Answer:
[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]
Step-by-step explanation:
[tex]Volume = Base \ Area\ * Height[/tex]
[tex]Height = \frac{Volume}{Base \ Area}[/tex]
Where [tex]Volume = x^4+4x^3+8x+4[/tex] and [tex]Area = x^3+3x^2+8[/tex]
Putting in the formula
[tex]Height = \frac{x^4 + 4x^3 + 3x^2 + 8x + 4}{x^3 + 3x^2 + 8}[/tex]
Doing long division, we get
[tex]Height = x + \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]
[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]
This is the simplifies form and it can't be further simplified.
Answer:
[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
Step-by-step explanation:
[tex]volume=base \: area \times height[/tex]
[tex]height=\frac{volume}{base \: area}[/tex]
[tex]\mathrm{Solve \: by \: long \: division.}[/tex]
[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]
[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]
[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
What is the product of 3x(x^2+4)?
0 + 3x + 4
3+ 12
31
124
Answer: i honestly dont know this seems very complicated
Step-by-step explanation:
Answer:
3x^3+12x
Step-by-step explanation:
Select all the equations where x=3 is a solution. A. x-3=0 B. 1+ x=2 C. 9-x=3 D. 6=2x E. 15x=3 F. x2=9
Answer:
A. x-3=0 D. 6=2x F. x^2=9
Step-by-step explanation:
Substitute x=3 into each equation
A. x-3=0 3-3 =0 0=0 x=3 is a solution
B. 1+ x=2 1+3 =2 4=2 false
C. 9-x=3 9-3 =3 6=3 false
D. 6=2x 6 = 2*3 6=6 x=3 is a solution
E. 15x=3 15*3 =3 45=3 false
F. x^2=9 3^2 = 9 9=9 x=3 is a solution
Find the value of x in the isosceles triangle shown below.
Answer:
the answer is x = sqrt 48
Step-by-step explanation:
a three dimensional figure with a circular base and a smooth face that diminishes to a single point
Answer:
I believe that the answer is a cone
Step-by-step explanation:
A cone is a three dimensional figure that has a circular base and a smooth face that goes up into a single point.
Please help with this
Answer:
B
Step-by-step explanation:
There are 90 passengers on a commuter flight from SFO to LAX, of whom 27 are traveling on business. In a random sample of five passengers, use the binomial model to find the approximate hypergeometric probability that there is at least one business passenger. A).1681 B).3602 C).8319 D).3087
Answer:
C). 0.83193
Step-by-step explanation:
There are total of 90 passengers of which 27 are for business.
The probability of passengers for business = 27/90
The probability of passengers for business p = 0.3
The probability of passengers not for business q = 1-The probability of passengers for business
= 1-0.3
= 0.7
Random sample of 5 passenger, probability of at least one business passenger = 1 - probability of no business passenger
probability of no business passenger
= 5C0(0.3)^0 * (0.7)^5
= 1 *1*0.16807
= 0.16807
probability of at least one business passenger = 1 - probability of no business passenger
= 1-0.16807
=0.83193
For the piecewise function, find the values g(-2), g(3), and g(4).
X +5, for x<3
g(x)=
6- X, for x>3
9(-2)=
g(3)=
9(4)=
Answer:
g(-2)= -2 + 5 =3 ( here we chose the function g(x)= x+5 as x< 3)
Step-by-step explanation:
g(3)= is not defined ( function is defined for x<3 and x>3 but not x=3)
g(4) = 6-4=2 ( here we chose the function g(x)= 6-x as x> 3)
The equation of the graphed line is 2x – y = –6. A coordinate plane with a line passing through (negative 3, 0) and (0, 6). What is the x-intercept of the graph? –3 –2 2 6
Answer:
-3
Step-by-step explanation:
-3 is the answer
Answer:
-3
Step-by-step explanation:
6th grade math help me, please:D
Answer:
the answer is c...............
The geometric probability function is f (x) = (1-P) x-1 P. what is the approximate probability of rolling a standard die and getting the first 6 on the 3rd try?
