Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide an arrival rate of 2.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution. What is the average number of cars in the system

Answers

Answer 1

Answer:

the average number of car(s) in the system is 1

Step-by-step explanation:

Given the data in the question;

Arrival rate; λ = 2.5 cars per hour

Service time; μ = 5 cars per hour

Since Arrivals follows Poisson probability distribution and service times follows exponential probability distribution.

Lq = λ² / [ μ( μ - λ ) ]

we substitute

Lq = (2.5)² / [ 5( 5 - 2.5 ) ]

Lq = 6.25 / [ 5 × 2.5 ]

Lq = 6.25 / 12.5

Lq = 0.5

Now, to get the average number of cars in the system, we say;

L = Lq + ( λ / μ )

we substitute

L = 0.5 + ( 2.5 / 5 )

L = 0.5 + 0.5

L = 1

Therefore, the average number of car(s) in the system is 1


Related Questions

Doyle Company issued $500,000 of 10-year, 7 percent bonds on January 1, 2018. The bonds were issued at face value. Interest is payable in cash on December 31 of each year. Doyle immediately invested the proceeds from the bond issue in land. The land was leased for an annual $125,000 of cash revenue, which was collected on December 31 of each year, beginning December 31, 2018

Answers

Answer:

f

Step-by-step explanation:

The answer to this math problem need help

Answers

Step-by-step explanation:

you know that you can copy and paste and give the answer

pls help me asap !!!

Answers

Answer:

11

Step-by-step explanation:

Hopefully you can see that this is an isosceles triangle and remembering the inequality theorem of a triangle (4,4,11 triangle cannot exist).  Iso triangle has two side the same length - as well as two angles the same.

can some0ne help me?

Answers

Answer:

(x - 2)/3

(x - 4)/-5 or (-x + 4)/5

Step-by-step explanation:

this is an inverse function, and to solve an inverse function you would :

swap x and g(x) without bringing the x coefficient with it, just simply swap the variables. Then, solve for g(x), and that's it

the first question's answer is :

g(x) = 3x + 2

x = 3(g(x)) + 2

x - 2 = 3(g(x))

(x - 2)/3 = g(x)

the second one is:

g(x) = 4 - 5x

x = 4 - 5(g(x))

x - 4 = -5(g(x))

(x-4)/-5 = g(x)

g(x) = 3x + 2

y = 3x + 2

x = 3y + 2

3y = x - 2

y = x/3 - 2/3

inverse g(x) = (x - 2) / 3

g(x) = 4 - 5x

y = 4 - 5x

x = 4 - 5y

5y = 4 - x

y = 4/5 - x/5

inverse g(x) = (4 - x) / 5

If a normally distributed population has a mean (mu) that equals 100 with a standard deviation (sigma) of 18, what will be the computed z-score with a sample mean (x-bar) of 106 from a sample size of 9?

Answers

Answer:

Z = 1

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean (mu) that equals 100 with a standard deviation (sigma) of 18

[tex]\mu = 100, \sigma = 18[/tex]

Sample of 9:

This means that [tex]n = 9, s = \frac{18}{\sqrt{9}} = 6[/tex]

What will be the computed z-score with a sample mean (x-bar) of 106?

This is Z when X = 106. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{106 - 100}{6}[/tex]

[tex]Z = 1[/tex]

So Z = 1 is the answer.

Use the commutative law of multiplication to rewrite 67 x 13.

A. 3 X 671
B. 13 x 67
C.6 X 7 X1 X3
D.80

Answers

Answer:

A. 671*3

B. 67*13

C. 3*1*7*6

D. 1*80

Answer this question that is given

Answers

Answer:

See explanation

Step-by-step explanation:

2) (10+4) x 2 = 28

3) (13 + 6) x 2 = 38

4) (8+4) x 2 = 24

5) (11+8) x 2 = 38

Answered by Gauthmath

Tyler and Gabe went to the arcade and played the same two games, Tyler played five rounds of each game for 30$. Write two equations for the amounts the two boys spent. Then find the cost for one round each game.

Answers

Equations:

1. (30)(5)= 150

2. 30 + 30 + 30 + 30 + 30 = 150

I round:

30 dollars divided by 5 rounds = 6 dollars per round.

The total amount spent by the two boys is $300.

What is algebraic expression?

An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -

2x + 3y + 5

2z + y

x + 3y

Given is that Tyler and Gabe went to the arcade and played the same two games. Tyler played five rounds of each game for 30$.

