Given that,
Sample size= 83
Mean number= 39.04
Standard deviation= 11.51
We know the critical t-value for 95% confidence interval which is equal to 1.989.
We also know the formula for confidence interval,
CI=( mean number - critical t-value*standard deviation/(sample size)^(1/2), mean number + critical t-value*standard deviation/(sample size)^(1/2))
So, we have
CI= (39.04 - 1.989*11.51/83^(1/2), 39.04 + 1.989*11.51/83^(1/2)
CI= (39.04 - 2.513,39.04 + 2.513)
CI= (36.527,41.553)
Therefore, 95% confidence interval for these data is (36.527,41.553), and this result interpret that the true value for this survey sample lie in the interval (36.527,41.553).
Direct variation is represented by the equation y = k × x and inverse variation is represented by y = k/x
Table 1:
y = k × x
30 = k × 5
30 = 5k
k = 30/5
k = 6
So,
<em>y = 30 </em>
<em>y = 30 k = 6</em>
<em>y = 30 k = 6x = 5</em>
<em>y = 30 k = 6x = 5Equation: y = 6x</em>
y = k × x
y = 10 × 8
y = 80
So,
<em>y = 80 </em>
<em>y = 80 k = 10</em>
<em>y = 80 k = 10x = 8</em>
<em>y = 80 k = 10x = 8Equation: y = 10x</em>
y = 3x
18 = 3x
x = 18/3
x = 6
So,
<em>y = 18</em>
<em>y = 18k = 3</em>
<em>y = 18k = 3x = 6</em>
<em>y = 18k = 3x = 6Equation: y = 3x</em>
y = 2x²
72 = 2x²
x² = 72/2
x² = 36
x = √36
x = 6
So,
<em>y = 72</em>
<em>y = 72k = 2</em>
<em>y = 72k = 2x = 6</em>
<em>y = 72k = 2x = 6Equation: y = 2x²</em>
Table 2:
y = k/x
5 = k/6
5 × 6 = k
30 = k
So,
<em>y = 5</em>
<em>y = 5k = 30</em>
<em>y = 5k = 30x = 6</em>
<em>y = 5k = 30x = 6Equation: y = 30/x</em>
y = k/x
y = 36/4
y = 9
So,
<em>y = 9</em>
<em>y = 9k = 36</em>
<em>y = 9k = 36x = 4</em>
<em>y = 9k = 36x = 4Equation: y = 36/x</em>
y = 60/x
20 = 60/x
20x = 60
x = 60/20
x = 3
So,
<em>y = 20</em>
<em>y = 20k = 60</em>
<em>y = 20k = 60x = 3</em>
<em>y = 20k = 60x = 3Equation: y = 60/x</em>
y = 24/x
y = 24/12
y = 2
So,
<em>y = 2</em>
<em>y = 2k = 24</em>
<em>y = 2k = 24x = 12</em>
<em>y = 2k = 24x = 12Equation: y = 24/x</em>
Read more:
brainly.com/question/472621
Answer:
x = 2.
Step-by-step explanation:
Solve for x:
0.3 (4 - x) = x - 1.4
Expand out terms of the left hand side:
1.2 - 0.3 x = x - 1.4
Subtract x from both sides:
1.2 + (-0.3 x - x) = (x - x) - 1.4
-0.3 x - x = -1.3 x:
-1.3 x + 1.2 = (x - x) - 1.4
x - x = 0:
1.2 - 1.3 x = -1.4
Subtract 1.2` from both sides:
(1.2 - 1.2) - 1.3 x = -1.2 - 1.4
1.2 - 1.2 = 0:
-1.3 x = -1.2 - 1.4
-1.2 - 1.4 = -2.6:
-1.3 x = -2.6
Divide both sides of -1.3 x = -2.6 by -1.3:
(-1.3 x)/(-1.3) = (-2.6)/(-1.3)
(-1.3)/(-1.3) = 1:
x = (-2.6)/(-1.3)
(-2.6)/(-1.3) = 2.:
Answer: x = 2.
I think the similar triangle is d and b for this question
