a tub shaped like a cylinder with a diameter of 18 inches, And a height of 20 inches Is filled to the top with water. Six spherical balls each with a diameter of 8 inches Are placed in the tub and they sink. some water overflows the tub, this amount equals a combined volume of the spheres. Find the exact and the approximate of water that remains in the tub.
The approximate amount of water that remains in the tub after the 6 spherical balls are placed in the tub are 3479.12 in³.
What is the approximate amount of water that remains in the tub?The first step is to determine the volume of the cylinder.
Volume of the tub = πr²h
Where:
r = radius = diameter / 2 = 18/2 = 9 inches h = height π = 3.143.14 x 9² x 20 = 5086.8 in³
The second step is to determine the volume of the 6 balls.
Volume of a sphere= 4/3πr³
r = diameter / 2 = 8/2 = 4 inches
6 x (3.14 x 4/3 x 4³) = 1607.68 in³
Volume that remains in the tub = 5086.8 in³ - 1607.68 in³ = 3479.12 in³
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If x^2 y^3 = 10 and x^3 y^2 = 8, what is the value of x^5 y^5
Step-by-step explanation:
so,
x²y³ = 10
x³y² = 8
what is the value of x⁵y⁵ ?
don't you see right away that 2+3 and 3+2 both equal 5 ?
so, x³x² = x⁵
y²y³ = y⁵
so, I only need to multiply both equations with each other. and I get
x²y³×x³y² = 10×8
x⁵y⁵ = 80
why ? because multiplications and exponents (which are nothing else than multiplications) are all communicative :
a×b = b×a.
Find the median of the data.
12, 10, 14, 9, 8, 9, 15, 15
Answer:
11
Step-by-step explanation:
First, order the numbers in the given set from least to greatest:
8 , 9 , 9 , 10 , 12 , 14 , 15 , 15
The median is the number found in the middle of the given set. If the amount of numbers in the set are even (as in this case), then you will find the mean of the two middle numbers.
In this case, the middle numbers are 10 & 12:
Find the mean. The mean is found by adding all the numbers together and dividing by the amount of numbers there is:
(10 + 12)/2 = (22)/2 = 11
11 is your median.
~
Answer:
11.
Step-by-step explanation:
12, 10, 14, 9, 8, 9, 15, 15
Arrange in ascending order:
8 9 9 10 12 14 15 15
Here, the median is the mean of the 2 middle numbers:
= (10+12) = 11.
PLEASE HELP ASAP!! DUE IN 10 MINUTES!! I'LL MARk BRAINLIEST ADN HIGH POINTS!! PLEASE HELP!!
Answer:
*speedrunning intensifies*
A:
Min is 15
LQ is 23
Median is 36
UQ is 38
B:
IQR is 38 minus 23, or 15, I guess that the data is not very consistent and it is spread out?
C:
Min is calculated by looking at the end of the far left line
LQ is the far left of the box
Median is the line inside the box
UQ is the the far right of the box
IQR is UQ subtract LQ
I answered because I wanted you to get brainliest!
A student used the equation below to create a table.
y=-3x - 5
The student used –2 as one of the values for the input. Which ordered pair could be taken from the table?
O (-11, -2)
O (-2,-11)
O (-2, 1)
O (1.-2)
Mark this and return
Save and Exit
Next
Submit
Answer:
second option -2, -11
Step-by-step explanation:
when you put -2 where x is then
y is -11
Before mr.wonsavage was a superhero in "wontropolis" he made wedding favors fof wedding receptions using peanuts and m&ms. pesnuts cost $3.50 per pound and m&ms cost $8 per pound. mr won wants to make 60 pounds of the peanut/m&ms mixture costings $6.00 per pound. how many pounds of peanuts and m&ms shoukd be mixed?
Answer:
10 pounds of copounds must be mixed
Step-by-step explanation:
Because if Mr wom wants 60 pounds if 1 cost &$6.00 he must take the prime number that can be multiplied by 6 to give us 60. The number is 10.
3B What is the value of account after 10 years,
if interest is paid at 3.7%, if no other deposits
or withdrawals are made?
