the intersection point is approximately (2.215421, 3.256684). For the first question, the initial value problem is given by the differential equation f'(u) = 5(cost - sinus) with the initial condition f(3xN) = 3.
To solve this problem, we can separate the variables and integrate both sides as follows:
f'(u) = 5(cosu - sinu)
∫ f'(u) du = ∫ 5(cosu - sinu) du
f(u) = 5sinu + 5cosu + C
Using the initial condition f(3xN) = 3, we can solve for the constant C:
f(3xN) = 5sin(3xN) + 5cos(3xN) + C = 3
C = 3 - 5sin(3xN) - 5cos(3xN)
Thus, the solution to the initial value problem is given by:
f(u) = 5sinu + 5cosu + 3 - 5sin(3xN) - 5cos(3xN)
For the second question, we are asked to find the intersection points of the two curves y = 16/* and y = x + 1 using Newton's method. To applyhttps://brainly.com/question/2228446 we need to find the function f(x) that represents the difference between the two curves:
f(x) = 16/x - (x + 1)
The intersection points correspond to the roots of f(x), which can be found using Newton's method:
x_{n+1} = x_n - f(x_n)/f'(x_n)
where x_n is the nth approximation of the root. We start with an initial guess of x_0 and iterate until we reach a desired level of accuracy. For example, if we start with x_0 = 1, the iterations are as follows:
x_1 = 1 - (16/1 - (1 + 1))/(16/1^2 + 1) = 2.5
x_2 = 2.5 - (16/2.5 - (2.5 + 1))/(16/2.5^2 + 1) = 2.267857
x_3 = 2.267857 - (16/2.267857 - (2.267857 + 1))/(16/2.267857^2 + 1) = 2.219208
x_4 = 2.219208 - (16/2.219208 - (2.219208 + 1))/(16/2.219208^2 + 1) = 2.215430
x_5 = 2.215430 - (16/2.215430 - (2.215430 + 1))/(16/2.215430^2 + 1) = 2.215421
Thus, the intersection point is approximately (2.215421, 3.256684).
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Melanie is making a piece of jewelry that is in the shape of a right triangle. The two shorter sides of the piece of jewelry are 4 mm and 3 mm. Find the perimeter of the piece of jewelry.
Therefore , the solution of the given problem of triangle comes out to be the jewellery's circumference is 12 mm.
What precisely is a triangle?If a polygon contains at least one more segment, it is a hexagon. It is a simple rectangle in shape. Anything like this can only be distinguished from a standard triangle form by edges A and B. Even if the edges are perfectly collinear, Euclidean geometry only creates a portion of the cube. A triangle is made up of a quadrilateral and three angles.
Here,
The lengths of all three sides must be added up in order to determine the jewellery's perimeter.
=> c²= a² + b²
where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.
=> A = 3mm, and B = 4mm.
Therefore, we can determine the length of the hypotenuse using the Pythagorean theorem:
=> c² = a²+ b²
=> c² = 3² + 4²
=> c² = 9 + 16
=> c² = 25
=> c = √25)
=> c = 5 mm
As a result, the hypotenuse is 5 mm long.
We total the lengths of all three sides to determine the jewellery's perimeter:
=> perimeter = 4mm, 3mm, and 5mm.
=> 12 mm is the diameter.
Therefore, the jewellery's circumference is 12 mm.
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LQ - 10.4 Areas in Polar Coordinates Show all work and use proper notation for full credit. Find the area of the region enclosed by one loop of the curve. • Include a sketch of the entire curve. r = 4cos (20) LQ - 10.3 Polar Coordinates Show all work and use proper notation for full credit. Find the slope of the tangent line to the given polar curve at the point specified by the value of e. TT r = 1-2sine, =
The area of the region enclosed by one loop of the curve r = 4cos(θ) is 4 square units. The slope of the tangent line to the polar curve r=1 - 2sin(θ) at θ = π/4 is 2 + √2.
Area of region enclosed by one loop of the curve r = 4cos(2θ)
The curve r = 4cos(2θ) has two loops, and we need to find the area of one loop, which is from θ = 0 to θ = π/4.
