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quester [9]
2 years ago
6

Exhibit 11-1 Last year, the standard deviation of the ages of the students at UA was 1.81 years. Recently, a sample of 10 studen

ts had a standard deviation of 2.1 years. We are interested in testing to see if there has been a significant change in the standard deviation of the ages of the students at UA. Refer to Exhibit 11-1. The test statistic is
Mathematics
1 answer:
rewona [7]2 years ago
3 0

Answer:

test statistic = 12.115

Step-by-step explanation:

Given data :

std = 2.1 years

n = 10

( std )^2 = 4.41

<u>determine the test statistic</u>

apply a two-tailed test ( chi squared test for one population variance )

test statistic

λ^2 = \frac{(n-1)s^2}{3.2761}   ( Referring to Exhibit 11-1 )

      = ( 10 - 1 )*(2.1)^2 / 3.2761

      = 12.115

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In Triangle XYZ, measure of angle X = 49° , XY = 18°, and
marissa [1.9K]

Answer:

There are two choices for angle Y: Y \approx 54.987^{\circ} for XZ \approx 15.193, Y \approx 27.008^{\circ} for XZ \approx 8.424.

Step-by-step explanation:

There are mistakes in the statement, correct form is now described:

<em>In triangle XYZ, measure of angle X = 49°, XY = 18 and YZ = 14. Find the measure of angle Y:</em>

The line segment XY is opposite to angle Z and the line segment YZ is opposite to angle X. We can determine the length of the line segment XZ by the Law of Cosine:

YZ^{2} = XZ^{2} + XY^{2} -2\cdot XY\cdot XZ \cdot \cos X (1)

If we know that X = 49^{\circ}, XY = 18 and YZ = 14, then we have the following second order polynomial:

14^{2} = XZ^{2} + 18^{2} - 2\cdot (18)\cdot XZ\cdot \cos 49^{\circ}

XZ^{2}-23.618\cdot XZ +128 = 0 (2)

By the Quadratic Formula we have the following result:

XZ \approx 15.193\,\lor\,XZ \approx 8.424

There are two possible triangles, we can determine the value of angle Y for each by the Law of Cosine again:

XZ^{2} = XY^{2} + YZ^{2} - 2\cdot XY \cdot YZ \cdot \cos Y

\cos Y = \frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ}

Y = \cos ^{-1}\left(\frac{XY^{2}+YZ^{2}-XZ^{2}}{2\cdot XY\cdot YZ} \right)

1) XZ \approx 15.193

Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-15.193^{2}}{2\cdot (18)\cdot (14)} \right]

Y \approx 54.987^{\circ}

2) XZ \approx 8.424

Y = \cos^{-1}\left[\frac{18^{2}+14^{2}-8.424^{2}}{2\cdot (18)\cdot (14)} \right]

Y \approx 27.008^{\circ}

There are two choices for angle Y: Y \approx 54.987^{\circ} for XZ \approx 15.193, Y \approx 27.008^{\circ} for XZ \approx 8.424.

6 0
3 years ago
There are 20 nickels in one dollar. Write an equation to find the number of nickels n in any number of dollars d
n200080 [17]

5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5

20 nickles

20•5=1.00

4 0
2 years ago
Abraham is taking his mother out to a restaurant for a mother's day dinner . He orders a meal that cost \$12 and his mom orders
White raven [17]

Answer:

$38.26

Step-by-step explanation:

add the amounts together and multiply by 0.075 and 0.15 add these answers to the original amount

6 0
3 years ago
Select the correct answer. One factor of the polynomial 213 3r2 – 3x + 2 is (t – 2), which expression represents the other facto
Darina [25.2K]

Answer:

(x - 2)(x + 1)(2x -1)

Step-by-step explanation:

We use synthetic division as a tool for factoring the given expression.  The coefficients of the terms given are {2, -3, -3, 2}.  If x - 2 is a factor of this expression, then 2 is a root.  We perform synthetic division as follows:

2   /    2     -3      -3     2

                  4       2     -2

    -------------------------------

          2      1        -1      0

Next, we determine whether or not (2x - 1)(x + 1) represents the remaining factor(s).  Using -1 as divisor, we get:

-1    /     2     1     -1

                   -2    1

     ---------------------

             2     -1     0

Since the remainder is zero, x + 1 must be a factor and (2x - 1) the third factor.  Answer D is correct.

4 0
2 years ago
The following system of equations is _____.
hoa [83]
The correct answer among the choices listed above is the second option. <span>The following system of equations is equivalent. This is because when written in the same form, one equation will yield to the same equation as the other.

</span>y = -1/3x +2/3 

<span>2x + 6y = 4
</span>6y = 4 - 2x
y = 2/3 - 1/3x
<span>y = -1/3x +2/3 </span>
3 0
3 years ago
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