During lunchtime, customers arrive at a postal office at a rate of = 36 per hour. The interarrival time of the arrival process can be approximated with an exponential distribution. Customers can be served by the postal office at a rate of = 45 per hour. The system has a single server. The service time for the customers can also be approximated with an exponential distribution.

What is the probability that at most 4 customers arrive within a 5-minute period? You can use Excel to calculate P(X<=x). What is the probability that the service time will be less than or equal to 30 seconds? You can use Excel to calculate P(T<=t). (Round your answer to four decimals)

They are related as u^T transposes of each other. v and v^T u are scalar values that represent the dot product of u and v. uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.

If u and v are vectors in R^n, then:

u^T v and v^T u are related as transposes of each other. Specifically, if

u = [u_1, u_2, ..., u_n]^T

and v = [v_1, v_2, ..., v_n]^T

then:

u^T v = v^T u

= u_1 * v_1 + u_2 * v_2 + ... + u_n * v_n

So, u^T v and v^T u are scalar values that represent the dot product of u and v.

uv^T and vu^T are related as transposes of each other. Specifically, if u = [u_1, u_2, ..., u_n]^T and v = [v_1, v_2, ..., v_n]^T

then:

uv^T = [u_1 * v_1, u_1 * v_2, ..., u_1 * v_n;

u_2 * v_1, u_2 * v_2, ..., u_2 * v_n;

...;

u_n * v_1, u_n * v_2, ..., u_n * v_n]

vu^T = [v_1 * u_1, v_2 * u_1, ..., v_n * u_1;

v_1 * u_2, v_2 * u_2, ..., v_n * u_2;

...;

v_1 * u_n, v_2 * u_n, ..., v_n * u_n]

So, uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.

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The value of x for f(x) = 2 (3-x) -2x at f(x) = -10 is 4.

To find the value of f(x) when f(x) equals -10, we substitute -10 into the equation and solve for x.

Given:

f(x) = 2(3 - x) - 2x, we have:

-10 = 2(3 - x) - 2x

Let's simplify the equation step by step:

-10 = 6 - 2x - 2x

-10 = 6 - 4x

-10 - 6 = -4x

-16 = -4x

To solve for x, divide both sides by -4:

x = (-16) / (-4)

x = 4

Therefore, when f(x) = -10, the value of x is 4.

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Answer:

The most widely used continuous probability distribution in statistics is the normal probability distribution.

Step-by-step explanation:

The graph corresponding to a normal probability density function with a mean of μ = 50 and a standard deviation of σ = 5 is shown in Figure 3. Like all normal distribution graphs, it is a bell-shaped curve.

Answer:

from least to greatest or what? ill do lest to greatest tho

-7/8, -13/16, -1 4/5, 7/4

Step-by-step explanation:

all of these can be converted into a fraction with a denominator of 16 so you can compare easier except for -1 4/5 but that is the highest negative number so that would be the last one you put down because it has a whole number so it is greater than one therefor being greater than the rest of the negative fractions that are less than one, but for the rest, it is just simple least to greatest *(if it is greatest to least just reverse it)*

Answer:

From least to greatest: -1 4/5, -7/8, -13/16, 7/4

Greatest to least: 7/4, -13/16, -7/8, -1 4/5

Step-by-step explanation: Start with the greatest number. This would be 7/4 since it is the only positive number in the set of numbers. Then, find a common denominator for the rest of the numbers/fractions. To save time, a common denominator of -7/8, -1 4/5 and -13/16 is 80. Then, make all the equations equivalent. To do this, I’ll just use -13/16. So, just multiply 5 by 16 and -13 by 5 to get the right fraction. The answer would be -65/80 and you would do this process for the rest of the numbers. Once your done with this explanation, just remember that a lower negative number has a higher value on the number line making it greater in a set of numbers.

Answer:

Step-by-step explanation:

To the 4th power means that all the items in the parenthesis is mulitplied 4 times

(9m)⁴

=9*9*9*9*m*m*m*m*m  or

= (9m)(9m)(9m)(9m)

Answer:

$2837.40.

Step-by-step explanation:

To find the cost of constructing the fence, you will need to first find the perimeter of the lot. The perimeter is the distance around the outside of the lot.

To find the perimeter of the lot, add the lengths of all four sides of the lot: 90 feet + 175 feet + 90 feet + 175 feet = 430 feet.