To find the area, we use the formula for the area enclosed by a polar curve
A = (1/2) ∫[a,b] r^2 dθ
where r is the polar function, and a and b are the angles of the region we want to find the area for.
So, the area of one loop is
A = (1/2) ∫[0,π/4] (4cos(2θ))^2 dθ
= 8 ∫[0,π/4] cos^2(2θ) dθ
Using the identity cos(2θ) = (cos^2θ - sin^2θ), we can rewrite the integrand as
cos^2(2θ) = (cos^2θ - sin^2θ)^2
= cos^4θ - 2cos^2θsin^2θ + sin^4θ
= (1/2) (1 + cos(4θ)) - (1/2) sin^2(2θ)
So, the integral becomes
A = 8 ∫[0,π/4] [(1/2) (1 + cos(4θ)) - (1/2) sin^2(2θ)] dθ
= 4 [θ/2 + (1/8)sin(4θ) - (1/4)θ - (1/8)sin(2θ)]|[0,π/4]
= 1 + (2/π)
Therefore, the area of one loop of the curve r = 4cos(2θ) is 1 + (2/π).
Slope of tangent line to the polar curve r = 1-2sinθ at θ = π/4
To find the slope of the tangent line, we need to take the derivative of the polar function with respect to θ:
dr/dθ = -2cosθ
Then, we can use the formula for the slope of the tangent line in polar coordinates
dy/dx = (dy/dθ) / (dx/dθ) = (r sinθ) / (r cosθ) = tanθ + r dθ/dθ
At the point specified by θ = π/4, we have
r = 1 - 2sin(π/4) = 1 - √2/2 = (2 - √2)/2
dθ/dθ = 1
So, the slope of the tangent line is
dy/dx = tan(π/4) + r dθ/dθ
= 1 + (2 - √2)/2
= (4 + 2√2)/2
= 2 + √2
Therefore, the slope of the tangent line to the polar curve r = 1-2sinθ at θ = π/4 is 2 + √2.
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As part of an exercise regimen, the probability of a person running outside is 0.45, the probability of a person joining a gym is 0.40, and the probability of a person both running outside and joining a gym is 0.25. what is the probability that a person either runs or joins a gym?
The probability that a person either runs outside or joins a gym is 0.60 or 60%.
To find the probability that a person either runs outside or joins a gym, you can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
where A is the event of running outside, B is the event of joining a gym, and "and" represents the intersection of both events.
Given:
P(running outside) = 0.45
P(joining a gym) = 0.40
P(both running outside and joining a gym) = 0.25
Plug these values into the formula:
P(either runs or joins a gym) = 0.45 + 0.40 - 0.25
Calculate the result:
P(either runs or joins a gym) = 0.60
Therefore, the 60% of person either runs outside or joins a gym
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4 Gabriela is building a wooden box with a rectangular base that is 18 in. By 15 in.
and is 15 in. Tall.
Part A
If she wants an open box without a top, how much wood will Gabriela use?
Strow your work
Gabriela will use 1620 square inches of wood to build the open box.
The amount of wood Gabriela will use depends on the surface area of the box, which is the sum of the areas of its six faces. Since the box is open on top, it will have five faces: four sides and a bottom.
The area of the bottom is the area of a rectangle with length 18 in. and width 15 in., which is:
Area of bottom = length x width = 18 in. x 15 in. = 270 in²
The area of each side is the product of the height and the length of the corresponding base, which is:
Area of each side = height x length = 15 in. x 18 in. = 270 in²
So the total surface area of the box is:
Total surface area = 2 x (Area of bottom) + 4 x (Area of each side)
= 2 x 270 in² + 4 x 270 in²
= 1620 in²
Therefore, Gabriela will use 1620 square inches of wood to build the open box.
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Figure anywhere on the grid on the right.
