First Part
Given that
[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]
We have that
[tex]Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{Diameter}{2})^{3} = \frac{4}{3} \pi 9^{3} = 972\pi cm^{3} \approx 3053.63 cm^{3}[/tex]
Second Part
Given that
[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]
If the Diameter were reduced by half we have that
[tex]Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{r}{2}) ^{3} = \frac{\frac{4}{3} \pi r^{3}}{8}[/tex]
This shows that the volume would be [tex]\frac{1}{8}[/tex] of its original volume
Step-by-step explanation:First Part
Gather Information
[tex]Diameter = 18cm[/tex]
[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]
Calculate Radius from Diameter
[tex]Radius = \frac{Diameter}{2} = \frac{18}{2} = 9[/tex]
Use the Radius on the Volume formula
[tex]Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi 9^{3}[/tex]
Before starting any calculation, we try to simplify everything we can by expanding the exponent and then factoring one of the 9s
[tex]Volume = \frac{4}{3} \pi 9^{3} = \frac{4}{3} \pi 9 * 9 * 9 = \frac{4}{3} \pi 9 * 9 * 3 * 3[/tex]
We can see now that one of the 3s can be already divided by the 3 in the denominator
[tex]Volume = \frac{4}{3} \pi 9 * 9 * 3 * 3 = 4 \pi 9 * 9 * 3[/tex]
Finally, since we can't simplify anymore we just calculate it's volume
[tex]Volume = 4 \pi 9 * 9 * 3 = 12 \pi * 9 * 9 = 12 * 81 \pi = 972 \pi cm^{3}[/tex]
[tex]Volume \approx 3053.63 cm^{3}[/tex]
Second Part
Understanding how the Diameter reduced by half would change the Radius
[tex]Radius =\frac{Diameter}{2}\\\\If \\\\Diameter = \frac{Diameter}{2}\\\\Then\\\\Radius = \frac{\frac{Diameter}{2} }{2} = \frac{\frac{Diameter}{2}}{\frac{2}{1}} = \frac{Diameter}{2} * \frac{1}{2} = \frac{Diameter}{4}[/tex]
Understanding how the Radius now changes the Volume
[tex]Volume = \frac{4}{3}\pi r^{3}[/tex]
With the original Diameter, we have that
[tex]Volume = \frac{4}{3}\pi (\frac{Diameter}{2}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{2^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{2 * 2 * 2} = \frac{4}{3}\pi \frac{Diameter^{3}}{8}\\\\[/tex]
If the Diameter were reduced by half, we have that
[tex]Volume = \frac{4}{3}\pi (\frac{Diameter}{4}) ^{3} = \frac{4}{3}\pi \frac{Diameter^{3}}{4^{3}}\\\\ = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 4 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{4 * 2 * 2 * 4} = \frac{4}{3}\pi \frac{Diameter^{3}}{8 * 8} = \frac{\frac{4}{3}\pi\frac{Diameter^{3}}{8}}{8}[/tex]
But we can see that the numerator is exactly the original Volume!
This shows us that the Volume would be [tex]\frac{1}{8}[/tex] of the original Volume if the Diameter were reduced by half.
PU
The data set below represents the different costs of a refrigerator at a local home improvement store.
$777, $498, $619. $379. $895, $1,256, $1,052
b. What is the median of the second half of the data? (third quartile) 379
T
Using the median concept, it is found that the third quartile is of is of $1,052.
What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
In this problem, the ordered data-set is:
$379, $498, $619, $777, $895, $1,052, $1,256.
Hence, the median of $777 divides the data-set into two halfs:
The first half is: $379, $498, $619.The second half is: $895, $1,052, $1,256.Hence, the third quartile, which is the median of the second half, is of $1,052.
More can be learned about the median concept at https://brainly.com/question/25215461
This is a spinner for a game board. color the spinner to show 20% chance of black and 80% chance of red.
Answer:
Step-by-step explanation:
Divide the circle into 10 parts and color 2 parts black and 8 parts red.
What is the probbability of flipping a coin 15 times and getting heads 6 times?
Answer:
if I'm wrong let me know 25
You invested $8,307 into stocks of a company that were priced at $12.75/sh. You decide to sell the stock. What is the sale amount if the stock is selling at $11.95/sh?
