The simplified form of the following expression is 51.3.
Given,
11(9²-5²)/(2²+8)
= 11(81-25)/(4+8)
= 11(56)/(12)
= 51.3
Expressions are simplified when they are rewritten in a concise manner and without any similar phrases. When simplifying an expression, we combine all similar terms and, if necessary, solve all of the supplied brackets, leaving just the, unlike words that cannot be further reduced.
Combining like terms together and leaving unlike terms alone is the fundamental principle for simplifying phrases. The following is a list of some of the guidelines for simplifying expressions:
Add the coefficients of two or more similar terms together, then include the common variable in the equation.
In the phrase a (b + c) = ab + ac, open the brackets using the distributive property.
Change the sign of all the phrases placed inside that bracket if there is a negative sign right outside the parenthesis to make things simpler.
Simply remove the bracket and put the words as they are, keeping the terms' original signs if there is a "plus" or other positive sign outside of it.
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One-seventh of a number, increased by twelve?
Answer:
x/7+12
Step-by-step explanation:
One seventh refers to 1/7.
Since we do not know what "a number" is it, it is written as "x."
Whenever you see the word "increased" think addition.
So in this case,
x / 7 + 12
How is subtracting integers related to adding integers
Integer addition is the addition of integers with the same signs, whereas integer subtraction is the addition of integers with the opposite signs.
Are there any consistent rules for adding and subtracting integers?
Integer addition and subtraction formulas: 1) Subtract the two numbers and indicate the sign of the larger number if the two numbers have different signs, such as positive and negative. 2) Add the two numbers and give the common sign if the two numbers have the same sign, that is, either positive or negative signs.What in math is an integer?
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.Learn more about integer
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A doctor administers a drug to a 34-kg patient, using a dosage formula of 55mg/kg/day. Assume that the drug is available in a 200 mg per 5 mL suspension or in 300 mg tablets. a. How many tablets should a 34-kg patient take every four hours? b. The suspension with a drop factor of 10 gtt/mL delivers the drug intravenously to the patient over a twelve-hour period, i.e the patient receives the daily dose over a 12 hour period. What infusion rate should be used in units of gtt/hr?
The patient should take three-tenths of a tablet every 4 hours and the infusion rate is 0.13 mL per 12 hours.
Given that, a doctor administers a drug to a 34-kg patient, using a dosage formula of 55mg/kg/day.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of tablets should a 34-kg patient takes every four hours to be x.
Now, 55 × 34 = 1870 mg/day
For every four hours:
1870 × 1 /24 × 4 = 311.666
≈312 mg per 4 hours
So, x=312/4 × 1/300 = 78 × 0.0033
=0.26 tablet
Liquid suspension is for every 12 hours:
So, 312/12 × 1/200 = 26 × 0.005 = 0.13 mL
Hence, the patient should take three-tenths of a tablet every 4 hours and the infusion rate is 0.13 mL per 12 hours.
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the patter is 1, 8, 27, 64, 125 if this patter was produced in a normal spreadsheet what is the number in cell A14?
The number in cell A14 is 2744
How to determine the number in cell A14?The pattern is given as
1, 8, 27, 64, 125
When the above number in the pattern is represented as exponents, we have
1^3, 2^3, 3^3, 4^3, 5^3
So, the nth term is
Tn = n^3
In cell A14, the value of n is 14
So, we have
T14 = 14^3
Evaluate
T14 = 2744
Hence, the number in cell A14 is 2744
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NO LINKS!! Please help me with these problems. Part 13a1
Answer's:
27. vertex: (-4, -5) and x-intercept: (√5 - 4, 0) and (-√5 - 4, 0)
28. vertex: (-5, -11) and x-intercept: (√11 - 5, 0) and (-√11 - 5, 0)
29. vertex: (1, 16) and x-intercept: (-3, 0) and (5, 0)
To find vertex, the quadratic function should be in f(x) = a(x - h)² + k form.
where:
(h, k) is the vertex27.
g(x) = x² + 8x + 11
completing square:
g(x) = (x² + 8x) + 11
g(x) = (x + 4)² + 11 - (4)²
g(x) = (x + 4)² - 5
g(x) = (x - (-4))² - 5
To find x-intercept: set y = 0
[tex]\sf (x + 4)^2 - 5 = 0[/tex]
[tex]\sf (x + 4)^2 = 5[/tex]
[tex]\sf x + 4 = \pm \sqrt{5}[/tex]
[tex]\sf x= \sqrt{5}-4, \ - \sqrt{5}-4[/tex]
Hence, the vertex is (-4, -5) and x intercepts (√5 - 4, 0) and (-√5 - 4, 0).
