For this case we have by definition, that the volume of a cone is given by:
[tex]V = \frac {1} {3} * \pi * r ^ 2 * h[/tex]
Where:
A: It is the cone radius
h: It's the height
They tell us that the diameter is 21 m, then the radius is half the diameter, that is: 10.5m. The height is 4m. Substituting the data:
[tex]V = \frac {1} {3} * \pi * (10.5) ^ 2 * 4\\V = \frac {1} {3} * \pi * 110.25 * 4\\V = 147 \pi[/tex].
Finally, the volume of the cube is[tex]147 \pi \ m ^ 3[/tex]
ANswer:
Option B
Answer:
147[tex]\pi[/tex]m^3
Step-by-step explanation:
Rhonda has $1.35 in nickels and dimes in her pocket. If she has six more dimes than nickels, which equation can be used to determine x, the number of nickels she has?
A: 0.05+0.10(6x)=1.35
B: 0.05(x+6)+0.10x=1.35
C: 0.05x+0.10(x+6)=1.35
D: 0.15(x+6)=1.35
Answer:
Option C. 0.05x+0.10(x+6)=1.35
Step-by-step explanation:
Remember that
1 nickel=$0.05
1 dime=$0.10
Let
x-----> the number of nickels
y----> the number of dimes
we know that
0.05x+0.10y=1.35 -----> equation A
y=x+6 ----> equation B
substitute equation B in equation A and solve for x
0.05x+0.10(x+6)=1.35
The correct equation that can be used to determine x, the number of nickels Rhonda has, is 0.05x + 0.10(x+6) = 1.35, which is option C from the ones presented.
Explanation:In this question, we are asked to find the equation that we can use to determine the number of nickels, represented by 'x', Rhonda has. Given that Rhonda has six more dimes than nickels, the cost of dimes in Rhonda's pocket can be represented by 0.10*(x+6) because each dime is worth $0.10 and she has six more dimes than nickels. Similarly, the cost of nickels in Rhonda's pocket could be represented as 0.05*x because each nickel is worth $0.05. As the total amount of money Rhonda has is $1.35, the two amounts should sum up to 1.35. Hence, the correct equation would be 0.05x + 0.10(x+6) = 1.35, so the answer is option C.
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Help, please! I have only a few minutes longer- 20 points.
Answer
The solution for the two system of equations is (-4,2)
Explanation
Equation for slope-intercept
The equation for slope-intercept form is y = mx + b
-mx represents the slope of the equation
-b represents the y-intercept
Determine the slope and the y-intercept
The slope of the two equations can be found based on what the number in front of the x is, this term is also called the coefficient.
The y-intercept is in the form of b and is substituted normally by a positive or negative integer.
Slope: 1/4 and 2
Y-intercept: 3 and 10
You must graph these, for this problem I have provided one for you.
Determining the solution
Since this problem requires you to find the solution based on the graph you must graph the two lines and the solution is the point in which the two lines intersect.
Based on the graph I have provided for you, we can determine that the solution is (-4,2)
Checking your work
In math it's very important to check your work: plug in the solution and if it is a perfect math then the solution is correct.
[tex]\frac{1}{4} (-4)+ 3 = 2[/tex]
The solution applies to the first equation, however we must now check for the second equation.
[tex]2(-4) + 10 = 2[/tex]
The solution also applies to the second equation, so we now know that this solution is correct.
The City Zoo collected $100 in one morning. An adult ticket is $5 each, and a child's ticket is $3. How many different combinations of adult and children's tickets would have totaled $100?
5
6
7
8
Final answer:
To calculate the number of different combinations of adult and children's tickets that would total $100, we can set up an equation: 5x + 3y = 100. We can find possible values of 'x' and 'y' that satisfy the equation. There are 6 different combinations of adult and children's tickets that would have totaled $100.
Explanation:
To calculate the number of different combinations of adult and children's tickets that would total $100, we can set up an equation:
5x + 3y = 100
Where 'x' represents the number of adult tickets and 'y' represents the number of children's tickets. We need to find whole number solutions for 'x' and 'y'.