The figure after changing the scale of the grid is added as an attachment
Drawing the figure after changing the scale of the gridFrom the question, we have the following parameters that can be used in our computation:
Old scale: 1 unit = 4 ft
New scale: 1 unit = 8 ft
Using the above as a guide, we have the following:
Scale = Old scale/New Scale
Substitute the known values in the above equation, so, we have the following representation
Scale: (1 unit = 4 ft)/(1 unit = 8 ft)
Evaluate
Scale: 1/2
This means that the figure on the new grid will be half the side lengths of the old grid
Next, we draw the figure
See attachment for the new figure
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See image for the work
The number of horizontal rails for 10 sections is
60The rule for the post is to multiply the number of section by 3
The rule for the rail is to multiply the post by 2
How to find the rulesThe rules is calculated using the unit value and comparing with other values
the rule for the number of post
1 section requires 3 posts hence multiplication by 3, comparing shows that multiplying by 3 gives the number of post
the rule for the number of rails
1 section requires 6 rails hence multiplication by 6, comparing shows that multiplying each section by 6 gives the correponding number of rails
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11. a bird makes a dive off a cliff to catch a fish in a lake. the path of the dive follows a
parabolic curve of the given function f(x) = (x-7)2 - 1 where f(x) represents the height of
the bird in meters, and x represents the time in seconds. how far was the fish from the bird?
The fish has located a horizontal distance of 7 meters away from the cliff.
How to find the distance between the bird and the fish?
To find the distance between the bird and the fish, we need to find the horizontal distance traveled by the bird during the dive. We can do this by finding the x-coordinate of the vertex of the parabolic curve, which represents the highest point of the dive.
The vertex of the parabolic curve of the given function f(x) = (x-7)^2 - 1 is at the point (7, -1). This means that the highest point of the bird's dive is reached at 7 seconds, and the bird is at a height of -1 meters at this point.
To find the distance traveled by the bird during the dive, we need to find the horizontal distance between the bird's starting point (the cliff) and the highest point of the dive (the vertex). The distance is given by the horizontal coordinate of the vertex, which is 7 seconds.
Therefore, the fish has located a horizontal distance of 7 meters away from the cliff, assuming that the bird started the dive from the edge of the cliff.
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Which statement correctly compares the values of 2s in 43,290 and 32,865?
A. 20 is 1 times the value of 200.
B. 200 is 1/20 the value of 2,000.
C. 200 is 10 times the value of 2,000.
Answer:
Step-by-step explanation:
The value of 2s in 43,290 is 2,000, while the value of 2s in 32,865 is 20.
B. 200 is 1/20 the value of 2,000.
This statement is correct, as 200 is 1/10 of 2,000, and there are two 0s in the value of 2s in 43,290 compared to one 0 in the value of 2s in 32,865.
Solve the following quadratic function by utilizing the square root method. Y=xsquared minus nine
The solution of the quadratic equation is y = (x + 3)(x - 3).
What is the solution of the quadratic equation?The solution of the quadratic equation is calculated by applying difference of two squares as shown below;
y = x² - 9
y = x² - 3²
the difference of two square of x² - 3² = (x + 3)(x - 3)
The solution of the quadratic equation is calculated as;
y = (x + 3)(x - 3)
Thus, solution of the quadratic equation has been determined using square root method.
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Identify the constant of proportionality in the situation
8. A plane travels 462.4 miles in 34 minutes.
Answer:
13.6 miles/minute
Step-by-step explanation:
We Know
A plane travels 462.4 miles in 34 minutes.
Identify the constant of proportionality in the situation..
We Take
462.4 / 34 = 13.6 miles/minute
So, the answer is 13.6 miles/minute
PLEASE ANSWER!!! FOR BRAINLY!!! ASAP!!
A system of linear equations is shown on the graph.
The graph shows a line that passes through negative 10 comma 10, negative 5 comma 9, and 0 comma 8. The graph also shows another line that passes through negative 8 comma 12, negative 5 comma 9, and 0 comma 4.
What is the solution to the system of equations?
A There are infinitely many solutions.
B There is no solution.
C There is one unique solution (−5, 9).
D There is one unique solution (0, 8).
Answer:
(-1/5)x + 8 = -x + 4
(4/5)x + 8 = 4
(4/5)x = -4
x = -5, so y = 9
C. There is one unique solution (-5, 9).
The arrow on this spinner is equally likely to land on each section. the arrow is spun 72 times. how many times do you expect the arrow to land on 4?
we know that the spinner has an equal chance of landing on each section. Since there are a total of six sections on the spinner, we can assume that the probability of the arrow landing on any one section is 1/6 or approximately 0.1667.
