1. A survey of local car dealers revealed that 64% of all cars sold last month had CD players,
28% had alarm systems, and 22% had both CD players and alarm systems.

a.
What is the probability one of these cars selected at random had neither a CD player nor
an alarm system?

b. What is the probability that a car had a CD player unprotected by an alarm system?


C.
What is the probability a car with an alarm system had a CD player?

D.
Are having a CD player and an alarm system disjoint events? Explain.

Using the specified oriented surface, the surface integral is F=y³i+8j-xk is a downward-pointing normal is -53/60.

Given that,

We have to find using the specified oriented surface, calculate the surface integral: F=y³i+8j-xk is a downward-pointing normal that is a part of the plane x+y+z=1 in the octant x,y,z≥0.

We know that,

Finding the surface integral of [tex]\int {} \,\int\limits_s {F} \, ds[/tex]

Here,

The surface of the plane's part is x+y+z=1;

In the 1st octant, x,y,z≥0, and the oriented surface F=y³i+8j-xk.

The plane x + y + z = 1

z=1-x-y

dz/dx=-1

dz/dy=-1

So, the surface is oriented downward

dS= (dz/dzi+dz/dyj-k)dxdy

dS=(-i-j-k)dxdy

So, we get

[tex]\int {} \,\int\limits_s {F} \, ds[/tex]

[tex]\int {} \,\int\limits_s {F} \, (dz/dzi+dz/dyj-k)dxdy[/tex]

-53/60

Therefore, Using the specified oriented surface, the surface integral is F=y³i+8j-xk is a downward-pointing normal is -53/60.

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Answer:

The answer is (10) 8' and (3) 12 A

Step-by-step explanation:

To build a wall that is 12' long and 8' high, you will need (10) 8' 2x4's and (3) 12' 2x4's. This will give you the necessary length for the bottom and top plates and 10 studs. Each stud should be spaced about 16" on center, so 10 studs will be enough to support the wall.

Answer:

-9/47

Step-by-step explanation:

[tex]4 \frac{1}{4}x-\frac{1}{3}x=-\frac{3}{4} \\ \\ \frac{17}{4}x-\frac{1}{3}x=-\frac{3}{4} \\ \\ 51x-4x=-9 \\ \\ 47x=-9 \\ \\ x=-\frac{9}{47}[/tex]

Answer:

Step-by-step explanation:

- 5/12

i did the test lol

The intersection of the two medians results in a 1:2 division. Consequently, the KP value is 15.5.

Given,

Triangle ABC is shown;

Triangle;-

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Here,

If AK = 31 and we are aware that the two medians coincide, then the division is 1:2.

Then,

KP/AK = 1/2

KP = AK / 2

KP = 31/2

KP = 15.5

Therefore,

The value of KP is 15.5 units.

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Answer:

C. $6,500

Step-by-step explanation:

Owner's equity is the amount of the business's assets that are owned by the owner or shareholders. It is calculated by subtracting the total liabilities from the total assets.

Given that Total assets = $34,500 and Total liabilities = $28,000, the owner's equity is:

Owner's equity = Total assets - Total liabilities

= $34,500 - $28,000

= $6,500

Therefore, the correct answer is C. $6,500.

Answer: Luisa is correct.

Step-by-step explanation: Luisa is correct. To find the solution to the equation, we need to isolate the radical expression on one side of the equation. If we subtract x from both sides, we get √5 + 4x - x = x - x, or √5 = 0. Since the square root of any number is always positive, this equation has no solution. Therefore, the solution is H = 5.

On the other hand, if we square both sides of the equation, we get 5 + 8x + 4x^2 = x^2. If we simplify this equation, we get x^2 + 8x - 5 = 0. This equation can be solved using the quadratic formula, which gives us x = (-8 +/- sqrt(64 + 20))/2. This simplifies to x = (-8 +/- sqrt(84))/2. The solutions to this equation are x = -1 and x = 5. However, since we squared both sides of the original equation, we have to check whether these solutions actually work in the original equation. Substituting x = -1 into the original equation gives us √5 + 4(-1) = -1, or √5 = -1. This is not a valid solution, since the square root of any number is always positive. However, substituting x = 5 into the original equation gives us √5 + 4(5) = 5, or √5 = 0. This is a valid solution, since the square root of any number is always positive. Therefore, the only solution to the original equation is x = 5, which is the solution that Luisa found.

