To find the diameter of a cone with a given volume and height, use the volume formula, substitute the given values, and solve for the radius. The calculated diameter of this cone is approximately 4.90 meters.
Explanation:To find the diameter of a cone given its volume and height, we can use the formula for the volume of a cone: V = (1/3)πr²h, where V is the volume, r is the radius of the base, and h is the height of the cone. Given that the volume (V) is 20π cubic meters and the height (h) is 10 meters, we can substitute these values into the formula and solve for r.
First, rearrange the formula to solve for r: r = √((3V)/(π×h)). Substitute V = 20π and h = 10 into the equation to get r = √((3×20π)/(π×10)) = √(6) meters. Therefore, the diameter of the cone, which is twice the radius, is 2×√(6) meters, or approximately 4.90 meters.
The diameter of the cone is [tex]\[ d = 4\sqrt{3} \][/tex]
To find the diameter of the cone, we first need to determine the radius of the cone's base. The volume V of a cone can be calculated using the formula:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
where r is the radius of the base and h is the height of the cone. Given that the volume V is [tex]\(20\pi\)[/tex] cubic meters and the height [tex]\(h\) is \(10\)[/tex] meters, we can set up the equation:
[tex]\[ 20\pi = \frac{1}{3} \pi r^2 \cdot 10 \][/tex]
[tex]\[ 60 = r^2 \cdot 10 \] \[ \frac{60}{10} = r^2 \] \[ r^2 = 6 \][/tex]
Taking the square root of both sides gives us the radius r:
[tex]\[ r = \sqrt{6} \][/tex]
Since the radius is half the diameter, we can find the diameter d by multiplying the radius by 2:
[tex]\[ d = 2r \] \[ d = 2\sqrt{6} \] \[ \sqrt{6} = \sqrt{2 \cdot 3} \] \[ \sqrt{6} = \sqrt{2} \cdot \sqrt{3} \] \[ \sqrt{6} = \sqrt{2} \cdot \sqrt{3} = 2\sqrt{3} \][/tex]
Thus, the diameter d of the cone is:
[tex]\[ d = 2 \cdot 2\sqrt{3} \][/tex]
[tex]\[ d = 4\sqrt{3} \][/tex]
Which expression is equivalent to
Answer:
j^13
Step-by-step explanation:
j j j j j j j j j j j j j j
There are 13 j's so we raise j to the 13 power
j^13
Answer:
c
Step-by-step explanation:
lol.................................
I need help please???
that anser you have highlighted it correct
Two lines, A and B, are represented by the following equations:
Line A: 3x + 3y = 12
Line B: x + y = 4
Which statement is true about the solution to the set of equations?
It is (12, 4).
There are infinitely many solutions.
It is (4, 12).
There is no solution.
Answer:it would be infinalty many
Step-by-step explanation:
The statement "There are infinitely many solutions" is true about the solution to the set of equations, as the lines represented are coincident.
To determine the solution to the set of equations, we can solve them simultaneously.
Given:
- Equation of Line A: 3x + 3y = 12
- Equation of Line B: x + y = 4
To find the solution, we can use methods like substitution or elimination. Here, let's use the elimination method:
Multiply the second equation by 3 to match the coefficients of \(y\) in both equations:
3(x + y) = 3(4)
3x + 3y = 12
Now, we can see that both equations represent the same line, so they are coincident or overlapping. Therefore, there are infinitely many solutions.
Hence, the statement "There are infinitely many solutions" is true about the solution to the set of equations.
i don't understand this. my teacher wasn't at school and this was homework
The answer would be A. 198 cm. To find the circumference of a circle you take c=2piR. You would find the circumference of the bigger wedges and divide by 2 since it makes up 1/2 the circle. Then you would do the same for the smaller wedges and it would be approximately 198 cm
Factor completely 25x^2-36
Rewrite it in the form; a^2 - b^2, where a = 5x and b = 6
(5x)^2 - 6^2
Use the Difference of Squares: a^2 - b^2 = (a + b)(a - b)
(5x + 6)(5x - 6)
To factor 25x^2-36 completely, we use the difference of squares formula which gives us the factorization (5x + 6)(5x - 6).
Explanation:To factor the expression 25x^2-36 completely, we can use the difference of squares formula. This formula states that a^2 - b^2 can be factored as (a + b)(a - b). In this case, our 'a' value is 5x and our 'b' value is 6. So we can factor 25x^2-36 as (5x + 6)(5x - 6).
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Cindy needs to work a total of 240 hours at her internship. Though she currently has 177.13 hours completed. How many more hours does Cindy need to complete her internship?
Answer:
62.87
Step-by-step explanation:
240-177.13=62.87
The mystery number is a three-digit number. Its digits are 1, 8, and 4.
• The 4 and the 8 are not next to each other.