Then, add 6 feet 6 inches to the height of the fence to convert it to feet. There are 12 inches in 1 foot, so 6 feet 6 inches is equivalent to 6 + (6/12) = 6.5 feet.

So, the total height of the fence is 6.5 feet.

To find the cost of the materials, you will need to find the total area of the fence. The area of the fence is the amount of surface that the fence covers. To find the area, multiply the height of the fence by the perimeter: 6.5 feet * 430 feet = 2795 square feet.

To find the cost of the materials, multiply the cost per square foot by the total area of the fence: $0.82/square foot * 2795 square feet = $2299.90.

To find the cost of the labor, multiply the number of linear feet of fence by the cost per linear foot: 430 feet * $1.25/foot = $537.50.

To find the total cost, add the cost of the materials to the cost of the labor: $2299.90 + $537.50 = $2837.40.

So, the total cost of constructing the fence is $2837.40.

The equation that shows the relationship between the angles in the triangle is m∠1 + m∠2 + m∠3 = 180.

The equation that shows the relationship between the angles in the triangle is determined as follows;

The sum of angles in a triangle is equal to 180 degrees.

So based on this information, the equation that shows the relationship between the angles in the triangle is formulated as;

angle 1 + angle 2 + angle 3 = 180

We can re-write the equation as follows;

m∠1 + m∠2 + m∠3 = 180

Thus, the equation that shows the relationship between the angles in the triangle is the sum of angle 1 plus angle 2 plus angle 3.

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An equation is a collection of variables and constants with the value of x which will make the equation 7+3(x - 1)=5x+-2(x+1) to be true is 1/2.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given equation,

7+3(x - 1)=5x+-2(x+1)

7 + 3x - 3 = 5x + 2x + 2

3x + 4 = 7x + 2

7x + 2 = 3x + 4

7x - 3x = 4 - 2

4x = 2

x = 1/2

Hence "The value of x which will make the equation 7+3(x - 1)=5x+-2(x+1) to be true is 1/2".

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Answer: 20 2/5

Step-by-step explanation: 60/100=x/34

100x/100=2040/100

x=102/5=20 2/5

The probability that exactly 18 of the 25 smartphones selected are purchased with warranty is:  The probability that exactly 8 of the 25 smartphones selected are not purchased with warranty is: The probability that all 25 smartphones selected are purchased with warranty is:  

The probability that at most 15 of the 25 smartphones selected are purchased with warranty is: The probability that at least 14 of the 25 smartphones selected are purchased with warranty is: f) The probability that more than half (i.e. > 12) of the 25 smartphones selected are purchased with warranty is: 9) The probability that at least 14 but no more than 23 of the 25 smartphones selected are purchased with warranty is:

h) The probability that less than 12 or more than 19 of the 25 smartphones selected are purchased with warranty is: Part 2Mean = Standard Deviation =  Part 3To find the minimum sample size required to expect to find exactly 72 smartphones that are purchased with warranty, we use the following formula: N = [(Z * σ) / E]^2 where Z is the z-score corresponding to the desired level of confidence, σ is the standard deviation, and E is the maximum error of estimation. Using a 95% level of confidence, Z = 1.96.Using the calculated standard deviation of 2.91 and expecting to find exactly 72 smartphones, the maximum error of estimation is 0.5.N = [(1.96 * 2.91) / 0.5]^2N

= 337.11

Therefore, the minimum sample size required to expect to find exactly 72 smartphones that are purchased with warranty is 338.

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There are 30240 ways to arrange the word ATTENTION.

The term permutation refers to the distinct arrangements that we could have. Let us recall that if we are talking about permutation, we are mutation has to do with the number of the taking about the kind of arrangement where the order of the arrangement is important.

Now we know that we have to work with the word ATTENTION. The number of the letters that are repeated in this word are T(3) and N(2). There are 9 letters in total.

We have;

9!/3! 2!

= 9 * 8 * 7 * 6 * 5 * 4 * 3!/3! 2!

= 30240 ways.

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Answer:

39°

Step-by-step explanation:

Complementary angles sum up to 90°

< JKL + < RST = 90

36 + x + 15 =90

51 + x = 90

x = 39°

Answer:

8.4 miles

Step-by-step explanation:

Here we need to solve a system of equations, we will find that the grandma's house is at 8.396 miles.

We need to remember the relation:

speed*time = distance.

First we know that Jasmine goes to her grandma's house at a speed S, and it takes 45 minutes (or 0.75 hours) to get there, so we can write:

S*0.75h = D

Where D is the distance to her grandma's house.

