A spherical shell has inner radius r and an outer radius r+h. Let h=0.1r. Find the volume of the shell in terms of r and then approximate the volume of the shell by 4πr^2h. Does this seem like a reasonable approximation if h is small compared to r?
Step-by-step explanation:
The volume of the shell is the volume of the outer sphere minus the volume of the inner sphere.
V = 4/3 π (r+h)³ − 4/3 π r³
V = 4/3 π (r³ + 3r²h + 3rh² + h³) − 4/3 π r³
V = 4/3 π r³ + 4π r²h + 4π rh² + 4/3 π h³ − 4/3 π r³
V = 4π r²h + 4π rh² + 4/3 π h³
If h = 0.1 r:
V = 4π r² (0.1 r) + 4π r (0.1 r)² + 4/3 π (0.1 r)³
V = 0.4π r³ + 0.04π r³ + 0.00133π r³
V = 0.44133π r³
Using the approximation:
V = 4π r² h
V = 4π r² (0.1 r)
V = 0.4π r³
The approximation is reasonable if h is small compared to r.
Janis is at the store shopping for snacks for her trip to the zoo. She purchases 9 / 11 pound of grapes, 1 3/4 pounds of bananas and 2 5/6 pounds of apples.
(A) what is the weight of each type of fruit in decimal form?
(B) Does the weight of each type of fruit in decimal form represent a rational number? Explain.
Answer:
A. What is the weight of each type of fruit in decimal form?
Grapes in decimal form = 0.8181 pounds
Bananas in decimal form = 1.75 pounds
Apples in decimal form = 2.8333 pounds
B. Does the weight of each type of fruit in decimal form represent a rational number? Explain.
Of course, each of the weights of the fruits in decimal form represent a rational number. The weights can be expressed as a fraction where both the numerator and the denominator in the fraction are integers, like we checked with 9/11, 1 3/4 and 2 5/6. The denominator in a rational number cannot be zero.
Step-by-step explanation:
1. Let's check the information provided to us to answer the questions correctly:
Janis purchased:
9/11 pounds of grapes
1 3/4 pounds of bananas
2 5/6 pounds of apples
2. What is the weight of each type of fruit in decimal form?
Grapes in decimal form = 0.8181 pounds
Bananas in decimal form = 1.75 pounds
Apples in decimal form = 2.8333 pounds
3. Does the weight of each type of fruit in decimal form represent a rational number? Explain.
Of course, each of the weights of the fruits in decimal form represent a rational number. The weights can be expressed as a fraction where both the numerator and the denominator in the fraction are integers, like we checked with 9/11, 1 3/4 and 2 5/6. The denominator in a rational number cannot be zero.
Complete the equation of the line through ( 2 , − 2 ) and ( 4 , 1 )
Answer:
Step-by-step explanation:
first we find the slope using the slope formula : (y2 - y1) / (x2 - x1)
(2,-2)....x = 2 and y = -2
(4,1)...x = 4 and y = 1
now sub
slope = (1 - (-2) / (4 - 2) = (1 + 2) / 2 = 3/2
y = mx + b
slope(m) = 3/2
(4,1)...x = 4 and y = 1
now sub and find b, the y int
1 = 3/2(4) + b
1 = 6 + b
1 - 6 = b
-5 = b
so ur equation is : y = 3/2x - 5 <===
(a - b)(a 2 + ab + b 2)
Please list the steps on how to solve this one.
The ratio of Geoff’s to Ethan’s age is 1:10.If the total of their ages is 88, how old is Ethan
Answer:
80 years old
Step-by-step explanation:
the ratio is 1:10 and their total is 88. Just by looking at it you can see that Geoff's age is 8 and Eathan is 80. The total is 88 and the ratio also matches.
1:10 1 times 10 is 10
8:80 8 times 10 is 80
Answer:
hi there!
The correct answer to this question is: 80 years old
Step-by-step explanation:
you first need to set up to equations:
in this case: I will use the variable "e" for Ethan and "g" for Geoff
e=10g
g + e = 88
since e = 10g, substitute that into the second equation and you get 10g + g = 88
you add the variables and you get 11g=88 then you divide 11 on both sides and you get 8 so geoff is 8
then you plug 8 back into the second equation and you get ethan's age which is 80
Write The Mixed Number As A Fraction Or The Fraction As A Mixed Number
Answer:
14.06=703/50
Step-by-step explanation:
14.06=703/50
Answer:
what is the number in the word problem
Step-by-step explanation:
Liz runs 8 feet per second. Katie runs 350 feet in 31 seconds. Katie runs 350 feet in 31 seconds. Stephanie runs 1 mile in 388 seconds. Stephanie runs 1 mile in 388 seconds. Noah runs 541 feet in 1 minute. Noah runs 541 feet in 1 minute.
