The length of the rectangle is 30 feet and the width of the rectangle is 15 feet.
Let l be the length l the rectangle and w be the width of the rectangle.
The area of a rectangular living room is 450 square feet.
⇒ A = l × w
⇒ 450 = l × w ................(1)
The length of the room is 15 feet less than three times the width.
So we get an expression,
l = 3w - 15
Substitute above vale of l in equation (1)
450 = (3w - 15) × w
450 = 3w² - 15w
3w² - 15w - 450 = 0
w² - 5w - 150 = 0
(w - 15)(w + 10) = 0
w - 15 = 0 or w + 10 = 0
w = 15 or w = -10
But width of the rectangle cannot be -10
So, w = 15 feet
and l = 3(15) - 15
l = 30 feet
Therefore, the length of the rectangular living room is 30 feet and the width is 15 feet.
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Help please!!!!!!!!!!!
Only #1 and 5 please show work THANK YOU
The single complex number corresponding to each expression:
1. √(-9) = 3i
2. √(-16) = 4i
3. √(-6)√(-24) = 12
4. √(-3)√(-75) = 15
5. (2+√(-12))/2 = 1 + 3i
6. (4 + √(-20))/2 = 2 + 5i
We represent √(-1) as i which is an imaginary number. Complex numbers are numbers of the kind a + ib, where a and b are real numbers.
Hence all real numbers are also complex numbers (i.e., when b = 0).
Also we use some formula for square roots:
√(ab) = (√a )(√b)
Now, to find the single complex number corresponding to each expression:
1. √(-9) = √(9) x √(-1) = 3i
2. √(-16) = √(16) x √(-1) = 4i
3. √(-6)√(-24) = √(-6 x -24) = √(144) = 12
4. √(-3)√(-75) = √(-3 x -75) = √(225) = 15
5. (2+√(-12))/2 = (2+√4√3√(-1))/2 = (2+2 x (√3)i)/2 = 1+(√3)i
6. (4 + √(-20))/2 = (4 + √4√5√(-1))/2 = (4 + 2 x (√5)i )/2 = 2 + (√5)i
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A catering service offers 8 appetizers, 9 main courses, and 3 desserts. A customer is to select 6 appetizers, 6 main courses, and 2 desserts for a banquet. Inhow many ways can this be done?
Given:
Number of appetizers offered = 8
Number of appetizers customer is to select = 6
Number of main courses offered = 9
Number of main courses customer is to select = 6
Number of desserts offered = 3
Number of desserts the customer is to select = 2
Let's determine how many ways this can be done.
This is a combination problem.
To determine the number of ways this can be selected, apply the combination formula below:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Thus, we have:
[tex]_nC_r=_8C_6\ast_9C_6\ast_3C_2[/tex]Solving further, let's apply the formula and combine:
[tex]\begin{gathered} _8C_6\ast_9C_6\ast_3C_2=\frac{8!}{6!(8-6)!}\ast\frac{9!}{6!(9-6)!}\ast\frac{3!}{2!(3-2)!} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{8!}{6!(2)!}\ast\frac{9!}{6!(3)!}\ast\frac{3!}{2!(1)!} \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} _8C_6\ast_9C_6\ast_3C_2=\frac{8\ast7\ast6!}{6!(2\ast1)}\ast\frac{9\ast8\ast7\ast6!}{6!(3\ast2\ast1)}\ast\frac{3\ast2!}{2!(1)} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{8\ast7}{2\ast1}\ast\frac{9\ast8\ast7}{3\ast2\ast1}\ast\frac{3}{1} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{56}{2}\ast\frac{504}{6}\ast\frac{3}{1} \\ \\ _8C_6\ast_9C_6\ast_3C_2=28\ast84\ast3 \\ \\ _8C_6\ast_9C_6\ast_3C_2=7056 \end{gathered}[/tex]herefore, there are
Consider a simple economy where the basket of goods used to calculate the CPI contains two items: shampoo and soap. The basket consists of 1 bottle of shampoo and 2 bars of soap. The prices are shown in the table.
Year Price of a Bottle of Shampoo Price of a Bar of Soap
Year 1 $6.50 $1.25
Year 2 $6.60 $1.30
Type the correct answer in the box. Round your answers to two decimal places, if necessary.
The CPI for year 2 is
.
