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kari74 [83]
3 years ago
11

In a circle, chords ST and RA intersect at Y such that SY is perpendicular to RY. The value of mSA + mRT is: a. 90º b. 180º c. 2

25º d. Undefined
Mathematics
1 answer:
pshichka [43]3 years ago
6 0

Answer:

a. 90º

Explanation:

The chords ST and RA intesect at Y, so that SY is now perpendicular to RY and they form an angle 90 degrees at that point. However angles mSA and mRT are both at the circumference of the circle(a chord is a line from point of a circle's circumference to the other) and are both 90 degrees because angle at the circumference is half of angle at the centre in same arc.

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1) The brain volumes (cm3) of 50 brains vary from a low of 910 cm3 to a high of 1492 cm3. Use the ange rule of thumb to estimate
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Answer:

1) The estimated standard deviation from the range rule is 145.5 cm3.

As it is 29.8 cm3 smaller than the exact standard deviation, we consider that the estimation is not accurate enough.

2) Brain volumes smaller than 921.1 cm3 can be considered significantly low.

Brain volumes bigger than 1417.5 cm3 can be considered significantly high.

A brain volume of 1457.5 cm3 is bigger than the expected maximum , so it can be considered significantly high.

Step-by-step explanation:

The range rule indicates the approximate relationship between the range (the difference between the maximum and minimum value) and the standard deviation:

s\approx\dfrac{R}{4}

1) If we have a sample of 50 brains volumes, and they range from 910 cm3 to 1492 cm3, we can estimate the standard deviation as:

s\approx\dfrac{\text{Max}-\text{Min}}{4}=\dfrac{1492-910}{4}=\dfrac{582}{4}=145.5

The exact standard deviation is 175.3 cm3.

The difference is 175.3-145.5=29.8 cm3, so the estimation is not accurate enough.

2) According to the range rule of thumb we expect to have a maximum value around 2 standard deviations above the mean, and a minimum value 2 standard deviations below the mean. We have a mean of 1169.3 cm3 and a standard deviation of 124.1 cm3, so the expected boundaries are:

\text{Min}=M-2s=1169.3-2*124.1=1169.3-248.2=921.1\\\\\text{Max}=M+2s=1169.3+2*124.1=1169.3+248.2=1417.5

A brain volume of 1457.5 cm3 is bigger than the expected maximum , so it can be considered significantly high.

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