[tex]3 \div 4 \frac{1}{2} \\ = 3 \div \frac{9}{2} \\ = 3 \times \frac{2}{9} \\ = \frac{2}{3} [/tex]
Answer:
[tex] \frac{2}{3} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
What is the area of this triangle?
Enter your answer in the box.
units2
Answer:
8 units^2
Step-by-step explanation:
The area of a tringle is 1/2 bh. The base, LK, measures 4 while the height is also 4(you can get these values by counting the squares). This means the area is:
1/2 * (4)(4) = 1/2 * 16 = 8 units^2
I need help
With these
Answer:
"A"
Step-by-step explanation:
a+b >c
a+c>b
b+c>a
~~~~~~~~~~~~
A. T,T,T
B. T,T,F
C. T,F,T
Rope pieces of lengths 45 cm, 75 cm and 81 cm have to be cut into same size pieces. What is the smallest piece length possible?
Answer:
2025 cm
Step-by-step explanation:
Given the length of pieces - 45 cm, 75 cm and 81 cm
To find the length of the rope we have to find the L.C.M. of 45, 75 and 81 :
3 | 45, 75, 81
| ________________
3 | 15, 25, 27
|________________
3 | 5, 25, 9
|________________
3 | 5, 25, 3
|________________
5 | 5, 25, 1
|________________
5 | 1, 5, 1
|________________
| 1, 1, 1
L.C.M. = 3 × 3 × 3 × 3 × 5 × 5
= 2025 cm
So, the least length of the rope should be 2025 cm which can be cut into a whole number of pieces of length 45 cm, 75 cm and 81 cm.
use undetermined coefficient to determine the solution of:y"-3y'+2y=2x+ex+2xex+4e3x
First check the characteristic solution: the characteristic equation for this DE is
r ² - 3r + 2 = (r - 2) (r - 1) = 0
with roots r = 2 and r = 1, so the characteristic solution is
y (char.) = C₁ exp(2x) + C₂ exp(x)
For the ansatz particular solution, we might first try
y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)
where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).
However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :
y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)
Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.
y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)
… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)
y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)
… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)
Substituting every relevant expression and simplifying reduces the equation to
(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)
… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]
… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]
= 2x + (1 + 2x) exp(x) + 4 exp(3x)
… … …
2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)
= 2x + (1 + 2x) exp(x) + 4 exp(3x)
Then, equating coefficients of corresponding terms on both sides, we have the system of equations,
x : 2a = 2
1 : -3a + 2b = 0
exp(x) : 2c - d = 1
x exp(x) : -2c = 2
exp(3x) : 2e = 4
Solving the system gives
a = 1, b = 3/2, c = -1, d = -3, e = 2
Then the general solution to the DE is
y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)
Which of the following behaviors would best describe someone who is listening and paying attention? a) Leaning toward the speaker O b) Interrupting the speaker to share their opinion c) Avoiding eye contact d) Asking questions to make sure they understand what's being said
The answer is A and D
good luck
What is the equation of a circle with center (1, -4) and radius 2?
Answer:
(x-1)^2 + (y+4)^2 = 4
Step-by-step explanation:
The equation for a circle is given by
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x-1)^2 + (y- -4)^2 = 2^2
(x-1)^2 + (y+4)^2 = 4
are ratios 2:3 and 8:12 equalvelent to eachother
Answer:
2:3 is equal to 8:12
Step-by-step explanation:
2:3
To get the first number to 8
8/2 = 4
Multiply by all terms 4
2*3 : 3*4
8:12
2:3 is equal to 8:12
8:12 = 8/12
= 2/3
= 2:3
Therefore 2:3 and 8:12 are equalent to each other.