In this simple economy where the market basket for CPI contains two items, the CPI for year 2 is 102.22%.
What is the CPI?The CPI means the Consumer Price Index.
The CPI economically indicates the inflationary trend, using a basket of selected consumer goods and services, and computes their total costs for each period.
The base year's total costs set to 100% are used to compare with the current year's.
Price 1 Bottle of 1 Bar of 2 Bars Total Cost
Shampoo Soap of Soap Mkt Basket
(a) (b) (c) (a) + (c)
Year 1 $6.50 $1.25 $2.50 $9.00
Year 2 $6.60 $1.30 $2.60 $9.20
CPI for Year 1 (base year) = 100% ($9/$9 x 100)
CPI for Year 2 = 102.22% ($9.20/$9 x 100)
Thus, year 2's Consumer Price Index is 102.22%, compared to year 1's.
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Answer:
102.22
Step-by-step explanation:
Edmentum.
find the standard error mean if O = 64 and n = 64
The standard error mean if σ = 64 and n = 64 is 8.
How can we obtain the standard error mean?The standard error mean is given by the formula σ/√N. In the question provided, we need to note that the standard error mean is designated by σM.
Now applying the formula, we will have this:
σM = 64 ÷√64
The root of 64 = 8.
Therefore, the standard error mean is equal to 64 divided by 8 which is 8.
So, we can arrive at the conclusion that given the standard error mean of σ = 64 and n = 64, the standard error mean will be 8.
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a picture is 5inches wide and 8inches tall:A photographer wants to use a scale factor of 2.5to enlarge a picture.what will the area of the picture be after it is elarged
We can determine the area of the enlarged picture as follows:
*First, we determine the new dimensions, that is:
[tex]5\cdot2.5\text{ = 12.5}[/tex][tex]8\cdot2.5=20[/tex]*Secondly, we find the area using the formula of area for a rectangle, that is:
[tex]A=20\cdot12.5\Rightarrow A=250[/tex]From this, we have that the area of the picture after being enlarged equals 250 in^2.
Henry is younger than Cameron. Their ages are consecutive odd integers. Find Henry's age if the sum of Henry's age and 2 times Cameron's age is 85.
Since we used x and x+2 as consecutive odd integers. "x" to represent Henry's age, Henry's age is 27. Since we used the expression "x+2" to represent Cameron's age, Cameron's age is "27+2" which is just 29.
How to do age sums?So the consecutive odd integers, just means they're separated by a value of 2. This can be generally expressed as "a and a+2" where the these two values would be consecutive odd integers assuming "a" is an integer.
So let's express the Henry's age as the variable "x", since it's unknown. Since Cameron is older, and by definition of a consecutive odd integer, Cameron's can be expressed as "x+2"
So the equation we need to set up is 2(Cameron's age) + (Henry's age) = 85
So we can substitute variables we defined to express Cameron and Henry's age:
2(x+2)+x= 85
Distribute the 2:
2x+4+x
Add like terms:
3x+4=85
Subtract 4 from both sides:
[tex]3x= 81[/tex]
Divide both sides by 3:
x=27
Since we used "x" to represent Henry's age, Henry's age is 27. Since we used "x+2" to represent the Cameron's age, Cameron's age is "27+2" which is just 29.
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24. Jenna wants to purchase a new guitar for $375. She currently has $45 in her savings account. If she plans to save $35 each week, how many weeks will it take her to save enough money to purchase the guitar? Choose the inequality that best represents this situation. A 45 + 35x < 375 B 35 + 45x < 375 C 45 + 35x > 375 D 35 + 45x > 375
Here, we want to select the inequality that best represents the situation
Let the number of weeks be x
Total value saved in x weeks at $35 per week will be 35 * x = 35x
Adding this to what she had initially, the total expression becomes 35x + 45
This sum must be the same or greater than what she plans to save
The inequality is thus;
[tex]35x\text{ + 45}\ge\text{ 375}[/tex]Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
The value of x of the Quadratic Equation, (x - 7)² = 36 when the right-hand side is positive is 13 and for the negative right-hand side, it is 1. So the value of x could be 13 and 1 both.
Split into two equations:
(x - 7)² = 36
(x- 7) = √36 or (x- 7) = -√36
For equation (x- 7) = √36 value of x:
x - 7 = √(6)²
x - 7 = 6
x = 13
For equation (x- 7) = -√36 value of x:
x - 7 = -√(6)²
x - 7 = - 6
x = 1
∴ value of x could be 13 and 1 both.