Are the ratios 5:4 and 20:16 equivalent?
Answer:
yes
Step-by-step explanation:
If you take 20 and divide by 4 you get 5. if you take 16 and also divide by 4, you will get 4.
how many integers from 100 to 999, inclusive, don't include the numbers 2,4,6,8? PLS HELP I WILL MARK BRAINLIEST
Answer:
243
Step-by-step explanation:
999-100= 899 integers
200s 400s 600s 800s excluded so 400 numbers excluded
899 - 400 = 499
20s 40s 60s 80s which are 40 integers x 4 = 160
499 - 160 = 339
2s 4s 6s 8s which are 4 integers x 6 x 4 ( 4 from each 100 ) = 96
339 - 96 = 243 integers
a newspaper editor hired a writer for jokes cartoons. the cost for 8 jokes and 6 cartoons is 610usd. the cost of 6 jokes and 8 cartoons is 510usd how much do a joke and a cartoon together cost
Answer:
a joke and a cartoon together cost $80
c=$15 j=$65
Step-by-step explanation:
j=joke
c=cartoon
8j +6c = 610
6j+8c = 510
Multiply the first by 8
Multiply the second by -6
64j +48c = 4880
-36j -48c = -3060
ADD both (c will cancel)
28j = 1820
j= 65
PLUG j
8(65) + 6c = 610
520+6c = 610
6c= 90
c = 15
j + c = 65+15 = 80
(NEED HELP ASAP)An urn contains three red marbles, and six blue marbles. What is the probability of selecting at random, without replacement, two blue marbles?
Answer:
6/9 or 1/3
Step-by-step explanation:
There is a total of 9 marbles of both colors in the bag.
(3 red marbles + 6 blue marble = 9 marbles)
This means the denominator of your probability will be 9. There are 6 blue marbles in the bag so, in conclusion, the probability that you will take a blue marble out of the bag is 6/9. Also, 6/9 when simplified, is 1/3.
Have a great rest of your day
#TheWizzer
6. Higher Order Thinking The manager of a restaurant wants to add two new side dishes to the menu. She surveys customers about side dish preferences and records the results in the table shown at the right. a. Find the experimental probability that a customer prefers either baked potato or asparagus. b. Find the experimental probability that a customer prefers either steamed broccoli or sweet potato.
Using it's concept, considering the number of desired and total outcomes, it is found that the probabilities are given by:
a. 0.6 = 60%.
b. 0.4 = 40%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In an experimental probability, these numbers of outcomes are taken from previous trials.
Researching the problem on the internet, it is found that there is a total of 127 + 44 + 95 + 104 = 370 customers.
Item a:
127 + 95 = 222 customers prefer either baked potato or asparagus, hence the probability is given by:
p = 222/370 = 0.6 = 60%.
Item b:
44 + 104 = 148 customers prefer either steamed broccoli or sweet potato, hence the probability is given by:
p = 148/370 = 0.4 = 40%.
More can be learned about probabilities at https://brainly.com/question/14398287
Mark rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a factor of 18.
Answer:
1/3
Step-by-step explanation:
Factors of 18 are 1,2,3,6,9
5 A bag of tiles contains 6 green, 4 yellow, and 5 blue tiles. If one tile is pulled at random what is the probability of NOT choosing a green tile.
Make sure to give your probability as a fraction in simplest form.
Answer:
3/5
Step-by-step explanation:
6+4+5 = 15
5+4 = 9
9/15 = 3/5
Answer:
3/5
Step-by-step explanation:
Since it given that a bag of tiles contains:
6 green
4 yellow
5 blue
To Find:
If one tile is pulled at random what is the probability of NOT choosing a green tile.
Solve:
knowing that there are a total of 15 tiles {6+5+4=15}
And there is 6 green tiles
Thus, 15 - 6 = 9
Hence, the probability of Not Choosing a green tiles before simplest form is 9/15
GCD - 3
Divide both the numerator and denominator by the GCD
9 ÷ 3/15 ÷ 3
Reduced fraction = 3/5
Therefore, the probability of Not choosing a green tiles is 3/5
~Lenvy~
An amount of R351 is made up with 114 coins (R2 coins and R5 coins only). How many R2 coins are there? How many R5 coin are there?