For automobile traffic, dB=81.987657 dB.

For quiet conversation is 40.33423 dB.

For fender guitar, 115.56302 dB.

For jet engine, 151.98657 dB.

(A)

The intensity of automobile traffic is, I=1.58x10^8 I.

Given: dB=10 log (I/I0)

Substituting the value of I,

dB= 10 log (1.58x10^8 I/I)

=10 log (1.58x10^8)

Using the logarithm property,

=10 (log (1.58)+log (10^8))

=10 (log (1.58)+8 log (10)

=10( log (1.58)+8(1)

=80+1.98657

=81.98657

Thus, for automobile traffic, dB=81.987657 dB.

B)

Quiet conversation, I=10800 I0

dB= 10 log (10800 I0/I0)

=10 log (10800)

=10 log (1.08x10^4)

=10 log (1.08)+log (10^4)

=10 (log (108)+4log (10))

=10 (log (1.08+4*(1))

=40+10 log (1.08)

=40+0.33423

=40.33423 dB.

Thus, for quiet conversation is 40.33423 dB.

C)

Fender guitar, I=3.16x10^11 I0

dB= 10 log (3.16x10^11 I0/I0)

=10 (log (3.16)+11)

=110+10 log (3.16)

=110+5.56302

=115.56302

Thus, for fender guitar, 115.56302 dB.

D)

Jet engine, I=1.58x10^5 I0

dB= 10 log (1.58x10^15 I0/I0)

=10 (log (1.58)+15)

=150+10 log (1.58)

=150+1.98657

=151.98657

Thus, for jet engine, 151.98657 dB.

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The true statements are

Consider the two points in the line

(-1, 1) and (3, 2)

The slope of the line = (2-1) / (3 -(-1))

= 1/4

The slope intercept form is

y = mx + b

2 = (1/4)3 + b

2 = 3/4 + b

b = 2 - (3/4)

b = 5/4

The equation of the line y = (1/4)x + 5/4

(3, 2) and (-1, 1) are points on the line

Consider the point (1, 3/2)

3/2 = (1/4)1 + 5/4

3/2 = 1/4 + 5/4

3/2 = 3/2

Therefore, (1, 3/2) is the solution of the line

It has infinitely many solutions

Therefore, the correct statements are statements A, B, C, E, F

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Answer:

80 Meters by 80 Meters

Step-by-step explanation:

Perimeter is the distance around the rectangle.  60+60+100+100 = 320

The perimeter is 320 meters.

Area = Length times width

The area would be

100x 60 = 6,000 [tex]m^{2}[/tex]

If we change the length and width to 80 meters we would have the same perimeter

80+80+80+80 = 320 Meters, but the area would be larger

Area = 80 x 80 = 6,400 [tex]m^{2}[/tex]

Answer:

24

Step-by-step explanation:

(9-3)×4

(6)×4

The answer is 24

Answer:

Step-by-step explanation:3.5 bytes

The family monthly payment on annual interest is 1691.

What is annual interest rate?

Calculation of amount payable to the bank

Cost of House  -  350000

Down payment 10%  -  35000

Amount payable  -  315000

]5% Annual interest rate and compounded monthly is 186.28030751

A) family monthly payment= Amount payable/Annuity factor =315000/186.28030751 =1691

B)Total interest paid on loan =293756.40

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Answer: Thermal energy

Step-by-step explanation:

Thermal energy is the sum of the kinetic and potential energy of all the particles in an object.

As per the statement in the question, the expression will be x + 52.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per given information in the question,

Let the unknown number is x.

The statement says that the number is more than 52.

