Answer:
Vertex: (3, 5)
Axis of symmetry: x=3
When you cough,the radius of your trachea (windpipe) decreases,affecting the speed S of the air in the trachea. If r0 is the normal radius of the trachea, the relationship between the speed S of the air and the radius r of the trachea during a cough is given by a function of the form
S(r) = (r0 - r) ar^2
where a is positive constant. Find the radius r for which the speed of the air is greatest.
Answer: 2r(0)/3.
Step-by-step explanation:
So, we are given one Important data or o or parameter in the question above and that is the function of the form which is given below(that is);
S(r) = (r0 - r) ar^2 -----------------------------(1).
We will now have to differentiate S(r) with respect to r, so, check below for the differentiation:
dS/dr = 2ar (r0 - r ) + ar^2 (-1 ) ---------;(2).
dS/dr = 2ar(r0) - 2ar^2 - ar^2.
dS/dr = - 3ar^2 + 2ar(r0) ------------------(3).
Note that dS/dr = 0.
Hence, - 3ar^2 + 2ar(r0) = 0.
Making ra the subject of the formula we have;
ra[ - 3r + 2r(0) ] = 0. -------------------------(4).
Hence, r = 0 and r = 2r(0) / 3.
If we take the second derivative of S(r) too, we will have;
d^2S/dr = -6ar + 2ar(0). -------------------(5).
+ 2ar(0) > 0 for r = 0; and r = 2r(0)/3 which is the greatest.
Answer:
[tex]r =\frac{2r_{0}}{3}[/tex]
Step-by-step explanation:
We need to take the derivative of S(r) and equal to zero to maximize the function. In this conditions we will find the radius r for which the speed of the air is greatest.
Let's take the derivative:
[tex]\frac{dS}{dr}=a(2r(r_{0}-r)+r^{2}(-1))[/tex]
[tex]\frac{dS}{dr}=a(2r*r_{0}-2r^{2}-r^{2})[/tex]
[tex]\frac{dS}{dr}=a(2r*r_{0}-3r^{2})[/tex]
[tex]\frac{dS}{dr}=ar(2r_{0}-3r)[/tex]
Let's equal it to zero, to maximize S.
[tex]0=ar(2r_{0}-3r)[/tex]
We will have two solutions:
[tex]r = 0[/tex]
[tex]r =\frac{2r_{0}}{3}[/tex]
Therefore the value of r for which the speed of the air is greatest is [tex]r =\frac{2r_{0}}{3}[/tex].
I hope it helps you!
The diameter of a circular placement is 42 centimeters what is the approximate area of the circular placement
What is the solution for the following equation? 2x+2=8
Answer:
x = 3
Step-by-step explanation:
2(x)+2=8
2*x+2-(8)=0
Pull out like factors :
2x - 6 = 2 • (x - 3)
2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
x-3 = 0
X=3
Answer:
x= 3
Step-by-step explanation:
2x+2=8
substact 2 from both sides of the eqation,
then you get 2x=6
then you divide each side by 2 and get x= 3
hope this helped, good luck !!
brainliest ?? :))
Mercury is a heavy metal that can cause severe health problems in even small concentrations. Fish and shellfish efficiently concentrate mercury into their flesh, so it is important to monitor seafood for its mercury content. An extensive study conducted in 1980 concluded that the mean mercury level in oysters from the White Bear estuary was 0.020 parts per million (ppm) with a standard deviation ppm. In 2012, a sample of 40 oysters from the same estuary exhibited a mean mercury concentration of . Can you conclude that the 2012 mercury concentration is lower than in 1980? Use the level of significance.
Answer:
The overview of the problem is listed in the segment below on the explanation.
Step-by-step explanation:
The given values are:
Sample mean, [tex]\bar{Z}=0.017[/tex]
The hypothesized mean value, [tex]\mu_{0}=0.02[/tex]
Population standard deviation, [tex]\sigma=0.036[/tex]
As we know, the status of the test is as follows:
⇒ [tex]z^* = \frac{\bar X - \mu_0}{\frac{\sigma}{\sqrt{n}}}[/tex]
On putting the values, we get
⇒ [tex]= \frac{0.017 - 0.02}{\frac{0.036}{\sqrt{40}}}[/tex]
⇒ [tex]=-0.5357[/tex]
Now, even though this is a one-sided check, here so the p-value is measured as:
[tex]p=P(Z<-0.5357)[/tex]
[tex]=0.2[/tex]
Consequently p-value > 0.05 the check isn't relevant so there is no data to suggest that perhaps the concentration of mercury fallen from 1980 until 2012.
6. The mean of 5 consecutive integers is 19. What is the difference between the largest and
the smallest of the 5 integers?
