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13 problems match “proportions”. Clear

Estimating frog population by recapture ●○○○○ 10 ptsOne day, 45 frogs were captured from a pond, marked and then returned to the pond. The next day, 40 frogs were observed in the pond, of which 10 had been marked the previous day. Assuming the marked frogs are equally distributed among all the frogs in the pond, what is the best estimate of the number of frogs living in the pond?
Estimating fish population by recapture ●○○○○ 10 ptsManagement staff caught 30 fish from a pond, marked them, and released them back into the pond. 10 days later, they caught 50 fish from the pond, of which 2 were marked. Assume the marked fish have mixed evenly through the pond, so the proportion marked in the second catch estimates the proportion marked in the whole pond. Based on this data, estimate the total number of fish in the pond.
Estimating fish population by capture-recapture ●○○○○ 10 ptsTo estimate the number of fish in a pond, $100$ fish were caught, tagged, and then released back into the pond. After some time, when the tagged fish had mixed completely with the rest of the fish, another $200$ fish were caught. If $10$ of them were tagged, estimate the total number of fish in the pond.
Pie graph angle for cherry pie ●○○○○ 10 ptsOf the 36 students in Richelle's class, 12 prefer chocolate pie, 8 prefer apple pie, and 6 prefer blueberry pie. Half of the remaining students prefer cherry pie and half prefer lemon pie. In Richelle's pie graph showing this data, how many degrees should she use for cherry pie?
Y-change on a line ●○○○○ 10 ptsMoving along a particular line in the Cartesian plane, when the $x$ -value increases by 3 units, the $y$ -value increases by 7 units. When the $x$ -value increases by 9 units, by how many units will the $y$ -value increase?
Central angle of a male 45-54 sector ●○○○○ 10 ptsTim wants to create a circle graph showing the number of physicians whose specialty is aerospace medicine. He knows the following information. - 53 male physicians are under 35 years of age. - 8 female physicians are under 35 years of age. - 155 male physicians are between 35 and 44 years of age. - 17 female physicians are between 35 and 44 years of age. - 145 male physicians are between 45 and 54 years of age. - 10 female physicians are between 45 and 54 years of age. - 98 male physicians are over 54 years of age. - 2 female physicians are over 54 years of age. He wants to include each of the eight groups in his graph. How many degrees would he use for the central angle of the "45-54 year-old males" sector? Express your answer to the nearest whole number.
Cans of red paint in a mixture ●○○○○ 10 ptsPaint is to be mixed so that the ratio of red paint to white paint is $3$ to $2$ . If Ben wants to make $30$ cans of the mixture and all cans hold the same volume of paint, how many cans of red paint will he need?
Percentage relation between three quantities ●○○○○ 10 ptsIf $x$ is $20\%$ of $y$ and $x$ is $50\%$ of $z$ , then what percentage is $z$ of $y$ ?
Fair council representation by enrollment ●○○○○ 10 ptsThe 7th and 8th grades have enrollments of 520 and 650 students respectively. The two grades have a total of 18 representatives on the Student Council. Assuming representation is fair when the seats are allotted in proportion to enrollment, how many representatives should the 8th grade have?
Basketball players at a middle school ●○○○○ 10 ptsThe ratio of basketball players to football players at Roward Middle School is $2:7$ . There are 54 basketball and football players in total. How many basketball players are there?