The dimensions of the box if it is to use the minimum possible amount of metal are,
⇒ 2.714 m, 2.714 m, 1.358 m
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A container with an open top is to have 10 m³ capacity.
Now,
Let the dimensions are x, y and z.
Since, Volume of box = 10 m³
Hence, We get;
⇒ xyz = 10
⇒ z = 10/xy
Since, A container is open in top.
Hence, The surface area = 2xz + 2yz + xy
Substitute z = 10/xy;
⇒ S.A = 2x (10/xy) + 2y (10/xy) + xy
= 20/y + 20/x + xy
For minimum metal;
⇒ d (S.A)/ dx = 0
⇒ - 20/x² + y = 0
⇒ y = 20/x² ..(i)
And, d (S.A) / dy = 0
⇒ - 20/y² + x = 0
⇒ x = 20/y² ..(ii)
Divide equation (i) and ((ii);
⇒ x = y
Hence, We get;
⇒ xyz = 10
⇒ x³ = 10
⇒ x = 2.714
And, y = 2.714
So, The value of z is,
⇒ z = 10/xy
⇒ z = 10 / 2.714×2.714
⇒ z = 1.358 m
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how do you get 3/8 from 13/8
You can get 3/8 from 13/8 by subtraction. The solution is 10 / 8
How to get 3/8 from 13/8In order to get 3/8 from 13/8 we would have to carry out a subtraction of fractions.
That is we would have: 13/8 - 3/8
take the lcm of the denominator
[tex]\frac{13 - 3}{8}[/tex]
= 10 / 8
Hence when we take 3 / 8 from 13 / 8, the solution that we would have would be from subtraction. This is 10 / 8
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a simple l cell organism divides in to 3 identical cells every 20 minutes, how many organisms will there be after 8 hours.
Step-by-step explanation:
Let’s see … one division every 20 minutes? That would be like <grinding noise> three binary doublings per hour, right? Now for the tough part … three doublings per hour, for eight straight hours? <more grinding noises> … Is that even mathematically possible? After much thinking, I decide that the total number of binary doublings has to be in the neighborhood of no less than eight times three!
Would you believe that 224=16777216 ? While mathematically true, it is not the answer to the posted question… Since we started at 0 minutes, there are only 23 buddings inside eight hours … so the answer has to be 223=8388608 , right?
Wrong again, this time forgetting all about the newlybud bacteria generations, that all go on budding side by side of their ancestors …
Now that you’ve caught on to the basic idea, I leave it to you to figure out the real answer! Keep in mind that after 20 minutes, you have two budding bacteria to reckon with, for 440 minutes … after 40 minutes another two (for 420 minutes), and so on, down the line.
Hint: the answer still is not 16777216 …
Answer:
after 1 division,there is 3 cell
after 2 divisions,there is 9 cell.
after 3 divisions,there is 27 cell
The above data takes the form of Geometric sequence.
3,9,27......,last term
here,Common ratio(r)=9/3=27/9=3
and,first term(a)=3
Let, n be the no.of divisions.
then, n=8 hrs/20 min=480 min/20min=24
Now,from the G.S,
last term=ar^n-1
=3×3^24-1
=9²³
Hence,9²³ organisms will there be after 8 hours
It can be written as 8.86293812×10²¹ as well
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24.
-2
2
NO
2
y-int=
slope =
equation:
y
2
X
On solving the provided question we can say that from data provided by the graph, we have a straight line, which means that the coordinates are equal. so the equation will be x = y = > x-y = 0
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle.
from data provided by the graphs,
we have a straight line,
which means that the coordinates are equal.
so the equation will be x = y
x-y = 0
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Huilan is 7 years older than Thomas. The sum of their ages is 79. What is Thomas’s age?
Answer:
To solve this problem, we can set up the following equation:
Huilan's age + Thomas's age = 79
Let H be Huilan's age and T be Thomas's age. We can then rewrite the equation as:
H + T = 79
We are told that Huilan is 7 years older than Thomas, so we can write the following equation:
H = T + 7
Substituting the second equation into the first equation, we get:
(T + 7) + T = 79
Combining like terms, we get:
2T + 7 = 79
Subtracting 7 from both sides, we get:
2T = 72
Dividing both sides by 2, we get:
T = 36
Therefore, Thomas's age is 36 years.
