Answer:
B.
Step-by-step explanation:
I don't know for a fact but i think its B. Sorry if I got it wrong.
Answer pllllllleeeaaaaasssss
(3.1) … … …
[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2x-y}{x-2y}[/tex]
Multiply the right side by x/x :
[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{2-\dfrac yx}{1-\dfrac{2y}x}[/tex]
Substitute y(x) = x v(x), so that dy/dx = x dv/dx + v :
[tex]x\dfrac{\mathrm dv}{\mathrm dx} + v = \dfrac{2-v}{1-2v}[/tex]
This DE is now separable. With some simplification, you get
[tex]x\dfrac{\mathrm dv}{\mathrm dx} = \dfrac{2-2v+2v^2}{1-2v}[/tex]
[tex]\dfrac{1-2v}{2-2v+2v^2}\,\mathrm dv = \dfrac{\mathrm dx}x[/tex]
Now you're ready to integrate both sides (on the left, the denominator makes for a smooth substitution), which gives
[tex]-\dfrac12\ln\left|2v^2-2v+2\right| = \ln|x| + C[/tex]
Solve for v, then for y (or leave the solution in implicit form):
[tex]\ln\left|2v^2-2v+2\right| = -2\ln|x| + C[/tex]
[tex]\ln(2) + \ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]
[tex]\ln\left|v^2-v+1\right| = \ln\left(\dfrac1{x^2}\right) + C[/tex]
[tex]v^2-v+1 = e^{\ln\left(1/x^2\right)+C}[/tex]
[tex]v^2-v+1 = \dfrac C{x^2}[/tex]
[tex]\boxed{\left(\dfrac yx\right)^2 - \dfrac yx+1 = \dfrac C{x^2}}[/tex]
(3.2) … … …
[tex]y' + \dfrac yx = \dfrac{y^{-3/4}}{x^4}[/tex]
It may help to recognize this as a Bernoulli equation. Multiply both sides by [tex]y^{\frac34}[/tex] :
[tex]y^{3/4}y' + \dfrac{y^{7/4}}x = \dfrac1{x^4}[/tex]
Substitute [tex]z(x)=y(x)^{\frac74}[/tex], so that [tex]z' = \frac74 y^{3/4}y'[/tex]. Then you get a linear equation in z, which I write here in standard form:
[tex]\dfrac47 z' + \dfrac zx = \dfrac1{x^4} \implies z' + \dfrac7{4x}z=\dfrac7{4x^4}[/tex]
Multiply both sides by an integrating factor, [tex]x^{\frac74}[/tex], which gives
[tex]x^{7/4}z'+\dfrac74 x^{3/4}z = \dfrac74 x^{-9/4}[/tex]
and lets us condense the left side into the derivative of a product,
[tex]\left(x^{7/4}z\right)' = \dfrac74 x^{-9/4}[/tex]
Integrate both sides:
[tex]x^{7/4}z=\dfrac74\left(-\dfrac45\right) x^{-5/4}+C[/tex]
[tex]z=-\dfrac75 x^{-3} + Cx^{-7/4}[/tex]
Solve in terms of y :
[tex]y^{4/7}=-\dfrac7{5x^3} + \dfrac C{x^{7/4}}[/tex]
[tex]\boxed{y=\left(\dfrac C{x^{7/4}} - \dfrac7{5x^3}\right)^{7/4}}[/tex]
(3.3) … … …
[tex](\cos(x) - 2xy)\,\mathrm dx + \left(e^y-x^2\right)\,\mathrm dy = 0[/tex]
This DE is exact, since
[tex]\dfrac{\partial(-2xy)}{\partial y} = -2x[/tex]
[tex]\dfrac{\partial\left(e^y-x^2\right)}{\partial x} = -2x[/tex]
are the same. Then the general solution is a function f(x, y) = C, such that
[tex]\dfrac{\partial f}{\partial x}=\cos(x)-2xy[/tex]
[tex]\dfrac{\partial f}{\partial y} = e^y-x^2[/tex]
Integrating both sides of the first equation with respect to x gives
[tex]f(x,y) = \sin(x) - x^2y + g(y)[/tex]
Differentiating this result with respect to y then gives
[tex]-x^2 + \dfrac{\mathrm dg}{\mathrm dy} = e^y - x^2[/tex]
[tex]\implies\dfrac{\mathrm dg}{\mathrm dy} = e^y \implies g(y) = e^y + C[/tex]
Then the general solution is
[tex]\sin(x) - x^2y + e^y = C[/tex]
Given that y (1) = 4, we find
[tex]C = \sin(1) - 4 + e^4[/tex]
so that the particular solution is
[tex]\boxed{\sin(x) - x^2y + e^y = \sin(1) - 4 + e^4}[/tex]
1) Prepare a post merger financial position for METRO using the pooling of interest method.
