Answer:
3² +2³= 9+8=17
2¹ - 3²= 2-9=8
Step-by-step explanation:
Answer:
1-7
Step-by-step explanation:
[tex]3^{2}[/tex] + [tex]2^{2}[/tex] (3x3) + (2x2x2) = 9 + 8 = 17
[tex]2^{1}[/tex] - [tex]3^{2}[/tex] = 2 - (3x3) = 2 - 9 = -7
√6/√3 I’m struggling on this question this symbol / means divide
Answer:
√2
Step-by-step explanation:
√3 x√2/√3 =√2
Answer:
[tex]\sqrt{2}[/tex]
explanation:
[tex]\frac{\sqrt{6} }{\sqrt{3} }[/tex]
= [tex]\sqrt{2}[/tex]
(Decimal: 1.414214)
A redwood tree casts a shadow that is 8 meters long. A carpool lane sign near the redwood
tree casts a shadow that is 4 meters long. If the redwood tree is 6 meters tall, how tall is the
carpool lane sign?
Answer:
Hey bro, solving this would be relatively simple. If the Redwood tree is 6 meters tall, then the height of the carpool lane sign can be easily calculated using similar triangles. Using the lengths of their respective shadows, the carpool lane sign should be 3 meters tall, because the ratio between the height of the Redwood tree and the carpool lane sign, is the same ratio as between their respective shadows (8 to 4). The based way to solve this problem would be to measure the length of the shadows, and then use the ratio to calculate the height of the carpool lane sign.
Answer:
You need to set up the problem to solve for X. X = how tall is the tree? Set up your problem in this fashion. Set up the formula then arrange to solve for X. X/9 (shadow of the tree) = 15 (how tall the building is)/6 (shadow of building) X= 15/6 * 9 To get X alone, you need to move 9 to the other side of the equation. multiply by 9 on each side. For X side, this nullifies 9 and gets 9 to the other side. X= 2.5*9 You have divided 15 by 6, now multiply by 9 to get final answer for X X=22.5 meters The tree is 22.5 meters tall.
Step-by-step explanation:
If this is not.. right ill do another answer!!
Write down the first two terms (and the error term) in the Taylor series expansion of f(h) = ln(3 - 2h) around h = 0, The error term should involve a mysterious unknown constant xi. There's no way to determine xi from the information given here: in practice, if you were to evaluate your Taylor expansion at, say, h =, you would know that xi elementof (0, 4) and you could get bounds on the error by bounding the derivatives of f(h) on this interval.
The Taylor series expansion of f(h) = ln(3 - 2h) around h = 0 is given by:
f(h) = f(0) + f'(0)h + R(h)
where f(0) = ln(3), f'(0) = -2/3, and R(h) is the remainder term.
To find the remainder term, we need to take the higher-order derivatives of f(h) and evaluate them at h = 0. We have:
f''(h) = 4/(3(3 - 2h))^2, f'''(h) = -32/(3(3 - 2h))^3, and so on.
Evaluating these at h = 0, we get f''(0) = 4/9 and f'''(0) = -32/27.
Thus, the remainder term can be expressed as:
R(h) = (1/2)f''(xi)h^2 = (1/2)(4/9)(xi)^2h^2 = (2/9)(xi)^2h^2
where xi is some unknown constant between 0 and 4.
Therefore, the first two terms in the Taylor series expansion of f(h) are:
ln(3) - (2/3)h
and the remainder term involves the unknown constant xi, given by R(h) = (2/9)(xi)^2h^2.
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One and Seventy One Hundredths
wright the number for the decimal names..
When one and seventy one hundredth is written in decimal form, it would be 1. 71
How to write as decimal ?A single part of something that has been evenly divided into one hundred parts is referred to as a hundredth in mathematics. The tenths place is represented by the first digit following the decimal. The hundredths place is represented by the digit that follows the decimal.
This means that when given the number one and seventy One Hundredths in words, then the number, " one " would be written before the decimal and the 71 would be 0. 71 as a hundredth figure.
When put together, this becomes:
= 1 + 0. 71
= 1. 71
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HELP FAST WILL GIVE BRAINLYEST AND 100 PTS
The correct answers are: a reflection across the x-axis and a translation 1, unit right, a rotation of 180° about the origin and a translation of 1 unit left.
How to check for congruence?To check for congruence, we need to verify that the two triangles have the same shape and size, which means that one triangle can be mapped onto the other using a sequence of transformations.
