A rectangular prism with a volume of 101010 cubic units is filled with cubes with side lengths of \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction unit.
How many \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction unit cubes does it take to fill the prism?
Answers
now, we're assuming that the prism has a volume of 10³ and is filled with cubes of sides 1/2 long, Check the picture below.
now notice the bottom-right part of the picture, if we put two small cubes next to each other, they add up to 1, so to get 10 units from that, we'll need 20 of those halves, or 20/2 = 10, meaning we'll need 20 cubes side by side to make a length of 10 horizontally.
The same will be true for getting cubes to make up 10 vertically, we'll need 20, the same is true to fill up from back to front, we'll need 20 cubes.
so we can say that the rectangular prism will need 20 cubes from front to back, 20 horizontally and 20 vertically, that'll be 20*20*20 cubes, or 20³ or 8000 cubes.
mind you that we used a Cube for the prism, but the same will be true if we were to rearrange the cubes and make the prism taller or wider, same 8000 cubes will fill it in.
Related Questions
How do I find the equation of the perpendicular bisector between (-2,5) and (2,-1)?
Answers
Answer:
[tex]y = \frac{2}{3} x + 2[/tex]
Step-by-step explanation:
Start by finding the slope of the given line.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope of given line
[tex] = \frac{5 - ( - 1)}{ - 2 - 2} [/tex]
[tex] = \frac{5 + 1}{ - 4} [/tex]
[tex] = \frac{6}{ - 4} [/tex]
[tex] = - \frac{3}{2} [/tex]
A perpendicular bisector cuts through the line at its midpoint perpendicularly.
The product of the slopes of two perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
[tex] - \frac{3}{2} m = - 1[/tex]
[tex]m = - 1 \div ( - \frac{3}{2} )[/tex]
[tex]m = - 1 \times ( - \frac{2}{3} )[/tex]
[tex]m = \frac{2}{3} [/tex]
[tex]y = \frac{2}{3}x + c[/tex], where c is the y-intercept.
To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.
[tex]\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}[/tex]
Midpoint of given line
[tex] = ( \frac{ - 2+ 2}{2} , \frac{5 - 1}{2} )[/tex]
[tex] =( \frac{0}{2} , \frac{4}{2} )[/tex]
= (0, 2)
[tex]y = \frac{2}{3} x + c[/tex]
When x= 0, y= 2,
2= ⅔(0) +c
2= 0 +c
c= 2
Thus, the equation of the perpendicular bisector is [tex]y = \frac{2}{3} x + 2[/tex].
A bath tub drained at a constant rate. The table shows the number of gallons of water left in the tub after being drained for two amounts of time
Answers
The rate at which the water was drained from the tank is 6 gallons of water per minute (option A)
To know the speed at which the tank was drained, we must carry out the following operations:
Taking into account the information provided by the table we establish how much water has been drained from the tank in 20 minutes.
450 gallons - 330 gallons = 120 gallons.
Subsequently, we must divide the amount of water (120 gallons) that was drained by the time it was drained (20 minutes).
120 gallons ÷ 20 minutes = 6 gallons / minute.
According to the above, we can establish that the bath drain rate is 6 gallons / minute (option A).
Note: This question is incomplete because there is some missing information. Here is the complete information:
What is the rate at which the water was drained from the tank?
6 gallons of water per minute. 11 gallons of water per minute. 45 gallons of water per minute. 120 gallons of water per minute.
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4781/32 without a decimal
Answers
Answer:
149(13/32)
Step-by-step explanation:
4781/32 and then take the remainder to make it an improper fraction
A camper attaches a rope to the top of her tent to give it more support. She stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. About how tall is her tent?
Answers
Answer:
5.3
Step-by-step explanation:
8^2 - 6^2 = x^2
64 - 36 = x^2
28 = x^2
Square root of 28 is approx 5.3
1.5kg : 350g solve the ratio
Answers
Step-by-step explanation:
convert kg into grams
1kg=1000g
1.5kg/350g=1.5×1000g/350
1500/350=300/70
=30/7
ratio will be 30:7
answer is 4.2g
The answer to the ratio is:
4.2g
First of all, we need to convert the kg to g
This can be done by multiplying the Kg by 1000
1.5kg x 1000= 1500g
Next, we solve the ratio since they are in the same parameters
This would be 1500g:350g
1500/350= 30/7.