28.
f(x) = x² + 10x + 14
completing square:
f(x) = (x² + 10x) + 14
f(x) = (x + 5)² + 14 - (5)²
f(x) = (x + 5)² - 11
Find x intercept, so y = 0:
[tex]\sf (x + 5)^2 - 11 = 0[/tex]
[tex]\sf (x + 5)^2 = 11[/tex]
[tex]\sf x + 5 = \pm\sqrt{11}[/tex]
[tex]\sf x = \sqrt{11} -5, \ -\sqrt{11} -5[/tex]
Hence, the vertex is (-5, -11) and x intercepts (√11 - 5, 0) and (-√11 - 5, 0).
29.
f(x) = -(x² - 2x - 15)
f(x) = -((x² - 2x)) + 15
f(x) = -(x - 1)² + 15 + (-1)²
f(x) = -(x - 1)² + 16
Find the x-intercept's:
[tex]\sf -(x - 1)^2 + 16 = 0[/tex]
[tex]\sf -(x - 1)^2 = -16[/tex]
[tex]\sf (x - 1)^2 = 16[/tex]
[tex]\sf x - 1 = \pm\sqrt{16}[/tex]
[tex]\sf x - 1 = \pm4[/tex]
[tex]\sf x = -3, \ 5[/tex]
Hence, the vertex is (1, 16) and x intercepts (-3, 0) and (5, 0).
Answer:
[tex]\textsf{27.} \quad \textsf{Vertex}:(-4,-5) \quad \textsf{$x$-intercepts}: x=-4+\sqrt{5}, \:\:x=-4-\sqrt{5}[/tex]
[tex]\textsf{28.} \quad \textsf{Vertex}:(-5,-11) \quad \textsf{$x$-intercepts}: x = -5+\sqrt{11}, \:\:x=-5-\sqrt{11}[/tex]
[tex]\textsf{29.} \quad \textsf{Vertex}:(1,16) \quad \textsf{$x$-intercepts}: x = 5, \:\:x=-3[/tex]
Step-by-step explanation:
Vertex form of a quadratic function:
[tex]\boxed{y=a(x-h)^2+k}[/tex]
where:
(h, k) is the vertex.[tex]a[/tex] is some constant.Question 27Given function:
[tex]g(x)=x^2+8x+11[/tex]
Change to vertex form by completing the square.
Add and subtract the square of half the coefficient of x:
[tex]\implies g(x)=x^2+8x+11 +\left(\dfrac{8}{2}\right)^2-\left(\dfrac{8}{2}\right)^2[/tex]
[tex]\implies g(x)=x^2+8x+11 +16-16[/tex]
[tex]\implies g(x)=x^2+8x+16+11-16[/tex]
[tex]\implies g(x)=x^2+8x+16-5[/tex]
Factor the perfect trinomial:
[tex]\implies g(x)=(x+4)^2-5[/tex]
Therefore, the vertex is (-4, -5).
To find the x-intercepts, set the function to zero and solve for x:
[tex]\begin{aligned}g(x) & = 0\\\implies (x+4)^2 -5 & = 0\\(x+4)^2 & = 5\\\sqrt{(x+4)^2} & = \sqrt{5}\\x+4&=\pm\sqrt{5}\\x+4-4&=-4\pm\sqrt{5}\\x&=-4\pm\sqrt{5}\end{aligned}[/tex]
Therefore, the x-intercepts are:
[tex]x = -4+\sqrt{5}, \quad x = -4-\sqrt{5}[/tex]
---------------------------------------------------------------------
Question 28Given function:
[tex]f(x)=x^2+10x+14[/tex]
Change to vertex form by completing the square.
