Wednesday
October 26, 2016

# Search: What is the probability that the random variable has a value greater than 4?

Number of results: 38,684

There is a 60% that your math teacher will give a pop quiz tonight and, due to the fact that you have a soccer game, there is an 85% chance you will not be able to do your math homework. You decide that you will do the homework if the probability of there being a pop quiz and ...
October 8, 2015 by Hannah

math solutions
solve the equation abx=cy for each of following the variable x the variable a the variable c solve the equation ay/x the variable y the variable z the variable x solve each of following for variable y 3y=ab ab=cy ayc=bx bx/y=R zy/x=b
October 6, 2008 by sherri

Intro to Local Area Networks
1. System A consists of a single ring with 100 stations, one per repeater. System B consists of four 25 stations rings linked by a bridge. If the probability of a link failure is , a repeater failure is , and a bridge failure is , derive an expression for parts (a) to (d). a) ...
March 18, 2010 by Ramie

HELP!! MATH!
A bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn. 1. What is the probability of selecting a purple marble and then a white marble? 2. What is the probability of selecting ...
May 18, 2015 by Anon101

statistics
The US Environmental Protection Agency reports the average fuel costs for various makes of cars. In recent years the fuel costs for mid‐size Japanese cars averaged \$1200. Suppose that the annual fuel costs for various makes of automobiles are normally distributed and ...
July 6, 2015 by meri

Algebra
The value of almost everything you own, such as a car, computer, or appliance, depreciates over time. When the value decreases by a fied amount each year, the depreciation is called straight-line depreciation. Suppose your car has an initial value of \$16,750 and depreciates \$...
March 12, 2012 by kim

statistics
the random variable x is normally distributed with a mean of 75 and a standard deviation of 15.0. For this distribution, what is the twenty-third percentile?
August 20, 2010 by marie

Math
Random variable X is normally distributed with mean 10 and standard deviation 2. Compute the following probabilities. a. Pr(X<10) b. Pr(X<11.04) I don't know where to start.
November 10, 2011 by Sally

Finite
Assume that the coin is weighted so that Pr[H] = [ 1/11], and that it is flipped 9 times. The random variable X is defined as the number of heads in the 9 flips. What is E[X]?
October 8, 2012 by Sam

College Statistics
A random variable X has a Gamma distribution with (alpha = a, beta = b). Show that P(X > 2ab) < (2/e)^a. hint: X > c is equivalent to e^Xt > e^ct
March 30, 2013 by Allie

Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals). c. P(z -1.5) d. P(z -2.5)
April 8, 2014 by Vanessa

Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals). a. P(z -1.5) b. P(z -2.5)
April 10, 2014 by Vanessa

math
find the cumulative function, mean and variance of the following continuous pdf of a random variable X. f(x)=x/2 for 0<x<1 f(x)= 1/2 for 1<x<=2 f(x)=(3-x)/2 for 2<x<3 f(x)=0 otherwise
January 20, 2016 by Zelalem Getnet

stats
Given that z is a standard normal random variable, find z for each situation (to 2 decimals). 1.The area between -z and z is 0.2128
April 13, 2016 by Anonymous

Probability
Consider a fire alarm that senses the environment constantly to figure out if there is smoke in the air and hence to conclude whether there is a fire or not. Consider a simple model for this phenomenon. Let Θ be the unknown true state of the environment: Θ=1 means ...
April 21, 2015 by qwerty

Math
Three hundred people apply for three jobs. 80 of the applicants are women If three persons are selected at random, what is the probability that one is a woman? (Round the answer to six decimal places.)(d) If three persons are selected at random, what is the probability that ...
September 21, 2015 by MiMi

Maths - Probability q2
Five cards are lettered A, B, C, D, E Three cards are chosen at random one after the other without replacement and are in the order shown below First, Second, Third What is the probability that the cards spell the word BED
May 13, 2013 by donald

Managerial ECON
The chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm’s short- run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC dollars per vacuum cleaner and Q number of vacuum ...
November 6, 2011 by lost