Answer:
We know that for a standard dice the probability of obtain a 6 is:
[tex] P=\frac{1}{6}[/tex]
And for this case our value of x=3 and replacing we got:
[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]
[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]
Step-by-step explanation:
For this case we have the following function:
[tex] f(x) = (1-P)^{x-1} P[/tex]
We want to find the approximate probability of rolling a standard die and getting the first 6 on the 3rd try
We know that for a standard dice the probability of obtain a 6 is:
[tex] P=\frac{1}{6}[/tex]
And for this case our value of x=3 and replacing we got:
[tex] f(x=3) = (1- \frac{1}{6})^{3-1} \frac{1}{6}[/tex]
[tex]f(x=3)=\frac{25}{36} \frac{1}{6}= \frac{25}{216}= 0.116[/tex]
Someone please help! Thxx
Answer:
E, needs more info to be determined
Step-by-step explanation:
We know that Kai takes 30 minutes round-trip to get to his school.
One way is uphill and the other is downhill.
He travels twice as fast downhill than uphill.
This means that uphill accounts for 20 minutes of the round-trip and downhill accounts for 10 minutes of his trip.
However, even with this information, we do not know how far his school is.
In order to figure out how far away his school is, we would need more information about the speed at which Kai is traveling.
Simply knowing that he travels twice as fast downhill is not enough.
This question could only be solved by knowing how many miles Kai travels uphill or downhill in a given time.
The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 3 m and w = h = 6 m, and l and w are increasing at a rate of 3 m/s while h is decreasing at a rate of 6 m/s. At that instant find the rates at which the following quantities are changing.
(a) The volume.
m3/s
(b) The surface area.
m2/s
(c) The length of a diagonal. (Round your answer to two decimal places.)
m/s
Answer:
a) The rate of change associated with the volume of the box is 54 cubic meters per second, b) The rate of change associated with the surface area of the box is 18 square meters per second, c) The rate of change of the length of the diagonal is -1 meters per second.
Step-by-step explanation:
a) Given that box is a parallelepiped, the volume of the parallelepiped, measured in cubic meters, is represented by this formula:
[tex]V = w \cdot h \cdot l[/tex]
Where:
[tex]w[/tex] - Width, measured in meters.
[tex]h[/tex] - Height, measured in meters.
[tex]l[/tex] - Length, measured in meters.
The rate of change in the volume of the box, measured in cubic meters per second, is deducted by deriving the volume function in terms of time:
[tex]\dot V = h\cdot l \cdot \dot w + w\cdot l \cdot \dot h + w\cdot h \cdot \dot l[/tex]
Where [tex]\dot w[/tex], [tex]\dot h[/tex] and [tex]\dot l[/tex] are the rates of change related to the width, height and length, measured in meters per second.
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the volume of the box is:
[tex]\dot V = (6\,m)\cdot (3\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot (3\,m)\cdot \left(-6\,\frac{m}{s} \right)+(6\,m)\cdot (6\,m)\cdot \left(3\,\frac{m}{s}\right)[/tex]
[tex]\dot V = 54\,\frac{m^{3}}{s}[/tex]
The rate of change associated with the volume of the box is 54 cubic meters per second.
b) The surface area of the parallelepiped, measured in square meters, is represented by this model:
[tex]A_{s} = 2\cdot (w\cdot l + l\cdot h + w\cdot h)[/tex]
The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time:
[tex]\dot A_{s} = 2\cdot (l+h)\cdot \dot w + 2\cdot (w+h)\cdot \dot l + 2\cdot (w+l)\cdot \dot h[/tex]
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the surface area of the box is:
[tex]\dot A_{s} = 2\cdot (6\,m + 3\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m+6\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m + 3\,m)\cdot \left(-6\,\frac{m}{s} \right)[/tex]
[tex]\dot A_{s} = 18\,\frac{m^{2}}{s}[/tex]
The rate of change associated with the surface area of the box is 18 square meters per second.
