(MRH CH03-B_6018) You are looking at web logs of users who click on your website. You see these coming in with an average rate of 5 unique users per minute. Each user clicks once then goes away. You want to figure out the probability that there will be more than 300 or users over the next hour. This can best be modeled by
O A binomial random variable with the chance of 5 successes out of n=10 trials, so p = 5/10 = 0.5
O A Poisson random variable with a mean arrival rate lambda = 5 users/minute 60 minutes/hour = 300 users per hour
O An exponentially distributed random variable with a mean arrival rate of 300 / 5 = 60 minutes per user
O A normally distributed random variable with mean 300 and standard deviation 60
O None of these

The area of the rectangle is 17 square units.

The area of a rectangle is the product between the two dimensions (length and width) of the rectangle.

Here we know that the vertices are:

A(-1, 9), B(0, 9), C(0, -8), D(-1, -8)

We can define the length as the side AB, which has a lenght:

L = (-1, 9) - (0, 9) = (-1 - 0, 9 - 9) = (-1, 0) ----> 1 unit.

And the width as BC, which has a length:

L = (0, 9) - (0, -8) = (0 - 0, 9 + 8) = (0, 17) ---> 17 units.

Then the area is:

A = (1 unit)*(17 units) = 17 square units.

Learn more about area at

https://brainly.com/question/24487155

#SPJ1

Answer:

QR = 15

Step-by-step explanation:

The product of the length of the secant segment and its external part equals the square of the length of the tangent segment.

(QR+5) *5 = 10^2

(QR+5) *5 = 100

Divide each side by 5.

(QR+5) *5/5 = 100/5

(QR+5)  = 20

Subtract 5 from each side.

QR = 20-5

QR = 15

Answer:

0, -7 or Slope is Undefined

Step-by-step explanation:

y2 - y1 / x2 - x1

(x2 - y2) (x1 - y1)

The system of equations that models the given scenario is t + u = 9 and 10t + u = 10u + t - 9.

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

The answer would be "t + u = 9 and 10t + u = 10u + t - 9".

This can be found if you replaced t with 4 and u with 5.

Adding the 2 digits would give you 9.

Use the formula "10t + u = 10u + t - 9".

Replace t and u with 4 and 5 then simplify. 10*4 + 5 = 10*5 + 4 - 9. Simplifying you'd get 45 = 54 - 9 or 45 = 45 which makes the statement true.

Thus making "t + u = 9 and 10t + u = 10u + t - 9" the answer.

To learn more about the equation from the given link

https://brainly.com/question/28218072

#SPJ4

The identities are represented as;

sin θ = 4/5

tan θ = 4/3

cos θ = 3/5

sec θ = 5/3

cosec θ = 5/4

cot θ = 3/4

To determine the values of the identities, we need to know that there are six trigonometric identities listed thus;

From the information given, we have that;

The opposite side of the triangle is 4

The adjacent side is 3

Using the Pythagorean theorem, we have that;

x² = 16 + 9

x = √25

x = 5

For the sine identity, we have;

sin θ = 4/5

For the tangent identity;

tan θ = 4/3

For the cosine identity;

cos θ = 3/5

For the secant identity;

sec θ = 5/3

For the cosecant identity;

cosec θ = 5/4

For the cotangent identity;

cot θ = 3/4

Learn more about trigonometric identities at: https://brainly.com/question/22591162

#SPJ1

Answer:

(15 1/2 ) divided by 2/5= 38 3/4 miles per hour

Answer:

......

Step-by-step explanation:............

