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4 years ago

What is the value of x if 5x+2=5^9

Mathematics

2 answers:

Nata [24]4 years ago

8 0

X=7
When solving for x as an exponent this is what you do. You have to get the bases (in this case 5) to be the same. In this case they already are. When they are the same you can then solve the exponents by themselves. this would x+2=9 you then solve like its a regular equation. x=7

VikaD [51]4 years ago

3 0

Answer:

Option C is correct

Value of x = 7

Step-by-step explanation:

Using the exponent rule:

$x^a = x^b$

⇒a = b

Solve the equation:

$5^{x+2} = 5^9$

Apply the exponent rule we have;

$x+2 = 9$

Subtract 2 from both sides we have;

$x = 7$

Therefore, the value of x is, 7

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Your charged 6% sales tax, you purchase a new bicycle and pay $27 in sales tax. What is the price of the bicycle?

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4 years ago

Read 2 more answers

triangle BCD is a right triangle the length of the hypotenuse is 20 cm the length of one of the legs is 15 cm what is the length

Troyanec [42]

Answer:

13.22

Step-by-step explanation:

The eqtn is

hypotenuse^2 = leg^2 + leg^2

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8 0

3 years ago

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.9 and a mean diameter of 200

ExtremeBDS [4]

Answer:

64.76% probability that the mean diameter of the sample shafts would differ from the population mean by less than .2 inches

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 $\sigma$ , 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:

$\mu = 200, \sigma = 1.9, n = 78, s = \frac{1.9}{\sqrt{78}} = 0.2151$

What is the probability that the mean diameter of the sample shafts would differ from the population mean by less than .2 inches?

This is the pvalue of Z when X = 200 + 0.2 = 200.2 subtracted by the pvalue of Z when X = 200 - 0.2 = 199.8. So

X = 200.2

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

By the Central Limit Theorem

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

$Z = \frac{200.2 - 200}{0.2151}$

$Z = 0.93$

$Z = 0.93$ has a pvalue of 0.8238

X = 199.8

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

$Z = \frac{199.8 - 200}{0.2151}$

$Z = -0.93$

$Z = -0.93$ has a pvalue of 0.1762

0.8238 - 0.1762 = 0.6476

64.76% probability that the mean diameter of the sample shafts would differ from the population mean by less than .2 inches

4 0

3 years ago

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Brrunno [24]

Answer:

The graph is attached

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Option C is likely the answer

A graph showing a range of negative three to two on the x and y axes. A solid line with arrows at both ends passes through the x axis at two and runs parallel to the y axis. The graph is shaded to the right of the line.

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3 years ago