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Step-by-step explanation:
Answer:
y= 3x
Step-by-step explanation:
The slope is just read. It is 3. It is the value of m in the general equation.
y = mx + b
y = 3x + b
To find b, use (-1,-3)
x = -1
y = -3 Substitute into the general equation
-3 = 3(-1) + b Simplify the right side
-3 = -3 + b Subtract -3 from both sides
b = 0
Answer: y = 3x
Using the z-distribution, it is found that the 90% confidence interval for mean calories in a 30-gram serving of all chocolate chip cookies is (143, 149).
We are given the <em>standard deviation</em> for the population, which is why the <em>z-distribution </em>is used to solve this question.
The information given is:
- Sample mean of
.
- Population standard deviation of
.
- Sample size of
.
The confidence interval is:
The critical value, using a z-distribution calculator, for a <u>95% confidence interval</u> is z = 1.645, hence:
![\overline{x} - z\frac{\sigma}{\sqrt{n}} = 146 - 1.645\frac{12}{\sqrt{35}} = 143](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20-%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%20146%20-%201.645%5Cfrac%7B12%7D%7B%5Csqrt%7B35%7D%7D%20%3D%20143)
![\overline{x} + z\frac{\sigma}{\sqrt{n}} = 146 + 1.645\frac{12}{\sqrt{35}} = 149](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%20%2B%20z%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%3D%20146%20%2B%201.645%5Cfrac%7B12%7D%7B%5Csqrt%7B35%7D%7D%20%3D%20149)
The 90% confidence interval for mean calories in a 30-gram serving of all chocolate chip cookies is (143, 149).
A similar problem is given at brainly.com/question/16807970
Answer: ![\frac{1}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D)
Step-by-step explanation:
1. Original Equation: ![4^4(4^-^7)(4)](https://tex.z-dn.net/?f=4%5E4%284%5E-%5E7%29%284%29)
2.Simplify: ![4^4(4^-^7)(4) ----> 4^4* 4^-^7 * 4\\](https://tex.z-dn.net/?f=4%5E4%284%5E-%5E7%29%284%29%20----%3E%204%5E4%2A%204%5E-%5E7%20%2A%204%5C%5C)
3.Apply exponent rule: ![4^4^-^7^+^1](https://tex.z-dn.net/?f=4%5E4%5E-%5E7%5E%2B%5E1)
4. Simplify: ![4^-^2\\](https://tex.z-dn.net/?f=4%5E-%5E2%5C%5C)
5.Apply exponent rule: ![\frac{1}{4^2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%5E2%7D)
6.Simplify: ![\frac{1}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D)