Answer:
[tex]\frac{dr}{dt} = 0.0535 ft/hr[/tex]
Step-by-step explanation:
Rate at which gas is escaping, dV/dt = 14 ft³/hr
Volume, V = 400 ft³
Volume of a sphere, [tex]V = \frac{4}{3} \pi r^{3}[/tex]................(1)
Differentiate both sides with respect to t
[tex]\frac{dV}{dt} = \frac{4}{3} \pi * 3r^{2}\frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt} =4\pi r^{2} \frac{dr}{dt}[/tex]........................................(2)
From equation (1)
[tex]400 = \frac{4}{3} \pi r^{3}\\\\ r = (\frac{1200}{4\pi } )^{1/3} \\\\r = 4.564 ft[/tex]
Substitute the value of r and dV/dt into equation (2)
[tex]14 =4\pi * 4.564^{2} \frac{dr}{dt}\\\\\frac{14}{261.79} = \frac{dr}{dt}\\\\\frac{dr}{dt} = 0.0535 ft/hr[/tex]
Find the midpoint of the line segment joining the points (-5, 2) and (3. -8).
Hey there! :)
Answer:
(-1, -3)
Step-by-step explanation:
Use the midpoint formula to derive the coordinates of the midpoint:
[tex](x_{m} ,y_{m} ) = (\frac{x_{1} +x_{2} }{2}, \frac{y_{1}+ y_{2} }{2} )[/tex]
Plug in the coordinates given:
[tex](\frac{-5+3 }{2}, \frac{2-8 }{2} )[/tex]
Simplify:
[tex](\frac{-2 }{2}, \frac{-6 }{2} )[/tex]
(-1, -3) are the coordinates of the midpoint.
Answer:
[tex]\boxed{Midpoint = (-1,-3)}[/tex]
Step-by-step explanation:
The coordinates are (-5,2) and (3,-8)
M(x,y) = [tex](\frac{x1+x2}{2} , \frac{y1+y2}{2} )[/tex]
M(x,y) = [tex](\frac{-5+3}{2} , \frac{2-8}{2} )[/tex]
M(x,y) = [tex](\frac{-2}{2} , \frac{-6}{2} )[/tex]
M(x,y) = (-1,-3)
A man is four times as old as his son. In 3 years, the father will be three times as old as the son. How old is each now?
The man is 27 years old and the son is 9 years old.
We can write the son's age as 'x', and therefore write the man's age as 4x. In 3 years, both their ages will increase by 3, so the son's age is now x + 3, and the man's age is 4x + 3.
We are told that the man is now 3 times older than his son, which means his current age, 4x + 3, is the same as 3 times the son's current age, which is x + 3.
Therefore we can write an equation:
4x + 3 = 3(x + 3)
4x + 3 = 3x + 9
- 3x
x + 3 = 9
- 3
x = 6
We can now substitute this in to find their current ages:
Son's age = x + 3 = 6 + 3 = 9
Man's age = 4x + 3 = 24 + 3 = 27
I hope this helps! Let me know if you have any questions :)
11/ 42 Marks
34%
ABC is a straight line and angle CBD = 116°
a) Work out the value of x.
C
+
B
b) P is a point on the minor arc AD.
Explain why angle APD = 116°
+
A
Р
Answer:
(a)x=128 degrees
(b)[tex]\angle APD\neq 116^\circ[/tex]
Step-by-step explanation:
[tex]\angle ABD+\angle CBD =180^\circ$ (Linear Postulate)\\\angle ABD+116^\circ =180^\circ\\\angle ABD=180^\circ-116^\circ\\\angle ABD=64^\circ[/tex]
(a) Now:
[tex]\angle AOD=2 \times \angle ABD$ (Angle at the centre is twice the angle at the circumference)\\x=2 \times 64^\circ\\x=128^\circ[/tex]
(b)
[tex]\angle APD=2 \times \angle ABD$ (Inscribed Angle Theorem)\\\angle APD=2 \times 64^\circ\\ \angle APD=128^\circ[/tex]
[tex]\angle APD\neq 116^\circ[/tex]
The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies: Number of Cars Arriving in a 10-Minute Interval Frequency 0 3 1 10 2 15 3 23 4 30 5 24 6 20 7 13 8 8 9 or more 4 150 Calculate mean and use Poisson probabilities. The expected frequency of exactly 3 cars arriving in a 10-minute interval is a. .1533. b. 26.145. c. .1743. d. 23.
Answer: c. 0.1743
Step-by-step explanation: Poisson Probability or Poisson Distribution is a discrete distribution that models the number of events ocurring in a given period of time.