We can start by finding the possible values of 'x' and 'y' that satisfy the equation and add up to $100. The possible combinations are:
x = 0, y = 33
x = 5, y = 31
x = 10, y = 29
x = 15, y = 27
x = 20, y = 25
x = 25, y = 23
Therefore, there are a total of 6 different combinations of adult and children's tickets that would have totaled $100.
Find the product.
y 5 · y 3
Answer: y8
Step-by-step explanation: You keep the base and add the exponents
The other answer is correct if you’re dealing with exponents. However, if your numbers are y5 x y3, then just multiply them: y5 x y3 = y15
This is because they are “like terms” can be directly multiplied
Determine the slope between the points (-3, 0) and (0, 5)
Thank you^^
The slope is 5/3.hope this helps
Answer:
slope = [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 5)
m = [tex]\frac{5-0}{0+3}[/tex] = [tex]\frac{5}{3}[/tex]
ALOT OF PONTS!!! HELPPP!!! Hi, I would greatly appreciate help with this. I have no idea how to do it.
A marble company has hired you as their new production manager. Your job is to choose the form of packaging for a new product from the five choices below. The package must hold at least 400 cubic inches. The cost of the cardboard for the packaging is $0.02 per square inch.
You should include the volume, total surface area, and materials cost for each solid given below, including the formulas you used and each step of your work. Make sure to use the formulas given in your lessons and round your answers to the nearest hundredth.
Solid 1 (rectangle):
Solid 2 (pyramid):
Solid 3 (cylinder):
Solid 4 (cone):
Solid 5 (sphere):
Write a paragraph that answers the following questions:
• Do all of the solids hold at least 400 cubic inches?
• Which solid is the most cost efficient (the packaging with the smallest materials cost that holds at least 400 cubic inches)?
• Would the most cost efficient solid work well for packaging? Why or why not?
• Which solid would you recommend using? Why?
Answer:
Logically, the answer is the sphere, as it is the figure which gives maximum volume for the same total surface area. But I'll just solve them like you want it.
I'm just writing the numerical values without the units.Please resolve
Solid 1: Square Prism with each side of the base equal to 8 in. and a height of 8 in.
Volume = 8^3 = 512
Area = 8^2 * 6 = 384
V/A Ratio = 1.33 (We need the highest ratio, that's why they hired us)
Cost = $7.68
Solid 2: Square Pyramid with each side of the base equal to 10 in. and a height of 15 in.
Volume = 1/3 * 10^2 * 15 = 500
Slant height = [(10/2)^2 + 15^2]^(1/2) = root of 250 = 15.81
Area = 2*10*15.81 + 10^2 = 416.23
V/A Ratio = 1.20
Cost = $8.34
Solid 3: Cylinder with a radius of 4 in. and a height of 10 in.
Volume = pi*4*4*10 = 502.65
Area = 2*pi*4*4 + 2*pi*4*10 = 351.86
V/A Ratio = 1.43
Cost = $7.04
Solid 4: Cone with a radius of 7 in. and a height of 10 in.
Volume = (1/3)*pi*7*7*10 = 513.13
Slant height = [(7^2)+(10^2)]^(1/2) = 12.21
Area = pi*7*12.21 + pi*7*7 = 422.37
V/A Ratio = 1.21
Cost = $8.45
Solid 5: Sphere with a radius of 5 in.
Volume = (4/3)*pi*(5^3) = 523.60
Area = 4*pi*(r^2) = 314.16
V/A Ratio = 1.67
Cost = $6.28
Hence, Solid 5 must be the packaging model opted for
Step-by-step explanation:
Logically, the answer is the sphere, as it is the figure which gives maximum volume for the same total surface area. But I'll just solve them like you want it.
I'm just writing the numerical values without the units.Please resolve
Solid 1: Square Prism with each side of the base equal to 8 in. and a height of 8 in.
Volume = 8^3 = 512
Area = 8^2 * 6 = 384
V/A Ratio = 1.33 (We need the highest ratio, that's why they hired us)
Cost = $7.68
Solid 2: Square Pyramid with each side of the base equal to 10 in. and a height of 15 in.
Volume = 1/3 * 10^2 * 15 = 500
Slant height = [(10/2)^2 + 15^2]^(1/2) = root of 250 = 15.81
Area = 2*10*15.81 + 10^2 = 416.23
V/A Ratio = 1.20
Cost = $8.34
Solid 3: Cylinder with a radius of 4 in. and a height of 10 in.
