Mathematics High School

The quality-control department of Starr Communications, a manufacturer of video-game DVDs, has determined from records that 1.5% of DVDs sold have video defects, 0.8% have audio defects, and 0.4% have both audio and video defects. What is the probability that a DVD purchased by a customer a. will have a video or audio defect? b. Will not have a video or audio defect?

Answers

Answer 1
Let A represents the event that DVD has a video effect. 
So, 
P(A) = 1.5 %

Let B represents the event that DVD has a audio defect.
So,
P(B) = 0.8 %

A ∩ B represents that DVD has both audio and video defect.
So,
P(A∩B) = 0.4%

Part a)
A ∪ B represents that DVD has a video or audio defect. 

P(A∪B) = P(A)+P(B)-P(A∩B) = 1.5 + 0.8 - 0.4 = 1.9%

Thus the probability that the DVD purchased by the customer has a video or audio defect is 1.9%.

Part b) 
The complement of P(A∩B) will represent the probability that the DVD does not have video or audio defect.

So, the probability that DVD purchased by customer does not have video or audio defect is 1 - 0.4 = 0.96%
Answer 2

Final answer:

The probability that a DVD will have a video or audio defect is 1.9%, calculated using the principle of inclusion-exclusion. The probability that a DVD will not have any defect is 98.1%, obtained by subtracting the probability of having a defect from 100%.

Explanation:

To solve the probability that a DVD purchased by a customer will have a video or audio defect or not, we can use the principle of inclusion-exclusion for probabilities.

According to the given data:

P(video defect) = 1.5%P(audio defect) = 0.8%P(both video and audio defects) = 0.4%

Part a: The probability that a DVD will have a video or audio defect (at least one type of defect) is calculated by adding the probabilities of each defect and subtracting the probability of both defects occurring, as these are counted twice.

P(either type of defect) = P(video defect) + P(audio defect) - P(both defects)

P(either type of defect) = 1.5% + 0.8% - 0.4% = 1.9%

Part b: To find the probability that a DVD will not have any defect, we subtract the probability of either defect from 100%.

P(no defect) = 100% - P(either type of defect)

P(no defect) = 100% - 1.9% = 98.1%

Therefore, the probability that a DVD will have a video or audio defect is 1.9%, and the probability that a DVD will not have any defect is 98.1%.

Related Questions

PLEASE HELP ME ON THIS QUESTION

THX
~BRAINLIEST AVAILABLE TO CORRECT ANSWER

Answers

g(x)=-f(x)-2
x=-2→g(-2)=-f(-2)-2=-(-1)-2=1-2→g(-2)=-1
x=-1→g(-1)=-f(-1)-2=-(1)-2=-1-2→g(-1)=-3
x=0→g(0)=-f(0)-2=-(3)-2=-3-2→g(0)=-5
x=1→g(1)=-f(1)-2=-(5)-2=-5-2→g(1)=-7

x       -2    -1   0     1
g(x)   -1   -3   -5   -7
Given the table for a linear function
f(x)={(-2,-1),(-1,1),(0,3),(1,5)}
Need to find g(x)=-f(x)-2

First step is to find f(x) in analytical form.
The slope-intercept form would be convenient because we can find both the slope and y-intercept.
In a typical linear function
f(x)=mx+c
m= slope, can be found by (y2-y1)/(x2-x1)
c= y-intercept  [value of y when x=0]

So here, taking points (0,3),(1,5)
m=(5-3)/(1-0)=2
c=3  [y-value when x=0]
=>
f(x)=2x+3
=>
g(x)
=-f(x)-2            [given]
=-(2x+3)-2       [don't forget the parentheses]
=-2x-3-2
=-2x-5  

Finally
g(-2)=-2(-2)-5=4-5=-1
g(-1)=-2(-1)-5=2-5=-3
g(0)=-2(0)-5=0-5=-5
g(1)=-2(1)-5=-2-5=-7
...

What would be the side length of the smallest square plate on which a 40-cm chopstick can fit along a diagonal without any overhang? (Correct answer will get reward)

Answers

The side length of the smallest square plate required to fit a 40-cm chopstick along its diagonal without any overhang is approximately 28.284 cm.

To find the side length of the smallest square plate in which a 40-cm chopstick can fit along a diagonal without any overhang, we can use the Pythagorean theorem. The diagonal of a square is the hypotenuse of a right-angled triangle formed by two sides of the square. Since the sides of the square are equal, if one side is s, then the diagonal d can be calculated using the equation d = s√2, where √2 is the square root of 2 (approximately 1.4142).

