Answer:
The answer is Nitrogen
Hope this helps :)
Can you help me with this?
16. The equatiοn οf the line in slοpe-intercept fοrm that passes thrοugh the pοint (-6, 5) and is parallel tο x + 2y = 14 is y = (-1/2)x + 2.
What is equatiοn οf line?The equatiοn οf a straight line is y = mx + c, y = m x + c m is the gradient and c is the height at which the line crοsses the y -axis, alsο knοwn as the y -intercept.
16. Tο write the equatiοn οf a line in slοpe-intercept fοrm, we need tο find the slοpe and the y-intercept οf the line.
Tο find the slοpe οf the line, we can rewrite the equatiοn x + 2y = 14 in slοpe-intercept fοrm y = mx + b by sοlving fοr y:
x + 2y = 14
2y = -x + 14
y = (-1/2)x + 7
The slοpe οf the line is -1/2.
Since the line we want tο find is parallel tο this line, it will have the same slοpe οf -1/2.
Nοw we can use the pοint-slοpe fοrm οf the equatiοn οf a line tο find the equatiοn οf the line that passes thrοugh the pοint (-6, 5) with a slοpe οf -1/2:
y - y1 = m(x - x1)
where (x1, y1) is the pοint (-6, 5), and m is the slοpe, -1/2.
y - 5 = (-1/2)(x - (-6))
y - 5 = (-1/2)x - 3
y = (-1/2)x + 2
17. The equation perpendicular to y = -(2/3)x + 4, passing through (-4, 6)
perpendicular equations slope would be negative reciprocal to the current line.
The slope in y = -(2/3)x + 4, is m = -(2/3),
The negative reciprocal of -(2/3) is 3/2
Now, applying the x and y values in pοint-slοpe fοrm
y - 6 = 3/2(x - (-4))
y = 3/2(x+4) + 6
y = (3/2)x + 6 + 6
y = (3/2)x + 12
18. Since the line we want tο find is parallel tο this line, it will have the same slοpe.
Lets find the slope using slope formula
[tex]\rm m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]\rm m = \dfrac{0 - (-1)}{2 - (-1)}[/tex]
[tex]\rm m = \dfrac{1}{3}[/tex]
Now, using the point slope form
y - 1 = 1/3(x - 3)
y = 1/3(x - 3) + 1
y = (1/3)x - 1 + 1
y = (1/3)x
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Dentify the solution to the following system of equations
Identify the solution to the following system of equations
No solution
(0. 29, 2. 73)
(0. 78, 0. 05) and (-4. 32, 12. 80)
( -1, 4. 5)
If m = 3/2, the two equations in the system are dependent and have an infinite number of solutions.
To do this, we can set the coefficients of x and y in the two equations equal to each other:
6 - 4m = 2k(2m - 1)
2n - 7 = 3k
Simplifying these equations, we get:
8m - 6 = 4km
2n - 7 = 3k
We can solve the first equation for k:
k = (8m - 6)/(4m)
Substituting this into the second equation and solving for n, we get:
n = (16m - 29)/(8m - 12)
Now we need to check if there are any values of m for which the equations are proportional. We can do this by checking if the expressions for k and n are the same for all values of m.
We find that the expressions for k and n are the same for m = 3/2.
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Complete Question:
Determine the values of m and n so that the following system of linear equations have infinite number of solutions:
(2m−1)x+3y−5=0
3x+(n−1)y−2=0
Help Me Find Y
Show Work
Answer:
y = 12
Step-by-step explanation:
if a tangent and a secant are drawn from an external point to a circle, then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant , that is
y² = 8(8 + 6 + 4) = 8 × 18 = 144 ( take square root of both sides )
y = [tex]\sqrt{144}[/tex] = 12
A friend is building a garden with two side lengths 16 ft and exactly one right angle. What geometric figures could describe how the garden might look?
SELECT ALL THAT APPLY:
A. Kite.
B. Isosceles right triangle
C. Quadrilateral
D. Parallelogram
(Remember it is multiple choice)
Answer:
B. Isosceles right triangle
C. Quadrilateral
D. Parallelogram
Step-by-step explanation:
Answer:
The geometric figures that could describe how the garden might look are B. Isosceles right triangle and C. Quadrilateral.
Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. )
P = $1300, r = 8. 5%, t = 11 years
n A
1 $
2 $
4 $
12 $
365 $
Continuous $
The complete table for the amount balance, A when P dollars is invested at rate r for t years and compounded n times per year is present in above figure 2.
