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3 years ago

Does anyone know how to solve 54 = 36 - 9b

Mathematics

2 answers:

Klio2033 [76]3 years ago

7 0

The answer would be -2

vodomira [7]3 years ago

6 0

Answer:

-2

Step-by-step explanation:

54 - 36 = 18

18 % -9 =-2

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3 years ago

For f(x)=2x+1 and g(x)=x^2-7, find (f.g)(x)

hram777 [196]

Option C (in the figure) is correct.

Step-by-step explanation:

We need to find (f.g)(x)

Given that $f(x)=2x+1\\g(x)= x^2-7$

Now finding (f.g)(x)

$(f.g)(x)= f(x).g(x)$

$(f.g)(x)= (2x+1)(x^2-7)\\(f.g)(x)=2x(x^2-7)+1(x^2-7)\\(f.g)(x)=2x^3-14x+x^2-7\\(f.g)(x)=2x^3+x^2-14x-7$

So, $(f.g)(x)=2x^3+x^2-14x-7$

Option C (in the figure) is correct.

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3 years ago

For 10.932, which digit is in the tenths place?

antiseptic1488 [7]

The 9 is in the tenths place.

6 0

4 years ago

Read 2 more answers

How do I do this????

Georgia [21]

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4 years ago

The mean output of a certain type of amplifier is 183 watts with a variance of 121. If 78 amplifiers are sampled, what is the pr

koban [17]

Answer:

0.8278 = 82.78% probability that the mean of the sample would differ from the population mean by less than 1.7 watts

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation(which is the square root of the variance) $\sigma$ , 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.

In this problem, we have that:

$\mu = 183, \sigma = \sqrt{121} = 11, n = 78, s = \frac{11}{\sqrt{78}} = 1.2455$

Probability that the mean of the sample would differ from the population mean by less than 1.7 watts?

This is the pvalue of Z when X = 183+1.7 =184.7 subtracted by the pvalue of Z when X = 183 - 1.7 = 181.3.

X = 184.7

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

By the Central Limit Theorem

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

$Z = \frac{184.7 - 183}{1.2455}$

$Z = 1.365$

$Z = 1.365$ has a pvalue of 0.9139

X = 181.3

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

$Z = \frac{181.3 - 183}{1.2455}$

$Z = -1.365$

$Z = -1.365$ has a pvalue of 0.0861

0.9139 - 0.0861 = 0.8278

0.8278 = 82.78% probability that the mean of the sample would differ from the population mean by less than 1.7 watts

4 0

3 years ago