The base of a solid is a circular disk with radius 4. Parallel cross sections perpendicular to the base are squares. Find the volume of the solid.
Answer:
the volume of the solid is 1024/3 cubic unit
Step-by-step explanation:
Given the data in the question,
radius of the circular disk = 4
Now if the center is at ( 0,0 ), the equation of the circle will be;
x² + y² = 4²
x² + y² = 16
we solve for y
y² = 16 - x²
y = ±√( 16 - x² )
{ positive is for the top while the negative is for the bottom position }
A = b²
b = 2√( 16 - x² ) { parallel cross section }
A = [2√( 16 - x² )]²
A = 4( 16 - x² )
Now,
VOLUME = [tex]\int\limits^r -rA dx[/tex]
= [tex]\int\limits^4_4 {-4(16-x^2)} \, dx[/tex]
= 4[ 16x - (x³)/3 ] { from -4 to 4 }
= 4[ ( 64 - 64/3 ) - (-64 = 64/3 0 ]
= 4[ 64 - 64/3 + 64 - 64/3 ]
= 4[ (192 - 64 + 192 - 64 ) / 3 ]
= 4[ 256 / 3 ]
= 1024/3 cubic unit
Therefore, the volume of the solid is 1024/3 cubic unit
If 8 x - 4 = 6 - 3 x then x =
Answer:
x = 10/11
Step-by-step explanation:
Your welcome! :)
Anyone know this? Please help
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
Answer:
C) f(x) = 1500(2.15)x
Step-by-step explanation:
Got it right on Edge :)
Consider the following data. 15,−4,−10,8,14,−10,−2,−11
Step 1 of 3: Determine the mean of the given data
Step 2 of 3: Determine the median of the given data.
Step 3 of 3: Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the mode(s), if any exist.
Answer:
(a) The mean is 0
(b) The median is -30
(c) The mode is unimodal
Step-by-step explanation:
Given
[tex]Data: 15,-4,-10,8,14,-10,-2,-11[/tex]
Solving (a): The mean.
This is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x =\frac{15-4-10+8+14-10-2-11}{8}[/tex]
[tex]\bar x =\frac{0}{8}[/tex]
[tex]\bar x =0[/tex]
Solving (b): The median
First, arrange the data
[tex]Sorted: -11,-10, -10, -4, -2,8,14,15[/tex]
There are 4 elements in the dataset. So, the median is the mean of the 4th and 5th item.
[tex]Median = \frac{-4-2}{2}[/tex]
[tex]Median = \frac{-6}{2}[/tex]
[tex]Median = -3[/tex]
Solving (c): The mode
The item that has occurs most is -10.
Hence, the mode is -10. The dataset is unimodal because it has only 1 mode (-10).
On a coordinate plane, a polygon has points (negative 3, 4), (3, 4), (3, negative 3), (negative 3, negative 2).
What points are the vertices of this polygon? Select all that apply.
(–3, –2)
(–2, –3)
(3, 4)
(–3, 4)
(3, 3)
(3, –3)
Answer:
(-3,-2)
(-3,4)
(3,4)
(3,-3)
Step-by-step explanation:
Answer:
cant see nun mind showing it
A multiple-choice test contains 25 questions, each with 4 answers. Assume a student just guesses on each question. (a) What is the probability that the student answers more than 20 questions correctly
Answer:
9.68*10^-10
Step-by-step explanation:
The problem above can be solved using the binomial probability relation :
Where ;
P(x = x) = nCx * p^x * q^(n-x)
n = number of trials = 25
p = 1/4 = 0.25
q = 1 - p = 0.75
x = 20
P(x > 20) = p(x = 21) + p(x = 22) +.. + p(x = 25)
Using the binomial probability calculator to save computation time :
P(x > 20) = 9.68*10^-10
A study of college football games shows that the number of holding penalties assessed has a mean of penalties per game and a standard deviation of penalties per game. What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be penalties per game or less
Answer:
The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
We have that:
The mean number of penalties per game is [tex]\mu[/tex] and the standard deviation is [tex]\sigma[/tex].
Sample of n games:
This means that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be X penalties per game or less?
The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.
what weight remains when 5/9 of a cake weighing 450 grams is eaten.
Please help me!! i have no clue how to do this unit :(
Answer:
the area is 27
Step-by-step explanation:
Answer:
the base of this shape is 6
lets break it up into a rectangle and a triangle
the rectangle is 6(base) time 3(height)=18
the triangle is 6(base) times 3(height) divided by two = 9
18 plus 9 = 27
Question 6. * The number of likes a social media post has generated has been tracked as a function of the number of min since it was posted. The data is shown in the table below, where t is the number of minutes and I is the number of likes. If an exponential model was used to fit this data, which of the following would be closest to its prediction for the number of likes after one hour
Answer:
Step-by-step explanation:
yes
Which of the following represents the ratio of the given side to the
hypotenuse?
HELP if you’re good at GEOMETRY!!
convert fraction to decimal 1/5 explanation
Answer: 0.2
Step-by-step explanation:
1 divided by 5 = 0.2
Answer:
0.2
Step-by-step explanation:
1/5 = 1 divided by 5.