Volume = pi*4*4*10 = 502.65
Area = 2*pi*4*4 + 2*pi*4*10 = 351.86
V/A Ratio = 1.43
Cost = $7.04
Solid 4: Cone with a radius of 7 in. and a height of 10 in.
Volume = (1/3)*pi*7*7*10 = 513.13
Slant height = [(7^2)+(10^2)]^(1/2) = 12.21
Area = pi*7*12.21 + pi*7*7 = 422.37
V/A Ratio = 1.21
Cost = $8.45
Solid 5: Sphere with a radius of 5 in.
Volume = (4/3)*pi*(5^3) = 523.60
Area = 4*pi*(r^2) = 314.16
V/A Ratio = 1.67
Cost = $6.28
Hence, Solid 5 must be the packaging model opted for
The circle with the center O has a radius of 4 centimeters . If x=30 degrees , what is the length of arc AB ?
Answer:
2π/3 cm
Step-by-step explanation:
The formula for arc length is s = rФ, where Ф is the central angle in radians.
Thus, we must convert 30° into radians: that'd be π/6 rad.
Then the arc length here is s = rФ = (4 cm)(π/6 rad) = 2π/3 cm
A solid right pyramid has a square base. The base edge length is 2 cm longer than the height of the pyramid.If the height is 6 cm, the volume of the pyramid is ____cm3.
Answer:
The volume of the pyramid is 128 cm³
Step-by-step explanation:
* Lets revise the volume of the pyramid
- The pyramid has one base and the number of side faces depends
on the number of sides of the base
- The volume of any pyramid is 1/3 × Area of its base × its height
* Lets solve the problem
- The pyramid has a square base
- It has four side faces all of them are triangles
- It has five vertices and eight edges
- The area of the base = s², where s is the length of the side of
the square
- The volume of the pyramid is 1/3 × s² × h, where h is the height
of the pyramid
- The base edge length of the base is 2 cm longer than the height
of the pyramid
- The height of the pyramid is 6 cm
∵ The length of the edge of the base is 2 cm longer than the
height of the pyramid
∵ The height of the pyramid (h) = 6 cm
∴ The edge length of the base = 6 + 2 = 8 cm
- The area of the base = s²
∵ s = 8 cm
∴ The area of the base (s²) = 8² = 64 cm²
- The volume of the pyramid = 1/3 × s² × h
∴ Its volume = 1/3 × 64 × 6 = 128 cm³
* The volume of the pyramid is 128 cm³
The correct answer is:
128 cm^3
Hope this helps
to cancel a term.its necessary to add the _____to both sides of the equation
Answer:
To cancel a term, it is necessary to add the opposite of the term to both sides of the equation
Step-by-step explanation:
Adding opposites creates a sum of zero. Zero added to anything else does not change the its value. So, adding the opposite of a term effectively removes it from (that side of) the equation.
These are the means and standard deviations for samples of prices from two different brands of shoes. Brand A Brand B Mean: $50 Mean: $40 Standard deviation: $5 Standard deviation: $8 Select the two true statements.
(a) The average price of brand A is higher than average price of brand B
(b) The price of brand B is more spread out than the price of brand A.
Mean of the distributions
The mean of the distributions for the individual samples is given as;
Mean of Brand A = $50
Mean of Brand B = $40
Standard deviation of the samplesStandard deviation of Brand A = $5
Standard deviation of Brand B = $8
From the mean and standard deviation of the samples we can conclude the following;
The average price of brand A is higher than average price of brand B.The price of brand B is more spread out than the price of brand A.Learn more about standard deviation here: https://brainly.com/question/12402189
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Final answer:
The two true statements are that Brand A's prices are less spread out than brand B's prices (C), reflected in the smaller standard deviation, and that Brand A has a higher average price than brand B (D), as indicated by their respective means.
