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.
The midpoint of segment AB has the coordinates M(-4,2). If the coordinates of endpoint A are (-6, -7), find the coordinates of endpoint B.
Given:
The midpoint of segment AB has the coordinates M(-4,2).
The coordinates of endpoint A are (-6, -7).
To find:
The coordinates of B.
Solution:
Let the coordinates of point B are (a,b).
Formula for midpoint:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
The midpoint of segment AB has the coordinates M(-4,2), so by using the above formula we get
[tex]M=\left(\dfrac{-6+a}{2},\dfrac{-7+b}{2}\right)[/tex]
[tex](-4,2)=\left(\dfrac{-6+a}{2},\dfrac{-7+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{-6+a}{2}=-4[/tex]
[tex]-6+a=-8[/tex]
[tex]a=-8+6[/tex]
[tex]a=-2[/tex]
And,
[tex]\dfrac{-7+b}{2}=2[/tex]
[tex]-7+b=4[/tex]
[tex]b=4+7[/tex]
[tex]b=11[/tex]
Therefore, the coordinates of point B are (-2,11).
2.
Jamie used a microscope to measure the diameter of a hair. She found that the
diameter of the hair was 0.000072 meter. How is this number written in scientific
notation?
A. 7.2x10.5
B. 7.2 x 106
C.7.2 x 105
D.7.2 x 10
Type Your
Answer:
7.2 *10⁻⁵
Step-by-step explanation:
Given the diameter of the hair expressed as 0.000072, we are to express it in scientific notation.
The standard form of scientific notation is expressed as;
A * 10ⁿ
A is a value from 1 to 9
n is any integer.
Rewriting 0.000072 in this form, we will need to shift the decimal point to the front 5 times to have;
0.000072 = 7.2 *10⁻⁵ where;
A = 7.2 and n = -5
Note that the power is a negative value since the value is less than 1.
A nursery has $55,000 of inventory in dogwood trees and red maple trees. The profit on a dogwood tree is 29% and the profit on a red maple tree is 18%. The profit for the entire stock is 20%. How much was invested in each type of tree?
Answer:
On dogwood $45,000 was invested
On red maple tree , $10,000 would be invested
Step-by-step explanation:
Let the amount invested on dogwood tree be d and the amount invested on red maple be r
Total is 55,000
Thus;
d + r = 55,000 ••••••(i)
Total profit is;
20/100 * 55,000 = 11,000
Profit on dogwood is;
29/100 * d = 0.29d
Profit on red maple is;
18/100 * r = 0.18r
Both equals 11,000
0.29d + 0.18r = 11,000 •••••••(ii)
From equation i, d = 55,000 - r
substitute into ii
0.29(55,000-r) + 0.18r = 11,000
15950- 0.29r + 0.18r = 11,000
4950 = 0.11r
r = 4950/0.11
r = 45,000
d = 55,000 - r
d = 55,000 - 45,000
d = 10,000
Helpppp pleaseeeeeeeeeeeee
Answer:
$1.30
Step-by-step explanation:
91/14/5
11.
Charlene and Danielle share some money in ratio 2:3
Danielle gets £25 more than Charlene.
How much does each girl receive?
Answer:
Charlene got £50
Danielle got £75
Step-by-step explanation:
Let Charlene get x
this means that Danielle will get x + 25
The ratio is thus;
x/x + 25 = 2/3
3x = 2(x + 25)
3x = 2x + 50
3x-2x = 50
x = £50
Charlene got this
The amount Danielle got will be
50 + 25 = £75
subtract -2/3- (-2/5)
Answer:
- 4/15
Step-by-step explanation:
The - and - make a + so -2/3 + 2/5
HOPE THIS HELPS
PLZ MARK BRAINLIEST
You have one type of nut that sells for $6.50/lb and another type of nut that sells for $8.60/1b. You
would like to have 14.7 lbs of a nut mixture that sells for $7.10/lb. How much of each nut will you
need to obtain the desired mixture?
You will need
____lbs of the cheaper nut
and
____lbs of the expensive nut.
Answer:
You buy 10.5 pounds of the $6.50/lb nuts and 4.2 pounds of the $8.60/lb nuts.
Step-by-step explanation:
Let x be the number of pounds of the cheaper nut.