Initial deposit $6500, then compounded annually
Answer:
$9,347.62
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $6,500r = 3.7% = 0.037n = 1t = 10 yearsSubstituting the given values into the formula and solving for A:
[tex]\implies \sf A=6500\left(1+\frac{0.037}{1}\right)^{10 \times 1}[/tex]
[tex]\implies \sf A=6500\left(1.037\right)^{10}[/tex]
[tex]\implies \sf A=9347.617232[/tex]
Therefore, the value of account after 10 years is $9,347.62
Let's see
[tex]\\ \rm\Rrightarrow A=P(1+r)^t[/tex]
P=6500r=3.7%t=10yearsSo
A:-
[tex]\\ \rm\Rrightarrow 6500(1+0.037)^{10}[/tex]
[tex]\\ \rm\Rrightarrow 6500(1.037)^{10}[/tex]
[tex]\\ \rm\Rrightarrow \$ 9347.6[/tex]
y X X
y = 85 when x = 17
Using the information above, write an equation for y in terms of x.
y=
?
Answer:
y= x5
Step-by-step explanation:
y = 5 times the number of x.
2x^2-8x factor
the folowing polynomials
Leslie keeps her goats
in a circular pen
enclosed by a fence.
The total length of the
fence is 100 yards.
What is the area of the
goat pen?
Answer:
Step-by-step explanation:
Circumference = 2 π r
100 = 2 π r
r = 100 / 2π
= 50/π
So the area = π r^2
= π * (50/π)^2
= 2500/π
= 795.8 yd^2.
if the diameter of a cone is 16cm and the height is 15cm what is the volume? I've tried the formula v=1/3*3.14*r^2*h but the answer wasn't on the choice pick even when I divided the diameter by 2 to get the radius which is 6. and I've tried leg^2 +leg^2=hypotenuse, but I probably did it wrong. If you find the answer could you show how you found it? I'll put u as the brainiest.
Answer:
V= volume of cone A=Ah A= πr2
A= area of base 3
H= height
V= (3.1416)(16)(15) 3.1416x16x15= 753.9
3
V= 753.9 753.9÷3= 251.3 cu. in
3
Volume of the cone is 251.3 cu. in
I hope this helps you. Good luck!
15. If m arc BY = 40 degrees, what is m angle YAC? the figure is not drawn to scale.
Using the tangent theorem and the inscribed angle theorem, the measure of angle YAC in the figure is: 70°.
What is the Tangent Theorem?The angle formed at the point of tangency of the radius and the tangent equals 90 degrees based on the tangent theorem.
What is the Inscribed Angle Theorem?According to the inscribed angle theorem, an inscribed angle equals the measure of the arc intercepted.
m∠BAY = 1/2(40) [inscribed angle theorem]
m∠BAY = 20°
m∠BAC = 90° [tangent theorem]
m∠YAC = 90 - 20
m∠YAC = 70°
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Sketch a graph of each of the four angles in the same coordinate plane. Label the ordered pairs that intersect the circle. The angles given are 30°, 150°, 210°, 330°
To Sketch a graph of each of the four angles of 30°, 150°, 210°, 330°, one can follow the example that is given in the image.
What is a sketch?In the mathematics, a sketch is known to be a given category that tells what a thing is all about.
Note that in sketching, one need to take not of the key points and angles and as such, To Sketch a graph of each of the four angles of 30°, 150°, 210°, 330°, one can follow the example that is given in the image.
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A cylinder has a volume of 72 cubic inches. What is the volume of a cone with the same height and radius as the cylinder? Explain.
This graph represents gasoline price trends in New Mexico.
First, the price of gasoline in New Mexico _______ (increases quickly, increases slowly, decreases slowly, decreases quickly) , and then it _____ (increases quickly, increases slowly, decreases slowly, decreases quickly)
Answer:
Increases slowly, increases quickly
Step-by-step explanation:
The first part of the graph is a slope that's not very steep, but in a positive direction. That means it's increasing slowly. The second segment has a much steeper slope, and it's going upwards, meaning it is increasing quickly.
I hope this helped!
