Answer:
[tex]\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}[/tex]
Step-by-step explanation:
Given that:
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz[/tex]
where;
the top vertex = (0,0,1) and the base vertices at (0, 0, 0), (1, 0, 0), (0, 1, 0), and (1, 1, 0)
As such , the region of the bounds of the pyramid is: (0 ≤ x ≤ 1-z, 0 ≤ y ≤ 1-z, 0 ≤ z ≤ 1)
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 \int ^{1-z}_0 (x^2+y^2) \ dx \ dy \ dz[/tex]
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 ( \dfrac{(1-z)^3}{3}+ (1-z)y^2) dy \ dz[/tex]
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \ dz \ ( \dfrac{(1-z)^3}{3} \ y + \dfrac {(1-z)y^3)}{3}] ^{1-x}_{0}[/tex]
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \ dz \ ( \dfrac{(1-z)^4}{3}+ \dfrac{(1-z)^4}{3}) \ dz[/tex]
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz =\dfrac{2}{3} \int^1_0 (1-z)^4 \ dz[/tex]
[tex]\iiint_W (x^2+y^2) \ dx \ dy \ dz =- \dfrac{2}{15}(1-z)^5|^1_0[/tex]
[tex]\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}[/tex]
www.g Suppose that 59% of people own dogs. If you pick two people at random, what is the probability that they both own a dog
Answer:
The value is [tex]P(O) = 0.3481[/tex]
Step-by-step explanation:
From the question we are told that
The proportion of people that own a dog is [tex]p = 0.59[/tex]
The number of people selected is n = 2
Generally the probability that the people selected owns a dog is mathematically represented as
[tex]P(O) = p^n[/tex]
=> [tex]P(O) = 0.59^2[/tex]
=> [tex]P(O) = 0.3481[/tex]
in 2016 the average Raleigh driver spent 18 hours in traffic jams, which accounted for 6% of their total driving time. How many hours did the average Raleigh driver spend behind the wheel in 2016
Answer: 300 hrs
The time spent behind the wheel by the average Raleigh driver in 2016 is 300 hrs
Step-by-step explanation:
Given that;
Raleigh driver spent 18 hours in traffic jams
And it accounts for 6% of their total driving time
Now
let total driving time be = x hrs
so
6% of total driving time = 18 hrs
6/100 × x = 18hrs
6x = 1800 hrs
x = 1800/6
x = 300 hrs
∴ The time spent behind the wheel by the average Raleigh driver in 2016 is 300 hrs
Use the table below to answer the following questions. a. Plot the points (x,y) in this table on a graph (except when x is 5)
Answer:no answers sorry
Step-by-step explanation:
No answers sorry
An executive invests 29,000, some at 8% and the rest at 7% annual interest. If he receives an annual return of $2,230, how much is invested at each rate?
Answer:
Amount invested in A (8%) = $20,000
Amount invested in B (7%) = $9,000
Step-by-step explanation:
Given:
Total amount invested = $29,000
Interest rate A = 8% = 0.08
Interest rate B = 7% = 0.07
Annual return = $2,230
Find:
Amount invested in each
Computation:
Assume;
Amount invested in A = x
Amount invested in B = 29,000 - x
So,
Interest receive from A = x × 0.08
Interest receive from A = 0.08 x
Interest receive from B = (29000 - x) × 0.07
Interest receive from B = 2,030 - 0.07 x
Annual return = Interest receive from A + Interest receive from B
2,230 = 0.08 x + 2,030 - 0.07 x
x = 20,000
Amount invested in A = $20,000
Amount invested in B = 29,000 - $20,000
Amount invested in B = $9,000
Matt is tiling his house and he needs to find out what are the largest square tiles that he could use to
tile an area 105 cm by 280 cm?
Answer:
the largest square tile is 35cmx35 cm
Step-by-step explanation:
1. Factorize 105 = 5*7*3=35*3
Factorize 280=10*7*4=2*5*7*4=35*8
The common factor is 35.
