Answer:
[tex]this \: proberbility \: is \: \frac{2}{5} [/tex]
Find the volume common to two spheres, each with radius r, if the distance between their centers is r/2. [Hint: It may be helpful to look at the previous question and see how it relates to this one. ] intersectingspheres
Answer:
The volume common to two spheres is [tex]V=\frac{27 \pi r^3}{32}[/tex]
Step-by-step explanation:
Let r be the radius of each sphere
We are given that distance between their centers is [tex]\frac{r}{2}[/tex]
Let [tex](\frac{-r}{4},0)[/tex] be the center of sphere 1 and [tex](\frac{r}{4},0)[/tex]be the center of sphere 2 .
Using the disk points
a=0 and b =[tex]\frac{3r}{4}[/tex]
[tex](x+(\frac{r}{4}))^2+y^2=r^2\\V=2 \int_{0}^{\frac{3r}{4}} \pi y^2 dx\\V=2 \int_{0}^{\frac{3r}{4}} \pi [r^2-(x+(\frac{r}{4}))^2]dx\\V=\frac{27 \pi r^3}{32}[/tex]
Hence the volume common to two spheres is [tex]V=\frac{27 \pi r^3}{32}[/tex]
In attached diagram, we can see 2 circumferences with radius r, and separated centers by r/2.
The solution is:
V = (11/12)×π×r³
Let´s call circumferences 1 and 2, by symmetry, rotating area A will produce a volume V₁ identical a V₂, Obtained by rotating area B ( both around x-axis), then the whole volume V will be:
V = 2× V₁
V₁ = ∫π×y²×dx (1)
Now
( x - r/2)² + y² = r² the equation of circumference 1
y² = r² - ( x - r/2)²
Plugging this value in equation (1)
V₁ = ∫π×[ r² - ( x - r/2)²]×dx with integrations limits 0 ≤ x ≤ r/2
V₁ = π×∫ ( r² - x² + (r/2)² - r×x )×dx
V₁ = π× [ r²×x - x³/3 + (r/2)²×x - (1/2) ×r×x²] evaluate between 0 and r/2
V₁ = π× [(5/4)×r²×x - x³/3 - (1/2) ×r×x²]
V₁ = π× [(5/4)×r² × ( r/2 - 0 ) - (1/3)×(r/2)³ - (1/2) ×r×(r/2)²]
V₁ = π× [ (5/8)×r³ - r³/24 - r³/8]
V₁ = π× (11/24)×r³
Then
V = 2× V₁
V = 2×π×11/24)×r³
V = (11/12)×π×r³
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I WILL GIVE BRAINLIEST
All of the following statements describe the relation shown except _____.
The diagram represents a function.
The inputs are {-1, 0, 3, 4}.
The outputs are {-2, -1, 1}.
This relation could also be represented as {(-1, 1), (0, -2), (3, 1), (4, -1)}.
Answer:
132
Step-by-step explanation:
Answer:
{-1, 0, 3, 4}.
Step-by-step explanation:
sorry if this is incorrect
There is no options to choose from and I need to find slope help due today
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
To find the slope we need two points.
A = ( -2 , 5 ) & B = ( 0 , 2 ) & C = ( 2 , -1 )
I choose A and B .
_________________________________
We have following equation to find the slope using two points.
[tex]slope= \frac{y(B) - y(A)}{x(B) - x(A)} \\ [/tex]
Now just need to put the coordinates in the above equation.
Let's do it...
[tex]slope = \frac{2 - 5}{0 - ( - 2)} \\ [/tex]
[tex]slope = \frac{ - 3}{2} \\ [/tex]
[tex]slope = - \frac{3}{2} \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
I suggest to find the slope using A , C
and B , C to can understand exactly what did I do buddy.
Good luck ♥️♥️♥️♥️♥️
If there are 9 rows of seats with 18 seats in each row there are also 6 rows of seats with 24 seats in each row how many seats are there in the auditorium
Answer:
306
Step-by-step explanation:
The number of rows times the number of seats in each row is equal to the stadium chair. Using this, 9 rows of seats with 18 seats in each row is 9(18) and 6 rows with 24 seats in each row is 6(24). Now we add 9(18) + 6(24), which is 162 + 144 which is 306 seats
What is the value of the unknown in the equation 3m + 7 = - 23?
Answer:
Step-by-step explanation:
3m + 7 = - 23
we pass the -7 to the right with a positive sign
3m = -23 - 7
we perform the sum of negative numbers
3m = -30
we pass the -3 to the right to divide
m = -30/3
we perform the division
m = -10
ignore the black words on the bottom but i’ll be giving brainliest!
Answer:
2. the figure has rotatinal symetry
Step-by-step explanation:
Answer:
1. x = 4; y = 7
2. rotational symmetry.
3. No. 360°÷ 50° is not a whole number, so the points will not be evenly spaced all the way around the center.
Step-by-step explanation:
hi again ♡
Form a polynomial function f(x) with the given degree and zeros. You can leave your answer in factored form.
Degree 7; zeros: -7, i, 3-1, -6i
Answer:
Your search - Form a polynomial function f(x) with the given degree and zeros. You can leave your answer in factored form. Degree 7; zeros: -7, i, 3-1, -6i - did not match any image results.
Suggestions:
Make sure all words are spelled correctly.
Try different keywords.
Try more general keywords.
Try fewer keywords.
write a verbal expression for x + y
(6. 10)
Ka, 8)
(4.b)
(2.2)
a. What is the slope of the line? Type the answer in the box below.
The slope of the ines
HELP ASAP I don’t get it
Answer:
-11/5
Step-by-step explanation:
In order to solve it u should open the mixed fraction ,i.e,
11/7÷-15/21
=11/7×-21/15
Cutting,
ans=-11/5
Mark me the brainliest
Answer:
Fraction: -11/5
Decimal form: -2.2
Mixed number form: -2 1/5
Step-by-step explanation:
Complete the function using the function y=-2x -6
-2
0
2
4
Helpppppppppppppppppppppppppppppppppppp
if the slope of ac 6 what is the slope of bc
Which equation could be used to generate the following table?
x y
-2 7
-1 6
0 5
1 4
2 3
a
y = -x + 5
b
y = x + 5
c
y = 5x - 1
d
y = -x - 5
Answer:
ur welcome
Step-by-step explanation:
x is first so -2 and -1 and 0 and 1 and 2 all cancel each other out so no worries there then on to the other side you add it all and boom you done
NEED HELP PLEASE !
Can you conclude that the following is a rhombus, rectangle, or square?
A parallelogram's diagonals form eight congruent angles at the vertices.
In a square, opposite sides are parallel, all sides are equal, and the angles made by the diagonals are equal, that is 45°.
What is a parallelogram?It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal.
In a rectangle, opposite sides are parallel and equal, but the angles made by the diagonals are different.
In a rhombus, opposite sides are parallel and all sides are equal, but the angles made by the diagonals are different.
In a square, opposite sides are parallel, all sides are equal, and the angles made by the diagonals are equal, that is 45°.
More about the parallelogram link is given below.
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A rectangle is dilated using a scale factor of 6. The
image is then dilated using a scale factor of 1/3. What
scale factor could you use to dilate the origianl
rectangle to get the final rectangle? Explain.
9514 1404 393
Answer:
2
Step-by-step explanation:
The second rectangle's dimensions are 1/3 of those after they were multiplied by 6, so are (6)(1/3) = 2 times the original dimensions.
A scale factor of 2 could be used to get the final rectangle.
Find the value of x.
Answer:
27=x
Step-by-step explanation:
Although it looks slanted, it is an 90 degree angle. Let's make an equation.
90= 55+x+8
90= 63+x
-63 -63
27=x
hope this helps!
Answer:
27
Step-by-step explanation:
180-90=90
90-55=35
35=x+8
X=27
The age of earth’s crust is 5 · 10^9 years. Express this number as an integer.
Answer:
5,000,000,000 (see below)
Step-by-step explanation:
Integers are whole numbers and their opposites. That doesn't include fractions or decimals, even if they're negative. Being negative doesn't do anything, really.
For example, 5 and –5 are integers, but 5.1 or –5.3 are not integers. They're decimals, which means they're rational.
Integers also include 0.
Whole numbers do not include 0, so they're only 1, 2, 3, 4, 5, 6, 7, 8, 9 . . . and so on.
All whole numbers are integers.
So in order to find 5 × [tex]10^{9}[/tex] as an integer, you'll have to multiply the 5 and [tex]10^{9}[/tex] together.
[tex]10^{9}[/tex] is simply nine zeros, so it's: 1,000,000,000.
5 × 1,000,000,000 = 5,000,000,000
5,000,000,000 is not a decimal or fraction—and it also isn't negative. That means it's a whole number. Which qualifies it as an integer as well.
(y^3)^2 without exponents
Answer:
y^6
Step-by-step explanation:
Answer:
[tex]y^{6}[/tex]
Step-by-step explanation:
Step 1:
( y³ )² Equation
Step 2:
[tex]y^{3 * 2}[/tex] Multiply
Answer:
[tex]y^{6}[/tex]
Hope This Helps :)
Which expression is equivalent to 32 ⋅ 3−5?