We can write the total amount spent by the two boys as -

total amount = 2 x cost of each game x total number of games played

total amount = 2 x 30 x 5

total amount = 10 x 30

total amount = 300

Therefore, the total amount spent by the two boys is $300.

To solve more questions on equivalent expression, visit the link-

https://brainly.com/question/1041084

#SPJ3

190 of 7
6 7 8 9 10
-3
4
5
6
The slope of the line shown in the graph is
and the intercept of the line is

Answers

Answer:slope 2/3

Y-int 6

Step-by-step explanation:

3 write the factor of the following (1) 48 (2) 36 (3) 28 (4) 100 (5) 125 ​

Answers

Answer:

FACTORING THE NUMBERS :-

well u didnt say to prime factors so i am writing all factors

1) 48 => 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48    ( all are plus and minus )

2) 36 => 1, 2, 3, 4, 6, 9, 12, 18 and 36    ( all are plus and minus )

3) 28 => 1, 2, 4, 7, 14 and 28    ( all are plus and minus )

4) 100 => 1, 2, 4, 5, 10, 20, 25, 50, and 100  ( all are plus and minus )

5) 125 => 1, 5, 25, 125   ( all are plus and minus )

is it worth brainliest...

yes ofc

Please help!!

Find BD​

Answers

Answer:  [tex]8\sqrt{2}[/tex]

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

Work Shown:

Focus entirely on triangle ABD (or on triangle BCD; both are identical)

The two legs of this triangle are AB = 8 and AD = 8. The hypotenuse is unknown, so we'll say BD = x.

Apply the pythagorean theorem.

[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\x = \sqrt{8^2 + 8^2}\\\\x = \sqrt{2*8^2}\\\\x = \sqrt{8^2*2}\\\\x = \sqrt{8^2}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]

So that's why the diagonal BD is exactly [tex]8\sqrt{2}\\\\[/tex] units long

Side note: [tex]8\sqrt{2} \approx 11.3137[/tex]

how many distinct permutations can be formed using the letters of the word robberies

Answers

Answer:

45360 arrangements

Step-by-step explanation:

Given the word 'robberies'

Number of letters = 9 letters in total

Repeated letters ; r = 2 ; b = 2 ; e = 2

Therefore, the number of distinct arrangement of letters is :

(total letters)! / repeated letters!

The number of distinct arrangement of letters is :

9! / (2! * 2! * 2!) = (9*8*7*6*5*4*3*2*1) / (2*2*2)

362880 / 8 = 45360 arrangements

Solve. x+y+z=6 3x−2y+2z=2−2x−y+3z=−4

Answers

Answer:

-4?

hope dis helps ^-^

Analyze the key features of the graph of the quadratic function f(x) = –x^2 + 4x – 3.
1. Does the parabola open up or down?
2. Is the vertex a minimum or a maximum?
3. Identify the axis of symmetry, vertex and the y-intercept of the parabola.

Answers

9514 1404 393

Answer:

downmaximumx=2; (2, 1), -3

Step-by-step explanation:

1. The negative leading coefficient (-2) tells you the parabola opens downward.

__

2. The fact that the parabola opens downward tells you the vertex is a maximum.

__

3. For quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For this parabola, that is x = -4/(2(-1)) = 2. The y-value of the vertex is f(2) = -2^2+4(2)-3 = -4+8-3 = 1. The y-intercept is the constant, c = -3.

axis of symmetry: x = 2vertex: (2, 1)y-intercept: (0, -3)

A shop sells a particular of video recorder. Assuming that the weekly demand for the video recorder is a Poisson variable with the mean 3, find the probability that the shop sells. . (a) At least 3 in a week. (b) At most 7 in a week. (c) More than 20 in a month (4 weeks).

Answers

Answer:

a) 0.5768 = 57.68% probability that the shop sells at least 3 in a week.

b) 0.988 = 98.8% probability that the shop sells at most 7 in a week.

c) 0.0104 = 1.04% probability that the shop sells more than 20 in a month.

Step-by-step explanation:

For questions a and b, the Poisson distribution is used, while for question c, the normal approximation is used.

Poisson distribution:

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^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of successes

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Poisson distribution can be approximated to the normal with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex], if [tex]\lambda>10[/tex].

Poisson variable with the mean 3

This means that [tex]\lambda= 3[/tex].

(a) At least 3 in a week.

