Answer:
21 students were in the class.
Step-by-step explanation:
The information in the question tells you that 4/7 of the class is girls.
That means that the remainder of the class is 1 - 4/7 = 3/7 boys
Let the total in the class = x
(3/7)x = 9 Multiply by 7
(3/7)*7*x = 9 * 7 Simplify the right and left
3x = 63 Divide by 3
3x/3 = 63/3
x = 21
There were 21 students in the class.
Answer:
a = 16 and b = 13
Step-by-step explanation:
The opposite sides of a parallelogram are congruent, so
CD = AB , that is
3a - 10 = 2a + 6 ( subtract 2a from both sides )
a - 10 = 6 ( add 10 to both sides )
a = 16
The diagonals of a parallelogram bisect each other, so
AO = CO , that is
2b = 26 ( divide both sides by 2 )
b = 13
Answer:
KM=9
JK= 12.69
Angle JKM=45 degrees
ML=18.97
MKL=60 degrees
Angle L=30 degrees
Step-by-step explanation:
Triangle JKM is a 45, 45, 90 degree triangle so that means both side lengths are equal and the hypotenuse is square root of 2 times a side length. This means, KM will be equal to 9 and JK will be equal to 9 times square root of 2. For triangle KML, you know that the triangle is a 30,60,90 degree triangle. This means the hypotenuse is a^2+b^2=c^2 where c is the hypotenuse. Since you know that a is 9 and c is 21, plug them into the equation to get 81+b^2=441. Subtract 81 from both sides to isolate b^2 to get 360. b^2 = 360. Then find the square root of 360 which is about 18.97. Therefore, b or ML is equal to 18.97. Also, because we know that MKL is a 30, 60, 90 triangle, we know that angle MKL is equal to 60 degrees. Because we know the angles of MKL(60) and KML (90), we do 180-90-60 to find angle L. Simplify 180-90-60 to 30 and that means that angle L is equal to 30 degrees. Since we know that JKM is a 45, 45, 90 degree triangle, we know that JKM is equal to 45 degrees. Therefore, KM is equal to 9, JK is equal to 9 times square root of 2 or 9 times 1.41 which is 12.69. Angle JKM is 45 degrees, ML is 18.97, angle MKL is 60 degrees, and angle L is 30 degrees.
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Answer:
b. 0.02
Step-by-step explanation:
The smaller the p-value, the stronger the evidence that you should reject the null hypothesis. In this case, this will mean rejecting that the proportions are not significantly different.
Usually, a p-value is considered to be statistically significant when p ≤ 0.05.
From the answer options provided, alternative b. 0.02 is the only one that represents the difference in proportions to be statistically significant (there is only a 2% chance that the proportions are not significantly different).
Therefore, the answer is b. 0.02