• The 1 comes before the 4.
What is the mystery number?
Answer:
814
Step-by-step explanation:
there has to be a number between 4,8
so either 4 can be at hundred position or 8 can be at hundredth position.
but since 1 comes before 4, then 1 has to be at tens place and 4 has to be at one's place.
so number is 814
Using the given clues, we can determine that the three-digit mystery number with digits 1, 8, and 4, where 1 comes before 4 and 4 is not next to 8, is 184.
The mystery number is a three-digit number where the digits are 1, 8, and 4. With the given clues that the digits 4 and 8 are not next to each other and that 1 comes before 4, we must arrange the digits accordingly.
Since we are told the exact sequence for 1 and 4, with 1 coming before 4, and knowing that 8 cannot be next to 4, the possible arrangement is: the digit 1 first, then 8, and finally 4.
Following these conditions, the mystery number is 184.
Help me answer this question:(
Answer: first option.
Step-by-step explanation:
To solve this problem you must plug the function h(x) into the function g(x):
[tex]g(x)=\sqrt{(2x-8)-4}[/tex]
Now you must simplify by adding like terms, as following:
[tex]g(h(x))=\sqrt{2x-12}[/tex]
Substitute x=10 into the fucntion. Therefore, you obtain the following result:
[tex]g(h(10))=\sqrt{2(10)-12}[/tex]
[tex]g(h(10))=2\sqrt{2}[/tex]
Answer:
The correct answer is first option 2√2
Step-by-step explanation:
It is given that, g(x) = √(x - 4) and h(x) = 2x - 8
To find g(h(x))
We have g(x) = √(x - 4) and h(x) = 2x - 8
h(x) = 2x - 8
g(h(x)) = √((2x - 8)- 4) = √(2x - 12)
To find the value of g(h(10))
g(h(x)) = √(2x - 12)
g(h(10)) = √(2*10 - 12) =√(20 -12) =√8 = 2√2
Therefore the correct answer is first option 2√2
Drag the correct steps into order to evaluate 42 + t6 for t = 12.
Answer:
42+ (12)6=
42+72=114
Step-by-step explanation:
use pemdas to eliminate parethesis then add them together
Answer:
1. 42 + t/6
2. 42 + 12/6
3. 42 + 2
4. 44
Step-by-step explanation:
-You start of with 42 + t/6. If t = 6
-If t = 6, the next step should be to replace t with 12 So it would be 42 + 12/6.
-If we have 12/6 we know to divide. 12 divided by 6 is 2. So we would replace 12/6 with 2. Now we have 42 plus 2
-42 plus 2 is 44.
Write 7,000,000+300,000+ 40,000+ 5,000+ 800+ 2 in word form
seven million+three hundred thousand+forty thousand+ five thousand+eight hundred+two
HOPE THIS HELPED!!
Can I have brain?
7,345,802
Seven million, Three hundred, fourty thousand, eight hundred two
A school is sending six teachers and some students to attend a technology fair the admission price for teachers is 8.50 each and the admission price for students is $6 each if the budget set aside by the school for this event is $250 at most how many students can attend the fair
The number of students attending the fair will be 33.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a school is sending six teachers and some students to attend a technology fair the admission price for teachers is 8.50 each and the admission price for students is $6 each if the budget set aside by the school for this event is $250.
The number of the students will be calculated as,
( 6 x 8.5 ) + N x 6 = 250
6N = 250 - 51
N = 199 / 6
N = 33
Hence, the number oof the students will be 33.
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shelby needs 4/8 of a cup of oatmeal for each batch if she wants to make 7 batches how much oatmeal will she need
what is 10 times as much as 430?
Answer:
4300
Step-by-step explanation:
430*10=4300
Answer:
43
Step-by-step explanation:
43 x 10 = 430
The tables show some input and output values:
Table A
Input Output
1 7
2 7
2 9
4 5
Table B
Input Output
6 1
7 3
8 2
9 5
Which tables represent functions?
Only A
Only B
Both A and B
Neither A nor B
Your answer would be Only B
Table A has a repeated number in the inputs, while Table B does not
In the tables, only B represents functions.
What is a function?A function is a relation in which each domain value has only one range value. If a domain has more than one image in the range, it is not a function.
We can determine which table is a function as follows:Observe table A.
We can see that the input value of 2 has two outputs.
This means that table A is not a function.
Observe table B.
In table B, all input values have one and only one output value.
This table represents a function.
Therefore we have found that, from the given tables, only B represents functions. The correct answer is option B.