The compound interest formula is written as A = P( 1 + r/n)ⁿᵗ
where, A--> total Amount of money after t years
P --> Principal
r --> Annual rate of interest (as a decimal)
t --> Number of years:
n--> number of times interest is compounded per year
Here, principle, P = $1300, rate of interest, r = 8.5% = 0.085 , time periods, t = 11 years. We have to complete the above table for compound interest.
Case 1: n = 1
Substitute the known values in above formula, A = 1300( 1 + 0.085/1)¹¹
= 1300( 1.085)¹¹
= 3,189.12
Case 2: n = 2
A = 1300( 1 + 0.085/2)²²
= 1300( 2.085/2)²²
= 1300( 1.0425)²²
= 3,248.01
I'll let you work out the cases where n = 4, 12 and 365 since all you need to do is place those in for n as done in the 1st 2 cases. For the Compounded continuously case, the formula becomes,
[tex] A = Pe^{rt}[/tex]
Where: A-> Total amount of money after t years
P --> Principal Amount
e --> Natural log constant:
r = Annual rate of interest (as a decimal)
Case: Continuous: e = 2.71828 (approx), r = 0.085
A = 1300( 2.71828)⁰·⁰⁸⁵⁽¹¹⁾
= 1300(e)⁰·⁹³⁵ = 3,311.34
Hence, required value is $3,311.3775.
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Complete question :
The above table completes the question.
Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. ) P = $1300, r = 8. 5%, t
= 11 years
4 more than 3 times a number is 5
Answer:
0.33
Step-by-step explanation:
To solve this, you first write the problem as an algebra equation as follows: 3x + 4 = 5
Then you solve the equation by subtracting 4 from both sides, and then divide both sides by 3. Here is the math to illustrate better:
3x + 4 = 5
3x + 4 - 4 = 5 - 4
3x = 1
3x/3 = 1/3
x = 0.33
Answer = 0.33
What is the measure of arc AC? PLS help
a family of five recently replaced its 5-gallon-per-minute showerheads with water-saving 2-gallon-per-minute showerheads. each member of the family averages 8 minutes in the shower per day. in a 30-day period, how many fewer gallons of water will the family use with the new showerheads? responses 60 60 800 800 2,400 2,400 3,600 3,600 7,200
The family will use 3,600 fewer gallons of water with the new showerheads in a 30-day period.
A family of five recently replaced its 5-gallon-per-minute showerheads with water-saving 2-gallon-per-minute showerheads. Each member of the family averages 8 minutes in the shower per day. In a 30-day period, the family will use 3,600 fewer gallons of water with the new showerheads. How many fewer gallons of water will the family use with the new showerheads?
Calculate the number of gallons used per person per shower before:
5 gal/min x 8 min = 40 gallons per person per shower.
The number of gallons used per person per shower after:
2 gal/min x 8 min = 16 gallons per person per shower.
The number of gallons used per person per day before:
40 gallons x 1 shower = 40 gallons per person per day.
The number of gallons used per person per day after:
16 gallons x 1 shower = 16 gallons per person per day
The number of gallons used per family per day before:
40 gallons x 5 people = 200 gallons per day
The number of gallons used per family per day after:
16 gallons x 5 people = 80 gallons per day
The number of gallons used per month before:
40 gallons x 5 people x 30 days = 6,000 gallons per month
The number of gallons used per month after:
16 gallons x 5 people x 30 days = 2,400 gallons per month
The family will use 6,000 - 2,400 = 3,600 fewer gallons of water with the new showerheads in a 30-day period. Therefore, the answer is 3,600.
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The cost price of 20 articles is the same as sellling price of 16 articles find the gain percent
If the cost price of 20 articles is the same as selling price of 16 articles, then the gain percentage is 25%
To find the gain percent, we first need to calculate the profit earned on the sale of the 16 articles.
Let the cost price of each article be "C" and the selling price of each article be "S".
Given that the cost price of 20 articles is the same as the selling price of 16 articles, we can write:
20C = 16S
We can simplify this equation to:
S = (20/16)C = (5/4)C
Now, let's calculate the profit earned on the sale of 16 articles:
Profit = Total Selling Price - Total Cost Price
Profit = 16S - 20C
Profit = 16(5/4)C - 20C
Profit = 5C/2
The profit earned is 5C/2. The profit percent can be calculated as:
Profit Percent = (Profit / Cost Price) x 100
Profit Percent = (5C/2) / (20C) x 100
Profit Percent = 25%
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The spinner above is used in a game. What is the theoretical probability of the given event with one spin?