c) The length of the diagonal, measured in meters, is represented by the following Pythagorean identity:
[tex]r^{2} = w^{2}+h^{2}+l^{2}[/tex]
The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time before simplification:
[tex]2\cdot r \cdot \dot r = 2\cdot w \cdot \dot w + 2\cdot h \cdot \dot h + 2\cdot l \cdot \dot l[/tex]
[tex]r\cdot \dot r = w\cdot \dot w + h\cdot \dot h + l\cdot \dot l[/tex]
[tex]\dot r = \frac{w\cdot \dot w + h \cdot \dot h + l \cdot \dot l}{\sqrt{w^{2}+h^{2}+l^{2}}}[/tex]
Given that [tex]w = 6\,m[/tex], [tex]h = 6\,m[/tex], [tex]l = 3\,m[/tex], [tex]\dot w =3\,\frac{m}{s}[/tex], [tex]\dot h = -6\,\frac{m}{s}[/tex] and [tex]\dot l = 3\,\frac{m}{s}[/tex], the rate of change in the length of the diagonal of the box is:
[tex]\dot r = \frac{(6\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot \left(-6\,\frac{m}{s} \right)+(3\,m)\cdot \left(3\,\frac{m}{s} \right)}{\sqrt{(6\,m)^{2}+(6\,m)^{2}+(3\,m)^{2}}}[/tex]
[tex]\dot r = -1\,\frac{m}{s}[/tex]
The rate of change of the length of the diagonal is -1 meters per second.
Look at the parallelogram ABCD shown below. The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent. Statement Reasons 1 . AB is parallel to DC and AD is parallel to BC - definition of parallelogram 2 . angle 1 = angle 2, angle 3 = angle 4 - if two parallel lines are cut by a transversal then the corresponding angles are congruent 3 . BD = BD - Reflexive Property 4 . triangles ADB and CBD are congruent - if two sides and the included angle of a triangle are congruent to the corresponding sides and angle of another triangle , then the triangles are congruent by SAS postulate 5 . AB = DC, AD = BC - corresponding parts of congruent triangles are congruent Which statement is true about the table? 1. It is not correct because it provides incorrect sequence of statement 2 and statement 4. 2. It is not correct because it does not provide correct reasons for statement 2 and statement 4. 3. It is accurate because it provides the correct sequence of statements. 4. It is accurate because it provides the correct reasons for the statements.
Answer:
Can you add the image so i can anwser?
Step-by-step explanation:
Find the intervals of convergence of f(x), f '(x), f ''(x), and ∫f(x) dx. (Be sure to include a check for convergence at the endpoints of the intervals. Enter your answer using interval notation.) f(x) = [infinity] (−1)n + 1(x − 8)n n8n n = 1
Answer: See solution and explanations in the attached documents
Step-by-step explanation:
See explanations in the attached documents
Two friends are playing tic-tac-toe. If Amy wins 3/8 of the time, Lily wins 3/10 of the time, and they tie the rest of the time, then what fraction of the time do they tie?
Answer:
13/40
Step-by-step explanation:
The period they have played can be divided into 3 parts:
● The time Amy wins
● The time Lily wins
● The time they tie
So the sum of them is the total time of playing.
Let A be the time Amy wins, L the tile Lily wins and T the time they tie .
●●●●●●●●●●●●●●●●●●●●●●●
Since we have expressed the times using fractions then the total period of playing is 1 wich is 100%.
So:
A + P + T = 1
3/8 + 3/10 + T = 1
Multiply 8 by 10 and 10 by 8 so that you get a common denominator.
Cross multiply the numerators and the denominators.
(3*10+3*8)/80 + T = 1
(30 + 24)/80 + T =1
54/80 + T = 1
(27*2)/(40*2) + T = 1
Simplify by 2
27/40 + T = 1
T = 1 - 27/40
Multiply one by 40 to get a common denominator
T = (40-27)/40
T = 13/40
So they have tied 13/40 of the time
Need help with this math problem
Answer:
4
Step-by-step explanation:
f(x) = 4 ^ ( x-2)
Let x=3
f(3) = 4 ^ ( 3-2)
= 4 ^ 1
= 4
Answer:
4
Step-by-step explanation:
4^(x - 2)
Plug x as 3.
4^(3 - 2)
Subtract.
4^(1)
4^1 = 4
which graph represents a function? Please help!
Answer:
The last graph (to the far right).
Step-by-step explanation:
As long as each x-value has one y-value, it is a function. However, the last graph has an x-value at -1 where there are two y-values. So, it does not pass the Vertical Line Test, and it is a relation rather than a function.
Hope this helps!
A movie theater has a seating capacity of 235. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1704, How many children, students, and adults attended?