The average value of both f(x) and g(x) on 0≤x≤2 is 1/4. The average value of (f.g) on 0≤x≤2 is 0 and the statement avg(f) . avg(g) = avg(f . g) is false.

avg value of a function = 1/(b - a) ∫f(x) with limts a and b. Here a and b are the constraints under which the average has to be calculated.

a)

Hence average value of f(x) on 0≤x≤2

= 1/2 ∫f(x)  with 0 and 2 as intervals

Since integration is basically the area under the curve we get

avg of f(x) = 1/2[area under curve from 0 to 1 + Area under the curve from 1 to 2]

Since from 0 to 1, the figure is a triangle and beyond that a straight line we get

1/2[1/2 X 1 X 1 + 0]

= 1/4 sq units

b)

Similarly, the average value of g(x) on 0 ≤ x ≤ 2

1/2[area from 0 to 1 + area from 1 to 2]

= 1/2[0 + 1/2]

= 1/4 sq units

c) here we need to find the average of f(x) . g(x)

Here we see that f(x) is 0 from x = 1 to x = 1 while g(x) id 0 from x = 0 from x = 1

Hence we see that on multiplying the functions, the resultant has to be a 0 function.

Hence its average value will be 0.

d)

Average(f) . Average(g) = 1/4 X 1/4

= 1/16

Average of (f.g) = 0

Hence the statement is false

To learn more about the average function visit

https://brainly.com/question/14402983

#SPJ4

Complete Question

The figure attached to the left is a graph of f(x), and below to the right is g(x).

The figure below to the left is a graph of f(x), a

(a) What is the average value of f(x) on 0≤x≤2? avg value = __________

(b) What is the average value of g(x) on 0≤x≤2? avg value = __________

(c) What is the average value of f(x) . g(x) on 0≤x≤2? avg value = _________

(d) Is the following statement true?

Average(f) . Average(g)=Average(f.g)

A. Yes

B. No

When the radius of the ripple is 3 feet, the area enclosed by the ripple is increasing at a rate of approximately 50.92 square feet per second.

To understand how the area of the ripple changes over time, let's start with the formula for the area of a circle:

A = πr²

where A is the area and r is the radius of the circle. Since the radius of the ripple is increasing at a constant rate of 2.7 ft/s, we can use the chain rule of differentiation to find the rate of change of the area with respect to time (t):

dA/dt = dA/dr x dr/dt

where dA/dt is the rate of change of the area, dA/dr is the derivative of the area with respect to the radius (which is 2πr), and dr/dt is the rate of change of the radius (which is given as 2.7 ft/s).

Substituting these values into the equation, we get:

dA/dt = 2πr x 2.7

Now, we can plug in the given value of the radius (r = 3 ft) to find the rate of change of the area at that point in time:

dA/dt = 2π(3) x 2.7

= 16.2π

≈ 50.92 ft²/s

To know more about area here

https://brainly.com/question/14994710

#SPJ4

Let's represent the speed of the plane in still air as "p" and the speed of the wind as "w".

When the plane is traveling with the wind, its speed is (p + w) and against the wind, its speed is (p - w).

Given that it travels d1 miles with the wind in t hours and d2 miles against the wind in the same time, we can form the following equations:

d1 = t(p + w)
d2 = t(p - w)

Now, we need to solve for "p" and "w". Divide the first equation by t, and the second equation by t as well:

d1/t = p + w
d2/t = p - w

Add the two equations together to eliminate "w":

(d1/t) + (d2/t) = 2p

Solve for "p":

p = (d1 + d2) / (2t)

Now, substitute the value of "p" in either equation to solve for "w":

w = (d1/t) - p

Once you have the specific values for d1, d2, and t, plug them into the equations to find the speed of the plane in still air (p) and the speed of the wind (w).

learn more about speed here:brainly.com/question/28224010

#SPJ11

We need to graph the next given inequalities:

For 2x+y<1.

We need to find the x-intercept and y-intercept

To find the y-intercept, set x=0

To find the x-intercept, set y=0

The symbol "<" means less than, so we get the next graph:

For the second inequality y>1/2x+2

To find the y-intercept, set x=0

Answer:

105 = (5x-70)

Step-by-step explanation:

You are trying to find x so you would have to place that in to finally get to the end where x = 5

The Malthusian law for population growth states that the rate of population growth is proportional to the current population size.

