Answer:
A
Step-by-step explanation:
for the relation to be a function then each value of x in the domain must map to exactly one unique value of y in the range
this is the case for A
in B : 3 → 2 and 3 → 8 ← not a function
in C : - 2 → 5 and - 2 → 7 ← not a function
in D : 2 → 2 and 2 → 3 and 3 → 3 and 3 → 2 ← not a function
Answer:
14,130 cm³
Step-by-step explanation:
V = 4/3πr³
= 4/3 x 3.14 x 15 x 15 x 15
= 20 x 225 x 3.14
= 706.5 x 20
= 14,130 cm³
Answer:
Option C. x^2-18x-81
Step-by-step explanation:
A. 16a^2-72a+81
x^2-2xy+y^2=(x-y)^2
x^2=16a^2→sqrt(x^2)=sqrt(16a^2)→x=sqrt(16) sqrt(a^2)→x=4a
y^2=81→sqrt(y^2)=sqrt(81)→y=9
2xy=2(4a)(9)→2xy=72a equal to the second term of the expression, then we can factor as a perfect square trinomial:
16a^2-72a+81=(4a-9)^2
B. 169x^2+26xy+y^2
a^2+2ab+b^2=(a+b)^2
a^2=169x^2→sqrt(a^2)=sqrt(169x^2)→a=sqrt(169) sqrt(x^2)→a=13x
b^2=y^2→sqrt(b^2)=sqrt(y^2)→b=y
2ab=2(13x)(y)→2ab=26xy equal to the second term of the expression, then we can factor as a perfect square trinomial:
169x^2+26xy+y^2=(13x+y)^2
C. x^2-18x-81
a^2+2ab+b^2=(a+b)^2
This expression does not factor as a perfect square trinomial because the third term is negative (-81).
D. 4x^2+4x+1
a^2+2ab+b^2=(a+b)^2
a^2=4x^2→sqrt(a^2)=sqrt(4x^2)→a=sqrt(4) sqrt(x^2)→a=2x
b^2=1→sqrt(b^2)=sqrt(1)→b=1
2ab=2(2x)(1)→2ab=4x equal to the second term of the expression, then we can factor as a perfect square trinomial:
4x^2+4x+1=(2x+1)^2
Answer:
2.897
Step-by-step explanation:
Let us find the mean and variance for the sample first.
105 104 110 112
114 106 108 109
Mean = sum/8 = 108.5
Variance = 12
Std dev = sq rt of variance = 3.464
Std error = std dev/ sq rt n
since n =8, we get std error = 1.225
Since sample size is small, df =8-1 =7
For 95% confidence intervals, t critical value for two tailed=2.365
Margin of error = std error x t critical = 1.225(2.365)
=2.897
