Add 10% of 300 to 50% of 20
Answer:
40
Step-by-step explanation:
10% of 300 = 300/10 = 30
50% of 20 = 20/2 = 10
30+10=40
Evaluate the triple integral.
E
y dV, where E = {(x, y, z) | 0 ≤ x ≤ 6, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y}
The definition of the set E gives you a natural choice for the limits in the integral:
[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x \int_{x-y}^{x+y} y \, dz \, dy \, dx[/tex]
Computing the integral, we get
[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x y ((x+y)-(x-y)) \, dy \, dx = 2 \int_0^6 \int_0^x y^2 \, dy \, dx[/tex]
[tex]\displaystyle \iiint_E y \, dV = 2 \int_0^6 \frac13 (x^3 - 0^3) \, dx = \frac23 \int_0^6 x^3 \, dx[/tex]
[tex]\displaystyle \iiint_E y \, dV = \frac23 \cdot \frac14 (6^4 - 0^4) = \boxed{216}[/tex]
The evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216
What is triple integral?Triple integral integrates the integrand over three dimensions.
Given that:
E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y}
Evaluating the integral:
[tex]I = \int \int \int _E y \: dV[/tex]
[tex]I = \mathlarger{\int_0^6 (\int_0^x (\int_{x-y}^{x+y} y\: dz)dy)dx}\\\\I = \int_0^6 (\int_0^x [yz]_{z=(x-y)}^{z=(x+y)}dy)dx\\\\I = \int_0^6 (\int_0^x y( (x+y) - (x-y)) \: dy)dx\\\\ I = \int_0^6 (\int_0^x y(2y) \: dy)dx\\\\I =2 \int_0^6 \left [\dfrac{y^3}{3}\right ]_{y=0}^{y=x} dx\\\\I = 2 \int_0^6 (x^3/3) dx\\\\I = \dfrac{2}{3} \left[\dfrac{x^4}{4} \right]_{x=0}^{x=6} = \dfrac{2}{3} \times \dfrac{6^4}{4} =216[/tex]
Thus, the evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216
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Please I need help fast
Answer:
55
Step-by-step explanation:
Combine both bases (15+7 = 22)
Divide by 2 (22/2 = 11)
Multiply by height (11 x 5 = 55)
lin ran 4 laps around the track in 5 minutes, if lin ran 21 laps, how long does it take her
Answer:
26 1/4 minutes or 1635 seconds
Step-by-step explanation:
Lin runs 4 laps in 5 minutes. You must turn this into a unit rate. In order to do this, you divide 4 laps by 4 to get 1 lap. To get the equivalent, you also have to divide 5 minutes (300 seconds) by 4. This will get you one lap for every 75 seconds. Because Lin ran 21 laps, see how many times 4 can go into 20 using a remainder if necessary. 4 can go into 21 5 times with a remainder of 1. 4*5=20 5*5=25. Now you add 75 seconds because you have an extra lap.
Help help help help help help
Answer:
Step-by-step explanation:
A' = (-1 + 4, 2 + 6) = (3, 8)
B' = (-2 + 4, -3 + 6) = (2, 3)
A' = (-5 + 4, -1 + 6) = (-1, 5)
A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained the wishes the estimate to be within three percentage points
with 90% confidence, assuming that
(a) he uses the estimates of 21.3% male and 19.5% female from a previous year?
(b) he does not use any prior estimates?
(a)n (Round up to the nearest whole number)
(b) (Round up to the nearest whole number.)
Using the z-distribution and the formula for the margin of error, it is found that:
a) A sample size of 54 is needed.
b) A sample size of 752 is needed.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
Item a:
The estimate is [tex]\pi = 0.213 - 0.195 = 0.018[/tex].