So Matt can tile 3 tiles 35x35 along the side 105 and 8 tiles along the side 280.
Total 24 pieces 35x35 are necessary to tile the area 105x 280 cm
( However the question is only about the largest tile that Matt could use and not about the quantity of the tiles)
one number is 7 more than twice the other number. if the sum of the two numbers is 19, find the two numbers
Answer:
4 and 15
Step-by-step explanation:
Let the two numbers be a and b.
The sum of the two is 19. Therefore:
[tex]a+b=19[/tex]
One number (let's use a) is 7 more than twice the other. Thus:
[tex]a=7+2b[/tex]
Solve for the system of equations. Substitute the second equation into the first:
[tex]a+b=19\\(7+2b)+b=19[/tex]
Subtract 7 from both sides:
[tex]2b+b=12[/tex]
Combine like terms:
[tex]3b=12[/tex]
Divide by 3:
[tex]b=4[/tex]
So, b is 4.
And since they add up to 19, this means that a is:
[tex]a+b=19\\a+4=19\\a=15[/tex]
So our numbers are 4 and 15
And we are done :)
Answer:
the equation is: 2x+7+x=43
the 2 numbers are: 12 and 31.
ayyyyyyyyyyyyyyyyyyyyyyyyyyyyyy please help me
The school paper charges $1.50 for an ad, plus 25 cents per word. Carl wants to spend only $12.00 on the ad.
What is the maximum number of words that can be in his ad?
Answer:
42 words
Step-by-step explanation:
To solve just solve 0.25x +1.50 = 12.00 for x
Composition of the functions is
____ commutative.
Answer:
Composition of functions is sometimes commutative.
Step-by-step explanation:
Composition of the functions is sometimes commutative.
Under certain circumstances, they can be commutative. However, this is not guaranteed.
Consider, for example, the functions:
[tex]\displaystyle f(x) = x^2 \text{ and } g(x) = x^3[/tex]
Composition of the two functions yields:
[tex]f(g(x))=(x^3)^2=x^6 \\ \\ \text{ and} \\ \\ g(f(x))=(x^2)^3=x^6[/tex]
In this case, the composition is commutative.
Composition of functions is sometimes commutative.
Commutativity refers to the ability to change the order of operations without affecting the result. In terms of functions, it means that the order in which you perform the composition matters.
For example, if we have two functions, f(x) and g(x), the composition of f(g(x)) is not necessarily equal to g(f(x)). In other words, the result of applying one function followed by another is generally different from the result of applying them in the opposite order.
This lack of commutativity is due to the fact that the output of one function becomes the input of the other.
Thus, Composition of functions is sometimes commutative.
Learn more about Commutative Property here:
https://brainly.com/question/28762453
#SPJ6
Reese loves to drink healthy green smoothies a 16 oz serving of smoothie has 170 calories how many calories are in a 24 oz smoothie
Answer:
255
Step-by-step explanation:
170/16 = 10.625
10.625 x 24 = 255
Gasoline at a particular gas station costs $2.78 per gallon. If Cory buys $18 of gas, how many gallons did he buy?
Answer:
Cory bought 6.474 gallons of gasolline.
Step-by-step explanation:
The total cost of gasoline ([tex]C[/tex]), measured in dollars, is given by the following expression:
[tex]C = n\cdot c[/tex]
Where:
[tex]n[/tex] - Amount of gasoline, measured in gallons.
[tex]c[/tex] - Unit cost, measured in dollars per gallon.
Given that [tex]C = \$\,18[/tex] and [tex]c = \$\,2.78\,\frac{1}{gal}[/tex], the amount of gasoline is cleared and calculated:
[tex]n = \frac{C}{c}[/tex]
[tex]n = \frac{\$\,18}{\$\,2.78\,\frac{1}{gal} }[/tex]
[tex]n = 6.474\,gal[/tex]
Cory bought 6.474 gallons of gasolline.
find pb, if pj=14 and jb= 28
Answer:
42
Step-by-step explanation:
Based on the information given, point j is the midpoint, as it is shared by both line segments. Set the equation:
pb = pj + jb
Note:
pj = 14
jb = 28
Plug in the corresponding numbers to the corresponding variables:
pb = pj + jb
pb = 14 + 28
pb = 42
pb = 42 is your answer.