Answered by Gauthmath must click thanks and mark brainliest
lim ₓ→∞ (x+4/x-1)∧x+4
It looks like the limit you want to find is
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4}[/tex]
One way to compute this limit relies only on the definition of the constant e and some basic properties of limits. In particular,
[tex]e = \displaystyle\lim_{x\to\infty}\left(1+\frac1x\right)^x[/tex]
The idea is to recast the given limit to make it resemble this definition. The definition contains a fraction with x as its denominator. If we expand the fraction in the given limand, we have a denominator of x - 1. So we rewrite everything in terms of x - 1 :
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(\dfrac{x-1+5}{x-1}\right)^{x-1+5} \\\\ = \left(1+\dfrac5{x-1}\right)^{x-1+5} \\\\ =\left(1+\dfrac5{x-1}\right)^{x-1} \times \left(1+\dfrac5{x-1}\right)^5[/tex]
Now in the first term of this product, we substitute y = (x - 1)/5 :
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(1+\dfrac1y\right)^{5y} \times \left(1+\dfrac5{x-1}\right)^5[/tex]
Then use a property of exponentiation to write this as
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \left(\left(1+\dfrac1y\right)^y\right)^5 \times \left(1+\dfrac5{x-1}\right)^5[/tex]
In terms of end behavior, (x - 1)/5 and x behave the same way because they both approach ∞ at a proportional rate, so we can essentially y with x. Then by applying some limit properties, we have
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = \lim_{x\to\infty} \left(\left(1+\dfrac1x\right)^x\right)^5 \times \left(1+\dfrac5{x-1}\right)^5 \\\\ = \lim_{x\to\infty}\left(\left(1+\dfrac1x\right)^x\right)^5 \times \lim_{x\to\infty}\left(1+\dfrac5{x-1}\right)^5 \\\\ =\left(\lim_{x\to\infty}\left(1+\dfrac1x\right)^x\right)^5 \times \left(\lim_{x\to\infty}\left(1+\dfrac5{x-1}\right)\right)^5[/tex]
By definition, the first limit is e and the second limit is 1, so that
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = e^5\times1^5 = \boxed{e^5}[/tex]
You can also use L'Hopital's rule to compute it. Evaluating the limit "directly" at infinity results in the indeterminate form [tex]1^\infty[/tex].
Rewrite
[tex]\left(\dfrac{x+4}{x-1}\right)^{x+4} = \exp\left((x+4)\ln\dfrac{x+4}{x-1}\right)[/tex]
so that
[tex]\displaystyle \lim_{x\to\infty} \left(\frac{x+4}{x-1}\right)^{x+4} = \lim_{x\to\infty}\exp\left((x+4)\ln\dfrac{x+4}{x-1}\right) \\\\ = \exp\left(\lim_{x\to\infty}(x+4)\ln\dfrac{x+4}{x-1}\right) \\\\ =\exp\left(\lim_{x\to\infty}\frac{\ln\dfrac{x+4}{x-1}}{\dfrac1{x+4}}\right)[/tex]
and now evaluating "directly" at infinity gives the indeterminate form 0/0, making the limit ready for L'Hopital's rule.
We have
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\ln\dfrac{x+4}{x-1}\right] = -\dfrac5{(x-1)^2}\times\dfrac{1}{\frac{x+4}{x-1}} = -\dfrac5{(x-1)(x+4)}[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1{x+4}\right]=-\dfrac1{(x+4)^2}[/tex]
and so
[tex]\displaystyle \exp\left(\lim_{x\to\infty}\frac{\ln\dfrac{x+4}{x-1}}{\dfrac1{x+4}}\right) = \exp\left(\lim_{x\to\infty}\frac{-\dfrac5{(x-1)(x+4)}}{-\dfrac1{(x+4)^2}}\right) \\\\ = \exp\left(5\lim_{x\to\infty}\frac{x+4}{x-1}\right) \\\\ = \exp(5) = \boxed{e^5}[/tex]
Which number line represents the solutions to 1-2x = 4?
Answer:
The third choice down
Step-by-step explanation:
|-2x| = 4
There are two solutions, one positive and one negative
-2x = 4 and -2x = -4
Divide by -2
-2x/-2 = 4/-2 -2x/-2 = -4/-2
x = -2 and x = 2
Find the missing side lengths leave your answer as a racials simplest form
Answer:
m=[tex]7\sqrt3[/tex]
n=7
Step-by-step explanation:
Hi there!
We are given a right triangle (notice the 90°) angle, the measure of one of the acute angles as 60°, and the measure of the hypotenuse (the side OPPOSITE from the 90 degree angle) as 14
We need to find the lengths of m and n
Firstly, let's find the measure of the other acute angle
The acute angles in a right triangle are complementary, meaning they add up to 90 degrees
Let's make the measure of the unknown acute angle x
So x+60°=90°
Subtract 60 from both sides
x=30°
So the measure of the other acute angle is 30 degrees
This makes the right triangle a special kind of right triangle, a 30°-60°-90° triangle
In a 30°-60°-90° triangle, if the length of the hypotenuse is a, then the length of the leg (the side that makes up the right angle) opposite from the 30 degree angle is [tex]\frac{a}{2}[/tex], and the leg opposite from the 60 degree angle is [tex]\frac{a\sqrt3}{2}[/tex]
In this case, a=14, n=[tex]\frac{a}{2}[/tex], and m=[tex]\frac{a\sqrt3}{2}[/tex]
Now substitute the value of a into the formulas to find n and m to find the lengths of those sides
So that means that n=[tex]\frac{14}{2}[/tex], which is equal to 7
And m=[tex]\frac{14\sqrt3}{2}[/tex], which simplified, is equal to [tex]7\sqrt3[/tex]
Hope this helps!