The mean, or expected value, of the observed frequencies is:
E(X) = ∑xP(x)
E(X) = 0*3/150 + 1*(10/150) + 2*(15/150) + 3*(23/150) + 4*(30/150) + 5*(24/150) + 6*(20/150) + 7*(13/150) + 8*(8/150) + 9*(4/150)
E(X) = 4.399
The Poisson distribution is calculated by:
P(X = k) = [tex]\frac{mean^{k}.e^{-mean}}{k!}[/tex]
The question asks for the expected frequency of exactly 3 cars:
P(X = 3) = [tex]\frac{4.399^{3}.e^{-4.399}}{3!}[/tex]
P(X = 3) = [tex]\frac{4.399^{3}.e^{-4.399}}{3.2.1}[/tex]
P(X = 3) = 0.1743
The expected frequency of exactly 3 cars is 0.1743
identify which graphs are functions and which graphs are not.
Answer:
Step-by-step explanation:
We will apply the vertical line test in the given graphs to test them for a function.
Option (1) [First in top row]
If we draw a vertical line from any point, none other point of the graph passes through it.
Therefore, Graph (1) is a function.
Option (2) [2nd in the top row]
When we draw a vertical line through (2, 1), another point (2, -1) will pass through this line.
Therefore, Graph (2) is not a function.
Option (3) [1st in the second row]
In this option when a vertical line is drawn from (2, 1) two more points (2, 2) and (2, 3) pass through this line.
Therefore, graph (4) is not a function.
Option (4). [2nd in the 2nd row]
In this graph only one point lie on the vertical lines drawn.
Therefore, Graph (4) is a function.
Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?
Answer:
paper = $4 and stapler = $7
Step-by-step explanation:
let p represent paper and s represent stapler, then
3p + 4s = 40 → (1)
5p + 6s = 62 → (2)
Multiplying (1) by 5 and (2) by - 3 and adding will eliminate p
15p + 20s = 200 → (3)
- 15p - 18s = - 186 → (4)
Add (3) and (4) term by term to eliminate p
2s = 14 ( divide both sides by 2 )
s = 7
Substitute s = 7 into either of the 2 equations and evaluate for p
Substituting into (1)
3p + 4(7) = 40
3p + 28 = 40 ( subtract 28 from both sides )
3p = 12 ( divide both sides by 3 )
p = 4
Thus package of paper costs $4 and stapler costs $7
Write an expression involving integers for each statement a) moving 4 steps left, then moving 9 steps right b) on 3 separate occasions, Shari lost 2 pencils
Answer:
a) x-4+9
b) x-2
For part b, I am not 100% sure about my answer, but I am sure about part a.
www.g A bag contains 3 white counters, 10 black counters, and 4 green counters. What is the probability of drawing (a) a white counter or a green counter
Answer:
41.18% probability of drawing a white counter or a green counter
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
There are 3+10+4 = 17 counters.
Of those, 3+4 = 7 are white or green
7/17 = 0.4118
41.18% probability of drawing a white counter or a green counter
Find the slope of the function when x=4
y=
2x+1/x2
Select one:
a. 386
b. 0.56 X
C. -0.16
d. 1/4
e. -0.125
Answer:
Option C.
Step-by-step explanation:
The given function is
[tex]y=\dfrac{2x+1}{x^2}[/tex]
We need to find the slope of the function when x=4.
Differentiate the given function w.r.t. x.
[tex]\dfrac{dy}{dx}=\dfrac{x^2\dfrac{d}{dx}(2x+1)-(2x+1)\dfrac{d}{dx}x^2}{(x^2)^2}[/tex] (Using quotient rule)
[tex]\dfrac{dy}{dx}=\dfrac{x^2(2+0)-(2x+1)(2x)}{x^4}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{2x^2-4x^2-2x}{x^4}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{-2x^2-2x}{x^4}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{-2x(x+1)}{x^4}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{-2(x+1)}{x^3}[/tex]
Now substitute x=4 in the above equation.
[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-2(4+1)}{4^3}[/tex]
[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-2(5)}{64}[/tex]
[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-10}{64}[/tex]
[tex]\dfrac{dy}{dx}_{x=4}=-0.15625[/tex]
[tex]\dfrac{dy}{dx}_{x=4}\approx -0.16[/tex]
Therefore, the correct option is C.
Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle shown below 18 and 80
Answer:
82 units.
Step-by-step explanation:
The Pythagorean Theorem is a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the legs.
In this case, 18 and 80 are the legs.
18^2 + 80^2 = c^2
324 + 6,400 = c^2
6,724 = c^2
c^2 = 6,724
c^2 = 82^2
c = plus or minus 82
Since measurements cannot be negative, the length of the hypotenuse is 82 units.
Hope this helps!
Answer:
82 units indeed!
Step-by-step explanation:
c = [tex]\sqrt{ 18^{2} + 80^{2} }[/tex]
c = 82
Find the product.
