The statement is expressed algebraically as
(x/43) - 87 = -75
Answer:
1M
Step-by-step explanation:
one in a million twiceu
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)
Hey there,
<u>What </u><u>are </u><u>the </u><u>values </u><u>of </u><u>a,</u><u> </u><u>b </u><u>and </u><u>c?</u>
5x² + 2 = 4x
5x² + 2 - 4x = 4x - 4x
5x² - 4x+ 2 = 0
<em>Quadratic </em><em>général </em><em>e</em><em>quation</em><em>:</em>
ax² + bx + c = 0
I hope this helps ✅(◠‿◕)
a. The value of x is 7
b. The measure of ∠1 is 99°
<h3>Calculating angles </h3>
From the question, we are to solve for x
From the given diagram, we can write that
m∠NMQ + m∠MQN + m∠QNM = 180° (<em>Sum of angles in a triangle</em>)
From the given information,
m∠NMQ = 5x +19
m∠MQN = 8x -11
m∠QNM = 11x + 4
Then,
5x + 19 + 8x -11 + 11x + 4 = 180
Collect like terms
5x + 8x + 11x = 180 - 19 + 11 - 4
24x = 168
∴ x = 168/24
x = 7
Hence, the value of x is 7
b.
Measure of ∠1 + m∠QNM = 180° (<em>Sum of angles on a straight line</em>)
∴ Measure of ∠1 = 180° - m∠QNM
But m∠QNM = 11x + 4
∴ m∠QNM = 11(7) + 4
m∠QNM = 77 + 4
m∠QNM = 81°
Then,
Measure of ∠1 = 180° - 81°
Measure of ∠1 = 99°
Hence, the measure of ∠1 is 99°
Learn more on Calculating angles here: brainly.com/question/25716982
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