Probability
thirty animals are to be used in a medical experiment on diet deficiency: 3 male and 7 female rhesus monkeys, 6 male and 8 female dogs. If one animal is selected at random, what is the probability of getting a chimpanzee or a dog?
July 29, 2013 by Lucy

math
It is known that the number of people who enter a bank during a time interval of t minutes is a Poisson random variable with the parameter t. The bank opens at 8am and you arrive at the bank at uniformly random time between 8am and 9am. Let X be the number of people who ...
May 3, 2013 by hao

math
It is known that the number of people who enter a bank during a time interval of t minutes is a Poisson random variable with the parameter t. The bank opens at 8am and you arrive at the bank at uniformly random time between 8am and 9am. Let X be the number of people who ...
May 3, 2013 by hsuan

math
Which statement is true about the value of (5−n)(5n)? a.For all n, the value of the expression is 0. b.For n<0, the value of the expression is greater than 1. c.For n<0, the value of the expression is less than 1. d.For all n, the value of the expression is 1.
December 4, 2015 by liliana

math/algebra
solve each of the following systems by substitution. 16) 5x -2y = -5 y - 5x = 3 20) 8x -4y = 16 y = 2x - 4 28) 4x -12y = 5 -x + 3y = -1 Step one: Solve on of the equations for one of the variables. y=2x-4 Step two:Substitute the expression for the variable found in step one ...
June 7, 2007 by Diana

statistics
From past experience it is felt that the random variable, X, the age of a mother at the birth of her first child, is normally distributed with a mean of 21.3 and a variance of 16. Find the probability that a randomly selected mother: (a) has her first child before age 16 (b) ...
January 26, 2011 by Tian

Probability/Statistics
Assume 20 oz. cola bottles are filled so that the mean amount of liquid contained in the bottle is 20 oz and the standard deviation is .12 oz. If a bottle is randomly selected, find the probability that the number of ounces in that bottle is greater than 20.21 oz.
June 21, 2008 by thomas

math prob
It is known that the number of people who enter a bank during a time interval of t minutes is a Poisson random variable with the parameter t. The bank opens at 8am and you arrive at the bank at uniformly random time between 8am and 9am. Let X be the number of people who ...
May 4, 2013 by hsuan

Probability
MY MAIN PROBLEM IS FIGURING OUT WHAT DISCRETE DISTRIBUTION TO USE, BERNOULLI, BINOMIAL, DISCRETE UNIFORM, GEOMETRIC NEGATIVE BINOMIAL, OR POISSON. Every time I choose one, it's the incorrect one. Is there some way I can easily find out which one to use...
March 6, 2008 by Amelie

statistics
Find the indicated binomial probabilities. Round to the nearest 3 decimal places. In a local college, 20% of the math majors are women. Ten math majors are chosen at random. 1) What is the probability that exactly 2 are women? 2) What is the probability that 2 or less women ...

MAths
A unit square is drawn in the Cartesian plane with vertices at (0,0),(0,1),(1,0),(1,1). Two points P,Q are chosen uniformly at random, P from the boundary of the square and Q from the interior of the square. The line L1 through P and Q is drawn. The probability that the points...
April 29, 2013 by ianian

Maths
2a) assume that adult males have footless which are normally distributed with mean 24.6 cm and standard deviation 1.05 cm. Calculate the probability that an adult male has a foot length is greater than 27 cm. My answer - 2 2b) assume adult females have foot lengths which are ...
March 3, 2016 by Anonymous

Probability
What is the probability of spinning a number greater than 5 OR less than 3 on this spinner? This problem has a picture of a spinner with 8 sections divided equally. The sections are labeled: 1,2,3,4,5,6,7,8.
February 18, 2008 by LiLY

Math
Someone tossed a coin 80 times.The coin landed on heads 60 times. Is the experimental probability greater than or less than theoretical probability?
March 19, 2013 by Taya

stat
Problem 2. THE PROBABILITY THAT A RANDOMLY CHOSEN SALES PROSPECT WILL MAKE A PURCHASE IS 0.20. IF A SALESMAN CALLS ON SIX PROSPECTS, A. WHAT IS THE PROBABILITY THAT HE WILL MAKE EXACTLY FOUR SALES? B. WHAT IS THE PROBABILITY THAT THE SALESMAN WILL MAKE FOUR OR MORE SALES? C. ...
May 1, 2012 by siddhi

algebra3
which inequality is tge solution of 6x negative 3 greater than or = to 7 plus 4x? a.}x is greater than or =to negative 5 b.}x is greater than or= to 5 c.}x is less than or = to 5 d.}x is less than or = to negative 5 Your problem: 6x - 3 ≥ 7 + 4x Solve an inequality like ...
January 11, 2007 by Darius Graham