P (5)
Answer:
B
Step-by-step explanation
so there is 8 numbers so when you spin you have a 1/8 chance of spinning the numberA grading machine can grade 96 multiple choice test in 2 minutes. if a teacher has 300 multiple choice test to grade, predict the number of minutes it will take the machine the grade the tests. please answer with details please
Answer:
6.25 minutes
Step-by-step explanation:
So, if there are 96 tests being graded in 2 minutes, the average per minute (using the equation 96/2 = average) would be 48 per minute. Next you would do 300/48 to get the number of minutes that it would take to grade that amount. The answer to that would be 6.25, So it would take approximately 6.25 minutes.
1 Write a positive or negative number to represent each change in the high temperature. Tuesday's high temperature was 4 degrees less than Monday's high temperature.
Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.
Average temperature is calculated as (Monday's temperature plus Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature)/Total days.
Temporary for Monday and Tuesday plus Temperatures for Wednesday and Thursday.
The sum of the temperatures for Monday, Tuesday, Wednesday, and Thursday is equal.
As stated, the 6.5 degree average for the days of Tuesday, Wednesday, Thursday, and Friday.
using the formula no.
Average temperature is equal to (Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature plus Friday's temperature)/Total days.
Thus, Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.
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the complete question is
Write a positive or negative number to represent each change in the high temperature.
1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature. ?
2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature. ?
3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature. ?
4. Friday’s high temperature was 2 degrees less than Thursday’s high temperature. ?
if belongs to the interval , at which values of does the curve have a tangent line parallel to the line ?
Answer:
you need to show the numbers
Step-by-step explanation:
Part of your summer job is to count the number mosquitoes that get caught in traps around your city. At one trap, you count mosquitoes each week ("week 0" means the first day you counted) and record the following numbers:
Use a calculator or graphing technology to determine which of the following functions matches the numbers you counted in these first few weeks.
A) M (w) = 4(w) + 8
B) M (w) = 1.5 (8^w)
C) M (w) = 8 (1.5^w)
D) w = 8 (1.5^M)
Therefore, the function that matches the mosquito counts is'(w) = 8([tex]1.5^{w}[/tex]).
by the question.
To determine which function matches the mosquito counts, we can plot the given data points on a graph and see which function fits the curve. Here are the counts for the first few weeks:
Week Mosquito Count
0 8
1 20
2 50
3 125
4 312
Plotting these points on a graph with weeks on the x-axis and mosquito count on the y-axis, we get:
mosquito graph
Looking at the graph, we can see that the curve increases rapidly and seems to be exponential. This rule out option A (which is linear), leaving us with options B, C, and D.
To determine which of these options matches the data, we can try plugging in the week numbers and seeing which one gives us values close to the actual counts. We can also use a calculator or graphing technology to help us with this.
Option B gives us the following mosquito counts for the first five weeks:
Week Mosquito Count
0 8
1 19.5
2 47.25
3 114.19
4 276.32
Option C gives us:
Week Mosquito Count
0 8
1 12
2 18
3 27
4 40.5
Option D is not a function of mosquito counts with weeks as the input variable, so we can rule it out.
Comparing the values from options B and C to the actual counts, we can see that option C is the closest match.
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It measure the degree of accuracy of the sample mean as an estimate of the population mean
Answer:
The answer is the standard error is a measure of the accuracy of the sample mean as an estimate of the population mean.
Step-by-step explanation:
A textbook has 428 pages numbered in order starting with 1. You flip to a random page in the book in a way that it is equally likely to stop at any of the pages. What is the probability that you turn to page 45? You can write your answer as a fraction, decimal, or percent What is the probability that you turn to an even numbered page? You can write your answer as a fraction, decimal, or percent
Answer:
(a) Since there are 428 equally likely pages, the probability of randomly turning to page 45 is 1/428, which is approximately 0.00234 or 0.234%.
(b) There are two possible cases for an even numbered page: either the last digit is 0, 2, 4, 6, or 8, or the page number ends in 00.
For the first case, there are 5 possible digits for the units place, and each of these digits can be followed by any one of the 5 possible digits for the tens place. So there are 5x5 = 25 even numbered pages that end in a non-zero digit.
For the second case, there are 4 possible digits for the hundreds place, and each of these digits can be followed by 00. So there are 4 even numbered pages that end in 00.