Now, if the arrow is spun 72 times, we can use this probability to calculate the expected number of times the arrow will land on 4. To do this, we simply multiply the probability by the number of spins, as follows:
Expected number of times arrow lands on 4 = Probability of arrow landing on 4 x Number of spins
Expected number of times arrow lands on 4 = 0.1667 x 72
Expected number of times arrow lands on 4 = 12
So, we can expect the arrow to land on 4 approximately 12 times out of 72 spins. Of course, this is just an expected value, and the actual number of times the arrow lands on 4 may vary from this value due to random chance.
In summary, if we assume that the arrow on the spinner is equally likely to land on each section, and it is spun 72 times, we can expect the arrow to land on 4 approximately 12 times based on probability calculations.
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Given the system of inequalities: 4x – 5y < 1 one-halfy – x < 3 which shows the given inequalities in slope-intercept form? y < four-fifthsx – one-fifth y < 2x 6 y > four-fifthsx – one-fifths y < 2x 6 y > negative four-fifthsx one-fifth y > 2x 6
y < four-fifthsx - one-fifth
y < 2x + 6
How to express the given inequalities in slope-intercept form?The given system of inequalities can be represented in slope-intercept form as follows:
y < (4/5)x - 1/5
y < 2x + 6
To convert the given inequalities into slope-intercept form, we rearrange each equation to solve for y
In the first inequality, we add 5y to both sides and then divide by 4 to isolate y. This gives us:
4x - 5y < 1
-5y < -4x + 1
y > (4/5)x - 1/5
In the second inequality, we add x to both sides and then divide by -1/2 to isolate y. This gives us:
1/2y - x < 3
1/2y < x + 3
y > 2x + 6
Therefore, the given inequalities in slope-intercept form are:
y < (4/5)x - 1/5
y > 2x + 6
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at a local farmers market a farmer pays $10 to rent a stall and $7 for every hour he stays there. if he pays $45 on saturday how many hours did he stay at the market
Answer: The answer is 5.
Step-by-step explanation:
You first set up the equation
10 + 7x = 45
You must put x because you don't know the number of hours he stays
You then subtract 10 from both sides of the numbers 10 and 45
That'll get you 7x = 35
To find out what x is you divide both sides by 7
7x divided by 7 is x
35 divided by 7 is 5
X = 5
PLEASE HELP ME ASSAP!!!!!!!!!
The slope of UF is 1/6
What is a slope of a line?The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
The slope is given = change in point on y axis/ change in point on x axis
slope = y2-y1/x2-x1
The cordinate of F = (-2,-3) and U ( 4, -2)
y1 = -3 and y2 = -2
x1 = -2 and x2 = 4
slope = -2-(-3)/4-(-2)
= -2+3/(4+2)
= 1/6
therefore the slope of UF is 1/6
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Will any ramp with one angle of 4. 8 degrees have a slope ratio of 1 : 12?
Yes, any ramp with an angle of 4.8 degrees will have a slope ratio of 1:12.
The slope ratio is the ratio of the vertical rise to the horizontal run of the ramp, and it is equivalent to the tangent of the angle of inclination of the ramp.
The tangent of 4.8 degrees is approximately 0.0084, which means that for every 1 unit of vertical rise, there is 0.0084 units of horizontal run. To convert this to a ratio, we can multiply both sides by 100 to get:
1 unit of rise : 100 x 0.0084 = 0.84 units of run
Simplifying this ratio by dividing both sides by 0.84, we get:
1 unit of rise : 1.19 units of run
which is equivalent to a slope ratio of 1:12 (since 12 = 1/0.084). Therefore, any ramp with an angle of 4.8 degrees will have a slope ratio of 1:12.
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Which of the following combinations of side lengths would NOT form a triangle with vertices X, Y, and Z?
A.
XY = 7 mm , YZ = 14 mm , XZ = 25 mm
B.
XY = 11 mm , YZ = 18 mm , XZ = 21 mm
C.
XY = 11 mm , YZ = 14 mm , XZ = 21 mm
D.
XY = 7 mm , YZ = 14 mm , XZ = 17 mm
The combination of side lengths that would not form a triangle is C.XY = 11 mm, YZ = 14 mm, XZ = 21 mm.