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Factor 8mn2 + 12mn completely. A 42mn’ +3mn) B 4mn(2 + 3n) C 4mn(2mn + 3) D 4mn(2n + 3)
Question 1Step 1: Problem
[tex]\text{Factor 8mn}^2\text{ + 12mn}[/tex]Step 2: Concept
Factor the highest common factor out.
Step 3: Method
[tex]8mn^2\text{ + 12mn = 4mn( 2n + 3)}[/tex]Step 4: Final answer
4mn(2n + 3)
Question 2
Step 1: Question
[tex]\text{Simplify }\frac{(1.24\text{ }\times10^2\text{ ) (3.6 }\times10^{-3})}{1.8\text{ }\times\text{ 10}}[/tex]Step 2: Concept
Apply laws of exponent
[tex]\begin{gathered} \text{Division law } \\ \frac{m^x}{m^y}=m^{x\text{ - y}}^{} \\ \text{Multiplication law} \\ m^x\text{ }\times m^y=m^{x\text{ + y}} \end{gathered}[/tex]Step 3: Method
[tex]\begin{gathered} =\text{ }\frac{(1.24\text{ }\times10^2\text{ )(3.6 }\times10^{-3})}{1.8\text{ x 10}} \\ =\text{ }\frac{1.24\text{ }\times\text{ 3.6 }\times10^{2\text{ + (-3)}}}{18} \\ =\text{ }\frac{4.464\text{ }\times10^{2\text{ - 3}}}{18} \\ =\text{ }\frac{4.464\text{ }\times10^{-1}}{18} \\ =\text{ }\frac{4.464}{18}\text{ }\times10^{-1} \\ =\text{ 0.248 }\times10^{-1} \\ =\text{ 2.48 }\times10^{-2} \end{gathered}[/tex]Step 4: Final answer
Option D is the correct answer
[tex]2.48\text{ }\times10^{-2}[/tex]
3 to 5 men and total of 224 people how many are men
When there are 3 women to to 5 men and there is a total of 224 people, the number of men will be 140 men.
How to illustrate the information?From the information, it was stated that there are 3 women to to 5 men and a total of 224 people.
Therefore, it should be noted that the fraction for men that illustrates the information will be:
= 5/(3 + 5) × 224
= 5/8 × 224
= 5 × 28
= 140
Therefore, the number of men is 140 men.
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Keisha rented a truck for one day. There was a base fee of $13.75, and there was an additional charge of 10 cents for each mile driven. The total cost, C (in
dollars), for driving x miles is given by the following.
C=0.10x+13.75
What is the total rental cost if Keisha drove 40 miles?
Answer:
I believe the answer is $17.75
Step-by-step explanation:
As if you have a base fee of 13.75 then 0.10 for each additional mile. Then 40 miles x 0.10 is 4. Hope this helps.
Renu's brother is 5 years younger than Renu. Now he is 30 years old. Connect their ages
The age of Renu and her brother is 35 and 30 years respectively.
Let the age of Renu be x
Then,
The age of her brother will be x-5
According to the question,
Age of Renu's brother is 35
So,
x-5 = 30
x = 30+5
x= 35
Hence, the age of Renu and her brother is 35 and 30 years respectively.
This question is related to the topic age problem. These problems aim is to find the age of certain people.
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Please help for number 1 2 and 3 and an explanation because I don't understand
The product of the numbers are-
107×11 = 117772×13 = 936466×27 = 12582What is defined as the product of number?In mathematics, a product is defined as the result of multiplying two or more numbers together.The amount of objects in a group is referred to as a multiplicand, and the number of these equal groups is referred to as a multiplier.A multiplier, a multiplicand, as well as the product comprise a multiplication expression.For the given number;
Part a: 107 × 11
1 0 7
× 1 1
---------
1 0 7
+ 1 0 7 x
-------------
1 1 7 7
--------------
Thus, 107×11 = 1177
Part b: 72×13
7 2
× 1 3
---------
2 1 6
+ 7 2 x
-------------
9 3 6
--------------
Thus, 72×13 = 936
Part c: 466×27
4 6 6
× 2 7
---------
3 2 6 2
+9 3 2 x
-------------
1 2 5 8 2
--------------
Thus, 466×27 = 12582
Therefore, product of the number are found.
