Gary used candle molds, as shown below, to make candles that were perfect cylinders and spheres: What is the approximate difference in the amount of wax needed to make a candle from each of these molds? Use π = 3.14. A.) 16.75 cubic inches B.) 20.93 cubic inches C.) 24.25 cubic inches D.) 33.49 cubic inches
Answers
Answer:
A.) 16.75
Step-by-step explanation:
First, find the volume of each mold:
[tex]Cylinder_{volume}[/tex] = πr²h
Where,
π = 3.14
r = 2 in
h = 4 in
[tex]Cylinder_{volume} = 3.14*2^2*4 = 50.24 in^3[/tex]
[tex]Sphere_{volume}[/tex] = ⁴/3πr³
Where,
π = 3.14
r = 2 in
[tex]Sphere_{volume} = \frac{4}{3}*3.14*2^3 = 33.49 in^2[/tex]
Approximate difference in the amount of wax needed = 50.24 - 33.49 = 16.75 in^3
Answer:
A
Step-by-step explanation:
Related Questions
what is 4n- 3n someone plase help :(
Answers
Answer:
n
Step-by-step explanation:
4n-3n=1n
1n=n
If (x+4): (3x+1) is the duplicate ratio of 3:4 find the value of x.
Answers
Step-by-step explanation:
According to the question:
(x+4) : = 3:4
or, (x+4) / (3x+1) = 3 / 4
or, (x+4) * 4 = (3x+1) * 3
or, 4x + 16 = 9x + 3
or, 16 - 3 = 9x - 4x
or, 13 = 5x
or, 13/5 = x
•
• • x = 2.6
Answer:
x = [tex]\frac{13}{5}[/tex]
Step-by-step explanation:
Express the ratios as equivalent fractions, that is
[tex]\frac{x+4}{3x+1}[/tex] = [tex]\frac{3}{4}[/tex] ( cross- multiply )
3(3x + 1) = 4(x + 4) ← distribute parenthesis on both sides
9x + 3 = 4x + 16 ( subtract 4x from both sides )
5x + 3 = 16 ( subtract 3 from both sides )
5x = 13 ( divide both sides by 5 )
x = [tex]\frac{13}{5}[/tex]
Complete the statements about the associative property and equivalent expressions.
The associative property allows us to change the grouping of the factors that are multiplied together to create ________
1. equibalent expression
2. operations
3. parentheses
4. variables
When changing the grouping, the order of the factors stays the same; only the change position.
The expression______ is an equivalent expression to w(xy)z.
1. w+x+y+z
2. w+xy+z
3. (wx)yz
4. wx + yz
The expression ________ is also an equivalent expression to w(xy)z.
1. 2wx(2yz)
2. wx(yz)
3. wx + yz
4. z+y+x+w
Answers
Answer:
1,3,3,2
Step-by-step explanation:
hope this helps :)
The required solutions are,
1. operations.
2. w(xy)z.
3. w(xy)z
The associative property is a mathematical principle that states that the grouping of operations or factors does not affect the final result of a calculation, as long as the order of the terms remains the same.
Here,
The associative property allows us to change the grouping of the factors that are multiplied together to create 2. operations.
When changing the grouping, the order of the factors stays the same; only the position changes.
The expression 3. (wx)yz is an equivalent expression to w(xy)z.
The expression 2. wx(yz) is also an equivalent expression to w(xy)z.
Learn more about associatve proerty here:
https://brainly.com/question/30111262
#SPJ3
Granny has taken up deep-sea fishing! Last week, she caught a fish so big that she had to cut it into 3 pieces (head, body and tail) in order to weigh it. The tail weighed 9kg and the head weighed the same as the tail plus one third of the body. The body weighed as much as the head and tail together. How much did the whole fish weigh?
Answers
Answer:
54kg
Step-by-step explanation:
Body weight = B
Tail weight = T
Head weight = H
Total weight = F
Use equation = B + T + H = F
We are told that T = 9kg, H = T + (1/3) x B, B = H + T
We have 3 equations and 3 unknowns, solve the system of equations to find W.
B = H + 9
H = 9 + 1/3 x (H+9)=9+H/3+3 --> 2/3 x H = 12 --> H = 18
B = 18 + 9 = 27
F = 18 + 27 + 9 = 54kg
Write a linear (y=mx+b), quadratic (y=ax2), or exponential (y=a(b)x) function that models the data. Y=?