Explanation:
The question involves comparing means and standard deviations for samples of prices from two different brands of shoes, Brand A and Brand B. To select the two true statements among the given options, we consider the provided statistics for each brand:
Brand A: Mean = $50, Standard deviation = $5Brand B: Mean = $40, Standard deviation = $8Now let's analyze the statements:
A. Brand A has a lower average price than brand B - This statement is false because the mean of Brand A ($50) is higher than the mean of Brand B ($40).B. Brand A's prices are more spread out than brand B's prices - This statement is false as well because Brand A has a smaller standard deviation ($5) compared to Brand B ($8), indicating less spread.C. Brand A's prices are less spread out than brand B's prices - This statement is true, reflecting the smaller standard deviation for Brand A.D. Brand A has a higher average price than brand B - This statement is true as explained earlier.Therefore, the two true statements are C and D: Brand A's prices are less spread out than brand B's prices, and Brand A has a higher average price than brand B.
Find the area of the quadrilateral QRST by using the formula for the area of a kite. HELP PLEASE!!!!
A. 15 units^2
B. 10 units ^2
C. 16 units ^2
D. 5 units ^2
ANSWER
A. 15 units^2
EXPLANATION
The area of kite is half the product of the diagonals.
The first diagonal has vertices at,
T(0,0) and R(5,5).
The length of this diagonal is
[tex]TR = \sqrt{ {5}^{2} + {5}^{2} } [/tex]
[tex]TR = \sqrt{25 + 25} [/tex]
[tex]TR = \sqrt{50} =5 \sqrt{2} [/tex]
The other diagonal has vertices at;
Q(0,3) and S(3,0).
The length of this diagonal is
[tex]QS = \sqrt{ {3}^{2} + {3}^{2} } [/tex]
[tex]QS = \sqrt{ 9+ 9 } [/tex]
[tex]QS = \sqrt{18} = 3 \sqrt{2} [/tex]
The area of the kite is
[tex] = \frac{1}{2} \times 3 \sqrt{2} \times 5 \sqrt{2} [/tex]
[tex] = 15 \: {units}^{2} [/tex]
PLEASE HELP ME SOLVE THIS QUESTION!!
***quickest and shortest way***
Answer:
1/4 bag for each batch.
Step-by-step explanation:
Start with 4 bags. If the cake requires 1/4 bag, then 3 3/4 bags of flour are left over for the cookies. That's rather a nice number when you are dealing with 15 batches of cookies.
Start by changing the 3 3/4 into a decimal.
3 3/4 = 3.75
Now divide 3.75 by 15
3.75 / 15 = 0.25 bags which is 1/4 bag. You only have to come up with one value so this one will do.
1. What are the coordinates of Z?
Answer:
A z coordinate is the third-dimensional coordinate in a volume pixel , or voxel . Together with x and y coordinates , the z coordinate defines a location in a three-dimensional space.
Step-by-step explanation:
Answer:
z coordinate =0 since this is xy plane.
Step-by-step explanation:
Given is a planar graph which contains a parallelogram.
The parallelogram is lying on xy plane.
The parallelogram is a planar figure drawn on xy plane.
We have in 3 dimensional cartesian system of coorindates in the xy plane z=0
Hence we have z coordinate =0
Find length JM in the image attached.
Answer:
12
Step-by-step explanation:
I find it convenient to use the following relation:
JL -KL +5 = JM
(x +7) -(2x -4) +5 = 3x . . . . . substituting values shown
16 -x = 3x . . . . . . . . . . . . . . . collect terms
16 = 4x . . . . . add x
4 = x . . . . . . . divide by 4
JM = 3x = 3·4 . . . . . . find the length of JM
JM = 12
What is the difference of the matrices shown below?
COF
8
12] 1-14
15
v
| 17
-3]
co
-11 271
19 -2
127-11)
Answer:
Option A is correct.
Step-by-step explanation:
We need to find the difference of two matrices.
The matrices are:
[tex]\left[\begin{array}{cc}-4&8\\3&12\end{array}\right] - \left[\begin{array}{cc}2&1\\-14&15\end{array}\right][/tex]
We will subtract each row entry of Matrix 1 from the corresponding row entry of Matrix 2.
[tex]\left[\begin{array}{cc}-4-2&8-1\\3+14&12-15\end{array}\right]\\\left[\begin{array}{cc}-6&7\\17&-3\end{array}\right][/tex]
So, We get the answer
[tex]\left[\begin{array}{cc}-6&7\\17&-3\end{array}\right][/tex]
which matches Option A.
