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Dovator [93]
3 years ago
12

to find the distance between a point x and an inaccessible point​ z, a line segment xy is constructed. measurements show that xy

=966 ​m, angle xyz​=38°24', and angle yzx=94°6'. find the distance between x and z to the nearest meter.

Mathematics
1 answer:
marshall27 [118]3 years ago
4 0

Answer:

\approx \bold{602\ m}

Step-by-step explanation:

Given the following dimensions:

XY=966 ​m

\angle XYZ​ = 38°24', and

\angle YZX = 94°6'

To find:

Distance between points X and Z.

Solution:

Let us plot the given values.

We can clearly see that it forms a triangle when we join the points X to Y, Y to Z and Z to X.

The \triangle XYZ has following dimensions:

XY=966 ​m

\angle XYZ​ = 38°24', and

\angle YZX = 94°6'

in which we have to find the side XZ.

Kindly refer to the image attached.

Let us use the Sine rule here:

As per Sine Rule:

\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}

Where  

a is the side opposite to \angle A

b is the side opposite to \angle B

c is the side opposite to \angle C

\dfrac{XZ}{sin\angle Y} = \dfrac{XY}{sin\angle Z}\\\Rightarrow \dfrac{966}{sin94^\circ6'} = \dfrac{XZ}{sin38^\circ24'}\\\Rightarrow XZ=\dfrac{966}{sin94^\circ6'} \times sin38^\circ24'\\\Rightarrow XZ=\dfrac{966}{0.997} \times 0.621\\\Rightarrow XZ=601.69 \m \approx \bold{602\ m}

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Out of a sample 650 high school students, 321 take the bus to school every day. construct a 99% confidence interval for the popu
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A 99% confidence interval for the population mean of high school students that take the bus to school every day is b) ci=(44.34%, 54.43%)

We need to find the 99% confidence interval for the population mean of high school students that take the bus to school everyday

A confidence interval is a range of estimates for an unknown parameter. The confidence interval is calculated at the specified confidence level; the most common is the 95% confidence level, but sometimes other levels are used, such as 90% or 99%.

The confidence interval of proportions is given by:

π ± z √(π (1-π) /n)

π is the sample proportion.

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n is the sample size.

For 99% confidence interval the value of z is 2.58

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The confidence interval is given by

=321/650 ± 2.58 √( (321/650) × [ 1 - (321/650) ] ÷ 650)

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