QuestionFour teams measured a neutron star's rotation. Given a reliable measurement of $0.310 \mathrm{~s}$ , find the most accurate and precise earlier measurements.

Studdy Solution

STEP 1

Assumptions1. The later and more reliable measurement of the neutron star's rotation period is0.310s. . The measurements given by the four research teams are as follows - Team A0.36s ±10% - Team B between0.295s and0.305s - Team C0.210s - Team D0.410s ±0.025s

STEP 2

First, we need to understand the terms "accuracy" and "precision". Accuracy refers to how close a measurement is to the true value, while precision refers to how close repeated measurements are to each other.

STEP 3

To find the most accurate measurement, we need to compare each team's measurement to the later and more reliable measurement of0.310s. The team with the measurement closest to0.310s has the most accurate measurement.

STEP 4

For team A, the measurement is0.36s ±10%. To find the range of this measurement, we need to calculate10% of0.36s and then add and subtract this from0.36s.
$Range =0.36s \pm10\% \times0.36s$

STEP 5

Calculate the range for team A.
$Range =0.36s \pm0.036s$

STEP 6

This gives us a range of0.324s to0.396s for team A. The later and more reliable measurement of0.310s is not within this range, so team A's measurement is not the most accurate.

STEP 7

For team B, the measurement is between0.295s and0.305s. The later and more reliable measurement of0.310s is not within this range, so team B's measurement is not the most accurate.

STEP 8

For team C, the measurement is0.210s. This is not close to the later and more reliable measurement of0.310s, so team C's measurement is not the most accurate.

STEP 9

For team D, the measurement is.410s ±.025s. To find the range of this measurement, we need to add and subtract.025s from.410s.
$Range =.410s \pm.025s$

STEP 10

This gives us a range of0.385s to0.435s for team D. The later and more reliable measurement of0.310s is not within this range, so team D's measurement is not the most accurate.

STEP 11

From the above steps, we can see that none of the teams' measurements are close to the later and more reliable measurement of0.310s. However, the measurement of team B is the closest, so team B's measurement is the most accurate.

STEP 12

To find the most precise measurement, we need to look at the range of each team's measurement. The team with the smallest range has the most precise measurement.

STEP 13

For team A, the range is0.036s (from0.324s to0.396s).

STEP 14

For team B, the range is0.010s (from0.295s to0.305s).

STEP 15

For team C, there is no range as only one measurement was given.

STEP 16

For team D, the range is0.050s (from0.385s to0.435s).

STEP 17

From the above steps, we can see that team B has the smallest range, so team B's measurement is the most precise.
The most accurate measurement was made by team B and the most precise measurement was also made by team B.

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QuestionFour teams measured a neutron star's rotation. Given a reliable measurement of $0.310 \mathrm{~s}$ , find the most accurate and precise earlier measurements.

Studdy Solution

STEP 1

Assumptions1. The later and more reliable measurement of the neutron star's rotation period is0.310s. . The measurements given by the four research teams are as follows - Team A0.36s ±10% - Team B between0.295s and0.305s - Team C0.210s - Team D0.410s ±0.025s

STEP 2

First, we need to understand the terms "accuracy" and "precision". Accuracy refers to how close a measurement is to the true value, while precision refers to how close repeated measurements are to each other.

STEP 3

To find the most accurate measurement, we need to compare each team's measurement to the later and more reliable measurement of0.310s. The team with the measurement closest to0.310s has the most accurate measurement.

STEP 4

For team A, the measurement is0.36s ±10%. To find the range of this measurement, we need to calculate10% of0.36s and then add and subtract this from0.36s.
$Range =0.36s \pm10\% \times0.36s$

STEP 5

Calculate the range for team A.
$Range =0.36s \pm0.036s$

STEP 6

This gives us a range of0.324s to0.396s for team A. The later and more reliable measurement of0.310s is not within this range, so team A's measurement is not the most accurate.

STEP 7

For team B, the measurement is between0.295s and0.305s. The later and more reliable measurement of0.310s is not within this range, so team B's measurement is not the most accurate.

STEP 8

For team C, the measurement is0.210s. This is not close to the later and more reliable measurement of0.310s, so team C's measurement is not the most accurate.

STEP 9

For team D, the measurement is.410s ±.025s. To find the range of this measurement, we need to add and subtract.025s from.410s.
$Range =.410s \pm.025s$

STEP 10

This gives us a range of0.385s to0.435s for team D. The later and more reliable measurement of0.310s is not within this range, so team D's measurement is not the most accurate.

