A child reshapes a cone made up of China clay of height 24 and radius 6 into a sphere.
The radius of the sphere is...
Answers
Answer:
6
Step-by-step explanation:
Volume of the cone = V=πr2h ^3=π·62·24 ^3≈904.77868
So, the volume of the sphere, will be the same too:
904.78 = 4/3 x pi x r^3
Solve:
904.78 = 4.18 x r^3
r^3 = 904.78 divided by 4.18
r^3 = 216.45
r = cube root of 216(approximate) = 6.
Hope this helps.
Good Luck
Related Questions
factorise this expression as fully as possible 2x^2+6x
Answers
Answer:
(Factor out 2x from the expression)
2x (x +3)
Renting a trailer for 4 days costs $84. Renting the trailer for 5 days costs $100. Which of the following linear equations represents the (days, cost)?
Answers
Answer:Y=16x+20
Step-by-step explanation:
Y=16x+20 thats tthe one that worked for me
please help,
These prisms have different shapes as end faces.
a) Complete this table.
Shape of end face No. of faces No. of edges No. of vertices
Triangle (3 sides) 5
9
6
Rectangle (4 sides)
00
Triangle
Pentagon (5 sides)
15
10
Hexagon (6 sides)
8
18
b) How many edges and vertices does a prism
with a 100-sided end face have?
edges
vertices
Pentagon
Answers
Answer:
Step-by-step explanation:
E=300.
V=200.
An equilateral triangle has sides 8 units long. An equilateral triangle with sides 4 units long is cut off at the top, leaving an isosceles trapezoid. What is the ratio of the area of the smaller triangle to the area of the trapezoid? Express your answer as a common fraction.
Answers
Answer:
1:3
Step-by-step explanation:
Please study the diagram briefly to understand the concept.
First, we determine the height of the isosceles trapezoid using Pythagoras theorem.
[tex]4^2=2^2+h^2\\h^2=16-4\\h^2=12\\h=\sqrt{12}\\ h=2\sqrt{3}$ units[/tex]
The two parallel sides of the trapezoid are 8 Inits and 4 units respectively.
Area of a trapezoid [tex]=\dfrac12 (a+b)h[/tex]
Area of the trapezoid
[tex]=\dfrac12 (8+4)*2\sqrt{3}\\=12\sqrt{3}$ Square Units[/tex]
For an equilateral triangle of side length s.
Area [tex]=\dfrac{\sqrt{3}}{4}s^2[/tex]
Side Length of the smaller triangle, s= 4 Units
Therefore:
Area of the smaller triangle
[tex]=\dfrac{\sqrt{3}}{4}*4^2\\=4\sqrt{3}$ Square units[/tex]
Therefore, the ratio of the area of the smaller triangle to the area of the trapezoid
[tex]=4\sqrt{3}:12\sqrt{3}\\$Divide both sides by 4\sqrt{3}\\=1:3[/tex]
which of the following shows the correct steps to find the value of 8^1/3? (1 point)
Answers
Answer:
8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2
Step-by-step explanation:
Options are below
8 to the power of 1 over 3 equals 4 to the power of 3 whole to the power of 1 over 3 equals 4 to the power of 3 multiplied by 1 over 3 equals 4
8 to the power of 1 over 3 equals 2 to the power of 3 whole to the power of 1 over 3 equals 2 to the power of 3 multiplied by 1 over 3 equals 2
8 to the power of 1 over 3 equals 2 to the power of 4 whole to the power of 1 over 3 equals 2 to the power of 4 multiplied by 1 over 3 equals 16
16 to the power of 1 over 4 equals 8 to the power of 2 whole to the power of 1 over 4 equals 8 to the power of 2 multiplied by 1 over 4 equals 8
Given:
8^1/3
if a power is raised to a power, we simplify it by multiplying the exponents; this will create a whole number exponent
if 8 can be rewritten as a number to the 3rd power.