We shall use the triangle inequality theorem to determine if a set of side lengths can form a triangle.
What is the triangle inequality theorem?The triangle inequality theorem says that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
We shall calculate each of the options:
For option A:
XY + YZ = 7 mm + 14 mm = 21 mm which is < XZ = 25 mm.
Therefore, option A does form a triangle.
For option B:
XY + YZ = 11 mm + 18 mm = 29 mm, which is > XZ = 21 mm.
YZ + XZ = 18 mm + 21 mm = 39 mm, which is > XY = 11 mm.
XY + XZ = 11 mm + 21 mm = 32 mm, which is > YZ = 18 mm.
Therefore, option B does form a triangle.
For option C:
XY + YZ = 11 mm + 14 mm = 25 mm, and is > XZ = 21 mm.
Therefore, option C does not form a triangle.
For option D:
XY + YZ = 7 mm + 14 mm = 21 mm, which is > XZ = 17 mm.
YZ + XZ = 14 mm + 17 mm = 31 mm, which is > XY = 7 mm.
XY + XZ = 7 mm + 17 mm = 24 mm, which is > YZ = 14 mm.
Therefore, option D does form a triangle.
Therefore, the combination of side lengths that would not form a triangle is XY = 11 mm, YZ = 14 mm, XZ = 21 mm.
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jack draw a number line on his paper jack drew a new point 45% of the distance from e to point j. between which two letters does the new point lie?
The two letters in which the new point lie include the following: C. between G and H.
What is a number line?In Geometry, a number line simply refers to a type of graph that is composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.
This ultimately implies that, all number lines would primarily increase in numerical value (number) towards the right from zero (0) and decrease in numerical value (number) towards the left from zero (0).
From the number line shown in the image attached below, we can logically deduce the following point:
|J - E| = 45% of x
|J - E| = 0.45x
|J - E| = GH
In conclusion, 45% is almost half way or 50% between E and J, which makes the distance between the two letters G and H, the new point.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
A cone has a radius of 3 inches and a slant height of 12 inches.
What is the exact surface area of a similar cone whose radius is 9 inches?
The surface area of the similar cone is 415.8 in²
What is surface area of a cone?A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex.
The surface area of a cone is expressed as;
SA = πr( r+l) where r is the radius and l is the slant height.
The slant height of the original cone =
l= √h²+r²
l = √12²+3²
l = √144+9
l = √153
l = 12.4 in
SA= 3π( 3+12.4)
SA = 3 × 15.4
SA = 46.2 in²
The surface area of similar cone with radius 9 inches is calculated by;
(3/9)² = 46.2/x
= 9/81 = 46.2/x
x = 46.2 × 81/9
x = 415.8in²
Therefore the surface area of the similar cone is 415.8 in³
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A family camping in a national forest builds a temporary shelter with a
tarp and a 4-foot pole. the bottom of the pole is even with the ground, and one corner
is staked 5 feet from the bottom of the pole. what is the slope of the tarp from that
corner to the top of the pole?
A family camping in a national forest used a 4-foot pole and a tarp to build a temporary shelter. One corner of the tarp was staked 5 feet from the bottom of the pole. The slope of the tarp from that corner to the top of the pole is 0.8 or 4/5.
We can draw a right triangle with the pole being the height, the distance from the pole to the stake being the base, and the slope of the tarp being the hypotenuse. The hypotenuse is the longest side of the triangle and is opposite to the right angle.
Using the Pythagorean theorem, we can find the length of the hypotenuse
hypotenuse² = height² + base²
hypotenuse² = 4² + 5²
hypotenuse² = 41
hypotenuse = √(41)
Therefore, the slope of the tarp is the ratio of the height to the base, which is
slope = height / base = 4 / 5 = 0.8
So the slope of the tarp from that corner to the top of the pole is 0.8 or 4/5.
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Find the side x, giving answer to 1 decimal place
Answer:
Set your calculator to degree mode.
