Boatesville is a 65 3/5 -kilometer drive from stanton. A bus traveling from stanton to boatesville is 24 1/3 kilometers from boatesville. How far has the bus traveled​

Answer:

0.6 or 3/5

Step-by-step explanation:

If cos(t) = 4/5, then, taking the arccos of both sides, t ≈ 36.86989765. Taking the sin of that gives you 0.6, or 3/5 in fraction form.

Answer:

11n

Step-by-step explanation:

7n+4n   (factorize out n)

= n (7 + 4)

= n (11)

= 11n

Answer:

11n

Step-by-step explanation:

Combining like terms just means adding together the numbers with the same variable. 7n and 4n both have an n attached, so you would add like normal to get 7n + 4n = 11n.

Answer:

a. t = 2.48 will be a period within 2009.

b. 56.16 million

Step-by-step explanation:

Here is the complete question

Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the early years but began to grow rapidly after 2005. But the iPod era is coming to a close. Smartphones with music and video

Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the

END OF THE IPOD ERA

players are replacing the iPod, along with the category of device it helped to create. Sales of the iPod worldwide from 2007

through 2011 (in millions) were

approximately

N(0= -2.65t2 + 13.13t+ 39.9 (0 < t< 4)

in year t, where t= 0 corresponds to 2007. Show that the worldwide sales of the iPod peaked sometime in 2009. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?

a. Show that the worldwide sales of the iPod peaked sometime in 2009

N(t) = -2.65t² + 13.13t + 39.9

To find the maximum value of N(t), we find dN(t)/dt and equate it to zero

dN(t)/dt = d[-2.65t² + 13.13t + 39.9]/dt

dN(t)/dt = -5.3t + 13.13 = 0

-5.3t = - 13.13

t = -13.13/(-5.3)

t = 2.477

t ≅ 2.48

d²N(t)/dt² =d[-5.3t + 13.13]/dt = -5.3 < 0. So, t = 2.48 is a maximum point

Since t = 2 is 2009 and t = 3 is 2010, t = 2.48 will be a period within 2009.

b. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?

The approximate largest number of ipods sold is when t = 2.48

N(2.48) = -2.65(2.48)² + 13.13(2.48) + 39.9

N(2.48) = -16.29856 + 32.5624 + 39.9

N(2.48) = 56.16384

N(2.48) ≅ 56.16 million

Answer:

The correct answer is x = 32.

Step-by-step explanation:

To solve this problem, we must remember the concept of supplementary angles.  Two angles that are supplementary together make an angle of 180 degrees (a straight line).

In this case, we can see that inside the triangle, we will have an angle of 80 degrees.  We know this because the angle at the top of the triangle is supplementary with the angle measuring 100 degrees, so its measure should be 180-100 = 80 degrees.

On the lower right hand of the triangle, a similar rationale can be applied.  The angle inside of the triangle must measure 68 degrees, since it is supplementary to an angle measuring 112 degrees, and 180-112=68.

Finally, to solve this problem, we must remember that the sum of the three interior angles of a triangle should be 180 degrees.  This lets us set up the following equation:

80+68+x = 180

Now, we can solve this equation. Our first step is to simplify the left side of the equation by adding together the constant terms.

148 + x = 180

Next, we should subtract 148 from both sides of the equation.

x = 180-148

x = 32

Therefore, the correct answer is x = 32 degrees.

Hope this helps!  

The probability that a randomly selected traveller who checks work email also uses a cell phone to stay connected is 57.5%.

The probability that someone who brings a laptop on vacation also uses a cell phone to stay connected is 70%.

If the randomly selected traveller checked their work email and brought a laptop, the probability that he/she uses a cell phone to stay connected is 58.8%.

We have,

Let:

C = Check work email

P = Use a cell phone to stay connected

L = Bring a laptop

Given information:

P(C) = 0.40 (Probability of checking work email)

P(P) = 0.30 (Probability of using a cell phone to stay connected)

P(L) = 0.25 (Probability of bringing a laptop)

P(C ∩ P) = 0.23 (Probability of both checking work email and using a cell phone to stay connected)

P(Neither) = 0.50 (Probability of neither checking work email, using a cell phone to stay connected, nor bringing a laptop)

Additional information:

P(C | L) = 0.84 (Probability of checking work email given that a laptop is brought)

P(P | L) = 0.70 (Probability of using a cell phone to stay connected given that a laptop is brought)

a. For the value of P(P | C), use the conditional probability formula:

P(P | C) = P(C ∩ P) / P(C)

P(P | C) = 0.23 / 0.40

P(P | C) = 0.575

b. For the value of P(P | L), use the conditional probability formula:

P(P | L) = P(P ∩ L) / P(L)

P (P | L) = 0.70

c. For the value of P(P | C ∩ L), use the conditional probability formula:

P(P | C ∩ L) = P(C ∩ P ∩ L) / P(C ∩ L)

Since we don't have the direct probability of P(C ∩ P ∩ L), we can use the information provided:

P(C | L) = 0.84

P(P | C ∩ L) = P(C | L) × P(P | L)

P(P | C ∩ L) = 0.84 × 0.70

P(P | C ∩ L) = 0.588

Thus, The probability that a randomly selected traveller who checks work email also uses a cell phone to stay connected is 57.5%.

The probability that someone who brings a laptop on vacation also uses a cell phone to stay connected is 70%.

If the randomly selected traveller checked their work email and brought a laptop, the probability that he/she uses a cell phone to stay connected is 58.8%.

Learn more about probability here:

brainly.com/question/14099682

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