The sample size is n for which M = 0.03, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.018(0.982)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.018(0.982)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.018(0.982)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.018(0.982)}}{0.03}\right)^2[/tex]
[tex]n = 53.1[/tex]
Rounding up, a sample size of 54 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.05[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
[tex]n = 751.7[/tex]
Rounding up, a sample of 752 should be taken.
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The temperature at the North Pole averages -36࿁F. This past winter, the temperature averaged -47࿁F. Write a correct statement that compares the absolute values of the two temperatures
Comparing the temperature average, it can be concluded that the current average temperature is higher than the past average by 11°F
The temperature difference between the present and past winter can be expressed thus :
Current temperature average = - 36°F Past average = - 47°FTemperature difference :
-36 - (-47) = 11°FTherefore, we can conclude that the current average temperature is higher than the past average by 11°F
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show your solution and answer the 4 questions.
Answer:
Step-by-step explanation:
1. When the number of kilograms of paper is doubled, the points will be doubled
2. 300÷ 5 = 60
They have to collect 60 Kg of papers to earn 300 points.
3) P = 5*n
P = 5n
4) We are not only reducing the waste, the collected paper can be reused or can be sent to recycling centers.
please answer fully ?/'//////////////////////
Answer:
17.5
Step-by-step explanation:
i solved it and got that answer. hope this helps =)
I need some help it is to early for my brain to work
Answer:
5 minimum 32 maximum
Step-by-step explanation:
f(x)=ax^2 +bx +c solve: heigh 275 width 290
Answer:
800 i think
Step-by-step explanation:
OMG HELP RN
Sarah climbed 3,600 feet of the way up Pikes Peak and then stopped to rest. After she stops, she continues to climb at a rate of 85 feet per hour for h hours. Which expression indicates her elevation, in feet, h hours after she stops?
A.
3,600 ÷ 85 × h
B.
3,600 + 85 × h
C.
(3,600 + 85) ÷ h
D.
3,600 - 85 × h
Answer: the answer is d hope this helps if not i'm sorry
Find the value of x and y.
(In picture)
Answer:
x is 4, and y is 3
Step-by-step explanation:
Three times eight M equals fourteen. Which of the following equations represents this statement?
Answer:
3x8m= 14 is the equation that matches the description.
Step-by-step explanation:
It is simply the number three, multiplied by eight with the variable m, and is equal to the number 14.
Find the slope of the line that contains the following pair of points:
(4,-5) and (-1, -3).
Step-by-step explanation:
slope is y2-y1/x2-x1
-3-4=-7
-1-4=-5
now that you have -7/-5, or negative seven fifths, simplify.
you get -0.4, or -2/5 as your slope
Hope this helps!!
WILL GIVE 100PTS
Find the slope of a line that passes through (-2, -3) and (1, 1).
A. 1 /3
B. 1
C. 2
D. 4/3
Answer:
D
Step-by-step explanation:
Y2-Y1/x2-x-1
Answer:
D
Step-by-step explanation:
Formula for slope is (y2-y1)/(x2-x1).
(1-(-3))/(1-(-2)) = 4/3
These tables of ordered pairs represent some points on the graphs of lines s and t.
Which system of equations is represented by lines s and t?
5x−2y=−157x+4y=20
3x+5y=−185x−9y=25
x+4y=−89x−y=21
2x−y=−142x+y=6
The equation of line S is y = 2x + 14 while that of line T is y = -2x + 6.
A linear equation is in the form:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept.
For line s, using the points: (-5, 4) and (4, 22). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-4=\frac{22-4}{4-(-5)} (x-(-5))\\\\y-4=2(x+5)\\\\ y=2x+14[/tex]
Line T passes through the points (-4, 14) and (5, -4). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-14=\frac{-4-14}{5-(-4)} (x-(-4))\\\\y-14=-2(x+4)\\\\ y=-2x+6[/tex]
Hence the equation of line S is y = 2x + 14 while that of line T is y = -2x + 6.
