Answer:
115Gallons
Step-by-step explanation:
1. Calculate the Volume - Volume of a cylinder is done by this formula, V=π*R^2*H.
3.14x1.5^2x4.5=V
V=31.79ft^3
2. Find the amount of Gallons it can hold total - V=31.79 Now per 1ft^3 its roughly 7.5 gallons. 31.79x7.5=238.44gallons
3. Find the amount occupied by the water currently in the barrel - So we need the middle point so we have something to go off of, now 2.5ft isn't half of 4.5, 2.25 is. So 238.44/2=119.22Gallons. Now 2.5 is 53.4% the difference is 3.4. So we need to take 119.22Gallons*.034=4.05 now add that to the 119.22 and you get 123.27 gallons used
4. How much is left over? - Take 238.44-123.27=115.17 more Gallons that the barrel can hold.
Hope this helped :)
Verify that sin 2x = 2 cot x sin2 x is an identity
Answer:
see explanation
Step-by-step explanation:
Verifying that the left side equals the right side
left side = sin2x = 2sinxcosx
Consider the right side
2cotxsin²x
= 2 × [tex]\frac{cosx}{sinx}[/tex] × sin²x ← cancel sinx on numerator/ denominator
= 2cosxsinx = left side ⇒ verified
Prove two triangles congruent by a side, a median drawn to that side, and the angle formed by the side and the median.
Let's call one triangle ABC, and M the midpoint of AB.
Let's call the other triangle DEF, and midpoint N of DE.
We have a congruent side, AB=DE, congruent medians CM=FN, and congruent angles, ∠AMC=∠DNF
AB ≅ DE Given
AM ≅ BM and DN ≅ EN Def median/midpoint
AM+BM=AB and DN+EN=DE Segment addition theorem
2AM=2BM=AB and 2DN=2EN=DE Substitution (eg BM for AM)
AM ≅ BM ≅ DN ≅ EN Transitivity, algebra
CM ≅ FN Given
∠AMC ≅ ∠DNF Given
ΔAMC ≅ ΔDNF Side Angle Side
AC ≅ DF CPCTC
∠BMC ≅ ∠ENF Supplements of congruent angles are congruent
ΔBMC ≅ ΔENF Side Angle Side
BC ≅ EF CPCTC
Δ ABC ≅ Δ DEF Side Side Side
bz is tangent to circle o. ac is a diameter. mbc=90. mcd=30. mde=20.
state the theorem(s) that you used to find the measures of angles 1-10.
Answer:
1. Arc angle
2. Angle at circumference
3. Base angle of an isosceles triangle
4. Sum interior of angles in a triangle
5. Sum interior of angles in a triangle
6. The sum of angles on a straight line
7. Sum interior of angles in a triangle
8. Sum interior of angles in a triangle
9. Angle from a tangent to the radius of a circle
10. Alternate angles of line crossing two parallel lines
Step-by-step explanation:
Here, we note that, the angles where derived as follows;
1. mBC = 90°, therefore, angle subtended by the arc BC at the center of the circle = 1 = 90°
2. 90° The angle at the center which is the straight line diameter with angle 180° = 2 × angle at the circumference
∴ The angle at the circumference, angle 2 = 180°/2 = 90°
3. Angle subtended by the sum of arcs CD + DE at the center = 50°, therefore, ∡EOC = 50° and ∡EOA = 180° - 50° = 130° (the sum of angles on a straight line), since ΔAOE is an isosceles triangle, therefore, ∡OAE = ∡OEA = (180° - 130°)/2 = 25°
4. ∡A + ∡E + ∡C = 180° (Sum interior of angles in a triangle)
∴ 25° + 90° + ∡C = 180°
Hence ∡C = 180° - (90° + 25°) = 65°
5. From arc CD = 30°, ∡COD = 30°, ∴ ∡OBD = 30° = base angle of isosceles triangle with sides equal to the radius
Hence ∡8 = 30° from ∡8 + ∡1 + ∡OBD = 180° which gives
∡8 + 90° + 30° = 180°, hence;
∡8 = 180° - (90° + 30°) = 60°
∡8 = opposite ∡8 = 60°
Opposite ∡8 + ∡C + ∡5 = 180° (Sum interior of angles in a triangle)
Therefore ∡5 = 180° - (opposite ∡8 + ∡C) = 180° - (60° + 65°) = 55°
6. Angles 6 plus angle 5 = 180° (The sum of angles on a straight line)
Therefore, ∡6 = 180° - ∡5 = 180° - 55° = 125°
7. ∡7 + opposite ∡5 + ∡E = 180° (Sum interior of angles in a triangle)
∡E + ∡2 = 180° (The sum of angles on a straight line)
∴ ∡E = 180° - ∡2 = 180° - 90° = 90°
Hence, ∡7 + opposite ∡5 + ∡E = 180° = ∡7 + 55° + 90° = 180°
∴ ∡7 = 35°
8. ∡8 = 60° as found above
9. ∡9 = 90° (Angle from a tangent to the radius of a circle)
10. ∡10 = ∡8 = 60° (Alternate angles).