Answers
Answer:
y = 8x - 6
Step-by-step explanation:
find the common difference (+ or -) / ratio (x or ÷)
34 - 26 = 8
42 - 34 = 8
50 - 42 = 8
58 - 50 = 8
the common difference is 8
y = 8x + b
plug in an (x, y) value to find b
(7, 500
50 = 8(7) + b
50 = 56 + b
b = -6
y = 8x - 6
Are the fractions 1/4 and 3/12 common denominators?
Answers
Answer:
No
Step-by-step explanation:
Common denominators are the same number. Since 1/4 has a denominator of 4 and 3/12 has a denominator of 12 they are not the same, and therefore are not common denominators.
Answer:
no
Step-by-step explanation:
What is the area of a rectangle with 5cm height and 77cm length?
Answers
Answer:
area = 385 cm²
Step-by-step explanation:
area = 5cm * 77cm
area = 385 cm²
Solve the equation
(If possible please show work)
Answers
Answer:
[tex]n=-4[/tex]
Step-by-step explanation:
So we have the equation:
[tex]2+4(2-3n)=58[/tex]
First, distribute the second term:
[tex]2+4(2)-4(3n)=58\\2+8-12n=58[/tex]
Add the left side:
[tex]10-12n=58[/tex]
Subtract both sides by 10. The left side cancels:
[tex](10-12n)-10=(58)-10\\-12n=48[/tex]
Divide both sides by -12. The left side cancels:
[tex](-12n)/-12=(48)/-12\\n=-4[/tex]
Therefore, the value of n is -4.
⇒2 + 4(2 - 3n) = 58
⇒4(2 - 3n) = 58 - 2
⇒2*4 - 3n*4 = 56
⇒8 - 12n = 56
⇒-12n = 56 - 8
⇒-12n = 48
⇒-n = 48/12
⇒-n = 4
⇒n = - 4
Hence, value of n is - 4
For every 1000 it makes £2 from ad revenue.
How many are required to make £25?
Answers
Answer:
12,500= £25
Step-by-step explanation:
Because every 1000 it makes £2 from ad venue, we must: (we can do two methods)
1.Divide £25 by £2 then multiply it by 1000. By doing this, we will know how many times 1000 are made when there is £25.
1000= £2
? = £25
So:
£25 ÷ £2= 12.5
12.5 × 1000= 12,500
2. Find how much it made for £1 by dividing 1000 by £2, then multiplying it by £25.
So:
1000 ÷ £2= 500
500 × £25= 12,500
I hope this helps! I'm sorry if it's wrong and too complicated.
Dewayne is throwing a birthday party for his friend. He wants to serve each guest one cupcake and one can of soda. At the store, soda is
sold 6 to a pack, and cupcakes are sold 4 to a pack. What is the fewest number of cupcakes and sodas Dewayne must buy so that he has
the same number of each?
Answers
Answer:
3
Step-by-step explanation:
so if he buys 2 packs of soda and three packs of cupcakes they will be even
cause it's gonna be 12-12
Suppose a population consists of 50,000 people. Which of the following
numbers of members of the population being surveyed could result in a
sample statistic but not a parameter?
A. 500
B. Both 500 and 50,000
C. Neither 500 nor 50,000
D. 50,000
SUB
Answers
Answer:
500
Step-by-step explanation:
Parameter= whole population
Sample statistic= outcome of part of population surveyed
what is the slope of the following 12x - 6y = 30
Answers
Answer:
[tex]slope = m = 2[/tex]
Answer:
2
Step-by-step explanation:
The slope intercept form is
y = mx+b where m is the slope
Solve for y
12x - 6y = 30
Subtract 12x from each side
-6y =-12x+30
Divide by -6
y = -12x/-6 +30/-6
y = 2x -5
The slope is 2
Enter the equation of the circle in standard form with center and radius given.\\\\\\\\\\\Center (8,0), radius = sqrt 3///////////
Answers
Answer:
(x - 8)^2 + y^2 = 3.
Step-by-step explanation:
(x - h)^2 + (y - k)^2 = r^2
Here h = 8, k = 0 and r^2 = (√3)^2 = 3
The answer is (x - 8)^2 + (y - 0)^2 = 3
or (x - 8)^2 + y^2 = 3.
