Answer:
length : 37 m
width : 8 m
Step-by-step explanation:
perimeter = 2×l(ength) + 2×w(idth) = 90
l = 5w - 3
=> 2×(5w-3) + 2w = 90
10w - 6 + 2w = 90
12w = 96
w = 8
=> l = 5w - 3 = 5×8 -3 = 40-3 = 37
If the integral of the product of x squared and e raised to the negative 4 times x power, dx equals the product of negative 1 over 64 times e raised to the negative 4 times x power and the quantity A times x squared plus B times x plus E, plus C , then the value of A B E is
Answer:
[tex]A + B + E = 32[/tex]
Step-by-step explanation:
Given
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
Required
Find [tex]A +B + E[/tex]
We have:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
Using integration by parts
[tex]\int {u} \, dv = uv - \int vdu[/tex]
Where
[tex]u = x^2[/tex] and [tex]dv = e^{-4x}dx[/tex]
Solve for du (differentiate u)
[tex]du = 2x\ dx[/tex]
Solve for v (integrate dv)
[tex]v = -\frac{1}{4}e^{-4x}[/tex]
So, we have:
[tex]\int {u} \, dv = uv - \int vdu[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = x^2 *-\frac{1}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x} 2xdx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} - \int -\frac{1}{2}e^{-4x} xdx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]
-----------------------------------------------------------------------
Solving
[tex]\int xe^{-4x} dx[/tex]
Integration by parts
[tex]u = x[/tex] ---- [tex]du = dx[/tex]
[tex]dv = e^{-4x}dx[/tex] ---------- [tex]v = -\frac{1}{4}e^{-4x}[/tex]
So:
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x}\ dx[/tex]
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} + \int e^{-4x}\ dx[/tex]
[tex]\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}[/tex]
So, we have:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} [ -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}][/tex]
Open bracket
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} -\frac{x}{8}e^{-4x} -\frac{1}{8}e^{-4x}[/tex]
Factor out [tex]e^{-4x}[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{x^2}{4} -\frac{x}{8} -\frac{1}{8}]e^{-4x}[/tex]
Rewrite as:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{4}x^2 -\frac{1}{8}x -\frac{1}{8}]e^{-4x}[/tex]
Recall that:
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C[/tex]
[tex]\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{64}Ax^2 -\frac{1}{64} Bx -\frac{1}{64} E]Ce^{-4x}[/tex]
By comparison:
[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]
[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]
[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]
Solve A, B and C
[tex]-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2[/tex]
Divide by [tex]-x^2[/tex]
[tex]\frac{1}{4} = \frac{1}{64}A[/tex]
Multiply by 64
[tex]64 * \frac{1}{4} = A[/tex]
[tex]A =16[/tex]
[tex]-\frac{1}{8}x = -\frac{1}{64}Bx[/tex]
Divide by [tex]-x[/tex]
[tex]\frac{1}{8} = \frac{1}{64}B[/tex]
Multiply by 64
[tex]64 * \frac{1}{8} = \frac{1}{64}B*64[/tex]
[tex]B = 8[/tex]
[tex]-\frac{1}{8} = -\frac{1}{64}E[/tex]
Multiply by -64
[tex]-64 * -\frac{1}{8} = -\frac{1}{64}E * -64[/tex]
[tex]E = 8[/tex]
So:
[tex]A + B + E = 16 +8+8[/tex]
[tex]A + B + E = 32[/tex]
what is 10000000000+10000000000
Answer:
20000000000000000000000000000
Select the correct answer. Which of the following is equal to the expression below? (8 - 320) 3 OA. 40 O B. 30 OC. 10 5 OD. 835
Answer:
Quesiton is not clear. here is the asnswer basing on our understand
Step-by-step explanation:
(8-32)3 = (-24*3) = =72
Of the men in the survey, what percent of them prefer movies? Write your answer as a percent and round to one decimal place.
