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Question Find the middle value mm and distance EE of the interval 6<μ<246<\mu<24, then write the interval as m±Em \pm E.

Studdy Solution

STEP 1

Assumptions
1. The interval is given by 6<μ<246 < \mu < 24.
2. The middle value of the interval is represented by mm.
3. The distance from the middle of the interval to either endpoint is represented by EE.
4. We are asked to express the interval in the format m±Em \pm E.

STEP 2

To find the middle value mm of the interval, we calculate the average of the two endpoints. The formula to find the midpoint mm is given by:
m=lower endpoint+upper endpoint2m = \frac{{\text{lower endpoint} + \text{upper endpoint}}}{2}

STEP 3

Now, plug in the values for the lower endpoint (6) and the upper endpoint (24) to calculate the middle value mm.
m=6+242m = \frac{6 + 24}{2}

STEP 4

Calculate the middle value mm.
m=302=15m = \frac{30}{2} = 15

STEP 5

To find the distance EE from the middle of the interval to either endpoint, we subtract the lower endpoint from the middle value mm or vice versa. The formula to find EE is:
E=∣m−lower endpoint∣orE=∣upper endpoint−m∣E = |m - \text{lower endpoint}| \quad \text{or} \quad E = |\text{upper endpoint} - m|

STEP 6

Using the lower endpoint (6) and the middle value mm (15) we have already found, calculate EE.
E=∣15−6∣E = |15 - 6|

STEP 7

Calculate the distance EE.
E=∣15−6∣=9E = |15 - 6| = 9

STEP 8

Now that we have both mm and EE, we can write the interval in the format m±Em \pm E.
m±E=15±9m \pm E = 15 \pm 9
Therefore, the interval can be expressed as 15±915 \pm 9.

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