Then, the expression according to the statement will be,

= x + 52

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The oldest Kim could be 7.

What is inequality?

The occurrence of an unfair and/or unequal distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different people and in various settings, the word "inequality" may indicate different things.

Here,

Given

Josh is 4 years older than 2 times Kim's age.

The sum of their ages is less than 25.

We have to find the age of Kim.

Let Kim's age be x.

Then Josh's age is (2x+4)

The total is

 x + (2x+4) < 25.

Simplify and solve the inequality for x

 3x + 4 < 25

3x < 25-4= 21

 x < 21/3 = 7

Hence,  the oldest Kim could be 7.

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The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of w is 3, so the degree of the polynomial is 3.

The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In this case, the leading coefficient is 12.

In summary, the polynomial -9-8w+3w+12w³ has degree 3 and leading coefficient 12.

Answer:

Step-by-step explanation:

Rick desposits 3$ into his account:

b=Rick's bank balance

b+3

The following week, he deposits 3 times that amount:

3*3=9

2nd week= b+9

Each ewek after that, he deposits 3 times the amount he did the previous week:

3rd week = b+9x3

3rd week = b+27

How much does it deposit in all during the first 3 weeks?

1st week = $3

2nd week = $9

3rd week = $27

3+9+27=39

Rick deposits $39 in the first 3 weeks

Answer for second question:

d=dollars

w=weeks

d=[tex]d=3^2[/tex]

"One who performs his duty without attachment, surrendering the results unto the Supreme Lord, is unaffected by sinful action, as the lotus leaf is untouched by water." - Krishna, Bhagavad Gita 5.10

Thanks, I hope I could help

Miraculous21

The period of some number of  consecutive days during which the team must  play exactly 14 games should be that 2 games plays at  these days  1,5,10,15,20,25,30 individually....

As there are 30 days in a month.

So we have to arrange these 14 games during this time period of 30 days,

Which will be arranged as:

suppose its 1 st month of 2023,

So,

2 games at day  =    1/1/2023

2 games at day   =    5/1/2023

2 games at day   =    10/1/2023

2 games at day   =    15/1/2023

2 games at day   =    20/1/2023

2 games at day   =    25/1/2023

2 games at day   =    30/1/2023  

So from here we conduct:

2+2+2+2+2+2+2=  14 games

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Step-by-step explanation:

If €2 of grapes cost $6

$1 =2/6

=€0.3

Answer:

450J/(kg-°C)​

Step-by-step explanation:

the basic stuff of temperature is 3.0kg×5.0°C ，then assumed to be x

the thermal energy was y

then it was a functions y=kx,the k was the specific heat of the material

[tex]k=\frac{6750}{15}[/tex]=450 J/kg·°C

The numeric value of the expression [(3 ⇑ 1) ⇑ 2] − [3 ⇑ (1 ⇑ 2)] is given as follows:

70.

The operator for this problem is given as follows:

a ⇑ b = a² + b².

Then the operations are made following the precedence of operations, due to the parenthesis, as follows:

Then the expression can be written as follows:

[(3 ⇑ 1) ⇑ 2] − [3 ⇑ (1 ⇑ 2)] = [10 ⇑ 2] − [3 ⇑ 5].

Then the operators are calculated as follows:

Finally, the subtraction is applied between these two results to obtain the numeric value of the expression, as follows:

104 - 34 = 70.

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Based on the information given in the question the  (0, 2kπ) maybe the spiral point or center point of the nonlinear system. The stability of (0, 2kπ) is indeterminate.

An equation comprising one or more functions and their derivatives is known as a differential equation in mathematics. A function's derivative expresses the rate of change of the function at a specific moment. It is mostly employed in the sciences of physics, engineering, and biology.

F = (1 + x) sin y = 0

G = 1 − x − cos y = 0

we know that all the critical points are (0, 2kπ), (2,(2k + 1)π). Since the F, G are

continuous differentiable, the system is almost linear near the critical points.

