Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Rosie went on a hiking trip. The first day she walked 18 kilometers. Each day since, she walked 90% of what she walked the day before. What is the total distance Rosie has traveled by the end of the 10^("th ") day? Round your final answer to the nearest kilometer. km

Rosie went on a hiking trip. The first day she walked 1818 kilometers. Each day since, she walked 90% 90 \% of what she walked the day before.\newlineWhat is the total distance Rosie has traveled by the end of the 10th  10^{\text {th }} day?\newlineRound your final answer to the nearest kilometer.\newlinekm \mathrm{km}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Weighted averages: word problemsright chevron icon

Full solution

Q. Rosie went on a hiking trip. The first day she walked 1818 kilometers. Each day since, she walked 90% 90 \% of what she walked the day before.\newlineWhat is the total distance Rosie has traveled by the end of the 10th  10^{\text {th }} day?\newlineRound your final answer to the nearest kilometer.\newlinekm \mathrm{km}
  1. Identify initial distance and decrease rate: Identify the initial distance walked and the daily decrease rate.\newlineRosie walked 1818 kilometers on the first day. Each subsequent day, she walked 90%90\% of the distance she walked the day before. This means there is a daily decrease rate of 10%10\% (100%−90%100\% - 90\%).
  2. Calculate distance on second day: Calculate the distance walked on the second day.\newlineTo find the distance walked on the second day, multiply the first day's distance by 9090%.\newlineDistance on second day = 18 km×90%=18 km×0.9=16.2 km18 \, \text{km} \times 90\% = 18 \, \text{km} \times 0.9 = 16.2 \, \text{km}
  3. Recognize pattern of distance walked: Recognize the pattern of distance walked each day.\newlineThe distance walked each day forms a geometric sequence where the first term is 18 km18\,\text{km} and the common ratio is 0.90.9 (90%90\% of the previous day).
  4. Use formula for sum of geometric sequence: Use the formula for the sum of the first nn terms of a geometric sequence to calculate the total distance.\newlineThe sum of the first nn terms of a geometric sequence is given by Sn=a⋅(1−rn)/(1−r)S_n = a \cdot \left(1 - r^n\right) / \left(1 - r\right), where aa is the first term, rr is the common ratio, and nn is the number of terms.
  5. Calculate total distance on 1010th day: Calculate the total distance walked by the end of the 1010th day.\newlineUsing the formula from Step 44, with a=18a = 18 km, r=0.9r = 0.9, and n=10n = 10:\newlineS10=18×(1−0.910)/(1−0.9)S_{10} = 18 \times (1 - 0.9^{10}) / (1 - 0.9)
  6. Perform calculations: Perform the calculations.\newlineS10=18×(1−0.910)/(1−0.9)S_{10} = 18 \times (1 - 0.9^{10}) / (1 - 0.9)\newlineS10=18×(1−(0.910))/0.1S_{10} = 18 \times (1 - (0.9^{10})) / 0.1\newlineFirst, calculate 0.9100.9^{10}:\newline0.910≈0.34870.9^{10} \approx 0.3487\newlineNow, substitute this value into the formula:\newlineS10=18×(1−0.3487)/0.1S_{10} = 18 \times (1 - 0.3487) / 0.1\newlineS10=18×0.6513/0.1S_{10} = 18 \times 0.6513 / 0.1\newlineS10=11.7234/0.1S_{10} = 11.7234 / 0.1\newlineS10=117.234S_{10} = 117.234
  7. Round final answer: Round the final answer to the nearest kilometer.\newlineS10≈117S_{10} \approx 117 kilometers

More problems from Weighted averages: word problems

Question
A monkey is swinging from a tree. On the first swing, she passes through an arc of 10 m 10 \mathrm{~m} . With each swing, she passes through an arc 910 \frac{9}{10} the length of the previous swing.\newlineWhat is the total distance the monkey has traveled when she completes her 25th  25^{\text {th }} swing? Round your final answer to the nearest meter.\newlinem
Get tutor helpright-arrow

