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4 years ago

Order of expression and simplify expressions

1 answer:

3 0

Answer:uidelines called the order of operations, which outlines the order in which parts of an expression must be simplified.

ORDER OF OPERATIONS

When simplifying mathematical expressions perform the operations in the following order:

1. Parentheses and other Grouping Symbols

Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.

2. Exponents

Simplify all expressions with exponents.

3. Multiplication and Division

Perform all multiplication and division in order from left to right. These operations have equal priority.

4. Addition and Subtraction

Perform all addition and subtraction in order from left to right. These operations have equal priority

Step-by-step explanation:

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3 years ago

Which polynomial is prime? 7x2 – 35x + 2x – 10 9x3 + 11x2 + 3x – 33 10x3 – 15x2 + 8x – 12 12x4 + 42x2 + 4x2 + 14

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Which estimation could be used to make sure the answer is reasonable?

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Answer: The amount left over was 4.05 L.

Estimation: 3.15 + 4.75 is about 7.

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The amount left over was about 3 L.

This is incorrect because 3.15+4.75 is closer to 8 than 7.

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8 L – 4 L = 4 L

The amount left over was a little less than 4 L.

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The correct answer is B.

Answer: The amount left over was 3.95 L.

Estimation: 3.15 + 4.75 is about 8.

8 L – 4 L = 4 L

The amount left over was a little less than 4 L.

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3 years ago

A municipal bond service has three rating categories (A, B, and C). Suppose that in the past year, of the municipal bonds issued

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Answer:

(a) The probability that the new municipal bond issued will receive an A rating given that it was issued by a city is 0.196.

(b) Thus, the probability of municipal bonds issued by suburbs is 0.325.

Step-by-step explanation:

The data provided is as follows:

P (A) = 0.70

P (B) = 0.20

P (C) = 0.10

P (c | A) = 0.50

P (s | A) = 0.40

P (r | A) = 0.10

P (c | B) = 0.60

P (s | B) = 0.20

P (r | B) = 0.20

P (c | C) = 0.90

P (s | C) = 0.05

P (r | C) = 0.05

(a)

The Bayes' theorem states that the conditional probability of an event Y $_{i}$ given that another event X has already occurred is:

$P(Y|X)=\frac{P(X|Y)P(Y)}{\sum\limits_{i} {P(X|Y_{i})P(Y_{i})}}$

Compute the probability that the new municipal bond issued will receive an A rating given that it was issued by a city as follows:

$P(A|c)=\frac{P(c|A)P(A)}{P(c|A)P(A)+P(c|B)P(B)+P(c|C)P(C)}$

$=\frac{(0.50\times 0.70)}{(0.50\times 0.70)+(0.60\times 0.20)+(0.10\times 0.90)}\\\\=\frac{0.35}{0.56}\\\\=0.196$

Thus, the probability that the new municipal bond issued will receive an A rating given that it was issued by a city is 0.196.

(b)

The law of total probability states that:

$P(X)=\sum\limits_{i} {P(X|Y_{i})}$

Compute the probability of municipal bonds issued by suburbs as follows:

$P(s)=P(s|A)P(A)+P(s|B)P(B)+P(s|C)P(C)$

$=(0.40\times 0.70)+(0.20\times 0.20)+(0.10\times 0.05)\\\\=0.28+0.04+0.005\\\\=0.325$

Thus, the probability of municipal bonds issued by suburbs is 0.325.

3 0

4 years ago