So, Option A is correct.
Answer:
A
Step-by-step explanation:
Subtract corresponding elements in second matrix from first matrix, that is
[tex]\left[\begin{array}{ccc}-4-2&8-1&\\3-(-14)&12-15&\\&&\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-6&7&\\17&-3&\end{array}\right][/tex]
Please please help me out
Answer:
18%
Step-by-step explanation:
The number of graduates on financial aid = 1879
The total number of students = 10730
Probability = [tex]\frac{1879}{10730}[/tex] × 100% = 0.175 × 100% ≈ 18%
Jimmy is trying to dive down and touch the bottom of the pool. On his first try he makes it 1/3 of the way to the bottom. On his second try he makes it 3/5 of the way to the bottom. Jimmys second dive was deeper than his first dive by what fraction of the pool?
Answer:
Jimmy's second dive was [tex]\frac{4}{15}[/tex] of the pool deeper than the first one
Explanation:
We are given that:
First dive was [tex]\frac{1}{3}[/tex] of the way to the bottom
Second dive was [tex]\frac{3}{5}[/tex] of the way to the bottom
We know that the second dive was deeper than the first one since [tex]\frac{3}{5} > \frac{1}{3}[/tex]
To know how much deeper the second dive was compared to the first one, we will simply subtract the depth of the first dive from that of the second one
Therefore:
The second dive was [tex]\frac{3}{5} - \frac{1}{3} = \frac{9}{15} - \frac{5}{15} = \frac{4}{15}[/tex] of the pool deeper than the first one
Hope this helps :)
Final answer:
Jimmy's second dive was 4/15 of the pool deeper than his first dive, calculated by finding a common denominator and subtracting the fractions representing the depth of each dive.
Explanation:
Jimmy's second dive was 3/5 of the way to the bottom of the pool, which is deeper than his first dive at 1/3 of the way. To find out how much deeper the second dive was compared to the first, we subtract the two fractions:
Second dive - First dive = 3/5 - 1/3
To subtract fractions, they must have a common denominator. Multiplying top and bottom of 3/5 by 3 and 1/3 by 5 gives us:
9/15 - 5/15 = 4/15
Therefore, Jimmy's second dive was 4/15 of the pool deeper than his first dive.
John owns an engine which receives heat input from a reservoir at 600 K and loses heat to a sink at 300 K. What is the maximum possible efficiency of this engine?
A.
25 percent
B.
50 percent
C.
75 percent
D.
100 percent
Answer:
D. 100 percent
Step-by-step explanation:
it is 100 percent because the reservoir is putting out 600k, but loses 300k, which would be easy to think it would be 50 percent because 300k is half of 600k, but however its peek outage is putting out 600k, therefore 600k = 600k, 100%.
A copy machine depreciates at the rate of 15% each year. If the original cost of the copy machine was $20,000, what is the approximate value of the machine at the end of 3 years?
$12,282.5 (20000x0.85x0.85x0.85)
The value of the copy machine depreciates at a rate of 15% each year. After calculating the depreciated value for 3 consecutive years, the copy machine that initially cost $20,000 is worth approximately $12,282.50 after 3 years.
Explanation:The original cost of the copy machine is $20,000. Given that the copy machine depreciates, or loses value, at a rate of 15% each year, we need to calculate the value of the copy machine each year for 3 years by subtracting 15% of its current value.
In the first year, the value of the copy machine would be $20,000 - (15% of $20,000) = $20,000 - $3,000 = $17,000. In the second year, we will take 15% off $17,000, so the value will be $17,000 - (15% of $17,000) = $17,000 - $2,550 = $14,450. Finally, in the third year, we will take 15% off $14,450, so the final value is $14,450 - (15% of $14,450) = $14,450 - $2,167.50 = $12,282.50. So, the approximate value of the machine at the end of 3 years is $12,282.50.Learn more about Depreciation here:https://brainly.com/question/17827672
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which one of the fololowing is equivalent to 9 1.5 =27
27 is equivalent to the number 9
Please answer this multiple choice question CORRECTLY for 30 points and brainliest!!