Answer:
41
Step-by-step explanation:
For this, you have to make two equations;
One that calculates the amount of coins
and one that calculates the amount of R
I'm going to set
R2 = x
R5 = y
To make this a bit easier to look at
So to do the number of coins, you want to do this:
x + y = 114
This is saying that the total amount of R2 coins plus the total amount of R5 coins will add up to 114
Then, you want to calculate the worth of them.
2(x) + 5(y) = 351
This is saying that for ever R2 coin there is, it will increase the total by 2, and every R5, it will increase the total by 5. When you add these together, it will come out to 351.
Then you have to solve the system of equations:
x + y = 114
2x + 5y = 351
-2 * (x + y = 114)
2x + 5y = 351
-2x + -2y = -228
2x + 5y = 351
3y = 123
y = 41
Since y is the amount of R5 coins, we know we have 41 R5 coins.
So the answer is
41
Re write the quadratic function in standard form y=(x+5)(x-2)
Answer:
y = x^2 + 3x - 10
Step-by-step explanation:
x*x + 5*x + -2*x + 5*-2
= x^2 + 3x + -10
PLEASE RATE!! I hope this helps!!
Use rounding to estimate the product of 5, 555 and 4, 444. Round both numbers to the nearest thousand to find your answer.
The solution is
Step-by-step explanation:
5,555 can be rounded up to 6,000 because the 5 next to the five thousand will make it go up. while the 4,444 will round to 4,000 . I don't have a clear answer but I hope this helps.
8 out of 9 people in a class of 360 people are right handed, what is the percentage or right handed people and left. Then how many people out of the class of 360 is left and right handed.
Answer:
88.889% are right handed, 11.111% are left handed, ~320 people are right handed in a class of 360, ~40 people are right handed.
Step-by-step explanation:
The fraction 8/9 is equal to .88889, or 88.889%
Likewise, the fraction 1/9 (remainder) is equal to .11111, or 11.111%
By multiplying 360 by these fractions to get the number of people who fit these criteria in the sample, you get:
360*8/9 = 320 people right handed.
360*1/9 = 40 people left handed.
Cheers!
please solve for x please use statement reason
AE || BC
===》 DCB angle = DAE angle
AC /
__________________________________
Thus :
DCB angle = x
And also we know that the submission of interior angles of any triangle must equals to 180 degrees so :
In BCD triangle :
B + C + D = 180
x + x + D = 180
D = 180 - 2x
__________________________________
In the other hand we know that :
BDC angle + BDA angle = 180
because they make a straight line together so ;
180 - 2x + 50 = 180
- 2x = 180 - 230
- 2x = - 50
x = 25
And we're done...
Have a great time ♡
Did i do this right?
Answer:
yes
Step-by-step explanation:
Urgente!!! Doy 20 puntos
Answer:
74-7, 0, +9Step-by-step explanation:
Hope this helps
How to illistrate 1/3×1/2
Answer:
=1/6
Step-by-step explanation:
thats the answer
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Answer:
The answer is 157 mm.
Step-by-step explanation:
Given;Diameter (d) = 50 mmπ = 3.14To Find;The circumference of the circle.Formula;C = πdNow,
C = πd
C = 3.14 × 50 mm
C = 157 mm
Thus, The circumference of the circle is 157 mm.
three subtracted from five times a number is -39. what number is?
A) Translate the statement above into an equation that you can solve to answer this question, Do not solve it yet. Use x as your variable.
The equation is _____
B) Solve your equation in part {A} for x
.Answer x=
Answer:
A) 5x - 3= -39
B) 5x = -39 + 3
5x = -36
x = -36/ 5
x= -7.2
Help me please, thank you
Answer:
Option D is your correct answer
I think it will help.
