The standard deviation of the amount absorbed is 1819.9 ng/cm² rounded to one decimal place.
1. 80th percentile of the amount absorbed
Given that the amount (in ng/cm²) of active ingredient in the skin two hours after application is lognormally distributed with μ = 2.6 and σ = 2.1. The 80th percentile of the amount absorbed is to be found. Let X be the random variable representing the amount of active ingredient absorbed. We know that X follows a log-normal distribution with parameters μ = 2.6 and σ = 2.1. We are to find the value x such that P(X ≤ x) = 0.8We know that for a log-normal distribution X ~ log N (μ, σ). Then we can obtain the corresponding normal distribution with mean and variance of ln(X) as follows:µ1 = ln(X) = µ, σ1^2 = ln(1 + (σ^2/µ^2)) = σ^2From the normal distribution, we can use the standard normal tables to determine the required probability. Thus Z = (ln(x) - µ)/σ and P(X ≤ x) = P(Z ≤ (ln(x) - µ)/σ) = 0.8We can use the standard normal tables to determine the z-score for P(Z ≤ z) = 0.8, which is 0.84. Then we can find ln(x) using:0.84 = (ln(x) - 2.6)/2.1 or ln(x) = 2.6 + (0.84)(2.1) = 4.374x = e^4.374 = 79.1 ng/cm²Therefore, the 80th percentile of the amount absorbed is 79.1 ng/cm² rounded to one decimal place.2. Standard deviation of the amount absorbedThe standard deviation of a lognormal distribution is given by σx = [(e^(σ^2) - 1)(e^(2μ + σ^2))]^(1/2)From the given data, we have μ = 2.6 and σ = 2.1. Therefore,σx = [(e^(2.1^2) - 1)(e^(2(2.6) + 2.1^2))]^(1/2) = 1819.9 ng/cm² rounded to one decimal place. Therefore, the standard deviation of the amount absorbed is 1819.9 ng/cm² rounded to one decimal place.
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solve x+8=3x wefsdf eferc4frtvtgervgbeg4t
Answer:
x = 4
Step-by-step explanation:
x + 8 = 3x
8 = 2x
x = 4
So, the answer is x = 4
Consider the following formulas.
a sin Bθ + b cos Bθ = a2 + b2 sin(Bθ + C), where C = arctan(b/a) and a > 0
a sin Bθ + b cos Bθ = a2 + b2 cos(Bθ − C), where C = arctan(a/b) and b > 0
Use the formulas given above to write the trigonometric expression in the form a sin Bθ + b cos Bθ.
11 cos (θ − π/ 4)
The trigonometric expression 11 cos (θ − π/4) in the form a sin Bθ + b cos Bθ is 11/√2 cos θ.
What is the trigonometric expression?
The write the trigonometric expression in the required, we can start by using the second formula:
a sin Bθ + b cos Bθ = a^2 + b^2 cos(Bθ − C)
where;
C = arctan(a/b) and b > 0Let a = 11 and b = 11/√2, and Bθ = θ − π/4.
Then C = arctan(a/b) = arctan(11/(11/√2)) = arctan(√2).
Substituting these values, we get:
11 cos (θ − π/4) = 11/√2 cos (θ − π/4 + arctan(√2))
= 11/√2 cos (θ - π/4 + π/4)
= 11/√2 cos θ
Thus, we have written the trigonometric expression 11 cos (θ − π/4) in the form a sin Bθ + b cos Bθ as 11/√2 cos θ.
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The Scale Used in a Map is 2 : 10,000. Two cities are 1450 km apart what will be the distance between these cities on the map? (Hint)= 2 : 10,000 means that 2cn on map corresponds with 10,000 cm of actual distance.
Answer:
3.44827586
Step-by-step explanation:
1450:10,000::x:2
=10,000x=2900
x= 10,000
----------
2900
x=3.44827586 km
when solving a word problem, Fiona got answer 2.05 yards. Her friend Marsha's answer was 41/2 yards. Their classmate Fredic got 20.5. What was the answer to the problem if two out of three fifth graders have the correct answer?
Answer:
2.05 yards, Fredic and Fioana's answers are in the same range.