Answer:
4
Step-by-step explanation:
The integers are
x
x+1
x+2
x+3
x+4
since they are consecutive
The largest is x+4
The smallest is x
Difference is
x+4 -x
4
Answer:
Step-by-step explanation:
If the least integer is n, it means the five consecutive integers are:
n,n+1,n+2,n+3,n+4
Summing all integers we have:
n + n+1+n+2+n+3+n+4
=5n+10
The mean of this integers is
5n+10 /5 =19
5n+10=19*5
5n + 10 = 95
5n = 95 - 10
5n =85
n=85/5=17
The smallest of the integer is n= 17
The largest integer is n + 4 =17+4=23
The difference between the least and largest integer would be;
Is 4
The sum of largest integer and the smallest integer is 23 + 17 = 40
Is 56 inches less than 5 feet? PLEASE THIS IS AN EMERGENCY! 40 POINTS IF YOU ANSWER! :D
Answer:
5ft. = 60 in. so yes, 5 feet is more than 56 inches
Step-by-step explanation:
1 ft. = 12 in. , so 5ft. = 60 in.
Answer:
Yes! 56 inches is less than 5 feet
Step-by-step explanation:
5 feet is 60 inches, so 56 inches is less than 60 inches
HOPE THIS HELPS !
PLEASE GIVE BRAINIEST
A 4-foot long steel pipe consists of two concentric cylinders, with the inner cylinder hollowed
out. The radius of the outside of the pipe is 6 inches and the radius of the inside of the pipe
is 5.75 inches.
HINT: The units of measure must be the same! Convert to inches and keep your answer in
terms of π.
A. Determine the volume of metal used to build the pipe.
B. If the pipe is to be powder-coated on the inside and outside surfaces, what is the total
surface area to be powder-coated?
Answer:
The pipe is formed by two concentric cylinders.The outside cylinder has 6 inches of radius.The inside cylinder has 5.75 inches of radius.To find the volume of the pipe, we need to subtract the inside cylinder volume from the outside cylinder volume.
Remember that the volume of a circular cylinder is
[tex]V=\pi r^{2} h[/tex]
Where [tex]r[/tex] is the radius and [tex]h[/tex] is the height.
Outside cylinder volume.[tex]V_{outside}=\pi r^{2}h= \pi (6in)^{2} (48in)=1,728 \pi in^{3}[/tex]
Inside cylinder volume.[tex]V_{inside}=\pi r^{2}h= \pi (5.75in)^{2} (48in)=1,587 \pi in^{3}[/tex]
Notice that we used the height 4 feet in inches units, that's why the height in the formulas is 48 inches, because each feet is equivalent to 12 inches.
Volume of the pipe.[tex]V_{pipe}=V_{outside} -V_{inside} =1,728 \pi in^{3}-1,587 \pi in^{3} =141 \pi in^{3}[/tex]
(A) Therefore, the volume of metal used to build the pipe is 141π cubic inches.
Now, to know the amount of powder-coat we must use, we need to find the surface area of the pipe, which is basically the sum of the surface area of both cylinders.
Surface area of outside cylinder.[tex]S_{outside}=2\pi r^{2}+2\pi rh=2 \pi (6in)^{2}+2 \pi (6in)(48in)= 72 \pi in^{2} +576 \pi in^{2} =648 \pi in^{2}[/tex]Surface area of the inside cylinder.[tex]S_{inside}=2\pi r^{2}+2\pi rh=2 \pi (5.75in)^{2}+ 2 \pi (5.75in) (48in)= 66.13 \pi in^{2} +552 \pi in^{2} =618.13 \pi in^{2}[/tex]
The total surface is[tex]S_{powder}=648 \pi in^{2} + 618.13 \pi in^{2} =1,266.13 \pi in^{2}[/tex]
(B) Therefore, we need 1,266.13π sqaure inches of powder to cover the whole pipe.
Answer:
A. volume of the metal used to build the pipe is 141[tex]\pi[/tex] cubic inches.
B. The total surface area to be powder coated is 1122.125 square inches.
Step-by-step explanation:
The length of the cylinder = 4 feet = 48 inches.
Radius of the outside of the pipe = 6 inches.