Therefore, to fit a 40-cm chopstick along the diagonal:

Let d = 40 cm.

Use the equation s√2 = 40 cm to find s, the side of the square.

s = 40 cm / √2.

s ≈ 28.284 cm when rounded to three decimal places.

So, the side length of the smallest square plate on which a 40-cm chopstick can fit along a diagonal without any overhang is approximately 28.284 cm.

Find the product by using the FOIL method

(11z-5y)(3z+2y)

Plz help!

Answers

33z squared -10y squared + 7zy
 = 33z^2+7zy-10y^2   thats the answer

2. Which is equal to log6?

log26

log62

log610

log106,

Answers

The Value of Log(6) = 0.77815125 the values given in different forms of Log are independent from each other and thus do not match any of the other listed values.

A 2-digit number is one more than 6 times the sum of its digits. If the digits are reversed, the new number is 9 less than the original number. Find the original number

Answers

43

hope this helps<3
   
 
:)

 
 
 
 
 

Find the area of a triangle with a base length of 3 units and a height of 4 units.

Answers

I will love to help you with this ! So You would use this formula A=1/2b*h 

So these are given so we plug them in 

A=1/2(3)(4)
A=6 units 


Hi there!

To find the area of a triangle, we need to multiply the base and the height of the triangle and divide the product by 2. 

So, the expression we would use to solve this is (3 * 4) / 2.

Let's solve:

(3 * 4) / 2
= 12 / 2
= 6

So, the area of the triangle is 6 units squared. 

Hope this helps!

Farmer Fran has some cows and some hens. Between them, they have 52 legs and 38 eyes. How many hens does Farmer Fran have? How many cows does Farmer Fran have?

Answers

Number of cows: c=?
Number of hens: h=?

Total number of legs: 4c+2h=52  (1)
Total number of eyes: 2c+2h=38 (2)

Subtracting equations (1) and (2)
4c+2h-(2c+2h)=52-38
4c+2h-2c-2h=14
2c=14
2c/2=14/2
c=7

Replacing c=7 in equation (2)
2(7)+2h=38
14+2h=38
14+2h-14=38-14
2h=24
2h/2=24/2
h=12

Answers:
Farmer Fran has 12 hens
Farmer Fran has 7 cows

Find the equation for the line that passes through the point (−1,2), and that is parallel to the line with the equation 3/2x−2y=2.

Answers

You can start with
.. (3/2)(x +1) -2(y -2) = 0 . . . . . the given line translated to the point (-1, 2)
.. 3(x +1) -4(y -2) = 0 . . . . . . . . multiply by 2
.. 3x +3 -4y +8 = 0 . . . . . . . . . eliminate parentheses
.. 3x -4y = -11 . . . . . . . . . . . . . . put in standard form (not necessary, but prettier)

What are the values of a and b in the equation (4x^a)^b = 256/x^8

Answers

b =  4 and a = -2

(4x^-2)^4
= 4^4 x^-8
= 4^4 / x^8
= 256/x^8

Answer:

The value of a is -2 and the value of b is 4.

Step-by-step explanation:

Given expression is,

[tex](4x^a)^b = \frac{256}{x^8}[/tex]

Using [tex](ab)^m=a^m.b^n[/tex] on left side,

[tex]4^b(x)^{ab}=\frac{4^4}{x^8}[/tex]     ( [tex]4^4 = 256[/tex] )

Using [tex]a^m=\frac{1}{a^{-m}}[/tex],

[tex]4^b(x)^{ab}=4^4 (x)^{-8}[/tex]

By comparing both sides,

We get,

b = 4 and ab = -8

⇒ a = -2

Hence, the value of a is -2 and the value of b is 4.

The explicit rule for a sequence is an=9(−5)n−1 .



What is recursive rule for the sequence?




an=5−(an−1),a1=9

an=−9(an−1),a1=5

an=9−(an−1),a1=5

an=−5(an−1),a1=9

Answers

Explicit rule is a(n) = 9*(-5)^(n-1)

The recursive rule is a(n) = -5*a(n-1); a(1) = 9

The first term is 9. Each new term is found by multiplying the previous term by -5

We can see this when we raise -5 to a whole number power. Eg: 9(-5)^3 = 9*(-5)*(-5)*(-5)

Answer: Choice D

Answer:

Option 4th is correct.

[tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]

Step-by-step explanation

The explicit sequence of the geometric sequence is given by:

[tex]a_n = a_1r^{n-1}[/tex]              ....[1]

where,

r is the common ratio

n is the number of terms

[tex]a_1[/tex] is the first term

As per the statement:

The explicit rule for a sequence is:

[tex]a_n=9(-5)^{n-1}[/tex]

On comparing [1] we have;

[tex]a_1 = 9[/tex] and r=  -5

Recursive formula for the geometric sequence is given by:

[tex]a_n = r \cdot a_{n-1}[/tex]  for [tex]n\geq 2[/tex]

Substitute the given values we have;

[tex]a_n = -5 \cdot a_{n-1}[/tex]

Therefore, the recursive rule for the sequence is, [tex]a_n = -5 \cdot a_{n-1}[/tex] , [tex]a_1 = 9[/tex]

Philip is going on a 400040004000-kilometer road trip with three friends. The car consumes 666 liters of gas per 100100100 kilometers, and gas costs \$1.50$1.50dollar sign, 1, point, 50 per liter. If Philip and his friends want to split the cost of gas evenly, how much should they each pay?

Answers

Let us calculate how much gas he will need for the trip. Since he needs 6 liters for 100 miles, he will need x for 4000 miles. Gas is proportional to mileage. Solving for x, x=4000/100 *6=240
In total, this will cost 240*1.5=360$. He has 3 friends, so they are 4 in total. Everyone will have to pay 360/4=90$
Let's calculate how much gas would car consume during the trip.
First, we will calculate how much it consumes per kilometer:
[tex]g_{ckm}=6/100=0.06\frac{l}{km}[/tex]
The total consumption for the whole trip would be:
[tex]g_t=L\cdot g_{ckm}=0.06\cdot 4000=240 l[/tex]
To get the total cost of the gas we multiply the total gas consumed by its cost:
[tex]C_t=g_t\cdot1.5=360\$[/tex]
So, each passenger must pay $90.

when the solutions to each of the two equations below are graphed in the xy coordinate plane, the graphs of the solutions intersect at two places. Write the y-coordinate of the points of intersection in the boxes below in order from smallest to largest. y=2x and y=x^2-3

Answers

The points of intersection are at (3, 6) and (-1, -2).

Since both of these equations have y isolated, we can set them equal to each other:

2x=x²-3

We want all of the variables on one side, so subtract 2x:
2x-2x = x²-3-2x
0=x²-3-2x

Write the quadratic in standard form:
0=x²-2x-3

This is easily factorable, as there are factors of -3 that will sum to -2.  -3(1)=-3 and -3+1=-2:
0=(x-3)(x+1)

Using the zero product property we know that either x-3=0 or x+1=0; therefore x=3 or x=-1.

Substituting this into the first equation (it is simpler):
y=2(3) = 6
y=2(-1)=-2

Therefore the coordinates are (3, 6) and (-1, -2).

Answer:

Step-by-step explanation:

From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

⇒ -3,  

⇒ 0.59,  

⇒ 3.41

Simplify these algebraic expressions: 12x + 3 − 4x + 7, 8 − 7x − 13 + 2x, −3x − 18 + 5x − 2

Answers

12x+3-4x+=8x-4
8-7x-13+2x=-5-5x
-3x-18+5x-2=-16x-2

The simplified expressions are:

12x + 3 − 4x + 7 = 8x + 10

8 − 7x − 13 + 2x = −5x − 5

−3x − 18 + 5x − 2 = 2x − 20

What is an expression?

A term is a single mathematical phrase. It might consist of only one variable—a letter—one number—positive or negative—or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. Coefficients are numbers that come before phrases.

To simplify each expression, we combine like terms:

Expression 1:

12x + 3 − 4x + 7 = (12x − 4x) + (3 + 7)

12x + 3 − 4x + 7 = 8x + 10

Expression 2:

8 − 7x − 13 + 2x = (−7x + 2x) + (8 − 13) = −5x − 5

Expression 3:

−3x − 18 + 5x − 2 = (−3x + 5x) + (−18 − 2) = 2x − 20.

Therefore, the simplified expressions are:

12x + 3 − 4x + 7 = 8x + 10

8 − 7x − 13 + 2x = −5x − 5

−3x − 18 + 5x − 2 = 2x − 20

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Find the value of z.