Plsss help meeeeeeeereeeee
Answer: 61 degrees
Step-by-step explanation:
just trust me
Answer:
You must know the value of x
Pls help question in photo
Therefore , the solution of the given problem of expressions comes out to be 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.
Expression : What is it?With shifting variables, estimates that mix joining, deactivating, and random division should be made. They could accomplish the following if they united: A math problem, some facts, and software. Formulas, parts, and arithmetic operations like additions, subtractions, omissions, and groupings can all be found in a declaration of truth. Both words and sentences can be evaluated and analysed.
Here,
The distributive property of multiplication must be used to multiply the two factors jointly in order to simplify the expression:
=> (x-1)(3x²-5x-3) = x(3x²) - x(5x) - x(3) - 1(3x²) + 1(5x) + 1 (3)
Condensing each term:
=> 3x³ - 5x²- 3x - 3x² + 5x + 3
=> 3x³ - 8x²+ 2x + 3
Therefore, 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.
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Shen does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at least 12 hours. He spends at most 9 hours on weight training. He spends at most 6 hours doing cardiovascular work. Let x denote the time (in hours) that Shen spends doing cardiovascular work. Let y denote the time (in hours) he spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.
PLEASE!!!!! GRAPH AND NUMBERS TOO!!!
The solution to the system of inequalities is the region enclosed in the triangle
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.
Let x denote the time (in hours) that Shen spends doing cardiovascular work. Let y denote the time (in hours) he spends on weight training.
Each week, he exercises for at least 12 hours, hence:
x + y ≥ 12 (1)
He spends at most 9 hours on weight training. Therefore:
x ≤ 6 (3)
He spends at most 6 hours doing cardiovascular work. Hence:
y ≤ 9 (3)
The solution to the system of inequalities is the darker region shown in the graph.
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fill the area for each of the composite shapes below
Step-by-step explanation:
1) 12×5=60
8×4=32
32÷2=16
60+16=82
2) 12×14=168
10×2=20
20÷2= 10
168+10+10=188
3) 4×4= 16
4×11=44
4×5=20
16+44+20=80
4) 8×4=32
3×3= 9
9÷2= 4.5
32+4.5=36.5
Write a system of equations to represent the number of each type of basket Jake scored. Explain your thinking.
The system of equations that represents the number of each type of basket Jake scored is given by:
x + y = 13
2x + 3y = 28
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of 2-point shots.
Variable y: Number of 3-point shots.
Jake scored 28 points in his basketball game by shooting only 2-point and 3-point shots, hence:
2x + 3y = 28.
He scored a total of 13 baskets, hence:
x + y = 13.
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Which two statements are true???????
The statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.
What are perpendicular and parallel lines?Geometry's use of parallel and perpendicular lines is crucial, and their distinctive qualities make it simple to distinguish between them. If two lines are in the same plane, are spaced equally apart, and never cross one another, they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees. Two straight lines are said to be parallel if they are located in the same plane and never cross one another. On the other hand, two lines are said to be perpendicular when they cross each other at a 90° angle.
From the given figure we observe that, the angle between the segments FG and HB is 90 degrees thus,
FG ⊥ HB.
Also, DE ⊥ HB, thus the segments FG ║ DE.
Hence, the statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.
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Find x.
Please help, and thank you!
Answer: 42
Step-by-step explanation:
We start by looking at the 49 degree angle. A common method of solving geometric problems is to bring things together. To follow this concept, we can say that the 49 degree angle has a vertical angle inside the triangle, which means that angle is 49 degrees. We now work with the 91 degree angle. We can see the 91 degree angle falls on a line, so the other side of the angle equals 180-91=89. All angles in a triangle add up to 180 degrees, so x + 49 + 89 = 180, so x=180 - 138 = 42.
Sleight #1 and Sleigh #2 headed in the opposite directions. If sleight #1 traveled at a speed of 20 mph and sleight #2 traveled at a speed of 45 mph, how many hours was it before they were 390 miles apart?
it takes 6 hοurs fοr the sleighs tο be 390 miles apart.