Mathematically, we can express this as:

dP/dt = rP

where P is the population size, t is time, and r is the growth rate.

Assuming a constant growth rate, we can integrate this equation to get:

ln(P) = rt + C

where C is an integration constant. We can solve for C using the initial population estimate:

ln(1200) = r(1980) + C

C = ln(1200) - r(1980)

Substituting the values of C and P from the second estimate (P=7500 in 2008), we get:

ln(7500) = r(2008) + ln(1200) - r(1980)

Solving for r, we get:

r = [ln(7500) - ln(1200)] / (2008 - 1980) = 0.0496

Using this value of r, we can predict the alligator population in 2020, which is 12 years after the second estimate (2008). We have:

ln(P) = rt + ln(7500)

ln(P) = 0.0496(12) + ln(7500) = 9.058

P = e^9.058 = 8656

Therefore, the estimated alligator population in the region in the year 2020 is 8656.

To learn more about Malthusian law please click on below link        

https://brainly.com/question/15210976

#SPJ4

"The result is irrational because it cannot be written as the ratio of two integers and its decimal expansion does not terminate or repeat.

1) Note that we have here two irrational numbers:

2) We can simplify a little bit more, the square root of 12 like this:

Note that now, we have two radicals with the same radicand. So we can proceed with that:

3) We can now answer the 2nd part.

"The result is irrational because it cannot be written as the ratio of two integers and its decimal expansion does not terminate or repeat.

Given:

novel: 3/4

dictionary: 4 1/2

Let's first convert the two given height into similar fractions (with the sa

Answer:

Step-by-step explanation:

1.

y=mx+b

slope=m=3     (4,2)

Hence y=3x+b    (1)

We substitute valueы of x=4 and y=2 into the equation (1):

2=3(4)+b

2=12+b

2-12=12+b-12

-10=b

Thus, b=-10

Hence y=3x-10

2.

y=mx+b

slope=m=-2     (0,3)

Hence y=-2x+b    (1)

We substitute valueы of x=0 and y=3 into the equation (1):

3=-2(0)+b

3=0+b

3=b

Thus, b=3

Hence y=-2x+3

3.

y=mx+b

slope=m=-1     (1,-7)

Hence y=-x+b    (1)

We substitute valueы of x=4 and y=2 into the equation (1):

-7=-(1)+b

-7=-1+b

-7+1=-1+b+1

-6=b

Thus, b=-6

Hence y=-x-6

And so on ...

The general form of an increasing exponential equation is:

With the following restrictions:

Here, A is the starting point (the y-intercept), because y = A when x = 0.

Hypothesis test used to test the batting average of the two given team national league and American league is given z-test.

As given in the question,

Given : Mean batting for American league is not equal to Mean batting for National league.

Therefore, hypothesis test used to test the batting average of the national league and American league is given z-test.

Learn more about hypothesis test here

brainly.com/question/17099835

#SPJ4

Given the information on the problem, we can draw the following right triangle:

we can find how high the ladder reach using the pythagorean theorem:

therefore, the ladder reaches 21 ft high up on the wall

a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

x = (3/2)k + (2/3)

Substituting this value of x into the equation of the curve, we get:

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

Learn more about " line and curve" : https://brainly.com/question/30162650

#SPJ11

Step-by-step explanation:

the work will be finished in 26 daysplease mark the answer as the brainliest

Let s be the speed of the slowest train and t the time it takes to travel 300 miles.