Therefore, the ratio would be 30:7
Finally when further broken down, it would be 4.2g
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a certain pharmaceutical company know that, on average 4% of a certain type of pill has an ingredient that is below the minimum strength and thus unacceptable. what is the probability that fewer that 5 in a sample of 20 pills will be acceptable?
Answers
Using the binomial distribution, it is found that there is a 0% probability that fewer that 5 in a sample of 20 pills will be acceptable.
For each pill, there are only two possible outcomes, either it is acceptable, or it is not. The probability of a pill being acceptable is independent of any other pill, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
The sample has 20 pills, hence [tex]n = 20[/tex].100 - 4 = 96% are acceptable, hence [tex]p = 0.96[/tex]The probability that fewer that 5 in a sample of 20 pills will be acceptable is:
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.96)^{0}.(0.04)^{20} = 0[/tex]
[tex]P(X = 1) = C_{20,1}.(0.96)^{1}.(0.04)^{19} = 0[/tex]
[tex]P(X = 2) = C_{20,2}.(0.96)^{2}.(0.04)^{18} = 0[/tex]
[tex]P(X = 3) = C_{20,3}.(0.96)^{3}.(0.04)^{17} = 0[/tex]
[tex]P(X = 4) = C_{20,4}.(0.96)^{4}.(0.04)^{16} = 0[/tex]
0% probability that fewer that 5 in a sample of 20 pills will be acceptable.
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HELP SOMEONE!!!!!! PLZZZZ!!!
Find all complex numbers $z$ such that $z^4 = -4.$
Answers
Since -4 = 4 exp(iπ), by DeMoivre's theorem and using the fact that cos and sin are both 2π-periodic,
[tex]z^4 = 4 \exp\left(i\pi\right) \implies z = 4^{1/4} \exp\left(\dfrac14 \left(i\pi + 2i\pi k\right)\right)[/tex]
where k = 0, 1, 2, or 3. Then the 4th roots of -4 are
[tex]k = 0 \implies z = 4^{1/4} \exp\left(\dfrac14 \left(i\pi+0\right)\right) = \sqrt2 \exp\left(i\dfrac\pi4\right)[/tex]
[tex]k = 1 \implies z = 4^{1/4} \exp\left(\dfrac14 \left(i\pi+2i\pi\right)\right) = \sqrt2 \exp\left(i\dfrac{3\pi}4\right)[/tex]
[tex]k = 2 \implies z = 4^{1/4} \exp\left(\dfrac14 \left(i\pi+4i\pi\right)\right) = \sqrt2 \exp\left(i\dfrac{5\pi}4\right)[/tex]
[tex]k = 3 \implies z = 4^{1/4} \exp\left(\dfrac14 \left(i\pi+6i\pi\right)\right) = \sqrt2 \exp\left(i\dfrac{7\pi}4\right)[/tex]
If [tex]f(x) = x[/tex]² [tex]-x+3[/tex], then what is the reaminder when [tex]f(x)[/tex] is divided by [tex]x+9[/tex]?
Answers
Answer:
Remainder is 93
Step-by-step explanation:
Use synthetic division:
-9 | 1 -1 3
____ -9 90
1 -10 | 93
Therefore, the remainder is 93
Salaar, Waleed and Muazzam share $ 256. Waleed;s share is four times as much as Salaar. And Salaar's share is one-third of muazzam's. How much is each of their share?
Answers
Answer:
S 32, W 128, M 96
Step-by-step explanation:
W = 4S
S = 1/3M, or 3S = M
S + W + M = 256
Substitute
S + 4S + 3S = 256
8S = 256, S = 32
S = 32
W = 4S = 128
M = 3S = 96
1 meter is equal to 100 centimeters or 1,000 millimeters. How many millimeters are in 2 meters, 17 millimeters?
Answers
Answer:
2,017
Step-by-step explanation: 2 meters= 2,000
So, 2,000+17= 2,017
2017 millimeters are in 2 meters, 17 millimeters as per the given unit conversion rate.
What is Unit conversion?A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).
Given, 1 meter is equal to 100 centimeters or 1,000 millimeters.
To calculate the total number of millimeters in 2 meters, 17 millimeters.
Since,
millimeters in 1 meter = 1000
Thus,
millimeters in 2 meter = 2000
millimeters in 2 meters, 17 millimeters = 2017
Therefore, there is 2017 mm in 2meteres, 17 mm as per the given unit conversion.
