Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A1 be the event that the receiver functions properly throughout the warranty period, A2 be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A1)= .95, P(A2) = .98, and P(A3) = .80.a. What is the probability that all three components function properly throughout the warranty period?b. What is the probability that at least one component needs service during the warranty period?c. What is the probability that all three components need service during the warranty period?

Answer:

A. 4×π×3²×[tex]10^{6}[/tex]

Step-by-step explanation:

r = 3×10² = 3×100 = 300

[tex]\frac{4}{3}[/tex]×π×300³=

[tex]\frac{4}{3}[/tex]×π×27,000,000=

[tex]\frac{108,000,000}{3}[/tex]×π=

36,000,000π

Answers solved:

A. 36,000,000π

B. 108,000,000π

C. 3,600,000π

D. 32,400,000π

The solution is Option A.

The volume of the air in the spherical ball is given by the equation

V = 4π ( 3 )² ( 10 )⁶ cm³

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

The Surface Area of a Sphere = 4πr²

The Volume of a Sphere = ( 4/3 ) πr³

where r is the radius of the sphere

Given data ,

Let the volume of the sphere be represented as V

Now , the radius of the spherical ball be r

The value of r = 3 ( 10 )² cm

So , the volume of the spherical ball = ( 4/3 ) πr³

Substituting the values in the equation , we get

Volume of the spherical ball V = ( 4/3 ) x π x [ 3 ( 10 )² ]³

On simplifying the equation , we get

Volume of the spherical ball V = ( 4/3 ) x π x ( 3 )³ ( 10 )⁶

Volume of the spherical ball V = 4 x π x ( 3 )² ( 10 )⁶

Therefore , the value of V is 4π ( 3 )² ( 10 )⁶

Hence , the volume of the spherical ball is 4π ( 3 )² ( 10 )⁶

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Answer:

f(c)=4f, left parenthesis, c, right parenthesis, equals, 4 for at least one ccc between -2−2minus, 2 and 11

Step-by-step explanation:

hope this helps

There is a root in the given equation ex = 6 − 5x, in the interval (0, 1).

It is required to find the functions has f(0) and f(1).

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

Using Intermediate value Theorem we have

If F(x) is continuous and f(a) and f(b) have opposite signs then there will be at a point  (a ,b)  whereby F(c) = 0

The equation is

[tex]f(x) = e^{x} - 6 + 5x = 0[/tex] on  interval [0, 1],

This shows that the F(x) is continuous on (0,1).

[tex]f(0) = e^{0} - 6 + 5*0 = -5\\ \\f(1) = e^{1} - 6 + 5*1 = e-1[/tex]

e = 2.7182

since the functions has f(0) and f(1) have opposite signs then there is at a point whereby F(c) = 0 ( intermediate value theorem fulfilled )

Hence, there is a root in the given equation ex = 6 − 5x, in the interval (0, 1).

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Answer:

c) The population is the parents of the pediatrician's patients; the sample is the

10

1010 parents of patients selected.

Step-by-step explanation:

Answer:

c) The population is the parents of the pediatrician's patients; the sample is the

10

1010 parents of patients selected.

Step-by-step explanation:

Answer:

Average Rate of Pay = $ 5.23 /hr

Step-by-step explanation:

We have a data in form of Hours of Baby Sitting and Amount of Pay. Since the Amount of pay depends upon the Hours of Baby Sitting. Thus, we take y = Amount of Pay, while x = Hours of Baby Sitting. So, the data becomes:

x (Hours) =   12      13      16      17       20

y ($)         =  54     56     65     64     100  

The statistical data calculated is:

∑x = 78,   ∑x² = 1258,   ∑y = 339,  ∑xy = 5504,   n = no. of data points = 5

Now, we use linear regression model to fit a straight line to this data.

y = a + bx   --------- eqn (1)

where,

b = [ n∑xy - ∑x.∑y]/[n∑x² -(∑x)²]

b = [ (5)(5504) - (78)(339)]/[(5)(1258) - (78)²]

b = 5.23

and,

a = (∑xy - b∑x²)/∑x

a = [5504 - (5.23)(1258)]/78

a = -13.83

Therefore, eqn (1) becomes:

y = -13.83 + 5.23x

The graph plot of this straight line fit is provided in the attachments.

Now, we derivate the equation with respect to x, to get the average rate of pay:

Average Rate of Pay = dy/dx = d/dx(-13.83 + 5.23x)

Average Rate of Pay = $ 5.23 /hr

How am I supposed to be able to answer a question without the info

Answer:

Find the volume of the prism shown below if the height is 3 inches.

Step-by-step explanation:

Answer:

(x + 5) (x - 7)

Step-by-step explanation:

To factor this trinomial, you must split the middle term (-2x) into two terms that can be added to get -2x, and multiplied to get -35:

[tex]x^2[/tex] - 2x - 35

[tex]x^2[/tex] - 7x + 5x - 35

Group:

([tex]x^2[/tex] - 7x)  (5x - 35)

Take out GCF (Greatest Common Factor):

x(x - 7)  5(x - 7)

(x + 5) (x - 7)

Answer:

–3

Step-by-step explanation:

i got 90% on my quiz also may i pleas get brainliest

Answer:

Figure D

Step-by-step explanation:

Point Symmetry is when every part has a matching part: the same distance from the central point. but in the opposite direction. Hope this helps! :)

Answer:

  B. ​False, because the description applies to a single solution. The solution set consists of all possible solutions.

Step-by-step explanation:

The choice of true or false revolves around whether a linear system can have more than one solution.

The problem statement does not say the equations are independent, a condition that must be satisfied if there is to be only one solution. Hence we must assume that the system may be dependent or even inconsistent, leading to zero, one, or an infinite number of solutions. The answer above carries its own explanation.