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Helpppppppppppppppppppppppppppp
Answer:
look at the photo...............Micah earns 2 points for every 3 questions he answers correctly on a test. If he answered 24 questions correctly, how many points did he earn?
Answer:
16 points.
Step-by-step explanation:
24*2/3 = 16.
Hope this helped!
*Sorry if I'm wrong, though I think I'm correct.*
Enjoy the rest of your day.
Answer:16
Step-by-step explanation: 24 divided by 3 because it is for every 3 questions. You get 8. He gets 2 points for every 3 questions so 8 times 2 is 16.
please help me
what is
28a+84b+92c=
If you see this can you answer this question.
Answer:
The last one
Step-by-step explanation:
-4 1/3 is less than -1 3/4 because its farther on the negative side and -1 3/4 is closer to the positive side
If an item that originally cost $20 is increased to $27, what is the percentage of increase in the item?
PLS HELP ASAP IM TAKING AN RXAM!!! 40 POINTS!!!!!!
Using data from the Internet, we've compiled a list of Presidents of the United States through 2012 to show party affiliations and ages during office. You completed a frequency table and bar graph using this data. The bar graph is shown below. Describe what you can say about this bar graph given the data and the graph.
The given bar graph shows the number of years that each president served in office, and the presidents of the United States are represented by the width of the bar graph.
What is a bar graph?A bar graph is one way of representing data, The height of the bar graph represents relative frequencies and the width of the bar graph represents
it's class width or an interval.
The height given bar graph represents no. of years each president lasted
and the width of the bar graph represents the Presidents of the United States.
R-Republican lasted the most no.of years which is 18 years and U-Union lasted the least no of years which is one.
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Evaluate. (w^2/x -3) ÷10 × z when w= -4, x = 0.8, and z = -4/5 Enter your answer as a simplified mixed number in the box.
Answer:
-1.36
Step-by-step explanation:
(-4^2/0.8-3)/10×-4/5=-1.36
Help me with this pls
Answer:
Step-by-step explanation:
geomtry plz help me 15 pointz
Answer:
m∠R=76°
Step-by-step explanation:
∠STR=∠RST=(2x+2)° (base angles of isos triangle)
2(2x+2)+(3x+1)=180 (angle sum of triangle)
4x+4+3x+1=180
7x+5=180
7x=180-5
=175
x=175÷7
=25
Hence, m∠R = (3x+1)°
= [3(25)+1]°
= (75+1)°
= 76°
Answer:
m∠R=76º
Step-by-step explanation:
All angles in a triangle add up to 180º.
The triangle given is an isosceles triangle.
(2x+2)+(3x+1)+(2x+2)=180
Remove parentheses.
2x+2+3x+1+2x+2=180
Collect like terms.
7x+2+1+2=180
Add.
7x+5=180
Subtract 5 from both sides of the equation.
7x=175
Divide 7 from both sides of the equation.
x=25
m∠R=(3x+1)º
3x25+1=76º
m∠R=76º
Hope this helps :)
what the estimated quotient for the following problem?
343.23 divdend by 18
Answer:
Step-by-step explanation:
17
343.23 /18 is 19.0683333333
so the closest number to that is 17, if not try 23!
Janelys buys milk and apples at the store.
• She pays a total of $41.22.
• She pays a total of $3.22 for the milk.
• She buys 8 bags of apples that each cost the same amount.
.
Write and solve an equation which can be used to determine x, how much each bag
of apples costs.
Answer:
Each bag costs $4.75
Step-by-step explanation:
41.22 = 3.22 + 8x
38 = 8x
4.75 = x
1.7 6/5
2.4 25/25
3.28/3
what is the lowest term?
Answer:
3.
[tex] \frac{28}{3} [/tex]
Step-by-step explanation:
number 1 equals 8 1/5
number 2 equals 5
number 3 equals 9 1/3
A wading pool containing 100 gallons of water is leaking at a rate of 5 gallons per minute. At this rate, it will be empty in 20 minutes.