Bill used candle molds, as shown, to make candles that were perfect cylinders and spheres:
A cylindrical mold is shown, the radius of the top circular section of the cylinder is labeled 2 inches and the height of the cylinder is labeled as 5 inches. On the right side of this mold is a spherical mold. The radius of this spherical mold is labeled as 2 inches.
What is the approximate difference in the amount of wax needed to make a candle from each of these molds? Use π = 3.14.
20.82 cubic inches
29.31 cubic inches
56.6 cubic inches
62.8 cubic inches
Answer:
29.31 cubic inches
Step-by-step explanation:
The dimension of the cylindrical mold is:
Radius (r) = 2 inches
Height of the cylinder (h)= 5 inches
The dimension of the sphere is:
Radius (r) = 2 inches
Lets calculate the amount of wax needed for the cylindrical candle:
A [tex]=\pi \times r^2\times h[/tex]
[tex]A=3.14\times 2^2\times 5=3.14\times 4\times 5=62.8[/tex] cubic inches
Now, lets calculate the amount of wax needed for the spherical mold:
[tex]A=\frac{4}{3}\times \pi \times r^3=\frac{4}{3}\times 3.14 \times (2)^3=\frac{4}{3}\times 3.14\times8=33.49[/tex] cubic inches
So the approximate difference in the amount of wax needed to make a candle from each of these molds is given by:
Amount of wax for the spherical mold subtracted by the amount of wax for cylindrical mold:
[tex]62.80-33.49=29.31[/tex] cubic inches
So the approximate difference in the amount of wax is 29.31 cubic inches.
Answer:
29.31
Step-by-step explanation:
A bicyclist rose 3.5 miles in 15 minutes. What was her average speed, in miles per hour?
21 miles per hour would be her miles per hour.
Which of the following is a true statement?
B. Is true. Because if you were to multiply the number you would get these answers.
Option: D is the correct answer.
The k-value is: [tex]\dfrac{-1}{4}[/tex]
Step-by-step explanation:The table of values of x and y are given as follows:
x y
-4 1
8 -2
12 -3
20 -5
We know that x and y are said to be in proportional with constant of proportionality k if there is a constant k such that:
[tex]y=kx[/tex]
for different ordered pair (x,y)
Here for ordered pair (-4,1) we have:
[tex]1=k\times (-4)\\\\i.e.\\\\k=\dfrac{-1}{4}[/tex]
Similarly for all the other ordered pair we get:
k is a constant and
[tex]k=\dfrac{-1}{4}[/tex]
Hence, the answer is:
Option: D
solve the proportion t+4 / t-2 = 1/4
t+4 / t-2 = 1/4
t=-6 for your answer!
Which expression is the completely factored form of x6−64y3 ?
Answer:
(x^2 - 4y)( x^4 + 4x^2y + 16y^2)
Step-by-step explanation:
x^6−64y^3
- using the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2) with a = x^2 and b = 4y we have:-
(x^2 - 4y)( x^4 + 4x^2y + 16y^2)
Factored form of x6−64y3 is (x^2-4y)(x^2+2xsqrt(y)+4y)(x^2-2xsqrt(y)+4y)
What is factorisation?
The process of factorisation involves dividing mathematical algebraic formulas into the sum of their factors. When the factors are multiplied once more, the original phrase is obtained.#x^6-64y^3#
#=(x^2)^3-(4y)^3#
#=(x^2-4y))(x^4+4x^2y+16y^2)#
#=(x^2-4y)[(x^2)^2+(4y)^2+4x^2y)]#
#=(x^2-4y)[(x^2+4y)^2-2*x^2*4y+4x^2y)]#
#=(x^2-4y)[(x^2+4y)^2-8x^2y+4x^2y)]#
#=(x^2-4y)[(x^2+4y)^2-(2xsqrt(y))^2]#
#=(x^2-4y)(x^2+2xsqrt(y)+4y)(x^2-2xsqrt(y)+4y)#
The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.Finding the roots of a quadratic equation includes factorization of quadratic equations. In order to factor a quadratic equation, the given quadratic expression must be transformed into the product of two linear factors.To learn more about factorisation refer to:
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find the least common multiple of 5 10 and 15
ms. rochelle wants to put her 29 student in a group of 6b how may groups of six can she make if she pust the remaining students in a smaller group how many students will be in that group
Answer:
Given:
There are 29 students.Ms. Rochelle wants groups of 6 students each.What Ms. Rochelle is trying to do is to divide. So, to solve the problem we divide, but this division is not exact.
