Answer: The total volume of the the cubes in the tower is 792 cubic centimetres (792 cm³)
Step-by-step explanation: We shall call the volume of the cube at the bottom VB, the volume of the cube at the middle VM, and the volume of the cube at the top VT. The tower is made up of cubes at different levels and at the bottom the cube measures 8 centimetres. The cube at the middle measures 2 cm less than the bottom cube, hence middle cube equals 8 minus 2 which equals 6 cm. The top cube measures 2 cm less than the middle cube, hence the top cube equals 6 minus 2 which equals 4 cm. The volume of each cube is given as;
Volume = L³
The length of a cube measures the same on all sides, that is, length, width and height. The length on all sides therefore of the bottom cube is 8 cm. The volume equals;
VB = 8³
VB = 512 cm³
The length on all sides of the middle cube is 6 cm (measures 2 cm shorter than the bottom cube). The volume of the middle cube equals;
VM = L³
VM = 6³
VM = 216 cm³
The length on all sides of the top cube is 4 cm (measures 2 cm shorter than the middle cube). The volume of the top cube equals;
VT = L³
VT = 4³
VT = 64
From the calculations shown, the total volume of the cubes in the tower is given as;
Total volume = VB + VM + VT
Total volume = 512 + 216 + 64
Total volume = 792 cm³
Total volume is 792 cubic centimetres.
Answer: The total volume of the cubes is 792 cm^3
Step-by-step explanation:
We have 3 cubes here.
And remember that the volume of a cube is equal to the length of one of the edges at the power of 3.
So for the bottom cube, we have that the edges are 8cm long, so the volume of this cube is:
V1 = 8cm^3 = 512cm^3
The edges of the next cube are 2cm shorter, so the edges are 6cm long.
Then the volume is:
V2 = 6cm^2 = 216cm^3
The top cube's edges are 2 cm shorter than the previous one, so the length of these edges is 4cm, then the volume is:
V3 = 4cm^3 = 64cm^3
Now, the total volume is equal to:
V = V1 + V2 + V3 = 512cm^3 + 216cm^3 + 64cm^3 = 792 cm^3
Jack found bought a apple that was 3 dollars and he also bought a 2 dollar pen what is his total amount
Answer:
5 dollars
Step-by-step explanation:
Answer:
5 dollars
Step-by-step explanation:
A rectangle has a length of 4 inches and area of 12 in.² what is the perimeter of the rectangle
Answer:
14 in
Step-by-step explanation:
breadth = 12/4 = 3
perimeter = 3+3+4+4 = 14
Mike bought 7 new baseball cards to add to his collection. The next day his dog ate half of his collection. There are now only 41 cards left. How many cards did Mike start with?
Answer: Mike started with 75 cards
Step-by-step explanation:
Hi, to answer this question we have to write an equation:
The number of cards mike started with (x) plus the new cards added (7) must be divided by 2 (since his dog ate half of his collection).
That expression must be equal to the number of cards left (41)
Mathematically speaking:
(x + 7) /2 = 41
Solving for x:
x+7 = 41x2
x+7 = 82
x = 82-7
x = 75 cards
Feel free to ask for more if needed or if you did not understand something.
I'm not the brightest, mind helping me out?
Answer:
C.
Step-by-step explanation:
Opposite means that they are the same value away from 0 just on the opposite side.
4 is opposite to -4
and 7 is opposite to -7
PLEASE HELP ASAP
Fiona must find the length indicated by the dotted line for
the tiles she is installing. She knows that each polygon is a
regular hexagon with a perimeter of 7.5 in.
What is the length of the dotted line? Round to the nearest
hundredth.
2.50 in.
3.75 in.
5.00 in.
6.25 in.
Answer:
3.75 in.
Step-by-step explanation:
Fiona must find the length indicated by the dotted line for the tiles she is installing. She knows that each polygon is a regular hexagon with a perimeter of 7.5 in.
3 regular hexagons are connected at their sides. A dotted line is drawn through the middle of the 3 hexagons. The top image is a reflection of the bottom image. The dotted line is the length of one side and the distance from one point of the hexagon to the opposite point.
What is the length of the dotted line? Round to the nearest hundredth.
2.50 in.
3.75 in.
5.00 in.
6.25 in.
The length of the dotted line in the hexagon is 3.75 cm.
What is a hexagon?A polygon with 6 sides is called a hexagon.