Therefore, there are 25 + 4 = 29 even numbered pages in total. Since there are 428 pages in the book, the probability of randomly turning to an even numbered page is 29/428, which is approximately 0.06776 or 6.776%.
Step-by-step explanation:
(a) Оскільки існує 428 рівноймовірних сторінок, ймовірність випадкового переходу на сторінку 45 дорівнює 1/428, що становить приблизно 0,00234 або 0,234%.
(b) Існує два можливих випадки, коли сторінка має парний номер: або остання цифра 0, 2, 4, 6 або 8, або номер сторінки закінчується на 00.
У першому випадку є 5 можливих цифр для позначення одиниць, і за кожною з цих цифр може слідувати будь-яка з 5 можливих цифр для позначення десятків. Таким чином, існує 5x5 = 25 парних сторінок, які закінчуються на ненульову цифру.
У другому випадку є 4 можливі цифри для сотень, і за кожною з цих цифр може стояти 00. Отже, є 4 парні сторінки, які закінчуються на 00.
Таким чином, всього є 25 + 4 = 29 парних сторінок. Оскільки в книзі 428 сторінок, ймовірність випадкового переходу на парну сторінку дорівнює 29/428, що становить приблизно 0.06776 або 6.776%.
Describe the relationship between n and 4 that makes the equation 7 x n/4 greater that 7
An Inequality is a relationship between two expressions or values that aren't equal. The relationship between n and 4 is given by the inequality n> 4.
We want to find a relation between n and 4 similar that
7 *( n/ 4)> 7
still, we get
If we now divide both sides of the former inequality by 7.
7 *( n/ 4)/ 7>7/7
n/ 4> 1
So n/ 4 must be lesser than 1.
A better way to show the relationship is to multiply both sides of the inequality by 4.
4 *( n/ 4)> 4 * 1
n> 4
So the relationship between n and 4 is that n must be lesser than 4.
In mathematics, an inequality is a relationship that results in an unstable comparison of two figures or other fine expressions. It's frequently used to compare two figures on a number line grounded on their size.
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Six more than the quotient of a number and 8 is equal to 4
use the variable x for the unknown number
!!!TRANSLATE INTO A EQUATION!!!
Answer:
x/8 + 6 = 4
Step-by-step explanation:
x / 8 + 6 = 4
x/8 = -2
x = 8*-2 = -16.
If Joe has 40 apples and bob steals 5, how many apples does Joe have
Joe aura 35 pommes.
40-5=35
At the book store, you purchased some $5 clearance mystery books and $12 regular-priced science fiction books. How many of each did you buy if you spent a total of $126?
Answer: View answer in explanation below.
Step-by-step explanation: Let's use variables to represent the unknown quantities.
Let x be the number of $5 clearance mystery books purchased.
Let y be the number of $12 regular-priced science fiction books purchased.
We can set up a system of equations based on the given information:
5x + 12y = 126 (total amount spent)
x + y = total number of books purchased
We need to solve for x and y.
Let's use the second equation to solve for one variable in terms of the other:
y = total number of books purchased - x
Now we can substitute this expression for y into the first equation:
5x + 12(total number of books purchased - x) = 126
Simplifying and solving for x:
5x + 12total number of books purchased - 12x = 126
-7x + 12total number of books purchased = 126
-7x = -12total number of books purchased + 126
x = (12total number of books purchased - 126)/7
Since x must be a whole number (you can't buy a fraction of a book), we need to find a value of total number of books purchased that makes x a whole number. We can start by trying different values of total number of books purchased:
If total number of books purchased is 10:
x = (12(10) - 126)/7 = -6/7 (not a whole number)
If total number of books purchased is 11:
x = (12(11) - 126)/7 = 6/7 (not a whole number)
If total number of books purchased is 12:
x = (12(12) - 126)/7 = 6/7 (not a whole number)
If total number of books purchased is 13:
x = (12(13) - 126)/7 = 12/7 (not a whole number)
If total number of books purchased is 14:
x = (12(14) - 126)/7 = 18/7 (not a whole number)
If total number of books purchased is 15:
x = (12(15) - 126)/7 = 24/7 (not a whole number)
If total number of books purchased is 16:
x = (12(16) - 126)/7 = 30/7 (not a whole number)
If total number of books purchased is 17:
x = (12(17) - 126)/7 = 36/7 (not a whole number)
If total number of books purchased is 18:
x = (12(18) - 126)/7 = 42/7 = 6 (a whole number)
So, you bought 6 $5 clearance mystery books and 12 - 6 = 6 $12 regular-priced science fiction books.