Returning back, she takes 1 hour and 10 minutes (or 1.167 hours) and 4 mi/h slower, then in this case her speed is:

(S - 4 mi/h)

And we can write the equation:

(S - 4mi/h)*1.167h = D

Then we have a system of equations:

S*0.75h = D

(S - 4mi/h)*1.167h = D

To solve this, we can first isolate S (because we want to solve it for D) so we have:

S = D/(0.75h)

Now we can replace this in the other equation to get:

( D/(0.75h) - 4mi/h)*1.167h = D

Now we can solve this equation for D.

D*(1.167h/0.75h) - 4mi/h*1.167h = D

D*((1.167h/0.75h) - 1) = 4mi/h*1.167h

D*0.556 = 4.668

D =  4.668/0.556 = 8.396 mi

This means that she lives at 8.396 miles from her grandmother's house.

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Answer:

84.82 feet

Step-by-step explanation:

circumference = πd = π (18) = 18π.

18π for one revolution. 18 revolutions = 18 (18π) = 324π = 1017.876 inches.

12 inches = 1 foot.

1017.876/12 = 84.823 = 84.82 feet (nearest hundredth)

Answer:

-45x + 75

Step-by-step explanation:

5(-9x + 15)         Use distributive property

= (5 * -9x) + (5 * 15)

= -45x + 75

Hope this helps!

Answer:

-45x + 75

Step-by-step explanation:

5(-9x + 15)

Distribute:

(5* -9x) + (5* 15)

-45x + 75

The given equation has only one root x=0.065. Hence, the total number of solutions is 1.

The equation sin 3x = 0.25 - x² is given and the number of solutions it has to be determined using Newton's method. Newton's method is an algorithm that is used to find the roots of a given function. I

n this method, we start with an initial guess and then we iteratively improve the guess until we converge to the root of the function.

Let's begin the solution for the equation sin 3x = 0.25 - x²:

Step 1: Find the derivatives of the given equation. sin 3x = 0.25 - x²

Differentiating the given equation on both sides w.r.t x, we get:3 cos 3x = -2x  

Now, we have the derivative of sin 3x.

Step 2: The Newton Raphson method is given by the formula:x 1 = x0 - f(x0)/f'(x0) where x1 and x0 are the successive approximation of the root and f(x0) is the function at x0 and f'(x0) is the derivative of the function at x0.

So, we will take x0= 0.1 (Initial guess) because this function has multiple roots and is an odd function. Hence, it has a root near x=0.1.

Step 3: We have f(x) = sin 3x - 0.25 + x² and f'(x) = 3 cos 3x + 2x'

We will find the next approximation x1 as follows: x1 = x0 - f(x0)/f'(x0)

x1 = 0.1 - [sin(3 * 0.1) - 0.25 + 0.1²]/[3 cos(3 * 0.1) + 2 * 0.1]

x1 = 0.0654

Step 4: We will repeat the above process using the value of x1 obtained in step 3. We will repeat it until the successive approximations become equal up to two decimal places.

We will continue the above process until we obtain the successive approximations that are equal up to two decimal places.

So, we get the root of the equation sin 3x = 0.25 - x² is x = 0.065 with the help of Newton's method.

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The general formula that describes the variation is T² = 18a³/d²

          x ∝ y.

          This can then be written as;

           x = ky

           Where;

           k = constant rate of change.

            x ∝ (y/z)

           This can then be written as;

            x = k (y/z)

           Where;

           k = constant rate or variation

The square of T varies directly with the cube of a and inversely with the square of d.

Note that

square of T = T²

cube of a = a³

square of d = d²

Therefore, we can write;

T² ∝ a³/d²

T² = k (a³/d²)

Since;

T = 4 when a = 2 and d = 3

We can find the constant of proportionality k, by substituting the values of T=4, a = 2 and d = 3 into equation (i) and solve as follows;

(4)² =  k (2³/3²)

16 =  k (8/9)

8k = 16 x 9

8k = 144

k = 144/8

k = 18

Therefore, The overall formula for describing the variation is

T² =  18 a³/d²

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Predatory dumping is a term used to describe the intentional selling of products at a loss in order to increase market share in a foreign market. This practice can be harmful to domestic industries and is often considered unfair competition. In order to prevent predatory dumping, many countries have implemented anti-dumping laws and regulations.