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71.841 to the nearest tenth
Answers
71.8
Step-by-step explanation:71.841:
The 4 represents the number that we'll be looking at since 4 is the next position to the right of 8, 8 is in the Tenths place. 4 is in the Hundredths place, and 4 will be the only number that could round up the 8.
How?In order to round, we need to remember how to round numbers:
If the digit is less than 5, the number to the left stays the same.If the digit is greater than, or equal to 5, the number to the left rounds up, or increases by 1. Solve:First, 4<5, meaning that 4 is less than 5.
#1 above is stating that the number to the left of 4 stays the same.
If we use that rule:
71.8 is our answer.
which holds the more capacity 0.75 litres or 350ml
Answers
Answer:
0.75 liters
Step-by-step explanation:
1000ml in 1 liter so 0.75*1000=750ml
750ml > 350ml
A police car leaves a crime scene heading east directly towards the hospital at 72 kilometres per hour. An ambulance leaves a quarter of an hour later and also heads directly east towards the hospital at 81 kilometres per hour. How long will it take for the ambulance to pass the police car?
Answers
It will take 2 hours for the ambulance to pass the police car.
Given that a police car leaves a crime scene heading east directly towards the hospital at 72 kilometers per hour, and an ambulance leaves a quarter of an hour later and also heads directly east towards the hospital at 81 kilometers per hour, to determine how long will it take for the ambulance to pass the police car, the following calculation must be performed:
72 x 0.25 = 18 81 - 72 = 9 18/9 = 2 72 x 0.25 + 72 x 2 = 162 81 x 2 = 162
Therefore, it will take 2 hours for the ambulance to pass the police car.
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There are 40 pupils in a class. 75% of them are present. How may are present? How many are absent?
with solution please :D
Answers
Answer:
30 are present 10 are absent
Step-by-step explanation:
75%=3/4
so 3/4 of them are absent
3/4(40)=30
and 40-30=10 are absent
Help help math math math
Answers
Answer:
pushin p
Step-by-step explanation:
pushin p
May has 10 sticker sheets with 8 stickers each and 15 pages with y stickers each. How many stickers does she have total.
A. (10 x 8) + (15y)
B 10 x ( 9 + 15 + y)
C. 10 + 8 + 15 + y
D, (10 x 15) + (8y)
Answers
Answer:
A
Step-by-step explanation:
Find the simple interest paid on a $200 investment at 4.4% annual interest for 60 days.
Answers
Step-by-step explanation:
hope it will help you...
more help... please... I'm very stuck
Answers
A) 5percent of 40=2 ( 0.05*40)
Since it’s increase add 2 to 40=42
F) 40percent of 25= 10 (0.4* 25)
25-10=15
PLEASE HELP WILL MARK BRAINIEST!!!!!
Answers
Answer:
a perpendicular line from a point on ab
Mrs. Lovejoy and Christi spent the day baking cookies. When they divided them into 8 stacks, they had 14 cookies in each stack. How many cookies did they have? Solve and label the word problem. Please I need help.
Answers
Answer:
they had 112 cookies
Step-by-step explanation:
14×8 = 112
Does the expressions
[tex] \sqrt{100 - 64} [/tex]
and
[tex] \sqrt{100 - \sqrt{64} } [/tex]
have the same value?
Answers
Answer:
No. they have a difference in value
the first ans is 6 while the second gives 9.56
The graphs below have the same shape. What is the equation of the blue graph?
G(x) =
O A. G(X) = x^2 + 1
O B. G(X) = (x - 1)^2
O C. G(X) = (x + 1)^2
O D. G(x) = x^2-1
Answers
Answer:
c) G(x) = (x + 1)**2
Step-by-step explanation:
A function left shift is x + shift and a right shift is x - shift.
Help help help help math math math math help
Answers
because 7 (14) + 9 is equal to 9 (14) - 19
Answer:
14
Step-by-step explanation:
because both sides need to be equal so if u plug in the 14 in x it gives you the same number for both sides 107.
A café has 60 tables. 35% of the tables have 2 chairs at each table. The remaining 65% of the tables have 4 chairs at each table. How many tables have 4 chairs?
Answers
The number of tables with 4 chairs are 39.
We have a café which has 60 tables. 35% of the tables have 2 chairs at each table. The remaining 65% of the tables have 4 chairs at each table.
We have to determine the number of tables having 4 chairs.
