A bag of trail mix weighs 1 and 1/3 lbs.How much will 2 and 1/2 bags weigh

Select all of the potential solution(s) of the equation 2log5x = log54.

Vanyuwa [196]

Answer:

x = ±2

Step-by-step explanation:

A equation is given to us , which is ,

$\longrightarrow 2log_5(x) = log_5 4$

From properties of logarithm we know that ,

$\longrightarrow alog\ m = log \ m^a$

Applying this to LHS , we have ;

$\longrightarrow log_5 x^2 = log_5 4$

Now the bases of logarithm on LHS and RHS is same . On comparing , we have ;

$\longrightarrow x^2 = 4$

Put square root on both sides,

$\longrightarrow x =\sqrt{4}$

Simplify ,

$\longrightarrow \underline{\underline{ x =\pm 2 }}$

This is the required answer.

6 0

2 years ago

What it the related equation for x+58=6

Rom4ik [11]

The answer for this problem would be -52 because when you do 58-6 it give you 52 so i tried -52+58 and what did it give me 6 so -52 is your answer hope that this helps and here is a tip: negative is the only way to go down in addtion just to let you know

6 0

3 years ago

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Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1

svet-max [94.6K]

Answer:

a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

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 normal distributions can be solved using 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.

Mean of 8.0 ounces and a standard deviation of 1.1 ounces.

This means that $\mu = 8, \sigma = 1.1$

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?

$n = 5$ means that $s = \frac{1.1}{\sqrt{5}} = 0.4919$

This probability is the pvalue of Z when X = 9.3. So

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

By the Central Limit Theorem

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

$Z = \frac{9.3 - 8}{0.4919}$

$Z = 2.64$

$Z = 2.64$ has a pvalue of 0.9959

0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?

$n = 6$ means that $s = \frac{1.1}{\sqrt{6}} = 0.4491$

This probability is 1 subtracted by the pvalue of Z when X = 9. So

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

$Z = \frac{9 - 8}{0.4491}$

$Z = 2.23$

$Z = 2.23$ has a pvalue of 0.9871

1 - 0.9871 = 0.0129

0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

8 0

3 years ago

Help please algebra

Sveta_85 [38]

It's the one in the top right corner. Since the inequality says 'greater than or equal to' the line has to be bold and the shaded area has to be above the line. Hope this helped!

5 0

3 years ago

What is 1.086 rounded to the nearest whole number

Andru [333]

1.086 rounded to the nearest whole number would remain as one.

This is due to the fact that the tenths place does not have any number, and due to this the whole number would remain one.

If the number were to change, it would look as the following:

1.5 rounded to the nearest whole number 2.

3 0

3 years ago

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