What is the probability of spinning a 1 and flipping heads
Answer:6/11
Step-by-step explanation:
The probability of spinning a 1 and flipping a heads is given by the equation A = 1/10
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability of spinning a 1 and flipping a heads be A
Now , the equation will be
The total number of values in the spinner = { 1 , 2 , 3 , 4 , 5 }
So , the number of possible outcomes = 5
The probability of spinning a 1 = 1 / number of possible outcomes
Substituting the values in the equation , we get
The probability of spinning a 1 = 1/5
The number of outcomes for flipping a coin = { heads , tails }
Now , the probability of flipping a head = 1/2
So , the probability of spinning a 1 and flipping a heads A = probability of spinning a 1 x probability of flipping a head
Substituting the values in the equation , we get
The probability of spinning a 1 and flipping a heads A = ( 1/5 ) ( 1/2 )
On simplifying the equation , we get
The probability of spinning a 1 and flipping a heads A = 1/10
The probability of spinning a 1 and flipping a heads A = 0.1
Hence , the probability is 1/10
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That’s the question?
Answer:
Domain: [0, 6]
Step-by-step explanation:
There's a rising slope between 0 and 6 and then it's decreasing for the rest.
I hope this helped and have a good rest of your day!
Write a four-sentence paragraph in which events are described in sequence.
Answer:
First, the girl walked to the tree. Next, she placed a towel underneath the tree. The, she sat down and took out her book. Finally, the girl took out her food and ate it while reading.
Step-by-step explanation:
It's simple, but it's in a sequence. I dont know if this was related to a passage, if so, could i see it?
Can someone please help me out
does anyone understand the Pythagorean Theorem
Answer:
a^2 + b^2 = c^2
Step-by-step explanation:
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
a^2 + b^2 = c^2
a = side of right triangle
b = side of right triangle
c = hypotenuse
*can only be used for a RIGHT triangle*
( hope i was able to help)
The area of Miguel’s rectangular garden is 450 square feet. The garden is 9 feet wide.
How many feet of fencing will Miguel need to buy to enclose the garden on all four sides?
Answer: 118 feet
Step-by-step explanation:
For a rectangular shape: Area = W × L
450 = 9 × L
450 ÷ 9
L = 50
Perimeter of a rectangular shape = 2L + 2W
Perimeter = (2 × 50) + (2 × 9)
= 100 + 18 = 118 feet
Of the 800 particapants in a marthon, 120 are running to raise money for a cause. How many particpants out of 100 are running for a cause?
Answer:
15
Step-by-step explanation:
800/8 = 100
sooo.......
120/8 = 15
15/100
hope this helps ! :)
1~ Please help. What is the measure of m∠P and m∠N?