Finding the length across one entire hexagon :-
We can draw 6 small triangles from the center of the hexagon. The top vertex of this triangle will be 60°; this is because there are 6 angles, and 360.
The sum of the measures of the angles in a triangle is 180°; taking out the top angle, we have 180-60 = 120°.
Since the triangle is isosceles, the base angles will be equal to 120/2 = 60
The bottom two angles will also be 60°.
This makes the triangle equiangular, which also makes it equilateral; all 3 sides will be 1.25.
Hence,
This means across the dotted line we have 1.25+1.25+1.25 = 3.75.
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2. The area of a rectangle is 56 square inches. The rectangle is 8 inches long. How wide is the rectangle?
A.15 inches
B. 7 inches
C.48 inches
D.20 inches
Answer:
B. 7 inches
Step-by-step explanation:
The area of a rectangle is given by
A = l*w where l is the length and w is the width
56 = 8*w
Divide each side by 8
56/8 = 8w/8
7 =w
Answer: 7 inches
Step-by-step-Explanation: The formula for the area of a rectangle is below shown below.
Area = length · width
Since we know that the area of the rectangle is 56 in² and the length of the rectangle is 8 inches, we have 56 = 8 · w.
Now to find w or the width of the rectangle, we divide
both sides of the equation by 8 to get 7 = w.
So the width of the rectangle is 7 inches.
Notice that we include inches in our final answer because we were given inches as units in the original problem.
Also notice that we don't ever have to draw a picture of the rectangle in this problem. We can find our answer by simply using the formula for the area of a rectangle.
Simplify the expression.
100^(1/2)-125^(1/3)
PLEASE HELP OFFERING 24 POINTS
Solve the equation x³ − 5 = 59
Answer:
4 = x
Step-by-step explanation:
x³ - 5 = 59 Add five to both sides of the equation.
x³ = 64 Now find the cubed root of 64
∛64 = 4
x = 4
find the x and the area of the shape perimeter is 64.5
Answer:
x=8
A = 192
Step-by-step explanation:
The perimeter is the sum of the outer lengths
17.9 + 22.6 + 3x = 64.5
Combine like terms
40.5 +3x = 64.5
Subtract 40.5 from each side
40.5 +3x -40.5 = 64.5 - 40.5
3x =24
Divide each side by 3
3x/3 = 24/3
x = 8
The area of a triangle is given by
A = 1/2 bh
The base is 3x = 3(8) =24
and the height is 2x = 2(8) =16
A = 1/2 (24) * 16
A =192
An elevator started on the 10th floor of a large hospital. it traveled up 4 floors, then down 6 floors, then down 2 more floors, and finally went back up 7 floors. Which floor was the elevator on when it stopped?
After a series of movements starting on the 10th floor, the elevator stopped on the 13th floor.
To determine which floor the elevator was on when it stopped, we need to perform a series of additions and subtractions based on the elevator's movements, as described:
The elevator started on the 10th floor.
It traveled up 4 floors: 10 + 4 = 14th floor.
Then down 6 floors: 14 - 6 = 8th floor.
Then down 2 more floors: 8 - 2 = 6th floor.
Finally, it went back up 7 floors: 6 + 7 = 13th floor.
After completing all these movements, the elevator stopped on the 13th floor.
Lena tried to solve a system of linear equations algebraically and in process found the equation 5=9. Lena thought something was wrong,so she graphed the equations and found that they were parallel lines. Explain whats Lenas graph and equation could mean.
Answer:
This means that there is no solution
Step-by-step explanation:
When solving for a system of linear equations, we are solving for the intersection point. If we cannot algebraically solve for a system, it automatically means you made a mistake or the lines are parallel. Since the two lines are parallel, there is no intersection point, so there is no solution
A recent study claims that business travelers spend an average of $41 per day on meals. A sample of 16 business travelers found that they had spent an average of $45 per day with a standard deviation of $3.65. If a = 0.05, what are the critical values?