Answers

It we’ll be number 3

1. _____ is exchanging one good for another without using money.
Credit
Barter
Negotiating
Brokering
2. A _____ has to be paid in full on the due date. (1 point)
Charge card
Credit card
Debit card
Check card
3. The _____ is the original amount owed on a loan. (1 point)
Loan due
Interest
Available balance
Principal
4. APR is used to calculate the _____. (1 point)
Loan amount
Interest accrued
Principal
Future earnings,

Answers

Barter is exchanging one good for another without using money. .A Credit card has to be paid in full on the due date. The Principal is the original amount owed on a loan. APR is used to calculate the Interest accrued.

The answers are:

1. Barter

2. charge card

3. principal

4. interest accured

Sara is 8 years old and her mom is 34 years old. In how many years will Sara be twice as young as her mom will be?

If x is the number of years, then the equation is ______
The answer is _____

Answers

Sara = 8 years old
Mom = 34 years old

Let the number of years be x when Sara will be twice as young as her mom will be.
2(8 + x) = 34 + x
16 + 2x = 34 + x
2x - x = 34 - 16
x = 18

Answer:
If x is the number of years, then the equation is 2(8 + x) = 34 + x
The answer is 18 

If the intquantity and decprice variables contain the numbers 3 and 15.75, respectively, the condition if intquantity > 0 andalso intquantity < 10 orelse decprice > 20 will evaluate to

Answers

if intquantity > 0 andalso intquantity < 10 orelse decprice > 20 
expression evaluates to
 (3>0 and 15.75<10  or  15.75>20)
which, using priority of operations, "and" has a higher precedence than "or",
=>
( (3>0 and 15.75<10)  or  15.75>20)
=>
( false or false )
=> 
false

12pts BRAINLIEST, THX, AND RATE AVAILABLE TO CORRECT ANSWER.

PLEASE HELP ME ON THIS

****RANDOM ANSWERS WILL BE REPORTED****

Answers

just get percentage, multiply by number of years, and add it to the base hope this helps and please give me brainliest

In the Citizens United case the Supreme Court interpreted political donations as __________.

Answers

 In the Citizens United case the Supreme Court interpreted political donations as __________.
A) only allowable for low-income candidates  

B) a restriction on equal access to democracy  

C) a form of speech protected by the Constitution  

D) an unconstitutional influence over policymakers

Answer:  C) a form of speech protected by the Constitution  

Page Reference:  33 Learning 
Objective: 2.2 Topic/A-head: Political System: 
Links Between Wealth and Power 
Skill Level: Understand the Concepts

Suppose a population of 175 crayfish doubles in size every month. the function f(x) = 175(2x) gives the population after x months. how many crayfish will there be after 1 year?

Answers

The first thing we will do in this case is to rewrite the expression correctly.
 We have then:
 f (x) = 175 * (2 ^ x)
 Then, you should know that 1 year contains 12 months.
 So we have that for x = 12:
 f (12) = 175 * (2 ^ 12)
 f (12) = 716800
 Answer:
 there will be 716800 crayfishes after 1 year

A tessellation is a (blank) patterns of figures?
reflecting
repeating
symmetrical,

Answers

the answer is symmetrical

How many solutions does the system have?

{y = −2x + 2
y = x^2 − 3x



Enter your answer in the box.

________

Answers

Answer:

The system has two solution

Step-by-step explanation:

we have

[tex]y=-2x+2[/tex] ----> equation A

[tex]y=x^{2}-3x[/tex] ----> equation B

Solve the system of equations by graphing

Remember that

The solution of the system of equations is the intersection point both graphs

There are two point of intersection between the two graphs

see the attached figure

therefore

The system has two solution

Which of the following points lies on the graph

Answers

Plug in each point. If both sides of the equation are true, then the point is on the graph.

(-3, 21)

y = x^2-2x+6
21 = (-3)^2-2(-3)+6
21=9+6+6
21=21

That works. If you are not 100% confident with your arithmetic, you can plug in the other points.

every day Josie bakery bakes muffins and bagels. the ratio of m7ffins to bagels is always the same. the table shows data about what Josie bakery bakes 3 days of the week. How many bagels did Josie bakery bakes on wednesday

Answers

180/300 = 165/x

x = (300*165)/180 = 275

Find the volume of the box. use the formula v = lwh. rectangular box with three sides visible, having width, length, and height of x plus two, two x minus one, and three x plus one respectively
a. 6x3 – 2
b. 6x2 – 13x2 – 3x – 2
c. 6x2– x – 1
d. 6x3 + 11x2 – 3x – 2

Answers

x + 2, 2x-1, 3x+1
Multiplying these all together will result in 
6x^3+11x^2−3x−2
Making the answer option D.