Answer:
Answer is option b)
Step-by-step explanation:
[tex]sum \: of \: opposite \: angles \: of \: a \: \\ cyclic \: quadrilateral \: is \: 180 \: degrees \\ from \: the \: diagram \\ 2x + 2x - 12 = 180 \\ 4x - 12 = 180 \\ 4x = 180 + 12 \\ 4x = 192 \\ x = \frac{192}{4} \\ x = 48 \\ angle \: P \: = 2x \\ \: \: \: = 2(48) \\ \: \: \: = 96 \: degrees \\ angle \: N \: = 2x - 12 \\ \: \: \: \: = 96 - 12 \\ \: \: \: = 84 \: degrees[/tex]
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
What is the area of the triangle shown below?
Answer:
65
Step-by-step explanation:
In order to find the area you have to complete a formula for triangles going Area = 1/2 bh ( bh means base time the height height is the 13 and the base is the 10 in the photo.)
math question screen shot down below
Answer:
B. 1/2
It will always be a 50/50 probability cause there are only 2 sides
Rachael is placing a protective cover on a glass case. The case is a cube and the perimeter of one face of the cube is 56 inches. How many square inches of the protective covering does she need for the case?
Answer:
to cover this cube she needs at least 1,176 square inches of protective covering.
Step-by-step explanation:
The surface area of a cube is given by the following formula:
surface area cube = 6*l²
While the perimeter of each face of the cube is:
perimeter face = 4*l
Where l is the length of each side of the cube. Applying the data from the problem we have:
56 = 4*l
l = 56/4= 14 inches
surface area cube = 6*(14)²
surface area cube = 6*(196)
surface area cube = 1,176 square inches.
Therefore to cover this cube she needs at least 1,176 square inches of protective covering.
After analyzing this number line, which set of numbers would all round to 0 when rounding to the nearest hundred?
A) 15, 35, 44
B) 35, 44, 50
C) 44, 50, 55
D) 55, 63, 69
HELP ASAP I WILL GIVE BRAINLIEST
Answer:
the numbers in Set A would round to 0
Step-by-step explanation:
What is cosA?
a. 12/13
b. 5/13
c. 5/12
Which decimal number rounds to 0.296?
A) 0.29463
B) 0.29547
C) 0.29563
D) 0.29657
E) 0.29659
Answer:
The answer should be C. 0.29563
Step-by-step explanation:
A bag of marbles has 6 red marbles and 7 green marbles in it. What is the percent probability of pulling a green marble out of the bag ? *
Answer:
If a bag contains 4 red marbles, 3 blue marbles, and 7 green marbles and a marble is randomly selected from the bag, what is the probability that it is blue? P=3/(3+4+7)=3/14 because each of 14 marbles is equally likely to be drawn.
Step-by-step explanation:
Write the English phrase as an algebraic expression. Let x represent the number.
6 more than four times a number
Answer: 4x + 6
Step-by-step explanation:
Answer: 4x + 6
Step-by-step explanation:
Remember: Use ALL numbers below or above
the true median (which was 55)
What is the UPPER quartile?
64.5
69
73
65
Answer:
upper:65 lower:44
Step-by-step explanation:
Name the values represented by the box plot.
Lower quartile:
Upper quartile:
Median:
Answer: The lower quartile is 10, the upper quartile is 21, and the median is 17.
Step-by-step explanation:
Answer:
It sould be 5,10,26
Step-by-step explanation:
Factor completely 2x2 − 32.
Answer:
2(1x1-16)
Step-by-step explanation:
1. Find the gcf (greatest common factor) which is 2
2. Divide by each of the factors and put it inside of the parentheses
Using the graph, determine the equation of the axis of symmetry.
Answer:
the answer is (-1, -9)
that is the axis of symmetry
This is an upward-facing parabola the axis of symmetry is a line of the form x = -a that is constant.
How to find the points symmetric over axes or origin?Let the point be (x,y)
Case 1: Symmetry with respect to the x-axis
The point becomes (x, -y) as the point flips itself up or down which changes its y coordinate to the negative of whatever it was previously. And no motion is done horizontally so no change in x coordinate.
Case 2: Symmetry with respect to y-axis
The point becomes (-x, y) as the point flips itself left or right which changes its x coordinate to negative of whatever it was previously. And no motion is done vertically so no change in y coordinate.
Case 3: Symmetry with respect to origin
Origin is point at (0,0)
Symmetry with this is a bit ill defined. We use a slant line as if its a diagonal of a square.