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a snack company makes 3 batches of a nut mix using the recipe shown.
each batch contains a different total amount of mix.
how much of each type of nuts should be in each batch
full question not given...please resend
Answer:
Please include the "recipe" so we can answer the question :/
The value of a stock increases at a rate of 1/2% per year. If the initial value of the stock $40 a share, when will the value of the stock be $50? Round your answer to the nearest tenth of a year
Answer:
After 45.7 years
Step-by-step explanation:
∵ r = 1/2% per year
∵ P0 = $40
∵ Pn = $50
∵ Pn = P0 ( 1 + r/100)^n-1
∵ P0 is initial value , Pn is the value after n years , is the rate
∴ 50 = 40 (1 + 0.5/100)^n-1
∴ 50/40 = (1.005)^n-1
∴ 1.25 = (1.005)^n-1 ⇒ insert ln in both sides
∴ ln(1.25) = (n-1)ln(1.005)
∴ n - 1 = ln(1.25)/ln(1.005)
∴ n = ln(1.25)/ln(1.005) + 1 = 45.7 years
Point: (-3, 7); Slope: 4
Answer:
y - 7 = 4(x + 3)
Step-by-step explanation:
Write the equation of a line using the point slope formula. Substitute m = 4 and the point (-3,7) in the formula.
[tex]y - y_1 = m(x-x_1)\\y - 7 = 4(x--3)\\y - 7 = 4(x+3)[/tex]
What is the probability of drawing a king first and then a jack from a standard deck of cards with replacement?
Answer:
1/169
Step-by-step explanation:
There are total 52 cards in deck. Also, there are 4 kings and 4 jacks in the deck.
Probability of choosing a king out of 4 kings and total there are 52 cards
∴ Ans1 = ⁴C₁/⁵²C₁ = 4/52 = 1/13
The cards are drawn with replacement so again there will be total 52 cards.
Probability of choosing a jack out of 4 jacks and total there are 52 cards
∴Ans2 = ⁴C₁/⁵²C₁ = 4/52 = 1/13
So, ans=Ans1 * Ans2 = 1/13 *1/13 = 1/169
The formula for the area of a trapezoid is A = 1/2 (b+b) h. Explain why the bases of a trapezoid need to be added in the formula
Step-by-step explanation:
Look at the picture.
We connect two congruent trapezoids as in the picture.
We created a parallelogram with a base length of b₁ + b₂ and a height h equal to the height of the trapezoid.
The formula of an area of a parallelogram:
[tex]A_p=(base)(height)\to A_p=(b_1+b_2)h[/tex]
The area of the trapezoid is half of the parallelogram area.
Therefore we have the formula of an area of trapezoid:
[tex]A_t=\dfrac{(b_1+b_2)h}{2}[/tex]
Therefore we need to be added the bases of a trapezoid.
which statement about the data set is true? (600,612,614,615,620,630,643,644,656)
Answer:
C
Step-by-step explanation:
Let's break down the definitions.
Median = the middle value in the number set
So yes this is an appropriate measure of center.
Mode = the most common value in the number set
Since this can be any number, this isn't an appropriate measure of center.
Mean = average
So yes this can also be an appropriate measure of center.
A salesperson makes a base salary of $2100 per month. Once he reaches $42,000 in total sales, he earns an additional 5% commission on the amount in sales over $42,000.
(1) Graph the function.
(2) If the salesperson had $80,000 in sales, how much was his salary?
(3) If the salesperson's total salary for a month was $4500, how much were his total sales for that month?
(4) Compute S(25000) and interpret what this means in the context of the problem.
Answer:
(1) Observe the attached image
(2) [tex]S = \$4,000[/tex]
(3) [tex]x = \$90,000[/tex]
(4) [tex]S = 2100[/tex]
Step-by-step explanation:
(1) Let's call S the salary for the month the seller wins.
Let's call x the amount of dollars reached by the sales of that month.
The seller earns a base salary of $ 2100 per month.
Then, if x> 42,000 he wins a commission of 5% on sales.
Then the equation modeling this situation is:
[tex]S =\left\{{{0.05(x-42,000)+2100\ if\ x>42,000} \atop{2,100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ if\ 0\leq x\leq42,000}}\right.[/tex]
The graph of the function is shown in the attached image.
(2) If x = 80,000, then your salary was:
[tex]S = 0.05(80000-42000) +2100\\\\S = \$4,000[/tex]
(3) If S was 4500 and we want to find x then we equal S to 4500 and solve for x.
[tex]S = 4,500 = 0.05(x-42,000) + 2,100\\\\\frac{2,400}{0.05} = (x-42,000)\\\\x = \frac{2400}{0.05} +42,000\\\\x = \$90,000[/tex]
(4) S (25000) means that x equals 25000. Since x represents sales, this means that during the month, the seller only reached $ 25,000.
Then [tex]x <42000[/tex]
Therefore [tex]S = 2100[/tex].
Find the value of x.
Answer options: 4, 6, 5, 7
Answer:
x = 6
Step-by-step explanation:
The radius in this case measures; 20/2 = 10 since the diameter is 20.
