On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
A. 0.027
B. 0.090
C. 0.417
D. 0.657
E. 0.900

Answer:

D

Step-by-step explanation:

((p^4*q)/p^8)^2.

p^4/p^8=p^(4-8)=p^-4=1/p^4

(q/p^4)^2=(q^2/p^8)

To simplify an algebraic expression, eliminate denominators, distribute factors, rearrange and combine like terms, and isolate the variable. Checking the reasonableness of the answer is also important after simplification.

To simplify an algebraic expression or equation involving variables, you should first look at what needs to be solved for and then work the problem out using only variables. This helps in minimizing calculation time and reducing the chance of errors. Here are some steps to simplify algebraic expressions:

Additionally, by variable rescaling and setting some limits for the error margin, you can further simplify the algebra by eliminating as many parameters as possible. Always check your final answer to ensure it's reasonable.

Answer:

We can do it with envelopes with amounts $1,$2,$4,$8,$16,$32,$64,$128,$256 and $489

Step-by-step explanation:

This give us the idea to put in each envelope an amount of money equal to the positional value of each digit in the representation of 1023. That is, we will put the bills in envelopes with amounts of money equal to $1,$2,$4,$8,$16,$32,$64,$128,$256 and $512.

However, a little modification must be done, since we do not have $1023, only $1,000. To solve this, the last envelope should have $489 instead of 512.

Observe that:

Answer:

540 feet

Step-by-step explanation:

225x(8/5)

360 feet in 1 hour

6 feet in 1 minute

540 feet in 90 minutes

The equivalent expressions of the given expressions is 540 feet in 90 minutes.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

The expression of 225 divided by 5/8 as 225 x 8/5.

225 x (8/5)

So, the quotient says a sloth may move 360 feet in 1 hour.

360 feet in 1 hour

Then, 6 feet in 1 minute

90 minutes as 1 1/2 hour.

Multiply by 1 1/2 to get feet in 90 minutes.

540 feet in 90 minutes

The equivalent expressions of the given expressions is 540 feet in 90 minutes.

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Answer:

Step-by-step explanation:

SOH CAH TOA can remind you of the relationships between triangle measures. The distance east is the side of the right triangle that is opposite the angle, so is related to the hypotenuse (ship's travel distance) by the sine function.

  sin(43°) = (travel distance)/(distance east)

So, ...

  (distance east) = (travel distance)·sin(43°)

Likewise, the cosine function can be used to find the distance south.

Then we have ...

  east = (130 km)sin(43°) ≈ 95 km

  south = (130 km)cos(43°) ≈ 89 km

Answer:

The length of the patio is 32 ft and the width is 13 ft

Step-by-step explanation:

see the attached figure to better understand the problem

Let

L ----> the length of his patio

W ---> the width of his patio

we know that

[tex]L+2W=58[/tex] ----> equation A

[tex]L=2W+6[/tex] ----> equation B

substitute equation B in equation A and solve for W

[tex]2W+6+2W=58[/tex]

[tex]4W+6=58[/tex]

[tex]4W=58-6[/tex]

[tex]4W=52[/tex]

[tex]W=13\ ft[/tex]

Find the value of L

[tex]L=2W+6[/tex]  ----> [tex]L=2(13)+6=32\ ft[/tex]

therefore

The length of the patio is 32 ft and the width is 13 ft

The required patio length(L) = 32 and width(w) = 13.

Given that,

Wayne is hanging a string of lights 58 feet long,

And the side along the house, is 6 feet long.

We have to find,

The length and width of the patio.

According to the question,

Let, the length of his patio be L and width w,

Wayne is hanging a string of lights 58 feet long around the three sides of his patio, which is adjacent to his house.

L + 2W = 58

And The length of his patio, the side along the house, is 6 feet longer than twice its width.

L = 2W + 6

Solving the equation putting the of L from equation 2 in equation 1,

= 2W + 6 + 2W = 58

= 4W = 58 - 6

= 4W = 52

= W = [tex]\frac{52}{4}[/tex]

= W = 13

And L = 2(13) + 6 = 32

Patio length(L) = 32 And width(w) = 13.

Hence , The required patio length(L) = 32 And width(w) = 13.