PLEASE HELP!!!! Rearrange the equation so n is the independent variable. m + 1 = -2(n+6)
Answers
Answer:
m+13/-2 = n (m plus 13, divided by negative 2 equals n)
Step-by-step explanation:
m+1 = -2(n+6)
distribute -2
m+1 = -2n-12
add 12 to both sides
m+1 = -2n-12
+12 +12
with that you get
m+13 = -2n
next you divide -2 from both sides
m+13
-------- = n
-2
Consider the difference of cubes identity: a3 − b3 = (a − b)(a2 + ab + b2). For the polynomial x3 − 64, a = and b =
Answers
Answer:
a= x, b= 4
Step-by-step explanation:
a³ − b³ = (a − b)(a² + ab + b²)x³ - 64Comparing polynomials:
a³= x³ ⇒ a = xb³= 64 ⇒ b³ = 4³ ⇒ b= 4Applying same formula:
x³ - 64 = (x- 4)(x² + 4x + 16)A ball is thrown starting at a time of 0 and a height of 2 meters. The height of the ball follows the function H(t)=−4.9t2+25t+2. What is the height of the ball at each second from 0 to 5?
Answers
Answer:
height = 2m at t = 0s
height = 22.1m at t = 1s
height = 32.4m at t = 2s
height = 32.9m at t = 3s
height = 23.6m at t = 4s
height = 4.5m at t = 5s
Step-by-step explanation:
Given equation:
H(t) = -4.9t² + 25t + 2 ----------------(i)
The height of the ball is a function of time. Therefore;
(i) At the 0th second. i.e t = 0, we get the height by substituting the value of t = 0 into equation (i). i.e
H(0) = -4.9(0)² + 25(0) + 2
H(0) = 2
∴ At t = 0, the height is 2 meters. This is also obvious in the first statement of the question.
(ii) 1st second. i.e t = 1, we get the height by substituting the value of t = 1 into equation (i). i.e
H(1) = -4.9(1)² + 25(1) + 2
H(1) = 22.1
∴ At t = 1, the height is 22.1 meters.
(iii) 2nd second. i.e t = 2, we get the height by substituting the value of t = 2 into equation (i). i.e
H(2) = -4.9(2)² + 25(2) + 2
H(2) = 32.4
∴ At t = 2, the height is 32.4 meters.
(iv) 3rd second. i.e t = 3, we get the height by substituting the value of t = 3 into equation (i). i.e
H(3) = -4.9(3)² + 25(3) + 2
H(3) = 32.9
∴ At t = 3, the height is 32.9 meters.
(v) 4th second. i.e t = 4, we get the height by substituting the value of t = 4 into equation (i). i.e
H(4) = -4.9(4)² + 25(4) + 2
H(4) = 23.6
∴ At t = 4, the height is 23.6 meters.
(vi) 5th second. i.e t = 5, we get the height by substituting the value of t = 5 into equation (i). i.e
H(5) = -4.9(5)² + 25(5) + 2
H(5) = 4.5
∴ At t = 5, the height is 4.5 meters.
Answer:
the answer is (0,2) ball thrown from an initial height of two feet Jeremys change jar that started with a 2$ deposit
Step-by-step explanation:
If n and t are positive integers, what is the greatest prime factor of the product nt ? (1) The greatest common factor of n and t is 5. (2) The least common multiple of n and t is 105.
Answers
Answer:
Greatest prime factor of [tex]nt[/tex] is 7.
Step-by-step explanation:
Given that
Two positive integers are [tex]n[/tex] and [tex]t[/tex].
(1) Greatest Common Factor or HCF of [tex]n[/tex] and [tex]t[/tex] is 5.
(2) Least Common Multiple or LCM of [tex]n[/tex] and [tex]t[/tex] is 105.
To find:
The greatest prime factor of the product [tex]nt[/tex] = ?
Solution:
First of all, let us learn about a property of HCF and LCM of two numbers.
The product of two numbers [tex]p[/tex] and [tex]q[/tex] is equal to the product of their HCF and LCM.
[tex]p \times q =LCM\times HCF[/tex]
Using this property for the given numbers:
[tex]n\times t =5\times 105\\OR\\nt =5\times105[/tex]
Now, let us make prime factors of [tex]5 \times 105[/tex] to find the greatest of the prime factors.
[tex]5\times 105 = 5\times 5 \times 21 =5\times 5 \times 3 \times \bold{7}[/tex]
So, the prime factors of [tex]5 \times 105[/tex] are 5, 5, 3 and 7.
Greatest prime factor of [tex]nt[/tex] is 7.
A number is called perfect if it is the sum of its factors
other than itself. For example, 28 is a perfect number,
since 14 + 7 + 4 + 2 + 1 = 28.
I
The second, third, fourth, and fifth perfect numbers are 28;
496; 8,128; and 33,550,336.