Step-by-step explanation:
Answer:
let Thomas age be a
there fore, hullans age is a+7
(a+7)+a=79
2a=79-7
2a=72
a=36
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Xavier buys 4 snacks and 2 cans of
soda. Each snack costs $1.25, and each
can of soda costs S dollars. Xavier's
total for the snacks and soda was $8.
How much did each can of soda cost
Total cost is the sum of all expenses incurred to produce a particular type of product. The answer is $1.50.
What is the definition of total cost?Total cost is the sum of all expenses incurred to produce a specific kind of output. Financial reporting, when overhead costs must be allocated to specific assets, is where the total cost approach is more useful from an accounting standpoint.
$8 was spent in total.
Xavier bought four $1.25 snacks.
4 x 1.25 = $5
The 2 cans cost $3 because 5 + 3 = 8, and we know how much the snacks cost ($5), making the total cost ($8).
Each can cost $1.50 because, if the price of the two cans was $3, we would have to divide it by two to get the price of the second can, which comes out to be $1.50. As a result, each can was $1.50.
Therefore, the answer is $1.50.
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A grocer wishes to make 50 kilos of tea by mixing two grades of tea worth rs.16 and rs.18 per kilo respectively .if he wishes to sell the mixed tea at rs.16.80 per kilo ,how many kilos of each grade of tea should he mix?
Answer:
11.1 and 38.9
Step-by-step explanation:
16x + 18 (1-x) = 16.89
2x = 1.11
x = 0.222
0.222 x 50 = 11.1
50-11.1 = 38.9
Melinda, Zachary, and heather went to the mall to shop for school supplies
Heather spend $33.1 on school supplies.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Melinda, Zachary, and heather went to the mall to shop for school supplies
Melinda spent $14.25 on her supplies.
Melinda=$14.25
Zachary spent $2.30 more than Melinda spent
Zachary=$14.25+$2.3
=$16.55
Heather spent 2 times as much money as Zachary spent
Heather=2×$16.55
=$33.1
Hence, Heather spend $33.1 on school supplies.
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Identify two angles that are marked congruent to each other on the diagram
below. (Diagram is not to scale.)
Answers:
TSO for the first boxQRP for the second boxExplanation:
The angles TSO and QRP are marked with the same double angle arc markers. This signifies they are congruent or the same measure. For example, they both could be 30 degrees each.
The naming "angle TSO" is the same as saying "angle OST". The order of the letters does not matter as long as point S is in the middle. Similarly, saying "angle QRP" is the same as "angle PRQ".
Question 1-1
Barrett earns $15 per hour cutting grass and $10 per hour tutoring reading. In one month, Barrett needs to save at least $400 for a
new lawnmower but does not want to work more than 35 hours.
Part A: Let z represent the hours cutting grass and y represent the hours tutoring. Given z 20 and y ≥ 0, select all the inequalities
that represent the situation.
On solving the inequality we know, Barrett should work 25 hours tutoring and 10 hours cutting grass to make $400.
What exactly does inequality mean?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality results from a lack of balance.
Solution:-
given,
z=hours of cutting grass
y=hours of tutoring
Two equation can be made using given condition
15z+10y=400
and
z+y=35
Solving both equation simultaneously,
we get
y=25
z=10
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Which equation represents a linear function that has a slope of 4/5 and a y-intercept of -6?
○ y=-6x+4/5
O y=4/5x-6
O y=4/5x+6
Oy=6x+ 4/5
Answer: y= -6x+4/5
Step-by-step explanation: We will compare these equations with standard form y=mx+c where m is the slope of the line and c is the y-intercept.
for line y= -6x+4/5
on comparing with y= mx+c
we have m= -6 and c= 4/5.
So, the first option is correct.
Find the total surface area of the net below
Therefore ,answering the offered question, we can state that the figure's surface area is SA = 2(9 11+11 9+11 * 11), which equals SA = 638 in2.