The expression for the volume of the box is given by 6x³+11x²-3x-2

What is volume?

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Given that, rectangular box with three sides visible, having width, length, and height of x plus two, two x minus one, and three x plus one

Height = x+2

Width = 2x+1

Length = 3x+1

Volume = HxLxW

Volume = (x+2)(2x+1)(3x+1)

= 2x²-x+4x-2(3x+1)

= (2x²+3x-2)(3x+1)

= 6x³+11x²-3x-2

Hence, The expression for the volume of the box is given by 6x³+11x²-3x-2

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What’s the value of x worth 15 points!

Answers

3x - 15 = 2x + 24
Opposite angles of a parallelogram are equal. You get a hint of that from the 2 acute angles which are both 2x.

Add 15 to both sides.
3x = 2x + 24 + 15
3x = 2x + 39 Subtract 2x from both sides.
3x - 2x = 39
x = 39

Hi there! :)

Answer:

x=39

*The answer must have a positive sign.*

Step-by-step explanation:

When the 2 acute angles in which means you had to used 2x from both sides of an equation.

First, only had to do is, add by 15 from both sides of an equation.

[tex]3x-15+15=2x+24+15[/tex]

Then, you add by the numbers from left to right.

[tex]24+15=39[/tex]

[tex]3x=2x+39[/tex]

Next, you subtract by 2x from both sides of an equation.

[tex]3x-2x=2x+39-2x[/tex]

Finally, you simplify.

[tex]x=39[/tex]

Final answer is x=39

Hope this helps!

Thanks!

Have a nice day! :)

:D

-Charlie

Let $G$ denote the centroid of triangle $ABC$. If triangle $ABG$ is equilateral with side length 2, then determine the perimeter of triangle $ABC$. 99 points! for right answer!

Answers

Hey there!

You are trying to find the perimeter of triangle ABC. Each side is 2. Since there are 3 sides on a triangle, multiply 2 by 3 to get 6. You do not need the centroid for this problem.

I hope this helps!

what effect does the value of the coefficient of x^2 have on the graph?

Answers

as the coefficient increases, the graph shrinks.
ex.)
for the graph of x^2, 5 of your data points will be (0,0),(1,1),(2,4),(3,9),(4,16)

when you multiply by a coefficient,
ex.)
for the graph of ax^2, a being a stand in for the coefficient, 5 of your data points will be (0,a×0), (1,a×1), (2,a×4), (3, a×9), (4,a×16)

if your coefficient,a, is equal to 4 your data points become: (0,0),(1,4),(2,8),(3,36),(4,64)

if you graph it out you will notice that your graph rises faster and faster incompariaon to the original.

hope this helps good luck

You deposit $1500 in an account that pays 7% annual interest. Find the balance after 2 years when the interest is compounded daily.

Answers

The balance after 2 years when the interest is compounded daily is

$1,725.39.

What is Compound Interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

Given:

P= $1500

R= 7%

T = 2 years

Now, using

A = P[tex](1 + r/n)^{nt[/tex]

A = 1,500.00[tex](1 + 0.07/365)^{(365)(2)[/tex]

A = 1,500.00[tex](1 + 0.00019178082191781)^{(730)[/tex]

A = $1,725.39

Hence, the balance is $1,725.39.

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Im learning Polynomials and we are learning the strategy grouping, can anyone please explain how to group polynomials and maybe give an example :) greatly appreciated

Answers

Grouping is when you have to terms that are the same inside the parenthesis and a different or same number outside the parenthesis and then the one inside the parenthesis u are going to group them not combined them and write them once and the numbers inside the parenthesis group them together by adding them and put parenthesis between them

Ex
5(4x+1)10(4x+1)
(5+10)(4x+1)
Grouping can mean different things in different contexts. In simple cases, polynomials are written in such a way that all you need to do is add parentheses to make groups. Usually we are interested in doing this so we can factor or simlify the result.

Example
  x^2 +2x +3x +6
  (x^2 +2x) +(3x +6) . . . . parentheses added to group pairs of terms
  x(x +2) +3(x +2) . . . . . . common factor pulled from the terms of each group
  (x +3)(x +2) . . . . . . . . . common factor removed to give factored result
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