Question Bill needs 864 tiles to tile a bathroom. He can buy tiles individually for $0.40 each, and he can buy them in boxes of 100 for $32.50 per box. What is the least amount that Bill must pay to buy the tiles he needs
The least amount that Bill must pay to buy the tiles he needs is $292.50
What is the least amount?The total cost of buying the tiles individually is : cost per tile x total tiles needed
$0.40 x 864 = $345.60
The total cost of buying the tiles in a box of 100 is : $32.50 x 9 = $292.50
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If cos is x=0.25, find sin x
A) sin x ≈ 0.97
B) sin x ≈ 0.75
C) sin x ≈ 0.0625
D) sin x ≈ 0.03
Answer:
In quadrant I, the answer is A. sin(x) ≈ 0.97
PLSSS HELPPPPP with b !!!
Step-by-step explanation:
your a. is wrong.
so, we need to do both.
a.
you did not really read carefully. DE = 4x and not 4.
DE = 4x does not mean x = 4. absolutely not.
so, you cannot just use x=4 in the first triangle.
but you are right, AB and DE correlate between the 2 congruent triangles.
therefore
3x + 6 = 4x
6 = x
so, AB = 3x + 6 = 3×6 + 6 = 18 + 6 = 24 ft
b.
congruent means that the sides and the angles are the same between the 2 triangles.
so,
6y + 12 = 8y + 2
12 = 2y + 2
10 = 2y
y = 5
so, the angle EDF is
8y + 2 = 8×5 + 2 = 40 + 2 = 42°
The hypotenuse of a right triangle measures 18 cm and one of its legs measures 10 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
Step-by-step explanation:
This sounds like a Pythagoras theorem question. So what I would do is 18^2 - 10^2= Ans
Then square root the answer
Answer: the answer is 15
Use the diagram to determine which of the statements must be true.
No lines are parallel.
c∥d
a∥b
c∥e
a∥c
d∥e
a∥e
b∥d
Answer:
d∥e
Step-by-step explanation:
The figure shows that line e is perpendicular to line b, and line d is perpendicular to line b.
Theorem: If two lines are perpendicular to the same line, then the lines are parallel.
Since lines d and e are perpendicular to the same line, b, then lines d and e are parallel.
Answer: d∥e
The area of a circle is 36 square feet. What is the diameter?
Answer:
The diameter is 6.76
Please read the exaplanation... it always helps!
Step-by-step explanation:
Area of circle = r^2 pi
if the area is 36 then...
36 = r^2 pi to solve for r divide both sides by pi
36/pi = r^2
11.45 = r^2 take the square root of both sides
√11.45 = r RADIUS = 3.38
then multiply by two since the diameter is 2 (radius) and you get...
diameter = 6.76
i hope this helpssssss!!!!!!!
Answer:
[tex]area = \pi {r}^{2} [/tex]
[tex]36 = 3.14 \times {r}^{2} [/tex]
[tex] \frac{36}{3.14} = {r}^{2} [/tex]
[tex] {r}^{2} = 11.46[/tex]
[tex]r = \sqrt{11.46} [/tex]
[tex]r = 3.39[/tex]
[tex]diameter = 2 \times radius[/tex]
[tex]diameter = 3.39 \times 2[/tex]
[tex] = 6.78[/tex]
c) If you are given a circle with center C, how do you locate the vertices of a square inscribed in circle C?
Answer: The square is inscribed in a circle that means the square is drawn inside a circle such that it's vertices lie on the circle.
You need to remember that the vertices of the square lie on the circumference of circle and the center of circle is also the midpoint of diagonals of the square i.e. Diagonal of the square is equal to diameter of the circle.
We could also see the image of such figure.
The following histogram represents the heights of the students in Ari's classroom. Identify at least three things that you
can infer from the histogram about the distribution's center, spread, and overall shape.
Answer:
We can identify that the histogram is skewed to the left (more on the left) the center would be 3 and the spread is saying more students are between 58-59 and 60-61 inches were as there is only 3 for the rest
Step-by-step explanation:
I hope this helps I have the same question and this is what I wrote for my answer
Jayne stacked 2 cubes on top of each other as shown. The edge length of the smaller cube is half the edge length of the cube below it. What is the surface area of the new figure?