What precisely is surface area?Surface area is a measure of how much space an object's surface takes up overall. The total area of a three-dimensional shape's surroundings is its surface area. Surface area refers to the total surface area of a three-dimensional shape. You may compute the contact area of a cube with six square faces by adding together their individual areas. Alternatively, you can use the following formula to name the box's dimensions: Surfaces (SA) = 21 h + 2 lw + 2 hw. A tri shape's surface area is calculated as the total amount of space it occupies.
Here,
Front = rear = 11*11
top = bottom = 9*11
sides = 11*9;
SA= 2(911+119+1111)
SA=2(9999 +121)
SA = 2(319) (319)
SA = 638 in²
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A recipe calls for 6 liters of oj, 3 liters of grape juice and 9.5 liters of ice water. How much grape juice and water will be used with 2 liters of Jo?
If we use 2 liters of OJ, you will need to change the recipe and use:
1 liter of grape juice.3.2 liters of water.How much grape juice and water it will need?We know that a recipe calls for 6 liters of OJ, 3 liters of grape juice and 9.5 liters of ice cream.
If instead we use 2 liters of OJ, then the ratio of the recipe that we use is given by the quotient below:
2L/6L = 1/3
So we will just use 1/3 of each of the amounts that the recipe calls, we will se:
(1/3)*3 liters of grape juice = 1 liter of grape juice.
(1/3)*9.5 liters of water = 3.2 liters of water.
These are the amounts that you need to use.
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Rahul and his children went into a restaurant that sells hamburgers for $8 each and tacos for $4 each. Rahul has $80 to spend and must buy at least 11 hamburgers and tacos altogether. If x represents the number of hamburgers purchased and y represents the number of tacos purchased, write and solve a system of inequalities graphically and determine one possible solution.
x+y≥11 and 8x+4y=80 are system of inequalities and the number of tacos are two.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that Rahul and his children went into a restaurant that sells hamburgers for $8 each and
tacos for $4 each.
Rahul has $80 to spend and must buy at least 11 hamburgers and tacos altogether.
Let x represents the number of hamburgers purchased and y represents the number of tacos purchased,
x+y≥11...(1)
8x+4y=80..(2)
8(11-y)+4y=80
88-8y+4y=80
88-4y=80
8=4y
y≥2
Hence, x+y≥11 and 8x+4y=80 are system of inequalities and the number of tacos are two.
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could u please help me
Answer:
there is not enough info but i think it would be (5,11)
Step-by-step explanation:
divide
Answer:
[tex]y=\dfrac{11}{4}x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Choose two (x, y) points from the given table:
Let (x₁, y₁) = (4, 11)Let (x₂, y₂) = (8, 22)Substitute them into the slope formula:
[tex]\implies \dfrac{22-11}{8-4}=\dfrac{11}{4}[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute point (4, 11) and the found slope into the point-slope formula and rearrange to slope-intercept form:
[tex]\implies y-11=\dfrac{11}{4}(x-4)[/tex]
[tex]\implies y-11=\dfrac{11}{4}x-11[/tex]
[tex]\implies y=\dfrac{11}{4}x[/tex]
Rewrite in simplest terms: 9(-6p-4)+3(3p-5)9(−6p−4)+3(3p−5)
The expression in the simplest form is -90p - 102
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.
We are given an expression as 9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)
Then Rewrite in simplest terms:
9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)
2 [ 9(-6p-4)+3(3p-5) ]
Solve the like terms;
2 [-54p - 36 + 9p - 15]
2 [-54p + 9p - 15 - 36]
2 x ( -45p - 51)
-90p - 102
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What value for the
constant, h, in the equation
shown below will result in an infinite number of
solutions?
6t + 18 = h(3x + 9)
Therefore , As a result, h = 2 is the answer to the equation in the given question.
Explain equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra is the fundamental foundation of mathematics.
Here,
The formula is as follows: 6x + 18 = h(3x + 9)
To ensure that the expression has an unlimited number of answers, h's value must be determined.
Take the expression now and continue solving it.
=> 6x + 18 = h(3x + 9)
=>3hx + 9h= 6x +8
The expression will have an endless number of solutions if the coefficients of the left-hand side and the right-hand side are equal.
Therefore, 3h = 6 and h = 2
As a result, h = 2 is the answer to the equation in the given question.