Answer: Stephanie is the fastest
Step-by-step explanation:
Here we have to find who runs faster:
Liz:
[tex]8 ft/s[/tex]
Katie:
[tex]\frac{350 ft}{31 s}=11.29 ft/s[/tex]
Stephanie:
[tex]\frac{1 mile}{388 s}. \frac{5280 ft}{1 mile}=\frac{5280 ft}{388 s}=13.60 ft/s[/tex]
Noah:
[tex]\frac{541 ft}{1 min}. \frac{1 min}{60 s}=9.01 ft/s[/tex]
As we can see after comparing, Stephanie is the fastest, since she travels more distance in less time.
Given: ΔPQR; ∠Q = 52°; p = 3; and q = 4. Find ∠P to the nearest tenth of a degree.
Answer:
36.2
Step-by-step explanation:
When ringing up a customer ,a cashier needs 27 seconds to process payment as well as 4 seconds to scan each item being purchased .If it takes 43 seconds to ring up a customer, how many items are being purchased
Answer:
The number of items are being purchased is 4 .
Step-by-step explanation:
Given as :
The time taken to process the payment = 27 seconds
The time taken to scan each items = 4 seconds
The total time taken to ring up a customer = 43 seconds
Let The number of items being purchased = n
Now, According to question
The total time taken to ring up a customer = The time taken to process the payment + The time taken to scan each items × The number of items being purchased
i.e 43 = 27 + 4 × n
Or, 4 × n = 43 - 27
Or, 4 × n = 16
∴ n = [tex]\dfrac{16}{4}[/tex]
I.e n = 4
So, The number of items being purchased = n = 4
Hence, The number of items are being purchased is 4 . Answer
a).$ -16.72
b).$75.50
c).$98.28
d).$16.72
e).$ -18.78
Option D
Money earned by Marty is $ 16.72
Solution:
Given that, Marty started a lawn mowing business
He kept track of his expenses and earnings in a table
Lawn Mower = - $49.99
Gasoline = - $8.79
Moyer's yard = $ 40
Griffen's yard = $ 35.50
To find: Money earned by Marty
Total money earned = lawn mower + gasoline + moyers yard + griffens yard
Total money earned = -49.99 - 8.79 + 40 + 35.50
Total money earned = -58.78 + 40 + 35.50
Total money earned = -18.78 + 35.50 = 16.72
Thus money earned by Marty is $ 16.72
The larger of two numbers is 20 more then the smaller. Four times the larger is 70 more then 5 times the smaller.find the numbers.
The larger number is 30 and smaller number is 10.
Step-by-step explanation:
Let,
Larger number = x
Smaller number = y
According to given statement;
The larger number is 20 more than the smaller.
x = y+20 Eqn 1
Four times the larger is 70 more then 5 times the smaller.
4x = 5y+70 Eqn 2
Putting value of x from Eqn 1 in Eqn 2
[tex]4(y+20)=5y+70\\4y+80=5y+70\\80-70=5y-4y\\10=y\\y=10[/tex]
Putting y=10 in Eqn 1
[tex]x=10+20\\x=30[/tex]
The larger number is 30 and smaller number is 10.
Keywords: linear equation, substitution method
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Find (3 × 104) + (7 × 102).
Solve for x: logx3=1/2
Answer:
x= 9
Step-by-step explanation:
Please see attached picture for full solution.
The number of transitions double every 24 months ,what type of relationship is it ?
Answer: gay
Step-by-step explanation: y = mc2
The rectangular rug in Marcia's living room measures 12 feet by 109 inches. What is the rug's area in square feet?
Answer:
109 square feet.
Step-by-step explanation:
109 in: = 109/12 = 9.0833333.... = 9 5/60 = (540+5)/60 = 545/60
Area = L*w
L = 545/60 feet
W = 12 feet
Area = 545/60 * 12
Area = 545*12/60
Area = 545 /5 = 109 square feet.
Answer:
109
Step-by-step explanation:
A large office desk has an area of 42 ft2. If the width is 3.5 feet write an equation to represent the area
Answer:
Step-by-step explanation:
A = L * W
A = 42
W = 3.5
now sub
42 = 3.5L <=== ur equation
When you roll two number cubes, what are the odds in simplest form against getting two numbers greater than 3?
