Have you ever been frustrated because you could not get a container of some sort to release the last bit of its contents? The ar
1 answer:
Answer:
Indeed. Ample evidence substantiates the assertion that the leftover toothpaste is considerably below 10% of the stated net amount.
To explain step-by-step:
The remaining toothpaste sample consists of: [.53,.65,.46,.50,.37].
This dataset has a size of n=5, with a mean of M=0.502 and a standard deviation of s=0.102.
The 10% of the advertised content calculates to:
Hypothesis testing regarding the population mean:
The assertion posits that the remaining toothpaste is substantially less than 10% of the advertised net amount.
Thus, the null hypothesis and alternative hypothesis can be stated as follows:
The significance threshold is set at 0.05.
To find the estimated standard error of the mean, we utilize the formula:
Subsequently, we can compute the t-statistic as follows:
The degrees of freedom applicable to this sample size is:
This is a left-tailed test with 4 degrees of freedom resulting in t=-2.148. Thus, the P-value is evaluated as (using a t-table):
Given that the P-value (0.049) falls below the significance threshold (0.05), we conclude that the effect is significant.
The null hypothesis gets rejected.
There is ample evidence that affirms the claim that the remaining toothpaste is considerably below 10% of the stated net content.
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Answer:
A) Maia had 1920 beads more.
B) Maia had 2544 beads at first.
Step-by-step analysis:
Let x denote the beads with Jenny and y for Maia.
The information provided states that Maia possesses 2064 beads more than Jenny, which can be represented mathematically as:
Additionally, after Maia made a necklace with 144 beads, she had five times more beads than Jenny.
This can also be formulated as an equation:
A) Since Maia had 2064 beads more than Jenny before using 144 beads, we calculate her final bead count by subtracting 144 from 2064.
Thus, Maia is left with 1920 beads more than Jenny.
B) To solve this system of linear equations, we will utilize the substitution method.
By inserting equation (1) into equation (2), we arrive at:
Now, let's divide our equation by 4.
Now, we'll substitute x=480 into equation (1) to isolate y.
Conclusively, Maia initially had 2544 beads.
Answer:
Error made by Andrew: He identified incorrect factors based on the roots.
Step-by-step explanation:
The roots of the polynomial consist of: 3, 2 + 2i, 2 - 2i. By the factor theorem, if a is a root of the polynomial P(x), then (x - a) must be a factor of P(x). According to this premise:
(x - 3), (x - (2 + 2i)), (x - (2 - 2i)) represent the factors of the polynomial.
<pBy simplification, we obtain:(x - 3), (x - 2 - 2i), (x - 2 + 2i) as the respective factors.
This is where Andrew's mistake occurred. Factors should always be in the form (x - a), not (x + a). Andrew expressed the complex factors incorrectly, resulting in an erroneous conclusion.
Thus, the polynomial can be expressed as: