A sphere with a 2-inch radius is packed in a cube so that all sided touch. How much empty space is left in the cube?.
The volume of the empty space is 30.49 cubic inches if the sphere with a 2-inch radius is packed in a cube so that all sided touch.
What is a cube?It is defined as three-dimensional geometry that has six square faces and eight vertices.
We have a sphere with a 2-inch radius is packed in a cube so that all sided touch.
The volume of the sphere = (4πr³)/3 = (4π(2)³)/3 = 33.51 cubic inches
The side length of the cube = 4 inches
Because diameter of the sphere is 4 inches and all sided touch to the cube face.
Volume of the cube = 4³ = 64
The volume of the empty space = 64- 33.51 = 30.49 cubic inches
Thus, the volume of the empty space is 30.49 cubic inches if the sphere with a 2-inch radius is packed in a cube so that all sided touch.
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Look at the following four expressions:
Expression A: (14647 + 2956) ÷ 6
Expression B: 6 x (14647 + 2956)
Expression C: (14647 + 2956) + 6
Expression D: (14647 + 2956) − 6
Which expression has the least value? (1 point)
Group of answer choices
Expression A
Expression B
Expression C
Expression D
Answer:
Expression D has the least value
Find arc QT.
Answers are:
A.71
B.23
C.46
D.142
Answer:
d)142º
Step-by-step explanation:
[tex]\widehat{AB}=2\times71\º=142\º[/tex]
How many solutions are there to the equation below?
6x +33 = 6(x+6)
Answer:
no solution
Step-by-step explanation:
6x + 33 = 6x + 36
33 ≠ 36
Answer:
no solutions
Step-by-step explanation:
6x + 33 = 6(x + 6) ← distribute parenthesis
6x + 33 = 6x + 36 ( subtract 33 from both sides )
6x = 6x + 3 ( subtract 6x from both sides )
0 = 3 ← not possible
This indicates the equation has no solution
]
How do I find the radius/x of a shaded region with it's area and/or angle measurement?
Answer:
[tex]x \approx 9.823\ ft[/tex]
Step-by-step explanation:
Remember that the area of a sector is defined as:
[tex]A = \frac{\theta}{360^\circ}\times \pi r^2[/tex]
In this problem, we are given the area [tex]A[/tex], and the angle [tex]\theta[/tex]. We can set up an equation to solve for the radius, which is x:
[tex]A = \frac{\theta}{360^\circ}\times \pi r^2\\128 = \frac{152}{360}\times \pi r^2\\128 \times \frac{360}{152} = \pi r^2\\\frac{5760}{19} = \pi r^2\\r = \sqrt{\frac{5760}{19 \pi}}\\r \approx 9.823[/tex]
Answer:
r ≈ 9.8 feet
Step-by-step explanation:
Formula of A Sector
Area (Sector) = πr² × θ/360°Substitute the given values in the formula to find r.
128 = 3.14 × r² × 152/36040.76 = r² × 19/45r² = 1834.2/19r² = 96.54r ≈ 9.8 feet'the largest prime number that is a factor of 42'
is multiplied by
'the smallest prime number that is a factor of 28'
Answer:
14.
Step-by-step explanation:
42 = 2 8 3 * 7
Largest prime factor = 7
28 = 2 * 2 * 7
Smallest prime factor = 2
Answer = 2*7 = 14.
.To help him start a business, Cameron took out a $10,000 loan from a bank. The loan has an annual interest rate of 5%. What expectation should Cameron have?
Answer:
[tex]A = 10,000(1.05t)[/tex] where t is in years
Step-by-step explanation:
I'm going to assume that the expectation that Cameron has is the amount of money after t years.
We can use the simple interest formula [tex]A = P(1+rt)[/tex] where A is the final amount, P is the principal, r is the rate, and t is time.
We can plug in 10,000 for P and 0.05 for r, giving us
[tex]A = 10,000(1.05t)[/tex]
Determine if the sequence is arithmetic. If it is, find the common difference.
1) 35, 32, 29, 26, ...
2) -3, -23, -43, -63, ...
Answer:
1) yes--common difference is 3.
what is the absolute value of 62
Answer:
62, since positive doesn't change to negative.
I would like help :)
Answer:
diameter - B
central angle - E
radius - A
tangent - D
minor arc - F
chord - C
Complete the table by giving the length and area for each
width. (The width is the side perpendicular to the building.)
width (feet) length (feet)
area (square feet)
10
30
40
W
of the play area
The values of length are 100, 60, and 40 feet respectively, area of the rectangle 1000 square feet, 1800 square feet, and 1600 square feet respectively.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We know the perimeter of the rectangle = 2(w+l)
The sum of w+w+l = 120 (given)
2w + l = 120
From the above equation, we can calculate the l of the rectangle:
We have w = 10 feet
l = 100 feet
Area = 10×100 = 1000 square feet
When w = 30
l = 60 feet
Area = 60×30 = 1800 square feet
When w = 40
l = 40 feet
Area = 40×40 = 1600 square feet
Thus, the values of length are 100, 60, and 40 feet respectively, area of the rectangle 1000 square feet, 1800 square feet, and 1600 square feet respectively.
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Evaluate: (-2)5
0-10
O 10
O-32
32
Answer:
By multiplying -2 by 5 you get:
Step-by-step explanation:
- 10
Find the center and radius of the circle represented by the equation below.
Find the length of the third side. If necessary, round to the nearest tenth.
Write an expression to represent:
"5 times the sum of 12
and a number"
5 (12 + x)
Step-by-step explanation:
Answer:
5(12+X)
Step-by-step explanation:
Help please i only have 5 mins left on my test please answer this
P(Head, Diamond AND Head, Heart) = ?
Using it's concept, it is found that the desired probability is given by:
P(Head, Diamond AND Head, Heart) = 1/64.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, each outcome is equally as likely, having a 1/8 probability, and they are independent.
Then:
P(Head, Diamond AND Head, Heart) = 1/8 x 1/8 = 1/64.
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PLEASE HELP FAST, I'LL MARK YOU AS BRAINLIST
Marcus walks halfway around a square gym with an area of 90,000m². How far did he walk
P+d= 19 9p+ 5.50d= 150 solve the system of equations , step by step
Answer:
d=6 & p=13
Step-by-step explanation:
1. P+d=19
×9
2. 9p +5.50d=150
×1
9p+9d=171
-
9p +5.50d=150
3.5d=21
d=6
Substituting d=6 in 1.
P+6=19
P=13
how to find slope within two sets of points
The slope within two sets of points is calculated using the slope equation [tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
What is slope?The slope of a line or points is the rate of change of the line.
This in other words means that, the vertical change per unit horizontal change
Assume that the points are given as:
(x1, y1) and (x2, y2)
The slope (m) of the points is:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
Hence, the equation of two sets of points is [tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
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For items 6-8
Write IMPOSSIBLE, UNLIKELY, AS LIKELY AS UNLIKELY, LIKELY and CERTAIN to describe each of the following statements.
6. ___________ The sun will rise tomorrow. (CAPSLOCK ALL LETTERS)
Answer: ________________
7. __________ Bats are birds. (CAPSLOCK ALL LETTERS)
Answer: __________________
8._________ The weather forecast says there is 50% chance of rain today, (CAPSLOCK ALL LETTERS
Answer: _________________
NONSENSE REPORT
A computer generates 50 integers from 1 to 8 at random. The results are recorded in this table.
Outcome 1 2 3 4 5 6 7 8
Number of times outcome occurred
5 8 9 7 4 6 5 6
What is the experimental probability of the computer generating a 2 or a 4?
12%
15%
22%
30%
The experimental probability of the computer generating a 2 or a 4 is 30% option fourth is correct.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
A computer generates 50 integers from 1 to 8 at random.
Total number of outcomes = 5+8+9+7+4+6+5+6 = 50
Computer generating a 2 = 8
Computer generating a 4 = 7
P(computer generating a 2) = 8/50
P(computer generating a 4) = 7/50
P(computer generating a 2 or a 4) = 8/50 + 7/50 = 15/50 or
= 0.3×100
= 30%
Thus, the experimental probability of the computer generating a 2 or a 4 is 30% option fourth is correct.
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I need an answer for this:
stirring a hot cup of tea causes a metal spoon to get warm which statement best explains why the spoon gets warm?
Answer:
here we go
Step-by-step explanation:
Stirring a cup of hot tea causes a metal spoon to get warm. Which statement best explains why the spoon gets warm? Heat energy transfers from the hot tea to the spoon.
Answer:
The molecules at the end of the spoon, in turn, collide with the molecules in the adjacent, cooler part, passing the kinetic energy on. This continues through the spoon until the handle molecules are also heated.Step-by-step explanation:
Stay safe, stay healthy and blessed.Have a good day !Thank youJeremy finished 3/5 of his homework what percent of homework did he finish
Answer:
60%
Step-by-step explanation:
Percent means per hundred. Change to "per hundred"
3/5 = 6/10 = 60/100
3/5 is 60%
OR
Divide 3/5 means 3÷5...
3÷5 = .6
Change decimal to percent by multiplying by 100.
.6 × 100 = 60
60%
Answer:
60%
Step-by-step explanation:
well if they only finished 3/5 it’s going to be
60/100 = 60%
General rule nth term)
6;11;16; 21; .....
Answer:
The rule is increase by 5. That means the next term would be 26.
A company that makes boxes finds that 7 out of 25 boxes are damaged. What percent of the boxes are damaged
Answer:
15%
Step-by-step explanation:
see the picture for explanation
Answer:
28%.
Step-by-step explanation:
That would be 100 * 7/25
= (100/25) * 7
= 4*7
= 28.
What is the circumference of this circle, in millimeters? use startfraction 22 over 7 endfraction for pi. a circle with radius 49 millimeters. 154 308 484 968
The circumference of the circle with a radius of 49mm is 308mm
How to find the circumference of a circle?The circumference of the circle is also known as its perimeter. The formula is expressed as:
C = 2pi r
r is the radius = 49mm
pi = 22/7
Substitute
C = 2 * 22/7 * 49
C = 2 * 22 * 7
C = 308mm
Hence the circumference of the circle with a radius of 49mm is 308mm
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Answer:
B
Step-by-step explanation:
How far does the unicycle move if the wheel turns once?
Pierre enters a 100m unicycle race. How many times must the wheel rotate completely in order for Pierre to travel 100m?
The unicycle would move 2.512 meters if the wheel turns once
The wheel needs to rotate completely 40 times in order for Pierre to travel 100m
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
a) The circumference of the wheel = π * diameter = 3.14 * 80 cm = 251.2 cm = 2.512 m
The unicycle would move 2.512 meters if the wheel turns once
b) For a 100m race:
Number of wheel rotation = 100 m / 2.512 m = 39.8
The wheel needs to rotate completely 40 times in order for Pierre to travel 100m
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2. What is the solution of matrix equation
[2 7
1 4] x=[2 5]
Answer:
(d) X = [-27, 8]
Step-by-step explanation:
The solution to the matrix equation can be found by left-multiplying both sides of the equation by the inverse of the coefficient matrix.
AX = B . . . . given
X = A⁻¹B
__
[tex]X=\left[\begin{array}{cc}2&7\\1&4\end{array}\right]^{-1}\left[\begin{array}{c}2\\5\end{array}\right] =\left[\begin{array}{cc}4&-7\\-1&2\end{array}\right]\left[\begin{array}{c}2\\5\end{array}\right] \\\\X=\left[\begin{array}{c}-27\\8\end{array}\right][/tex]
_____
Additional comment
A calculator or spreadsheet can help with this. The solution can also be found by row-reducing the augmented matrix.
What is the median of this data set?
22, 37, 49, 15, 72
А. 39
В. 37
С. 47
D. 49
Find the measure of each side of a square
that has an area of 225 square centimeters.