We have
8 = 2*2*2 = 2³
Therefore,
8^1/3=(2^3)^1/3
=2^3×1/3
=2^3/3
=2^1
=2
The diagram represents 6x2 – 7x + 2 with a factor of 2x – 1. A 2-column table with 2 rows. First column is labeled 2 x with entries 6 x squared, negative 4 x. Second column is labeled negative 1 with entries negative 3 x, 2. Both rows are labeled with a question mark. What is the other factor of 6x2 – 7x + 2? 3x – 2 3x – 1 3x + 1 3x + 2
Answers
Answer:
( 3x -2)
Step-by-step explanation:
6x^2 – 7x + 2
We know that the constant only has factors of 1 and 2
Since the middle term is negative we know that that we are subtracting
A negative times a negative is positive for the final term
A negative plus a negative is negative for the middle term
( -1 ) ( -2)
We have to determine how to break up 6x^2
1x * 6x
2x*3x
3x*2x
6x*1x
We are given that one factor is 2x-1
( 2x -1 ) ( -2)
That means the other factor of 6x^2 is 3x ( 2x*3x)
( 2x -1 ) ( 3x -2)
Answer:
3x-2
Step-by-step explanation:
6x² – 7x + 2= 6x² -3x- 4x + 2= 3x(2x-1)- 2(2x-1)= (2x-1)(3x-2)Factors are:
2x-1 and 3x-2--------------
3x – 2 correct3x – 1 incorrect3x + 1 incorrect3x + 2 incorrectThe points (-2,4), (0,8), (1,10), and (3,14) are on a line. Which of the following statements are true?
Answers
Answer: y = 2x+8
Check out this graph I supplied you with!
Which statement illustrates the distributive property?
3 (4 + 5) = 3 (4) + 5
3 (4 + 5) = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = Left-bracket 3 (4) right-bracket + Left-bracket 3 (5) Right-bracket
Answers
Answer:
B. 3(4 + 5) = 3(4) + 3(5)
3 left-bracket (4) (5) right-bracket = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = Left-bracket 3 (4) right-bracket + Left-bracket 3 (5) Right-bracket
Step-by-step explanation:
Distributive property of multiplication over addition:
a(b + c) = ab + ac
You have
3(4 + 5), so following the pattern above, you should get:
3(4 + 5) = 3(4) + 3(5)
Answer:
b
Step-by-step explanation:
I took the test
A company borrows 60,000 for 10 years at a simple interest rate of 8.5%. Find the interest paid on the loan and the total amount paid.
Answers
Answer: 51,000 ; 111,000
Step-by-step explanation:
The formula to calculate the simple interest is: PRT/100
where,
P = principal = 60,000
R = rate = 8.5%
T = time = 10 years
Simple interest =(60000 × 8.5 × 10)/100
= 5100000/100
= 51,000
Total Amount Paid= Principal + Interest
= 60,000 + 51,000
= 111,000
Which one of the following numbers is divisible by 11?
A. 924711
B. 527620
C. 320793.
D. 435854
Answers
Answer:
320793
Step-by-step explanation:
320793 / 11 = 29163
As a project for math class, two students devised a game in which 3 black marbles and 2 red marbles are put into a bag.
First the players must decide who is playing black marbles and who is playing red marbles. Then each player takes a
turn at drawing a marble, noting the color, replacing the marble in the bag, and then drawing a second marble and noting
the color before returning it to the bag. The point scheme for the game is detailed in the table below.
Point Values for Marble Game
Black Marble Points
Red Marble Points
Both black: +2 points
Both red: +4 points
Different colors: -1 point
Different colors: -1 point
Both red: 0 points
Both black: 0 points
If Seth is challenged to a game by a classmate, which statement below is correct in all aspects in helping him make the
correct choice?
Since E(black) = 0.24 and E(red) = 0.16, Seth should choose to play black marbles.
E(red) will be twice that of E(black), so Seth should choose to play red marbles.
Since E(red) = E(black), it is a fair game, so it doesn't matter which color Seth chooses.
Answers
Answer:
The first option
Step-by-step explanation:
The correct answer is the first option, since E(black) = 0.24 and E(red) = 0.16, Seth should choose to play black marbles.
Answer:
I believe its A: Since E(black) = 0.24 and E(red) = 0.16, Seth should choose to play black marbles.
Step-by-step explanation:
edg 2020
Find the values of the variables and the measures of the angles
Answers
Answer:
Add each given variable
(6x + 10) + (x + 2) + x = 8x + 12
The sum of all the angles equals 180ᴼ
8x + 12 = 180
Subtract 12 from both sides
8x = 168
Divide by 8 on both sides
x = 21
Now plug in 21 for each x to find the measure of each angle.