This will also apply to any fraction
Fraction = Numerator divided by Denominator
Complete the remainder of the table for the given function rule:
Y=3x-5
[X] -6 -3 0 3 6
[Y] -23 ? ? ? ?
answer is
(Y)=-23,-14, -5,4,13
hope this will help you
PLEASE HELP
Libby flips a quarter 2 times in a row.
What is the probability of the quarter landing on heads at least 1 time?
A. 1/4
B. 1/3
C. 3/4
D. 1/2
Five minivans and three trucks are traveling on a 3.0 mile circular track and complete a full lap in 98.0, 108.0, 113.0, 108.0, 102.0, 101.0, 85.0, and 95.0 seconds, respectively. Assuming all vehicles are traveling at constant speeds, what is the time-mean speed of the minivans
Answer:
The time-mean speed of the minivans is of 105.8 seconds.
Step-by-step explanation:
Mean of a data-set:
The mean of a data-set is the sum of all values in the data-set divided by the number of values.
Five minivans, times of: 98.0, 108.0, 113.0, 108.0, 102.0, in seconds.
Thus, the mean is:
[tex]M = \frac{98 + 108 + 113 + 108 + 102}{5} = 105.8[/tex]
The time-mean speed of the minivans is of 105.8 seconds.
3. Find the value of:
a) 9²
b) 15²
c) (0.2)²
d) (0.7)
Answer:
Step-by-step explanation:
9^2
=9*9
=81
15^2
=15*15
=225
(0.2)^2
=0.2 * 0.2
=0.04
(0.7)
=0.7
What is the value of x
Answer:
18°
Step-by-step explanation:
Know that the intersection of two lines and the angles opposite each other are equal
3t+12=66
Subtract 12 from both sides
3t=54
Divide 3 from both sides
t=18
pls help me on this ..
Given : Scale drawing of Angel's rectangular room is 5cm by 7 cm
We know that, Area of a rectangle is given by : Length × Width
⇒ Area of Angel's rectangular room = (5 cm × 7 cm) = 35 cm²
Given : The scale is 1 cm = 4 feet
⇒ Area of Angel's rectangular room in square feet = 35 × (4 feet)²
⇒ Area of Angel's rectangular room in square feet = 35 × 16 feet²
⇒ Area of Angel's rectangular room in square feet = 560 feet²
Which table represents a linear function?
Answer:
Option 3 (C)
Step-by-step explanation:
It is the only one that changes the same amount every time ( times 2 )
Think you can figure out the correct answer here
The answer would be 30 because the triangle is 10, the circle is 5, and each black triangle is 2 which would be 10 plus 5 which is 15 then times 2 which is 30.
Answer:
20?
Step-by-step explanation:
If 3 triangles = 30 they we could assume that each triangle = 10
10 + 10 + 10 = 30
If one triangle = 10 then the 2 circles would = 5 in the 2nd equation
10 + 5 + 5 = 20
If 1 circle = 5 then the 1 full squares would = 4
5 + 4 + 4 = 13
1 triangle = 10 , 1 circle = 5, Half a square = 2
10 + 5 * 2 = ?
Using PEMDAS we would multiply 2 and 5 first to get 10
10 + 10 = 20
Find the surface area of the square pyramid 8mm 6mm
Answer:
136 mm²
Step-by-step explanation:
[tex]A=a^{2} +2a\sqrt{\frac{a^{2} }{4} } +h^{2}[/tex]
[tex]A=6^{2} +2(6)\sqrt{\frac{6^{2} }{4} } +8^{2}[/tex]
[tex]A=36 +12\sqrt{\frac{36 }{4} } +64[/tex]
[tex]A=36 +12\sqrt{9 } +64[/tex]
[tex]A=36 +12(3)+64[/tex]
[tex]A=36 +36+64[/tex]
A = 136
find the mesure of angle b
Answer:
It's C
Step-by-step explanation:
because there is a 90 degrees sigh behind it and those two angles need to add up to 90
Answer:
31
Step-by-step explanation:
b+59=90
b=90-59
b=31
hope it helps
HELP ASAP!!!
(Question and answers pictured)
9514 1404 393
Answer:
(d) reflection about the x-axis, up 6 units
Step-by-step explanation:
The parent function y=1/x is multiplied by -1, which reflects it over the x-axis. Then 6 is added, which shifts it up 6 units.