Using the Law of Sines:
7/sin(40°) = x/sin(81°)
x = 7sin(81°)/sin(40°) = 10.8
Answer:
10.8=x
Step-by-step explanation:
Using the Law of Sines, we can put together the fact that
[tex]\frac{sin A}{a} =\frac{sinB}{b}[/tex]
Substitute our given values from the triangle:
[tex]\frac{sin 81}{x} =\frac{sin40}{7}[/tex]
Turn the sines into a decimal:
[tex]\frac{0.9876}{x} =\frac{0.6427}{7}\\[/tex]
cross multiply using butterfly method
0.988·7=0.643x
solve for x
6.916=0.643x
divide both sides by 0.643
10.8=x (round to nearest tenth)
Hope this helps! :)
Assume the base is 2.
a = 5
b = 4
c= 0
Therefore, the equation for graph C is Y = a ^b + c
Y = 5 ^4 + 0
What is a graph?A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Graphs are a popular tool for graphically illuminating data relationships.
A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.
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During the first year with a company, Finley was paid an annual salary of $56,000, with a 6% raise for each following year. Which equation represents Finley's annual salary, f (n), during the nth year?
f (n) = 56,000(0.94n)
f (n) = 56,000(1.06n)
f (n) = 56,000(0.06n – 1)
f (n) = 56,000(1.06n – 1)
The correct equation that represents Finley's annual salary, f(n), during the nth year is: [tex]f(n) = 56,000(1.06)^(n-1)[/tex] Thus, option D is correct.
What is an equation?
Finley's annual salary increases by 6% each year. This means that the salary for the second year is 6% more than the salary for the first year, the salary for the third year is 6% more than the salary for the second year, and so on.
To find an equation for Finley's annual salary during the nth year, we can use the initial salary of $[tex]56,000[/tex] and the fact that the salary increases by 6% each year. One way to write this equation is:
[tex]f(n) = 56,000(1.06)^(n-1)[/tex]
Here, the expression (1.06)^(n-1) represents the 6% increase in salary each year, starting from the second year (hence the (n-1) exponent). Multiplying this by the initial salary of $56,000 gives the salary for the nth year.
Therefore, the correct equation that represents Finley's annual salary, f(n), during the nth year is:[tex]f(n) = 56,000(1.06)^(n-1)[/tex]
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A small barbershop, operated by a single barber, has room for at most two customers. potential customers arrive at a poisson rate of three per hour, and the successive service times are independent exponential random variables with mean 1 4 hour. (a) what is the average number of customers in the shop
The average number of customers in the shop is 7.5
How we find the average number of customers in the shop?The average number of customers in the shop can be calculated using the M/M/2 queuing model. In this model, we assume that the arrivals follow a Poisson distribution, and the service times follow an exponential distribution.
The subscript "2" in M/M/2 refers to the fact that there are two servers or service channels available.
Using Little's Law, the average number of customers in a stable system is equal to the product of the arrival rate and the average time spent in the system.
Thus, to calculate the average number of customers in the shop, we need to find the average time spent in the system.
The average time spent in the system can be calculated as the sum of the average time spent waiting in the queue and the average time spent being served. Using the M/M/2 queuing model,
the average time spent waiting in the queue can be calculated as [tex](λ^2)/(2μ(μ-λ))[/tex], where λ is the arrival rate and μ is the service rate. In this case, λ=3 and μ=1/2 since there is one barber who can serve one customer at a time.
Thus, the average time spent waiting in the queue is [tex](3^2)/(21/2(1/2-3))[/tex] = 9/4 hours. The average time spent being served is the mean service time, which is 1/4 hour. Therefore, the average time spent in the system is 9/4 + 1/4 = 5/2 hours.
Finally, using Little's Law, the average number of customers in the shop is λ times the average time spent in the system, which is 3*(5/2) = 15/2 or 7.5 customers.
However, since the shop can only accommodate at most two customers at a time, the actual number of customers in the shop would be either one or two.
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Help I don't know what I did wrong.
[tex]4\sqrt{125} -2\sqrt{243} -3\sqrt{20}+5\sqrt{27}[/tex]
ASAP PLEASE HELP!!
I’ll give brianest
Given that the length of arc DC is 9. 77 inches and the radius of the circle is 8 inches.
to the nearest degree, what is the mZDPC?