(6[21] + 10) = 126 + 10 = 136ᴼ
(21 + 2) = 23ᴼ
x = 21ᴼ
Find the value of x.
helpppp pleaseee!!
Answers
Answer:
x = 50
Step-by-step explanation:
Since this is a quadrilateral, the sum is 360 degrees
2x+x+10 + 3x+x = 360
Combine like terms
7x+10 =360
Subtract 10 from each side
7x+10-10 = 360-10
7x = 350
Divide by 7
7x/7 = 350/7
x = 50
Answer:
[tex]x = 50[/tex]
Step-by-step explanation:
Sum of the interior angles in a quadrilateral
= 360°
Let's solve now
[tex]x + 10 + 3x + x + 2x = 360 \\ 7x + 10 = 360 \\ 7x = 360 - 10 \\ 7x = 350 \\ \frac{7x}{7} = \frac{350}{7} \\ x = 50[/tex]
hope this helps you.
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 247 days and standard deviation sigma equals 16 days. Complete parts (a) through (f) below.
Answers
Answer:
The answer is given below
Step-by-step explanation:
a) What is the probability that a randomly selected pregnancy lasts less than 242 days
First we have to calculate the z score. The z score is used to determine the measure of standard deviation by which the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that Mean (μ) = 247 and standard deviation (σ) = 16 days. For x < 242 days,
[tex]z=\frac{x-\mu}{\sigma}=\frac{242-247}{16}=-0.31[/tex]
From the normal distribution table, P(x < 242) = P(z < -0.3125) = 0.3783
(b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
If a sample of 17 pregnancies is obtained, the new mean [tex]\mu_x=\mu=247,[/tex] the new standard deviation: [tex]\sigma_x=\sigma/\sqrt{n} =16/\sqrt{17} =3.88[/tex]
c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 242 days or less
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{17} }=-1.29[/tex]
From the normal distribution table, P(x < 242) = P(z < -1.29) = 0.0985
d) What is the probability that a random sample of 49 pregnancies has a mean gestation period of 242 days or less?
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{49} }=-2.19[/tex]
From the normal distribution table, P(x < 242) = P(z < -2.19) = 0.0143
(e) What might you conclude if a random sample of 49 pregnancies resulted in a mean gestation period of 242 days or less?
It would be unusual if it came from mean of 247 days
f) What is the probability a random sample of size 2020 will have a mean gestation period within 11 days of the mean
For x = 236 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{236-247}{16/\sqrt{20} }=-3.07[/tex]
For x = 258 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{258-247}{16/\sqrt{20} }=3.07[/tex]
From the normal distribution table, P(236 < x < 258) = P(-3.07 < z < 3.07) = P(z < 3.07) - P(z < -3.07) =0.9985 - 0.0011 = 0.9939
PLSSSSSSSSSSSSSSSSSS HELP I JUST DONT GET IT write in standard form a) 456000 b) 0.00034 c) 16×10with a seven in the right corner of the 10
Answers
Answer:
A) 4.56000 x 10^5
B) 3.4 x 10^-4
C) 160000000
Step-by-step explanation:
Please mark me the brainliest answer!
Answer:
Step-by-step explanation:
a) 456000 = 4.5* 10⁵
b) 0.00034 = 3.4 *10⁻⁴
c) 16 *10 = 1.6 * 10²
Ice is placed around a bowl of water to lower the temperature. The equation D=−75t+22 shows the time, t, measured in minutes and temperature, D, measured in degrees Celsius. Which statement is correct?
Answers
Answer:
d) Before cooling begins, the temperature of the water is 22°C
Step-by-step explanation:
Option A
If t=7 minutes
D=-7/5t+22
=-7/5(7)+22
=-49/5+22
=-49+110/5
=61/5
=12.2°C
Change in temperature=12.2°C-22°C
=-9.8°C
Option B
If t=5 minutes
D=-7/5t+22
=-7/5*5+22
=-7+22
=15°
Change in temperature=15°-22°
=-7°
Option C
The temperature of the ice must be less than 22°C
Option D
D=-7/5t+22
When ice is not placed, t=0
D=-7/5t+22
=-7/5(0)+22
=0+22
=22
Temperature of the water before cooling=22°
Answer:
D
Step-by-step explanation:
Helppp!!!! please!!!