Posted 10 months ago

Question
SE=σn S E=\frac{\sigma}{\sqrt{n}} \newlineThe given equation relates the standard error, SE S E , of a sample mean to the population standard deviation, σ \sigma , and the size of the sample, n n . Which of the following equations correctly gives the size of the sample in terms of the standard error and the population standard deviation?\newlineChoose 11 answer:\newline(A) n=(σSE)2 n=\left(\frac{\sigma}{S E}\right)^{2} \newline(B) n=σ2SE n=\frac{\sigma^{2}}{S E} \newline(C) n=(σSE) n=\sqrt{\left(\frac{\sigma}{S E}\right)} \newline(D) n=σSE n=\frac{\sqrt{\sigma}}{S E}
Get tutor helpright-arrow

Posted 10 months ago

Question
Avery is designing a large rectangular sign. They want the sign to have an area of 2 m2 2 \mathrm{~m}^{2} and a width of 45 m \frac{4}{5} \mathrm{~m} .\newlineHow tall should the sign be?\newlinem
Get tutor helpright-arrow

Posted 10 months ago

Question
The bacteria in a Petri dish culture are self-duplicating at a rapid pace.\newlineThe relationship between the elapsed time t t , in minutes, and the number of bacteria, B(t) B(t) , in the Petri dish is modeled by the following function.\newlineB(t)=10⋅2t12 B(t)=10 \cdot 2^{\frac{t}{12}} \newlineHow many bacteria will make up the culture after 120120 minutes?\newlineRound your answer, if necessary, to the nearest hundredth.\newlinebacteria
Get tutor helpright-arrow

Posted 10 months ago

Question
A large brine tank containing a solution of salt and water is being diluted with fresh water.\newlineThe relationship between the elapsed time, t t , in hours, after the dilution begins, and the concentration of salt in the tank, S(t) S(t) , in grams per liter (g/l) (\mathrm{g} / \mathrm{l}) , is modeled by the following function.\newlineS(t)=500⋅e−0.25t S(t)=500 \cdot e^{-0.25 t} \newlineWhat will the concentration of salt be after 1010 hours?\newlineRound your answer, if necessary, to the nearest hundredth.\newlineg/11
Get tutor helpright-arrow

Posted 10 months ago

Question
After the closing of the mill, the town of Sawyerville experienced a decline in its population.\newlineThe relationship between the elapsed time, t t , in years, since the closing of the mill, and the town's population, P(t) P(t) , is modeled by the following function.\newlineP(t)=12,000⋅2−t15 P(t)=12,000 \cdot 2^{-\frac{t}{15}} \newlineIn how many years will Sawyerville's population be 90009000 ? Round your answer, if necessary, to the nearest hundredth.\newlineyears
Get tutor helpright-arrow

Posted 10 months ago

Question
Carlos has taken an initial dose of a prescription medication.\newlineThe relationship between the elapsed time t t , in hours, since he took the first dose, and the amount of medication, M(t) M(t) , in milligrams ( mg \mathrm{mg} ), in his bloodstream is modeled by the following function.\newlineM(t)=20⋅e−0.8t M(t)=20 \cdot e^{-0.8 t} \newlineIn how many hours will Carlos have 1mg 1 \mathrm{mg} of medication remaining in his bloodstream?\newlineRound your answer, if necessary, to the nearest hundredth.\newlinehours
Get tutor helpright-arrow

Posted 10 months ago

Question
To take a taxi, it costs $3.00 \$ 3.00 plus an additional $2.00 \$ 2.00 per mile traveled. You spent exactly $20 \$ 20 on a taxi, which includes the $1 \$ 1 tip you left.\newlineHow many miles did you travel?\newlinemiles
Get tutor helpright-arrow

Posted 9 months ago

Question
Polygon Y Y is a scaled copy of Polygon X X using a scale factor of 13 \frac{1}{3} .\newlinePolygon Y′ Y^{\prime} 's area is what fraction of Polygon X X 's area?
Get tutor helpright-arrow

Posted 9 months ago

Question
You pick a card at random, put it back, and then pick another card at random.\newline44\newline55\newline66\newline77\newlineWhat is the probability of picking a number greater than 55 and then picking a 44 ?\newlineWrite your answer as a percentage.
Get tutor helpright-arrow

Posted 1 month ago

View all (19)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant