Answer:
1 cup
Step-by-step explanation:
3 1/3 - 2 1/3 = 1 cup
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.
How many unique ways are there to arrange the letters in the word PRIOR?
Answer:
60
Step-by-step explanation:
Answer:
it is 60
Step-by-step explanation:
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.
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.
Which goes with which
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
Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo.
Suppose it takes about 0.5 seconds to hear the echo. How far away is the canyon wall, in feet?
feet
Now let's generalize that result. Suppose it takes n seconds to hear the echo. How far away is the canyon wall, in terms of n?
Answer:
The sound takes time to go to a point and reflect back to your position.
It means the sound went twice a distance.
=> Suppose it takes about 0.5 seconds to hear the echo, the canyon wall would be [750 x (0.5/3600)]/2 = 0.052 miles
=> Suppose it takes about n seconds to hear the echo, the canyon wall would be [750 x (n/3600)]/2 miles
Hope this helps!
:)
The distance the canyon wall is away is 33000 feet.
The distance the canyon is away in terms of n is 66000n feet.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Speed = 750 miles per hour
Time = 0.5 seconds
Distance = Speed x Time
Now,
1 mile = 5280 feet
750 miles = 3960000 feet
1 hour = 60 seconds
So,
Speed = (3960000/60) feet per second
Distance = 66000 x 0.5 feet = 33000 feet
This means,
The canyon wall is 33000 feet away.
Now,
For n seconds,
The canyon wall is 66000n feet away.
Thus,
The canyon wall is 33000 feet away.
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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
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?
Find the volume of a block of woods
Answer:volume=125 cm^3
Surface area=150 cm^2
Step-by-step explanation:
Part A:
volume=length x width x height
volume=5 x 5 x 5
Volume=125 cm^3
Part B:
Surface area=6x5x5
Surface area=150 cm^2
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
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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
Calcula el 23 % de 175
Answer:40.25
Step-by-step explanation:
23% of 175
23/100 x 175
(23 x 175)/100
4025/100=40.25
What is the volume of a sphere with a diameter of 6 m, rounded to the nearest tenth of a cubic meter?
Answer:113 cubic meter
Step-by-step explanation:
Diameter=6
Radius=r=6/2
Radius=r=3
π=3.14
Volume of sphere=4/3 x π x r x r x r
Volume of sphere=4/3 x 3.14 x 3 x 3 x 3
Volume of sphere=(4x3.14x3x3x3) ➗ 3
Volume of sphere=339.12 ➗ 3
Volume of sphere=113.04
Volume of sphere =113 cubic meter
On the first day of school, each student is given $0.50 to attend. On day two, each student earns $1.00. on day 3, $2.00, etc. How much do students earn on the 9th day
Answer:
255.50
Step-by-step explanation:
If each day the number is doubled, then all you must do is keep on doubling to the ninth day and then add it all together
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
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.
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.
What are prime number
A prime number is a special number because it means that it only has one factor pair and that factor pair is always 1 and the number itself.
In other words, prime numbers are the numbers
divisible by 1 and the number itself.
For example, let us take 2.
2 has only two factors and those are 1 and 2 so it's prime.
Similarly, 7 is also a prime number because it has only two factors
and these are 1 and the number itself which is 7.
Answer:
A number that is only divisible by itself and 1
Step-by-step explanation:
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%
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Given the equation StartFraction 2 x + 2 Over y EndFraction = 4 w + 2 what is the value of x?
Question:
Given the equation (2x + 2)/y = 4w + 2.
What is the value of x?
Answer:
x = 2wy + y - 1
Step-by-step explanation:
Given
(2x + 2)/y = 4w + 2
Required
Find x
To find the value of x; the following steps will be used.
First, Multiply both sides by y
y * (2x + 2)/y = (4w + 2) * y
2x + 2 = 4wy + 2y
Subtract 2 from both sides
2x + 2 - 2 = 4wy + 2y - 2
2x = 4wy + 2y - 2
Multiply both sides by ½
½ * 2x = ½(4wy + 2y - 2)
x = ½(4wy + 2y - 2)
Open bracket
x = ½ * 4wy + ½ * 2y - ½ * 2
x = 2wy + y - 1
Hence, the value of x is 2wy + y - 1
Answer:
B
Step-by-step explanation:
I took the test
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:
Factor.
Z^2- 3z – 18
Answer:
(z-6)(z+3)
Step-by-step explanation:
Answer:
Step-by-step explanation:
z^2-6z + 3z -18
z(z-6)+3(z-6)
(z+3)(z-6)
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.
Which number line represents the solution set for the inequality 2x24?
+
-10
-8
-6
4
- 2
0
2
4
6
8
10
+
+
+
+
+
-4
-10
-8
-6
-2
0
+
6
+
10
2
4
8
+
+
-10
-8
--6
-4
O
-2
2
4
6
8
10
-10
-8
--6
-4
-2
0
2
4
6
8
10
Answer:
the answer is what I think 46
The solution of the inequality - 1/2x ≥ 4 is shown in Option 2.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
Inequality is,
⇒ - 1/2x ≥ 4
Now, We can simplify as;
⇒ - 1/2x ≥ 4
⇒ 1/2x ≤ - 4
⇒ x ≤ - 8
When we plot this inequality on a number line,
An arrow starting with a solid point from x = -8 and arrow directing towards negative numbers will represent the given inequality.
Hence, Option (2) will be the answer.
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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!
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!
Find the radius of Circle M, if the area of a sector is 36.07 cm^2 and the central angle of that sector is 58º. Round your answers to the hundredths place if necessary
Answer:
r = 5.97 cm
Step-by-step explanation:
The area of the sector is given by the following equation:
[tex]A = r*S = 2\pi*r^{2}*\frac{58}{360}[/tex]
Where:
r: is the radius
A: is the area
The radius is:
[tex]r = \sqrt{\frac{A}{2*\pi*58/360}} = \sqrt{\frac{36.07 cm^{2}}{2*\pi*58/360}} = 5.97 cm[/tex]
Therefore, the radius of Circle M is 5.97 cm.
I hope it helps you!
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
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
