answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Yakvenalex
9 days ago
5

A marathon runner runs at the rate of 9 mph for the complete course. A track man runs at 12 mph. If together they run for 3 hrs.

, 1 min. to complete a total of 28 miles, how far did the marathon runner run? 24 3/5 miles 21 miles 20 4/5 miles
Mathematics
2 answers:
lawyer [12.1K]9 days ago
7 0
To start, it’s important to arrange all the data provided to avoid any confusion. We will mark the marathon runner's information with a subscript of 1 and the trackman's data with a subscript of 2. Our first step will involve calculating the total time:

t₁ + t₂ = 3 hours and 1 minute

To maintain uniformity, we need to convert the minute into hours. 
1 minute (1 hour/60 minutes) = 1/60
Total time therefore equals 3 + 1/60 = 3.0167 hours

So, we have the equation: t₁ + t₂ = 3.0167 hours ----> equation 1

Next, we establish the equation for the total distance, which arises from multiplying speed by time to yield distance. Hence, we get:

9t₁ + 12t₂ = 28 miles ----> equation 2

With two unknowns and two equations, we can solve the system:

t₁ = 3.0157 - t₂
Substituting into the second equation gives us 9(3.0167 - t₂) + 12t₂ = 28
Thus, we find t₂ = 0.2832 hour, and 
t₁ = 3.0157 - 0.2832 = 2.733 hours

Consequently, the distance covered by the marathon runner would be
9*2.733 = 24.597 or roughly 24 3/5.
Svet_ta [12.2K]9 days ago
6 0

Result:

24 3/5

Detailed explanation:

You might be interested in
Circle 1 has center (−4, −7) and a radius of 12 cm. Circle 2 has center (3, 4) and a radius of 15 cm.
Svet_ta [12291]
Answer with explanation: Given that Circle 1 has a center at (−4, −7) and a radius of 12 cm, while Circle 2's center is at (3, 4) with a radius of 15 cm. Two circles are similar if one can be transformed and scaled to fit over the other, creating identical circles. The circles qualify as similar because the transformation rule (x,y) → (x+7,y+11) can be applied to Circle 1, followed by dilation using a scale factor of 5/4. Since Circle 1's center is at (-4,-7), we translate it to (3,4) through (-4+7,-7+11). With Circle 1 having a radius of 12 and Circle 2 having 15 cm, we denote the scale factor as k.
7 0
10 days ago
Read 2 more answers
A=9y+3yx solve for y
Inessa [12160]
The solution for y is y = \frac{a}{3(3 + x)}
3 0
1 month ago
Read 2 more answers
A spring stretches by 21.0 cm when a 135 n object is attached. what is the weight of a fish that would stretch the spring by 49
Inessa [12160]
When the stretch is proportional to the weight, it can be expressed as:
weight/(49 cm) = (135 N)/(21 cm)
weight = (49/21)×135 N
weight = 315 N

The fish's weight would be 315 N.
8 0
1 month ago
In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1,014 adults aged 18 and
babunello [11329]

Answer:

(b)E(x)=1.3087

(c)Variance of x =1.7119

(d)E(y)=2.0447

Step-by-step explanation:

The random variable x refers to the average number of cups of coffee consumed daily.

The total number of respondents equals 1014

(a) Probability distribution for x.

\left|\begin{array}{c|cccccc}x&0&1&2&3&4\\\\P(x)&\dfrac{365}{1014}&\dfrac{264}{1014}&\dfrac{193}{1014}&\dfrac{91}{1014}&\dfrac{101}{1014} \end{array}\right|

(b) Expected value for x

E(x)=\left(0\times\dfrac{365}{1014}\left)+\left(1\times\dfrac{264}{1014}\left)+\left(2\times\dfrac{193}{1014}\left)+\left(3\times\dfrac{91}{1014}\left)+\left(4\times\dfrac{101}{1014}\right)

E(x)=1.3087

(c) Variance for x

Variance =\sum (x-\mu)^2P(x)

\left|\begin{array}{c|cccccc}x&0&1&2&3&4\\(x-\mu)^2&1.7167&0.0953&0.4779&2.8605&7.2431\\\\P(x)&\dfrac{365}{1014}&\dfrac{264}{1014}&\dfrac{193}{1014}&\dfrac{91}{1014}&\dfrac{101}{1014} \\\\(x-\mu)^2P(x)&0.6179&0.0248&0.0910&0.2567&0.7215\end{array}\right|

Variance, \sum (x-\mu)^2P(x)=1.7119

(d)

\left|\begin{array}{c|cccccc}y&1&2&3&4\\\\P(y)&\dfrac{264}{649}&\dfrac{193}{649}&\dfrac{91}{649}&\dfrac{101}{649} \end{array}\right|

E(y)=\left(1\times\dfrac{264}{649}\left)+\left(2\times\dfrac{193}{649}\left)+\left(3\times\dfrac{91}{649}\left)+\left(4\times\dfrac{101}{649}\right)

E(y)=2.0447

The expected value for y surpasses that of x.

6 0
26 days ago
Based on FAA estimates the average age of the fleets of the 10 largest U.S. commercial passenger carriers is 13.4 years with a s
Leona [12115]
The result is 0.0129. The data to consider includes the mean and standard deviation for the random variable associated with the fleets' ages. Calculating the Z-score for x = 14 and using the standard normal distribution table yields the probability that the average age of the 40 sampled airplanes is at least 14 years, rounded to four decimal places as 0.0129.
6 0
19 days ago
Other questions:
  • If the clothing maker bought 500 m2 of this fabric, how much money did he lose? Use 1tepiz=0.625dollar and 0.9144m=1yard.
    9·2 answers
  • A parallelogram has a base of 9 units and a corresponding height of 2/3 units. What is the area
    11·1 answer
  • Maria works as a ride loader on "Space Mountain". She averages twenty passengers every twenty minutes. Sal also works as a ride
    13·1 answer
  • Let c1(t) = eti + (sin(t))j + t3k and c2(t) = e−ti + (cos(t))j − 6t3k. Find the stated derivatives in two different ways to veri
    10·1 answer
  • If rs 500 amounts to Rs 725 at 9% simple interest in sometime ,what will Rs 600amount to at 11% in same time?
    14·1 answer
  • The oblique rectangular prism below has a length of 6 cm, a width of 8 cm, and a height of 7 cm.What is the area of the base of
    6·2 answers
  • 20 POINTS Compost costs $10 per cubic yard and topsoil costs $2 per cubic yard. Maria needs more than 10 cubic feet of topsoil.
    14·2 answers
  • A small business makes cookies and sells them at the farmer's market. The fixed monthly cost for use of a Health Department–appr
    8·1 answer
  • Kelsey's school can be represented by Point A(9,9). Point A can be translated 6 units left and 5 units down to create 'A', the l
    11·1 answer
  • Meryl needs to add enough water to 11 gallons of an 18% detergent solution to make it a 12% detergent solution. which equation c
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!