Solve (2^2x+1)-9(2^x)+4=0

Mathematics

1 answer:

BartSMP [9]3 years ago

8 0

Answer:

x₁ = - 1

x₂ = 2

Step-by-step explanation:

2²ˣ⁺¹ - 9ₓ2ˣ + 4 = 0

2²ˣₓ2 - 9ₓ2ˣ + 4 = 0

2ˣ = n

2n² - 9n + 4 = 0

2n² - n - 8n + 4 = 0

n(2n - 1) - 4(2n - 1) = 0

(2n - 1)(n -4) = 0

2n - 1 = 0 => n₁ = 1/2

n - 4 = 0 => n₂ = 4

2ˣ = 1/2 => 2ˣ = 2⁻¹ => x₁ = - 1

2ˣ = 4 => 2ˣ = 2² => x₂ = 2

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Consider a normal distribution curve where the middle 85 % of the area under the curve lies above the interval ( 8 , 14 ). Use t

NeTakaya

Answer:

$\mu = 11$

$\sigma = 2.08$

Step-by-step explanation:

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.

Middle 85%.

Values of X when Z has a pvalue of 0.5 - 0.85/2 = 0.075 to 0.5 + 0.85/2 = 0.925

Above the interval (8,14)

This means that when Z has a pvalue of 0.075, X = 8. So when $Z = -1.44, X = 8$ . So