Scientists determined that the cause of death in many prawns off the coast of Chile was a nutrient deficiency. So, they set out to determine if the distribution of plants in the ocean near the coast was out of proportion when compared to the ideal environment: 40% Kelp, 25% Phytoplankton, 25% Coral and 10% Other (mostly nutrient-low seaweed). In randomly chosen areas along the coast, they sampled 240 plants.
KELP PHYTOPLANKTON CORAL OTHER
84 67 57 32
In an ideal environment how many of the 240 plants would you expect to be Kelp?
If a goodness of fit test is conducted, what is the null Hypothesis?
If a goodness of fit test is conducted, what is the alternative Hypothesis?
What is the probability of getting the observed values or values as extreme from the ideal?
Is there enough evidence to conclude that the environment for prawns is not ideal? Base this conclusion on p-value and a level of significance of 0.05 or 5%.
Answer:
Step-by-step explanation:
80% off of the sale price $90 what is the original price
Answer: So that means the answer is $112.5
Step-by-step explanation:Percent of Discount is 80%. Sale Price is $90. The original price,. = 90 x 100 / 80. = 9000/80. = 112.5. Therefore, $112.5 is the original price.
YES THIS IS RIGHT!!!!
The mayor of a town sees an article that claims the national unemployment rate is
8%. They suspect that the unemployment rate is lower in their town, so they plan to take a sample of 200 residents to test if the proportion of residents that are unemployed in the sample is significantly lower than the national rate. Let p represent the proportion of residents that are unemployed.
Which of the following is an appropriate set of hypotheses for the mayor's significance test?
Choose 1 answer:
The required correct answers are [tex]$$H_0: p = 0.08$$[/tex] , [tex]$$H_a: p < 0.08$$[/tex].
What is Hypothesis test?Let p be the proportion of residents in the town who are unemployed. The null hypothesis [tex]$H_0$[/tex] is that the proportion of unemployed residents in the town is the same as the national unemployment rate of 8%. The alternative hypothesis [tex]$H_a$[/tex] is that the proportion of unemployed residents in the town is significantly lower than the national unemployment rate.
Using the appropriate notation, the hypotheses can be expressed as:
$H_0: p = 0.08$
$H_a: p < 0.08$
Therefore, the appropriate set of hypotheses for the mayor's significance test are:
[tex]$$H_0: p = 0.08$$[/tex]
[tex]$$H_a: p < 0.08$$[/tex]
Note that this is a one-tailed test since the alternative hypothesis is only considering the possibility of the proportion being lower than the national unemployment rate
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Sally has 3:4 as many beads as Kelly. Kelly has 18 more beads than Sally. Find the average number of beads the girl have
The average number of beads that the girls have is 63
Let's start by using algebra to represent the given information:
Let b be the number of beads that Sally has.
Then, Kelly has 3/4 times as many beads as Sally, which can be expressed as (3/4)b.
Also, we know that Kelly has 18 more beads than Sally, which can be expressed as (b + 18).
Putting these together, we can write the equation:
(3/4)b = b + 18
Solving for b, we get:
b = 72
So, Sally has 72 beads, and Kelly has (3/4) × 72 = 54 beads.
The average number of beads that the girls have is (72 + 54)/2 = 63 beads
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Baseball hats are on sale for 12% off the original price of the sale price is $12.50 what was the original price? round the answer to the nearest cent
The original price of the baseball hat before 12% off in the sale was $14.20.
What is a percentage?A number can be expressed as a fraction of 100 using a percentage. It frequently serves to indicate a portion of a total and is represented by the sign %. We may state that 25% of the class is made up of guys, for instance, if there are 100 pupils in the class and 25 of them are male.
The Roman term per centum, which meaning "by the hundred," is where the word "percent" originates.
Let us suppose the original price of the baseball hat = x.
Given that, baseball hats are on sale for 12% off the original price.
That is,
12.50 = x(1 - 12/100)
12.50 = x(100 - 12)/100
12.50 = x(0.88)
x = 14.2
Hence, the original price of the baseball hat was $14.20.
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write the force equation for the following system b and b are the coefficient of viscious friction and force case by this friction is
The force equation for the system is F = bV - bF, where F is the force of friction, V is the velocity of the object, and b is the coefficient of viscous friction.
Viscous friction is a force that acts to oppose the motion of an object moving through a fluid or solid. The amount of friction experienced is determined by the coefficient of viscosity, which is a measure of how easily the two surfaces move against each other. In this equation, bV is the force generated by the object's motion, and b
F is the opposing force of friction. Together, these two forces determine the net force acting on the object.