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***** 6. A certain movie is 105 minutes long. It started at 6:15 pm. During the movie, there were two commercial breaks, one lasting 9 minutes and one lasting 6 minutes. At what what time did the movie finish
According to the given conditions in the question, the movie did finish at 8:15pm exactly.
What is the average movie length in hollywood?The average movie length of movies in hollywood is around 120 -130 mins per movie. However this fact can vary as per the genre and type of the film.
How are movies helping to improve world economy?The movie business, usually referred to as the film industry, has a big influence on the economy. For those involved in the industry, such as performers, directors, camera operators, sound technicians, special effects designers, and theater owners, the creation and distribution of films can result in jobs and financial gain.
The local economy can benefit from the tourists that movies can bring to an area where a movie is being made or is located. The money made by persons employed in the film business is likely to be spent on other goods and services, stimulating extra economic activity. As a result, the film industry may also have a "multiplier impact" on the economy.
So according to the question, the movie itself started at 6:15 pm, and it lasted for 105 mins , also adding the time for commercials of 9 mins and 6 mins , which ultimately added 15 more mins, the total screen time would be ,
105 + 15 = 120 mins
Which is equal to 2 hrs, so the movie finished at 8:15 pm.
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Jose has a points card for a movie theater.
• He receives 50 rewards points just for signing up.
• He earns 3.5 points for each visit to the movie theater.
• He needs at least 85 points for a free movie ticket.
Write and solve an inequality which can be used to determine x, the number of visits
Jose can make to earn his first free movie ticket.
Answer:
x ≥ 10
Step-by-step explanation:
Total Points = 50 + 3.5x
Total Points ≥ 85
50 + 3.5x ≥ 85
3.5x ≥ 35
then divide both sides by 3.5
x ≥ 10
Please help
Which poly nominal has the zeros 1,-2i and 3
The polynomial has the zeros 1,-2i and 3 is = x³ - 5x² + 11x -15.
What does a polynomial in mathematics mean?A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, as well as division (No division operation by a variable).
How can you recognize a polynomial?A polynomial function is a function that only uses non-negative numeric powers or only positive integer exponents of something like a variable in an equation, such as the quadratic equation, cubic equation, etc. As an illustration, the polynomial 2x+5 has an exponent of 1.
According to the given information:given zeros are 1-2i and 3 .
The polynomial function p(x) is
[x - (1+2i)] × [x - (1 - 2i)] × (x - 3)
[(x - 1) - 2i] × [(x - 1) + 2i] × (x - 3)
[(x - 1)² - (2i)² × (x - 3)]
∴ (x² - 2x + 1 + 4)(x - 3)
∴ (x² - 2x + 5)(x - 3)
The polynomial has the zeros 1,-2i and 3 is = x³ - 5x² + 11x -15.
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Determine the amount of a semi-annual coupon paid for a 3% bond with a face value of 80,000 which matures after 15years.
The amount (present value) of a semi-annual coupon paid for a 3% bond with a face value of 80,000 which matures after 15 years is $80,000.
What is the price of a bond?The price of a bond is its present value.
The present value can be determined as the discounted cash inflows.
In this situation, we can determine the present value of the bond using an online finance calculator as follows:
N (# of periods) = 30 (15 years x 2)
I/Y (Interest per year) = 3%
PMT (Periodic Payment) = $1,200
FV (Future Value) = $80,000
Results:
Present Value (PV) = $80,000.00
Sum of all periodic payments = $36,000.00
Total Interest = $36,000.00
Thus, the amount of the bond is $80,000.
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12 Aftab wants a patio in his garden. He is going to use concrete slabs to make the patio. Each concrete slab is a square with sides of length 0.5 m. A sketch of the planned patio is shown below. 3 m Patio 3 m 2
(a) What is the area of Aftab's patio? Give units with your answer.
Aftab pays £3.10 per concrete slab. (b) How much will it cost Aftab to buy enough concrete slabs to make the patio?
Answer:
5-3=2m
3x2=6m^2
Step-by-step explanation:
I can’t explain
LETTER B I DON’T KNOW THE ANSWER
Bob's Gift Shop sold 550 cards for Mother's Day. One salesman, Anand, sold 4% of the cards sold for Mother's Day. How many cards did Anand sell?
22 cards were sold by the Anand.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Bob's Gift Shop sold 550 cards for Mother's Day.