Radius of the inside of the pipe = 5.75 inches
A. volume of the metal used to build the pipe = volume of the outside pipe - volume of the inside pipe
volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
volume of the outside pipe = [tex]\pi[/tex][tex]r^{2}[/tex]h
= [tex]\pi[/tex] × [tex]6^{2}[/tex] × 48
= 1728[tex]\pi[/tex] cubic inches
volume of the inside pipe = [tex]\pi[/tex][tex]r^{2}[/tex]h
= [tex]\pi[/tex] × [tex]5.75^{2}[/tex] × 48
= 1587[tex]\pi[/tex] cubic inches
volume of the metal used to build the pipe = 1728[tex]\pi[/tex] - 1587[tex]\pi[/tex]
= 141[tex]\pi[/tex] cubic inches
B. Total surface area of a hollow cylinder = 2[tex]\pi[/tex] ( [tex]r_{1}[/tex] + [tex]r_{2}[/tex]) ( [tex]r_{2}[/tex] - [tex]r_{1}[/tex] + h)
where [tex]r_{1}[/tex] is the inner radius and [tex]r_{2}[/tex] is the outer radius.
= 2[tex]\pi[/tex] (6 + 5.75)(5.75 - 6 + 48)
= 2[tex]\pi[/tex] (11.75 × 47.75)
= 1122.125[tex]\pi[/tex] square inches
The total surface area to be powder coated is 1122.125 square inches.
Morgan is throwing a pizza party. She has 1 7/8 pounds of cheese available and she needs 1/5 pound of cheese to make each pizza. How many full pizzas can Morgan make with the amount of cheese she has?
We have been given that Morgan is throwing a pizza party. She has 1 7/8 pounds of cheese available and she needs 1/5 pound of cheese to make each pizza. We are asked to find the number of full pizzas that Morgan can make with the amount of cheese she has.
To solve our given problem, we will divide total amount of cheese by amount of cheese used to make each pizza.
[tex]\text{Number of pizzas}=1\frac{7}{8}\div \frac{1}{5}[/tex]
[tex]\text{Number of pizzas}=\frac{15}{8}\div \frac{1}{5}[/tex]
Now we will convert our division problem into multiplication problem by flipping the 2nd fraction.
[tex]\text{Number of pizzas}=\frac{15}{8}\times \frac{5}{1}[/tex]
[tex]\text{Number of pizzas}=\frac{75}{8}[/tex]
[tex]\text{Number of pizzas}=9\frac{3}{8}[/tex]
We are asked to find the number of full pizzas and we can see that Morgan can make 9 full and [tex]\frac{3}{8}[/tex] pizzas.
Since there are 9 full pizzas, therefore, Morgan can make 9 full pizzas with the amount of cheese she has.
8 cm
Answer:
cm
Part B
Find circumference of the circle. Use
= 3.14.
A 25. 12 cm
B 50.24 cm
C 73.06 cm
D
200.96 cm
Answer:
D.200.96 cm
Step-by-step explanation:
Given radius (R) = 8
Diameter = 2R = 16
Circumference = 2πR
= 16π
= 50.265482457437
Area = πR2
= 64π
= 201.06192982975
Please Help me
A restaurant has a build your own personal pizza on their express lunch menu. A customer can only choose one item from each category. The table below shows the different choices. How many different ways can a person order a lunch pizza?
A. 3
B. 9
C. 18
D. 27
How many strings can be formed by ordering the letters MISSISSIPPI which
contain no two I’s are consecutive ?
Answer:
Total number of strings = 7350
Step-by-step explanation:
Given:
MISSISSIPPI
Required:
Number of strings to contain no two consecutive I's
To do this, we start by calculating the number of strings that can be formed without any I;
We're left with MSSSSPP
7 characters in total
4 S and 2 P
The number of strings is calculated as follows
Number of strings = [tex]\frac{7!}{4!2!}[/tex]
Number of strings = [tex]\frac{7*6*5*4!}{4!*2*1}[/tex]
Number of strings = [tex]\frac{7*6*5}{2*1}[/tex]
Number of strings = 7 * 3 * 5
Number of strings = 105
Then we count the number of possible spaces of I; This is as follows
-M-S-S-S-S-P-P-
This is represented by the - sign.