Answer:
40%Step-by-step explanation:
There are 20 men and 8 of them prefer movies.
P = 8/20 = 0.4 = 40%please help me with this !!
Answer:
m∠J = 32°
m∠G = 78°
Step-by-step explanation:
ΔHJI ≈ ΔGEF respectively means;
∠H ≅ ∠G
∠I ≅ ∠E
∠J ≅ ∠F
Therefore;
Since ∠F = 32°, then ∠J = 32°
Since ∠H = 78°, then ∠G = 78°
Hope this helps!
A baby whale gains about 250 pounds a day. It was 250 pounds at birth. Find an equation to find the number of days it will take for a baby to weigh its first ton.
Answer:
8 days
Step-by-step explanation:
1 ton=2,000 pounds and If you divide 2,000÷250=8 days. It will talk 8 days for the baby whale to weigh his first ton.
One bag contains 6 red, 2 blue, and 3 yellow balls. A second bag contains 2 red, 4 blue, and 5 yellow balls. A third bag contains 3 red, 7 blue, and 1 yellow ball. One bag is selected at random. If 1 ball is drawn from the selected bag, what is the probability that the ball drawn is yellow?
Answer:
2 is the probability
Step-by-step explanation:
8;3;-2:-7:12 calculate the nth term
Answer:
45544554554554445455544
Step-by-step explanation:
Suppose that inches of wire costs cents.
At the same rate, how many inches of wire can be bought for cents?
Answer:
11 inches
Step-by-step explanation:
Given :
15 in of wire = 90 cents
At the same rate :
x inch of wire = 66 cents
Cross multiply :
90x = 15 * 66
90x = 990
x = 990 / 90
x = 11
11 inches of wire
Helpppppppp me plzzzzzzz
Answer:
Length of Line AC = 26 units
Step-by-step explanation:
Given:
Line AC = [3x + 1] + 8
Line BC = [x - 2] + 2
Find:
Length of Line AC
Computation:
Line AB ║ Line L
So,
Using Mid-Point theorem;
[3x + 1] / 8 = [x - 2] / 2
2[3x + 1] = 8[x - 2]
6x + 2 = 8x - 16
8x - 6x = 16 + 2
2x = 18
x = 9
So,
Line AC = [3x + 1] + 8
Line AC = [3(9) + 1] + 8
Line AC = [27 + 1] + 8
Line AC = 28 + 8
Length of Line AC = 26 units
A survey was done on the number of people in eachcar leaving a Shopping
Centre. The results are summarised in the following table:
Number of People
in Each Car
Frequency
1
45
2
198
3
121
4
76
5
52
6
13
a. What is the Mode number of people in each car?
b. What is the Median number of people in each car?
c. What is the Mean number of people in each car? Give your answer to 1
decimal place.
Answer:
a) Mode number = 2
b) Median = 64.5 = 4 people in car as 0.5 in 64.5 is close to 76
= 4 people
c) Mean number is 505/6 = 84.1666666667 then we see where 84.16 lies and see this lies with = 3 people
Step-by-step explanation:
45 is 1
198 is 2
121 is 3
76 is 4
52 is 5
13 is 6
Mode we look for the highest frequency and see 198 is the amount and 2 people in car is the subject, we give the subject and that is 2 people in car is the highest frequency and would be the mode.
Median is shown in the answer as we add up.
Mean we add up all frequency and divide by the amount of subjects = 6.
a) Mode number = 2
b) Median = 13, 45, 52, here 76, 121, 198 mid number between
= (76-52 )/ 2 + (52)= 24 /2 + (52) = 12 + 52 + 0.5 if even number
median = 64.5 in a cumulative graph though which is not asked here it would be exactly half of 505 = 257.5 and interquartile we half again and add on 257.5 and show the range values interquartile as 1/2(252.5) and 1/2(252.5+ 505) = 126.25 as one value and 757.5 as the other by drawing a horizontal line from y axis to the points so vertical lines can represnt the cars median and interquartile.
c. Mean number is 505/6 = 84.1666666667 then we see where 84.16 lies and see this lies with 3 seats
For cumulative frequency we can relist numbers like this
45
45 +198 = 243
243 + 121 = 364
364+76 = 440
440 + 52 = 492
492+13 = 505 to plot graph.