Hey there! :)
Answer:
118 children
58 students
59 adults
Step-by-step explanation:
We can solve this problem by setting up a system of equations:
Let a = adults
2a = children (since double the # of adults were children), and
s = students
Set up the equations:
1704 = 5(2a) + 7s + 12(a)
1704 = 10a + 7s + 12a
235 = 2a + a + s
Simplify the equations:
1704 = 22a + 7s
235 = 3a + s
Subtract the bottom equation from the top by multiplying the bottom equation by 7 to eliminate the 's' variable:
1704 = 22a + 7s
7(235 = 3a + s)
1704 = 22a + 7s
1645 = 21a + 7s
---------------------- (Subtract)
59 = a
This is the number of adults. Substitute this number into an equation to solve for the number of students:
235 = 3(59) + s
235 = 177 + s
s = 58.
Since the number of children is equivalent to 2a, solve:
2(59) = 118 children.
Therefore, the values for each group are:
118 children
59 adults
58 students.
Answer:
adults: 59, students:58 and children 118
Step-by-step explanation:
let A for adults, and C = children and S for students
There are half as many adults as there are children=
A=C/2 , C=2A
A+C+S=235 or
A+2A+S=235 first equation
3A+S=235
12A+5C+7S =1704 or
12A+10A+7S=1704
22A + 7S=1704 second equation
3A+S=235 first
solve by addition and elimination
22A+7S=1704
21 A+7S=1645 subtract two equations
A=59 adults
C=2A=2(59)=118
substitute in :A+S+C=235
S=235-(118+59)=58
check: 5C+7S+12A=1704
5(118)+7(58)+12(59)=1704
Betty has $33 to buy plants for her greenhouse. Each plant costs $8. How
many plants can she buy? Do not include units in your answer.
Answer:
4 plants
Step-by-step explanation:
If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4
(8 * 4 is 32)
She will have one dollar left but she can't buy another plant since that's not enough.
Answer:
4 plants
Step-by-step explanation:
Take the amount of money she has and divide by the cost per plant
33/8
The amount is 4 with 1 dollar left over
4 plants
if the probability of drawing a red card from a box is 3/8, what are the odds against drawing a red card from the box
Answer: 5/8
Step-by-step explanation:
Simply do 8/8(1)-3/8 to get 5/8
Hope it helps <3
what is this? 15.8 = d/25
Answer:
395
Step-by-step explanation:
15.8=d/25
multiply both sides by 25 to remove the denominator
25×15.8=d
d=395
Solve of the following equations for x: 3x = 5
Answer: 1.7
Step-by-step explanation:
5 divided by 3=1.666666667
1.6 and next 6 in line is over 5 so the 6 turns to a 7
3*1.7= 5.1 but when rounded 1 tells 5 to stay down so it = 5
Which group of plants were the first to adapt to life on land? flowering pine mosses conifers
Answer:
mosses
Step-by-step explanation:
use socratic
Mosses are also known as the amphibian of the plant kingdom. The mosses were the first plant that can even survive on the land.
Bryophytes:It is the group of small plants that complete its life cycle in both land and water. They were the first plants to adapt to live on the land.For example- mosses.Conifers, pines, and flowering plants developed much later after the evolution of bryophytes.
Therefore, the mosses were the first plant that can even survive on the land.
Learn more about Bryophytes:
https://brainly.com/question/841138
One bag of dog food has 13kg. Vet order dog to eat 683 grams a day. How many bags of dog for will you need to buy for 1yr.
Answer:
20 bags
Step-by-step explanation:
683✖️19=12977
683✖️365=249295
249295/13000=19.17
--> 20 bags
the product of 12 and K is 84 solve for K K =
Answer: k = 7
Step-by-step explanation:
12k=84
Divide(12)
k=7
Hope it helps <3
Answer:
7Step-by-step explanation:
The product of 12 and k is 84
let's create an equation:
[tex]12k = 84[/tex]
Divide both sides of the equation by 12
[tex] \frac{12 \: k}{12} = \frac{84}{12} [/tex]
Calculate
[tex]k = 7[/tex]
Hope this helps...
Best regards!!
A P E X!!!! URGENT :The annual interest rate of Belinda's savings account is 8.6% and simple interest is calculated quarterly. What is the periodic interest rate of Belinda's account?