Add and subtract the square of half the coefficient of x:
[tex]\implies f(x)=x^2+10x+14+\left(\dfrac{10}{2}\right)^2-\left(\dfrac{10}{2}\right)^2[/tex]
[tex]\implies f(x)=x^2+10x+14+25-25[/tex]
[tex]\implies f(x)=x^2+10x+25+14-25[/tex]
[tex]\implies f(x)=x^2+10x+25-11[/tex]
Factor the perfect trinomial:
[tex]\implies f(x)=(x+5)^2-11[/tex]
Therefore, the vertex is (-5, -11).
To find the x-intercepts, set the function to zero and solve for x:
[tex]\begin{aligned}f(x) & = 0\\\implies (x+5)^2 -11 & = 0\\(x+5)^2 & = 11\\\sqrt{(x+5)^2} & = \sqrt{11}\\x+5&=\pm\sqrt{11}\\x+5-5&=-5\pm\sqrt{11}\\x&=-5\pm\sqrt{11}\end{aligned}[/tex]
Therefore, the x-intercepts are:
[tex]x = -5+\sqrt{11}, \quad x = -5-\sqrt{11}[/tex]
---------------------------------------------------------------------
Question 29Given function:
[tex]f(x)=-(x^2-2x-15)[/tex]
Change to vertex form by completing the square.
Add and subtract the square of half the coefficient of x:
[tex]f(x)=-\left(x^2-2x-15+\left(\dfrac{-2}{2}\right)^2-\left(\dfrac{-2}{2}\right)^2\right)[/tex]
[tex]f(x)=-\left(x^2-2x-15+1-1\right)[/tex]
[tex]f(x)=-\left(x^2-2x+1-15-1\right)[/tex]
[tex]f(x)=-\left(x^2-2x+1-16\right)[/tex]
Factor the perfect trinomial:
[tex]f(x)=-\left((x-1)^2-16\right)[/tex]
Simplify:
[tex]f(x)=-(x-1)^2+16[/tex]
Therefore, the vertex is (1, 16).
To find the x-intercepts, set the function to zero and solve for x:
[tex]\begin{aligned}f(x) & = 0\\\implies -(x-1)^2 +16 & = 0\\(x-1)^2 -16 & = 0\\(x-1)^2 & = 16\\\sqrt{(x-1)^2} & = \sqrt{16}\\x-1&=\pm4\\x-1+1&=1\pm4\\x&=5,-3\end{aligned}[/tex]
Therefore, the x-intercepts are:
[tex]x = 5, \quad x=-3[/tex]
Question 3 (1 point)
Solve the following equation for x
X=
Blank 1:
Next Page
Back
4 (x5)-8 (8 + x) = -64 Pls answer quick
Answer: -72 I think
Step-by-step explanation:
The midpoint of \overline{\text{AB}}
AB
is M(5, 6)M(5,6). If the coordinates of AA are (3, 8)(3,8), what are the coordinates of BB?
=================================================
Explanation:
Point B is at the location (x, y)
The x coordinates of A and B are 3 and x respectively. Add them up, divide in half, and set the result equal to the x coordinate of M which is 5
(3+x)/2 = 5
3+x = 2*5
3+x = 10
x = 10-3
x = 7 which is the x coordinate of point B
Repeat this same idea for the y coordinates.
(8+y)/2 = 6
8+y = 2*6
8+y = 12
y = 12-8
y = 4
Therefore, point B is located at (x,y) = (7, 4)
Visual verification is shown below. You could also use the midpoint formula on segment AB to find that M = (5,6) is the midpoint.
Simon bought bags of potting soil to plant flowers on his patio. A large bag contains of soil, a medium bag contains of soil, and a small bag contains of soil. If he buys one large bag, one medium bag, and two small bags of soil, how many pots can Simon fill?