Answers
Answer:
your answer is b
hope this helps
Step-by-step explanation:
Answer:
B. m<DYZ = 90 deg
Step-by-step explanation:
There's a mistake in this problem. DY is a radius, so D is the center of the circle, but the circle is called circle O. Is the center D or O?
In any case, a radius that intersects a tangent at 90 degree angles.
m<DYZ = 90 deg
What are the solutions to the quadratic equation below? x^2+34x-72=0
Answers
Answer:
( x + 36 ) ( x - 2 ) = 0
Step-by-step explanation:
x^2 + 36x - 2x -72 = 0
x ( x + 36 ) - 2 ( x + 36 ) = 0
( x + 36 ) ( x - 2 ) = 0
ASAP! A boat travelling at top speed upstream moves at 15km/hr. When it travels downstream, again at top speed< it moves at 25km/hr. What is the boat's top speed in still water?
Answers
Answer: 20km/h
Step-by-step explanation:
20km/h. Simply average 15 and 25 by doing (15+25)/2
Hope it helps <3
there were 7 little cherries for every 2 big cherries. if there were 630 cherries in the box, how many little cherries were there? (please also answer the question in the picture)
Answers
Answer:
1)2205little cherries
2)0.5.
Step-by-step explanation:
1)7little=2big
?=630big
7×630=2205little cherries
2
2)²/5x=¹/10what is the value of 10x-2
first find the value of x that is ¹/10÷²/5=¼
so x is ¼
insert the value ie 10×¼-2
=2.5-2
=0.5
F(x)=x^2. What is g(x)?
Answers
Answer:
g(x)= 5x
Step-by-step explanation:
You should go back to the graph and notice that the abscissa 1 goes with the ordinate 5.
Now ask yourself how do I get 5 using 1. There many ways but notice that the function is growing and both functions f and g geow the same way. Wich mean that g(x)= 5x is a valid option.
notice that 0 is going with o at the ordinate.
some little calculations . m=(5-0)/(1-0)= 5
so the function is g(x)=5x+p
p is 0 since it is the first ordinate
so g(x)= 5x
urn I contains 1 red chip and 2 white chips; urn II contains 2 red chipsand 1 white chip. One chip is drawn at random from urn I and transferred to urnII. Then one chip is drawn from urn II. Suppose that a red chip is selected from urnII. What is the probability that the chip transferred was white
Answers
Answer:
Following are the answer to this question:
Step-by-step explanation:
In the question first calls the W if the transmitted chip was white so, the W' transmitted the chip is red or R if the red chip is picked by the urn II.
whenever a red chip is chosen from urn II, then the probability to transmitters the chip in white is:
[tex]P(\frac{w}{R}) = \frac{P(W\cap R)}{P(R)} \ \ \ \ \ _{Where}\\\\P(R) = P(W\cap R) + P(W'\cap R) \\[/tex]
The probability that only the transmitted chip is white is therefore [tex]P(W) = \frac{2}{3}\\[/tex], since urn, I comprise 3 chips and 2 chips are white.
But if the chip is white so, it is possible that urn II has 4 chips and 2 of them will be red since urn II and 2 are now visible, and it is possible to be: [tex]P(\frac{R}{W}) = \frac{2}{3}[/tex]
[tex]P(W\cap R) = P(W) \times P(\frac{R}{W}) \\[/tex]
[tex]= \frac{2}{3}\times \frac{2}{4} \\\\= \frac{2}{3}\times \frac{1}{2} \\\\= \frac{2}{3}\times \frac{1}{1} \\\\=\frac{1}{3}\\\\= 0.333[/tex]
Likewise, the chip transmitted is presumably red [tex](P(W')= \frac{1}{3})[/tex]and the chip transferred is a red chip of urn II [tex](P(\frac{R}{W'})= \frac{3}{4}[/tex], and a red chip is likely to be red [tex](\frac{R}{W'})[/tex].
Finally, [tex]P(W'\cap R) = P(W') \times P(\frac{R}{W'})\\[/tex]
[tex]= \frac{1}{3} \times \frac{3}{4} \\\\ = \frac{1}{1} \times \frac{1}{4} \\\\=\frac{1}{4}\\\\= 0.25[/tex]
The estimation of [tex]P(R)[/tex] and [tex]P(\frac{W }{R})[/tex] as:
[tex]P(R) = 0.3333 + 0.25\\\\ \ \ \ \ \ \ \ \ \ = 0.5833 \\\\ P(\frac{W}{R}) = \frac{0.3333}{0.5833} \\\\\ \ \ \ \ \ \ = 0.5714[/tex]
. Find the measure of angle A.