Answer:
Metro and Medec
METRO
Post-merger Financial Position, using the pooling of interest method:
Pre-merger Financial Positions:
Metro (RM ‘000)
Assets
Current assets 120
Fixed assets 830
Total assets 950
Liabilities and Equities
Current liabilities 40
Long term debt 200
Common stock (RM1 par) 480
Capital surplus 120
Retained earnings 110
Total liabilities and equity 950
Earnings available to
common stockholders 230
Common Dividends 150
Addition to Retained Earnings 80
Step-by-step explanation:
Pre-merger Financial Positions:
Metro (RM ‘000) Medec(RM ‘000)
Assets
Current assets 50 70
Fixed assets 650 180
Total assets 700 250
Liabilities and Equities
Current liabilities 30 10
Long term debt 140 60
Common stock (RM1 par) 400 80
Capital surplus 50 70
Retained earnings 80 30
Total liabilities and equity 700 250
Earnings available to
common stockholders 100 130
Common Dividends 50 100
Addition to Retained Earnings 50 30
Exchange ratio = 1:2
Which figure can be formed from the net?
pls answer fast for brainiest !
Answer:
It should be the top right one
(with 6ft as the height)
Step-by-step explanation:
Answer:
It must be the lower to the left choice.
Step-by-step explanation:
As you can see, the net we have is composed of only triangles.
So we should be choosing a figure with a triangular base.
Our answers are narrowed down into the top right and lower left choices because both figures have triangular bases.
The other person down there chose the top right choice and was incorrect, so the answer should be the lower to the left figure.
Also, its the lower left figure because look at the triangular base, it is an isosceles meaning that two sides have the same length.
If the net says that the long side measures 9 ft, then the other two sides should be the same length and shorter than 9 ft. So the answer is the lower left figure.
Hope this helps
identify an equation in slope-intercept form for the line parallel to y=-3x+7 that passes through (2,-4)
Answer:
y = -3x + 2
Step-by-step explanation:
If two lines are parallel to each other, they have the same slope.
The first line is y = -3x + 7. Its slope is -3. A line parallel to this one will also have a slope of -3.
Plug this value (-3) into your standard point-slope equation of y = mx + b.
y = -3x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (2, -4). Plug in the x and y values into the x and y of the standard equation.
-4 = -3(2) + b
To find b, multiply the slope and the input of x (2)
-4 = -6 + b
Now, add 6 to both sides to isolate b.
2 = b
Plug this into your standard equation.
y = -3x + 2
This equation is parallel/perpendicular to your given equation (y = -3x + 7) and contains point (2, -4)
Hope this helps!
Which of the following is a polynomial
A. 1-5x^2/x
b. 11x
c. 2x^2- square root x
d. 3x^2+6x
Answer:
B and D are polynomial
Step-by-step explanation:
An algebraic expression with non-zero coefficients and variables having non-negative integers as exponents is called a polynomial.
A)
If it is [tex]1 -\frac{5x^{2}}{x }=1-5x[/tex] , then it is a polynomial.
But if it is [tex]\frac{1-5x^{2}}{x}[/tex] then it is not a polynomial
Yes again but pls if you don’t know don’t answer.
Answer:
90deg +20deg.
Step-by-step explanation:
Angle RST can be broken down into RSQ and QST, whose measures are 90 deg and 20 deg, respectively. So you just add up the two parts to get the whole.
Hope this helps!
Please I need help!!!!!!!!
Answer:
10 is the correct answer
Answer:
Go with the third option 10!
i hope this helped!
-2,6,-18,54, what is the common ratio of the sequence
Answer:
2
Step-by-step explanation:
Answer:
Common Ratio=-3
Step-by-step explanation:
To find any common ratio in a sequence, always take the second number in the sequence and divide it by the first number. However, you must be careful because the common ratio should only be negative if the values in the sequence are alternating between negative and positive. Therefore, if the sequence of numbers is simply decreasing in value, this does not mean that the common ratio is negative. The common ratio would still be positive. If the sequence is decreasing in value, this means that the common ratio would be a fraction or a decimal less than one.
If m and n are positive integers and m^2 - n^2 = 9, which of the following could be the value of
n?