Which expression is equivalent to
128xy
5 ? Assume x > 0 and y> 0.
2xy5
Moto
8
yax
8
BV
y
8.VY
X
Answer:
[tex]\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{128x^8y^3}[/tex] --- the complete expression
Required
The equivalent expression
We have:
[tex]\sqrt{128x^8y^3}[/tex]
Expand
[tex]\sqrt{128x^8y^3} = \sqrt{128* x^8 * y^3}[/tex]
Further expand
[tex]\sqrt{128x^8y^3} = \sqrt{64 * 2* x^8 * y^2 * y}[/tex]
Rewrite as:
[tex]\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2* 2 * y}[/tex]
Split
[tex]\sqrt{128x^8y^3} = \sqrt{64 * x^8 * y^2} * \sqrt{2 * y}[/tex]
Express as:
[tex]\sqrt{128x^8y^3} = (64 * x^8 * y^2)^\frac{1}{2} * \sqrt{2y}[/tex]
Remove bracket
[tex]\sqrt{128x^8y^3} = (64)^\frac{1}{2} * (x^8)^\frac{1}{2} * (y^2)^\frac{1}{2} * \sqrt{2y}[/tex]
[tex]\sqrt{128x^8y^3} = 8 * x^\frac{8}{2} * y^\frac{2}{2} * \sqrt{2y}[/tex]
[tex]\sqrt{128x^8y^3} = 8 * x^4 * y * \sqrt{2y}[/tex]
[tex]\sqrt{128x^8y^3} = 8 x^4 y \sqrt{2y}[/tex]
I need help guys thanks so much
Answer: C
Step-by-step explanation:
There is a sales tax of S6 on an item that costs 888 before tax. The sales tax on a second item is $21. How much does the second item cost before tax?
Step-by-step explanation:
before Tax
Coast = 888
in 2ND Item = $21
• 888/21
= $42.28
A rocket is launched at t = 0 seconds. Its height, in meters above sea-level, is given by the equation
h = -4.9t2 + 112t + 395.
At what time does the rocket hit the ground? The rocket hits the ground after how many seconds
Answer:
Step-by-step explanation:
In order to find out how long it takes for the rocket to hit the ground, we only need set that position equation equal to 0 (that's how high something is off the ground when it is sitting ON the ground) and factor to solve for t:
[tex]0=-4.9t^2+112t+395[/tex]
Factor that however you are factoring in class to get
t = -3.1 seconds and t = 25.9 seconds.
Since time can NEVER be negative, it takes the rocket approximately 26 seconds to hit the ground.
Which points lie on the graph of f(x) = loggx?
Check all that apply.
Step-by-step explanation:
f(x)=log(x)
=d(log(x)/dx)
=>y=1/x
SOMEONE HELP ME PLEASE
Answer:
9/25
Step-by-step explanation:
3 novels , 1 bio , 1 poetry = 5 books
P( novel) = novels / books
= 3/5
Book is returned
3 novels , 1 bio , 1 poetry = 5 books
P( novel) = novels / books
= 3/5
P(novel, return, novel) = 3/5 * 3/5 = 9/25
how long does it take for a deposit of $900 to double at 2% compounded continuously?
how many years does it take to double ? ___ years __ days
9514 1404 393
Answer:
34.6574 years34 years, 239.94 daysStep-by-step explanation:
For continuous compounding the "rule of 69" applies. That is the doubling time can be found from ...
t = 69.3147/r . . . . where r is the interest rate in percent.
Here, r=2, so ...
t = 69.3147/2 = 34.6574 . . . years
That's 34 years and 240 days.
I NEED HELP THANK YOU!!
Answer:
rt3/2
Step-by-step explanation:
first off cosine is the x coordinate
now if you do't want to use a calculator, you can use use the unit circle.
360 - 330 = 30 (360 degrees is a whole circle)
a 30 60 90 triangle is made, then use the law for 30 60 90 triangles:
if the shortest leg is x, the other leg is x*rt3 and the hypotenuse is 2x.
Answer:
D
Step-by-step explanation:
cos 330 = cos (360-330)
= cos 30
= √3 /2
The median for the given set of six ordered data values is 29.5
9 12 25_ 41 50
What is the missing value?
