 4
Answer:
1
Step-by-step explanation:
Remainder if 7*7*7... 124 times is divided by 4
The remainder when (7^124) / 4
Using python console:
a = 7**124
b = 4
c = a%b
print(c)
Output = 1
Hence, the remainder when 7^124 is divided by 4 is 1
6 friends all use $2 off coupons to buy themselves movie tickets. They spend a total of $42 Write the equation
Answer:
(C / n) + 2
Step-by-step explanation:
Amount spent (C) = 42
Number of friends (n) = 6
Coupon on ticket = $2
Original price of ticket will be :
Cost per coupon ticket = (Total amount spent / number of friends)
(Total amount spent / number of friends) + coupon on ticket
= (C / n) + 2
= (42 /6) + 2
= 7 + 2
= 9
Simplify the expression below: (3−13)2+1442−5·2
Answer:
1412
Step-by-step explanation:
2*(3 - 13) + 1442 - (5 * 2)
Distribute the 2 to the 3 and -13, and multiply 5 and 2 together.
6 - 26 + 1442 - 10
Now simplify the expression by adding and subtracting the terms.
1412 is the answer.
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