We know that:

Since the second train has a speed of s+20 mph and travels the same 300 miles using 4 hours less time, then:

Isolate t from the first equation:

Substitute the expression for t in the second equation to find an expression only in terms of s:

Use the distributive property to rewrite the product of the quantities on the left hand side of the equation:

Simplify the products when possible. 4h times 20 mph is equal to 80 miles:

Substract 300 miles from both sides of the equation:

Multiply both sides by s:

This is a quadratic equation for s. Write the equation in standard form:

Use the quadratic formula to isolate s:

Observe that the term -4(-4h)(20mph)(300miles) is equal to +96000 squared miles, and 80 miles squared is equal to 6400 squared miles:

Factoring out the units, we get:

Since the square root of 102400 is equal to 320:

Taking the positive value of the plus/minus sign, we get:

Taking the negative value of the plus/minus sign, we get:

Since we first stated that s*t=300 miles and the time cannot be a negative number, the only acceptable answer is s=30 mph.

Since the velocity of the second train is s+20 mph and s=30mph, then the velocity of the second train is 50 mph.

Check the answer by verifying if all the conditions are satisfied. The problem says that the second train arrives 4 hours earlier.

The first train takes a time of 300 miles / 30 mph = 10 h.

The second train takes a time of 300 miles / 50 mph = 6h, 4 hours earlier.

Therefore, the velocities of the trains are 30 mph and 50 mph.

Answer:

Step-by-step explanation:

Formula: Y= mx+b

m = slope    |    b = y-intercept

Equation: Y>2x+1

The Y-Intercept is the (1)

Shade above the dotted line because it is >.

You always shade on the left if the left side of the equation is > than the right.

If ≥ Then the line is Solid  ||||  If > Then the line is dotted.

The statement is sometimes true. It depends on the relationship between the radius of the cone, the height of the cone, and the height of the prism.

The volume of a cone is given by the formula\(V_{cone} = (1/3)\pi r^2h\), where r is the radius of the cone and h is the height of the cone.

The volume of a prism is given by the formula\(V_{prism} = Bh\), where B is the base area of the prism and h is the height of the prism.

To determine if the statement is true, we need to compare the volumes of the cone and the prism.

If the base area of the cone is 3 times as great as the base area of the prism, it means that \(B_{cone} = 3B_{prism\).

Substituting these values into the volume formulas, we have \(V_{cone} = (1/3)\pi r^2h\) and \(V_{prism} = 3B_{prism} h\).

By comparing these formulas, we can see that the volume of the cone is indeed three times the volume of the prism, given the condition that \(B_{cone} = 3B_{prism\).

However, it is important to note that this relationship depends on the specific values of the radius and height of the cone and the height of the prism. If these values do not satisfy the condition \(B_{cone} = 3B_{prism\), then the statement would not hold true. Therefore, the statement is sometimes true, but it is not always true.

Learn more about cone here: https://brainly.com/question/16419032

#SPJ11

Answer:

x=4

Step-by-step explanation:

3x+2+5x-10=24

8x-8=24

8x=32

x=4

Answer:

x=4

Step-by-step explanation:

Let me know if you need step by step, it doesn't look like it though.

I hope this helps!!

Answer:

A. M= 20

B. r = 6

Step-by-step explanation:

M=kr³

where k is the constant

M= 160 , r 4

160= k(4)³

k = 160/4³= 2.5

A. when r= 2 , M= kr³

M= 2.5(2)³ = 20

B. when M= 540, find r

M= kr³

r³ = M/k

r³ = 540/2.5

r³= 216

r = 6

Answer:

40x+65y≤2,400 and x+y≤45

Step-by-step explanation:

the unit normal vector to the curve with vector equation \vec r \, (t) =<1^t,\ln(4/t^2), \, \ln(e/(t^4)) > r (t)=<1 t ,ln(4/t 2 ),ln(e/(t 4 ))> at the point where t=2t=2 is \vec n = <0,0,-1>

A unit normal vector is a normal vector with magnitude 1, and it points in the direction that is perpendicular to the tangent to the curve at a given point.

To determine the unit normal vector to a curve, it's important to find the tangent first and then find the normal. In this case, we're looking for the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2.

