Answer:
1.) mean
2.) H0 : μ = 64
3.) 0.0028
4) Yes
Step-by-step explanation:
Null hypothesis ; H0 : μ = 64
Alternative hypothesis ; H1 : μ < 64
From the data Given :
70; 45; 55; 60; 65; 55; 55; 60; 50; 55
Using calculator :
Xbar = 57
Sample size, n = 10
Standard deviation, s = 7.14
Test statistic :
(xbar - μ) ÷ s/sqrt(n)
(57 - 64) ÷ 8 / sqrt(10)
Test statistic = - 2.77
Pvalue = (Z < - 2.77) = 0.0028 ( Z probability calculator)
α = 10% = 0.1
Reject H0 ; if P < α
Here,
P < α ; Hence, we reject the null
Answer:
5. (x, y) ⇒ (x +5, y +1)
6. (x, y) ⇒ (x +4, y -1)
Step-by-step explanation:
A translation rule will generally have the form ...
(x, y) ⇒ (x +h, y +k)
where (h, k) is the horizontal and vertical distance to the right and up that the figure is being translated.d
5) The image is 5 units right and 1 unit up from the original, so in the above formula, (h, k) = (5, 1) and the translation rule is ...
(x, y) ⇒ (x +5, y +1)
__
6) The image is 4 units right and 1 unit down from the original, so (h, k) = (4, -1) and the transformation rule is ...
(x, y) ⇒ (x +4, y -1)
1/3(12x-24)=16
*3 *3
12x-24=48
+24 +24
12x=72
/12 /12
x=6
Answer:
(-2, -1).
Step-by-step explanation:
y = x² + 4x + 3
Completing the square:
y = (x + 4/2)^2 - (4/2)^2 + 3
y = (x + 2)^2 - 4 + 3
y = (x + 2)^2 - 1.
This is vertex form and the coordinates of the vertex are (-2, -1).
Answer:
Step-by-step explanation:
It can be convenient to compute the length of the hypotenuse of this triangle (AC). The Pythagorean theorem tells you ...
AC^2 = AB^2 + CB^2
AC^2 = 4^2 + 3^2 = 16 + 9 = 25
AC = √25 = 5
The altitude divides ∆ABC into similar triangles ∆AHB and ∆BHC. The scale factor for ∆AHB is ...
scale factor ∆ABC to ∆AHB = AB/AC = 4/5 = 0.8
And the scale factor to ∆BHC is ...
scale factor ∆ABC to ∆BHC = BC/AC = 3/5 = 0.6
Then the side AH is 0.8·AB = 0.8·4 = 3.2
And the side CH is 0.6·BC = 0.6·3 = 1.8
These two side lengths should add to the length AC = 5, and they do.
The remaining side BH can be found from either scale factor:
BH = AB·0.6 = BC·0.8 = 4·0.6 = 3·0.8 = 2.4
_____
The sides of interest are ...
AH = 3.2
CH = 1.8
BH = 2.4
