The set of rental car rates making it more economical for Jamal than employing taxi services is outlined as A = {x | 0 ≤ x < 26} [where x represents dollars]. The step-by-step breakdown is as follows: Let the rental cost be $x per day. With Jamal's trip extending over 4 days, factoring in $24 for gas, and estimating taxi costs at around $128, an inequality emerges: 128 > 24 + 4x. Thus simplifying leads to 4x < 104 and consequently x < 26.
Total time taken = 9.0252 *10^12 s.
Step-by-step explanation:
Data provided:
- Distance from Earth to Alpha Centauri: 4.3 light years.
- Distance from Earth to Sirius: 8.6 light years.
- Probe speed: V = 18.03 km/s.
- 1 AU equals 1.58125 x 10^-5 light-years.
Objective:
Determine the total time the probe has been in motion from leaving Earth to reaching Sirius.
Solution:
- Journey is tracked for each destination sequentially:
Earth ------> Alpha Centauri: d_1 = 4.3 light years
Alpha Centauri ------> Earth: d_2 =4.3 light years
Earth ------> Sirius: d_3 = 8.6 light years
Sum of distances = D = 17.2 light years.
- Now, we convert the total distance into kilometers (SI units):
1 AU ----------> 1.58125 x 10^-5 light-years
x AU ----------> 17.2 light years.
- By proportions:
x = 17.2 / (1.58125 x 10^-5) = 1087747.036 AU.
Also,
1 AU ---------------------> 149597870700 m
1087747.036 AU ----> D m.
- Using proportions:
D = 1087747.036*149597870700 = 1.62725*10^17 m.
- Finally, applying the speed-distance-time formula:
Time = Distance traveled (D) / V
Time = 1.62725*10^17 / (18.03*10^3).
Final answer: Time = 9.0252 *10^12 s.
Answer: 0.12
Step-by-step explanation:
There are a total of 65 candy bars. Within this amount;
2 candy bars contain 300 to 350 calories
1 candy bar contains 350 to 400 calories
4 candy bars contain 400 to 450 calories
1 candy bar contains 450 to 500 calories
Thus, the overall ratio of candy bars with more than 300 calories is;
= (2 + 1 + 4 + 1) / 65
= 8/65
= 0.12
A is confirmed as correct since -13 falls within the domain of g(x), and 20 is included in its range. For g(x), the inequality holds: -20 < -13 < 5 and -5 < 20 < 45. B is incorrect since the number 4 exists within the domain of g(x), but -11 is not within its range, represented by -20 < 4 < 5 and -11 < -5. C is likewise incorrect, as it is stated that g(0) equals -2. D is also false since 7 does not belong to the domain of g(x).