To find the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2, it is necessary to find the tangent to the curve and then find the normal. This is a crucial step in understanding the geometry of curves in 3D space.

To find the tangent to the curve, we'll differentiate the vector equation with respect to t and evaluate it at t = 2. The derivative of \vec r (t) is given by:

d\vec r/dt = <1, -2t^-3, -4e^-t^-4>

So the tangent to the curve at t = 2 is:

d\vec r/dt = <1, -2(2)^-3, -4e^-2^-4> = <1, 1.5, -1.648721>

Next, we'll find the normal to the tangent by taking the cross product of the tangent with a fixed vector, for example, the unit vector i = <1,0,0>. The cross product of two vectors results in a vector that is perpendicular to both of them.

The cross product of the tangent and the unit vector i is given by:

\vec T x \vec i = <1, 1.5, -1.648721> x <1,0,0> = <0,0,-1.5>

Since the magnitude of the normal is not 1, we'll normalize it by dividing it by its magnitude:

\vec n = \vec T x \vec i / ||\vec T x \vec i|| = <0,0,-1.5> / ||<0,0,-1.5>|| = <0,0,-1>

So the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2 is given by:

\vec n = <0,0,-1>

This is the unit normal vector that points in the direction that is perpendicular to the tangent to the curve at t = 2. The magnitude of 1 ensures that it's a unit vector and the direction points towards the normal direction.

To know mare about unit normal vector  refer here:

https://brainly.com/question/29752499#

#SPJ11

Answer:

\(3k (m + \frac{1}{3}n)\)

Step-by-step explanation:

Sum of m and one - third of n is :

                                     \(= m + \frac{1}{3}n\)

Product of 3k to  the sum is :

                                     \(=3k \times (m + \frac{1}{3}n)\)

The optimal values of L and K that maximize output while satisfying the cost constraint are L = 10/3 and K = 10.

Q = 10L⁰.⁷⁵K⁰.⁵, w = 5, r = 4, and the cost constraint = 60, we have to find the values of L and K using the Lagrange method which maximizes the output for the firm.

Let's formulate the Lagrange equation:

For Q = 10L⁰.⁷⁵K⁰.⁵, we have that the marginal products are

MPL = ∂Q/∂L = 7.5K⁰.⁵L⁻.²⁵ and

MPK = ∂Q/∂K = 5L⁰.⁷⁵K⁻.⁵.

The Lagrange function to maximize Q subject to the cost constraint is: L(K, λ) = 10L⁰.⁷⁵K⁰.⁵ + λ[60 - 5L - 4K]

Differentiate L(K, λ) w.r.t. L, K, and λ and set them to zero:

∂L(K, λ)/∂L = 7.5K⁰.⁵L⁻.²⁵ - 5λ = 0  ...........(1)

∂L(K, λ)/∂K = 5L⁰.⁷⁵K⁻.⁵ - 4λ = 0 ...........(2)

∂L(K, λ)/∂λ = 60 - 5L - 4K = 0 ...........(3)

From (1), we get:λ = 1.5K⁰.⁵L⁰.²⁵ .........(4)

Substituting (4) in (2), we get:

5L⁰.⁷⁵K⁻.⁵ - 6K⁰.⁵L⁰.²⁵ = 0  

=> 5L⁰.⁷⁵K⁻.⁵ = 6K⁰.⁵L⁰.²⁵K/L = (5/6) L⁰.⁵/(0.5)K⁰.⁵

=> L/K = (5/6) (2) = 5/3

Now from (3), we have: 60 = 5L + 4K

Substituting L/K = 5/3 in the above equation, we get:

60 = 5 (5/3) K + 4K

Simplifying this equation, we get:

K = 6L = 10K = 10

From the above solutions, we can conclude that the values of L and K using the Lagrange method which maximizes the output for the firm are:

L = 5K/3 = 10/3 and K = 10.

You can learn more about constraint at: brainly.com/question/17156848

#SPJ11