~
pj=14
jb=28
p=14/j
b=28/j
pb=(14/j)×28/j
pb=392/j²
j²=9.333≅
pb=392/9.333
pb=42.0015≅42
Luis is 4 years older than Colleen. In 4 years the sum of their ages will be 52. How old is Luis now?
Answer:
x: Colleen
Luis: x+4
x+x+4=52
2x+4=52
2x=48
x=24: Colleen
x+4=28 Luis
Find the distance between the two points in simplest radical form.
(3,7) and (9,9)
Answer:
The answer is
[tex]2 \sqrt{10} \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(3,7) and (9,9)
The distance between them is
[tex]d = \sqrt{ ({3 - 9})^{2} + ({7 - 9})^{2} } \\ = \sqrt{ ({ - 6})^{2} + ({ - 2})^{2} } \\ = \sqrt{36 + 4} \\ = \sqrt{40} [/tex]We have the final answer as
[tex]2 \sqrt{10} \: \: units[/tex]Hope this helps you
The least expensive type life insurance is ______
Answer:
Whole life policies
Step-by-step explanation:
Whole life policies are the least expensive way to meet your life insurance needs. The advantages of whole life insurance policies are that they provide long-term coverage, the rates are fixed, and they have a savings or cash value feature.
2/9 * 5/6
Multiply. Write the answer as a fraction in simplest form.
Answer:
5 / 27
Step-by-step explanation:
How did Sam’s fixed mindset prevent him from succeeding when the material got harder?
Answer: he gave up so he wasn’t able to do it
Step-by-step explanation:
PLSSS HELP MARKING BRAINLIST PLSSSS GUYS NO ONE IS GOING TO HELP ME?
Answer:
top
question 1 is 25
question 2 is 0.2
------------------------------
bottom
question 3 is the second graph
the last question is the first graph
Step-by-step explanation:
A rectangular flower bed has a length of 1/2 yard. The width of the flower bed is 3/4 yard. What is the area of the flower bed?
Answer:
The answer is 4 whole 2 by 3 (4 2/3).
Step-by-step explanation:
(3/4) x = 3 1/2
3 x / 4 = 7/2
3 x = 14
x = 14/3 = 4 2/3.
The sum of three consecutive integers is 162 . What are the integers?
Answer:
53 54 55
Step-by-step explanation:
Consecutive Integers are integers that go one after the other unless explained otherwise, so 53, 54 and 55 add up to 162.
ANSWER
X=52
x+2=54
x+4=56
these are the three consecutive integers
Evaluate the expression for x = 5 and y = 3.
3x – 4y2
A. 9
B. 27
C. 39
D. 81
Find all zeros of ƒ(x)=x4–22x3+121x2.Then determine the multiplicity at each zero. State whether the graph will touch or cross the x-axis at the zero.
Answer:
0, 11, both multiplicity 2touch, not cross, at each 0Step-by-step explanation:
The function factors as ...
f(x) = x^4 -22x^3 +121x^2
f(x) = x^2(x^2 -22x +121)
f(x) = x^2(x -11)^2
The zeros are x=0 and x=11, each of multiplicity 2.
Because the multiplicity is even, the graph will touch at each zero, not cross.
Given a standard day, at what altitude is the true airspeed of an aircraft approximately twice of what the airspeed indicator reads
Answer:
40000ftMSL
Step-by-step explanation:
We know that airspeed is measured using a pilot tube
And the air pressure is a function of density given as
Pressure= 1/2 xdensityx V²
So at 40,000ftMSL
Is this is replaced for V in the equation then the density of air will be 1/4 that of sea level
So since we are deriving velocity from pressure and pressure is 1/4 so the velocity Will be half of its pressure since velocity is squared from The equation above
You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You also know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?
