Hey ! there
Answer:
- Length of x is <u>7</u><u> </u><u>cm</u>
Step-by-step explanation:
In this question we are provided with a right angle triangle having <u>h</u><u>ypotenuse 25</u><u> </u><u>cm </u><u>,</u><u> </u><u>base </u><u>2</u><u>4</u><u> </u><u>cm </u><u>and </u><u>perpendicular</u><u> </u><u>x</u><u> </u><u>.</u> And we are asked to find the <u>length of</u> <u>x </u><u>.</u>
For finding the length of x we'll use Pythagorean Theorem . Pythagorean Theorem states that sum of square of perpendicular and base is equal to the square of hypotenuse in right angle triangle that is ,
<u>Where </u><u>,</u>
- H refers to <u>Hypotenuse</u>
- P refers to <u>Perpendicular</u>
<u>SOLUTION</u><u> </u><u>:</u><u> </u><u>-</u>
Here in the triangle ,
- Hypotenuse is <u>2</u><u>5</u><u> </u><u>cm</u>
- Base is <u>2</u><u>4</u><u> </u><u>cm</u>
- Perpendicular is <u>x</u>
<u>Applying</u><u> </u><u>Pythagorean</u><u> </u><u>Theorem</u><u> </u><u>:</u>
<u></u>
On squaring 24 and 24 we get ,
Subtracting 576 on both sides :
We get ,
Applying square root on both sides :
We get ,
- <u>Henceforth</u><u> </u><u>,</u><u> </u><u>length</u><u> </u><u>of </u><u>x </u><u>is </u><u>❝</u><u> </u><u>7</u><u> </u><u>cm </u><u>❞</u><u> </u><u>.</u>
<u>Verifying</u><u> </u><u>:</u><u> </u><u>-</u>
We are verifying our answer by substituting all the values of hypotenuse , perpendicular and base in Pythagorean Theorem . So ,
- ( 25 )² = ( <u>7</u> )² + ( 24 )²
<u>Therefore</u><u>,</u><u> our</u><u> answer</u><u> is</u><u> correct</u><u> </u><u>.</u>
<h2>
<u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>
Answer:
Decison region :
Reject H0 : if χ² > 6.251
12.229
Step-by-step explanation:
Given :
Manufacturer A B C D
Unacceptable 29 17 9 22
Acceptable 171 183 191 178
Total 200 200 200 200
H0: There is no relationship between quality and manufacturer.
H1: There is a relationship.
Testing using the goodness of fit :
Chisquare = (observed - Expected)² / Expected
Expected Values:
19.25 19.25 19.25 19.25
180.75 180.75 180.75 180.75
Chi-Squared Values:
4.93831 0.262987 5.45779 0.392857
0.525934 0.0280083 0.581259 0.0418396
χ² = 4.93831 + 0.262987 + 5.45779 + 0.392857
+ 0.525934 + 0.0280083 + 0.581259 + 0.0418396 = 12.229
Degree of freedom, df = (4-1)(2-1) = 3*1= 3
The critical value,
χ² at 0.10, 3 = 6.251
Decison region :
Reject H0 : if χ² > 6.251
Reject H0 : 12.229 > 6.251
Step-by-step explanation:
The line passes through the origin and point (30,3)
so, slope of the graph( miles per minute)= 3/30 = 1/10 miles per minute
Or, slope of the graph miles per hour
option B