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use the roster method to write the set of natural numbers less than 6
What is the answer to this question?
In the given angle, the value of x is 9°.
What are angles?In Euclidean geometry, an angle is a shape created by two rays that share an endpoint and are referred to as the angle's sides and vertex, respectively. The plane that contains the rays contains the angles created by two rays. The meeting of two planes can also result in an angle. They are referred to as dihedral angles.As we can see that the two triangles are congruent as 2 pairs of sides are similar to each other.
Hence, the angle between them is also similar.So, with this the equation will be:
3x + 15 = 423x = 42 - 153x = 27x = 27/3x = 9Therefore, in the given angle, the value of x is 9°.
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If you were to write an essay on an eyeball what would you write? Please help me i can’t do this!
Answer:
Should the essay be 3-5 paragraphs? Also I can't write the essay here or otherwise your school will find out you plagiarized it.
Step-by-step explanation:
I can send it to you privately.
Determine if the two figures below are congruent. Use the drop-down menus below to justify why. Which point on Figure 2 corresponds to point CC on Figure 1?
From the figure, we observe that,
Non-rigid motions are used to map figure 1 onto figure 2.
Here, resizing (stretching horizontally, vertically, or both ways) is a non-rigid transformation.
So, the answer is,
The figures are congruent because non-rigid motions are used to map figure 1 onto figure 2.
The point corresponding to point C is H.
The converse of the proposition "If it is cold, then I will not go walking" is:
A. If it is not cold, then I will go walking.
B. If it is not cold, then I will not go walking.
C. If I did not go walking, then it is cold.
D. If I go walking, then it is not cold.
Answer:
C. If I did not go walking, then it is cold.
Step-by-step Explanation:
A conditional statement is a hypothesis followed by a conclusion. The hypothesis in this example being “If it is cold” and then followed by a conclusion “I will not go walking”.
A converse statement swaps the hypothesis and the conclusion of a conditional statement.
help meeeeeeeeeeeeeee
Answer: What do you need help with?
Step-by-step explanation:
1: Comment what u need help with
2: We will help you
3: You have been helped :)
Answer:
After doing the math I got 74.44
Need to know what goes in the 4 boxes above, and the last box
Given that Owen moves half the number of boxes moved by Ariana.
So you can put 2 in the left side upper box, and 1 in the left side lower box.
Now, it is mentioned that Owen mobes 12 boxes. So the corresponding number of boxes moved by Arianna is to be obtained.
So you have to put 12 in the right side lower box. And a variable (say 'x') in the right side upper box.
The vaue of 'x' is to be calculated.
Cross multiply the terms,
[tex]\begin{gathered} 1\cdot x=2\cdot12 \\ x=24 \end{gathered}[/tex]Thus, the value of 'x' is 24.
Therefore, Arianna can move 24 boxes in the time when Owen moves 12 boxes.
A group of coworkers put their money together to buy raffle tickets and won $1500. if we use the variable w to represent the number of coworkers, which of these represents how much prize money each person gets?
The equation which represent the prize money given to each person is $1500/w.
What is described as the unitary method?The unitary method is a process that determines the value of a single unit from of the worth of multiple units, as well as the value of different components from the price of a single unit.It is a technique that we employ for the majority of math calculations.For the given condition in question;
Let 'w' be the number of coworkers.
The total money given to buy raffle tickets and won $1500.
This cam be written as;
w worker -------> $1500.
For 1 worker, use unitary method.
Divide both side by w.
1 worker -------> $1500/w.
Thus, the prize money given to each worker is $1500/w.
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Find the slope m of the line passing through the given pair of points. (If an answer is undefined, enter UNDEFINED.)
(6, 5) and (−9, 5)
Answer:
m= 0
Step-by-step explanation:
Since the two points have the same y-coordinates, the line passing through them is a horizontal line. Horizontal lines have a slope of zero.
Prove:
[tex]\boxed{slope = \frac{y_1 - y_2}{x_1 - x_2} }[/tex]
Slope between (6, 5) and (-9, 5)
[tex] = \frac{5 - 5}{ - 9 - 6} [/tex]
[tex] = \frac{0}{ - 15} [/tex]
= 0
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One morning in Atlanta, Tina observed that the temperature was 72 degrees. Later the temperature rose 21 degrees and then dropped 11 degrees. She then flew to New York where the temperature was 67 degrees.