STEP 11

From the above steps, we can see that none of the teams' measurements are close to the later and more reliable measurement of0.310s. However, the measurement of team B is the closest, so team B's measurement is the most accurate.

STEP 12

To find the most precise measurement, we need to look at the range of each team's measurement. The team with the smallest range has the most precise measurement.

STEP 13

For team A, the range is0.036s (from0.324s to0.396s).

STEP 14

For team B, the range is0.010s (from0.295s to0.305s).

STEP 15

For team C, there is no range as only one measurement was given.

STEP 16

For team D, the range is0.050s (from0.385s to0.435s).

STEP 17

From the above steps, we can see that team B has the smallest range, so team B's measurement is the most precise.
The most accurate measurement was made by team B and the most precise measurement was also made by team B.

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QuestionFour teams measured a neutron star's rotation. Given a reliable measurement of 0.310 s0.310 \mathrm{~s}0.310 s, find the most accurate and precise earlier measurements.

Studdy Solution

STEP 1

Assumptions1. The later and more reliable measurement of the neutron star's rotation period is0.310s. . The measurements given by the four research teams are as follows - Team A0.36s ±10% - Team B between0.295s and0.305s - Team C0.210s - Team D0.410s ±0.025s

STEP 2

First, we need to understand the terms "accuracy" and "precision". Accuracy refers to how close a measurement is to the true value, while precision refers to how close repeated measurements are to each other.

STEP 3

To find the most accurate measurement, we need to compare each team's measurement to the later and more reliable measurement of0.310s. The team with the measurement closest to0.310s has the most accurate measurement.

STEP 4

For team A, the measurement is0.36s ±10%. To find the range of this measurement, we need to calculate10% of0.36s and then add and subtract this from0.36s.Range=0.36s±10%×0.36sRange =0.36s \pm10\% \times0.36sRange=0.36s±10%×0.36s

STEP 5

Calculate the range for team A.Range=0.36s±0.036sRange =0.36s \pm0.036sRange=0.36s±0.036s

STEP 6

This gives us a range of0.324s to0.396s for team A. The later and more reliable measurement of0.310s is not within this range, so team A's measurement is not the most accurate.

STEP 7

For team B, the measurement is between0.295s and0.305s. The later and more reliable measurement of0.310s is not within this range, so team B's measurement is not the most accurate.

STEP 8

For team C, the measurement is0.210s. This is not close to the later and more reliable measurement of0.310s, so team C's measurement is not the most accurate.

STEP 9

For team D, the measurement is.410s ±.025s. To find the range of this measurement, we need to add and subtract.025s from.410s.Range=.410s±.025sRange =.410s \pm.025sRange=.410s±.025s

STEP 10

This gives us a range of0.385s to0.435s for team D. The later and more reliable measurement of0.310s is not within this range, so team D's measurement is not the most accurate.

STEP 11

From the above steps, we can see that none of the teams' measurements are close to the later and more reliable measurement of0.310s. However, the measurement of team B is the closest, so team B's measurement is the most accurate.

STEP 12

To find the most precise measurement, we need to look at the range of each team's measurement. The team with the smallest range has the most precise measurement.

STEP 13

For team A, the range is0.036s (from0.324s to0.396s).

STEP 14

For team B, the range is0.010s (from0.295s to0.305s).

STEP 15

For team C, there is no range as only one measurement was given.

STEP 16

For team D, the range is0.050s (from0.385s to0.435s).

STEP 17

From the above steps, we can see that team B has the smallest range, so team B's measurement is the most precise.The most accurate measurement was made by team B and the most precise measurement was also made by team B.

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QuestionFour teams measured a neutron star's rotation. Given a reliable measurement of $0.310 \mathrm{~s}$ , find the most accurate and precise earlier measurements.

For team A, the measurement is0.36s ±10%. To find the range of this measurement, we need to calculate10% of0.36s and then add and subtract this from0.36s.
$Range =0.36s \pm10\% \times0.36s$

Calculate the range for team A.
$Range =0.36s \pm0.036s$

For team D, the measurement is.410s ±.025s. To find the range of this measurement, we need to add and subtract.025s from.410s.
$Range =.410s \pm.025s$

From the above steps, we can see that team B has the smallest range, so team B's measurement is the most precise.
The most accurate measurement was made by team B and the most precise measurement was also made by team B.