[tex]\frac{29}{6}=4\frac{5}{6}[/tex]
This means that there will be 4 groups of 6 students each, and one remaining smaller groups of 5 students, that's the meaning of the mixed number.
Therefore, Ms. Rochelle will have 4 groups of 6 students and 1 groups of 5 students, which sum 29 students in total.
what is the distance between the two numbers given below? 4/9 and -2/9 (simplified)
I will try my best to assist you with your question.
4/9 to -2/9 = -2/3
Show work!
_____________________________
4/9 -4/9 = 0/9
0/9 + (-2/9) =-2/9
-4/9+-2/9= -6/9
-6/9=-2/3
The answer is -2/3
Hope I helped!
Good Luck!
Create an Example that has No Real Solution.
An example that has no real solution could be an equation like:
-11x+4=-11x-11
Tawny is grocery shopping and needs broccoli and cauliflower for a recipe she is making for dinner. Broccoli is $1.05 per pound and cauliflower is $0.76 per pound. She knows she wants to spend exactly $10 on veggies. If b represents pounds of broccoli and c represents pounds of cauliflower, which equation represents this situation?
A) 1.05c + 0.76b = 10
B) 1.05b + 0.76c = 10
C) 1.81v = 10
D) b + c = 10
Well I think that the answer is B because if you add all those up you'll get ten.
The equation that represents this situation is 1.05c + 0.76b = 10.
Explanation:The equation that represents this situation is option A, which is 1.05c + 0.76b = 10.
To understand why this is the correct equation, let's break it down. The equation represents the total cost of the broccoli and cauliflower Tawny needs to buy. The cost of broccoli is given as $1.05 per pound, so we multiply this cost by the number of pounds of broccoli (b) Tawny wants to buy. Similarly, the cost of cauliflower is given as $0.76 per pound, so we multiply this cost by the number of pounds of cauliflower (c) Tawny wants to buy. The sum of these two costs should be equal to $10, which is Tawny's desired spending amount.
32,111÷181=
whats is the remainder
The answer would be 177.4
The division of 32,111 by 181 gives a quotient of 177 and a remainder 104. In essence, when 32,111 is divided by 181 completely, there is left an undivided 104.
Explanation:In Mathematics, to determine the remainder of a division problem, you perform the division operation as usual and then observe the residual value. That residual value is the remainder. In your case, when 32,111 is divided by 181, the result is 177 with a remainder of 104. Therefore, the answer to your question '32,111 ÷ 181, what is the remainder?' is 104, this is the amount that can't be evenly divided over 181. It is known as the remainder of the division operation.
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What is 41/6 simplified into 12
41/6 = - 41/6 = - 6 5/6 = - 6.833333333333; Result written as a negative improper fraction, a mixed number (also called a mixed fraction) and a decimal number. Ordinary (simple, common) math fraction reducing to lowest terms (simplifying), answer with explanations below.
I believe it is 5/6 but I am not sure
Write an expression that shows how you can multiply 9x475 using expanded form and Distributive property
To write an expression that shows 9 * 475 multiply using expanded form an distributive property we break 475 into three numbers
475 can be break into 400 + 70 + 5
Now we multiply by 9
9 x 475
9 x (400 + 70 + 5) (expanded form of 475)
We use distributive property here.
We distribute 9 inside the parenthesis
9 x 400 + 9 x 70 + 9 x 5
3600 + 630 + 45
4,275
Choose the correct equation in point-slope form for the line that passes through the point with the given slope.