What was the change in temperature from when Tina left Atlanta and arrived in New York?
A:5°
B:6°
C:14°
D:15°
If She then flew to New York where the temperature was 67 degrees. The change in temperature from when Tina left Atlanta and arrived in New York is : D:15°.
Change in temperatureGiven :
Beginning temperature = 72 degrees
Increase in temperature = 21 degrees
Decrease in temperature = 11 degrees
Temperature outside Atlanta = 67 degrees
First step is to calculate the temperature in Atlanta using this formula
Temperature = (Beginning temperature + Increase in temperature - Decrease in temperature )
Let plug in the formula
Temperature = 72 + 21 -11
Temperature = 82 degrees
Second step is to calculate the change in temperature
Change in temperature = Temperature in Atlanta - Temperature in New York
Change in temperature = 82 degrees - 67 degrees
Change in temperature = 15 degrees
Therefore the correct option is D.
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Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,4) and parallel to x + 2y = 7.a) The equation of the line in slope-intercept form is(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)b) The equation of the line in standard form is(Type your answer in standard form.)
For this type of question the first step is to calculate the slope of the line given by th equation x+2y=7, for this we recall the slope intercept form ( y=mx+b) and put the equation in that form
[tex]y=-\frac{x}{2}+\frac{7}{2}[/tex]Then, m=-1/2. Now, since the equation of the line we are looking for is parallel to the previous line the slope must be the same, now we recall the point slope equation
[tex]\begin{gathered} (y-y_1)=m(x-x_1) \\ \end{gathered}[/tex]Substituting m=-1/2, and recalling that the line is passing through (-3,4) we get that the point slope equation the line is :
[tex]\begin{gathered} y-4=-\frac{1}{2}(x-(-3)) \\ y-4=-\frac{1}{2}x-\frac{3}{2} \end{gathered}[/tex]Finally to put it in the slope intercept form, we solve the equation for y:
[tex]y=-\frac{1}{2}x+\frac{5}{2}[/tex]For part b) we recall that the standard form of the equation of a line is:
[tex]\begin{gathered} C=Ax+By \\ \text{where C, A and B are real and whole numbers if possible} \end{gathered}[/tex]Now, we solve for the constant of the equation:
[tex]\begin{gathered} \frac{5}{2}=y+\frac{1}{2}x \\ 5=2y+x \end{gathered}[/tex]The last equation is the standard form of the equation of the line.
The miles Jack has driven, y, varies directly with x, the number of hours driven. If Jack drove 175 miles in 2.5 hours, find the number of hours it would take Jack to travel 665 miles.
If the miles Jack has driven, y, varies directly with x, the number of hours driven. If Jack drove 175 miles in 2.5 hours, the number of hours it would take Jack to travel 665 miles is 9.5 hours.
Determining the number of hours to travelLet x represent the number of hours it would take Jack to travel
Formulate an equation
175 / 2. 5 = 665 / x
The denominator cannot equal 0 because the fraction is defined
so,
x ≠ 0
Hence,
1750 × 25x / 25 = 665 × 25x /x
Reduce the fraction
1750x = 665 × 25
1750x = 16,625
Divide both side by 1750x
x = 16,625 / 1750
x = 9.5
Therefore it will take Jack 9.5 hours.
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In 9.5 hours Jack can travel for 665 miles.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Suppose 2 pens cost 10 dollars, therefore 1 pen costs (10/2) = 5 dollars.
From this unitary value, we can determine the cost of any no. of pens.
Given, Jack drove 175 miles in 2.5 hours.
∴ In one hour Jack can drive (175/2.5) miles.
= 70 miles.
So, to travel 665 miles Jack needs (665/70) hours.
= 9.5 hours or 9 hours and 30 minutes.
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Gary is buying a $1,250 computer on the installment plan. He makes a down payment of $150. He has to make monthly payments of $48.25 for 2 years. What is the total finance charge?
The total finance charge on the computer purchased on finance by Gary is $58.00
What is finance charge?
