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Vinvika [58]
3 years ago
5

Factor 9y2 - 12y + 4. (3 y - 2)(3 y + 2) (3 y - 4)( y + 1) (3 y - 2) 2

Mathematics
1 answer:
lozanna [386]3 years ago
8 0

Answer:

(y - 2)²

Step-by-step explanation:

9y² - 12y + 4 ← is a perfect square of the form

(ax - b)² = a²x² - 2abx + b²

Compare like terms with 9y² - 12y + 4, thus

a² = 9 ⇒ a = 3

b² = 4 ⇒ b = 2 and

- 2ab = - 2 × 3 × 2 = - 12

Thus

9y² - 12y + 4 = (3y - 2)²

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he one‑sample t statistic from a sample of n = 23 observations for the two‑sided test of H 0 : μ = 15 versus H α : μ > 15 has
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Answer:

t = 2.24

The first step is calculate the degrees of freedom, on this case:  

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Since is a one side right tailed test the p value would be:  

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Step-by-step explanation:

Data given and notation  

\bar X represent the mean height for the sample  

s represent the sample standard deviation

n=23 sample size  

\mu_o =15 represent the value that we want to test

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is higher than 15, the system of hypothesis would be:  

Null hypothesis:\mu \leq 15  

Alternative hypothesis:\mu > 15  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

For this case the statistic is given:

t = 2.24

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=23-1=22  

Since is a one side right tailed test the p value would be:  

p_v =P(t_{(22)}>2.24)=0.01776  

And for this case we can conclude that:

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Chris is constructing a diagram for a deck he is restructuring in his backyard. The deck will be in the shape of a square, and h
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4 0
2 years ago
Need help with number 4
zmey [24]
<span>–6(x – 2y) when x = –3 and y = –5
so
</span><span>–6(x – 2y) 
= </span><span>–6(-3 – 2(-5))
= -6(-3 + 10)
= -6(7)
= -42

answer
</span><span>A. -42</span>
3 0
3 years ago
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