Answer:
34
Step-by-step explanation:
let the missing value is x
(25+x) /2 = 29.5
25+x = 29.5(2)
25+x = 59
x = 59-25
x = 34
On the first day of travel, a driver was going at a speed of 40 mph. The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles, find the total distance traveled in the two days.
The Total mileage is "400" and the further solution can be defined as follows:
Let t become the time he spent commuting on the first day of his vacation.
It is then calculated as [tex]t + 2[/tex].
[tex]\to 40\times(t+2) = 60(t) + 20 \\\\\to 40t+80 = 60t + 20 \\\\\to 80-20 = 60t + 40t \\\\\to 60 = 20t \\\\\to t=\frac{60}{20} \\\\\to t=\frac{6}{2} \\\\\to t= 3\\\\[/tex]
It traveled [tex]40\times (3 + 2) + 20 = 40\times 5 + 20 = 200+20=220[/tex] miles on its first day of operation.
The car traveled [tex]180\ miles[/tex] on the second day, which was [tex]60 \ miles \times 3[/tex].
So,
Total mileage= first day traveled + second day traveled [tex]= 220+ 180= 400 \miles[/tex]
Learn more:
Total distance traveled: brainly.com/question/20670144
A survey of 30-year-old males provided data on the number of auto accidents in the previous 5 years. The sample mean is 1.3 accidents per male. Test the hypothesis that the number of accidents follows a Poisson distribution at the 5% level of significance.
No. of accident No. of males
0 39
1 22
2 14
3 11
>=4 4
Required:
a. What's the Expected probability of finding males with 0 accidents?
b. What's the Expected probability of finding males with 4 or more accidents?
Answer:
0.2725
0.0431
Step-by-step explanation:
The distribution here is a poisson distribution :
λ = 1.3
The poisson distribution :
p(x) = [(e^-λ * λ^x)] ÷ x!
Expected probability of finding male with 0 accident ; x = 0
p(0) = [(e^-1.3 * 1.3^0)] ÷ 0!
p(0) = [0.2725317 * 1] ÷ 1
p(0) = 0.2725317
= 0.2725
2.)
P(x ≥ 4) = 1 - P(x < 4)
P(x < 4) = p(x = 0) + p(x. = 1) + p(x = 2) + p(x = 3)
p(x = 0) = p(0) = [(e^-1.3 * 1.3^0)] ÷ 0! = 0.2725
p(x = 1) = p(1) = [(e^-1.3 * 1.3^1)] ÷ 1! = 0.35429
p(x = 2) = p(2) = [(e^-1.3 * 1.3^2)] ÷ 2! = 0.23029 p(x = 3) = p(3) = [(e^-1.3 * 1.3^3)] ÷ 0! = 0.09979
P(x < 4) = 0.2725 + 0.35429 + 0.23029 + 0.09979 = 0.95687
P(x ≥ 4) = 1 - 0.95687 = 0.0431
A computer system uses passwords that are exactly six characters and each character is one of the 26 letters (a–z) or 10 integers (0–9). Suppose that 10,000 users of the system have unique passwords. A hacker randomly selects (with replace- ment) one billion passwords from the potential set, and a match to a user’s password is called a hit. (a) What is the distribution of the number of hits? (b) What is the probability of no hits? (c) What are the mean and variance of the number of hits?
Answer:
The number of hits would follow a binomial distribution with [tex]n =10,\!000[/tex] and [tex]p \approx 4.59 \times 10^{-6}[/tex].
The probability of finding [tex]0[/tex] hits is approximately [tex]0.955[/tex] (or equivalently, approximately [tex]95.5\%[/tex].)
The mean of the number of hits is approximately [tex]0.0459[/tex]. The variance of the number of hits is approximately [tex]0.0459\![/tex] (not the same number as the mean.)
Step-by-step explanation:
There are [tex](26 + 10)^{6} \approx 2.18 \times 10^{9}[/tex] possible passwords in this set. (Approximately two billion possible passwords.)
Each one of the [tex]10^{9}[/tex] randomly-selected passwords would have an approximately [tex]\displaystyle \frac{10,\!000}{2.18 \times 10^{9}}[/tex] chance of matching one of the users' password.
Denote that probability as [tex]p[/tex]:
[tex]p := \displaystyle \frac{10,\!000}{2.18 \times 10^{9}} \approx 4.59 \times 10^{-6}[/tex].