A) 1
B) 16
C) 9
D) 4
Answer:
4
Problem:
If m and n are positive integers and m^2 - n^2 = 9, which of the following could be the value of
n?
A) 1
B) 16
C) 9
D) 4
Step-by-step explanation:
One approach would be to plug in the choices and see.
If n=1, then we have m^2-1=9.
This would give m^2=10 after adding 1 on both sides. There is no integer m when squared would give us 10. ( Square root of 9 is a decimal )
If n=16, then we would have m^2-256=9.
This would give m^2=265 after adding 256 on both sides. There is no integer m when squared would give us 265. ( Square root of 265 is a decimal )
If n=9, then we would have m^2-81=9.
This would give m^2=90 after adding 81 on both sides. There is no integer m when squared would give us 90. ( Square root of 90 is a decimal )
If n=4, then we would have m^2-16=9.
This would give m^2=25 after adding 16 on both sides. There is an integer m when squared would give us 25. ( Square root of 25 is a 5)
A rectangle's length is three times as long as it is wide. Which expression represents the change in area if the width of the rectangle is increased by 1?
1. 3x^2
2. 3x
3. 3x^2+3x
4. the area increases by 3
Step-by-step explanation:
Let's say the rectangle's width is equal to y. We know that the length is three times the width, so the length = 3 * y. We also know that the area for a rectangle is equal to length * width, so the area, z, is equal to
(3*y) * y = z
3 * y² = z
Now, let's increase the width of the rectangle by 1. We can replace y with y+1 (as y+1 is 1 greater than y), and 3 * y with 3 * (y+1) to get
3*(y+1) * (y+1) = new area
(3y+3)*(y+1) = new area
3y²+3y +3 y + 3 = new area
3y² + 6y + 3 = new area
The difference in area is equal to the new area subtracted by the old area, or
3y²+6y+3 - 3y² = 6y +3. The variable for x is not given, so if x = (2y+1), the answer would be the second choice. However, solely using the information given, it is impossible to determine a solution outside of saying that it is not option 4, as 6y + 3 ≠ 3
Can you tell me the procedure of these
x-7 = -2
x-1 = 7
9-x = -10
for maths answer this question please
4x-9=6-9
Answer:
x = 1.5
Step-by-step explanation:
First, calculate 6-9, which is -3.
Then we add 9 on both sides so that on the left, we only have 4x, and on the right, we have 6.
Then divide by 4 on both sides to get x = 1.5
Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. Write the formula for this sequence in the form an = a1 ⋅ rn−1. Explain how you arrived at your answer.
Answer:
[tex]a_n = 4.5 * 3^{n-1}[/tex]
Step-by-step explanation:
Given
[tex]a_4 = 121.5[/tex]
[tex]r = 3[/tex]
Required
[tex]a_n = a_1 * r^{n -1}[/tex]
Substitute 4 for n in [tex]a_n = a_1 * r^{n -1}[/tex]
[tex]a_4 = a_1 * r^{4 -1}[/tex]
[tex]a_4 = a_1 * r^3[/tex]
Substitute 121.5 for [tex]a_4[/tex]
[tex]121.5 = a_1 * 3^3[/tex]
[tex]121.5 = a_1 * 27[/tex]
Solve for a1
[tex]a_1 = \frac{121.5}{27}[/tex]
[tex]a_1 = 4.5[/tex]
So, we have:
[tex]a_n = a_1 * r^{n -1}[/tex]
[tex]a_n = 4.5 * 3^{n-1}[/tex]
Answer:
First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.
Step-by-step explanation:
sample answer on edge ;)
The greatest common factor of 45a^2b^3 and 18a^4b
Answer:
9a²b
Step-by-step explanation:
Hi there!
We need to find the greatest common factor out of 45a²b³ and 18[tex]a^{4}[/tex]b
We can split apart the monomials to make it easier
45a²b³ is 45*a²b³
18[tex]a^{4}[/tex]b is 18*[tex]a^{4}[/tex]b
First, let's find the GCF out of 45 and 18 (the number coefficients)
we can find all of the multiples of the 2 numbers:
45 is made up of 9 and 5
9 is made up of 3 and 3
so 3*3*5 is 45
18 is made up of 2 and 9
9 is made up of 3 and 3
so 2*3*3 is 18
3*3 is in both 45 and 18, so 9 is the GCF out of 45 and 18
Now let's find the GCF out of a²b³ and [tex]a^{4}[/tex]b
a²b³ made up of a² and b³
so a²b³ is a*a*b*b*b
[tex]a^{4}[/tex]b is made up of [tex]a^{4}[/tex] and b
so [tex]a^{4}[/tex]b is a*a*a*a*b
a*a*b is in both a²b³ and [tex]a^{4}[/tex]b, so the GCF out of a²b³ and [tex]a^{4}[/tex]b is a²b
Now multiply 9 and a²b together, as they are only the GCF of the parts of the monomials
9*a²b=9a²b
there's the greatest common factor of the 2 monomials
Hope this helps!