For the first sequence of transformations (a reflection across the x-axis and a translation 1 unit right), we can reflect triangle ABC across the x-axis, which will map (-6, 2) to (-6, -2), (-4, 6) to (-4, -6), and (-2, 2) to (-2, -2). We can then translate the reflected triangle 1 unit to the right, which will map (-6, -2) to (-5, -2), (-4, -6) to (-3, -6), and (-2, -2) to (-1, -2). This mapped triangle is triangle ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.
For the second sequence of transformations (a rotation of 180° about the origin and a translation of 1 unit left), we can rotate triangle ABC 180° about the origin, which will map (-6, 2) to (6, -2), (-4, 6) to (4, -6), and (-2, 2) to (2, -2). We can then translate the rotated triangle 1 unit to the left, which will map (6, -2) to (5, -2), (4, -6) to (3, -6), and (2, -2) to (1, -2). This mapped triangle is also ADEF, and since it was obtained by a sequence of transformations, we can conclude that ABC is congruent to ADEF.
Therefore, the correct answers are:
a reflection across the x-axis and a translation 1 unit right
a rotation of 180° about the origin and a translation of 1 unit left.
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Name the line of reflection that maps each pre-image to its image.
Answer: X axis , Y axis , y=-2
Step-by-step explanation:
2. Assume a firm operating in a purely competitive market has a constant selling price of
GH 60, a fixed cost of GH¢450 and a variable cost of GH¢35 an item. Derive;
a)
b)
c)
The total revenue function.
The total cost function.
The profit function.
The total revenue function is 60x.
The total cost function is 35x + 450.
The profit function is 25x - 450.
How derive the total revenue function, the total cost function and thee profit function?Since we have a constant selling price of GH 60, a fixed cost of GH¢450 and a variable cost of GH¢35 an item.
Let x be the number of items
Total revenue function = constant selling price * x
Total revenue function = 60x
Total Cost Function = Variable cost + Fixed cost
Total Cost Function = 35x + 450
Profit function = Total revenue function - Cost function
Profit function = 60x - (35x + 450)
Profit function = 60x - 35x - 450
Profit function = 25x - 450
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Dave Drinks a 12-ounce cup of coffee each morning on his way to work. This cup of coffee contains 136 mg of caffeine.
The caffeine in his system decreases about 40% every hour.
Function to calculate amount of coffee in Dave's system after x hours
= y = 135(0.6)ˣ
What is exponential expression?An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to.
Given,
Dave drinks 12-ounce cup of coffee each morning
One cup has 136 mg of caffeine
caffeine in his system decreases about 40% every hour
In x hours,
Amount of caffeine in his system
y = a(1 - 40/100)ˣ
or
y = 136(1-0.4)ˣ
y = 135(0.6)ˣ
Hence, y = 135(0.6)ˣ is the function to calculate amount of caffeine in system of Dave after x hours.
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In ΔFCE, the ratio of ∠F to ∠C is 2:5. The measure of ∠E is one hundred ten degrees more than the sum of the measures of ∠F and ∠C. What is the measure of each angle in ΔFCE?
Answer:70
Step-by-step explanation:
Given: <f and <c ratio 2:5
To find: <f and <c
Solution: 2x+5n=180' minus 110'
7n=70'
x=10'
<f= 2x10=20'
<e= 5x10=50'
The sum of <F and <E
= 20'+50'=70'
The critical points of a rational inequality are –1, 3, and 4. Which set of points can be tested to find a complete solution to the inequality? x = 1 and x = 3.5 x = –1, x = 3, and x = 4 x = –2, x = 2, and x = 5 x = –3, x = 1, x = 3.5, and x = 5
The possible set of inequalities are;
x = -3,
x = -1,
x = 1,
x = 3,
x = 5.
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
The critical points of a rational inequality are the x-values at which the inequality changes direction (from "<" to ">" or vice versa). In this case, the critical points are -1, 3, and 4.
To find the complete solution to the inequality, we need to test points on either side of the critical points. For example, if we test a value less than -1, such as -2, and find that it satisfies the inequality, then all values less than -1 also satisfy the inequality. On the other hand, if a value less than -1 does not satisfy the inequality, then no values less than -1 satisfy the inequality.
Therefore, a complete solution to the inequality can be found by testing values around each critical point. A common set of points to test for this purpose is the critical points themselves, and values just less than and just greater than each critical point.
So, a possible set of points to test to find the complete solution to the inequality is:
x = -3,
x = -1,
x = 1,
x = 3,
x = 5.
These points bracket the critical values and allow us to determine which intervals of values satisfy the inequality.
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F and H are sets of real numbers defined as follows.
Lemon disinfectant is mixed 4 oz to one gallon. How many lemon disinfectant needs to be added to 6 gallons of water?
Answer:
If the ratio of lemon disinfectant to water is 4 oz to one gallon, then we can say that for each gallon of water, we need 4 oz of lemon disinfectant. To find how much lemon disinfectant is needed for 6 gallons of water, we can multiply the amount needed for one gallon by the number of gallons:
4 oz/gallon * 6 gallons = 24 oz
Therefore, we need 24 oz of lemon disinfectant to be added to 6 gallons of water.
Step-by-step explanation:
Answer:
Given: x * 4 oz = 6 gallons.
First, multiply 4 oz and x:
4x = 6 gallons.
Then convert 6 gallons to oz:
4x = 768 oz.
Then divide both sides by 4:
x = 192.
2 rectangular pyramids are connected at their bases. The total height of the 2 figures if 10 units. The base edge lengths are 9 units and 1.5 units. The height of each pyramid is 5 units.
Which statements about the composite figure are true? Check all that apply.
The composite figure consists of two rectangular pyramids.
The composite figure can be broken down into rectangular prisms.
The volume of the composite figure is
1.5(9)(5) + 1.5(9)(5).
The total volume is 45 units3.
The total volume is 90 units3.
The composite figure consists of two rectangular pyramids, volume is 45 unit³.
What is rectangular pyramid?Pyramids are three-dimensional structures having triangle faces and have an encompassing polygon shape at its base. If the base of a pyramid is rectangular, then it is called a rectangular pyramid.
Given,
Total height of two rectangular pyramids = 10 units
height of each pyramid is 5 unit.
Base lengths are 9units and 1.5 units.
Both are connected at their bases.
Dimensions are same of both pyramids
Composite figure consists of two rectangular pyramids.
Volume of the composite figure
= 2(length × width × height)/3
= 2(9×1.5×5)/3
= 2(13.5×5)/3
= 2(67.5)/3
= 135/3
= 45 unit³
Hence, 45 unit³ is volume of composite figure, that consists of two rectangular pyramids.
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Answer:A D
Step-by-step explanation:
statistics is the science of average - elucidate this statement
Answer:
The average of all the data is calculated in statistics.
However, statistics is a field that goes beyond average and is not a complete science of it.
There are other additional statistical tools.
which explains how statistics is an extension of mathematics.
What is the correct sequence of steps for calculating 96 on a scientific calculator?
First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6. Then the value you get is 531,441.
What is the value of the expression?At the point when the important parts and fundamental cycles of a mathematical technique are given qualities, the articulation's outcome is the consequence of the calculation it portrays.
The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.
The expression is given below.
⇒ 9⁶
First press button 9, then press the button on which the (^) sign is mentioned. Then button press 6.
The value of the exponent numerical expression 9⁶ will be 531,441.
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The correct question is given below.
What is the correct sequence of steps for calculating 9⁶ on a scientific calculator?
Which letter
A
B
C
D
Answer:
Step-by-step explanation:
a
Answer:
ITS A
Step-by-step explanation:
The reason why is because that dude up there said the same thing so yeah..
What values of x
and y
satisfy the system {y=−2x+3
{y=5x−4?
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The required solutions of the given system of equation are x = 1 and y = 1.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
According to question:To find the values of x and y that satisfy the system, we need to solve the equations simultaneously:
y = -2x + 3 ... (1)
y = 5x - 4 ... (2)
Setting the right-hand sides of (1) and (2) equal to each other, we get:
-2x + 3 = 5x - 4
Simplifying this equation, we get:
7x = 7
Dividing both sides by 7, we get:
x = 1
Substituting x = 1 into either equation (1) or (2), we get:
y = -2(1) + 3 = 1
Therefore, the only solution that satisfies both equations is x = 1 and y = 1.
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Avery had $25.83 in her wallet. If she bought lunch with 7 3/4 dollars from her wallet, how much money did she have in her wallet after lunch?
Answer: $ 18.08
Step-by-step explanation:
Given: Money in wallet = $25.83
Given: Money spent = $7.75
To find: Money left in the wallet after lunch = money in the wallet - money spent
= $(25.83-7.75)
= $ 18.08
Noah is making mini berry pies. For the filling, he mixes 1 pound each of raspberries, blueberries, and blackberries. Then, he scoops 6 ounces of the filling into each mini pie tin. If he wants to use up all of his filling, how many mini pies can he make?
Farid is able to produce 8 small pies.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
Given: For the filling, Farid blends 1 pound of each blackberries, blueberries, and raspberries. Following that, he spoons 6 ounces of the filling into each tiny pie pan.
We need to find How many tiny pies can be made if he wants to use all of the filling.
Raspberries, blueberries, and blackberries, each weighing 1 pound, are combined by Faris for the filling.
3 pounds of filler total from 1+1+1= 3*16 ounces.
1 pound equals 16 ounces. = 48 ounces
Each little pie tin is filled with 6 ounces of filling by Faris.
48 ounces divided by 6 ounces equals 8 mini pies.
Hence, the Farid made 8 mini pies with 6 ounces.
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there are 36 boys and 45 girls in the track meet.the coach wants an equal number of boys and girls on each team.what is the greatest number of boys and girls the coach can have on one team.how many teams will he have
the coach can form 4 teams of 9 boys and 9 girls each, and there will be 9 players left over who cannot form a complete team.
What is greatest common divisor?The GCD (Greatest Common Divisor), also known as the HCF (Highest Common Factor), is the largest positive integer that divides two or more integers without leaving a remainder.
For example, the GCD of 12 and 18 is 6, because 6 is the largest positive integer that divides both 12 and 18 without leaving a remainder.
Given by the question.
To form teams with an equal number of boys and girls, we need to find the greatest common divisor (GCD) of 36 and 45.
The prime factorization of 36 is 2^2 x 3^2, and the prime factorization of 45 is 3^2 x 5.
The common factors are 3^2 = 9. Therefore, the GCD of 36 and 45 is 9.
This means that the coach can form teams of 9 boys and 9 girls each.
To find out how many teams he can form, we need to divide the total number of boys and girls by the number of players on each team:
Number of teams = Total amount of players / Number of players per team
Number of teams = (36 + 45) / 18
Number of teams = 81 / 18
Number of teams = 4 with a remainder of 9
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Mr. Sanchez made a apple pie. The circumstances of his pie was 28.26 inches.
? What was the diameter of the pie?
The diameter of the pie is approximately 9 inches
What is a diameter ?
Diameter can be defined as the double of the radius
To determine the diameter of the pie, we need to use the formula for the circumference of a circle:
C = 2πr
where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
In this case, we are given that the circumference (circumstances) of the pie is 28.26 inches, so we can set up the equation:
28.26 = 2πr
To solve for the radius, we can divide both sides of the equation by 2π:
r = 28.26 / (2π)
r ≈ 4.5
So the radius of the pie is approximately 4.5 inches. To find the diameter, we just need to double the radius:
d = 2r
d ≈ 9
Therefore, the diameter of the pie is approximately 9 inches.
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An airplane fies 3,780 miles in 7.5 hours. What is the speed of the airplane in miles per hour? Use the equation d=rt, where d is distance, r is rate, and t is time.
The airplane's speed ismiles per hour.
Answer:
504
Step-by-step explanation:
3780÷7.5=504
504 mph because 504 x 7.5 = 3780
Please give good review. :)
Evaluate y (x ÷2) if x = 20 and y = 10
Answer:
100
Step-by-step explanation:
1.) Plug in the values of x and y into the equation
10(20/2)
2.) Divide 20 by 2
10(10)
3.) Multiply 10 by 10
100
Question 3 Charlie has a total of $7 in quarters and nickels. He has twice as many nickels as quarters. In which system of equations does q represent the number of quarters he has and n represent the number of nickels?
Answers are linked below. I need help like fast
A system of equations where n is the number of nickels and q is the number of quarters he has is represented by (C) 25q + 5n = 7, n = 2q.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
Let's learn more about math equations in this tutorial.
So, we know that nickels are double quarters.
And nickels are represented by n and quarters are represented by q.
Then, we can write as:
n = 2q
Then, the equation that represents the situation will be:
25q + 5n = 7
Therefore, a system of equations where n is the number of nickels and q is the number of quarters he has is represented by (C) 25q + 5n = 7, n = 2q.
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If $16,000 is invested at 10% for 20 years, find the future value if the interest is compounded daily.
YZ = 9, LM = 3, MN = 2, and the measure of angle Z = 100 degrees. What additional information is needed to prove the triangles are similar by SAS?
The additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem is; MN/LK||MN.
What is SAS (Side-Angle-Side) similarity theorem?The SAS (Side-Angle-Side) similarity theorem states that if two triangles have two pairs of corresponding sides that are in proportion, and the included angles are congruent, then the triangles are similar.
In this case, we are given that ΔLKN and ΔKNM share the angle at vertex K, and we know that LN/MN and LK/KN are in proportion.
However, we need to establish that MN/LK||MN, that means MN is parallel to LK and forms a transversal with LN.
This information is necessary to establish that the included corresponding sides are congruent, which is required for the triangles to be similar.
Therefore, the additional piece of information needed to prove that ΔLKN ~ ΔKNM by the SAS similarity theorem.
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To save for retirement, a student invests $70 each month in an ordinary annuity with 3% interest compounded monthly. Determine the accumulated amount in the student's annuity after 30 years.
The accumulated amount will be $_______?
(Round to the nearest cent as needed.)
The accumulated amount will be $133.
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 student invests $70 each month in an ordinary annuity with 3% interest compounded monthly.
We know that;
⇒ Simple interest = P × r × t
Where, P is principle amount , 'r' is rate and t is time.
Here, P = $70
r = 3%
n = 30 years
Substitute all the values, we get;
Hence, We get;
⇒ Interest = P × r × t
⇒ Interest = 70 × 0.03 × 30
⇒ Interest = $63
Hence, The accumulated amount will be ;
⇒ P + Interest
⇒ $70 + $63
⇒ $133
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Let A be an mxn matrix, and let u and v be vectors in Rn with the property that Au = 0 and Av 0. Explain why A(u + v) must be the zero vector. Then explain why A(cu + dv) -0 for each pair of scalars c and d.
Suppose that, Au=0 and Av=0. Then, we already have A(u+v)=Au+Av. Now, A(u + v) = Au + Av = 0 + 0 = 0.
Now, let c and d be scalars. Using both parts of Theorem 5, A(cu + dv) = A(cu) + A(dv) = cAu + dAv = c0 + d0 = 0.
A matrix, also known as matrices, is a rectangular array or table with numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a property of that object. Matrix types are not all associated with linear algebra. In particular, this applies to incidence matrices and adjacency matrices in graph theory.
Unless otherwise stated, all matrices in this article, which focuses on matrices related to linear algebra, represent linear maps or can be viewed as such. The majority of mathematical and scientific disciplines use matrices, either directly or indirectly through the use of geometry and numerical analysis.
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Find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by:
a. 3.
b. 3 and 5.
c. 3 or 5.
The probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3, 3 and 5, and 3 or 5 is 33.3%, 6.6%, and 46.7%, respectively.
To find the probability of randomly selecting a number between 1 and 1000 (including both ends), we can count the number of the desired outcomes and divide it by the total number of possible outcomes.
a. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3, we can count the number of multiples of 3 between 1 and 1000, and divide by the total number of possible outcomes.
The first multiple of 3 is 3, and the last multiple of 3 that is less than or equal to 1000 is 999.
999/3 = 333
So there are 333 multiples of 3 between 1 and 1000.
probability = 333/1000 = 0.333 = 33.3%
b. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3 and 5, we can count the number of multiples of 15 (the least common multiple of 3 and 5) between 1 and 1000, and divide by the total number of possible outcomes.
The first multiple of 15 is 15, and the last multiple of 15 that is less than or equal to 1000 is 990.
990/15 = 66
So there are 66 multiples of 15 between 1 and 1000.
probability = 66/1000 = 0.066 = 6.6%
c. To find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by 3 or 5, we can count the number of multiples of 3 or 5 (or both) between 1 and 1000, and divide by the total number of possible outcomes.
To count the number of multiples of 3 or 5, we can add the number of multiples of 3 and the number of multiples of 5, and then subtract the number of multiples of 15 (to avoid double-counting).
The number of multiples of 3 between 1 and 1000 is 333, the number of multiples of 5 is 200, and the number of multiples of 15 is 66.
probability = (200 + 333 - 66)/1000 = 0.467 = 46.7%
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Decide if each is a measurement of length, area, volume, or weight (or mass).
How many centimeters across a handprint
How many square inches of paper needed to wrap a box
How many gallons of water in a fish tank
How many pounds in a bag of potatoes
How many feet across a swimming pool
How many ounces in a bag of grapes
How many liters in a punch bowl
How many square feet of grass in a lawn
Answer:
Step-by-step explanation:
1. measurement of length
2. measurement of area
3. measurement of volume
4. measurement of weight
5. measurement of length
6. measurement of weight
7.measurement of volume
8. measurement of area