µ

Fx Fy Gx Gy=µsin y (1 + x) cos y−1 sin y

The linear system near critical point (2,(2k + 1)π) is

du/dt = −3v, dv/dt = −u

where u = 2 + x, v = (2k + 1)π + y. The eigenvalues of the linear system are −√3,√3,hence the critical point (2,(2k + 1)π) is saddle point and unstable. The linear system

near critical point (0, 2kπ) is

du/dt = v

dv/dt = −u, where u = x, v = 2kπ + y. The eigenvalues of the linear system are −i, i, hence the

critical point (0, 2kπ) is center point and stable of the corresponding linear system. Then (0, 2kπ) maybe the spiral point or center point of the nonlinear system. The stability of (0, 2kπ) is indeterminate.

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Answer:

y = 3x + 37

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 8, 13 ) and (x₂, y₂ ) = (- 6, 19 )

m = [tex]\frac{19-13}{-6-(-8)}[/tex] = [tex]\frac{6}{-6+8}[/tex] = [tex]\frac{6}{2}[/tex] = 3 , then

y = 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 8, 13 ) , then

13 = 3(- 8) + c = -24 + c ( add 24 to both sides )

37 = c

y = 3x + 37 ← equation of line

Answer:

Hola cómo te llamas Hola

Answer:

Step-by-step explanation:

The slope of the graph of y = -3x is -3. The slope of a line is the amount that the line rises or falls for every unit it moves horizontally. In this case, the line rises by -3 units for every 1 unit it moves horizontally. This means that the slope of the line is -3.

The value of the missing coordinate, r as required to be determined from the given information is; r = 2.

It follows from the task content that the value of the missing coordinate, r is to be determined from the task content.

On this note, since the given points are; (-7, r) and (-3, 14) and the slope of the line through them is; 3.

It follows from the slope formula;

m = (y₂ - y₁) / (x₂ - x₁) that;

3 = ( 14 - r ) / ( -3 -(-7) )

-9 + 21 = 14 - r

r = 14 + 9 - 21

r = 2.

On this note, the required value of the missing coordinate, r is; 2.

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The correlation between the obesity rate and the mortality rate is moderately strong.

In math correlation is defined as the a statistical measure that expresses the extent to which two variables are linearly related

Here we have given that Colorectal cancer (CRC) is the third most commonly diagnosed cancer among Americans (with nearly 147.000 new eases), ami the third leading cause of cancer death (with over 50.000 deaths annually).

Here the Research was done to determine whether there is a link between obesity and CRC mortality rates among African Americans in the United States by county.

And we need to find the correlation between obesity rates and mortality rates.

While we looking into the given question we have identified that the regression analysis was carried out to find the relationship between the obesity and CRC mortality rates so the response variable is mortality rate and input variable is obesity.

Therefore, the correlation is moderately stronger than the analyzed data.

Therefore, option (c) is correct.

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Moment generating function of a random variable is the expectation of a random variable. The moment generating function of the geometric(p) distribution is given by pe^{t}/ (1 - (1 - p)e^{t}.

A moment generating function can be described as

MGFₓ(t) = E( e^{tx})

For continuous x

E( e^{tx}) = ∫ₓ e^{tx}×f(x)×d(x) where f(x) is the probability density function.

For discrete x

E( e^{tx}) = ∑ₓ e^{tx}×P(x) where P(x) is the probability mass function.

A geometric distribution is a discrete probability distribution that provide us the probability that the 1st occurrence o success would need k independent trials of success probability p each. Thus probability mass function of geometric distribution is

P(X = k) = (1 - p)^{k} × p

So moment generating function can be obtained by

MGFₓ(t) = E( e^{tx}) = ∑ₓ e^{tx}×P(x)

MGFₓ(t) = ∑ₓ (e^{kt} × (1 - p)^{k} × p)

MGFₓ(t) = p×∑ₓ (e^{t} × (1 - p))^{k}

|e^{t} × (1 - p)| < 1 so applying property of sum of infinite geometric progression we have

MGFₓ(t) = p× e^{t}/ (1 - (1 - p)e^{t}

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