Can someone please help me with one of these problems? If you can do both, it'd be even better. Thanks!
2 answers:
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Answer:
<em>a</em> = -10 and <em>b</em> = 18.
Step-by-step explanation:
Let <em>w</em> represent the width of the rectangle.
We are given that the perimeter of the rectangle is 20 cm, this means that:
Let's put <em>w</em> in terms of <em>x</em>. Divide both sides by two:
And solve for <em>w:</em>
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So, the rectangle measures <em>x</em> by (10 -<em> x</em>) cm.
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According to the Pythagorean Theorem:
<em>a</em> and <em>b</em> are the legs and <em>c</em> is the hypotenuse.
Substitute <em>x</em> for <em>a, w</em> for <em>b</em>, and 8 for <em>c:</em>
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Simplify and substitute:
Square:
Isolate the equation. So:
Since the leading coefficient is one, divide both sides by two:
Therefore, <em>a</em> = -10 and <em>b</em> = 18.
Answer:
a) test statistic = 2.12
b) p-value = 0.017
c) we reject the Null hypothesis
Step-by-step explanation:
Given data :
N = 200
girls (x) = 115 , Boys = 85
p = x / n = 115 / 200 = 0.575
significance level ( ∝ ) = 0.1
<em>aim : test whether the proportion of girls births after the treatment is greater than 50% that occurs without any treatment </em>.
<u>A) Determine the test statistic </u>
H0 : p = 0.5
Ha : p > 0.5
to determine the test statistic we will apply the z distribution at ( ∝ ) = 0.1
Z - test statistic = ( 0.575 - 0.5) / = 2.12
<u>b) determine the p-value</u>
The P-value can be determined using the normal standard table
P-value = 1 - p(Z< 2.12 ) = 1 - 0.9830 = 0.017
c) Given that the p value ( 0.017 ) < significance level ( 0.1 )
we will reject the H0 because there is evidence showing that proportion of girls birth is > 50%