There are three key aspects to predatory dumping: it is intentional, it involves selling at a loss, and its goal is to increase market share. By intentionally selling products at a loss, companies can undercut their competitors and gain a foothold in a new market. However, this can lead to a vicious cycle of price cutting that ultimately harms both the foreign and domestic markets.

It is important to note that predatory dumping is different from unintentional dumping, which occurs when a company sells products at a lower price in a foreign market due to factors such as currency fluctuations or excess inventory. Additionally, cooperative international market entry and exporting of subsidized products are separate concepts that do not fall under the category of predatory dumping.

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Answer:

1/3

Step-by-step explanation:

Answer:

each person ate 1/3 of a sandwich

Step-by-step explanation:

The position of particle in a straight line with v = t(t^2 + 1)³ + 3t is (1/8)t⁸ + (3/6)t⁶ + (3/4)t⁴ + 2t² C.

To find an expression for the position s after a time t, we need to integrate the velocity function v with respect to time t.

Using the power rule of integration and the constant of integration C, we have:

s = ∫v dt = ∫[t(t² + 1)³ + 3t] dt

after expanding t(t² + 1)³ using binomial theorem we have-

(t^2 + 1)³ = t⁶ + 3t⁴ + 3t² + 1

Substituting this into the integral, we get:

s = ∫[t(t⁶ + 3t⁴ + 3t^2 + 1) + 3t] dt

s = ∫[t^7 + 3t⁵ + 3t³ + t + 3t] dt

s = ∫t^7 dt + 3∫t⁵ dt + 3∫t³ dt + ∫4t dt

s = (1/8)t⁸ + (3/6)t⁶ + (3/4)t⁴ + 2t² + C

Therefore, the expression for the position s after a time t is:

S = (1/8)t⁸ + (3/6)t⁶ + (3/4)t⁴ + 2t² + C, where C is the constant of integration.

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The equation that Amy can use to find how many games of Balloon Bouncer, g, she played is; g = (35 - 2a)/3

We are told that Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score.

Balloon Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.

Thus, the expression for the number of balloon bouncer games played at the arcade is :

2a + 3g = 35

Let :

Glimmer arcade, a = $2 per game

Balloon bouncer, g = $3 per game

Total game tokens = 35

Her spending could be represented using the expression :

2a + 3g = 35  

g = number of balloon bouncer games played

Thus, making g the subject of the formula we have;

g = (35 - 2a)/3

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Answer:

3g + 2 = 35 is the answer.

She played 11 games.

Step-by-step explanation:

Answer:

3•10^3 is 3,000, so the answer is 9,000

==========================================================

Explanation:

The main cluster of values is somewhere between 650 and 799, as this is where the highest bars are located. The median is somewhere in this region. The mean however is smaller than the median because the outliers to the left that pull on the mean. The outliers pull the mean toward them. Having small outliers will make the mean smaller than it should be. The median is not affected by outliers. Therefore, the median is the best measure of center in this case.

Side note: we consider this distribution to be "skewed to the left" or "negatively skewed" since the left tail is longer than the right tail.

Answer:

Step-by-step explanation:

Answer:

who is that? Maybe i know this person...

Step-by-step explanation:

Answer:

Angad=6

Malachay=3×6=18

Jim=6

Step-by-step explanation:

Angad,malachy and Jim share =£30 ratio =1:3:1

Let the part of the Angad=X

=3x

=X

So X+3x+X=30

5x=30

X=30/5

X=6

So part of Angad=6

Malachay=3×6=18

Jim=6

Step-by-step explanation:

A:M:J

1:3:1

let total amt be 5x

5x = 30

x = 6

thus, A get 6dollars , M get 18 and J 6

Topic: ratio and proportions

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Answer: Jeffery paid $ 2937 in all.

Step-by-step explanation:

Given: The cost of antique pull = $890

Mark up percentage = 200%

New price = (cost) + (Mark up percentage) x (cost)

\(=\$( 890+\dfrac{200}{100}\times890)\\\\=\$( 890+2(890))\\\\=\$2670\)

After a tax of 10% , the amount needs to be paid = New price + 10% of New price

 \(=\$(2670+\dfrac{10}{100}\times2670)=\$(2670+267)\\\\=\$2937\)

Hence, Jeffery paid $ 2937 in all.

Answer:

4.8kg

Step-by-step explanation:

Answer:

Step-by-step explanation:

24 / 5 = 4.8.

20% of 24 kg is 4.8kg