In total, there are 8 spaces, the 4 I's can occupy
There number of selection is as follows
[tex]\left[\begin{array}{c}8&\\4&\\\end{array}\right] = \frac{8!}{4!*4!}[/tex]
[tex]\left[\begin{array}{c}8&\\4&\\\end{array}\right] = \frac{8 * 7 * 6 * 5 * 4!}{4!*4*3*2*1}[/tex]
[tex]\left[\begin{array}{c}8&\\4&\\\end{array}\right] = \frac{8 * 7 * 6 * 5}{4*3*2*1}[/tex]
[tex]\left[\begin{array}{c}8&\\4&\\\end{array}\right] = 70[/tex]
Total number of strings = 105 * 70
Total number of strings = 7350
Find the sum of the geometric series 1−0.99+0.99^2−0.99 ^3 +...−0.99
Answer:
0.28
Step-by-step explanation:
The sum of the geometric value progression is S = 0.28
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the sequence be A = { 1 - 0.99 + 0.99² - 0.99³... - 0.99⁷⁹ }
So , A = 1 - { 0.99 - 0.99² + 0.99³... + 0.99⁷⁹ }
Let the first term of the GP be a₁ = 0.99
Now , the common ratio of GP , r = 0.99
And , the number of terms in GP = 80
And , Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
On simplifying , we get
S₈₀ = 0.99 ( 1 - 0.99⁸⁰ ) ( 1 - 0.99 )
On further simplification , we get
S₈₀ = 0.7224
So , the sum of the GP is S = 1 - S₈₀ = 0.28
Hence , the sum of GP is 0.28
To learn more about geometric progression click :
https://brainly.com/question/1522572
#SPJ3
15. When coffee is packed by machine into 16-ounce cans, the amount can vary. The mean weight is 16.1 ounces and the standard deviation is 0.04 ounce. The weight of the coffee approximates a normal distribution. a. What percent of the cans of coffee can be expected to contain less than 16 ounces of coffee
TBH i found it online because im not that smart but the answer is
.6 %
and if the online question is correct there is another question connected to the question you asked, which the answer is 98.8%
can u pls gimme brainly?
Identify the graph of the equation... Then find q to the nearest degree.
16x^2+2xy+y^2-16=0
Answer:
ellipse ; 4 degrees
Step-by-step explanation:
edge’s possible answer 2020
Given f(x) = -4x + 7 and g(x) = x, choose
the expression for (fºg)(x).
Answer:
-4x^2+7x
Step-by-step explanation:
Multiply -4x+7 and x.
You get -4x^2+7x.
are 19/8 and 2.375 equivalent and why
Answer:
Yes.
Step-by-step explanation:
They are equivalent because if you divide 19 by 8, the result is 2.375.
Answer:
yes
Step-by-step explanation:
convert 19/8 into a decimal:
[tex]\frac{19}{8}[/tex]=2.375
2.375=2.375
Hope this helps!
what is (4 to the square root of 81)5?
Answer:
1310720
Step-by-step explanation:
Find out the frist part "4 to the square root of 81" 262144
then times it by 5
to get 1310720
A physical education class has 21 boys and 9 girls. Each day, the teacher randomly selects a team captain. Assume that no student is absent. What is the probability that the team captain is a girl two days in a row?
The probability of choosing a captain that is a girl two days in a row is
9
%.
Answer:9%
U already provided the answer. Anyways have a good day!!
The probability of choosing a captain that is a girl two days in a row is 9%
How to determine the probability?The given parameters are:
Boys = 21
Girls = 9
The total number of students is
Total = 21 + 9
Total = 30
This means that the probability of selecting a girl is:
P(Girl) = 9/30
For two days, the required probability is
P = 9/30 * 9/30
Evaluate
P = 9%
Hence, the probability of choosing a captain that is a girl two days in a row is 9%
Read more about probability at:
https://brainly.com/question/251701
#SPJ2
Find the area of the shaded region and choose the appropriate result?
Answer:
Option B
Step-by-step explanation:
The figures are made out of squares.
[tex]\text {Formula for area of a square: } A =s^2\\s-\text {Length of side.}[/tex]
Square 1 (the gray square):
The side measure is 4 cm.
[tex]A = 4^2 = 16cm^2[/tex]
Square 2 (white square):
The side measure is 2 cm.
[tex]A=2^2=4cm^2[/tex]
Subtract the area of the white square from the gray square to get the area of the shaded region:
[tex]16 - 4 =12[/tex]
The shaded region is [tex]12cm^2[/tex].
Option B should be the correct answer.
Brainilest Appreciated!
The ratio of sailboats to dinghies in the bay was 5 to 7 If there were 70
sailboats in the bay, how many dinghies were there?
Answer:
98
Step-by-step explanation:
Let the sailboats be s and the dinghies be d.
We have that:
s : d = 5 : 7
In other words:
s / d = 5 / 7
If there are 70 sailboats, this implies that s = 70
=> 70 / d = 5 / 7
=> d = (70 * 7) / 5 = 490 / 5 = 98
There will be 98 dinghies.
A G.P has a common ratio of 2 find the value of 'n' for which the sum 2n terms is 33 times the sum of n?
a line is perpendicular to y=-4x-2 and intersects the point (0,9). what is the equation for this perpendicular line?