One salesman, Anand, sold 4% of the cards sold for Mother's Day.
We need to find the number of cards sold by Anand
Convert 4% to decimal by dividing 4 by 100
4/100=0.04
Now multiply 0.04 with 550
0.04×550
22
Hence, 22 cards were sold by the Anand.
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1. Explain how place-value blocks can
help you with division.
Using place value along with division facts in a division equation, helps in dividing larger numbers easily. Place value counters and tape diagrams are often used to represent division using place value.
What is division?
With the arithmetic operation of division, we can divide a collection of items into equal pieces. Typically, it is represented by the symbol "÷".
The bigger amount that is divided into equal halves is called the dividend.
The number of groups that divide the payout is known as the divisor. Following division, the result is the quotient.
The value of a digit in a number is determined by its place in the number, or place value.
Divide larger numbers simply by applying place value and division facts in a division equation. Place value division is frequently shown using tape diagrams and place value counters.
Example - 4 ÷ 2 = 2
In the first equation, the digits are 4 and 2. We can write it as 4 ones ÷ 2 ones = 2 ones (using the division fact).
Example - 40 ÷ 20 = 2
For the second equation, the digits are the same, but a zero has been added after 4, and the quotient thus has one zero at the end. So, we can write it as 4 tens ÷ 2 ones = 2 tens (using place value and the division fact).
Example - 400 ÷ 200 = 2
Similarly, for the third division equation, the same digits are present, but the number of zeros has increased. We are dividing 4 hundreds ÷ 2 ones = 2 hundreds (using place value and the division fact).
Therefore, place value blocks help in division for making it simpler.
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What is a quadratic function (f) whose zeros are -2 and -11
Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.
What are quadratic equations explain?Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.
What are the ways to solve a quadratic equation?The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.
Now we have [tex]x1[/tex]=2 [tex]x2[/tex]=-11
then quadratic function will be
(x+2) (x+11)
[tex]x^2+2x+11x+22[/tex]
[tex]x^2+13x +22[/tex]
this is our required quadratic equation.
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Complete question is: Write a quadratic function f whose zeros are 2 and -13.
Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.
What are quadratic equations explain?Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.
What are the ways to solve a quadratic equation?The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.
Now we have x¹ = 2 x² = -11
then quadratic function will be
(x+2) (x+11)
x² + 2x + 11x + 22
x² + 13x + 22
This is our required quadratic equation.
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The complete question is-
Write a quadratic function f whose zeros are 2 and -13.
Could you please help me
A tank is 80c ,nu 60cm by 75cm, find the volume of water that will fill up
A tank that is 80 cm tall and has a base that is 60 cm by 75 cm.
To find the volume of the tank, you can use the formula for the volume of a rectangular prism, which is:
Volume = length * width * height
Using the dimensions given, we can plug them into the formula as follows:
Volume = 60 cm * 75 cm * 80 cm = 4,500 cm^3
This means that the tank has a volume of 4,500 cubic centimeters, and it would take 4,500 cubic centimeters of water to fill it up
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Answer:
Step-by-step explanation:
To find the volume of water that will fill up a tank that is 80 cm tall, 60 cm wide, and 75 cm deep, you can use the formula for the volume of a rectangular prism. The formula for the volume of a rectangular prism is length x width x height, so in this case, the formula would be:
60 cm x 75 cm x 80 cm = 36,000 cm^3
So the volume of water that will fill up the tank is 36,000 cubic centimeters.
Alternatively this also can be written as 806075 cubic cms
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Which integer in the set has the greatest value (4, -4, -3, 3)?
A. 4
B. 3
C. -3
D. -4
Answer:
A. 4
Step-by-step explanation:
4 is a positive number which is larger to 3 and bigger than negative numbers.
Answer:
Step-by-step explanation:
i\
i \
i \
i /
i /
Tyler is 30 years younger than Naeste 9years ago
Answer:
i dont understand this question but i think maybe 21
Step-by-step explanation:
30-9 =21
Answer:
21
Step-by-step explanation:
please help me this would make my day ^^
Ray YW bisects ∠XYZ such that m∠XYW = (3x−7)° and m∠WYZ=(2x+1)°.
Find the value of x.