Please help!! I will give brainliest :)
Answer: I think its 75 percent
Step-by-step explanation:
Answer:
75%
Step-by-step explanation:
The shaded is part of the poster 9/12
To convert 9/12 into a percent
100 ÷ 12 = 8.3333333333333
[tex]\frac{9*8.3333333333}{12*8.3333333333} = \frac{75}{100}[/tex]
Which of the following is equivalent to 1 and
5/8
Evaluate the function when x= -3, 0, and 1.
f(x) = 5 + 5x - 7
Answer:
f(-3) = -17
f(0) = -2
f(1) = 3
Step-by-step explanation:
f(-3) = 5 + 5(-3) - 7
5 -15 - 7
-10 - 7
=-17
f(0) = 5 + 5(0) -7
5 + 0 - 7
5 - 7
=-2
f(1) = 5 + 5(1) - 7
5 + 5 - 7
10 - 7
=3
The side of a goal in soccer is the shape of a right trapezoid. The dimensions are shown below. What is the area of the net needed for both sides of the goal? Чft 8 ft 10 ft
Answer:
[tex]61^{2}[/tex]
Step-by-step explanation:
So area equals {(B+b) x h} / 2 the two bases are 4 and 10 which is 14 the height is 8 so 14 times 8 is 112. 112 divided by 2 is 61. I hope this helps.
Dylan purchased a new car in 1993 for $26,300. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was $2,700 in the year 2001, then what would be the predicted value of the car in the year 2006, to the nearest dollar?
The predicted value of the car in the year 2006 to the nearest dollar would be $651.
What is the predicted value of the car?The first step is to determine the rate of depreciation
g = (FV/PV)^(1/n) - 1
Where:
FV = value of the car in 2001
PV = value of the car in 1993
n = number ofyears = 8
(2700/26,300)^(1/8) - 1 = -24.76%
Now determine the value of the car in 2006
2700x ( 1 - 0.2476)^5 = $651
To learn more about depreciation, please check: https://brainly.com/question/25552427
Abby is shooting a rocket off the top of a 128 foot tall building at a velocity of 96 feet per second. The equation to represent this is h(t) = -16t? +960 + 128 where h(t) represents the height of the rocket and t is the time after takeoff.
What is the maximum height of the rocket?
How many seconds does ot take to get to the maximum height?
Find the time it takes (in seconds) for the rocket to crash to the ground.
Answer:
a) 272 feet
b) 3 seconds
c) 7.123 seconds
Step-by-step explanation:
A graphing calculator provides an easy way to answer questions about the parameters of a quadratic function. Here the graph shows ...
a) the maximum height is 272 feet
b) it takes 3 seconds to get there
c) the rocket crashes after about 7.123 seconds
__
You can solve this algebraically by rewriting the equation in vertex form.
h(t) = -16t² +96t +128 . . . . . . given
h(t) = -16(t² -6t) +128 . . . . . . . factor out leading coefficient
h(t) = -16(t² -6t +9) +128 -(-16)(9) . . . . complete the square
h(t) = -16(t -3)² +272 . . . . . . write in vertex form
The vertex of the height function is (3, 272) meaning the rocket reaches a maximum height of 272 feet after 3 seconds.
__
The zero of the function can be found to be ...
0 = -16(t -3)² +272
0 = (t -3)² -17 . . . . . . divide by -16
t -3 = ±√17 . . . . . . add 17, take the square root
t = 3 +√17 ≈ 7.123106 . . . . . positive time value for h(t) = 0
It takes about 7.12 seconds for the rocket to crash.
In 1994, the moose population in a park was measured to be 4180. By 1999, the population was measured again to be 3480. If the population continues to change linearly: Find a formula for the moose population, P, in terms of t, the years since 1990. P(t)=? What does your model predict the moose population to be in 2002?
"If the population continues to change linearly", meaning the pattern or equation is the equation of a straight line.
[tex](\stackrel{x_1}{1994}~,~\stackrel{y_1}{4180})\qquad (\stackrel{x_2}{1999}~,~\stackrel{y_2}{3480}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3480}-\stackrel{y1}{4180}}}{\underset{run} {\underset{x_2}{1999}-\underset{x_1}{1994}}}\implies \cfrac{-700}{5}\implies -140[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4180}=\stackrel{m}{-140}(x-\stackrel{x_1}{1994}) \\\\\\ y-4180 = -140x + 279160 \\\\\\ y = -140x+283340~\hfill \boxed{P(t)=-140t+283340}[/tex]
what if t = 2002?
[tex]P(2002)=-140(2002)+283340\implies P(2002)= 3060[/tex]
How many more quarters does
Tommy need before he has $3.00
in quarters?