What are Distance and velοcity ?velοcity is a unit οf measurement fοr the Distance an οbject travels in a
the predetermined periοd οf time. Here is a wοrd equatiοn that illustrates the cοnnectiοn between space, speed, and time: velοcity is calculated by
dividing the tοtal Distance traveled by the jοurney time.
Since the sleighs are traveling in οppοsite directiοns, their distances frοm each οther are increasing at a cοmbined rate οf 20 mph + 45 mph = 65 mph. We can use the fοrmula:
distance = rate x time
Let's call the time it takes fοr the sleighs tο be 390 miles apart "t". Then we can write:
390 = 65t
Sοlving fοr "t", we can divide bοth sides by 65:
t = 6
Therefοre, it takes 6 hοurs fοr the sleighs tο be 390 miles apart.
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First, find the length of each edge of the cube one side is 3
(6-y) (6-y)=0
Solve.
Answer:
6
Step-by-step explanation:
y is 6..
Which statements must be true? Check all that apply.
A'A = C'C
C'Q = QC
Line P T⊥ A'A
C'C ⊥ B'B
A'A || B'B
m∠TRB = 90°
The true statements based on the shape in the given image are:
C'Q = QCLine P T⊥ A'AA'A || B'Bm∠TRB = 90°What is the Reflection of Triangles?The result of flipping a triangle on a coordinate system based on a line of reflection is a figure known as a triangle reflection.
Let's say we wish to mirror the triangle A B C over the -axis or the line. The image that results from reflecting the triangle, if A B C is the pre-image, is A ′ B ′ C ′. When using triangle reflections, the final image will keep the triangle's shape.
With this explanation in mind and from the image provided, C'Q = QC because they are parallel to each other.
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rohan had 36 pens . he gave 15 of them to mike and 11 of them to karan . what fraction of his original 36 pens does rohan have left ? write two equivalent fractions for that amount ?
Answer: 10/36 or 5/8
Step-by-step explanation:
Let’s start by solving how many pens Rohan has left. 36-11-15=36-26=10. Rohan has 10 pens left. Now to solve the fraction of pens Rohan has left, we divide our 10 by 36, or 10/36. Another fraction of this could be 5/18, because both the denominator and numerator have 2 as a factor.
Which expression does not have the same value as −2+3×6/5
a (2 * 9 + 14) / 10
b (5 * 8 - 8) / 10
c (5 * 4 + 12) / 10
d is 5 * 8 / 10 - 8
Five friends went to an amusement park. The group wanted to calculate the total cost, so Kathie wrote the expression 5x + 70. Each of her friends wrote expressions, too.
Determine which friends' expressions are equivalent to Kathie's. Show or explain your reasoning.
Kathie: 5x+70
Stephanie: 3(x+30)+2x−20
Jon: 3x+30+2x−20
Mary: 5(x+14)
Nicole: 3(x+30−20)+2x
Answer:
Stephanie Mary and Nicole
Step-by-step explanation:
SOMEBODY HELP ME OUT
Answer:
Below
Step-by-step explanation:
Area of a triangle = 1/2 base * height
this triangle has base = 4 ( 3 in) = 12 in and height = 3 (3 in) = 9 in
area = 1/2 * 12 * 9 = 54 in^2
54 in^2 * $ 2.75 /in^2 = $ 148.50
If the window is scaled down by .5 then the dimensions would be
base = 6 in height = 4.5 in
area = 1/2 * 6 * 4.5 = 13.5 in^2
cost would be 13.5 in^2 * $ 2.75/in^2 =~ $37.13
What is the value of the first term in the
sequence below?
Rule:
Start at ?
Add 3 then divide by 2 each time
5
3.5-
4 -3.5
The first term in the given sequence is 5
How to determine the first term in the sequenceFrom the question, we have the following parameters that can be used in our computation:
Rule:
Start at 5Add 3 then divide by 2 each timeThe sequence starting at 5 and following the given rule is:
5(5+3)/2 = 4, (4+3)/2 = 3.5, (3.5+3)/2 = 3.25, (3.25+3)/2 = 3.125, ...The first term in the sequence is simply the starting number, which is 5.
Hence, the value of the first term in the sequence is 5.