(3b + 6at)(b - at)
Answer:
3bat + 3b² - 6a²t²
Step-by-step explanation:
First you have to expand it to get;
3b(b - at) + 6at(b - at)
Then you can now multiply.
3b² - 3bat + 6bat - 6at²
Group like terms
6bat - 3bat + 3b² -6at²
3bat + 3b² - 6a²t²
okay the answer is attached. i was the first to answer, but brainly decided to delete it >:(
Adding polynomials, whine one is correct?
Hey there! :)
Answer:
P = 48xy + 4 units.
Step-by-step explanation:
To find the perimeter of a square, the formula P = 4s (where 's' is the side-length):
Substitute in 12xy + 1 for s:
P = 4(12xy + 1)
Distribute the 4:
P = 4(12xy) + 4(1)
P = 48xy + 4 units.
Use ￢, →, ∧ and ∨ to express the following declarative sentences in propositional logic; in each case state what your respective propositional atoms p, q, etc. a) If interest rates go up, share prices go down. b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. c) Today it will rain or shine, but not both. d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. e) My sister wants a black and white cat.
Answer:
a) If interest rates go up, share prices go down : this will be assigned p→q
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r)
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q)
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r)
e) My sister wants a black and white cat. p∧q
Step-by-step explanation:
A statement is said to be propositionally logical if the statement that can be assigned either true or false.
∧and
∨or
¬not
→implies
a) If interest rates go up, share prices go down : this will be assigned p→q implies because the occurrence of event (share prices go down) depends on the possibility of the other event happening.
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r) : either of the two of the other events (i.e. he has sold his car or he has not paid his mortgage ) can only occur if the first event occur
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q) : either of the events can occur but not both i.e. they are mutually exclusive
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r) either of the two of the other events (i.e. they had a cup of coffee together or they took a walk in the park ) can only occur if the first event (Sam met Jane yesterday) occur
e) My sister wants a black and white cat. p∧q : both events can only occur together
Which linear inequality is represented by the graph?
HELPPPP!!!
Answer:
b
Step-by-step explanation:
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation?
there are 480 students in a class. the ratio of boys to girls is 1:3 how many students in the class are boys
Answer:
120
Step-by-step explanation:
480/(1+3)
480/4
= 120
1 × 120 : 3 × 120
120 : 360
Boys to girls are in the ratio 120:360.
There are 120 boys.
Evaluate
[tex]lim \: f(x) \: as \: x \: approaches \: 0[/tex]
knowing that
[tex] \frac{1}{2} - {x}^{2} \leqslant 1 - f(x) \leqslant \frac{1}{2} [/tex]
for all instances of x
Answer:
f(0) = 1/2
Step-by-step explanation:
At x=0, the inequality tells you ...
1/2 ≤ 1 -f(0) ≤ 1/2
That is, ...
1 - f(0) = 1/2
f(0) = 1/2
[tex]\boxed{\lim\limits_{x\to 0}{f(x)}=\dfrac{1}{2}}[/tex]
If (a+1) and (a-1)= 35 what is a?? Helpppppppppp
Answer:
There is no real number that can satisfy this equation
Step-by-step explanation:
a+1=35 and a-1=35 ⇒ a+1=a-1⇒ a-a = -1-1⇒ 0= -2 That's absurd so a has no real solutionPlease help! Which of the following statements about the image below is true??
Answer:
The second one is correct.
Step-by-step explanation:
SWX is 108 because it is supplementary with RWS which is 72 degrees. Then, you just minus 72 from 180 and that is 108.
Answer:
The answer is B. The measure of angle SW X is 108 degrees
Step-by-step explanation:
We know that angle RWS is 72 degrees and it's on the same line as SW X. Since a line is always 180 degrees we subtract 72 from 180 and get our answer.
A rectangle measures 18 cm by 3 cm what is its area
Answer:
54 cm²
Step-by-step explanation:
Area of a Rectangle Formula: A = lw
We are given 18 as l and 3 as w, so simply plug it into the formula:
A = 18(3)
A = 54
How do you write 49 in scientific notation? ____× 10^____
Answer:
4.9 × 10^1
hopefully this helped :3
Answer:
4.9 * 10 ^1
Step-by-step explanation:
We want one digit to the left of the decimal
49
4.9
We moved the decimal one place to the left
One is the exponent. Since we moved to the left the exponent is positive
4.9 * 10 ^1
What is 27 rounded to the nearest ten? Use the number line to find the answer.
A number line from 10 to 50. An arrow points to 27.
The number 27 when rounded to the nearest ten using the number line will give the number 30.
On the number line, the numbers are marked from 10 to 50.
So, the tens are 10, 20, 30, 40, and 50.