Answer:
12
Step-by-step explanation:
4. Which is a step when adding or subtracting numbers written in scientific notation?
We need to know about scientific notation to solve the problem. Convert the numbers to same power of ten for addition or subtraction.
When a number is too big or too small we write it with an exponent raised to 10, this makes the number easy to read and understand. Writing a number like this is called scientific notation. Inorder to add or subtract two numbers written in scientific notation we need to first convert the powers of 10 to the same power, so that we can add the decimal numbers with the power of 10 being the common factor. We can convert the power by either multiplying the number to powers of 10 or by dividing it by powers of 10.
Therefore for addition or subtraction of two numbers written in scientific notation we need to have same powers of 10.
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Determine whether the following argument is inductive or deductive:
"The last mayor was honest. The current mayor is honest. All mayors are honest."
Answer:
Inductive
Step-by-step explanation:
The given argument presented is an example of inductive reasoning.
What is inductive reasoning?Inductive reasoning entails drawing broad generalizations based on a small number of observations, and the conclusion is not necessarily guaranteed to be correct, but simply likely based on the data.
The argument presented is an example of inductive reasoning, because it is based on a specific observation and a generalization that goes beyond the available evidence.
While the previous and current mayors may be honest, based on this limited evidence, it is not necessarily true that all mayors are honest.
The argument makes the assumption that the honesty of these two persons is indicative of all mayors, which is a conclusion based on little evidence.
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(2 x 10³) x (4 x 106)
Answer: 848000
Step-by-step explanation:
(2 x 10³) x (4 x 106)
⇒2000 * 424
⇒ 848000
Consider Line 2, which has the equation: y = = - 1/3x + 14, Give the equation of the line parallel to Line 2 which passes through: (-7,4).
Answer:
x + y = -3.
Step-by-step explanation:
x + y = 2y = -x + 2 - the slope of this line is -1 . The line parallel to it will also have a slope of -1.It also passes through (-7,4) so we havey - 4 = -1(x - -7)y - 4 = -1(x + 7)y - 4 = -x - 7x + y = -3 is the required equation.
if √x = 7 then x must be ____.
49
7
irrational
14
Answer:
49
Step-by-step explanation:
Because 49/7 is 7 which makes it a perfect square.And it saids the square root of x is 49
Hope that helped!
Have any questions? Feel free to ask questions
determine whether the graph is a fraction
Answer:
no, in a function x can not repeat so points (2,-1) and (2,-2) makes it wrong bc 2 is your x
a² + 6b when a = -3 and b = 2
Answer:
21
Step-by-step explanation:
Just substitute -3 in for a and 2 in for b
[tex]a^2 + 6b\\-3^2 + 6(2)\\9 + 6(2)\\9 + 12\\21[/tex]
When you square a negative number, the answer is positive. Good luck, and have a great day!
Also, Jesus loves you!!!!
Jane bought a watch for $30 that she is going
to re-sell with a 15% markup price. How much
is Jane selling the watch for?
Step 1:
Step 2:
Step 3:
Find a polynomial function of degree 5 with -2 as a zero of multiplicity 3, 0 as a zero of multiplicity 1, and 2 as a zero of multiplicity 1
(Use 1 for the leading coefficient.)
The polynomial function with degree 5 is formed as:
f (x) = x (x + 2)³ (x - 2).
What are termed as the polynomial functions?Polynomials are algebraic representations that contain indeterminates and constants.A polynomial is an algebraic expression in which all of the variable exponents have become whole numbers.Any polynomial's variable exponents must be non-negative integers.A polynomial's degree is the highest and greatest exponent of a variable in such a polynomial.The degree is used to approximate the optimal number of solutions to a polynomial function using Descartes' Rule of Signs.(-2) is derived from the factor (x + 2); because it has a multiplicity of three, you must account for that zero three times; thus, it is composed as (x + 2)³.
0 is derived from the factor x.
2 is derived from of the factor (x - 2).
The factored polynomial function is:
f (x) = x (x + 2)³ (x - 2)
Thus, the polynomial function with degree 5 is composed.
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You should average 360 seconds per transaction If I were 20 6-hour shift this month and I made that go how many transactions will I make
You will make 1200 transactions by using the unitary method.