The chord measuring 16 units has been bisected, hence each portion measures 8 units.
We now apply Pythagoras theorem since we are dealing with a right angled triangle with 2 given sides;
x^2 = 10^2 - 8^2
x^2 = 36
x = 6
Final answer:
Without a specific equation or sufficient context, it is not possible to determine the correct value of x from the provided answer options (4, 6, 5, 7). The provided excerpts mention various unrelated values and scenarios involving x.
Explanation:
The specific value of x is not provided in the context of the information given, making it impossible to accurately determine its value. The excerpts given mention several different equations and scenarios, including various values for x such as x=3, x=-7, and instances where x=1 is a solution. However, these are not directly related to a given problem or an equation we can solve in this context.
Moreover, references to checking answers online with exercise codes and the mention of convergence related to initial guesses suggests that these excerpts are from a discussion involving solving equations using numerical methods, possibly from a textbook or set of course notes. To find the correct value of x, we would need to know the specific equation or problem we are trying to solve.
Without a clear and specific equation to solve, or additional context, we cannot accurately determine which of the answer options (4, 6, 5, 7) is the correct value of x.
help please and thank you
Your answer should be A.
Answer:
The answer is C because both ordered pair when they are substituted into the equation, both sides equal to each other.
Explanation:
All you do is substitute. (x,y)
A:
Substitute
11 = 8(1) + 3
Multiply the inside parentheses by the outside number
11 = 8 + 3
Add them together to get the solution.
11 = 11
Both sides equal to each other so that means that it is a solution to the equation.
B:
Substitute
-5 = 8(-1) + 3
Multiply the inside parentheses by the outside number
-5 = -8 + 3
Add them together to get the solution.
-5 = -5
Both sides equal to each other so that means that it is also a solution to the equation.
D:
Both ordered pair gives you an equal solution to both sides.
Is 0.166 rational or irrational?
Answer:
the Answer is irrational
Step-by-step explanation:
Which formula should be used to find the area of the composite shape?
The last option seems the best one: the figure is composed of a square/rectangle and a triangle. The area of the rectangle is the product of its dimension (i.e. [tex]lw[/tex]), while the area of the triangle is half the product of the base and height ([tex]\frac{1}{2}bh[/tex]).
The sum of the two areas is the area of the composite shape.
ANSWER
area equals half of base times height plus length times width so d
simplify (6 to the power of negative 2), (3 to the power of negative 3), (3 times 6)the power of 4.
Answer:
[tex]( {6}^{ - 2}) ( {3}^{ - 3}) ( {3 \times 6})^{4} = \frac{ {3}^{4} {6}^{4} }{ {3}^{3} {6}^{2} } = 3( {6}^{2} ) = 3(36) = 108[/tex]
Help please please anyone can you explain please
I can't read it well, but if u need to learn the volume of the cube do this. Count the number of squares. Top is 8. So bottom is 8. =16
Front is 12. So back is 12. =24
Side is 6. So other side is 6. =12.
16+24+12=42.
42 is ur volume.
Ta Da!
(X+1)-(-2x - 5)
Help
answer: 3x + 6
x + 1 + 2x + 5 = 3x + 6
remember to first distribute the negative to both terms in the second parentheses which makes the 2x and 5 both positive and then just combine like terms . pls mark brainliest
Answer:
3x+6 is the answer
Step-by-step explanation:
Find the center, vertices, and foci of the ellipse with equation 3x2 + 6y2 = 18.
3x^2 +6y^2 = 18
Divide each term by 18 to make the right side equal 1:
3x^2/18 + 6y^2/18 = 1
Simplify each term:
x^2/6 + y^2/3 = 1
The form of an eclipse is written as (x-h)^2/a^2 + (y-k)^2/b^2 =1
Match the values in the ellipse to the standard form:
a = √6
b=√3
k = 0
h = 0
The center = (h,k) = (0,0)
Vertex is h +a, k = (√6,0) and (-√6,0)
Focus is h+c,k = (√3,0) and (-√3,0)
Help Please! Thanks so much if u do
Janette went to Tire Mart and paid $122.57 per tire for 4 tires and a flat rate fee for installation for a total of $555.28 before taxes. Monique went to Fast Wheels and paid $136.71 per tire for 4 tires and a flat rate fee for installation for a total of $585.34 before taxes. The difference in the amount that they paid in installation charges is $
Answer:
$65
Step-by-step explanation:
Let's add up the flat rate and the cost of four tires:
flat rate + 4($122.57/tire) = $555.28
We are to solve for "flat rate." First, multiply out 4($122.57/tire), obtaining a tire cost of $490.28 total. Subtracting this tire cost from the $555.28 Janette paid the shop, we get "flat rate" = $555.28 - $490.28, or $65.
Thus, the installation charge ("flat rate") must have been $65.