Considering the surface area of a cube, and that the figure has two cubes, the total surface area is of 1470 m².
What is the surface area of a cube?The surface area of a cube of edge length a is given by:
S(a) = 6a².
In this problem, we have two cubes, one with a = 14 m and the other with a = 7 m. Hence, the total surface area, in m², is given by:
S(a) = 6 x 14² + 6 x 7² = 1470.
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The volume of a sphere with radius r
is given by the formula V=4/3 π r^3.
Find the volume of a sphere with radius 10 cm is?
Answer:
4186.6 cm³[tex] \: [/tex]
Step-by-step explanation:
In the question, it is given that a sphere has a radius of 10 cm and we have to find the volume of the sphere.
To Find the volume of the cone, we must know this formula :
[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { Volume_{(sphere) }= \dfrac{4}{3} \: \pi {r}^{3}}}}}}}} \\ \\[/tex]
Now, we will substitute the values in the formula :
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= \dfrac{4}{3} \: \times 3.14 \times {(10)}^{3}}}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= \dfrac{4}{3} \: \times 3.14 \times 1000}}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= \dfrac{4}{3} \: \times 3140}}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= \dfrac{4 \times 3140}{3} }}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= \dfrac{12560}{3} }}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= 4186.6 }}}}}} \\ \\[/tex]
Therefore,
The volume of the sphere is 4186.6 cm³Given :
Radius of sphere is 10 cm.To Find :
Volume of sphere.Solution :
As we know that volume of sphere is calculated by the formula :
V = 4/3 πr³Here,
V is volume r is radius Value of π is 22/7Putting the values in the formula,
>> V = (4 / 3) × (22 / 7) × (10)³
>> V = (4 / 3) × (22 / 7) × (10 × 10 × 10)
>> V = (4 / 3) × (22 / 7) × (10 × 100)
>> V = (4 / 3) × (22 / 7) × 1000
>> V = 4 × 22 × 1000 / 3 × 7
>> V = 88 × 1000 / 3 × 7
>> V = 88000 / 3 × 7
>> V = 88000 / 21
>> V = 4190.47 cm³
-1+4x^{3}-\frac{x^{5}}{5}+x^{2}-3x
−1+4x
3
−
5
x
5
+x
2
−3x
Answer:
here is the graph
Step-by-step explanation:
A bag of colored paper clips contains 3 red clips
and 6 green clips. What's the probability of
pulling out a red clip and then a green clip?
(Assume that you don't put the first red paper
clip back in the bag.) Write your answer as a
fraction.
Answer:
1/5
Step-by-step explanation:
solution [ calculation of probability ]
P= (3/3+6) × (6/3+6-1)
=3/9×6/10
=1/5
In a class of 30 students, 18 have a cat and 17 have a dog. There are 7 students who
have a cat and a dog. What is the probability thatla student chosen randomly from the
class has a cat and a dog?
The probability of having cats and dogs is 7/30.
What is probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an occurrence may be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
Definitions of Probability Theory Terms
The probability terminology listed below aid in a better comprehension of probability concepts.
Experiment: A trial or procedure carried out to generate a result is referred to as an experiment.
Sample Space: A sample space is the collection of all potential results of an experiment. Tossing a coin, for instance, has two possible outcomes: head or tail.
Favorable Consequence: An occurrence is deemed to have generated the desired outcome or an anticipated event if it did so. For instance, if we roll two dice and receive the total of the two numbers as 4, the possible/favorable possibilities are (1,3), (2,2), and (3,1).
Trial: To conduct a trial is to conduct a random experiment.
Given:
total students = 30
students have cat = 17
student have dog = 17
students have both =7
So, the probability of having cats and dogs
=7/30
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Consider the cone with slant height of 13 m and perpendicular height of 12 m: a) Find the length of the radius, r. b) Find the length of the diameter of the cone's base.
Answer:
Step-by-step explanation:
answer question in pic, thanks!!
Answer:
6.42 %
Step-by-step explanation:
3412.23 = 2500(1+i)^5
i = 6.42%