A. 4:1
B. 1:4
C. 3:1
D. 1:3
PLEASE ANSWER
Option B
When you roll two number cubes, the odds in simplest form against getting two numbers greater than 3 is 1 : 4
Solution:The probability of an event is given as:
[tex]\text {probability of an event }=\frac{\text { number of favorable outcomes }}{\text { total number of possible outcomes }}[/tex]
Given that,
Tow number cubes are rolled
To find: Probability of getting two numbers greater than 3
On a number cube there are 6 numbers {1, 2, 3, 4, 5, 6} Out of which 3 numbers are greater than 3 {4, 5, 6}
So, total number of possible outcomes = 6
Favourable outcomes = number greater than 3 = 3
When you roll one number cube, probability of getting number greater than 3:
[tex]\text { Probability (number greater than } 3 \text { ) }=\frac{3}{6}[/tex]
When you roll two number cubes, probabilty is given as:
[tex]\text { Probability (number greater than }3)= \frac{3}{6} \times \frac{3}{6}=\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}[/tex]
[tex]Probability = \frac{1}{4}[/tex]
In ratio form we can write as 1 : 4
Option B is correct
Answer:
Actually... It's A
Step-by-step explanation:
Odd against is not 1:4, it's most likely 4:1
1:4 is odds in favor, not odds against.
The area of one rectangle is 36 square
feet. The area of a second rectangle is
21 square feet. The rectangles have the
same width and the dimensions are
whole numbers. What is the width of
both rectangles?
Answer:
The width of both rectangles are [tex]\frac{36}{l},\frac{21}{L}[/tex].
Step-by-step explanation:
Given : The area of one rectangle is 36 square feet. The area of a second rectangle is 21 square feet. The rectangles have the same width and the dimensions are whole numbers.
To find : What is the width of both rectangles?
Solution :
According to question, the two rectangles have the same widths but they have different lengths.
Let the width of both rectangle be 'w'
Let the length of one rectangle be 'l'
Let the length of second rectangle be 'L'
The area of the rectangle is [tex]\text{Area}=\text{Length}\times \text{Width}[/tex]
The area of one rectangle,
[tex]36=l\times w[/tex]
[tex]w=\frac{36}{l}[/tex]
The area of second rectangle,
[tex]21=L\times w[/tex]
[tex]w=\frac{21}{L}[/tex]
The width of both rectangles are [tex]\frac{36}{l},\frac{21}{L}[/tex].
A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 40 books. A total of 8 boxes were sent which can hold 260 books altogether. Determine the number of small boxes sent and the number of large boxes sent.
Answer:
5 large boxes
3 small boxes
Step-by-step explanation:
Create two equations to represent the problem.
let "a" be the number of small boxes
let "b" be the number of large boxes
20a + 40b = 260 This equation shows the numbers of books
a + b = 8 This equations shows the number of boxes
Solve the system of equations (solve for a and b). We can solve using the substitution method.
Rearrange a + b = 8 to isolate one of the variables.
a = 8 - b New equation that represents "a"
Since we know an equation for "a", we can substitute what "a" equals into the other equation. There will only be one variable in the equation, so we can solve by isolating. Isolate by doing reverse operations.
Substitute "a" for 8 - b
20a + 40b = 260
20(8 - b) + 40b = 260 Distribute 20 over the brackets by multiplying
160 - 20b + 40b = 260 Collect like terms (numbers with same variables)
160 + 20b = 260 Start isolating "b". Subtract 160 from both sides
20b = 260 - 160
20b = 100 Divide both sides by 20
b = 5 Number of large boxes
Substitute "b" for 5 in the simplest equation
a + b = 8
a + 5 = 8 Subtract 5 from both sides to isolate "a"
a = 8 - 5
a = 3 Number of small boxes
Therefore there were 5 large boxes and 3 small boxes sent.
Answer:
s = the number of small boxes
L = the number of large boxes
System of Equations:
25s+40L=250
s+l=7
Step-by-step explanation:
graph the function y=1/7x+2
Answer:
x - 0, 1
y - 2, 15/7
HEEEEELLLPPPP!!! I really need this to be answered im soo confused!!
Answer:
C
Step-by-step explanation:
∠ AFD = ∠ AFC + ∠ CFD
Given ∠ CFA = 90° and
∠ CFD = 90° - ∠ EFD, that is
∠ CFD = 90° - 62° = 28°, thus
∠ AFD = 90° + 28° = 118° → C
Answer:
answer is c. 118
angle AFC+ angleCFD = angle AFD..
[ANGLE AFD =AFC + CFD][ANGLE CFD = 90 -62 ]
i need help. i dont understand-
Answer:
39 degrees
Step-by-step explanation:
The square indicates a right angle, or 90 degrees. 90-51=39.