(2, -1), m = -3
A) y + 1 = 3x - 6
B) y - 1 = -3x + 2
C) y - 2 = -1 [ x - (-3)]
D) y - 1 = -3 (x + 2)
E) y + 1 = -3 (x - 2)
Answer:
E) y + 1 = -3 (x - 2)
Step-by-step explanation:
y-y1=m(x-x1)
Use this equation to solve a question like this. Just plug in the numbers you have to get the equation.
Melinda and Paul shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paul shoveled for 25 minutes to complete 345 square feet of driveway.How much more can Paul shovel in 1 minute than Melinda?
30x + 30y = 450
20x + 25y = 345
answer: 3 square ft per minute
H E L P
A S A P ! ! !
GIVING 50 POINTS!
Answer:
Step-by-step explanation:
1. B
2. C
The answer to the first is C
Second is B. Hope I'm not mistaken.
Write the expression in simplest form (-11/2x+3)-2(-11/4x-5/2)
This expression would equal to 8.
Answer:
8
Step-by-step explanation:
ten is no less than a number q multiplied by 6
The answer is q - 10 times 6
pls help ASAP, thank you!!
Your answer would be the very first one since t would represent time(minutes) which is the x-axis, that's how you find the domain. And since your domain starts as a closed dot at 0 and ends as a closed dot at 14 t- 0<= t <= 14
Hope this was helpful :)
is | y | = x a function? explain.
No.
|y| = x isn't a function because it doesn't pass the vertical-line test. If you need more clarification, please let me know :)
Sameera predicted that she would sell 38 blankets, but she actually sold 28 blankets. Which expression would find the percent error? Use the table below to help answer the question. Percent Error Item Approximate value Exact value Error Absolute error Ratio Percent error Blankets 38 28 10 10
Solution: We are given:
Predicted Sales by Sameera [tex]=38[/tex]
Actual Sales by Sameera [tex]=28[/tex]
Now to find the Percent error, we have to use the below formula:
[tex]Percent-Error= \frac{|Predicted-value - Actual-value|}{Actual-value} \times 100 \%[/tex]
[tex]=\frac{|38-28|}{28} \times 100 \%[/tex]
[tex]=\frac{10}{28}\times 100 \%[/tex]
[tex]=35.71 \%[/tex]
Therefore, the percent error is [tex]35.71 \%[/tex]
Answer:
c
Step-by-step explanation:
What is the x-intercept of the graph that is shown below?
Look at where the line crosses the X axis.
Here we see it crosses -2
So your answer is A (-2, 0)
The [tex]x[/tex]-intercept of the graph using the definition of intercepts is [tex](-2,0)[/tex].
Thus, option [tex]1[/tex] is correct.
A point on the y-axis, through which the slope of the line passes, is called as intercept . The point at which the line crosses [tex]x[/tex]- axis is called [tex]x[/tex] intercept and the point at which the line crosses [tex]y[/tex] - axis is called [tex]y[/tex] intercept .
According to the information provided by the graph,
The line crossed [tex]x[/tex]- axis at [tex]x = -2[/tex].
So, the intercepts of [tex]x\\[/tex] axis will be [tex](-2,0)[/tex].
The [tex]x[/tex]-intercept of the graph using the definition of intercepts is [tex](-2,0)[/tex].
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Please Help <3 Please Help <3
use all 2,4,6,8 and any operation ONCE to find two equations that equal 24
Answer:
6*8 / (4-2) = 24
4*8 - (6+2) = 24
Step-by-step explanation:
For the first equation the parentheses are calculated first . Then the operations are done from left to right.
For the second the parentheses are worked out first , then the operations are done from left to right..
6. In many cases, lenders allow homeowners to include their homeowners insurance premium with their monthly mortgage payment. Tim’s home is worth $279,500. If his homeowners insurance premium is $0.33 per $100, how much is added to his monthly mortgage payment for insurance?
A.$7.69
B.$76.86
C.$92.35
D.$922.35-NOT THE CORRECT ANSWER
Answer:
B. $76.86
Step-by-step explanation:
Step 1: Insurance premium is $0.33 per $100.
Step 2: In 279500, there are 2795 hundreds of dollar.
Step 3: find the premium.
2795*0.33 = 922.35
This is premium per year.
Step 4: There are 12 months in a year.