Please help asap i will give brainliest. Find the exact perimeter and area of the triangle.
Answer:
perimeter=9cm
Area=2cm^2
step by step explanation:
Firstly solve the sides that don't have figures using trigonometry
#1..sin15°=opposite/hypotenuse
sin15=opposite/4
opposite=sin15×4
=1.035, round off to 1cm
Then find the value of the base
tan15=opposite/adjacent
tan15=1/adjacent
1=tan15adjascent
1/tan15=adjacent
adjacent or base=3.7 round off to 4cm
After finding these values find the perimeter
p=side+side+side
p=4cm+4cm+1cm
p=9cm
Find the area
1/2bh
1/2×4×1
A=2cm2
Find m<1. Please answer by tomrrow
Answer:
59
Step-by-step explanation:
Just get the supplement of 121.
So angle 1 is 180-121 = 59 degrees
find the exact value of 6cos(105°)
Answer:
[tex]-\frac{3(\sqrt{6}-\sqrt{2})}{2}\text{ or } \frac{-3\sqrt{6}+3\sqrt{2}}{2}}\text{ or }\frac{3(\sqrt{2}-\sqrt{6})}{2}[/tex]
Step-by-step explanation:
There are multiple ways to achieve and even express the exact answer to this problem. Because the exact value of [tex]6\cos(105^{\circ}})[/tex] is a non-terminating (never-ending) decimal, it does not have a finite number of digits. Therefore, you cannot express it as an exact value as a decimal, as you'd either have to round or truncate.
Solution 1 (Cosine Addition Identity):
Nonetheless, to find the exact value we must use trigonometry identities.
Identity used:
[tex]\cos(\alpha +\beta)=\cos \alpha \cos \beta-\sin \alpha \sin \beta[/tex]
Notice that [tex]45+60=105[/tex] and therefore we can easily solve this problem if we know values of [tex]\cos(45^{\circ})[/tex], [tex]\cos(60^{\circ})[/tex], [tex]\sin (45^{\circ})[/tex], and [tex]\sin(60^{\circ})[/tex], which is plausible as they are all key angles on the unit circle.
Recall from either memory or the unit circle that:
[tex]\cos(45^{\circ})=\sin(45^{\circ})=\frac{\sqrt{2}}{2}[/tex] [tex]\cos(60^{\circ})=\frac{1}{2}[/tex] [tex]\sin(60^{\circ})=\frac{\sqrt{3}}{2}[/tex]Therefore, we have:
[tex]\cos(105^{\circ})=\cos(45^{\circ}+60^{\circ}}),\\\cos(45^{\circ}+60^{\circ}})=\cos 45^{\circ}\cos 60^{\circ}-\sin 45^{\circ}\sin 60^{\circ},\\\cos(45^{\circ}+60^{\circ}})=\frac{\sqrt{2}}{2}\cdot \frac{1}{2}-\frac{\sqrt{2}}{2}\cdot \frac{\sqrt{3}}{2},\\\cos(105^{\circ})=\frac{\sqrt{2}}{4}-\frac{\sqrt{6}}{4},\\\cos(105^{\circ})={\frac{-\sqrt{6}+\sqrt{2}}{4}}[/tex]
Since we want the value of [tex]6\cos 105^{\circ}[/tex], simply multiply this by 6 to get your final answer:
[tex]6\cdot {\frac{-\sqrt{6}+\sqrt{2}}{4}}=\frac{-3\sqrt{6}+3\sqrt{2}}{2}}=\boxed{\frac{3(\sqrt{2}-\sqrt{6})}{2}}[/tex]
Solution 2 (Combination of trig. identities):
Although less plausible, you may have the following memorized:
[tex]\sin 15^{\circ}=\cos75^{\circ}=\frac{\sqrt{6}-\sqrt{2}}{4},\\\sin 75^{\circ}=\cos15^{\circ}=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]
If so, we can use the following trig. identity:
[tex]\cos(\theta)=\sin(90^{\circ}-\theta)[/tex] (the cosine of angle theta is equal to the sine of the supplement of angle theta - the converse is also true)
Therefore,
[tex]\cos (105^{\circ})=\sin (90^{\circ}-105^{\circ})=\sin(-15^{\circ})[/tex]
Recall another trig. identity:
[tex]\sin(-\theta)=-\sin (\theta)[/tex] and therefore:
[tex]\sin (-15^{\circ})=-\sin (15^{\circ})[/tex]
Multiply by 6 to get:
[tex]6\cos (105^{\circ})=-6\sin (15^{\circ})=-6\cdot \frac{\sqrt{6}-\sqrt{2}}{4}=\boxed{-\frac{3(\sqrt{6}-\sqrt{2})}{2}}[/tex] (alternative final answer).
