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Naily [24]
3 years ago
6

Replace ? with an expression that will make the equation valid.

Mathematics
1 answer:
AlexFokin [52]3 years ago
6 0

Answer:

4x³

Step-by-step explanation:

d/dx ln(x⁴ + 7) = 1/(x⁴ + 7) × _?

To obtain the missing expression, let us simplify d/dx ln(x⁴ + 7). This can be obtained as follow:

Let y = ln (x⁴ + 7)

Let u = (x⁴ + 7)

Therefore,

ln(x⁴ + 7) = ln u

Thus,

y = ln u

dy/du = 1/u

Next, we shall determine du/dx. This is illustrated below:

u = (x⁴ + 7)

du/dx = 4x³

Finally, we shall determine dy/dx of ln (x⁴ + 7) as follow:

dy/dx = dy/du × du/dx

dy/du = 1/u

du/dx = 4x³

dy/dx = 1/u × 4x³

But:

u = (x⁴ + 7)

Therefore,

dy/dx = 1/(x⁴ + 7) × 4x³

Thus, the missing expression is 4x³

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Answer:

A) zero; cannot

Step-by-step explanation:

In line with the principle of rational expectations, expectation errors are unpredictable. The expectations of all available information will not differ from the optimal projections.The word optimal projection is inexorably intertwined with the best guess in rational expectations theory.

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3 years ago
You toss two 6-sided dice one right after the other. What is the probability of rolling a 3, then rolling a different odd number
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1/18.
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Answer:

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Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Suppose that 10% of the undergraduates at a certain university are foreign students, and that 25% of the graduate students are f
Deffense [45]

Answer:

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Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Foreign

Event B: Undergraduate.

There are four times as many undergraduates as graduate students

So 4/5 = 80% are undergraduate students and 1/5 = 20% are graduate students.

Probability the student is foreign:

10% of 80%

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10% of 80%. So

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0.6154 = 61.54% probability that the student is an undergraduate

8 0
3 years ago
Find the measure of angle C of a triangle ABC, if: d m∠A = 60°+α, m∠B = 60°−α
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Answer:

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