  False, for the reason given

Answer:

2n/3

Step-by-step explanation:

hope this helps!! moo

Answer:

no this game is not fair due to the fact that u have a 2/6 chance to win

Answer:

a. a reflection over the x-axis and then a reflection over the y-axis

Step-by-step explanation:

If you plot it on a graph (you can use Desmos), you can see the triangles and only a. a reflection over the x-axis and then a reflection over the y-axis makes sense.

Answer:

thats c

Step-by-step explanation:

Answer:

y = (1/2) x -10

Step-by-step explanation:

Perpendicular lines are lines make right angles. The slopes of perpendicular lines are opposite reciprocals !

2x + y = -7 rewrite in form y=

y = -7 -2x

slope of this line is -2

perpendicular lines are opposite reciprocals so the line p has a slope = 1/2

line p passes through (8, -6) so plug in point into equation of p and get ?

y = 1/2 x +?

-6 =1/2(8) +?

-6 =4 + ? subtract 4 from both sides

-6-4 = ?

-10 = ?

y = (1/2) x -10

Answer:

  -3

Step-by-step explanation:

An increase in x-value from 9 to 10 is an increase of 1 unit. The slope of -7 tells you that the corresponding change in y will by -7 units:

  v = 4 -7 = -3

The value of v is -3.

_____

Alternate solutions

You can see this easily on a graph, or you can use the equation of the line. We have a point and a slope, so the point-slope form is useful.

  y = m(x -h) +k

  y = -7(x -9) +4

For x=10, the value of y is ...

  v = -7(10 -9) +4 = -7 +4

  v = -3

Answer:

You are correct

Step-by-step explanation:

x - 8 < 23

Add 8 to both sides

x - 8 + 8 < 23 + 8

Simplify

x < 31

Yes, you are correct.

Answer: 4

Step-by-step explanation:

First you need to convert to pints.

Your conversion factors are:

1 gallon = 8 pints

1 quart = 2 pints

[tex]3gallons(\frac{8pints}{1gallon}) =24pints[/tex]

[tex]10quarts(\frac{2 pints}{1quart})=20pints[/tex]

To find the difference, subtract.

24-20=4

Answer: D

Step-by-step explanation:

 2x + (2x +4 ) =40

x= 9

2(9) +4 =22

Answer:

210 pounds because after 7 days (week) thats how much bambo the panda will eat

Step-by-step explanation:

90 pounds = 3 days

6 days = 180 pounds

1 day = 30 pounds

180 +30= 210 pounds

Answer:

26.31 units

Step-by-step explanation:

Given: Points [tex](-10,12),(-6,-14)[/tex]

To find: Distance between the given points

Solution:

Let [tex](x_1,y_1)=(-10,12)\,,\,(x_2,y_2)=(-6,-14)[/tex]

The distance formula is used to find the distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex]

According to distance formula,

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\sqrt{(-6+10)^2+(-14-12)^2}\\ =\sqrt{16+676}\\ =\sqrt{692}\\ =26.31[/tex]

So, distance between the given points is 26.31 units

Answer:

5 seconds

Step-by-step explanation:

(60 / seconds = GPM)

60 / 5 = 12 GPM

12 GPM = 60 seconds

Simplified

1 Gallon is 5 seconds

Answer:

5

Step-by-step explanation:

Answer:

c= 5 yards.

Step-by-step explanation:

4*1.5=6

30/6= 5

Answer:

A = 19.47

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hypotenuse

sin A = 2/6

Take the inverse sin of each side

sin ^-1 ( sin A) = sin ^-1 (2/6)

A =19.47122063

To the nearest hundredth

A = 19.47

Answer:

  it is not on the graph

Step-by-step explanation:

Put the given values into the equation and see if it is true:

  -2(2) +1/3(6) = -1

  -4 +2 = -1 . . . . . . . .FALSE

The point is not on the graph of the equation.

Answer:

2x3 - x2 - 50x + 25

Step-by-step explanation:

So the first thing you would do is multiply (x - 5)(x + 5)

x2 + 5x - 5x - 25

then you would simplify

x2 - 25

then you would multiply it by 2x - 1

(x2 - 25)(2x - 1)

2x3 - x2 - 50x + 25

so your answer is  

2x3 - x2 - 50x + 25

Answer:

The correct option is;

D. 30 and 40

Step-by-step explanation:

Here, we have that the rhombus is a quadrilateral with equal and parallel sides hence the length of the diagonals will be

2 × 25×sinθ  and 2 × 25× cosθ

Therefore tanθ = (2 × 25×sinθ)/(2 × 25× cosθ) = (sinθ)/(cosθ)

Therefore, the root of the sum squares of both diagonals = 50

Therefore, we analyze each of the options as follows

For A. we have √(22² + 40²) = 45.65 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

For B. we have √(26² + 36²) = 44.41 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

For C. we have √(26² + 48²) = 55.59 ≠ 50 therefore these are not the length of diagonals of the rhombus in question

For D. we have √(30² + 40²) = 50 therefore these are possible lengths of diagonals of the rhombus in question.

Answer:

-5

Step-by-step explanation:

-4x-12=8

     +12.  +12

-4x=20

Divide -4 on both sides

20/-4

x= -5

Answer:

Weight of decaf coffee = 5 pounds.

Weight of regular coffee = 8 pounds.

Step-by-step explanation:

(a) Let x be the weight of decaf coffee and y the weight of regular coffee. Then:

x + y = 13

2x + 3y = 34

(b) From the first equation x = 13 - y, so substituting for x in second equation:

2(13 - y) + 3y = 34

26 - 2y + 3y = 34

y = 34 - 26 = 8.

Substituting for y in the first equation:

x + 8 = 13

x = 5.

Answer:

B

Step-by-step explanation:

In the attached file