Answer:
[tex] df = n-1= 16-1 =15[/tex]
And the significance level is [tex]\alpha=0.05[/tex] and since we are conducting a bilateral test then the critical values are founded with the t distribution with 15 degrees of freedom and we got:
[tex] t_{\alpha/2}= \pm 2.131[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=45[/tex] represent the sample mean
[tex]s=3.65[/tex] represent the sample standard deviation
[tex]n=16[/tex] sample size
[tex]\mu_o =41[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to determine the true mean is 41 per day, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 41[/tex]
Alternative hypothesis:[tex]\mu \neq 41[/tex]
We need to find the degrees of freedom first:
[tex] df = n-1= 16-1 =15[/tex]
And the significance level is [tex]\alpha=0.05[/tex] and since we are conducting a bilateral test then the critical values are founded with the t distribution with 15 degrees of freedom and we got:
[tex] t_{\alpha/2}= \pm 2.131[/tex]
A cylinder has a base diameter of 10m and a height of 14m. What is its volume in cubic m, to the nearest tenths place?
Answer:
1099.6 m³
Step-by-step explanation:
The formula for the volume of a cylinder of radius r and height h is
V = πr²h. In this case, the radius, r, is half the diameter, 10 m: r = 5 m, and the height is 14 m.
Thus, the volume of this cylinder is
V = π(5 m)²(14 m) = 1099.6 m³ (to the nearest tenths place).
The volume of the cylinder is approximately 1099.6 cubic meters to the nearest tenth place.
What is a cylinder?A cylinder is a 3D solid form made up of two bases that are parallel and identical and are connected by a curving surface. These bases resemble spherical disks. The axis of the cylinder form is a line drawn through the center or connecting the centers of two circular bases.
The formula for the volume of a cylinder is:
V = πr²h
where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is the mathematical constant pi (approximately equal to 3.14159).
To find the radius of the cylinder, we need to divide the diameter by 2:
r = d/2 = 10m / 2 = 5m
Now we can plug in the values:
V = πr²h = π(5m)²(14m) = 350π m³
To approximate the value to the nearest tenths place, we can substitute the value of π as 3.14159 and use a calculator to evaluate the expression:
V ≈ 350 × 3.14159 ≈ 1099.56 ≈ 1099.6
Therefore, the volume is 1099.6 cubic meters.
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There are 10 students participating in a spelling bee. In how many ways can the students who go first, second, and third in the bee be chosen?
Answer:
90
Solution:
The 1st choice is 1 of 10.
The 2nd is one of 9.
Therefore, 10 times 9= 90
An expression is shown. 3/5÷5/8 What is the value of the expression?
Answer:
24/25
Step-by-step explanation:
3/5×8/5
24/25
what is p if 7/p = 3/10
Answer:
23 1/3 or 70/3 =p
Step-by-step explanation:
7/p = 3/10
Using cross products
7*10 = 3p
70 = 3p
Divide each side by 3
70/3 = 3p/3
70/3 =p
or as a mixed number
23 1/3 =p
Match the following items.
1. a2 +2ab + b2
factor
2. a2 - b2
(a + b)2
3. a2 -2ab + b2
(a-b)(a2 + ab + b2)
4. a3 - b3
joint variation
5. a3 + b3
(a + b)(a - b)
6. divisor
(a - b)2
7. process
direct variation
8. a simplified procedure that temporarily omits variables
synthetic division
9. y = 10x
combined variation
10. xy = 18
algorithm
11. y = 4xz
(a + b)(a2 - ab + b2)
12. y = 4x/z
inverse variation
Step-by-step explanation:
The following match
* a² + 2ab + b² and (a + b)²
* a² - b² and (a - b)(a + b)
* a² - 2ab + b² and (a - b)²
* a³ - b³ and (a - b)(a² + ab + b²)
* a³ + b³ and (a + b)(a² - ab + b²)
* y = 10x Direct variation
* xy = 18 Algorithm
* y = 4xz Joint variation
* y = 4x/z Inverse variation
Kale can typed 165 words in 3 minutes. How can this ratio be written to show words per minute?
Answer:
55 words per minute
Step-by-step explanation:
165/3
Final answer:
The ratio of words typed per minute for Kale who typed 165 words in 3 minutes is calculated by dividing the number of words by the number of minutes, resulting in 55 words per minute.
Explanation:
To calculate the number of words typed per minute, you take the total number of words typed and divide it by the number of minutes it took to type them. In this case, Kale typed 165 words in 3 minutes, so the ratio of words to minutes is:
165 words / 3 minutes = 55 words per minute
This ratio indicates the typing speed, measured in words per minute (wpm), which is a common way to express typing efficiency.
What is the final amount if 457 is decreased by 1% followed by a further 3% decrease? Give your answer rounded to 2 DP.
