Question

parks rachelle wants to determine the best state park for hiking and fishing. part a use the metric to calculate a score for each park. round to the nearest tenth. park score = 100\left0.2\left(\frac{\text{online rating}}{5}\
ight) + 0.4\left(\frac{\text{miles of trails}}{25}\
ight) + 0.4\left(\frac{\text{fish weight}}{10}\
ight)\
ight \

$$\begin{array}{|l|c|c|c|c|} \\hline \\text{state park} & \\text{online star rating} & \\text{hiking trails (mi)} & \\text{best fish (lb)} & \\text{park score} \\\\ \\hline \\text{gooseberry falls} & 4.8 & 20 & 9.8 & \\bigcirc \\\\ \\hline & 4.3 & 14 & 8.2 & \\bigcirc \\\\ \\hline \\text{lake maria} & 4.9 & 25 & 7.3 & \\bigcirc \\\\ \\hline \\text{maplewood} & 4.3 & 15.8 & 10.1 & \\bigcirc \\\\ \\hline \\text{camden} & & & & \\\\ \\hline \\end{array}$$

Explanation:

Gooseberry Falls

Step1: Calculate each term

First term: $0.2\times\frac{4.8}{5}=0.2\times0.96 = 0.192$
Second term: $0.4\times\frac{20}{25}=0.4\times0.8 = 0.32$
Third term: $0.4\times\frac{9.8}{10}=0.4\times0.98 = 0.392$

Step2: Sum the terms and multiply by 100

Sum: $0.192 + 0.32 + 0.392 = 0.904$
Score: $100\times0.904 = 90.4$

Lake Maria (Wait, correction: The second park is the one with 4.3,14,8.2? Wait, the table: Let's re - check the park names. Wait, the first park is Gooseberry Falls (4.8,20,9.8), then the next row: maybe a typo? Wait, the table as per the image:

Wait, the table rows:

1. Gooseberry Falls: Online Rating 4.8, Trails 20, Fish 9.8
2. Then a row with 4.3,14,8.2 (let's assume park name is, say, Park X? Wait, the user's table: "Gooseberry Falls" then a row with 4.3,14,8.2 (maybe "Another Park"), then Lake Maria: 4.9,25,7.3, Maplewood:4.3,15.8,10.1, Camden: (maybe incomplete). But let's do Lake Maria:

Lake Maria

Step1: Calculate each term

First term: $0.2\times\frac{4.9}{5}=0.2\times0.98 = 0.196$
Second term: $0.4\times\frac{25}{25}=0.4\times1 = 0.4$
Third term: $0.4\times\frac{7.3}{10}=0.4\times0.73 = 0.292$

Step2: Sum the terms and multiply by 100

Sum: $0.196+0.4 + 0.292=0.888$
Score: $100\times0.888 = 88.8$

Maplewood

Step1: Calculate each term

First term: $0.2\times\frac{4.3}{5}=0.2\times0.86 = 0.172$
Second term: $0.4\times\frac{15.8}{25}=0.4\times0.632 = 0.2528$
Third term: $0.4\times\frac{10.1}{10}=0.4\times1.01 = 0.404$

Step2: Sum the terms and multiply by 100

Sum: $0.172+0.2528 + 0.404=0.8288$
Score: $100\times0.8288 = 82.9$ (rounded to nearest tenth)

The park with 4.3,14,8.2 (let's call it Park Y)

Step1: Calculate each term

First term: $0.2\times\frac{4.3}{5}=0.2\times0.86 = 0.172$
Second term: $0.4\times\frac{14}{25}=0.4\times0.56 = 0.224$
Third term: $0.4\times\frac{8.2}{10}=0.4\times0.82 = 0.328$

Step2: Sum the terms and multiply by 100

Sum: $0.172 + 0.224+0.328 = 0.724$
Score: $100\times0.724 = 72.4$

(Assuming we need to calculate for each park as per the table. If only Gooseberry Falls was needed, the score is 90.4)

Answer:

Gooseberry Falls: 90.4; Park with (4.3,14,8.2): 72.4; Lake Maria: 88.8; Maplewood: 82.9 (depending on which park is required. If it's Gooseberry Falls, the answer is 90.4)