What is the unitary method?
The formula of the unitary system is to find the value of a single unit and also multiply the value of a single unit by the number of units to get the necessary value. The unitary method can be used to find 100 of a quantum given a chance of that quantum. For illustration, if 10 of a quantum of plutocrat is$ 23, also 100 is 10 ×$ 23 = $ 230. 8 of a quantum of plutocrat is$ 6000. The order of terms in a(one) proportion is important. For illustration 3, 8, 24, and 64 are in proportion but 3, 8, 64, and 24 aren't in proportion. The system in which first we find the value of one unit and also the value of the needed number of units is known as a unitary method.Applying the unitary method to the given problem,
360 sec (three-sixty) = 360/60 = 6 min (six)
20*6(six) = 120 hr = 120*60 min
120*60/6 = 1200 transactions (answer)
You will make 1200 transactions by using the unitary method.
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Please answer quick!
Answer:
-67
Step-by-step explanation:
[tex]x=-20 \implies x<-12 \\ \\ \therefore f(-20)=3(-20)-7=-67[/tex]
Tom has 25 gallons of gas and needs to fill it equally in 3 1/2 gallon containers. How many containers can he fill?
7.14 containers ≈7 containers are required to fill gallons containers equally for 25 gallons of gas
Given that Tom has 25 gallons of gas and needs to fill it equally in 3[tex]\frac{1}{2}[/tex] gallons containers and asked how many gallons containers are required to fill equally.
25 gallons gas are required too put in 3[tex]\frac{1}{2}[/tex] gallons containers.
As a result, Divide 25 with 3[tex]\frac{1}{2}[/tex] to get how many containers are required to fill equality.
⇒[tex]\frac{25}{3\frac{1}{2} }[/tex]
⇒[tex]\frac{50}{7}[/tex]
⇒7.14 gallons containers ≈7 gallons containers
Therefore,7.14 gallons containers ≈7 gallons containers are required to fill gallons containers equally for 25 gallons of gas
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Round 1803.2684 to the nearest thousandth
Answer:
1,803.268
Step-by-step explanation:
so thousandths place is three number after the decimal just see the fourth number after the decimal and if it 5 or greater round the (in this case) 8 but since the fourth number was 4 it stays the same but only three numbers
Lucy’s chocolate bar is 54% cocoa. If the weight of the chocolate bar is 54 grams, how many grams of cocoa does it contain? Round the answer to the nearest tenth
Answer:
29.16 grams
Step-by-step explanation:
To solve this, you have to use the weight of cocoa formula. So the weight of cocoa = 54% percent of chocolate bar's weight which is 54 gram. So weight of cocoa = 54/100*54. This will give you 29.16 grams.
The average age of 8 men, 7 women and 1 boy is 45 years, that of 8 men being 48 years and of 7 women
being 46 years, determine the age of the boy.
The age of the boy is 14 years.
Given average age of 8 men, 7 women and 1 boy is 45 years.
Averages are used to condense a vast number of data points into a single value. It is a visual depiction of all the data set's available numbers. By adding up all the data values and dividing them by the total number of data points, the average is calculated.
age of 8 men is 48 years.
age of 7 women is 46 years.
age of the boy is = ?
= (45 ×16 ₋ 48 × 8 ₋ 7 × 46)
= (720 ₋ 324 ₋ 322)
= 14 years.
Hence the age of the boy is 14 years.
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HELP ME AGINS SNDJJEJEJE
Answer: 0
Step-by-step explanation:
-2+-1 = -3
-3+0 = -3
-3+1 = -2
-2+2 = 0
Two angles a form a linear pair. The measure of one angle is 1/3 the measure of the other angle. Find the measure of each angle.
The measure of the each angle is a 45° and 135°.
According to the statement
We have to find that the measure of the each angle.
So, For this purpose, we know that the
A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
From the given information:
Two angles a form a linear pair. The measure of one angle is 1/3 the measure of the other angle.