This is [tex]P(X \geq 3)[/tex]. So

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which:

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

Then

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

So

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0498 + 0.1494 + 0.2240 = 0.4232[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 1 - 0.4232 = 0.5768[/tex]

0.5768 = 57.68% probability that the shop sells at least 3 in a week.

(b) At most 7 in a week.

This is:

[tex]P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]

[tex]P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680[/tex]

[tex]P(X = 5) = \frac{e^{-3}*3^{5}}{(5)!} = 0.1008[/tex]

[tex]P(X = 6) = \frac{e^{-3}*3^{6}}{(6)!} = 0.0504[/tex]

[tex]P(X = 7) = \frac{e^{-3}*3^{7}}{(7)!} = 0.0216[/tex]

Then

[tex]P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 + 0.1008 + 0.0504 + 0.0216 = 0.988[/tex]

0.988 = 98.8% probability that the shop sells at most 7 in a week.

(c) More than 20 in a month (4 weeks).

4 weeks, so:

[tex]\mu = \lambda = 4(3) = 12[/tex]

[tex]\sigma = \sqrt{\lambda} = \sqrt{12}[/tex]

The probability, using continuity correction, is P(X > 20 + 0.5) = P(X > 20.5), which is 1 subtracted by the p-value of Z when X = 20.5.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20 - 12}{\sqrt{12}}[/tex]

[tex]Z = 2.31[/tex]

[tex]Z = 2.31[/tex] has a p-value of 0.9896.

1 - 0.9896 = 0.0104

0.0104 = 1.04% probability that the shop sells more than 20 in a month.

The probability of the selling the video recorders for considered cases are:

P(At least 3 in a week) = 0.5768 approximately.P(At most 7 in a week) = 0.9881 approximately.P( more than 20 in a month) = 0.0839 approximately.

What are some of the properties of Poisson distribution?

Let X ~ Pois(λ)

Then we have:

E(X) = λ = Var(X)

Since standard deviation is square root (positive) of variance,

Thus,

Standard deviation of X = [tex]\sqrt{\lambda}[/tex]

Its probability function is given by

f(k; λ) = Pr(X = k) = [tex]\dfrac{\lambda^{k}e^{-\lambda}}{k!}[/tex]

For this case, let we have:

X = the number of weekly demand of video recorder for the considered shop.

Then, by the given data, we have:

X ~ Pois(λ=3)


Evaluating each event's probability:

Case 1: At least 3 in a week.

[tex]P(X > 3) = 1- P(X \leq 2) = \sum_{i=0}^{2}P(X=i) = \sum_{i=0}^{2} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 3) = 1 - e^{-3} \times \left( 1 + 3 + 9/2\right) \approx 1 - 0.4232 = 0.5768[/tex]

Case 2: At most 7 in a week.

[tex]P(X \leq 7) = \sum_{i=0}^{7}P(X=i) = \sum_{i=0}^{7} \dfrac{3^ie^{-3}}{i!}\\\\P(X \leq 7) = e^{-3} \times \left( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120 + 729/720 + 2187/5040\right)\\\\P(X \leq 7) \approx 0.9881[/tex]

Case 3: More than 20 in a month(4 weeks)

That means more than 5 in a week on average.

[tex]P(X > 5) = 1- P(X \leq 5) =\sum_{i=0}^{5}P(X=i) = \sum_{i=0}^{5} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 5) = 1- e^{-3}( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120)\\\\P(X > 5) \approx 1 - 0.9161 \\ P(X > 5) \approx 0.0839[/tex]


Thus, the probability of the selling the video recorders for considered cases are:

P(At least 3 in a week) = 0.5768 approximately.P(At most 7 in a week) = 0.9881 approximately.P( more than 20 in a month) = 0.0839 approximately.

Learn more about poisson distribution here:

https://brainly.com/question/7879375

[tex]\sqrt{25}[/tex]

Answers

Answer:

5

Step-by-step explanation:

Calculate the square root of 25 and get 5.

5 I just thought of what # gets me to 25

hlo anyone free .... im bo r ed

d​

Answers

Step-by-step explanation:

Excuse me! Who r u? where r u frm? tell me tht frst.

Answer:

Oop

Step-by-step explanation:

I’m bored

Solve x∕3 < 5 Question 5 options: A) x ≥ 15 B) x > 15 C) x < 15 D) x ≤ 15

Answers

Answer:

C

Step-by-step explanation:

Given

[tex]\frac{x}{3}[/tex] < 5 ( multiply both sides by 3 to clear the fraction )

x < 15 → C

You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten.

Answers

Answer:

[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]

Step-by-step explanation:

There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.