7=1/3(8x+3)
Solve for x in simplest form
Answer:
x=2 1/4
Step-by-step explanation:
Let's swap it around so its 1/3(8x+3)=7
Now you multiply both sides by 3 to make it 1(8x+3)=21
That means its 8x+3= 21
Subtract both sides by 3 to get rid of it
Now you have 8x=18
Which equals to x= 18/8
Which equals 2 1/4
Which of the equations listed below are linear equations
C=2 pie r
A= pie r squared
V=4/3 pie rcubed
Answer:
[tex]\large\boxed{C=2\pi r}[/tex]
Step-by-step explanation:
A linear equation is an equation in which a variable is in the first power.
The formula of a Circumference of a circle
[tex]C=2\pi r\\\\2,\ \pi-\text{numbers}\\r-\text{variable}\\\\\boxed{\bold{YES}}[/tex]
The formula of an Area of a circle
[tex]A=\pi r^2\\\\\pi-\text{number}\\r^2-\text{variable in the second power}\\\\\boxed{\bold{NO}}[/tex]
The formula of a volume of a sphere
[tex]V=\dfrac{4}{3}\pi r^3\\\\\dfrac{4}{3},\ \pi-\text{numbers}\\r^3-\text{variable in the third power}\\\\\boxed{\bold{NO}}[/tex]
How do you find the slope of a line? Answer it in your OWN OPINION.
You divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
Best of Luck to you.
A young sumo wrestler decided to go on a special diet to gain weight rapidly
W represents the wrestlers weight (in kilograms) after t months
W=80+5.4t
What was the wrestlers weight before his special diet
The weight of wrestler was 80 kg before the special diet
Step-by-step explanation:
Given function is:
[tex]W=80+5.4t[/tex]
We can substitute the values of t to find the weight after t number of months
When we have to find the initial weight , t has to be put equal to zero
So,
[tex]W = 80+5.4t\\t = 0\\W = 80 + 5.4(0)\\W = 80+0\\W = 80[/tex]
Hence,
The weight of wrestler was 80 kg before the special diet
Keywords: Functions, variables
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Answer:
80
Step-by-step explanation:
i'm not sure but the answer for people on khan
Using V = lwh, what is an expression for the volume of the following rectangular prism?
The dimensions of a prism are shown. The height is StartFraction 5 Over 2 x + 8 EndFraction. The depth is StartFraction x + 4 Over 4 EndFraction. The length is StartFraction 12 Over x EndFraction.
StartFraction 15 Over 2 x EndFraction
StartFraction 3 x + 12 Over 2 x + 8 EndFraction
StartFraction 15 Over 2 x + 2 EndFraction
Fifteen-eighths
Answer:
Volume of the rectangular prism is given by,
[tex]\frac {15}{2x}[/tex] unit .
Step-by-step explanation:
According to the question,
height of the prism = [tex]\frac {5}{2x + 8}[/tex] unit = h (say)
depth of the prism = [tex]\frac {x + 4}{4}[/tex] unit = w (say)
length of the prism = [tex]\frac {12}{x}[/tex] unit = l (say)
So,
the volume of the rectangular prism,
V = lwh
= [tex]\frac {5}{2x + 8} \times \frac {x + 4}{4} \times \frac {12}{x}[/tex] unit
= [tex]\frac {15}{2x}[/tex] unit
Answer:
A
Step-by-step explanation:
what is the inverse of g (x)=2x-3
Answer:
g^-1 (x)=1/2x+3/2
Step-by-step explanation:
y=2x-3
x=2y-3
2y=x+3
y=1/2x+3/2
How many solutions does the system have?
x=y-2
-3x+3y=6
Answer:
Infinitely many solutions.Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x=y-2&(1)\\-3x+3y=6&(2)\end{array}\right\qquad\text{substitute (1) to (2)}\\\\-3(y-2)+3y=6\qquad\text{use the distributive property}\\-3y+6+3y=6\qquad\text{combine like terms}\\(-3y+3y)+6=6\\6=6\qquad\bold{TRUE}\\\\\text{That is why the system of equations has infinitely many solutions.}[/tex]
At the start of the month, Jodie had sold 885 copies of her new book. At the end of the month, she had sold 1,364 copies of her book. If each book profits $13.97, approximately how much did the book profit in the entire month? A. $6,706 B. $31,486 C. $19,096 D. $12,390
Option B
Profit earned in the entire month is $ 31486
Solution:
Given that At the start of the month, Jodie had sold 885 copies of her new book
At the end of the month, she had sold 1,364 copies of her book
Each book profits $13.97, approximately
To find: profit earned in entire month
Total books earned = 885 + 1364 = 2249
Profit earned from 1 book = $ 13.97 ≈ 14
Therefore profit earned from 2249 books is found by multiplying profit earned from 1 book by 2249
profit earned from 2249 books = Profit earned from 1 book x 2249
profit earned from 2249 books = 14 x 2249 = 31486
Therefore profit earned in the entire month is $ 31486