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Answer:

Expected Value = -$42 (loss of 42 dollars)

Step-by-step explanation:

Complete Question Below:

"There is a 0.9986 probability that a randomly selected 33​-year-old male lives through the year. A life insurance company charges ​$182 for insuring that the male will live through the year. If the male does not survive the​ year, the policy pays out ​$110 comma 000 as a death benefit. If a 33-year-old male purchases the policy, what is his expected value?"

We can say P(survival) = 0.9986 and thus P(not survival) = 1 - P(survival) = 1-0.9986 = 0.0014

Also,

In case 33 year old doesn't live, the payment would be 100,000 - 182 = $99,818

And

In case 33 year old lives, the payment is

-$182

We know, the expected value is the sum of the product of each possibility with its probability.

[tex]ExpectedValue=\Sigma x*p(x)=(99818)(0.0014)+(-182)(0.9986)=-42[/tex]

This means a loss of $42 (or -$42)

Answer:

The answer is true.

Step-by-step explanation:

An ad valorem tax is based on the assessed value of a property. These include property taxes on real estate, sales tax on consumer goods etc,

When you are earning rent from a property, then you have to pay some tax for it, that will surely affect the amount of ad valorem property taxes levied on the properties.

Therefore, the answer is true.

Answer:

12.83

Step-by-step explanation:

S = 12.091

N = 12

We must find the 12th point, X

The formula of S² (variance) as a function of µ (media) is as follows:

S² = (1/N Ʃ Xi²) - µ²

S² = 146.2

Multiplying both members by N,  

N S² = Ʃ Xi² – N µ²

On the other hand,

µ = (25 + 41 + 49 + 25 + 30 + 13 + 31 + 34 + 27 + 54 + 38 + X) / 12

µ = (367 + X) / 12

Replacing,

12 x 146.2 = 13607 + X² – 12 (367 + X)² / 144

1754.4 = 13607 + X² – 0.0833 (134689 + 734 X + X²)

1754.4 = 13607 + X² – 11219.5 – 61.14 X – 0.0833 X²

0.92 X² – 61.14 X + 633.1 = 0

This is solved by finding the two values of X that satisfy the equation.

The solution requires solving the quadratic formula,

X12 = (-b ± √(b² - 4ac)) / 2a

The values are:

X1 = 12.83

X2 = 53.62

Since we know that the value is 25 or less, the answer is 12.83

The twelfth data point in the data set is x = 16.32

Let x be the value of the twelfth data point. We know that the sample standard deviation of the 12 points is 12.091. We can use the following formula to calculate the sample standard deviation:

s = √((Σ((xₙ - M)²) / (n - 1)))

where:

We can plug in the given values to get the following equation:

if x is the missing data point then:

M = (25 + 41 + 49 + 25 + 30 + 13+ 31 + 34 + 27 + 54 + 38 + x)/12

M = 30.6+ x/12

And we know that:

s = 12.091

n = 12

Replacing these values we get:

12.091 = √((Σ((xₙ - 30.6 - x/12)²) / (12 - 1)))

Apply the square in both sides:

146.19 = (Σ((xₙ - 30.6 - x/12)²) / (11)

Multiply both sides by 11:

146.19*11 = Σ((xₙ - 30.6 - x/12)²

1,608.12 = Σ((xₙ - 30.6 - x/12)²

Now we can solve the right side:

1,608.12 = (-5.6 -  x/12)² + (10.4 - x/12)² + (18.4-   x/12)² + (-5.6 -  x/12)² + (-0.6  -  x/12)² + (-17.6  -  x/12)² + (0.4  -  x/12)² + (3.4  -  x/12)² + (-3.6  -  x/12)² + (23.4  -  x/12)² + (7.4  -  x/12)² + ( x -    x/12)²

Now we can graph this, the positive solution is x = 16.32

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Answer:

  A = 7

  B = 2

Step-by-step explanation:

The question is asking for the simplified form of √(-98). You are expected to know that √-1 = i, and you are expected to be able to factor the number 98.

[tex]\sqrt{-98}=\sqrt{(-1)(7^2)(2)}=7i\sqrt{2}[/tex]

Matching parts of the simplified expression to the form you are given, you see that ...

  A = 7

  B = 2

Answer:

Step-by-step explanation:

(a) If we let k = f(m), we can solve for m to find f⁻¹(k).

  k = 1.609344m

  k/1.609344 = m = f⁻¹(k)

__

(b) Since k is the number of kilometers in m miles, m is the number of miles in k kilometers.

