Answer:
the 90% confidence interval is ( 48.684 , 51.316 )
Step-by-step explanation:
Given that :
the sample size = 36
Sample Mean = 50
standard deviation = 4.80
The objective is to calculate a 90% confidence interval.
At 90% confidence interval ;
the level of significance = 1 - 0.9 = 0.1
The critical value for ![z_{\alpha/2} = z_{0.1/2}](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%20%3D%20z_%7B0.1%2F2%7D)
= 1.645
The standard error S.E = ![\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
=![\dfrac{4.8}{\sqrt{36}}](https://tex.z-dn.net/?f=%5Cdfrac%7B4.8%7D%7B%5Csqrt%7B36%7D%7D)
![=\dfrac{4.8}{6}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B4.8%7D%7B6%7D)
= 0.8
The Confidence interval level can be computed as:
![\bar x \ \pm z \times \ \dfrac{ \sigma }{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cbar%20x%20%20%5C%20%5Cpm%20z%20%5Ctimes%20%5C%20%5Cdfrac%7B%20%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%7D)
For the lower limit :
![\bar x \ - z \times \ \dfrac{ \sigma }{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cbar%20x%20%20%5C%20-%20z%20%5Ctimes%20%5C%20%5Cdfrac%7B%20%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%7D)
![=50 \ - 1.645 \times \ \dfrac{ 4.8 }{\sqrt{36}}](https://tex.z-dn.net/?f=%3D50%20%5C%20-%201.645%20%20%5Ctimes%20%5C%20%5Cdfrac%7B%204.8%20%7D%7B%5Csqrt%7B36%7D%7D)
![=50 \ - 1.645 \times \ 0.8 }}](https://tex.z-dn.net/?f=%3D50%20%5C%20-%201.645%20%20%5Ctimes%20%5C%200.8%20%7D%7D)
=50 - 1.316
= 48.684
For the upper limit :
![\bar x \ - z \times \ \dfrac{ \sigma }{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cbar%20x%20%20%5C%20-%20z%20%5Ctimes%20%5C%20%5Cdfrac%7B%20%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%7D)
![=50 \ + 1.645 \times \ \dfrac{ 4.8 }{\sqrt{36}}](https://tex.z-dn.net/?f=%3D50%20%5C%20%2B%201.645%20%20%5Ctimes%20%5C%20%5Cdfrac%7B%204.8%20%7D%7B%5Csqrt%7B36%7D%7D)
![=50 \ + 1.645 \times \ 0.8 }}](https://tex.z-dn.net/?f=%3D50%20%5C%20%2B%201.645%20%20%5Ctimes%20%5C%200.8%20%7D%7D)
=50 + 1.316
= 51.316
Thus, the 90% confidence interval is ( 48.684 , 51.316 )
Ok so we can model this like
![1.89+0.25x=3.8](https://tex.z-dn.net/?f=1.89%2B0.25x%3D3.8)
This is because the initial price was 1.89$ for the drink, then for every refill, it was a quarter extra. To solve for x we start by subtracting 1.89 from both sides.
![0.25x=1.91](https://tex.z-dn.net/?f=0.25x%3D1.91)
So now we divide by 0.25 or multiply by 4 and we get
![x=7.64](https://tex.z-dn.net/?f=x%3D7.64)
But x cannot be a fraction. So we round this to the least integer, or 7
Given:
-2y + 5z = -3 <span>(first equation)
</span>y = -5x - 4z - 5 (second equation)
x = 4z + 4 <span>(third equation)<span>
</span></span>
Solution:
PART 1
Substitute x with (4z + 4) in the second equation
y = -5x - 4z - 5
y = -5(4z + 4) - 4z - 5
Then simplify
y = -20z - 20 - 4z - 5
add like terms
y = -20z - 4z - 20 - 5
y = -24z - 25
PART 2 : Find the value of z
We got y is equal to (-24z - 25). Substitute y with (-24z - 25) in the first equation, and we'll find the value of z.
-2y + 5z = -3
-2(-24z - 25) + 5z = -3
48z + 50 + 5z = -3
add like terms
48z + 5z = -3 - 50
53z = -53
z = -53/53
z = -1
The value of z is equal to -1
PART 3: Find y and x
Find the value of y by substitution of -1 in the place of z.
y = -24z - 25
y = -24(-1) - 25
y = 24 - 25
y = -1
The value of y is equal to -1
Find the value of x by substitution of -1 in the place of z.
x = 4z + 4
x = 4(-1) + 4
x = -4 + 4
x = 0
The value of x is equal to 0
Answer:
12 = 3/4x, x - 4.8 = 9, and x - 3.1x = 14.7 + 12 are all equations because you have an equal sign that has you solve for each side and you can solve for the variable, unlike with the other ones you can't solve for the variable.
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
18-4