Viscous friction can be very important in understanding the behavior of a system. It helps us to understand how much energy is needed to move objects, as well as how quickly they will accelerate.
Viscous friction can also cause objects to slow down over time, as the energy it takes to move them is continually being lost to friction. Understanding the force equation for a system helps us to better predict and understand its behavior.
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Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary.W = {[\begin{array}{ccc}a\\b\\c\\\d\end{array}\right] : 3a+b=c, a+b+2c=2d}
An appropriate theorem to show that the given set, W, is a vector space. A specific example can be
[tex]\left[\begin{array}{ccc}p\\q\\r\end{array}\right][/tex] , -p- -3q = s and 3p = -2s - 3r
Sets represent values that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.
The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.
The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.
The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.
Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is
S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties
u +v =y+ u and (u + v)+w=u + (v +W).
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Why is pi important in math?
In the figure below, m 24 = 106°. Find mZ1, m/2, and m 23. 1 X 3 2 ترا = 0° m 22 = ° m2 1 = m 23 = °
Answer:
m<1=74
m<2=106
m<3=74
Step-by-step explanation:
m<1:
=180-106
=74
m<2:
=106
m<3;
if m<1 is 74, m<s will also be 74
Suppose 30% of the restaurants in a certain part of a town are in violation of the health code. A health inspector randomly selects nine of the restaurants for inspection. (Round your answers to four decimal places.)
(a) What is the probability that none of the restaurants are in violation of the health code?
(b) What is the probability that one of the restaurants is in violation of the health code?
(c) What is the probability that at least two of the restaurants are in violation of the health code?
a)The probability that none of the restaurants are in violation of the health code is approximately 0.0482.
b)The probability that one of the restaurants is in violation of the health code is approximately 0.3729.
c)The probability that at least two of the restaurants are in violation of the health code is approximately 0.4681.
(a) Probability that none of the restaurants are in violation of the health code:
Let E be the event that a restaurant is in violation of the health code, and let F be the event that a restaurant is not in violation of the health code. Therefore, probability that a restaurant is in violation of the health code is:
P(E) = 0.30
,then the probability that a restaurant is not in violation of the health code is:
P(F) = 1 - P(E) = 1 - 0.30 = 0.70
The health inspector selects 9 restaurants. The probability that none of the restaurants are in violation of the health code is:
P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) = (0.70)^9 ≈ 0.0482.
Therefore, the probability that none of the restaurants are in violation of the health code is approximately 0.0482.
(b) Probability that one of the restaurants is in violation of the health code:
The health inspector selects 9 restaurants. We want to find the probability that one of the restaurants is in violation of the health code. We can use the product rule of probability for this. Let us assume that the health inspector selects the first restaurant and that it is in violation of the health code. The probability of that happening is:
P(E) = 0.30
Then the probability that the other eight restaurants are not in violation of the health code is:
P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) × P(F) = (0.70)^8
Then, the health inspector could have selected the restaurant that is in violation of the health code from any of the 9 restaurants. So, we have to multiply by 9.
P(one restaurant in violation of health code) = 9 × P(E) × P(F)^8≈ 0.3729
Therefore, the probability that one of the restaurants is in violation of the health code is approximately 0.3729.
(c) Probability that at least two of the restaurants are in violation of the health code:
Let X be the random variable that denotes the number of restaurants that are in violation of the health code. Then, X can take on values 0, 1, 2, 3, ..., 9.The probability that at least two of the restaurants are in violation of the health code is the same as the probability that two or more are in violation of the health code:
P(X ≥ 2) = P(X = 2) + P(X = 3) + · · · + P(X = 9)
We can use the sum rule of probability for this.Let us calculate the probability that exactly k of the 9 restaurants are in violation of the health code:
P(X = k) = (9Ck) P(E)k P(F)9−k = (9Ck) (0.30)k (0.70)9−k
Then:P(X ≥ 2) = P(X = 2) + P(X = 3) + · · · + P(X = 9)= ∑ (9Ck) (0.30)k (0.70)9−k, where k = 2, 3, ..., 9
= 1 − [P(X = 0) + P(X = 1)]= 1 − [1 × (0.70)^9 + 9 × (0.30)(0.70)^8]≈ 0.4681
Therefore, the probability that at least two of the restaurants are in violation of the health code is approximately 0.4681.
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