At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just

[tex]\frac{4}{52}[/tex]

After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is

[tex]\frac{4}{51}[/tex]

Now to get the total probability we need to multiply the two probabilities together

[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]

Một công ty sản xuất ván trượt có thể bán một cái ván trượt với giá $60.

Tổng chi phí cho sản xuất bao gồm chi phí cố định là $1200 và chi phí để sản xuất một cái ván trượt là $35.

Nếu công ty đó bán được 80 cái ván trượt thì công ty đó

Answers

can you translate so I can help you out

A rectangle has a length of 7 in. and a width of 2 in. if the rectangle is enlarged using a scale factor of 1.5, what will be the perimeter of the new rectangle

Answers

Answer:

27 inch

Step-by-step explanation:

Current perimeter=18

New perimeter=18*1.5=27 in

The PTA sells 100 tickets for a raffle and puts them in a bowl. They will randomly pull out a ticket for the first prize and then another ticket for the second prize. You have 10 tickets and your friend has 10 tickets. What is the probability that your friend wins the first prize and you win the second prize?

Answers

Jÿïôò śfrtÿ hjkÿï èrï

5x-22 3x +105 x minus 22 3 X + 10 ​

Answers

-291x+10

:)))))) Have fun

-5 + 3 and also what is 1/4 of 24
What is the answer i am struggling

Answers

Answer:

-5+3=-2

1/4 of 24 = 6

Step-by-step explanation:

PLEASEE HELP ME ASAPPP (geometry)

Answers

Answer:AE=EC và BF=FC => EF là đường trung bình của tam giác ABC

=> EF // và bằng 1/2 AB

=> AB = 16

Step-by-step explanation:

Answer:

AB=16

Step-by-step explanation:

Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.

The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle.

AD=DB

AD+DB=AB=2EF

AB=2×8=16

a farmer needs 5 men to clear his farm in 10 days. How many men will he need if he must finish clearing the farm in two days if they work at the same rate?

Answers

Answer:

25 workers

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

,

the number of multiples of a given number is infinite ( )​

Answers

Answer:

make an 8 horizontal

oooookkkk

Answer:

TRUE

The number of multiples of a given number is finite is a false statement. The number of multiples of a given number is infinite.

Examples:

Multiples of 2 = 2,4,6,8,10,…..

Multiples of 3 = 3,6,9,12,15,18,…

Multiples of 4 = 4, 8, 12, 16, 120, 24….

∴ The number of multiples of a given number is infinite .

Answer From Gauth Math

There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.10 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.04 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. What is the probability that the first machine produces an acceptable cork

Answers

Answer:

0.6827

Step-by-step explanation:

Given that :

Mean, μ = 3

Standard deviation, σ = 0.1

To produce an acceptable cork. :

P(2.9 < X < 3.1)

Recall :

Z = (x - μ) / σ

P(2.9 < X < 3.1) = P[((2.9 - 3) / 0.1) < Z < ((3.1 - 3) / 0.1)]

P(2.9 < X < 3.1) = P(-1 < Z < 1)

Using a normal distribution calculator, we obtain the probability to the right of the distribution :

P(2.9 < X < 3.1) = P(1 < Z < - 1) = 0.8413 - 0.1587 = 0.6827

Hence, the probability that the first machine produces an acceptable cork is 0.6827

Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print​ lengths, foot​ lengths, and heights of males. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Based on these​ results, does it appear that police can use a shoe print length to estimate the height of a​ male? Use a significance level of α=0.01

Answers

It does not appear that police can use a shoe print length to estimate the height of a​ male.

The given parameters are:

[tex]\begin{array}{cccccc}{Shoe\ Print} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ Height (cm) & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]

Rewrite as:

[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]

See attachment for scatter plot

To determine the correlation coefficient, we extend the table as follows:

[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} & y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} & x^2 & {817.96} & {864.36} & {1036.84} & {1049.76} & {745.29} & y^2 & {29756.25} & {31222.89} & {35494.56} & {28934.01} & {32112.64} & x \times y & {4933.5} & {5194.98} & {6066.48} & {5511.24} & {4892.16} \ \end{array}[/tex]

The correlation coefficient (r) is:

[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]

We have:

[tex]n =5[/tex]

[tex]\sum xy =4933.5+5194.98+6066.48+5511.24+4892.16 =26598.36[/tex]

[tex]\sum x =28.6+29.4+32.2+32.4+27.3=149.9[/tex]