Therefore, his month mortgage payment = 922/35 = $76.86
Thank you.
A tuxedo rental shop rents tuxedos with sleeve lengths from 20 inches to 40 inches. The shop says the length of the sleeves should be about 1.2 times a person's arm length. Write and solve a compound inequality that represents the arm lengths of people the shop does not provide tuxedos for.
Let the person's arm length be = x
Condition is : sleeve lengths available from 20 inches to 40 inches and the length of the sleeves should be about 1.2 times a person's arm length.
So, the inequality equation becomes:
[tex]20\leq1.2x\leq40[/tex]
This gives x=[tex]\frac{20}{1.2}=16.66[/tex] or [tex]16\frac{2}{3}[/tex]
or x=[tex]\frac{40}{1.2}[/tex]=33.33 or [tex]33\frac{1}{3}[/tex]
Hence, the shop does not provide tuxedos to people with arm length less than 16.66 inches and greater than 33.33 inches.
Answer:
Step-by-step explanation:
Let the arm length of tuxedo be x which varies from 20 inches to 40 inches.
If length of the sleeves is about 1.2 times a person's arm length.
Then the arm length of a person will be 1.2x.
Inequality for the arm length will be
20 < 1.2x < 40
Now we divide this inequality by 1.2
[tex]\frac{20}{1.2}<x<\frac{40}{1.2}[/tex]
16.67 < x < 33.33
This inequality represents the arm length of people having arm length between 16.67 and 33.33 inches.
tuxedo rental shop does not provide tuxedos to the persons having arm length less than 16.67 and greater than 33.33.
I really need some help with this. Please no guesses, I need an exact answer. Thank you in advance.
Help!
"Stacy is planting a vegetable garden. She has 27 tomato plants, 45 bean plants, and 54 carrot plants. Stacy wants each row of her garden to have the same number of each type of plant. What is the greatest number of rows that Stacy can have if she wants to use all of her plants? How many of each type of plant will she have in each row?"
To determine the number of rows and the number of each type of plant Stacy can have, we need to find the greatest common factor (GCF) of the plant counts. The GCF represents the number of plants in each row. The GCF of 27, 45, and 54 is 9, so Stacy can have 9 rows with 3 tomato plants, 5 bean plants, and 6 carrot plants in each row.
Explanation:To determine the greatest number of rows that Stacy can have in her vegetable garden while still using all of her plants, we need to find the greatest common factor (GCF) of the numbers 27, 45, and 54. The GCF will represent the number of plants Stacy can have in each row.
First, we can find the GCF of 27 and 45 by listing their factors:
27: 1, 3, 9, 27
45: 1, 3, 5, 9, 15, 45
The greatest common factor of 27 and 45 is 9.
Next, we find the GCF of 9 and 54:
9: 1, 3, 9
54: 1, 2, 3, 6, 9, 18, 27, 54
The greatest common factor of 9 and 54 is 9.
Therefore, Stacy can have 9 rows in her garden, and each row will have 3 tomato plants, 5 bean plants, and 6 carrot plants.
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May I get some help please?
See the attached picture:
what is 2 to the -10th power
[tex]2^{-10} = \frac{1}{2^{10}} = \frac{1}{1024}[/tex]
A negative power is equal to 1/that to the positive power.
Final answer:
2 to the -10th power equals 1/1024 or 0.0009765625 in decimal form. It is calculated by taking the reciprocal of 2 raised to the 10th power, following the rules of negative exponents.
Explanation:
The student is asking about 2 to the -10th power, which is a mathematical expression involving negative exponents. When dealing with negative exponents, it's important to remember that a negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. Therefore, to calculate 2 to the -10th power, we use the following steps:
Identify the base (2) and the negative exponent (-10).
Understand that a negative exponent means the reciprocal is taken.
Calculate the reciprocal of the positive exponent: 2¹⁰.
Since 2¹⁰ is 1024, the reciprocal is 1 divided by 1024.
So, 2 to the -10th power equals 1/1024, which can also be written as 0.0009765625 in decimal form. This concept is crucial for understanding scientific notation, where negative exponents represent small numbers.