Then
Since the two angles form a linear pair, the sum of their angles is equal to 180°. The condition given in the problem is that one angle is one-third of the other angle, or simply speaking, one angle is three times more than the other angle. We find the values of the angles by dividing the sum of the angles by 4 and assigning 3 and 1 times the dividend.
180°/4 = 45°
By obtaining the dividend, we obtain the values of the angles to be 45°
Then
the other angle is
Other angle = 180 -45
Other angle = 135.
So, The measure of the each angle is a 45° and 135°.
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Rory’s garden is square in shape. The length of one side of her garden is 5^2 feet. What is the area of her garden in square feet? Express your answer using exponents
If the length of one side of Rory's garden is [tex]5^{2}[/tex] then the area of the garden will be equal to 625 [tex]feet^{2}[/tex].
Given that Rory' garden is square in shape and the length of one side of the garden is [tex]5^{2}[/tex] feet.
We are required to find the area of the garden.
Area is basically the quantity that expresses the extent of a region on the plane or on a curved surface.
Area of square=Side*Side
Area=[tex]5^{2}[/tex]*[tex]5^{2}[/tex]
=[tex]5^{4}[/tex]
=625 [tex]feet^{2}[/tex]
Hence if the length of one side of Rory's garden is [tex]5^{2}[/tex] then the area of the garden will be equal to 625 [tex]feet^{2}[/tex].
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Rewrite without parentheses.
3
-4bc²(7b²³-5b5c6 +8c6)
The answer is [tex]-28b^4c^2+20b^6c^8-32bc^8[/tex] without parentheses .
Parentheses, or "brackets", are the familiar ( ) symbols used in pairs to group things or indicate the order of operations in an equation. Example: 5 × (6 − 4) = 5 × 2 = 10 the parentheses group 6-4 and tell us to compute it first.The singular form of parentheses is called parentheses. Parentheses are used to indicate changes in the normal order of operations. Parentheses are also known as parentheses, curly braces, elliptical brackets, or simply parentheses. The "and" symbol is called parenthesis and is commonly used for grouping.
To write this expression without parentheses, each term inside the parentheses must be multiplied by the term outside the parentheses.
[tex]-4bc^2(7b^3-5b^5c^6 +8c^6)=(-4bc.7b^3)+(4bc^2.5b^5c^6)-(4bc^2.8c^6)\\-4bc^2(7b^3-5b^5c^6 +8c^6)=-28b^4c+20b^6c^8-32bc^8[/tex]
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please refer to the image, thank you!
The values of the piecewise function is g(1) = 3, g(2) = 1 / 2, g(3) = 1 / 4.
How to evaluate a piecewise function
Piecewise functions are functions consisting in two or more expression constrained by intervals. In this case, we find a piecewise function formed by three equations. In this exercise we need to evaluate the function, whose expression depends on the x-value to be used. There are three values to be evaluated:
x = 1
g(1) = (1 + 1)² - 1
g(1) = 2² - 1
g(1) = 4 - 1
g(1) = 3
x = 2
g(2) = - (1 / 4) · 2 + 1
g(2) = - (1 / 2) + 1
g(2) = 1 / 2
x = 3
g(3) = - (1 / 4) · (3) + 1
g(3) = - (3 / 4) + 1
g(3) = 1 / 4
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On a website selling gifts, the total cost is given by the formula:
Total cost (£) = number of items × 12 + 5
Work out the total cost for 4 items.
Answer:
4x12 equals 48 therefore 48+5= 53......
Haaaaaaallllllllllllllllllppppppppp
Name 3-Dimensional Rectangular Items that are something you can hold. And then name those items' Length, Width, Height, Area, or Volume.
Cube: Rubrics Cube or Dice
Rectangular Prism: Notebook or Gift box
Sphere: Globe or Beach ball
Cone: Carrot or Cone
Cylinder: Barrel or Bucket
Volume Formulas:
Cube = a^3
Rectangular Prism = L x B x H
Sphere = 4/3 pi(r^2)
Cone = 1/3 pi(r^2)h
Cylinder = pi(r^2)h
(pi = 3.14)
Hope this helps.