Answer:
438.86
Step-by-step explanation:
1. 457 x 0.99 = 452.43 - Decreased by 1%
2. We need to decrease 452.43 again but this time by 3% - 452.43 x 0.97
3. This gives us an answer of 438.8571
4. Finally we need to round this to 2DP, the 7 (438.8571) rounds up so the number to the left increases. This leaves an answer of 438.86
Hope this helps :D
What is the measure of x?
115°
105°
15°
285°
Answer: B. 105
Step-by-step explanation:
180 - 75 = 105
Hope this helps!
20 POINTS!!!! PLZ HELP WILL MARK BRAINLEST 20 POINTS!!!!
Answer:
[tex]10\pi[/tex]
Step-by-step explanation:
The penguin swam around half of the perimeter, or circumference, of the pool. The first step is to calculate that. You can find the circumference of a circle by multiplying the diameter by pi. Therefore, the circumference of this island is 20pi. Half of that is [tex]10\pi[/tex] meters. Hope this helps!
Answer:
10 meters
Step-by-step explanation:
20 / 2 = 10
how to change the format of the equation y-5=x
Ethan Purchased a gently used minivan 2 years ago. the current value of the van is $8000 the vans value depreciated by 11% each year. how much does Ethan pay for the van?
Answer:
18,736.80
Step-by-step explanation:
Final answer:
To determine the original purchase price of the van, we apply the formula for exponential decay and find that Ethan paid approximately $10,100.45 for the van two years ago, taking into account a depreciation rate of 11% per year.
Explanation:
To find how much Ethan paid for the van, we need to work backwards from the current value and consider the annual depreciation rate.
To do this, we can use the formula for exponential decay which is final value = initial value × (1 - rate of depreciation)number of years. Given the final value ($8000) and the depreciation rate (11% or 0.11), we need to solve for the initial value, which represents the price Ethan paid for the van.
Let's set up the equation:
8000 = initial value × (1 - 0.11)2
8000 = initial value × (0.89)2
8000 = initial value × 0.7921
Initial value = 8000 / 0.7921
Initial value ≈ $10,100.45
Therefore, Ethan paid approximately $10,100.45 for the van.
The percentage profit on an MP3 player purchased for $320 and later sold for $350 is
Answer:
The profit percentage in MP3 player is 9.37 %.
Step-by-step explanation:
Cost price of MP3 player is $320
Selling price of MP3 player is $350.
Here, selling price is more than cost price. It means there is profit in MP3 player.
Profit = SP - CP
Profit = 350 - 320
Profit = $30
Profit percentage is given by :
[tex]\% P =\dfrac{{SP}-{CP}}{{CP}}\times 100\\\\\% P=\dfrac{30}{{320}}\times 100\\\\\% P=9.37\%[/tex]
The profit percentage in MP3 player is 9.37 %.
can you actually help me with this so i can finish the math work if so thank you so much
Answer:
adbbcbaca
Step-by-step explanation:
What is the mean of the data set below? Round to the nearest tenth when necessary. 40, 40, 52, 41, 62
Answer:
47
Step-by-step explanation:
add all the numbers and divide them by however many numbers there are.
Answer: The mean is 47.
There are 5 numbers.
To find the mean of them we add them and divide the sum by 5.
Mean = [tex]\frac{\left(40+40+52+41+62\right)}{5}=\frac{235}{5}=47[/tex]
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C/ 8= 9. What does c equal
Answer: 72
72/8 will get you 9. To see if the answer is correct Multiply 9*8.
Answer:
72
Step-by-step explanation:
c/8 = 9
Multiply each side by 8
c/8 * 8 =9*8
c = 72
Need help now please answer
Answer:
10 cm
Step-by-step explanation:
We want to find TS = ST
ST = CD from the second statement of congruence
CD = IJ from the first statement of congruence
We know IJ = 10
That means ST = 10
after making 20 servings of pasta, a chef has used 30 cloves of garlic. how many cloves are used to make 10 servings?
Answer:
15
Step-by-step explanation:
Easy question, Easy points LIMTED TIME. LOTS OF POINTS
Topic: Volume
Answer:
V = 77 m^3
Step-by-step explanation:
We want the volume of the cylinder
V = pi r^2 h
We know the diameter not the radius
r = d/2 = 7/2 = 3.5
V = 3.14 * (3.5)^2 (2)
V = 76.93 m^3
To the nearest cubic meter
V = 77 m^3
The answer is 77 m^3
Quick question though... Why say "easy" and ask for an answer?