What is 10% of 250 ?The 10% of 250 will be -
[tex]\frac{10}{100} \times 250[/tex] = 25
According to question, we have -
Percentage of tables with 2 chairs = 35%
Percentage of tables with 4 chairs = 65%
Total number of tables = 60
Therefore -
Number of tables with 2 chairs = [tex]\frac{35}{100} \times 60[/tex] = 21
Therefore, number of tables with 4 chairs will be = 60 - 21 = 39
Hence, the number of tables with 4 chairs are 39.
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There are 39 tables that have 4 chairs.
i.e. the number of tables with 4 chairs is: 39.
Here, we have to find the number of tables that have 4 chairs, we first need to calculate how many tables have 2 chairs, and then subtract that number from the total number of tables.
Given that 35% of the tables have 2 chairs, we can calculate the number of tables with 2 chairs as follows:
Number of tables with 2 chairs = 35% of 60 tables
Number of tables with 2 chairs = 0.35 * 60
Number of tables with 2 chairs = 21 tables
Now, to find the number of tables with 4 chairs:
Number of tables with 4 chairs = Total number of tables - Number of tables with 2 chairs
Number of tables with 4 chairs = 60 tables - 21 tables
Number of tables with 4 chairs = 39 tables
So, there are 39 tables that have 4 chairs.
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1. Find the area of the sector by multiplying the area of the circle by the ratio of the _________________________ to 360.
2. Subtract the area of the triangle from the area of the sector.
length of the radius
length of the diameter
measure of the central angle
circumference of the circle
Answers
Answer: measure of the central angle
Step-by-step explanation: trust
Answer:
measure of the central angle
Step-by-step explanation:
evaluate the expression for h= -6.
Answers
Answer:
63-|-6| = 57
Step-by-step explanation:
63-|-6|
63-6
57
Answer:
57
Step-by-step explanation:
Substitute -6 for variable h.
[tex]63-|(-6)|\\63-6\\57[/tex]
Find the value of x need help
Answers
Answer:
x=-10
Step-by-step explanation:
since there's a given 120 degrees, and it's a isosceles triangle, we know that the line adds up to 180 (where the 120 degrees is). so 120+x=180, the interior angle measures 60 degrees. That being said, the 3 angles measure 60 degrees also. now there's a right angle mark on top, so we find the angle of the smaller triangle (near angle 2) by doing 90-60=30 degrees.
angle 2 is said to be x+160, and there's a line, which tells us that they must add to 180.. so x+160+30=180
x+190=180
x=-10.
Integer Exponents
#1: Simplify the expression below using properties of exponents. Write your
answer using positive exponents. *
5-2
Answers
Answer:
Step-by-step explanation:
5 - 2 cannot be further simplified? No properties of exponents can be used due to already knowing the answer of the top of your head, it could be a mistype though, or I'm just very very d*mb.
3x2 - 4x – 7
factor
Answers
Answer:
3x2 = 6
6-4x-7
(6-4x) - 7
2x - 7 = messi ok no xd
3.5-
Step-by-step explanation:
Answer:
[tex](3x-7)(x+1)[/tex]
Step-by-step explanation:
Use the slide-and-divide method:
[tex]3x^2-4x-7[/tex]
[tex]x^2-4x-21[/tex] <-- Multiply last term by the leading coefficient 3
[tex](x-7)(x+3)[/tex] <-- Factor
[tex](3x-7)(x+1)[/tex]
LCM of two numbers is 1134 and HCF is 18. if one of the numbers is 162, find the other. number.
Answers
=====================================================
Work Shown:
Let x and y be the two numbers.
We're given x = 162 and the variable y is unknown.
We're also given LCM = 1134 and HCF = 18
So,
LCM = (x*y)/HCF
1134 = 162*y/18
1134 = (162/18)y
1134 = 9y
9y = 1134
y = 1134/9
y = 126
The other number is 126
---------------------
Notice that
162 = 18*9126 = 18*7showing that 18 is the highest common factor (HCF) of the numbers 162 and 126. This partially confirms the answer.
Now let,
A = multiples of 162B = multiples of 126So,
A = 162, 324, 486, 648, 810, 972, 1134, 1296, ...B = 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, ...We see that 1134 is in each list of multiples and the smallest such common item. So the lowest common multiple (LCM) of 162 and 126 is 1134. This helps fully confirm the answer.