The mZDPC is approximately 15 degrees.
How we find the mZDPC?We know that the length of an arc of a circle is given by the formula:
length of arc = (central angle / 360°) × 2πr
where r is the radius of the circle.
In this case, the length of arc DC is 9.77 inches and the radius of the circle is 8 inches. Let's use the above formula to find the central angle mZDPC:
9.77 = (mZDPC / 360°) × 2π(8)
Simplifying this equation, we get:
mZDPC = (9.77 / (2π(8) / 360°))
mZDPC = (9.77 / 0.670206) degrees
mZDPC ≈ 14.58 degrees
Rounding to the nearest degree, we get:
mZDPC ≈ 15 degrees
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The human gestation times have a mean of about 266 days, with a standard deviation of about 10 days. Suppose we took the average
gestation times for a sample of 100 women.
days
Where would the center of the histogram be?
What would the standard deviation of that histogram?
My sample shows a mean of 264. 8 days. What is my z-score?
days (Round to the thousandth place)
My sample shows a mean of 264. 8 days. What is my z-score?
(Round to the tenth place)
The z-score is -1.2, rounded to the tenths place.
The center of the histogram would be around the population mean of 266 days.
The standard deviation of the histogram would be the standard error of the mean, which is the standard deviation of the population divided by the square root of the sample size. Thus, the standard deviation of the histogram would be 10 / sqrt(100) = 1 day.
To calculate the z-score for a sample mean of 264.8 days, we can use the formula:
z = (sample mean - population mean) / (standard deviation / sqrt(sample size))
Substituting the given values, we get:
z = (264.8 - 266) / (10 / sqrt(100)) = -1.2
Therefore, the z-score is -1.2, rounded to the tenths place.
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Victoria will deposit $2000 in an account that earns 5% simple interest every year. Her friend Corbin will deposit $1800 in an account that earns 9% interest compounded annually. The deposits are made on the same day, and no additional money will be deposited or withdrawn from the accounts. Which statement about the balances of Victoria and Corbin's accounts at the end of 3 years is true?
Corbin's account will have a higher balance than Victoria's account at the end of 3 years" is true.
How to calculate account balance at the end of 3 years?To calculate the balance at the end of 3 years, we can use the simple interest formula for Victoria's account and the compound interest formula for Corbin's account.
For Victoria's account:
Simple interest = P * r * t
= 2000 * 0.05 * 3
= $300
Balance after 3 years = P + Simple interest
= 2000 + 300
= $2300
For Corbin's account:
Balance after 3 years = [tex]P * (1 + r)^t[/tex]
= 1800 * (1 + 0.09)³
= $2401.40
Therefore, the statement "Corbin's account will have a higher balance than Victoria's account at the end of 3 years" is true.
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How do you do this problem?
Knowing that tan(x) = 3/5 and using a trigonometric identity, we will get that:
tan(2x) = 1.875
How to find the tangent of 2x?There is a trigonometric identity we can use for this, we know that:
[tex]tan(2x) = \frac{2tan(x)}{1 - tan^2(x)}[/tex]
So we only need to knos tan(x), which we already know that is equal to 3/5, then we can replace it in the formula above to get:
[tex]tan(2x) = \frac{2*3/5}{1 - (3/5)^2}\\\\tan(2x) = \frac{6/5}{1 - 9/25} \\tan(2x) = 1.875[/tex]
That is the value of the tangent of 2x.
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A culture of bacteria has an initial population of 65000 bacteria and doubles every 2
hours. Using the formula Pt = Po 2a, where Pt is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 13 hours, to the nearest whole number?
.
The population of bacteria in the culture after 13 hours is approximately 1,656,320.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
We have the initial population, Po = 65000, and the doubling time, d = 2 hours. To find the population after 13 hours, we need to use the formula:
[tex]Pt = Po * 2^{(t/d)[/tex]
where Pt is the population after t hours, Po is the initial population, t is the time in hours, and d is the doubling time.
Substituting the given values, we get:
Pt = 65000 x [tex]2^{(13/2)[/tex]
Pt ≈ 1,656,320
Rounding this to the nearest whole number, we get:
The population of bacteria in the culture after 13 hours is approximately 1,656,320.
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