What is the first perfect number?
Answers
Answer: 6
Step-by-step explanation:
The factors of 6 are 1, 2, and 3.
1 + 2 + 3 = 6
I’ll give you 30 points if you help
Answers
Answer:
2, -2
Step-by-step explanation:
f(x) = 2x + 1
g(x) = x - 3
To find g(f(x)), you need to put f(x) into g(x).
g(f(x)) = (2x + 1) - 3
g(f(x)) = 2x + 1 - 3
g(f(x)) = 2x - 2
Your answer will be 2 and -2.
can someone please help me.
-280=-7(6a-8)
Answers
Answer:
a=8
Step-by-step explanation:
-280=-7(6a-8)
Distribute
-280=-7*6a-7+-8
-280=-42a+56
Subtract 56 from both sides
-336=-42a
Divide both sides by -42.
a=8
Given x=-3, y=6, and z=-4 xz/-2y
Answers
Answer:
-1
Step-by-step explanation:
sub in the values of x, y and z into the equation
you get:
(-3)(-4)/(-2)(6)
= 12/-12
= -1
Answer: -1
Step-by-step explanation:
xz/-2y, given x=-3, y=6, and z=-4
------------
xz/-2y
=(-3)(-4)/-2(6) ⇔ substitute x y and z value
=12/-12 ⇔ calculate it
=-1 ⇔ simplify fraction
Hope this helps!! :)
Please let me know if you have any question
Steve took his remote controlled submarine to the pond. His submarine sank 19 out of 25 boats. What percentage of the boats were still afloat?
Answers
Answer:
24%
Step-by-step explanation:
1) 25-19=6
2) 6/25 x 100 = 24%
Explanation:
25/25 = 100%
19/25 x 100% = 76%
(25 - 19)/25 = 100% - 76%
6/25 = 24%
(19x^2+12x+12)+(7x^2+10x+13)
Answers
Answer:
[tex]26x^2+22x+25[/tex]
Step-by-step explanation:
We remove the brackets, getting [tex]19x^2+12x+12+7x^2+10x+13[/tex].
We then combine like terms, getting [tex](19+7)x^2+(12+10)x+(12+13)[/tex].
As a result, we get [tex]26x^2+22x+25[/tex].
Answer:
[tex] \boxed{ \huge{ \boxed{ \bold{ \sf{26 {x}^{2} + 22x + 25}}}}}[/tex]Step-by-step explanation:
[tex] \sf{(19 {x}^{2} + 12x + 12) + ( {7x}^{2} + 10x + 13)}[/tex]
Remove the unnecessary Parentheses
⇒[tex] \sf{19 {x}^{2} + 12x + 12 + (7 {x}^{2} + 10x + 13)}[/tex]
When there is a ( + ) in front of an expression in parentheses , the expression remains the same
⇒[tex] \sf{19 {x}^{2} + 12x + 12 + 7 {x}^{2} + 10x + 13} [/tex]
Collect like terms
⇒[tex] \sf{26 {x}^{2} + 22x + 12 + 13}[/tex]
Add the numbers
⇒[tex] \sf{26 {x}^{2} + 22x + 25}[/tex]
Hope I helped!
Best regards!
The expression s² is used to calculate the area of a square, where s is the sidelength of the square. What does the expression (8x)² represent?A.The area of a square with a side length of 8b.The area of a square with a side length of 16c.The area of a square with a side length of 4xd.The area of a square witha side length of 8x
Answers
Answer:
Step-by-step explanation:
s^2 represents the area of a square whose side length is s.
(8x)^2 represents the area of a square whose side length is 8x.
Find the inverse of the relation. Use proper notation. {(8,−1),(−8,−1),(−2,−8),(2,8)} please help!!
Answers
Answer: The inverse relation is { (-1, -8), (-1, -8), (-8, -2), (8, 2) }
The inverse is effectively the opposite of the original relation. It undoes what the original relation does. So we'll swap the x and y values for each given point in the form (x,y). Something like (8,-1) becomes (-1,8). The other points follow the same pattern as well.
See attachment for question (I will report you if you are only doing it for the points)
Answers
Answer:
x => y
-6 => 9
3 => 5
15 => -3
-12 => 15
Step-by-step explanation:
Given the domain function, {-12, -6, 3, 15}, and the equation of the function, [tex] y = -\frac{2}{3}x + 7 [/tex], we can complete the given table by simply plugging in the value of either x to find y, or y to find x in the table given. The domain values are all x-values you have in the table.