In golf, scores are often written in relationship to par, the average score for a round at a certain course. Write an integer to represent a score that is 7 under par.
Answer:
-7
Step-by-step explanation:
If it is 7 below (a key word, which you can connect to 'negative'), then you just write it as -7.
PLEASE HELP!!! WILL GIVE BRAINLIEST!!!!!!
Answer:
78.93 yan ats yung sagot hula ko
Answer:
it is 78.93 yun
hope this will help you
There is a high-speed rail track between London and Manchester.
The length of this track is 210 miles.
A train departs London at 11:20 and arrives in Manchester at 13:28
The train company claims
the average speed of this train is 104 miles per hour.
Is the average speed of this train 104 miles per hour?
(4)
Use the box below to show clearly how you get your answer.
Answer:
Step-by-step explanation:
this is the famous dirt formula, :P I made it up :D
D=rt ( notice it looks like Dirt , kinda, but it also means it dirt simple )
D= distance
r = rate ( think speed or how fast)
t = time ( in what ever units of time you want to use, seconds, minutes, hours )
13:28 - 11:20 = 128 minutes ( b/c the question is asking in MPH convert to hours) 2.4666667 hours
210 miles = r * 2.46666667
210 / 2.46666667 = r ( in MPH) ( does anyone else find it odd that they are saying miles in London instead of kilometers? :/ )
85.135 MPH = rate
so no, not even close to 104 MPH :/
Answer:
Average speed is 98 mph
Step-by-step explanation:
[tex]\frac{distance (miles)}{time (hours)}[/tex] = speed [tex]\frac{mile}{hours}[/tex] (miles per hour is a ratio)
The time is 2 hours and 8 minutes.
[tex]\frac{8}{60}[/tex] = .13333 ( 8 minutes / 60 minutes in a hour)
So time is 2.133333 hours .
Divide the distance 210 by the time 2.13333 and get the speed.
Its 98.437..
Round to 98 miles per hour.
If 2x^2 + 3x + 3 = Kx - K has real roots, find the possible values of k.
Answer:
Step-by-step explanation:
Dd
Which choice is equivalent to √10*√5
Answer:
5√2
Step-by-step explanation:
Given √10*√5
Using surd, the expression can be evaluated further as :
√10*√5 = √50
√50 can be expressed as :
√50 = √25*2 = √25 * √2
√25 = 5
Hence,
√50 = √25 * √2 = 5√2
Hence, √10*√5 = 5√2
Which formula can be used to describe the sequence?
O f(x + 1) = f(x)
O f(x + 1) = - f(x)
O f(x) = f(x + 1)
O f(x) = - 3 f(x + 1)
Answer:
f(x+1) = -3/4 × f(x)
Step-by-step explanation:
first of all, the sign of the numbers in the sequence is alternating. so, there must be a "-" involved.
that eliminates the first and third answer options.
and the absolute values of the numbers in the sequence are going down. |f(x+1)| < |f(x)|
that eliminates the fourth answer option, as this says that
|f(x)| < |f(x+1)|. and that is the opposite of how the actual sequence behaves.
Rewrite in simplest terms: (9x+5)-(-2x+10)(9x+5)−(−2x+10)
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { 18 {x}^{2} - 69x - 55}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] = (9x + 5) - ( - 2 x+ 10)(9x + 5) - ( - 2x + 10)[/tex]
[tex] = (9x + 5) + 2x (9x + 5) - 10(9x + 5) - ( - 2x + 10)[/tex]
[tex] = 9x + 5 + 18 {x}^{2} + 10 x- 90x - 50 + 2x - 10[/tex]
Collect the like terms.