The finance charge on the computer purchase is the excess of the total payments over the principal of the loan, where the principal is the purchase price of $1,250 minus the down payment of $150
principal=purchase price-down payment
principal=$1,250-$150
principal=$1,100
total payments=monthly payment*number of months in 2 years
total payments=$48.25
total payments=$48.25*24
total payments=$1,158.00
total finance charge=total payments-principal
total finance charge=$1,158.00-$1,100.00
total finance charge=$58.00
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In a 7-card poker, played with a standard 52-card deck, 52C7, or 133,784,560, different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by . Shown to the right is the number of ways a particular type of hand can occur and its associated probability. Find the probability of not being dealt this type of hand.
If the probability of being dealt this type of hand is 7654/133,784,560. the probability of not being dealt this type of hand is: 0.999944..
ProbabilityProbability of complement of the event A =P (Ac) = 1- P(A)
A = event of the particular type of hand
Probability of A :
P(A) = n (A) / n(S)
P(A) = 7480 / 133,784,560
Ac = event of not being dealt of this type of hand
Probability of Ac:
P (Ac) = 1- P(A)
P (Ac) = 1- 7480 / 133,784,560
P (Ac) = 133, 777,080 / 133,784,560
P (Ac) = 0.999944
Therefore the probability of not being dealt this type of hand is 0.999944.
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The complete question is :
In 7 card poker,played with a standard 52 card deck 52C7 or 133,784,560 different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by 133,784,560. The probability of being dealt this type of hand is 7654/133,784,560. Find the probability of not being dealt this type of hand.
TRUE OR FALSE? For any real number x > 0 log 3 x > log ₂ x.
======================================================
Explanation:
We can use a counter-example.
Pick any positive real number you want to replace x.
I'll pick x = 7
Use the change of base formula to get the following
[tex]\log_{3}(\text{x}) = \frac{\log(\text{x})}{\log(3)}\\\\\log_{3}(7) = \frac{\log(7)}{\log(3)}\\\\\log_{3}(7) \approx \frac{0.8451}{0.4771}\\\\\log_{3}(7) \approx 1.7713\\\\[/tex]
and
[tex]\log_{2}(\text{x}) = \frac{\log(\text{x})}{\log(2)}\\\\\log_{2}(7) = \frac{\log(7)}{\log(2)}\\\\\log_{2}(7) \approx \frac{0.8451}{0.3010}\\\\\log_{2}(7) \approx 2.8076\\\\[/tex]
---------------------------
So if x = 7, then we have,
[tex]\log_{3}(\text{x}) > \log_{2}(\text{x})\\\\\log_{3}(7) > \log_{2}(7)\\\\1.7713 > 2.8076\\\\[/tex]
The last statement is false, so the first statement is false when x = 7.
It turns out that you could pick any positive real number for x and will always get a false statement when saying [tex]\log_{3}(\text{x}) > \log_{2}(\text{x})[/tex]
Among 6225 cases of heart pacemaker malfunctions, 346 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in 3
different pacemakers randomly selected from this batch of 6225 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire
batch will be accepted? Is this procedure likely to result in the entire batch being accepted?
The probability is. This procedure is
(Round to three decimal places as needed.)
to result in the entire batch being accepted.
P ( All three are not caused by firmware ) = 8423 %
The probability that the entire batch will be accepted = 0.8423
We are told that out of the 6225 cases of heart pacemaker malfunctions, 346 were found to be caused by firmware.
Thus,
Cases not caused by firmware = 6225 - 346 = 5879
So, the probability of the first case not being affected by the firmware is;
P( first case not caused by firmware ) = 5879/6225
Also,
The probability of the second case not being affected by the firmware is given as;
P(second case not caused by firmware|first case not affected by firmware) = 5878/6224
Similarly,
The probability of the third case not being affected by the firmware is given as;
P(third case not caused by firmware | first and second not caused by firmware) = 5877/6223
Now that we have the three probabilities, it is clear that the occurrences are not independent because the likelihood of one event depends on the likelihood of the others.
Thus, we will make use of the general multiplication rule which is;
P(A & B) = P(B) × P(A|B)
Thus;
P( All three not caused by firmware ) = P(first case not caused by firmware ) × P( second case not caused by firmware | first case not affected by firmware) × P( third case not caused by firmware | first and second not caused by firmware)
Substituting the values,
P(All three not caused by firmware) = ( 5879/6225 ) × ( 5878/6224 ) × ( 5877/6223 )
P(All three are not caused by firmware) = 0.84232558432 = 84.23 %
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