Answer:
EH = 3.31
Step-by-step explanation:
We have been given a right angle triangle EKL. As KH has been given as the altitude (perpendicular) of the right angled triangle, and K is the right angle, we can say that EK is tthe base of the triangle and EH is the only side lleft, which is the hypotenuse of the triangle.
Where,
EK = Base = 3
KH = perpendicular altitude
EH = Hypotenuse
m<K = 90
m<E = 25
We know that
cosθ = Base/ Hypotenuse
cos 25 = 3/ EH
EH = 3/cos25
EH = 3.31
Perpendicular alitutude can also be calculated by using the formula for tanθ.
Answer:
1 no
2 no
3 no
4 yes
5 no
Step-by-step explanation:
Answer:
1) The linear regression model is y = -0.0348·x + 13.989
2) The correlation coefficient is -0.0725
3) The strength of the model is strong - association
Step-by-step explanation:
1)
X Y XY X²
27 13 351 729
65 12 780 4225
83 11 913 6889
109 10 1090 11881
142 9 1278 20164
175 8 1400 30625
∑ 601 63 5812 74513
From y = ax + b, we have
b = 1/n(∑y -a∑x) = 1/6(63 - (0.0348)×601) = 13.989
Therefore, the linear regression model is y = -0.0348·x + 13.989
2)
![r = \frac{n\sum xy - \sum x\sum y }{\sqrt{[n\sum x^{2}-\left (\sum x \right )^{2}] [n\sum y^{2}-\left (\sum y \right )^{2}]}} = \frac{6 \times 5812 - 601 \times 63}{\sqrt{[6 \times 74513-601^{2}] [6 \times 3969 - 63^2]} } = - 0.0725](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bn%5Csum%20xy%20-%20%5Csum%20x%5Csum%20y%20%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E%7B2%7D-%5Cleft%20%28%5Csum%20x%20%20%5Cright%20%29%5E%7B2%7D%5D%20%5Bn%5Csum%20y%5E%7B2%7D-%5Cleft%20%28%5Csum%20y%20%20%5Cright%20%29%5E%7B2%7D%5D%7D%7D%20%20%3D%20%5Cfrac%7B6%20%5Ctimes%205812%20%20-%20601%20%5Ctimes%2063%7D%7B%5Csqrt%7B%5B6%20%5Ctimes%2074513-601%5E%7B2%7D%5D%20%5B6%20%20%5Ctimes%203969%20-%2063%5E2%5D%7D%20%7D%20%3D%20-%200.0725)
3) The strength is - association.
Answer:
students preferred alternative music
= 461/1940 ×100%=23.7%
Answer:
- addition property of equality
- integers are closed to addition
- identity element
- multiplication property of equality
- commutative property of multiplication; reals are closed to multiplication; identity element
Step-by-step explanation:
<u>Given</u>:
c/2 -5 = 7
Step 1: c/2 -5 +5 = 7 +5
Step 2: c/2 +0 = 12
Step 3: c/2 = 12
Step 4: 2(c/2) = 12(2)
Step 5: c = 24
<u>Find</u>:
The property that justifies each step of the solution.
<u>Solution</u>:
Step 1: addition property of equality (lets you add the same to both sides)
Step 2: integers are closed to addition
Step 3: identity property of addition (adding 0 changes nothing)
Step 4: multiplication property of equality
Step 5: closure of real numbers to multiplication; identity property of multiplication
_____
It is hard to say what "property" you want to claim when you simplify an arithmetic expression. Above, we have used the property that the sets of integers and real numbers are closed to addition and multiplication. That is, adding or multiplying real numbers gives a real number.
In Step 5, we can rearrange 2(c/2) to c(2/2) using the commutative property of multiplication. 2/2=1, and c×1 = c. The latter is due to the identity element for multiplication: multiplying by 1 changes nothing.
Apart from the arithmetic, the other properties used are properties of equality. Those let you perform any operation on an equation, as long as you do it to both sides of the equation. The operations we have performed in this fashion are adding 5 and multiplying by 2.