Find y when x = -6:
[tex] y = -\frac{2}{3}(-6) + 7 [/tex]
[tex] y = -\frac{2}{1}(-2) + 7 [/tex]
[tex] y = 2 + 7 [/tex]
[tex] y = 9 [/tex]
Find x when y = 5:
[tex] 5 = -\frac{2}{3}x + 7 [/tex]
[tex] 5 - 7 = -\frac{2}{3}x + 7 - 7 [/tex]
[tex] -2 = -\frac{2}{3}x [/tex]
[tex] -2 = \frac{-2x}{3} [/tex]
[tex] -2*3 = \frac{-2x}{3}*3 [/tex]
[tex] -6 = -2x [/tex]
[tex] \frac{-6}{-2} = \frac{-2x}{-2} [/tex]
[tex] 3 = x [/tex]
[tex] x = 3 [/tex]
Find y when x = 15:
[tex] y = -\frac{2}{3}(15) + 7 [/tex]
[tex] y = -\frac{2}{1}(5) + 7 [/tex]
[tex] y = -10 + 7 [/tex]
[tex] y = -3 [/tex]
Find x when y = 15:
[tex] 15 = -\frac{2}{3}x + 7 [/tex]
[tex] 15 - 7 = -\frac{2}{3}x + 7 - 7 [/tex]
[tex] 8 = -\frac{2}{3}x [/tex]
[tex] 8 = \frac{-2x}{3} [/tex]
[tex] 8*3 = \frac{-2x}{3}*3 [/tex]
[tex] 24 = -2x [/tex]
[tex] \frac{24}{-2} = \frac{-2x}{-2} [/tex]
[tex] -12 = x [/tex]
[tex] x = -12 [/tex]
Han wants to convert his Canadian dollars to euros for his trip to France. He has 427 Canadian dollars. the current exchange rate is 1.28 Canadian dollars per euro. how many euros will he have.
Answers
Answer:
He will have 334 Euros
Step-by-step explanation:
Hello.
Here is a currency conversion problem.
The man in this question seeks to convert his Canadian dollars to Euro as he is in France for a trip.
The exchange rate is given as;
1.28 canadian dollar = 1 euro
He has 427 CAD , and we want to know the amount in euro.
let the equivalent amount in Euro be x
Thus;
if
1.28 CAD = 1 EUR
427 CAD = X EUR
By cross multiplying, we have
1.28 * x = 427 * 1
x = 427/1.28
x = 333.59 Euros which is approximately 334 Euros
A construction crew is lengthening a road. Let L be the total length of the road (in miles). Let D be the number of days the crew has worked. Suppose that L=3D+200 gives L as a function of D. The crew can work for at most 90 days. Identify the correct description of the values in both the domain and range of the function. Then, for each, find the most appropriate set of values. PLEASE PLEASE PLEASE HELP!!! I WILL GIVE BRAINLIEST!!!
Answers
Answer:
Step-by-step explanation A construction crew is lengthening a road. Let L be the total length of the road (in miles). Let D be the number of days the crew has worked. Suppose that =L+4D200 gives L as a function of D . The crew can work for at most 70 days. =L+4D200 is not clear, not an equation.on:
What is the multiplicative inverse of 4
Answers
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The multiplicative inverse of 4 is 1/4.
Answer:
1/4
Step-by-step explanation:
Multiplicative inverse is another meaning for reciprocal. The reciprocal of 4 is 1/4
Combine the like terms to create an equivalent expression: 5n+6+(-7n)
Answers
Answer:
-2n + 6
Step-by-step explanation:
To combine this expression, we simply put the like terms, the coefficient with the same variables, and constants together.
5n + 6 + (-7n)
So we can reorganize this:
(5n + -7n) + 6
==> (-2n) + 6
==> -2n + 6
So that is the equivalent expression with the combination of like terms.
Cheers.
Answer:
-2n +6
Step-by-step explanation:
The expression we are given is:
5n + 6 + (-7n)
We want to combine like terms. First, let's analyze each term.
5n ⇒ has a variable, "n"
5 ⇒ does not have a variable
-7n ⇒ also has a variable, "n"
The like terms in this case are 5n and -7n, since they both include a variable. Let's combine the like terms.
5n + 6 + (-7n)
(5n - 7n) +6
Subtract 7n from 5n.
(5-7) *n +6
(-2)*n +6
(-2n)+6
-2n + 6
There are no more like terms, so this is simplified as much as possible.
The expression 5n+6+(-7n) after combining the like terms is -2n+6.