[tex] = 18 {x}^{2} + (9x + 10x- 90x + 2x) + (5 - 50 - 10)[/tex]
[tex] = 18 {x}^{2} + (21x - 90x) +(5 - 60)[/tex]
[tex] = 18 {x}^{2} - 69x - 55[/tex]
[tex]\boxed{ Note:}[/tex][tex]\sf\pink{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
Suppose you just received a shipment of 14 televisions. Three of the televisions are defective. If two televisions are randomly selected , compute the probability that both televisions work. What is the probability at least one of the two televisions does not work?
Answer:
Probability of defective televisions : Now, If two televisions are randomly selected, then the probability that both televisions work. Hence, the probability that both televisions work is 0.5289 . Hence, the probability at least one of the two televisions does not work is 0.4711.
A fashion designer wants to know how many new dresses women buy each year. A sample of 650 women was taken to study their purchasing habits. Construct the 95% confidence interval for the mean number of dresses purchased each year if the sample mean was found to be 5.6. Assume that the population standard deviation is 1.3.
g At a certain gas station, 30% of all customers use the restroom. What is the probability that, out of the next 10 customers, (a) exactly 4 will use the restroom
Answer:
[tex]P(x=4) = 0.200[/tex]
Step-by-step explanation:
Given
[tex]n=10[/tex] --- selected customers
[tex]x = 4[/tex] --- those that are expected to use the restroom
[tex]p =30\% = 0.30[/tex] --- proportion that uses the restroom
Required
[tex]P(x = 4)[/tex]
The question illustrates binomial probability and the formula is:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n - x}[/tex]
So, we have:
[tex]P(x=4) = ^{10}C_4 * (0.30)^4 * (1 - 0.30)^{10 - 4}[/tex]
[tex]P(x=4) = ^{10}C_4 * (0.30)^4 * (0.70)^6[/tex]
[tex]P(x=4) = 210* (0.30)^4 * (0.70)^6[/tex]
[tex]P(x=4) = 0.200[/tex]
Eight more than one-half of a number is twenty-two. Find the number.
Answer:
Below.
Step-by-step explanation:
22-8 = 14x2 = 28.
A town has a current population of 4,000. The population increased 4 percent per year for the past four years, Emergency response professionals
make up 3 percent of the town's population.
Part A
Write a function that represents the population (p) of the town in terms of the number of years (1) for the last four years.
Answer:
p=c(1+r)^t so the population will be 4679.43424 or rounded to 4679
Step-by-step explanation:
p=c(1+r)^t
p=4,000(1+.04)^t
p=4,000(1.04)^t
p=4,000(1.04)^4
p=4679.43424
p= the population you are solving for
c= the initial amount of the population
(1+r)= the rate of change
t= the period of time
The exponential equation that represents the population of the town in terms of the number of years : [tex]p=4000 (1+0.4)^{t}[/tex]
What is an exponential equation?An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.
It is similar to the amount received after investing a certain amount compounded annually.
Given,
Initial population = 4000
Rate of increase = 4%
Let current population be p.
Let number of years passed be t.
The exponential equation will be: [tex]p=4000 (1+0.4)^{t}[/tex]
(The population of the town has grown exponentially. This means that:
Initial population = 4000
Population in year I = 4000 + 4% of 4000 = 4000(1 + 0.4)
Population in year II = 4000 + 4% of 4000(1 + 0.4) = 4000(1 + 0.4)(1+0.4)
and this goes on.)
Learn more about exponential equation here
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(3 points) Buchtal, a manufacturer of ceramic tiles, reports on average 3.1 job-related accidents per year. Accident categories include trip, fall, struck by equipment, transportation, and handling. The number of accidents is approximately Poisson. Please upload your work for all of the parts at the end. (0.5 pts.) a) What is the probability that more than one accident occurs per year
Answer:
0.8743 = 87.43% probability that more than one accident occurs per year
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Buchtal, a manufacturer of ceramic tiles, reports on average 3.1 job-related accidents per year.
This means that [tex]\mu = 3.1[/tex]
What is the probability that more than one accident occurs per year?
This is:
[tex]P(X > 1) = 1 - P(X \leq 1)[/tex]
In which
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
Then
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3.6}*(3.6)^{0}}{(0)!} = 0.0273[/tex]
[tex]P(X = 1) = \frac{e^{-3.6}*(3.6)^{1}}{(1)!} = 0.0984[/tex]
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0273 + 0.0984 = 0.1257[/tex]
[tex]P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1257 = 0.8743[/tex]
0.8743 = 87.43% probability that more than one accident occurs per year