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Manny walked around a basketball court the court is 27 m long and 17 m wide what is the perimeter A. G, O. N, S. A. Grade 4 pls help
A basketball court takes the shape of a rectangle and the perimeter of a rectangle is =88m
The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.
Each form has a different perimeter depending on its measurements. The perimeter is only ever stated as the circle's diameter when referring to a circle. So we must add all of the sides of each polygon to determine its perimeter, which is the same for all polygons.
A basketball court takes the shape of a rectangle and the perimeter of a rectangle is calculated by the formula:
= Length + Length + Width + Width
Slotting the figures in will give:
= 27 + 27 + 17 + 17
= 88 m
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• F(x)=x3+2x2+5+10 factor
Answer:
F(x)=x^3+2x^2+15
Step-by-step explanation:
Please ASAP Help
Will mark brainlest due at 12:00
Answer:
the midpoint is at -8
Step-by-step explanation:
using two water heaters as the inspection unit, calculate the center line and control limits that are consistent with the past 22 days of inspection data. (c) what is the probability of type i error for the control chart in part (b)?
The probability is 0.05.
When using two water heaters as the inspection unit, the center line and control limits consistent with the past 22 days of inspection data are calculated as follows:
Center line (CL) = (X1 + X2)/2
Upper control limit (UCL) = CL + 3 * s/2
Lower control limit (LCL) = CL - 3 * s/2
Where X1 and X2 are the means of the two water heaters, and
s is the standard deviation of the sample data.
The probability of type I error for the control chart in part (b) is typically set at 0.05,
meaning that there is a 5% chance of rejecting the null hypothesis when it is actually true.
Complete question:
When using two water heaters as the inspection unit, (b) calculate the center line and control limits that are consistent with the past 22 days of inspection data. (c) what is the probability of type i error for the control chart in part (b)?
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The computer lab at school has a new computer system. The system had a total cost of $1895. There is a special printer that can be added to the system. The printer can be purchased separately for $649. Write an equation and solve to determine the cost of the system with the printer.
Answer:
meaning the computer is $1246
Step-by-step explanation:
$1895-$649=$1246
Eimy and Enerlyn are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Eimy sold 6 apple pies and 8 lemon meringue pies for a total of $208. Enerlyn sold 6 apple pies and 2 lemon meringue pies for a total of $88. Find the cost each of one apple pie and one lemon meringue pie
The cοst each οf οne apple pie is $8 and οne lemοn meringue pie is $20.
What is apple pie?Apples serve as the primary filling in fruit pies, which are knοwn as apple pies. Apple pies are cοmmοnly served with whipped cream, cheddar cheese, custard, ice cream, οr custard. The upper crust οften has pastry abοve and belοw the filling and may be sοlid οr latticed. The bοttοm crust can be baked separately tο prevent it frοm becοming sοggy. Deep dish apple pies typically just feature the tοp crust. The tarte tatin's crust is baked οn tοp, even thοugh it is placed οn the bοttοm when it is served.
Suppοse the cοst οf each apple pie is x and οne lemοn meringue pie is y.
Eimy sοld 6 apple pies and 8 lemοn meringue pies fοr a tοtal οf $208.
Then, 6x+8y= 208
Or, 6x=208-8y…………(1)
Enerlyn sοld 6 apple pies and 2 lemοn meringue pies fοr a tοtal οf $88.
Then, 6x+2y=88……………(2)
Putting the value οf 6x in equatiοn nο 2
208-8y+2y=88
Or, -6y=88-208
Or,y=120/6=20
Putting the value οf y in equatiοn 1
6x= 208-8*20
Or, x= 48/6
Or, x= 8
Hence the cοst each οf οne apple pie is $8 and οne lemοn meringue pie is $20.
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what do the slopes from part a and b tell you about the relationship between all points in the table
The slope of the line is 1. Two different points have the same slope.
What is tilt?Rise or fall is a number or ratio that determines the direction or slope of the line. The slope of a straight line is the ratio of the slope of the straight line to the course of the straight line. The point is:
-XY
twenty-five
−2 1
0 3
-7 -4
The slope of a straight line is generally calculated using the formula:
slope = [tex](y_{2} - y_{1} ) / (x_{2} - x_{1} )[/tex]
Points (2, 5) and (-2, 1) of part (A).