6.5x + 8.6(14.7-x) = 7.1*14.7
6.5x + 126.42 - 8.6x = 104.37
2.1x = 22.05
x = 10.5
archilles ordered a pizza with 16 slices every hour he ate half of the remaining slice
Answer:
so there is 8 slice left
Step-by-step explanation:
Sam wrote his bike 2/5 of a mile and walked another 3/4 of a mile how far did he travel?
Answer:
1.15 miles
Step-by-step explanation:
Answer:
24/20
Step-by-step explanation:
Changed denominator to 20 since 4 and 5 both go into 20. Got 8/20 and 15/20. Added and got 24/20. As a mixed number it is 1 1/5/ Hope this helps!
Charlotte had to distribute 71 dollars among 6 people. What is left with Charlotte after distribution if all six got maximum equal dollars?
Answer:
5?
Step-by-step explanation:
need a math genius to help
Answer:
Angle 8
Step-by-step explanation:
Angle 8 is the corresponding angle to angle 4. Corresponding angles are angles that are in the same relative position at each intersection. Since the lines are parallel they are also congruent. If you look at the lines both angle 8 and 4 are on the bottom right side of the intersection, therefore they are corresponding angles.
Which equation represents the graph of function j?
Answer:
Hi your answer is... B... Because The following radical phrase does not have to be negativeAnswer: C or j(x) = (-x + 4)^1/2
Step-by-step explanation:
Got it right on the test
HELP ME PLEASEE ASAPAPAP PLEASE PLEASE PLEASE PLEASE!!!!!!!!!!!
Answer: AEC = 80
X=30
YW ;)
y= p2 + qr write p in terms of y, q and r
Step-by-step explanation:
y=p²+qr
y-qr=p²
p=√y-qr
now, is it fine..
Iris wants to buy two necklaces, one for her sister and one for herself. The necklace for her sister costs $42.00, and the necklace for herself costs $28.00. The sales tax on the purchases is 8%. Find the total cost of Iris’s purchases, including sales tax. If necessary, round your answer to the nearest cent.
Answer:
$75.60
Step-by-step explanation:
First, find the total cost without tax:
42 + 28
= 70
Then, to find the price with sales tax, multiply this by 1.08:
70(1.08)
= 75.6
So, the total cost of her purchases was $75.60
what is the answer 42 ounces to 5 pounds in simplest form
42 ounces is equivalent to 2.625 pounds.
To convert 42 ounces to pounds, we divide by the conversion factor of 16 ounces per pound, since there are 16 ounces in a pound:
= 42 ounces / 16 ounces per pound
= 2.625 pounds
Now, to express 2.625 pounds in simplest form.
Since it is in decimal form, so we don't need to simplify it further.
Therefore, 42 ounces is equivalent to 2.625 pounds.
Learn more about Unit Conversion here:
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ctions and Models
Algebra I
Which of the following options results in a graph that shows exponential decay? (2 points)
Of(x) = 0.6(2)*
O f(x) = 3(0.7)
O f(x) = 0.4(1.6)*
O f(x) = 20(3)*
3. (04.03 LC)
Answer:
i need help
Step-by-step explanation:
I dont understand
The volume of a right circular cone is 300 cubic inches. What is the volume, in cubic inches, of a right cylinder th
has the same base and height as the cone?
Answer:
The volume of the cylinder is 900 cubic inches
Step-by-step explanation:
Given
Let V1 represent the volume of a cone and V2 represents the volume of a cylinder
[tex]V_1 = 300in^3[/tex]
Required
Determine the volume of a cylinder with same dimension
The volume of a cone is calculated as:
[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]
The volume of a cylinder is calculated as:
[tex]V_2 = \pi r^2h[/tex]
Since, the cone and cylinder have the same dimensions, we can substitute [tex]\pi r^2h[/tex] for [tex]V_2[/tex] in [tex]V_1 = \frac{1}{3}\pi r^2h[/tex]
So, we have:
[tex]V_1 = \frac{1}{3} * V_2[/tex]
Multiply both sides by 3
[tex]3 * V_1 = \frac{1}{3} * V_2 * 3[/tex]
[tex]3 * V_1 = V_2[/tex]
[tex]V_2 = 3 * V_1[/tex]
Substitute [tex]300in^3[/tex] for [tex]V_1[/tex]
[tex]V_2 = 3 * 300in^3[/tex]
[tex]V_2 = 900in^3[/tex]
Hence, the volume of the cylinder is 900 cubic inches
Solve: x=4+(4x-4)1/2
Answer:
x = 10
Step-by-step explanation:
x = 4 + (4x-4) ^ (1/2)
First, we rewrite the expression:
x = 4 + (4x-4) ^ (1/2)
x = 2 (2+ (x-1) ^ (1/2))
x = 4 + 2 (x-1) ^ (1/2)
From here we get a solution for x = 10
To check it we substitute x = 10 in the expression:
10 = 4 + 2 (10-1) ^ (1/2)
10 = 4 + 2 (9) ^ (1/2)
10 = 4 + 2 (3)
10 = 4 + 6
10 = 10
Answer:
The solution is:
x = 10
Answer:
C. x = 10
Step-by-step explanation:
edgen 2020
I need some assistance please
Answer:
2x + y = 20 . y=3x
2x + 3x = 20
5x = 20
x/5 = 20/5
x = 4
(4,0)
The time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with l=0.0003
a. What proportion of the fans will last at least 10,000 hours?
