Answer: 4x² + 3x + 52
Step-by-step explanation:
1. rearrange & simplify terms:
(4x² - 4 + 6) + (3x - 7² + 1) . . .
(4x² + 2) + (3x + 49 + 1) . . .
(4x²+2) + (3x + 50).
2. combine like terms in standard form:
<u>4x² + 3x + 52</u>
Answer:
the height is 7.5
Step-by-step explanation:
30 divided by 4 = 7.5
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval is ![-0.00870](https://tex.z-dn.net/?f=-0.00870%20%3Cp_1%20-p_2%20%3C%20-0.007297)
Step-by-step explanation:
From the question we are told that
The first sample size is ![n_1 = 1068000](https://tex.z-dn.net/?f=n_1%20%20%3D%20%201068000)
The first proportion ![\r p_1 = 0.084](https://tex.z-dn.net/?f=%5Cr%20p_1%20%3D%200.084)
The second sample size is ![n_2 = 1476000](https://tex.z-dn.net/?f=n_2%20%20%3D%20%201476000)
The second proportion is ![\r p_2 = 0.092](https://tex.z-dn.net/?f=%5Cr%20p_2%20%3D%20%200.092)
Given that the confidence level is 95% then the level of significance is mathematically represented as
![\alpha = (100 - 95)\%](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%20%28100%20-%2095%29%5C%25)
![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%200.05)
From the normal distribution table we obtain the critical value of
the value is
![Z_{\frac{\alpha }{2} } =z_c= 1.96](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%3Dz_c%3D%20%201.96)
Now using the formula from the question to construct the 95% confidence interval we have
![(\r p_1 - \r p_2 )- z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2} }](https://tex.z-dn.net/?f=%28%5Cr%20p_1%20-%20%5Cr%20p_2%20%20%29-%20z_c%20%5Csqrt%7B%20%5Cfrac%7B%5Cr%20p_1%20%5Cr%20q_1%20%7D%7Bn_1%7D%20%2B%20%5Cfrac%7B%5Cr%20p_2%20%5Cr%20q_2%20%7D%7Bn_2%7D%20%7D%20%3Cp_1%20-p_2%20%3C%20%20%28%5Cr%20p_1%20-%20%5Cr%20p_2%20%20%29%2B%20z_c%20%5Csqrt%7B%20%5Cfrac%7B%5Cr%20p_1%20%5Cr%20q_1%20%7D%7Bn_1%7D%20%2B%20%5Cfrac%7B%5Cr%20p_2%20%5Cr%20q_2%20%7D%7Bn_2%7D%20%7D)
Here ![\r q_1 = 1 - \r p_1](https://tex.z-dn.net/?f=%5Cr%20q_1%20%3D%20%201%20-%20%5Cr%20p_1)
=> ![\r q_1 = 1 - 0.084](https://tex.z-dn.net/?f=%5Cr%20q_1%20%3D%20%201%20-%200.084)
=> ![\r q = 0.916](https://tex.z-dn.net/?f=%5Cr%20q%20%3D%20%200.916)
and
![\r q_2 = 1 - \r p_2](https://tex.z-dn.net/?f=%5Cr%20q_2%20%3D%20%201%20-%20%5Cr%20p_2)
=> ![\r q_2 = 1 - 0.092](https://tex.z-dn.net/?f=%5Cr%20q_2%20%3D%20%201%20-%200.092)
=> ![\r q_2 = 0.908](https://tex.z-dn.net/?f=%5Cr%20q_2%20%3D%200.908)
So
![(0.084 - 0.092 )- (1.96)* \sqrt{ \frac{0.092* 0.916 }{1068000} + \frac{0.084* 0.908 }{1476000} }](https://tex.z-dn.net/?f=%280.084%20-%200.092%20%29-%20%281.96%29%2A%20%20%5Csqrt%7B%20%5Cfrac%7B0.092%2A%200.916%20%7D%7B1068000%7D%20%2B%20%5Cfrac%7B0.084%2A%200.908%20%7D%7B1476000%7D%20%7D%20%3Cp_1%20-p_2%20%3C%20%20%280.084%20-%200.092%20%29%2B%20%281.96%29%2A%20%20%5Csqrt%7B%20%5Cfrac%7B0.084%2A%200.916%20%7D%7B1068000%7D%20%2B%20%5Cfrac%7B0.092%2A%200.908%20%7D%7B1476000%7D%20%7D)
![-0.00870](https://tex.z-dn.net/?f=-0.00870%20%3Cp_1%20-p_2%20%3C%20-0.007297)
Answer:
-10
Step-by-step explanation:
Let x = number
10 less than a number is the same number doubled
x-10 = 2x
Subtract x from each side
x-10-x = 2x-x
-10 = x
The number is -10
<span>A. 0.1
The residual is the difference between the observed value and the predicted value for a data point. You obtain it by subtracting the predicted value from the observed value. So the predicted value is:
y = -0.2x + 1.9
y = -0.2*5 + 1.9
y = -1 + 1.9
y = 0.9
Therefore the residual is:
r = 1 - 0.9
r = 0.1
And the value of 0.1 matches option "A".</span>