Given a population comprised of 30 bats, 15 gloves, and 60 balls, if sampling is random and one at a rime without replacement, what is the probability of obtaining a bat, a glove, and a bat in that order if three objects are sampled from the population?
April 30, 2009 by Lou

Algebra 2
Suppose the experimental probability is 1/3 that a carton of eggs contains at least one broken egg. Use the simulation of 20 trials to find the experimental probability that 3 cartons selected at random contain only unbroken eggs.
November 2, 2010 by bc

math
Two cards are selected at random without replacement from a well-shuffled deck of 52 playing cards. Find the probability of the given event. (Round your answer to three decimal places.) find the probability that A pair is not drawn.
November 8, 2011 by Rico

Math Help ASAP SETS & Probability
Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 2 10 17 29 Female 7 15 4 26 Total 9 25 21 55 If one student was chosen at random, find the probability that the student got a C.
October 1, 2016 by Amanda

math
1. The table shows the results of spinning a four-colored spinner 50 times. Find the experimental probability and express it as a decimal. P(not red) = ? red | blue | green | yellow ---------------------------------------- 20 | 10 | 9 | 11 (1 point) a 0.6 b 0.4 c 0.2 <...
June 1, 2016 by Kawaii_potato

statistics
B} The average number of mosquitoes in a stagnant pond is 70 per square meter with a standard deviation of 8. If 36 square meters are chosen at random for a mosquito count, find the probability that the average of those counts is more than 70.9 mosquitoes per square meter. ...
November 12, 2014 by Loren

Elementary Statistic
twenty-five percent of all death are caused by diseases of the heart Ischemic heart disease accounts for 16.4% of all death and heart failure for 2.3% choose one death at random. What is the probability that it is from ischemic heart disease given that it was from heart ...
June 24, 2015 by Angela

Math
A department store is holding a drawing to give free shopping sprees to two lucky customers. There are 15 customers who have entered the drawing: 4 live in the town of Gaston, 6 live in Pike, and 5 live in Wells. In the drawing, the first customer will be selected at random, ...
February 21, 2011 by Rachal

elementry math
A box contains three black balls and two gold balls. A ball is selected at random, its color is recorded, and it is then replaced. A second ball is then selected at random and its color recorded. The outcome associated with this type of selection is an ordered pair (first draw...
January 10, 2010 by katie

math
2) In a certain instant lottery game, the chances of a win stated as "3 in 23". Express the indicated degree of likelihood as a probability value between 0 and 1 3) A certain company reduced its management staff from 20 managers to 16. The company claimed that 4 managers were ...
March 15, 2012 by Jamie

Probability
There are 3 lucky tickets among 10 lottery tickets. 3 tickets are drawn at random. What is a probability that one ticket selected randomly from those three is lucky? PLEASE HELP
October 20, 2010 by JHONY

Statistics-Probability
An instructor will choose 3 problems from a set of 7 containing 3 hard and 4 easy problems. If the selection is made at random, what is the probability that only the hard problems are chosen?
February 5, 2013 by Steven

stat
the average number of pushups a United States Marine does daily is 300, with a standard deviation of 50. A random sample of 36 marines is selected. What is the probability that the sample mean is at most 320 push-ups? With a mean of 300, you are looking for a sample using a ...
April 15, 2007 by Anonymous

chin
You want to set up a games stall at the Winter Wonderland. You have a single pack of 52 cards and decide to play card games with your customers. The game is designed as follows. A customer draws 4 cards at random. For every “Ace” that the customer draws, he/she wins £3 and for...
November 13, 2014 by lee

statistics
You want to set up a games stall at the Winter Wonderland. You have a single pack of 52 cards and decide to play card games with your customers. The game is designed as follows. A customer draws 4 cards at random. For every “Ace” that the customer draws, he/she wins £3 and for...
November 13, 2014 by lee

