The original total of the ingredients was 40 dollars
Answer: C. A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.
Explanation: The One-Sample Proportion Test is used to assess whether a population proportion (P1) is significantly different from a hypothesized value (P0). This procedure calculates sample size and statistical power for testing a single proportion using either the exact test or other approximate z-tests.
To write a null hypothesis, first, start by asking a question. Rephrase that question in a form that assumes no relationship between the variables. In other words, assume a treatment has no effect. Write your hypothesis in a way that reflects this.
A null hypothesis is a hypothesis that says there is no statistical significance between the two variables. It is usually the hypothesis a researcher or experimenter will try to disprove or discredit. An alternative hypothesis is one that states there is a statistically significant relationship between two variables.
<span>I note that this problem starts out with "Which is a factor of ... " This implies that you were given several answer choices. If that's the case, it's unfortunate that you haven't shared them.
I thought I'd try finding roots of this function using synthetic division. See below:
f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35
Please use " ^ " to denote exponentiation. Thanks.
Possible zeros of this poly are factors of 35: plus or minus 1, plus or minus 5, plus or minus 7. Use synthetic division; determine whether or not there is a non-zero remainder in each case. If none of these work, form rational divisors from 35 and 6 and try them: 5/6, 7/6, 1/6, etc.
Provided that you have copied down the function
</span>f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35 properly, this approach will eventually turn up 1 or 2 zeros of this poly. Obviously it'd be much easier if you'd check out the possible answers given you with this problem.
By graphing this function, I found that the graph crosses the x-axis at 7/2. There is another root.
Using synth. div. to check whether or not 7/2 is a root:
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7/2 / 6 -21 -4 24 -35
21 0 -14 35
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6 0 -4 10 0
Because the remainder is zero, 7/2 (or 3.5) is a root of the polynomial. Thus, (x-3.5), or (x-7/2), is a factor.
The summation indicates the sum from n = 1 to n = 3 of the expression 2(n+5).
2 (n+5) = 2n + 10
2n + 10 denotes an Arithmetic Series, with a common difference of two and first term as 12.
For n =1, it equals 12
For n = 2, it equals 14
For n = 3, it equals 16
So the sum from n=1 to n=3 will be 12 + 14 + 16 = 42
Sum of an Arithmetic Series can also be written as:
Using the value of a₁ and d, we can simplify the expression as:
This expression is equivalent to the given expression and will yield the same result.
For n=3, we get the sum as:
S₃ = 3(11+3) = 42