b. What proportion of the fans will last at most 7000 hours?
Answer: 0.0497870 ; 0.87754
Step-by-step explanation:
Given that :
λ = 0.0003
Defining a continuous distribution function :
F(x) = 1 - e^-λx = 1 - e^-0.0003x ; x ≥ 0
a. What proportion of the fans will last at least 10,000 hours?
P(x ≥ 10000) = e^-0.0003(10000) = 0.0497870
b. What proportion of the fans will last at most 7000 hours?
P(x ≥ 7000) = 1 - p(x ≤ 7000) = 1 - e^-0.0003(7000)
1 - 0.12245642825 = 0.87754
Geometry please help
The amount of money earned by bank customers based on the amount of principal in their savings account is _______________.
Answer:
interest
Step-by-step explanation:
An insurance company has written 100 policies for $75,000, 500 policies for $25,000, and 1000 policies for $10,000 for people of age 20. If experience shows that the probability that a person will die at age 20 is 0.0015, how much can the company expect to pay out during the year the policies were written? The company can expect to pay out _____ $ over the year after the policies were written.
Answer:
The company can expect to pay out $45,000 over the year after the policies were written.
Step-by-step explanation:
This can be determined as follows:
The probability that a person will die at age 20 = 0.0015
Revenue from 100 policies = 100 * $75,000 = $7,500,000
Revenue from 500 policies = 500 * $25,000 = $12,500,000
Revenue from 1000 policies = 1000 * $10,000 = $10,000,000
Total revenue from all policies = Revenue from 100 policies + Revenue from 500 policies + Revenue from 1000 policies = $7,500,000 + $12,500,000 + $10,000,000 = $30,000,000
Expected amount to pay out during the year the policies were written = Total revenue from all policies * The probability that a person will die at age 20 = $30,000,000 * 0.0015 = $45,000
Therefore, the company can expect to pay out $45,000 over the year after the policies were written.
Which equation can be used to find 55 percent of 900?
StartFraction 55 times 1 Over 900 times 1 EndFraction = StartFraction 55 Over 900 EndFraction
StartFraction 100 times 16.36 Over 55 times 16.36 EndFraction = StartFraction 1636 Over 899.8 EndFraction
StartFraction 900 times 9 Over 100 times 9 EndFraction = StartFraction 8100 Over 900 EndFraction
StartFraction 55 times 9 Over 100 times 9 EndFraction = StartFraction 495 Over 900 EndFraction
Answer:
the answer is A
Step-by-step explanation:
igot a 100
Answer:
D
Step-by-step explanation:
If 5 workers complete one task in 7 days, then how many days will 7 workers take to complete the same task?
Answer: 5 days
Step-by-step explanation:
5*7=35 - means the total amount of the days to complete the job by 1 worker is 35 days
So 7 workers can do this job in
35:7=5 days
What is the value of the expression, if p=42?
Then whats p+22
Answer:
64
Step-by-step explanation:
Answer:
64
Step-by-step explanation:
p=42 and p+22=?
Substitute:
(42)+22=?
Add:
(42)+22=64
help me please click link to go to question
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Answer:
okay thank you. ummmm yes well it's not loading
You start at (5, -4). You move down 1 unit. Where do you end?
Answer:
(5,-5)
Step-by-step explanation:
You're only moving down one number on the y-axis, so you go from -4 to -5, and your x-value remains the same
Which system of linear inequalities is represented by this graphed solution?
Answer:
There is no picture.....
Step-by-step explanation:
what graphed solution?