But if there was group of measures or time etc then we would always plot the highest of each set for cumulative x axis and use the 2 values to see the ratio for histograms ie) 198/2 = 99 so that all values are read in equal proportions and 2 is a data below the graph not on the graph as 2 does not show as a box count just a name below on x axis. So we have to use the ratio as explained for histograms.
Please Answer Correctly - Will Give Branliest & Extra Points. (links or unidentified/wrong answers will be reported and auto banned)
Answer:
Step-by-step explanation:
11 no
46+4x=90 degree(being perpendicular)
4x=90-46
x=44/4
x=11
12 no
They are complementary angles
6 no
angle B+27=180 degree(being straight line)
angle B=180-27
angle B=153
10 no
angle 38 +angle DFE=180 degree(being supplementary)
angle DFE=180-38
angle DFE=142 degree
5 no
They are vertically opposite angles.
7 no
angle AGF and angle CGD (because they have common arm and vertex)
Answer:
Solution given:
11.4x+46=90[being right angle]
4x=90-46
x=44/4
x=11
12.
Complementary angles
5.
vertical
6.
<ABD+27=180°[linear pair]
<ABD=180-27
<ABD=153° degree
10.
<DFE+38=180[being supplementary]
<DFE=180-38
<DFE=142 degrees.
7.
angle DGE and angle DGC
8.
<AGB and <AGE
B Reading Choose the best estimate for the multiplication problem below. 85 x 86
A. 8100
B. 10,400
C. 12,200
Answer:
A. 8100
Step-by-step explanation:
85 x 86
To estimate, we multiply 85*100, which is the easiest multiplication, as a multiplication by 100 is the same as placing two zeros at the end of the number.
85*100 = 8500
Since 86 < 100, 85*86 < 8500. Thus, the correct estimate is given by option A.
Lynn is tracking the progress of her plant's growth. Currently the plant is 11 The plant grows 1.2 cm per day. Find an equation that represents the plant's height after any given number How tall is the plant after 9 days?
Answer:
the equation is 11+1.2d= h so the height after 9 days would be 21.8cm
Step-by-step explanation:
Answer:
f(h) = 11 + 1.2h
f(9) = 21.8 cm
Step-by-step explanation:
let 'h' = height
f(h) = 11 + 1.2h
height after 9 days:
f(9) = 11 + 1.2(9)
= 11 + 10.8
= 21.8 cm
Find the length of side y.
y=_ft
Answer:
y = 5.66388 feet, (round that to whatever you need to round to)
Step-by-step explanation:
cos (51) = y/9
cos(51)*9=
y = 5.66388 feet
The measure of an angle is 89. Find the measure of its supplementent
a. 91
b. 89
c.90
d. 80
Answer:
A) 91
Step-by-step explanation:
Supplementary angels are 2 angels whos sum is 180
To find the supplement of angle 89, substract 89 from 180
180-89 = x
91 = x
A personnel psychologist studying adjustment to the job of new employees found a correlation of .3 between amount of education and rating by job supervisors 2 months later. The psychologist now plans to use the amount of education to predict supervisors’ later ratings. Indicate the independent/predictor variable, dependent/criterion variable, and beta. Write the Z-score prediction model; give the predicted Z-scores for supervisor ratings for employees with the amount of education Z-score of -1.5, -1, -.5
Answer:
the predictor variable is: amount of education
the criterion variable is: the Supervisors' rating
the beta is: .3
the Zy scores are -0.45, -0.3, 0.15
Step-by-step explanation:
r=beta which is the same; hence correlation equals regression
use this formula for the Z-scores
Zy= (beta) (Zx)
zy=(.3) (-1.5) = -0.45
(E) -1.5;
Zy=-0.45
(F)-1,
Zy=-0.3
(G)-.5.