A
160°
Answers
Answer:
20°
Step-by-step explanation:
A= 360°- (160°+2*90°)= 20°
CD=17 AM=5 CD=? I've tried everything but I can't figure it out.
Answers
Answer:
We can prove that ΔTMB ≅ ΔTMD and ΔTMA ≅ ΔTMC by ASA. This means that BM = MD = BD / 2 = 8.5 and that AM = CM = 5 which means that CD = MD - CM = 8.5 - 5 = 3.5.
What is the decimal expansion of 2/3
Answers
Answer:
[tex]0.\overline{6}[/tex]
Step-by-step explanation:
It is a repeating decimal fraction:
[tex]\dfrac{2}{3}=0.6666...=0.\overline{6}[/tex]
__
You can see this if you do the long division. Each step is the same as the one before.
The radius of a circle is 2 feet. What is the area of a sector bounded by a 180° arc?
Answers
Answer:
[tex]\boxed{Area = 3.14 ft^2}[/tex]
Step-by-step explanation:
Radius = r = 2 feet
Angle = θ = π/2 (In radians) = 1.57 radians
Area of Sector = [tex]\frac{1}{2} r^2 \theta[/tex]
Area = [tex]\frac{1}{2} (4)(1.57)[/tex]
Area = 2 * 1.57
Area = 3.14 ft²
Answer:
[tex]\bold{2\pi\ ft^2\approx6,28\ ft^2}[/tex]
Step-by-step explanation:
360°:2 = 180° so the area of a sector bounded by a 180° arc is a half of area of a circle of the same radius.
[tex]A=\frac12\pi R^2=\frac12\pi\cdot2^2=\frac12\pi\cdot4=2\pi\ ft^2\approx2\cdot3,14=6,28\ ft^2[/tex]
Evaluate: m - 12 when m = 23.
Answers
Answer:
11
Step-by-step explanation:
sub 23 with m
23 - 12 = 11
Write a set of data that contains 12 values for which the box plot has no whiskers. State the median, first and third quartiles, and lower and upper extreme
Answers
Answer:
The data set is:
S = {4.5, 4.5, 4.5, 4.5, 6, 8, 10, 12, 13.5, 13.5, 13.5, 13.5}
Step-by-step explanation:
Consider the ordered data set:
S = {4.5, 4.5, 4.5, 4.5, 6, 8, 10, 12, 13.5, 13.5, 13.5, 13.5}
The lower extreme is: 4.5
The upper extreme is: 13.5
The median for an even number of observations is the mean of the middle two values.
[tex]\text{Median}=\frac{6^{th}+7^{th}}{2}=\frac{8+10}{2}=9[/tex]
The first quartile (Q₁) is defined as the mid-value between the minimum figure and the median of the data set.
Q₁ = 4.5
The 3rd quartile (Q₃) is the mid-value between the median and the maximum figure of the data set.
Q₃ = 13.5
A box plot that has no whiskers has, Range = Interquartile Range.
Compute the range as follows:
[tex]Rangw=Max.-Min.=13.5-4.5=9[/tex]
Compute the Interquartile Range as follows:
[tex]IQR=Q_{3}-Q_{1}=13.5-4.5=9[/tex]
Thus, the box pot for the provided data has no whiskers.
Solve for x 3 x − 2 = 2 x − 4
Answers
Answer:
x= -2
Step-by-step explanation:
Answer: x=-2
Step-by-step explanation: first subtract 2x from both sides leaving you with x-2=-4
Then add 2 to both sides, leaving you with x=-2
Please help ASAP I’m very unsure on how to do these 2 questions please give answers for both :)
Answers
Answer:
1) Option 2
2) Option 1
Step-by-step explanation:
1) 3a-2b
Where a = 3, b = 2
=> 3(3)-2(2)
=> 9-4
=> 5
2) 5c+3d
Where c = 4, d = -5
=> 5(4) + 3(-5)
=> 20 - 15
=> 5
Answers:
5, 5
Step-by-step explanation:
Put a as 3 and b as 2 and evaluate:
3(3) - 2(2)
9 - 4
= 5
Put c as 4 and d as -5 and evaluate:
5(4) + 3(-5)
20 - 15
= 5