Answer:
Row B. J becomes (-2,-3), K becomes (-2,-5), and L becomes (1,-5)
The correct answer is B.
The coordinates of the triangle are ...
J = (-5, -1)
K = (-5, -3)
L = (-2, -3)
All you have to do is add 3 to all of the x's of the coords
And subtract 2 from all of the y's of the coords
21. what are the excluded values of the function? y= 5/6x-72
A. 0
B. 12
C. 72
D. 11
22. what are the excluded values of the function? y= 6/x^2-25
A. x=/ 5, -5
B. x=/ 5
C. x=/ -5
D. x=/ 1/6
you have to calculate the SID number and then take it upon yourself and divided X it's actual number and then there's a chance and the answer would be c.72
Please help it would mean so much!!
4x-3(x-2)=21
4x-3(x-2)=21
4x-3x+6=21
4x-3x=21-6
x=15
is this right? let's check
4(15)-3(15-2) = 21? yes
For this case we have the following expression, we must find the value of the variable "x":
[tex]4x-3 (x-2) = 21[/tex]
We apply distributive property to the terms of the parenthesis taking into account that:
[tex]- * + = -\\- * - = +\\4x-3x + 6 = 21[/tex]
We add similar terms:
[tex]x + 6 = 21[/tex]
We subtract 6 on both sides of the equation:
[tex]x = 21-6\\x = 15[/tex]
Now, the value of x is 15
Answer:
[tex]x = 15[/tex]
HELP HELP!!
What is the distance between the vertices of the graphs corresponding to y = x2 + 2 and y = 3x2 + 2?
A.0
B.2
C.3
D.4
Answer:
0
Step-by-step explanation:
[tex]p_1:~~y = x^2+2\\p_2:~~y = 3x^2+2\\ \\ V{p_1} = \Big(-\dfrac{b}{2a}, -\dfrac{\Delta}{4a}\Big) = \Big(-\dfrac{0}{2}, -\dfrac{0^2-4\cdot 2}{4}\Big) = \Big(0,2\Big) \\ \\ Vp_2 = \Big(x_V, -\dfrac{\Delta}{4a}\Big) = \Big(0, -\dfrac{0^2-4\cdot 3 \cdot 2}{4\cdot 3}\Big) = \Big(0,2\Big) \\ \\ \\ \text{The distance is }0,~~\text{Because the vertices are equal.}[/tex]
The distance between the vertices of the graphs is 0.
Explanation:The distance between the vertices of the graphs corresponding to y = x2 + 2 and y = 3x2 + 2 can be found by finding the x-coordinates where the graphs intersect. To do this, we set the two equations equal to each other:
x2 + 2 = 3x2 + 2
Subtracting 2 from both sides gives: x2 = 3x2
Subtracting x2 from both sides gives: 0 = 2x2
Dividing both sides by 2 gives: 0 = x2
This equation has only one solution: x = 0. Therefore, the distance between the vertices of the graphs is 0.
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How many vertices does a dodecahedron have
Answer:
20
Step-by-step explanation:
A dodecahedron is a three-dimensional figure made out of 12 regular pentagons. It resembles a soccer ball, just more rough on the edges.
So, it has 12 faces made out of regular pentagons. Each summit/vertex is a meeting point for 3 different pentagons.
So, you can easily calculate the number of vertices:
How many pentagon vertices in total?
12 pentagons with 5 vertices / pentagon = 60 vertices in total
But each vertex meets with two others... so you have to divide the number of total vertices by 3... so 60 / 3 = 20.
Answer:
12 faces
Step-by-step explanation:
~apex
If the length of side a is 16 centimeters, the length of side b is 10 centimeters, and m = 42°, what is the measure of ? Round your answer to two decimal places.
Answer:Substitute the given values in the Law of Sines and find that the measure is 24.72°
The measure of the missing angle is approximately 113.28°.
Assuming that the missing angle is opposite to side c, we can use the Law of Sines to find the measure of the missing angle. The Law of Sines states that for any triangle ABC:
a/sin(A) = b/sin(B) = c/sin(C)
Substituting the given values, we have:
16/sin(42°) = 10/sin(B) = c/sin(C)
Solving for sin(B), we get:
sin(B) = 10*sin(42°)/16 ≈ 0.4182
Using the inverse sine function, we can find the measure of angle B:
B ≈ sin⁻¹(0.4182) ≈ 24.72°
Now, we can use the fact that the angles of a triangle add up to 180° to find the measure of the missing angle:
A + B + C = 180°
A + 42° + 24.72° = 180°
A ≈ 113.28°
Therefore, the measure of the missing angle is approximately 113.28°.