[tex]\sum y =172.5+176.7+188.4+170.1+179.2=886.9[/tex]

[tex]\sum x^2 =817.96+864.36+1036.84+1049.76+745.29=4514.21[/tex]

[tex]\sum y^2 =29756.25+31222.89+35494.56+28934.01+32112.64=157520.35[/tex]

Calculate mean of x and y

[tex]\bar x = \frac{\sum x}{n} = \frac{149.9}{5} = 29.98[/tex]

[tex]\bar y = \frac{\sum y}{n} = \frac{886.9}{5} = 177.38[/tex]

Calculate SSx and SSy

[tex]SS_x = \sum (x - \bar x)^2 =(28.6-29.98)^2 + (29.4-29.98)^2 + (32.2-29.98)^2 + (32.4-29.98)^2 + (27.3-29.98)^2 =20.208[/tex]

[tex]SS_y = \sum (y - \bar x)^2 =(172.5-177.38)^2 + (176.7-177.38)^2 + (188.4-177.38)^2 + (170.1-177.38)^2 + (179.2-177.38)^2 =202.028[/tex]

Calculate [tex]\sum(x - \bar x)(y - \bar y)[/tex]

[tex]\sum(x - \bar x)(y - \bar y) = (28.6-29.98)*(172.5-177.38) + (29.4-29.98)*(176.7-177.38) + (32.2-29.98)*(188.4-177.38) + (32.4-29.98)*(170.1-177.38) + (27.3-29.98) *(179.2-177.38) =9.098[/tex]

So:

[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]

[tex]r = \frac{9.098}{\sqrt{20.208 * 202.028}}[/tex]

[tex]r = \frac{9.098}{\sqrt{4082.581824}}[/tex]

[tex]r = \frac{9.098}{63.90}[/tex]

[tex]r = 0.142[/tex]

Calculate test statistic:

[tex]t = \frac{r}{\sqrt{\frac{1 - r^2}{n-2}}}[/tex]

[tex]t = \frac{0.142}{\sqrt{\frac{1 - 0.142^2}{5-2}}}[/tex]

[tex]t = \frac{0.142}{\sqrt{\frac{0.979836}{3}}}[/tex]

[tex]t = \frac{0.142}{\sqrt{0.326612}}[/tex]

[tex]t = \frac{0.142}{0.5715}[/tex]

[tex]t = 0.248[/tex]

Calculate the degrees of freedom

[tex]df = n - 2 = 5 - 2 = 3[/tex]

The [tex]t_{\alpha/2}[/tex] value at:

[tex]df =3[/tex]

[tex]t = 0.248[/tex]

[tex]\alpha = 0.01[/tex]

The value is:

[tex]t_{0.01/2} = \±5.841[/tex]

This means that we reject the null hypothesis if the t value is not between -5.841 and 5.841

We calculate the t value as:

[tex]t = 0.248[/tex]

[tex]-5.841 < 0.248 < 5.841[/tex]

Hence, we do not reject the null hypothesis because they do not appear to have any correlation.

Read more about regression at:

https://brainly.com/question/18405415

The distance between Ali's house and 1 point
college is exactly 135 miles. If she
drove 2/3 of the distance in 135
minutes. What was her average speed
in miles per hour?

Answers

First we have to figure out how long it would take for the full voyage and that would be 135 + (135 x 1/3) and the answer to that would be 135 + 45 = 180 and that means that 180 is the total minutes it would take to travel the whole trip, now we have to calculate average speed which would be 135(distance)/180(time) which would end up being 135 miles/ 3 hours, now we divide the entire equation by 3 which would be 45/1
CONCLUSION ——————————
Ali would be driving 45 miles per hour

Ali's average speed was 40 miles per hour.

What is an average speed?

The total distance traveled is to be divided by the total time consumed brings us the average speed.

How to calculate the average speed of Ali?

The total distance between the college from Ali's house is 135 miles.

She drove 2/3rd of the total distance in 135 minutes.

She drove =135*2/3miles

=90miles.

Ali can drive 90miles in 135 mins.

Therefore, her average speed is: 90*60/135 miles per hour.

=40 miles per hour.