The number 27 has to be rounded to the nearest ten.
The one position will be 0.
Now, 27 lies in between the tens 20 and 30 on the number line.
Now, it is required to find which number is 27 closer to.
There are 7 units from 20 to 27.
But there are only 3 units far from 27 to 30.
So, 27 can be rounded to 30 to the nearest ten.
Learn more about Rounding Off here :
https://brainly.com/question/24234983
#SPJ6
10 + 6 ÷ 2 =
2(5) - 7 =
36 - (4 +8) ÷ 4 =
(2 x 5) -4 =
Complete the square to rewrite y = x2 - 6x + 16 in vertex form. Then state
whether the vertex is a maximum or minimum and give its coordinates.
Answer:
y = x² + 6x + 16
= (x² + 6x + 9) - 9 + 16
= (x + 3)² + 7 ← vertex form
Therefore, vertex is (-3, 7) and since the coefficient of (x + 3)² is positive the vertex is a minimum.
Answer:
minimum (3,7)
Step-by-step explanation:
While the Pareto distributions are continuous, they tend to be used to model discrete data in humanities and actuarial sciences. Moreover, with its roots in power functions, Pareto distributions may be used in the growing popularity of the studies of networks. The probability density function (PDF) for a Pareto distribution is
Answer:
Step-by-step explanation:
While the pareto distributions are continuous in nature, they are sometimes used to model discrete data in fields such as Social Sciences, Humanities, Geophysics, and Actuarial Sciences.
The Pareto Distribution is a power-law probability distribution used in studies of observable phenomena.
The probability density function (PDF) for a Pareto Distribution is:
Xn = 1
for various Alpha levels
Where Xn is the probability value of X
As Alpha tends to infinity, the pareto distribution tends to ¶ [X-Xn]
Where ¶ is the Dirac Delta function.
Simple linear equations
Check Whether the value given in the brackets is the root of the given equation or not (nessessary steps is needed)
a) 4x = -4 [x=-1]
b) 2(x-3) =-12 [x=3]
c) 8x - 4x = 24 [x = 1/2]
d) 9x - 4x = 24 [x=18]
Answer: Evaluate the Function, right?
Hello!
~~~~~~~~~~~~~~~~~~
A) 4x = -4 [x=-1] =
4x = -4 =
x = -1 = x = -1
( The steps : Substitute the given value into the function and evaluate.)
B) 2(x-3) =-12 [x=3] =
2 ( x - 3) = -12 = x = -3
x = 3 = x = 3
( The steps : Substitute the given value into the function and evaluate.)
C) 8x - 4x = 24 [x = 1/2] =
8x - 4x = 24 = x = 6
x = 1/2 = x = 1/2
( The steps : Substitute the given value into the function and evaluate.)
D) 9x - 4x = 24 [x=18] =
9x - 4x = 24 = x = 24/5
x = 18 = x = 18
( The steps : Substitute the given value into the function and evaluate.)
~~~~~~~~~~~~~~~~~~
Step-by-step explanation: All the steps are the same. Substitute the given value into the function and evaluate.
Hope this helped you!
Given that (0,0) is on the graph of f(x), find the
corresponding point for the function
f(x) – 5.
Answer:
(0, -5)
Step-by-step explanation:
You have (x, f(x)) = (0, 0) and you want (x, f(x) -5).
That would be ...
(x, f(x) -5) = (0, 0 -5) = (0, -5)
1. A circus elephant is being led up a 12-foot-long ramp to a trailer that is 4 feet above
the ground.
4ft
12 ft
Which equation could be used to find the angle between the ramp and the ground?
f(X)=3x-12 what is f(2)
Answer:
The answer is - 6Step-by-step explanation:
f(X)=3x-12
To find f(2) substitute the value in the bracket which is 2 into f(x)
That's
f(2) = 3(2) - 12
= 6 - 12
= - 6
Hope this helps you
Answer:
-6
Step-by-step explanation:
Please help me.What type of polygon would a peice of an icosahedron at a vertex create? Explain why.
Answer:
Regular Pentagon
Step-by-step explanation:
A regular icosahedron is a twenty-faced polyhedron, each face being an equiangular triangle. Each vertex is joined together by 5 faces, therefore the polygon formed at each vertex is a regular pentagon.
We can also figure out the number of faces at each vertex using Euler's formula
F+V=E+2
F=number of faces = 20
E=number of edges = number of triangular faces * edges/triangle /2
(since each edge is shared between two faces)
= 20*3/2
=30
Number of vertices
= E+2-F = 30+2-20 = 12
So number of edges meeting at each vertex
= 30 / (12/2) = 30/6 = 5
(12/2 because each edge joins two vertices).
See attached figure, courtesy of Wikipedia.