The transformations are ...
reflection about the x-axis, up 6 units
Determine whether the stochastic matrix P is regular. Then find the steady state matrix X of the Markov chain with matrix of transition probabilities P. P=
0.22 0.20 0.65
0.62 0.60 0.15
0.16 0.20 0.20
Answer:
Step-by-step explanation:
Given that:
[tex]P = \left[\begin{array}{ccc}0.22&0.20&0.65\\0.62&0.60&0.15\\0.16&0.20&0.20\end{array}\right][/tex]
For a steady-state of a given matrix [tex]\bar X[/tex]
[tex]\bar X = \left[\begin{array}{c}a\\b\\c\end{array}\right][/tex]
As a result P[tex]\bar X[/tex] = [tex]\bar X[/tex] and a+b+c must be equal to 1
So, if P[tex]\bar X[/tex] = [tex]\bar X[/tex]
Then;
[tex]P = \left[\begin{array}{ccc}0.22&0.20&0.65\\0.62&0.60&0.15\\0.16&0.20&0.20\end{array}\right]\left[\begin{array}{c}a\\b\\c\end{array}\right] =\left[\begin{array}{c}a\\b\\c\end{array}\right][/tex]
[tex]\implies \left\begin{array}{ccc}0.22a+&0.20b+&0.65c\\0.62a+&0.60b+&0.15c\\0.16a+&0.20b+&0.20c\end{array} \right = \left \begin{array}{c}a ---(1)\\b---(2)\\c---(3)\end{array}\right[/tex]
Equating both equation (1) and (3)
(0.22a+ 0.2b + 0.65c) - (0.16a + 0.2b + 0.2c) = a - c
0.06a + 0.45c = a - c
collect like terms
0.06a - a = -c - 0.45c
-0.94 a = -1.45 c
0.94 a = 1.45 c
[tex]c =\dfrac{ 0.94}{1.45}a[/tex]
[tex]c =\dfrac{ 94}{145}a --- (4)[/tex]
Using equation (2)
0.62a + 0.60b + 0.15c = b
where;
c = 94/145 a
[tex]0.62a + 0.60b + 0.15(\dfrac{94}{145}) a= b[/tex]
[tex]0.62a + 0.15(\dfrac{94}{145}) a= -0.60b+b[/tex]
[tex]0.62a + (\dfrac{141}{1450}) a= 0.40b[/tex]
[tex](0.62+\dfrac{141}{1450}) a= 0.40b[/tex]
[tex](\dfrac{62}{100}+\dfrac{141}{1450}) a= 0.40b[/tex]
[tex](\dfrac{1043}{1450})a= 0.40b[/tex]
[tex](\dfrac{1043}{1450})a= \dfrac{4}{10} b[/tex]
[tex](\dfrac{1043 \times 10}{1450 \times 4})a = \dfrac{4}{10} \times \dfrac{10}{4}[/tex]
[tex]b = (\dfrac{1043}{580}) a --- (5)[/tex]
From a + b + c = 1
[tex]a + \dfrac{1043}{580}a + \dfrac{94}{145} a = 1[/tex]
[tex]a + \dfrac{1043}{580}a + \dfrac{94*4}{145*4} a = 1[/tex]
[tex]a + \dfrac{1043}{580}a + \dfrac{376}{580} a = 1[/tex]
[tex]\dfrac{580+ 1043+376 }{580} a= 1[/tex]
[tex]\dfrac{1999}{580} a= 1[/tex]
[tex]a = \dfrac{580}{1999}[/tex]
∴
[tex]b = \dfrac{1043}{580} \times \dfrac{580}{1999}[/tex]
[tex]b = \dfrac{1043}{1999}[/tex]
[tex]c = \dfrac{94}{145} \times \dfrac{580}{1999}[/tex]
[tex]c= \dfrac{376}{1999}[/tex]
∴
The steady matrix of [tex]\bar X[/tex] is:
[tex]\bar X = \left[\begin{array}{c}\dfrac{580}{1999} \\ \\ \dfrac{1043}{1999}\\ \\ \dfrac{376}{1999}\end{array}\right][/tex]
For f(x) = 3x +1 and g(x) = x - 6, find (f- g)(x).
A. K - 3x-7
B. 3x - 17
c. -x + 3x + 7
D. -x + 3x - 5
SUBND
Answer:
c. -x + 3x + 7 = 2x+7
Step-by-step explanation:
f(x) = 3x +1 and g(x) = x - 6
f-g = 3x +1 - ( x - 6)
Distribute the minus sign
= 3x+1 - x+6
= 2x +7
Graph the image of kite JKLM after a translation 3 units up.
Simplify the following completely, show all work. √-45
Answer:
[tex]3\sqrt{5}i[/tex]
Step-by-step explanation:
[tex]\sqrt{-45}[/tex]
[tex]\sqrt{-9*5}[/tex]
[tex]\sqrt{-9}\sqrt{5}[/tex]
[tex]3i\sqrt{5}[/tex]
[tex]3\sqrt{5}i[/tex]
Hurry which one ITS NOT 270
A.84
C.128
D.540
Answer:
84 cm^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh where b is the length of the base and h is the height
A = 1/2 ( 5+9) * 12
A = 1/2 (14) * 12
A =84
NEED HELP ASAP!!
use the vertical line test to determine if the relation whose graph is provided is a function
(graph and answers pictured)
Answer:
Yes, this graph represents a function
Step-by-step explanation:
The function passes the vertical line test, which tests for if any input has more than one unique output by moving a vertical line from left to right. If the vertical line doesn't pass 2 or more points at a time, then the function is indeed a function.
Answer:
The graph does represent a function
Step-by-step explanation:
The function is at about 30y = x^3
