Help me please!<br> 1+9^4=?

timofeeve [1]

The question above was not written properly

Complete Question

Lacey and Haley are rewriting expressions in an equivalent, simpler form.

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

Answer:

a) Haley is correct, Lacey simplified wrongly.

b) Haley is incorrect

Step-by-step explanation:

a. Haley simplified x³⋅ x² and got

x⁵

Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

For Question a, when it comes to simplifying algebraic expression that has to do with powers, there are certain rules that should be followed.

For example

x^a × x^b = x^(a + b)

For Haley, she simplified x³⋅ x² and got

x⁵

She is correct because this follows the product rule of powers or exponents above

= x³⋅ x² = x³+² = x⁵

For Lacey she is wrong because:

x³ + x² ≠ x⁵

x³ + x² when simplified as quadratic equation = x²(x + 1)

b. Haley simplifies 3⁵⋅ 4⁵ and gets the result 12^10, but Lacey is not sure.

Is Haley correct? Be sure to justify your answer.

For question b, when we have two distinct or different numbers with the same power(exponents) the rule states that:

x^a × y^a = (x × y)^a = (xy)^a

Haley is simplified wrongly. She did not apply the rule above

Haley simplified 3⁵⋅ 4⁵ = (3 × 4) ⁵+⁵

= 12^10, this is wrong.

The correct answer according to the rule =

3⁵⋅ 4⁵ = (3 × 4) ⁵ = 12⁵

Therefore,

3⁵⋅ 4⁵ ≠ 12^10

3⁵⋅ 4⁵ = 12⁵

Haley is wrong.

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The web logs of a certain website show that the average number of hits in an hour is 75 with a standard deviation equal to 8.6.

Wittaler [7]

Answer:

a) There is a 10.75% probability of observing less than 60 hits in an hour.

b) The 99th percentile of the distribution of the number of hits is 95.21 hits.

c) There is a 24% probability of observing between 80 and 90 hits an hour

Step-by-step explanation:

Problems of normally distributed samples 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

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

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. The sum of the probabilities is decimal 1. So 1-pvalue is the probability that the value of the measure is larger than X.

In this problem, we have that

The web logs of a certain website show that the average number of hits in an hour is 75 with a standard deviation equal to 8.6, so $\mu = 75, \sigma = 8.6$ .