Slope = [tex]( 1 - 5 ) / ( -2 - 2 )[/tex]
Slope = -4 / -4 = 1
Split (B) at the points ( 0, 3 ) and ( -7, - 4 ).
Slope = [tex]( -4 - 3 ) / ( -7 - 0 )[/tex]
Slope = -7 / -7 = 1
The slope of the line at two different points is the same.
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Complete question is: A table with certain points is shown. x 2 −2 0 −7 y 5 1 3 −4 Part A: Choose two points from the table and calculate the slope between them. Show all necessary work. (4 points) Part B: Choose two different points from the table and calculate the slope between them. Show all necessary work. (4 points) Part C: What do the slopes from parts A and B tell you about the relationship between the points? Explain.
20 POINTS
Given: CD is an altitude of ΔABC
Prove:
[edAsset type="image" caption="" figure="false" alt="" class="block-center img-responsive " /edAsset]In an Image of a Triangle ACB with b is the length between AC, a is the length between CB and c is the base length between AB. D is a point between AB at the Right angle forming DCB
Proof:
Statements Reasons
1. CD is an altitude of ΔABC. Given
2. ∠ADC and ∠BDC are right angles. Definition of altitude
3. ΔADC and ΔBCD are right triangles. Definition of right triangles
4.
Definition of sine
5. ? Multiplication property of equality
6. b sin(A) = a sin(b) Substitution property of equality
7.
Division property of equality
Which statement completes this proof?
A.
CD = b sin(B) and CD = a sin(A)
B.
b = CD sin(A) and a = CD sin(B)
C.
CD = b sin(A) and CD = a sin(B)
D.
b = CD sin(B) and a = CD sin(A)
In the triangle , the cοrrect οptiοn is B) b = CD sin(A) and a = CD sin(B).
What is triangle?A triangle is a fοrm οf pοlygοn with three sides; the intersectiοn οf the twο lοngest sides is knοwn as the triangle's vertex. There is an angle created between twο sides. One οf the crucial elements οf geοmetry is this.
Certain fundamental ideas, including the Pythagοrean theοrem and trigοnοmetry, rely οn the characteristics οf triangles. The angles and sides οf a triangle determine its kind.
Here the given triangle CD is altitude.
According to the given statement table , in 4th statement we have definition of sine , Then
=> Sin(A) = [tex]\frac{CD}{b}[/tex] and Sin(B) = [tex]\frac{CD}{a}[/tex]
Here simplifying this sine equation for a and b then,
=> b = CD sin(A) and a = CD sin(B).
Hence the correct option is B) b = CD sin(A) and a = CD sin(B).
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Calculate the perimeter of the following.
In September 1998 the population of the country of West Goma in millions was modeled by f(x)=17.9e0.002x. At the same time the population of East Goma in millions was modeled by g(x)=13.6e0.017x. In both formulas x is the year, where x=0 corresponds to September 1998. Assuming these trends continue, estimate what the population will be when the populations are equal.A. 19 millionB. 18 millionC. 17 millionD. 1 million
Option B, 18 million, is the answer to this question.
In September 1998, the population of West Goma in millions was modeled by the function f(x) = 17.9e0.002x, and the population of East Goma in millions was modeled by the function g(x) = 13.6e0.017x. Here, x represents the year, with x=0 corresponding to September 1998.
To find out the point of intersection where the populations are equal, we equate both formulas and solve for x:
17.9e0.002x = 13.6e0.017x
Taking the natural logarithm of both sides of the equation gives:
x ln(17.9) + 0.002x = x ln(13.6) + 0.017x
Simplifying and rearranging terms, we get:
ln(17.9) - ln(13.6) = (0.017 - 0.002)x
0.079 = 0.015x
Solving for x, we get:
x = 5.27 years
Since x is the year, when x = 5.27, it corresponds to the year 1998 + 5.27 ≈ 2003.
When the populations are equal, the population will be f(5.27) ≈ 18 million for West Goma.
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