__

In summary ...

  (a) f⁻¹(k) = k/1.609344

  (b) f⁻¹(k) is the exact number of miles in k kilometers

Answer:

Step-by-step explanation:

An  way  to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Answer: You only have 5 samples, always when you want to do statistics, you need a large sample size.

let's suppose you throw a dice 5 times, the results that it shows are 1,4,2,1,4. If you make statistics whit that numbers, you will think that the 1 and 4 have a bigger possibility than the other numbers, but that can't be, if you throw the dice enough times you will se that all numbers have the same possibility.

Answer:

5/8 after subtraction :)

Step-by-step explanation:

Answer:  The answer is:  62.5 % (left over).

______________________________________________

Step-by-step explanation:

______________________________________________

[tex]\frac{1}{4} + \frac{1}{8} = ?[/tex]   ;  

Change "(1/4)" to: "(?/8)" ;

What is "(?)" ?  ;

→  (1/4) = (?/8) ;

notice the denominators;

(1/4) = (?/8) ;  In the first fraction, how does the "denominator", "4" ;  turn to "8" ?   Specifically, since we dealing with "fractions", what number do we multiply "4" by, to get:  "8" ??? ;

→  " 4  * ? = 8 " ?? ;

→  " 8 ÷ 4 = ? " ;

               = 2 ;

______________________________________________

so  " 1/4 = ?/8 " ;

Since we multiply the denominator, "4" ;  by "2" , to get:  

                     "8" (the denominator in the other fraction);  

we multiply the numerator, "1" ; by "2" ; to get:

                     "2" (the denominator in the other fraction):

______________________________________________

   →  " [tex]\frac{1}{4} = \frac{(1*2)}{(4*2)} = \frac{2}{8}[/tex] ;

______________________________________________

Now, the amount of the pizza that "you" ate is:  "(2/8)" ;

The amount of the pizza eaten by "your dog" is: "(1/8)" ;

Let's add up the amount of pizza eaten:

[tex]\frac{2}{8} + \frac{1}{8}  = \frac{(2+1)}{8} = \frac{3}{8}[/tex] .

The total amount of the pizza would be:  " [tex]\frac{8}{8}[/tex] " .

Note:  " [tex]\frac{8}{8}[/tex] = 8 ÷ 8 = 1 whole [pizza].

To find the amount left over,  subtract the amount eaten; "(3/8)" ; from the whole pizza; "(8/8)" ; as follows:

______________________________________________

   →  [tex]\frac{8}{8} - \frac{3}{8} = \frac{(8-3)}{8} = \frac{5}{8}[/tex] .

______________________________________________

Now, the question asks, what percent is left over? ;

So, we convert "(5/8)" into a percentage;

Change "(5/8)" to: "(?/100)" ;

  →  Notice the denominators;

(5/8) = (?/100) ;  In the first fraction, how does the "denominator", "8" ;  turn to "100" ?   Specifically, since we dealing with "fractions", what number do we multiply "8" by, to get:  "100" ??? ;

→  " 8  * ? = 100 " ?? ;

→  " 100 ÷ 8 = ? " ;

                  = 12.5 ;

______________________________________________

so  " 5/8 = ?/100 " ;

Since we multiply the denominator, "8" ;  by "12.5" , to get:  

                     "100" (the denominator in the other fraction);  

we multiply the numerator, "5" ; by "12.5" ; to get:

                     "2" (the denominator in the other fraction):

______________________________________________

   →  " [tex]\frac{5}{8} = \frac{(5*12.5)}{(100*12.5)} = \frac{62.5}{100}[/tex] ;

______________________________________________

   →  [tex]\frac{62.5}{100} = 62.5 % .

______________________________________________

Hope this helpful to you!

       Wishing you the best!

______________________________________________

Answer:

Step-by-step explanation:

The magnitude of a fraction of a fraction (their product) is always smaller than the magnitudes of either fraction. So, if both decimals are positive, the result is less than either factor.

___

Negative numbers are less than 1, so there can be several cases of interest when one or both numbers are negative.

Both numbers negative

The product will be positive, so will be greater than either negative factor.

__

One number negative, the other number positive

The product will be negative, so will be less than the positive factor and greater than the negative factor. (Multiplying a negative number by a positive fraction moves it closer to zero on the number line, hence to a value that is greater than the negative factor.)

A plane traveling at a speed of 4000 miles per hour would take approximately 6.25 hours to travel around a planet with a circumference of 25,000 miles.

To solve this question, we will use the concept of time, speed, and distance. We know that the plane travels at a speed of 4000 miles per hour and the Earth's circumference is 25000 miles. Thus to compute the time it would take for the plane to travel around the planet, we can use the relation 'Time = Distance / Speed'.

The distance in this case is the circumference of the Earth, which is 25000 miles and the speed is the plane's speed, which is 4000 miles/hour. So, we simply divide 25000 miles by 4000 miles/hour:

Time = 25000 / 4000 = 6.25 hours

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Answer:

Step-by-step explanation:

There are 5 green marbles among the 10 in the bag, so the probability of drawing one at random is 5/10 = 0.50.

The odds in favor of drawing a green marble will be the ratio of the number of green marbles to the number that are not green: 5 : 5. Usually, the odds are expressed using integers with no common factors, so they would be written as 1 : 1.

Answer:

The value of a+b is 4.

Step-by-step explanation:

The given function is

[tex]\[f(x) = \left\{ \begin{array}{cl} 9 - 2x & \text{if } x \le 3, \\ ax + b & \text{if } x > 3. \end{array} \right.\][/tex]

It is given that for some constants a and b the function f has the property that f(f(x))=x for all x.

For x≤3,

[tex]f(x)=9-2x[/tex]

For x>3,

[tex]f(x)=ax+b[/tex]

At x=0,

[tex]f(0)=9-2(0)=9[/tex]

[tex]f(f(0))=f(9)\Rightarrow a(9)+b=9a+b[/tex]

Using property f(f(x))=x,

[tex]f(f(0))=0[/tex]

[tex]9a+b=0[/tex]                     .... (1)

At x=1,

[tex]f(1)=9-2(1)=7[/tex]

[tex]f(f(1))=f(7)\Rightarrow a(7)+b=7a+b[/tex]

Using property f(f(x))=x,

[tex]f(f(1))=1[/tex]

[tex]7a+b=1[/tex]                     .... (2)

Subtract equation (2) from equation (1).

[tex]9a+b-(7a+b)=0-1[/tex]    

[tex]2a=-1[/tex]

Divide both sides by 2.

[tex]a=-\frac{1}{2}[/tex]

Substitute this value in equation (1).

[tex]9(-\frac{1}{2})+b=0[/tex]

[tex]b=\frac{9}{2}[/tex]

The value of a is [tex]-\frac{1}{2}[/tex] and value of b is [tex]\frac{9}{2}[/tex]. The value of a+b is

[tex]a+b=-\frac{1}{2}+\frac{9}{2}[/tex]

[tex]a+b=4[/tex]

Therefore the value of a+b is 4.

Answer:

Step-by-step explanation:

The area formula is ...

  A = πr²

When r = 1/4 in, the area is ...

  A = π(1/4 in)² = π/16 in²

__

The circumference formula is ...

  C = πd

When the diameter is 3/4 in, the circumference is ...

  C = π(3/4 in) = (3/4)π in

Answer:

14,740

Step-by-step explanation:

The mean of a set of data is another way of saying the average

To find the average you find the sum of all the numbers/amount of numbers

In this case it would be 221,100/15

Answer:

20 months

Step-by-step explanation:

Let x be the number of months. The cost  equation for each dealer is the total of the down payment and the total monthly contribution. Thus,

Deal 1 cost = $2,350 + $175x

Dealer 2 cost =$2,850 + $150x

The number of months after which the costs from both dealers are equal is calculated by equating the costs for both dealers. Therefore,

$2,350 + $175x = $2,850 + $150x

$175x -$150x =$2,850 -$2,350

   $25x =$500

        x= $500/$25

         x = 20 months

Answer:

  d.  √34 ≈ 5.82

Step-by-step explanation:

Both of choices B and D are valid calculations and should have resulted in the same estimate. Choice B, however, is incorrectly rounded, leaving choice D as the better answer.

___

The other answer choices do not result in a number between 5 and 6, so are clearly incorrect.

Answer:

  129°

Step-by-step explanation:

If CE is between CD and CF, then angle DCF is the sum of the given angles:

  75° +54° = 129°

Answer:

129

Step-by-step explanation:

bc it just is right

Westbound boats speed = X

Southbound boats speed = X + 5

In 3 hours they are 27 miles apart:

3X + 3(x+5) = 27

Simplify:

3x + 3x +15 = 27

Combine like terms:

6x + 15 = 27

Subtract 15 from both sides:

6x = 12

Divide both sides by 6:

x = 12/6

x = 2

Westbound was 2 miles per hour

Southbound was 2 +5 = 7 miles per hour

Check:

2 miles per hour x 3 hours = 6 miles

7 miles per hour x 3 hours = 21 miles

21 + 6 = 27 miles

Answer:

x = 2.4

Step-by-step explanation:

To find the value when f(x) = x, you just have to replace f(x) for x

[tex]f(x) =-\frac{1}{4}x +3 \\x = - \frac{1}{4}x +3 \\x +\frac{1}{4}x=3 \\\frac{5}{4} x= 3 \\ x = 3*\frac{4}{5} \\x = 2.4[/tex]

Answer:

540°

Step-by-step explanation:

The sum of the interior angles of a polygon is:

(n-2)*180

where n = number of sides

Here you have :

(5 - 2)*180 = 540°

Answer:

  x = -5, x = -6

Step-by-step explanation:

After canceling common terms from numerator and denominator, there are two factors remaining in the denominator that can become zero. The vertical asymptotes are at those values of x.

[tex]\displaystyle F(x)=\frac{x\frac{2x}{2}}{x(x+5)(x+6)}=\frac{x}{(x+5)(x+6)}[/tex]

The denominator will be zero when ...

  x + 5 = 0 . . . . at x = -5

  x + 6 = 0 . . . . at x = -6

Answer:

p= 0.555 ; E= 0.222; then we have 0.555 +/- 0.222

Step-by-step explanation:

The confidence interval goes from 0.333 to 0.777.

To find the p, we need to locate the median of that series of numbers.

The median is 0.555 as is the middle value of that interval.

Now the E corresponds to the deviation or the Error that we can measure.

And since we know that our variance ranges between 0.333 and 0.777, we can sustract 0.333 to p and we can get 0.222. We can also check if we add 0.222 to p, and we can get 0.777.

Answer:

The demand equation is: D=-4p+23

Step-by-step explanation:

To get started, we should keep in mind that the market price (p=3) occurs when supply equals demand ,therefore when p=3

S=2(3)+5=11

Thus, when p=3 D=11 and, according to the problem  when p=1 D=19.

We already know two points on the demand curve. Great!

The demand equation is linear, so it has form D=bp+c.

The variable b is the slope of  the demand linear equation . It can be computed through the formula

[tex]b=\frac{y2-y1}{x2-x1}[/tex].  equation 1

Substituting the two points (3,11) and (1,19) on equation 1.

[tex]b=\frac{19-11}{1-3} =\frac{8}{-2}[/tex]

b=-4

Now we can find the value of  intercept of the demand equation c trough point-slope form y-y1=b(x-x1).

We can use any of the points. Let's take (3,11) and write in point-slope :

y-11=-4(x-3)

y=-4x+11+12

y=-4x+23

Rewrite the linear equation according our variables D and p

D=-4P+23

Finally we found the demand equation !

Answer:

Step-by-step explanation:

Look at the picture.

The lines l and m are parallel, therefore alternate interior angles are congruent.

Therefore [tex]\beta=50^o[/tex]

Supplementary angles add up to 180°.

Therefore

[tex](5x-16)+\theta=180[/tex]          add 16 to both sides

[tex]5x+\theta=196[/tex]         subtract 5x from both sides

[tex]\theta=196-5x[/tex]

We know: the sum of the triangle angle measures is 180°.

Therefore we have the equation:

[tex]50+2x+196-5x=180\\\\-3x+246=180\qquad\text{subtract 246 from both sides}\\\\-3x=-66\qquad\text{divide both sides by (-3)}\\\\x=22[/tex]

Answer:

75 = 32 + 6 + x

Answer:

I believe it would be the first option on edge

Step-by-step explanation:

X + 6 + 32 = 75