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masya89 [10]
3 years ago
11

Factor quadratic trinomials 27x^2-90x+27

Mathematics
1 answer:
igor_vitrenko [27]3 years ago
8 0
27x^2-81x-9x+27      In this case, just in your mind multiply 27 (coefficient of x^2) by the constant value 27(the end value of the quadratic trinomial). Then find factors that give you the value -90 when you add and 729 (27*27) when you multiply.

Factorise the values
 27x( x-3)-9(x-3)

Which will give you

(27x-9)(x-3)
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A certain shampoo is available in two sizes. A 23.7-ounce bottle costs $4.97 . A 33.8 -ounce bottle costs $7.48 . Find the unit
Eddi Din [679]

Answer:

23.7 ounce = 20 cents per ounce

33.8 ounce = 22 cents per ounce

The 23.7 ounce bottle is a better deal because it is only 20 cents per ounce, rather than 22 cents per ounce.

6 0
3 years ago
Suppose 41%41% of American singers are Grammy award winners. If a random sample of size 860860 is selected, what is the probabil
Doss [256]

Answer:

99.72% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question:

n = 860, p = 0.41

So

\mu = 0.41, s = \sqrt{\frac{0.41*0.59}{860}} = 0.0168

What is the probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%?

This is the pvalue of Z when X = 0.41 + 0.05 = 0.46 subtracted by the pvalue of Z when X = 0.41 - 0.05 = 0.36. So

X = 0.46

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.46 - 0.41}{0.0168}

Z = 2.98

Z = 2.98 has a pvalue of 0.9986

X = 0.36

Z = \frac{X - \mu}{s}

Z = \frac{0.36 - 0.41}{0.0168}

Z = -2.98

Z = -2.98 has a pvalue of 0.0014

0.9986 - 0.0014 = 0.9972

99.72% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%.

7 0
3 years ago
Please help will give brainliest
mylen [45]
3 ,4,5 .....................
8 0
3 years ago
Write the following inequality in slope-intercept form. −8x + 4y ≥ −52
Shkiper50 [21]
-8x+4y<span>≥-52 

Add 8x to both sides: 
</span>-8x+8x+4y≥8x-52 

Now we have: 
4y≥8x-52 

Divide everything by 4. 

Final answer: 
y≥4x-13


4 0
4 years ago
Read 2 more answers
A parallelogram has a base of 14 centimeters and a height of 20 centimeters.What is the area of the parralegram
Drupady [299]

Answer:

44444444444444444444444444444444444444444444467

Step-by-step explanation:

5 0
4 years ago
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