Learn about average speed here :

https://brainly.in/question/14787217

#SPJ2

Other Questions
what expression is equivalent to (-7-x-5)-(3x+x) Write the equation of a line in slope intercept form that passes through the two points. (-1,3) and (2,9) The author describes the research of Cyrus Thomas most likely because it:A.discredits the hypothesis that mounds were built by a vanished culture.B.supports the hypothesis that people from the area that is now Mexico influenced Native American mound building.C.establishes when mound building occurred in the eastern Woodlands.D.challenges the diffusion hypothesis put forth by archaeologist c. Compare Mainframe and Minicomputers with their key featuresplzzz help describe the react of clans after hearing islam's message by muhammad convert f(x) = 5x(x 6) to standard form NEED HELP ASAP!!!!!!! Describe how to make a template If the body temperature of a person is recorded as 98.6F, what is the persons body temperature in C? 3799209 plz help me on this Write a 500-750 word essay informing the audience why an item you care about is superior to all others. Model your style of writing after "Modern Faithful Steed." Include solid facts as to why the item you selected is superior. True or False: This funding structure incentivizes schools to seek out and serve lower-performing students. True False Please help me ASAP??!!!! Date: Pages The recent price of a car is Rs. 10.00,000: If its price reduces by to1 yearly after how many year its price will be Rs 7, 29,000? who is responsible for collecting the data for GDP in India Which of these products is negative? Select all that apply. -8 (-3) -2 8 0 (-2) 15 (-5) -8 (-9) Library services reportNew challenge1 There has been a huge increase in the number of people interested in researching their ancestry, and genealogy has become a multi-billion-dollar industry. A British government ancestry site recently received more than 50 million hits, and access had to be restricted to cope with the demand. Due to this surge in interest, we have decided that our library records department will need to be reorganized in terms of staffing. In the past, we have received occasional requests for assistance in tracing documentation relating to family and business histories, but in the last two years the number of requests has reached a level that cannot be addressed by the existing staff alone. We are currently in the process of recruiting two additional specialists.Family history2 Traditionally, genealogy was thought of as finding out about your family tree. The idea was to find out who came before you, going as far back in history as possible. However, nowadays it is more common to want to find out as much detail about the people as possible, so what was a purely factual quest has become a historical process. This is an area that we are able to address, as our records include diaries and other documents that contain information and clues that can help build a more complete picture.Medicine and law3 In the past, most genealogical searches could be classified as vanity searches, because the motivation was to prove family nobility. However, this is no longer the case. One of the driving forces of the increased interest in genealogy has been in relation to illness. Genetics are now recognized as significant in predicting the likelihood of suffering from many types of diseases, including cancer and heart disease. There may also be a legal dimension to the searches, because inheritance claims often rely on ancestry. In both of these cases, we, as a department, must be particularly careful in relation to possible lawsuits, and we will be providing legal training to all relevant staff.Naming conventions4 The key starting point for any genealogical search is through surnames. Although first names, maiden names, and middle names are all significant, it is through surnames that most family history can be traced. For this reason, the department will be updating all of our databases with surname information. This is a skilled job, as spellings are often changed on documents as a result of clerical error. All staff will be involved in this process after appropriate training.Commercial aspects5 As mentioned earlier, genealogy is no longer a vanity hobby but has become a lucrative business. As a nonprofit organization, it is not our intention to compete in this market; however, we will need to cover the costs of increased staffing and training, so we will be charging a nominal fee for our services. The finance department is currently assessing the charges, which will be detailed in our next report. The fees will be reviewed on an annual basis.6 We thank all staff in advance for your cooperation in this exciting new opportunity for our department. Please make sure that you keep well informed of any updates on the website.Match the heading (1-5) with five main ideas (A-H)1. New challenge 2. Family history 3. Medicine and law 4. Naming conventions 5. Commercial aspects A. People from European countries are more interested in genealogy than people from elsewhere.B. Interest in genealogy has grown dramatically in recent years.C. People want to find out more details about the lives of their ancestors.D. Advanced technology is necessary for conducting detailed genealogy searches.E. Issues related to genetics and inheritance are of increasing importance in genealogy searches.F. People conducting ancestry searches tend to be males over the age of 45.G. The most vital piece of information in a genealogy search is a persons last name.H. The area of genealogy is becoming financially rewarding. What component is an example of skill-related fitness What happens in Diabetes? please make rough draft of this pre writing of 150 wordsWhen I was at primary school in 2nd grade. I was a very geeky and scrawny socially awkward type person. I had only two friends both of there name was "Austin" but I don't remember their Last names. I was at music class and the who's name I also forgot. Decided last minute to hold a talent show. No one really did anything but a very unintelligent little Luke Oden. Decided to sing the ninjago season 1 theme song. I went up and sang my song. It was terrible and I was bullied for a couple of months after.