statistics
You want to set up a games stall at the Winter Wonderland. You have a single pack of 52 cards and decide to play card games with your customers. The game is designed as follows. A customer draws 4 cards at random. For every “Ace” that the customer draws, he/she wins £3 and for...
November 13, 2014 by sana

math
CountingOutcomes and Theoretical Probability A computer store sells 4 models of computer (m1,m2,m3 m4. Each model can be fitted with 3 sizes of hard drive (A,B,C,) 1- Find the sample space. 2- What is the probability of choosing a model with a size C hard drive? 3- What is the...
January 31, 2010 by Julainna

stat probability
At a certain college, there were 780 science majors, 320 engineering majors, and 390 business majors. If one student was selected at random, the probability that they are a business major is?
April 8, 2013 by Lynn

algebra
A bag contains 9 marbles: 2 are green, 4 are red, and 3 are blue. Laura chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue? Write your answer as a fraction in simplest form.
November 29, 2015 by denora

PROBABILITY
There are 3 lucky tickets among 10 lottery tickets. 3 tickets are drawn at random. What is a probability that one ticket selected randomly from those three is lucky?
October 12, 2010 by OMER

PROBABILITY
There are 3 lucky tickets among 10 lottery tickets. 3 tickets are drawn at random. What is a probability that one ticket selected randomly from those three is lucky?
October 13, 2010 by JHONY

PROBABILITY
There are 3 lucky tickets among 10 lottery tickets. 3 tickets are drawn at random. What is a probability that one ticket selected randomly from those three is lucky?
October 20, 2010 by JHONY

PROBABILITY
There are 3 lucky tickets among 10 lottery tickets. 3 tickets are drawn at random. What is a probability that one ticket selected randomly from those three is lucky?
October 21, 2010 by JHONY

statistics and probability
A shipment of 20 computers contains 4 defective machines.Two computers are selected at random without replacement and tested for being detective. (a). is this a binomial experiment? why or why not solution. Yes. because each trial can result in just two possible outcomes. (b...
December 3, 2015 by masinde

Algebra 2
suppose the experimental probability is 1/3 that a carton of eggs contains at least one broken egg. Use a stimulation of 20 trials to find the experimental probability that three cartons selected at random contain only unbroken eggs.
September 10, 2015 by Liliya

Science
Which of the following best describes the dependent variable in an experiment? A- the variable that is measured B- the variable that is manipulated C- the variable that you can see D- the variable that is most common (My guess is A) Photosynthesis is the process whereby plants...
September 20, 2014 by Skye

Statistics/Probability
A certain brand of candies have a mean weigh of 0.8576 g and a standard deviation of 0.0523. A sample of these candies came from a package containing 447 candies,and the package label stated the net weight is 381.3 g. (If every package has 447 candies, the mean weight of the ...
March 5, 2015 by slomomo

Math
Did I answer this problem right? A bag contains 13 marbles of which 10 are red. A marble is selected at random and replaced. A second marble is then selected at random. What is the probability that both marbles are red? 100/169. Thanks.
August 7, 2009 by B.B.

math
a bag contains 6 blue marbles and 10 red marbles. If you choose one marble at random, and then another marble at random, what is the probability that both marbles are blue?
July 22, 2016 by carol

math
A bucket contains 7 red, 3 blue, 2 black and 1 yellow ball of the same size. A random selection of 5 balls is taken from the bucket. find the probability that the random selection will contain atleast 1 red ball?
August 17, 2011 by Mahalakshmi

Statistics/Probability
The standard deviation of the masses of articles in a large population is 4.55 kg. Random samples of size 100 are drawn from the population. Find the probability that a sample mean will differ from the population mean by less than 0.8 kg.
July 17, 2014 by Koylar

Statistics
To determine whether themean nicotine content of a brand of cigarettes is greater than the advertised value of 1.4 milligrams, a health advocacy program tests: Ho: mu = 1.4 Ha: mu > 1.4 The calculated value of the test statistic is z = 2.42. ==> How do I calculate the p-...
February 27, 2011 by Emily