The point is reflected to its diagonally opposite quadrant to whatever coordinate it belongs to.
Since diagonally opposite reflection causes both x and y axis to become negative of what it was before, thus,
The point becomes (-x,-y)
The axis of symmetry is where the left side is the mirror image of the right side.
Since this is an upward-facing parabola the axis of symmetry is a line of the form x = -a that is constant.
It will be the x coordinate of the vertex
x = 1
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Solve for y :
y/5 + 7 = -3
Y is equal to -50. (y= -50)
Step-by-step explanation: Solve for y
by simplifying both sides of the equation, then isolating the variable.y=−50
Which of these systems of linear equations has no solution? 2 x + 8 y = 15. 4 x + 16 y = 30. 2 x minus y = 18. 4 x + 2 y = 38. 4 x + 7 y = 17. 8 x minus 14 y = 36. 4 x minus 3 y = 16. 8 x minus 6 y = 34. 100points
Answer:
4 x minus 3 y = 16. 8 x minus 6 y = 34
Step-by-step explanation:
2 x + 8 y = 15. 4 x + 16 y = 30.
Multiply the first equation by 2
4x +16y = 30
They are identical so they are the same line so there are infinite solutions
2 x - y = 18. 4 x + 2 y = 38.
Multiply the first equation by 2
4x -2y = 36
Add to the first equation
4x -2y = 36
4 x + 2 y = 38.
-----------------------
8x =74
This has a solution
4 x + 7 y = 17. 8 x - 14 y = 36.
Multiply the first equation by 2
8x +14y = 34 add to the second equation
8x +14y = 34
8 x - 14 y = 36.
------------------------
16x = 70
This has a solution
4 x - 3 y = 16. 8 x - 6 y = 34.
Multiply the first equation by -2
-8x + 6y = -32
Add to the second
-8x + 6y = -32
8x - 6y = 34
---------------------------
0 = 2
This is never true so there is no solution
Answer:
Last one:
4x minus 3y = 16
8x minus 6y = 34
Step-by-step explanation:
4x - 3y = 16
y =(4x - 16)/3
y = (4/3)x - 16/3
8x - 6y = 34
y =(8x - 34)/6
y = (4/3)x - 17/3
These are two distinct parallel lines, hence will never meet
Therefore no solutions
Which is a description of rational numbers? a)Their decimal expansions can be infinitely repeating b) They are all numbers except zero c)They are always positive
what is the 50th term of the sequence that begins -2, 4, 10, 16
290
294
292
296
Answer: 292
Step-by-step explanation:
The formula is: [tex]a_n=a_1+(n-1)d[/tex]
Where;
[tex]a_n=[/tex] [tex]n^t^h[/tex] term or the term we're trying to find.
[tex]a_1=[/tex] First term
[tex]d=[/tex] Common difference.
To find the common difference, take [tex]a_2-a_1[/tex], or [tex]a_3-a_2[/tex] or [tex]a_4-a_3[/tex]
4-(-2)=?
4+2=?
6 -> this is our common difference
---------------------------------
10-4=?
6 -> this is our common difference
--------------------------------
16-10=?
6 -> this is our common difference
------------------------------------------------------------
Knowing this, we plug into the formula the number we're trying to find.
[tex]a_n=a_1+(n-1)d\\a_5_0=-2+(50-1)6\\a_5_0=-2+(49)6\\a_5_0=-2+294\\a_5_0=292[/tex]
Answer:
C. 292
Step-by-step explanation:
Which of these groups of values plugged into the TVM Solver of a graphing calculator will return the amount of a 20-year loan with an APR of 19.2%, compounded monthly, that is paid off with monthly payments of $510? site:brainly.com
Answer:
my answer was B.
Step-by-step explanation:
I chose C and i got it wrong
What is $526.36 rounded to the nearest 10 dollars?
526.36 rounded will be =
= 530
What is the answer please help me
Answer:
Step-by-step explanation:
the first one is D
Answer:
first one is 180
Step-by-step explanation:
