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kherson [118]
2 years ago
10

Try to estimate the probability you'd turn on the radio and hear a song you were thinking about. In other words, estimate the pr

obability of the combined event P(thinking of a song)P(turn on the radio and hear the song).
Take these factors into account:

The likelihood you'd hear the song during a randomly selected time of day (think about how frequently the song plays, at what times of day, and on what stations).
The likelihood your radio will be tuned to a station that plays the song.
The likelihood you'll be thinking of the song at a randomly selected time of day. (Remember that if the song gets a lot of airplay it's more likely that you'll be thinking of it.)

Required:
If the combined events were to occur once, would the probability present compelling evidence that the event wasn't merely a chance occurrence? What if it happened twice in one day?
Mathematics
1 answer:
Black_prince [1.1K]2 years ago
8 0

Probabilities are used to determine the likelihood of events

The value of the probability P(thinking of a song)P(turn on the radio and hear the song) is 0.056

<h3>How to estimate the probability</h3>

To calculate the probability, we make use of the following representations:

  • Event A represents the likelihood of thinking of a song
  • Event B represents the likelihood of turning on the radio and hearing the song

So, we have:

P(thinking of a song)P(turn on the radio and hear the song) = P(A) * P(B)

Assume that:

P(A) = 0.12 and P(B) = 0.47

So, we have:

P(thinking of a song)P(turn on the radio and hear the song) = 0.12* 0.47

Evaluate the product

P(thinking of a song)P(turn on the radio and hear the song) = 0.0564

Approximate

P(thinking of a song)P(turn on the radio and hear the song) = 0.056

Hence, the value of the probability P(thinking of a song)P(turn on the radio and hear the song) is 0.056

Read more about probabilities at:

brainly.com/question/25870256

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g Use this to find the equation of the tangent line to the parabola y = 2 x 2 − 7 x + 6 at the point ( 4 , 10 ) . The equation o
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Answer:

The tangent line to the given curve at the given point is y=9x-26.

Step-by-step explanation:

To find the slope of the tangent line we to compute the derivative of y=2x^2-7x+6 and then evaluate it for x=4.

(y=2x^2-7x+6)'          Differentiate the equation.

(y)'=(2x^2-7x+6)'       Differentiate both sides.

y'=(2x^2)'-(7x)'+(6)'    Sum/Difference rule applied: (f(x)\pmg(x))'=f'(x)\pm g'(x)

y'=2(x^2)'-7(x)'+(6)'  Constant multiple rule applied: (cf)'=c(f)'

y'2(2x)-7(1)+(6)'        Applied power rule: (x^n)'=nx^{n-1}

y'=4x-7+0               Simplifying and apply constant rule: (c)'=0

y'=4x-7                    Simplify.

Evaluate y' for x=4:

y'=4(4)-7

y'=16-7

y'=9 is the slope of the tangent line.

Point slope form of a line is:

y-y_1=m(x-x_1)

where m is the slope and (x_1,y_1) is a point on the line.

Insert 9 for m and (4,10) for (x_1,y_1):

y-10=9(x-4)

The intended form is y=mx+b which means we are going need to distribute and solve for y.

Distribute:

y-10=9x-36

Add 10 on both sides:

y=9x-26

The tangent line to the given curve at the given point is y=9x-26.

------------Formal Definition of Derivative----------------

The following limit will give us the derivative of the function f(x)=2x^2-7x+6 at x=4 (the slope of the tangent line at x=4):

\lim_{x \rightarrow 4}\frac{f(x)-f(4)}{x-4}

\lim_{x \rightarrow 4}\frac{2x^2-7x+6-10}{x-4}  We are given f(4)=10.

\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}

Let's see if we can factor the top so we can cancel a pair of common factors from top and bottom to get rid of the x-4 on bottom:

2x^2-7x-4=(x-4)(2x+1)

Let's check this with FOIL:

First: x(2x)=2x^2

Outer: x(1)=x

Inner: (-4)(2x)=-8x

Last: -4(1)=-4

---------------------------------Add!

2x^2-7x-4

So the numerator and the denominator do contain a common factor.

This means we have this so far in the simplifying of the above limit:

\lim_{x \rightarrow 4}\frac{2x^2-7x-4}{x-4}

\lim_{x \rightarrow 4}\frac{(x-4)(2x+1)}{x-4}

\lim_{x \rightarrow 4}(2x+1)

Now we get to replace x with 4 since we have no division by 0 to worry about:

2(4)+1=8+1=9.

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Answer:

  6 inches long and 4 inches wide

Step-by-step explanation:

The dimensions of the actual crate are 20 times those on Jacob's drawing. The dimensions on the builder's drawing are 1/10 of those, so (1/10)(20) = 2 times the dimensions on Jacob's drawing.

The dimensions on the builder's scale drawing are 6 inches long by 4 inches wide.

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Question 7 of 10
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Answer:

  • Option B

Step-by-step explanation:

Given Equation :

\qquad \sf \dashrightarrow \: 3(4x+3) = 2x - 5(3 - x) + 2

Using distribute property:

\qquad \sf \dashrightarrow \: 12x + 9 = 2x - 15 + 5x + 2

Adding the like terms we get :

\qquad \sf \dashrightarrow \: 12x + 9 = 2x  + 5x  - 15 + 2

\qquad \sf \dashrightarrow \: 12x + 9 = 7x  - 13

Transposing the variables on the right side and constant terms on the left side :

\qquad \sf \dashrightarrow \: 12x  - 7x =   - 13 - 9

\qquad \sf \dashrightarrow \: 5x =   - 22

Dividing both sides by 5 :

\qquad \sf \dashrightarrow \:  \dfrac{5x}{5}  =  \dfrac{ - 22}{5}

\qquad \bf \dashrightarrow \:  x =  \dfrac{ - 22}{5}

3 0
3 years ago
The elevation at ground level is 0 feet. An elevator starts 90 feet below ground level. After traveling for 15 seconds, the elev
defon

Unfortunately there was no choice in which we can choose our answer to this item. However, looking into the situation given in this item, it may be deduced that the distance traveled by the elevator after 15 seconds is equal to 70 ft. The rate of change in elevation of the elevator is therefore 70ft/15s which is also equal to 4.67 ft/s. 

7 0
3 years ago
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