Math
In a game, you have a 1/27 probability of winning \$100 and a 26/27 probability of losing \$4. What is your expected value?
March 16, 2015 by Marli

probability
if for two random variables X and Y,is Y=-X then ñ=1
November 4, 2011 by alex

Math
The odds of rolling two dice and the sum being greater than 9 are 6 to 30. What is the probability that the sum of two rolled dice is less than or equal to 9? I got 1/5 because its greater? help.
August 28, 2015 by Jacqueline

Math-Probability
Suppose an urn contains 8 red,5 white and 7 blue marbles.If 3 marbles are drawn at random from the urn with replacement,what is the probability that three marbles are the same color?Give answer in a reduced fraction.
November 14, 2013 by Melina

Math
An unfair coin with Pr[H]=0.25 is flipped 95 times. A random variable X is defined as the number of heads that occur. Find the standard deviation. Any help??
April 2, 2012 by Tiffany

elementary stats
A binomial random variable is based on n = 28 and p = 0.7. Find x2P(x). (Give your answer correct to two decimal places.) 1
March 30, 2013 by Toni

Statistics
Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is \$120,000. This distribution follows the normal distribution with a standard deviation of \$38,000. (A) If we select a random sample of 58 ...
April 11, 2014 by Student5

probability---normal distribution
population size=50 population mean= 80m standard deviation = 0.70m what proportion would have average meter of 89 or more? ---------------------------- now I know how to solve this problem if the question is worded "what proportion would have average meter Greater than 89?" ...
September 4, 2011 by Alex

prob
Consider the triangle with vertices (0; 0), (1; 0) and (0; 1). Let Z be a uniform random variable in the interval [0; 1]. Draw a vertical line that intersects the x axis at Z. This line divides the triangle in two pieces. Select a point (X; Y ) uniformly at random from the ...
May 3, 2013 by hsuan

algebra 1
1. MULTI-STEP PROBLEM There are 5743 known amphibian species in the world. Of these, 1856 species are judged to be at risk of extinction, and another 113 species may already be extinct. a. Find the probability that an amphibian species chosen at random is at risk of ...
May 17, 2016 by Ruby

Help ASAP
A jar contains 5 red marbles, numbered 1 to 5, and 12 blue marbles numbered 1 to 12. a) A marble is chosen at random. If you're told the marble is red, what is the probability that it has the number 3 on it? b) The first marble is replaced, and another marble is chosen at ...
October 8, 2016 by Anonymous

Stats
I have a test on this tomorrow and I swear he didn't teach this and the book's not helping either, so maybe u can: A hwy engineer knows that his crew can lay 5 miles of hwy on a clear day, 2 miles on a rainy day, and only 1 mile on a snowy day. Suppose that the probabilities ...
November 14, 2012 by Jessica

Math
1. Suppose a and b are integers, and the absolute value of a is > than the absolute value of b. Must a be greater than b? Use examples to support your answer. 2. Do decimals have opposites? Explain. 3. For what values of x does the absolute value of x equal negative x?
September 22, 2013 by Calla

statistic****help*****
Show all your work. Indicate clearly the methods you use because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation. A simple random sample of adults living in a suburb of a large city was selected. The age and ...
March 19, 2014 by akiba

math
Taylor surveys students in one grade level who own at least one pet. She finds that 50% of the students surveyed own 2 pets, 3 students own 3 pets each, and 2 students own 4 pets each. Eight of the students in the grade own 1 pet. Considering the number of pets as the random ...
May 19, 2014 by Anonymous

math
Please help with this question. A bag contains 10 marbles of which 3 are red. A marble is selected at random and replaced. A second marble is then selected at random. What is the probability that both marbles are red?
July 30, 2010 by jackie

statistics
Find the indicated binomial probabilities. Round to the nearest 3 decimal places. In a local college, 20% of the math majors are women. Ten math majors are chosen at random. 1) What is the probability that exactly 2 are women? 2) What is the probability that 2 or less women ...