ŷ = 26 + 7.8x
ŷ = 7.8 + 26x
ŷ = -502 + 0.078x
ŷ = 0.078 - 502x
What are the greatest and the least
6-digit numbers that have a 9 in the hundreds place and 3 fewer
hundred thousands than hundreds?
Answer:
Greatest = 699,999
Least = 600,900
Step-by-step explanation:
6 digit numbers
9 in the Hundred place
3 fewer hundred thousands than hundred
9 - 3 = 6
Hundred thousand = 600,000
Hence, greatest 6 digit number
Hth__TTh__Th__H__T__U
6____9____9___9__9__9
600,000 + 90,000 + 9,000 + 900 + 90 + 9
= 699,999
Hence, least 6 digit number
Hth__TTh__Th__H__T__U
6____0____0___9__0__0
600,000 + 00000 + 0000 + 900 + 00 + 0
= 600,900
Two partners are starting a wedding planning business. The total investment is $45,000. Their investments are in the ratio 4:5. How much does each
investor contribute?
$20,000 and $25.000
$5,000 and $40.000
$15,000 and $30.000
$10,000 and $35.000
Answer:
Hey there!
Think of 45000 being split to 9 pieces.
Each piece would be 5000 dollars.
Thus, the ratio would be 20000 to 25000
Hope this helps :)
One partner will bring $20,000 and the other will bring $25,000.
The total investment is $45,000 and they will contribute by the ratio, 4:5.
First add up the ratio as this will form the denominator:
= 4 + 5
= 9
The amount that the first partner will pay is:
= Proportion / 9 x Total investment
= 4 / 9 x 45,000
= $20,000
The other partner will bring:
= 5 / 9 x 45,000
= $25,000
The partners will therefore bring $20,000 and $45,000
Find out more at https://brainly.com/question/23766289.
PLEASE HELP!
2x+2y = 5
3x + 3y = 7
How many solutions does the system of equations above have?
Answer: no solution or zero solutions.
Step-by-step explanation:
Given System of equations
2x+2y = 5
3x + 3y = 7
have No solution
Given :
2x+2y = 5
3x + 3y = 7
We write the given equation in y=mx+b form and then we compare the slope 'm'
Solve each equation for y
[tex]2x+2y=5\\2y=-2x+5\\Divide \; by 2\\y=-1x+\frac{5}{2}[/tex]
Slope of first equation is -1
[tex]3x+3y=7\\3y=-3x+7\\Divide \; by \; 3\\y=-1x+\frac{7}{3}[/tex]
Slope of second equation is -1
Slope of both the equations are equal . So the lines are parallel to each other.
Hence , No solution
Learn more : brainly.com/question/17705616
On a number line suppose point E has a coordinate of 1, and EG=11 What are the possible coordinates of G?
Answer:
- 10 and 12
Step-by-step explanation:
On a typical number line, we have basically two directions that we can move on. Either to the left where the numbers are negative, of to the right where the numbers are positive.
Given that point E has a coordinate of 1 on a number line, and we are told that the distance between E and another point on the number line is 11 (EG), the possible coordinates of point G are two (either we are moving to the right or to the left). Therefore, possible coordinates of G are:
1 - 11 = -10 (to the left)
1 + 11 = 12 (to the right)
find the difference of 5.95 and 4.7
Answer:
1.25 is your answer.
what does x=?........................
Answer:
x = -25 / 3
Step-by-step explanation:
10 / 3 = x / (-5/2)
10 / 3 * (-5 / 2) = x
x = -50 / 6
x = -25 / 3
Answer:
[tex]x=\frac{-25}{3}[/tex]
Step-by-step explanation:
[tex]\frac{10}{3}=\frac{x}{\frac{-5}{2} } \\\\\frac{-5}{2}*\frac{10}{3}=\frac{x}{\frac{-5}{2} }*\frac{-5}{2} \\\\\frac{-25}{3} =x\\\\x=\frac{-25}{3}[/tex]