Answer:
The answer is 2.15%
Step-by-step explanatio
In which table does y vary inversely with x? A. x y 1 3 2 9 3 27 B. x y 1 -5 2 5 3 15 C. x y 1 18 2 9 3 6 D. x y 1 4 2 8 3 12
Answer:
In Table C, y vary inversely with x.
1×18 = 18
2×9 = 18
3×6 = 18
18 = 18 = 18
Step-by-step explanation:
We are given four tables and asked to find out in which table y vary inversely with x.
We know that an inverse relation has a form given by
y = k/x
xy = k
where k must be a constant
Table A:
x | y
1 | 3
2 | 9
3 | 27
1×3 = 3
2×9 = 18
3×27 = 81
3 ≠ 18 ≠ 81
Hence y does not vary inversely with x.
Table B:
x | y
1 | -5
2 | 5
3 | 15
1×-5 = -5
2×5 = 10
3×15 = 45
-5 ≠ 10 ≠ 45
Hence y does not vary inversely with x.
Table C:
x | y
1 | 18
2 | 9
3 | 6
1×18 = 18
2×9 = 18
3×6 = 18
18 = 18 = 18
Hence y vary inversely with x.
Table D:
x | y
1 | 4
2 | 8
3 | 12
1×4 = 4
2×8 = 16
3×12 = 36
4 ≠ 16 ≠ 36
Hence y does not vary inversely with x.
You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friend walks 205 yards due west from your position and takes a bearing on the cabin of N 23.9°E. How far are you from the cabin? asap would be great also running out of points srry
Answer:
462.61 yards.
Step-by-step explanation:
To solve, you need to find the measurement of the angle that forms a 90 degree angle with the 23.9 degree angle.
90 - 23.9 = 66.1 degrees.
Now that you have the angle, you can use TOA to solve for x (TOA = Tangent; Opposite over Adjacent).
tan(66.1) = x / 205
x / 205 = tan(66.1)
x = tan(66.1) * 205
x = 2.256628263 * 205
x = 462.6087939
So, you are about 462.61 yards from the cabin.
Hope this helps!
x+15=6 What does x equal?
Answer:
x=-9
Step-by-step explanation:
6-15=-9
Answer:
-9
Step-by-step explanation:
When you add some thing to a negative that means you are actually subtract that number
i need these THREE questions ANSWERED please!!!! please i really need these done!!!
Step-by-step explanation:
8. As the name implies, a box-and-whisker plot looks like a box with two whiskers. The box is the middle 50%. The whiskers are the bottom 25% and the top 25%.
First, we need to sort the numbers from smallest to largest. Starting with Set A:
Set A = {56, 57, 62, 68, 71, 82, 84, 92, 97, 101, 103, 106}
Now we find the median of the set, or the middle number. Set A has 12 data points. Since 12 is an even number, the median will be the average of the 6th and 7th numbers.
M = (82 + 84) / 2 = 83
Next, we find the median of the lower half. There are 6 numbers in the lower half, so the median is the average of the 3rd and 4th numbers.
Ml = (62 + 68) / 2 = 65
Now we find the median of the upper half. Again, there are 6 numbers in the upper half, so the median will be the average of the 3rd and 4th numbers.
Mu = (97 + 101) / 2 = 99
So the left whisker is from 56 to 65.
The box is from 65 to 99.
The right whisker is from 99 to 106.
Don't forget to mark the median, 83.
Repeat for Set B.
Set B = {36, 37, 42, 46, 48, 56, 58, 63, 69, 72, 75, 78}
M = (56 + 58) / 2 = 57
Ml = (42 + 46) / 2 = 44
Mu = (69 + 72) / 2 = 70.5
So the left whisker is from 36 to 44.
The box is from 44 to 70.5.
The right whisker is from 70.5 to 78.
The median is 57.
By graphing both on the same number line, we can easily compare them.
9. To make a dot plot, draw a number line starting from the smallest number and ending at the largest number. For each number, draw a dot every time the number appears in the set. For example, the number 3 appears twice in Set A, so draw two dots on 3. You may find it helpful to sort the data first.
10. Draw a dot plot of the set to determine the shape.