GEOMETRY
The squares of a 3×3 grid of unit squares are coloured randomly and independently so that each square gets one of 5 colours. Three points are then chosen uniformly at random from inside the grid. The probability that these points all have the same colours can be expressed as a...
March 27, 2013 by Anonymous

math
Hi! I'm Maddie. I need some help on my homework. Here are three problems I need help with: A bowl contains only red marbles, blue marbles and green marbles. The probability of selecting a red marble from the bowl is 3/13. The probability of selecting a blue marble from the ...
August 21, 2013 by Maddie

Math : Probability and Standard Deviation
This is a word problem. "We know that for certain workers the mean wage is \$5/hr with a standard deviation of \$.50. We need to find out if a worker is chosen at random what is the probability that the workers' wage is between \$4.50 and \$5.50? Assume a normal distribution of ...
October 23, 2007 by Tiffany Johnson

Math help.
1. 1 • 12 numerical expression variable expression; a is the variable variable expression; there is no variable variable expression; l is the variable 2. f ÷ 7 variable expression; there is no variable numerical expression variable expression; g is the variable variable ...
September 17, 2014 by Anonymous

Statistics and Probability
A research manager at Coca-Cola claims that the true proportion, p, of cola drinkers that prefer Coca-Cola over Pepsi is greater than 0.50. In a consumer taste test, 100 randomly selected people were given blind samples of Coca-Cola and Pepsi. 58 of these subjects preferred ...
March 23, 2011 by Adam

Computer Science
public class RandomPhoneNumber { public static void main(String[] args) { int num1=(int)(Math.random()*7); int num2=(int)(Math.random()*7); int num3=(int)(Math.random()*7); int set1=(int)(100+Math.random()*642); int set2=(int)(1000+Math.random()*8000); System.out.println("Your...
October 30, 2012 by Sarah

STATISTIC***HELP
Show all your work. Indicate clearly the methods you use because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation. A simple random sample of adults living in a suburb of a large city was selected. The age and ...
March 18, 2014 by KIBA

Math
The following equation has denominators that contain variables. for this equation write the value or values of the variable that make a denominator zero. these are the restrictions on the variable. keeping the restrictions in mind, solve the equation. 2/11x plus 1/4 equals 81/...
April 22, 2016 by Anonymous

Probability
Let X be the number of successes in 25 independent trials with probability 1/10 of success in each trial. Let m be the most likely value of S. Find m.
March 31, 2013 by Claire

Statistics
A paper manufacturer claims that fewer than 1 in 100 of its reels (2 ton rolls) of paper is flawed. A customer has just received a large shipment of these reels and proceeds to check a random sample of 600 of them for flaws. Of this sample, 14 reels are found to be flawed. ...
February 26, 2007 by Jason L

statistics
The power of a significance test for a particular value of the parameter is computed to be 0.93. Which statement below is true? a) The probability of committing a Type I error is 0.07. b) The probability of committing a Type I error is 0.93. c) The probability of committing a ...
April 17, 2012 by Anna

Chemistry
Would the value of molar absorbitivity value be greater, less, or equal for the absorbance of light at 550nm vs 650 nm?
November 13, 2013 by Anonymous

statistics & probability
according to a survey, 30% of 18-25 year olds have blue eyes. In a random sample of 8 people in this age group what is the probability that exactly 0 have blue eyes?
June 27, 2013 by Madison

pre-algebra
Rewrite the equation so the variable is alone. Solve to find the value of the variable. 42=-2h Divide both sides by 2. Then change the signs of both sides. That will provide the answer. Possibly in 1 step: Divide by -ve 2
March 15, 2007 by Julia

statistics
One student is selected at random from a student body. Suppose the probability that this student is female is 0.5 and the probability that this student works part time is 0.6. Are the two events "female" and "working" mutually exclusive?
October 5, 2010 by nasta

Probability
2/3 people at a spa are there to lose weight. There are 10 people there and I approach one. What is the probability that the person is there to lose weight? The random variables are based on 10 rolls of a dice. 1(1)+ 2(2)+ 3(1)+ 4(2)+ 5(1)+ 6(3) {1=4=3=8=1=18}= 35 Please help ...
March 8, 2013 by kathy

probability
A random sample of six integers in the interval [1,42] is to be drawn. The numbers are selected randomly, one after the other, and repeats are allowed. What is the probability the six numbers in the sample will all be different?
September 4, 2013 by zach