Answer:
y=(1/4)x + 9 OR y=x/4 +9
Step-by-step explanation:
Perpendicular lines have a slope/gradient of -1/n
Because the slope of this line is -4, the slope of a line perpendicular to it would be 1/4.
y=(1/4)x+b
(0,9) is the y-intercept, so b = 9
y=(1/4)x + 9 OR y=x/4 +9
You score a 65% on your AP Statistics Exam and a 78% on your Economics Exam. The AP Statistics scores were normally distributed with an average of 60% and a standard deviation of 6%. The Economics scores were also normally distributed with an average of 75% and standard deviation of 2.5%. In which class did you perform better relative to the class average? Be sure to justify your answer.
Answer:
His economics grade had a higher z-score, so you performed better relative to the class average in economics.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In which class did you perform better relative to the class average?
In whichever class you had the higher z-score.
Statistics:
Scored 65, mean 60, standard deviation 6. So [tex]X = 65, \mu = 60, \sigma = 6[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{65 - 60}{6}[/tex]
[tex]Z = 0.83[/tex]
Economics:
Scored 78, Mean 75, Standard deviation 2.5. So [tex]X = 78, \mu = 75, \sigma = 2.5[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{78 - 75}{2.5}[/tex]
[tex]Z = 1.2[/tex]
His economics grade had a higher z-score, so you performed better relative to the class average in economics.
GIVING BRANLIEST Which prism has a greater surface area?
2 prisms. A rectangular prism has a length of 12 inches, height of 8 inches, and width of 6 inches. A triangular prism has a rectangular base with a length of 6 inches and height of 12 inches. 2 rectangular sides are 12 inches by 10 inches. The triangular sides have a base of 6 inches an height of 8 inches.
The rectangular prism has a greater surface area by 72 square inches.
The rectangular prism has a greater surface area by 88 square inches.
The triangular prism has a greater surface area by 72 square inches.
The triangular prism has a greater surface area by 88 square inches.
Answer:
Rectangular prism
Step-by-step explanation:
Five subtracted from the product of 8 and x is greater than or equal to 51.
1/5 of the shoes in a factory are green. If you pick a shoe, replace it, pick another shoe and replace it, and pick a third shoe, what is the probability that none of the shoes are green? The answer needs to be in fraction form.
Answer: I believe it’s 3/5
Step-by-step explanation:
Answer:
7/5
Step-by-step explanation:
just add gtwebtewgbrwgragtgwgtrwgtwebgrw
The diameter of a cylindrical water tank is 8 ft, and its height is 9 ft. What is the volume of the tank?
Use the value 3.14 for it, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
The volume of the tank is [tex]452\ \text{feet}^3[/tex].
Step-by-step explanation:
We have,
Diameter of a cylindrical water tank is 8 ft
Height of the water tank is 9 ft.
It is required to find the volume of the tank. The volume of a cylindrical shaped object is given by :
[tex]V=\pi r^2h[/tex]
r is radius of cylindrical tank, r = 4 ft
Plugging all the values in above formula,
[tex]V=3.14\times (4)^2\times 9\\\\V=452.16\ \text{feet}^3[/tex]
or
[tex]V=452\ \text{feet}^3[/tex]
So, the volume of the tank is [tex]452\ \text{feet}^3[/tex].
Mr. Marchand cut a pizza into 8 equal slices. He ate 2 slices.
Write 2 equivalent fractions to describe how much pizza Mr. Marchand ate.
Write 2 equivalent fractions to describe how much pizza was left
Answer:
He ate 1/4 or 4/16 of the pizza. There are 3/4 or 9/12 of the pizza left.
Answer:
a)
2/8 = 1/4 = 3/12
b)
6/8 = 3/4 = 9/12
1. To measure the resting heart rate of an animal biologist use the function h(m) = 530m-C), where h
is resting heart rate in beats per minute, given the mass m in pounds.
Part A: What is a feasible domain for the function him?
Answer:
Step-by-step explanation:
In mathematics, the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall. It is the set X in the notation f: X → Y. Since a function is defined on its entire domain, its domain coincides with its domain of definition, the subset of the domain for which the function associates an image. However this coincidence is no longer true for a partial function since the domain of definition of a partial function can be a proper subset of the domain.
x^2 = 8x - 15
.......................
Answer: x= 5
Step-by-step explanation: Lets solve by completing the square.
You first need to get -15 by itself.
x^2-8x=15 Now you need to complete the square my finding a perfect constant that will go with x^2-8x, then add it to the other side containing -15 to balance the equation out.
-8x/2= -4^2=16 This will be the perfect square.
x^2-8x+16 = -15 + 16
(x-4)^2 = 1 factor into a binomial, then use the square root on both sides.
√ x-4 ^ 2 = √ 1
x-4 = 1
x=5