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A ceiling light has a cross-section in the shape of a parabola. The parabola is 24 cm wide and 9 cm deep. The lightbulb is located at the focus of the parabola. How far from the vertex is the lightbulb?
Answer:
4 cm
Step-by-step explanation:
The equation of a parabola with its vertex at the origin can be written as ...
y = 1/(4p)x^2
The problem statement tells us that one point on the parabola is (x, y) = (12, 9). We can put these values into the equation and solve for p, the distance from the focus to the vertex.
9 = 1/(4p)(12^2)
9×4/144 = 1/p = 1/4 . . . . . . . . multiply by the inverse of the coefficient of 1/p
Then p = 4, and the bulb is 4 cm from the vertex.
A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles? A. 27 π cubic inches B. 36 π cubic inches C. 53 π cubic inches D. 86 π cubic inches E. 98 π cubic inches
Answer:
A. 27 π cubic inches
Step-by-step explanation:
The volume of a cylinder is calculated using the formula;
[tex]Volume=\pi r^2h[/tex]
From the given information, the smallest candle has a radius of 0.5 inches and a height of 3 inches.
We substitute [tex]r=0.5[/tex] and [tex]h=3[/tex] into the given formula.
The vlume of the smallest candle is
[tex]Volume=\pi \times0.5^2\times 3[/tex]
[tex]Volume=\frac{3}{4}\pi in^3[/tex]
from the given information, the other two candles are scaled versions of the smallest, with scale factors of 2 and 3.
The volume of the other two candles will be [tex]2^3\times \frac{3}{4}\pi=6\pi in^3[/tex] and [tex]3^3\times \frac{3}{4}\pi=\frac{81}{4}\pi in^3[/tex]
The wax needed to create one set of candle is
[tex]\frac{3}{4}\pi+6\pi+\frac{81}{4}\pi=27\pi\: in^3[/tex]
The correct answer is A
Answer:
27 pi in³
Step-by-step explanation:
I just took a test on Plato/Edmentum with this question and this was the right answer
~Please mark me as brainliest :)
To take a taxi it costs $3.00 plus an additional $2.00 per mile traveled. You spent exactly $20 on a taxi, which includes the $1 tip you left. How many miles did you travel?
This is a basic algebraic word problem. Make x equal the miles you traveled. multiply that by 2 and add the 3 initial dollars, then add the one dollar tip, finally make all this equal to 20. So your equation should look like this:
2x + 3 + 1 = 20
add the 3 and 1:
2x + 4 =20
move the 4 to the right side:
2x = 16
devide both sides by 2:
x = 8
So you traveled 8 miles.
Costs $17.60 for a pack of 4 padlocks.Find the unit price in dollars per padlock.If necessary, round your answer to the nearest cent
4=$17.60
1=$17.60/4
1=$4.40
Hole this helps :)
The unit price of a padlock, when rounded to the nearest cent, is $4.40 per padlock.
To calculate the unit price of a padlock, you'll need to determine the cost per individual padlock within a pack. In this scenario, you have a pack of 4 padlocks that costs $17.60. To find the cost of a single padlock, you can use the following formula:
Unit Price = Total Cost / Number of Padlocks
In this case:
Total Cost = $17.60
Number of Padlocks = 4
Now, let's calculate the unit price:
Unit Price = $17.60 / 4 padlocks
Unit Price = $4.40 per padlock
So, the unit price of each padlock is $4.40 when rounded to the nearest cent.
Understanding the unit price is essential for making informed purchasing decisions. It allows you to compare prices and determine whether buying in bulk (in this case, a pack of 4 padlocks) is more cost-effective than purchasing items individually.
In summary, the unit price of a padlock is $4.40 per padlock when rounded to the nearest cent. This information helps consumers assess the value of buying items in larger quantities and ensures they get the best deal for their money.
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