For any one of the [tex]10^{9}[/tex] randomly-selected passwords, let [tex]1[/tex] denote a hit and [tex]0[/tex] denote no hits. Using that notation, whether a selected password hits would follow a bernoulli distribution with [tex]p \approx 4.59 \times 10^{-6}[/tex] as the likelihood of success.
Sum these [tex]0[/tex]'s and [tex]1[/tex]'s over the set of the [tex]10^{9}[/tex] randomly-selected passwords, and the result would represent the total number of hits.
Assume that these [tex]10^{9}[/tex] randomly-selected passwords are sampled independently with repetition. Whether each selected password hits would be independent from one another.
Hence, the total number of hits would follow a binomial distribution with [tex]n = 10^{9}[/tex] trials (a billion trials) and [tex]p \approx 4.59 \times 10^{-6}[/tex] as the chance of success on any given trial.
The probability of getting no hit would be:
[tex](1 - p)^{n} \approx 7 \times 10^{-1996} \approx 0[/tex].
(Since [tex](1 - p)[/tex] is between [tex]0[/tex] and [tex]1[/tex], the value of [tex](1 - p)^{n}[/tex] would approach [tex]0\![/tex] as the value of [tex]n[/tex] approaches infinity.)
The mean of this binomial distribution would be:[tex]n\cdot p \approx (10^{9}) \times (4.59 \times 10^{-6}) \approx 0.0459[/tex].
The variance of this binomial distribution would be:
[tex]\begin{aligned}& n \cdot p \cdot (1 - p)\\ & \approx(10^{9}) \times (4.59 \times 10^{-6}) \times (1- 4.59 \times 10^{-6})\\ &\approx 4.59 \times 10^{-6}\end{aligned}[/tex].
What is the equation of a line that passes through the point (1,8) and is perpendicular to the line whose equation is y=x/2+3?
Answer:
m=1/2
y-8=1/2(x-1)
y-8=1/2x-1/2
multiply through by 2
2y-16=x-1
2y-16+1-x=0
2y-15-x=0
2y-x-15=0
find the mid-point of the line segment joining the points (10, 13) and (-7, 7)?
Answer:
(3/2,10)
Step-by-step explanation:
Mid point is ((10-7)/2,(13+7)/2)=(1.5,10)
Which ratio is equal to 27 : 81?
Answer:
1:3
Step-by-step explanation:
27 : 81
Divide each side by 27
27/27 : 81/27
1:3
Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm
0.08 cm/min
Step-by-step explanation:
Given:
[tex]\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}[/tex]
Find [tex]\frac{dr}{dt}[/tex] when diameter D = 20 cm.
We know that the volume of a sphere is given by
[tex]V = \dfrac{4\pi}{3}r^3[/tex]
Taking the time derivative of V, we get
[tex]\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt} = 4\pi\left(\dfrac{D}{2}\right)^2\dfrac{dr}{dt} = \pi D^2\dfrac{dr}{dt}[/tex]
Solving for [tex]\frac{dr}{dt}[/tex], we get
[tex]\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})[/tex]
[tex]\:\:\:\:\:\:\:= 0.08\:\text{cm/min}[/tex]
If sin x = –0.1 and 270° < x < 360°, what is the value of x to the nearest degree?
Answer:
354°15'38.99''
Step-by-step explanation:
Most of the heat loss for outdoor swimming pools is due to surface
evaporation. So, the greater the area of the surface of the pool, the greater
the heat loss. For a given perimeter, which surface shape would be more
efficient at retaining heat: a circle or a rectangle? Justify your answer.
Answer:
rectangle
Step-by-step explanation:
Perimeter of 20 feet
rectangle (square is technically a rectangle):
sides 5 and 5
5*5 = 25ft²
Circle:
20/(2π) = 3.18309...
3.1809...²π = 31.831ft²
Max area of rectangle (i.e. square) has a smaller area than a circle.
Find the Z scores for which 5% of the distributions area lies between negative Z & Z
Answer:
0.475: Z = -0.062706778
0.525: Z = 0.062706778
Step-by-step explanation:
find the equation of Straight line which passes through the point A(-5,10) makes equal intercept on both axes.
Answer:
y = -x + 5
Step-by-step explanation:
The point is in quadrant 2, so the line must pass through points that look like (a, 0) and (0, a) where a is a positive number. The slope of such a line is -1.
If (x, y) is a point on the line, then the slope between points (x, y) and (-5, 10) is 1, and you can write
[tex]\frac{y-10}{x-(-5)}=-1\\y-10 = -1(x+5)\\y-10=-x-5\\y=-x+5[/tex]