Answer:
91
Step-by-step explanation:
Using the PEMDAS method (parentheses exponenets multiplication division addition subtraction), we know that since 3-5 is not in parentheses, we have to multiply before we subtract. So first, we must multiply 32 x 3 to get a product of 96. Then we must subtract, 96 - 5 = 91. Therefore, your answer is 91.
Hope this helped! Good luck!
Solve the simple equation.
5(2d+2) = 3 (8d-5)
Answer:
d = 25/14
Step-by-step explanation:
5(2d+2) = 3 (8d-5)
10d + 10 = 24d - 15 | +15
10d + 25 = 24d | - 10d
25 = 14 d | :14
d = 25/14
Ruben bought 666 comic books for \$21$21dollar sign, 21. Each comic book was the same price. What was the cost for 111 comic books?
Answer:
Each comic book is $3.30
Step-by-step explanation:
$21 divided by 6= $3.50
Answer:
Each comic book is $3.30
Step-by-step explanation:
$21 divided by 6= $3.50
7. A fish tank hold 100 gallons of water and is losing water at a rate of 1 gallons per hour. A second fish tank
contains 40 gallons of water is having 2 gallons added per hour. After how many hours will the first tank
have less water than the second? Which inequality represents the situation?
a. 100+ h > 40 - 2h
c. 40-h > 100 + 5h
b. 100-h< 40 + 2h
d. 100-h > 40 + 2h
OA
OB
ОС
D
D
Question 8
My
Answer:
B
Step-by-step explanation:
the first fish tank has 100 gallons of water and 1 gallon is removed every hour which makes 100-h
the second tank has 40 gallons in it and 2 gallons are added every hour which makes 40+2h
after 20 hours the second tank will have more gallons than the first tank
this means that 40+2h would be greater than 100-h since it's also asking you "After how many hours will the first tank have less water than the second?"
Which is a factor of
25
x
2
−
40
x
+
16
?
A.
5
x
−
4
B.
5
x
+
8
C.
5
x
+
4
D.
5
x
−
8
Answer:
OOOOOOOOOOOOOO9ONOOOOOOOOOOOORewrite the following expression: x^-7
the heights of adult males are approximately normally distributed with a mean of 70 inches and a standard deviation of 3 inches. an adult male is categorized as shirt if he is less than 64 inches tall and categorized as tall if he is in the top 2% of adult males in term of height. how tall does an adult make need to be to be assigned to the tall category.
Answer:
76.2
Step-by-step explanation:
Use a calculator or chart to find the z-score associated with the probability.
P(Z > z) = 0.02
P(Z < z) = 0.98
z = 2.054
Find the height.
z = (x − μ) / σ
2.054 = (x − 70) / 3
x = 76.2
2d + 7 = 9
Hellllllpppppp
Answer:
Doesn't 2+7 = 9 itself?
Step-by-step explanation:
George is 2 in. taller than the quotient of Myron's height and 3. Let M represent Myron's height, in inches. Write an expression that represents George's height, in inches.
Answer:
G = M/3 + 2
Step-by-step explanaion
We can interpret the quotient of Myrons height and 3 as "M/3" and we add "+2" to account for the "2 in. taller" part of the problem. We can also represent George's height using "G"
The expression that represents George's height, in inches is G = M/3 + 2
What is algebra?
Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
Given:
George is 2 in. taller than the quotient of Myron's height and 3.
let M represent Myron's height, in inches.
and, the quotient of Myrons height and 3 can be written as
=M/3
Now, add 2 to Myron's height.
Then George's height will be
G = M/3 + 2
Learn more about algebra here:
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Find values of a and b that make both equalities true: a/b = 2/5 and 22/a = 11/6 .
Answer:
a=32b=80Step-by-step explanation:
Find values of a and b that make both equalities true:
a/b = 2/5 and 22/a = 11/6 .
given that 22/a=11/16
cross multiply
11a=22x16
11a=352
a=352/11
a=32
put a=32 in a/b = 2/5 to find b we have
32/b=2/5
cross multiply we have
2b=32x5
2b=160
divide both sides by 2 we have
b=160/2
b=80
Answer:
Step-by-step explanation:
First, we will start by solving: 22/a = 11/6
Solving for a
We can first cross multiply and we get this: 22 x 6 = 11a, Simplified it would be 132 = 11a. Now we know that a = 12.
Solving for b
Now knowing a = 12 we can get this. 12/b = 2/5 same thing, cross multiply. That would be: 12 x 5 = b x 2, Simplified: 60 = 2b so b = 30
Order these numbers from least to greatest.
8.506, 8.6, 8.5612, 8.56
Answer:
It goes 8.506, 8.56, 8.5612, 8.6
Happy to Help