Zy=-0.15
What is the area of the base of the cone below? 12ft v=90ft^3
Answer: C 22.5 ft2!
Step-by-step explanation:
i took the test, have a great day:) <3
Answer:
right
Step-by-step explanation:
Answer fast will give brainiest
Answer:
Step-by-step explanation:
1). If two right triangles are congruent by HL property of congruence,
Their corresponding sides will be congruent.
By this property,
x - 4 = y + 3
x - y = 7 -----(1)
x = 2y ------(2)
By substituting x = 2y in equation (1),
2y - y = 7
y = 7
From equation (1)
x - 7 = 7
x = 15
2). If both the right triangles are congruent by HL property of congruence,
Their height and and hypotenuse will be congruent.
y + x = x + 7
y = 7
y + 5 = 2y - x
y - 2y + 5 = -x
-y + 5 = -x
x = y - 5
By substituting y = 7 in the equation,
x = 7 - 5
x = 2
Answer for brainlest
Answer:
Step-by-step explanation:
angle 3 and angle 4 are co interior angles.so,
angle 3+angle 4=180 degree
sum of co interior angle is always 180 degree.
Answer: Angle 3 and 5 = 180° because consecutive angles formed by parallel lines are supplementary
Step-by-step explanation:
It should be noted that Angle 3 and 5 = 180° because consecutive angles formed by parallel lines are supplementary.
For example, if angle 3 is 60°, the value of angle 5 will be:
= 180° - 60°
= 120°
A man buys a marker at Rs. 40 and sells it at Rs. 50. What is the profit percentage?
Answer:
may be 10%hope it helps uh
Convert 10π/6 radians into degrees.
We know that ,
[tex]\pi rad = 180^o[/tex]
SOLUTION :Using Unitary Method ,
[tex]\implies 1 \ rad = \dfrac{180^o}{\pi } [/tex]
Therefore ,
[tex]\implies \dfrac{10\pi}{6} rad = \dfrac{10\pi}{6} * \dfrac{180^o}{\pi } [/tex]
[tex]= \boxed{\red{ 300^o }}[/tex]
Required answer !
if a news paper costs 25p how much would 3 weeks . if the the paper is puplished six days each week
The best i could find out is 450p
show that the subset is the partial ordering on the power set of S.
refer to the attachment
Naeem bought a dirtbike. The original price
was $1,800, but he got a discount of 30%. What
was the discounted price of the dirtbike?
Answer:
$1,260
Step-by-step explanation:
30% off
pay 70%
70% = 0.7
1,800 * 0.7 = 1,260
$1,260
Tickets for the school play cost $5 for students and $8 for adults. For one performance, 128 tickets were sold for $751. How many tickets were for adults and how many were for students?
HELPPPPPPPPPPPPPPPPPPPPP
Answer:
2
35
6
Step-by-step explanation:
14/7=2
5*7=35
42/7=6
Solve 7/w+4 =5/w+4-6/w
Answer:
w=-1+[tex]\sqrt{2}[/tex], w=-1-[tex]\sqrt{2}[/tex]
Step-by-step explanation:
PLS ANWER ASAP!! person with correct answer will be marked brainliest
Answer:
62 degrees since there are supplementary angles
Step-by-step explanation:
∠PQO= 180 degrees - 118 degrees
∠PQO= 62 degrees is the answer.
∠PQO= 180°-∠RQO -------(Supplementary Angles)
∠PQO= 180° - 118°
∠PQO= 62° answer.
Help I need this answer ASAP
Answer: c
Step-by-step explanation: because yes
Answer:
d po answer
yan po sinagot ko
hehe