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1 year ago

Name the property used in each step.

Mathematics

1 answer:

jarptica [38.1K]1 year ago

5 0

Answer:

$\begin{aligned}ab(a+b) & = (ab)a+(ab)b & & \textsf{Distributive Property of Addition} \\& = a(ab)+(ab)b & & \textsf{Commutative Property of Multiplication} \\& = (a \cdot a)b + a(b \cdot b) & & \textsf{Associative Property of Multiplication}\\& = a^2b+ab^2 & & \textsf{Property of Exponents}\end{aligned}$

Step-by-step explanation:

Distributive Property of Addition

Multiplying a number by a group of numbers added together is the same as multiplying each number separately.

Addition: a(b + c) = ab + ac

Subtraction: a(b - c) = ab – ac

Commutative Property

Changing the order or position of two numbers does not change the end result.

Applies to addition and multiplication only.

Addition: a + b = b + a

Multiplication: a × b = b × a

Associative Property

Grouping of numbers by parentheses in a different way does not affect their sum or product.

Applies to addition and multiplication only.

Addition: (a + b) + c = a + (b + c) = (a + c) + b

Multiplication: (a × b) × c = a × (b × c) = (a × c) × b

Property of Exponents

The exponent of a number shows how many times it should be multiplied by itself.

a × a × a = a³

b × b × b × b = b⁴

Learn more about Property Laws here:

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The time between arrivals of customers at the drive-up window of a bank follows an exponential probability distribution with a m

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Answer:

a) 50.34% probability that the arrival time between customers will be 7 minutes or less.

b) 24.42% probability that the arrival time between customers will be between 3 and 7 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Mean of 10 minutes:

This means that $m = 10, \mu = \frac{1}{10} = 0.1$

A. What is the probability that the arrival time between customers will be 7 minutes or less?

$P(X \leq x) = 1 - e^{-\mu x}$

$P(X \leq 7) = 1 - e^{-0.1*7} = 0.5034$

50.34% probability that the arrival time between customers will be 7 minutes or less.

B. What is the probability that the arrival time between customers will be between 3 and 7 minutes?

$P(3 \leq X \leq 7) = P(X \leq 7) - P(X \leq 3)$

$P(X \leq x) = 1 - e^{-\mu x}$

$P(X \leq 7) = 1 - e^{-0.1*7} = 0.5034$

$P(X \leq 3) = 1 - e^{-0.1*3} = 0.2592$

$P(3 \leq X \leq 7) = P(X \leq 7) - P(X \leq 3) = 0.5034 - 0.2592 = 0.2442$

24.42% probability that the arrival time between customers will be between 3 and 7 minutes

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3 years ago

plz hurryA 3-column table with 6 rows. Column 1 is labeled Number Rolled with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Obse

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Answer:

The complete table is shown below.

Step-by-step explanation:

The data provided is:

Number Rolled Observed Frequency Relative frequency

1 10 $\frac{10}{60}=\frac{1}{6}$

2 12 $\frac{12}{60}=\frac{1}{5}$

3 10 $\frac{10}{60}=\frac{1}{6}$

4 10 $\frac{10}{60}=\frac{1}{6}$

5 8 $\frac{8}{60}=\frac{2}{15}$

6 10 $\frac{10}{60}=\frac{1}{6}$

TOTAL 60 1

The complete table is shown above.

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Answer:

y intercept (0, 4)

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I hope this is good enough:

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2 years ago

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Answer:

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Step-by-step explanation:

You can't factor the expression evenly, so use the quadratic formula.

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