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ikadub [295]
3 years ago
10

Simplify: Negative two and one-third minus negative ten and one-sixth(20 points)

Mathematics
1 answer:
slamgirl [31]3 years ago
8 0

Given:

The expression is

-2\dfrac{1}{3}-\left(-10\dfrac{1}{6}\right)

To find:

The value of the expression.

Solution:

We have,

-2\dfrac{1}{3}-\left(-10\dfrac{1}{6}\right)=-2\dfrac{1}{3}+10\dfrac{1}{6}

Convert the mixed fraction in improper fraction.

=-\dfrac{2\times 3+1}{3}+\dfrac{10\times 6+1}{6}

=-\dfrac{6+1}{3}+\dfrac{60+1}{6}

=-\dfrac{7}{3}+\dfrac{61}{6}

Taking LCM, we get

=\dfrac{-2(7)+61}{6}

=\dfrac{-14+61}{6}

=\dfrac{42}{6}

Convert it into mixed fraction.

=\dfrac{6(7)+5}{6}

=7\dfrac{5}{6}

Therefore, the correct option is C.

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Susan needs 228 ounces of fruit juice for a party. She is choosing between two brands of juice. She finds the unit rate of each
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Answer:

"Brand A costs approximately $0.21 per ounce, and Brand B costs approximately $0.18 per ounce."

In order to find the rounded cost per one item (in this case, per one ounce) Susan needs to divide the total price between the number of units and after that, round the result obtained up to the nearest cent.

Therefore:

Brand A

2.55$/12 ounces= 0.2125 $/ounce

As the third decimal digit, 2, is closer to 0 than to 9, then we maintain the second decimal digit as 1.

The price per unit of brand A after rounding it up is 0.21 $ per ounce

Brand B

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2 years ago
The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that
wlad13 [49]

Answer:

a) 0.0821

b) 0.0111

c) 0.0041

Step-by-step explanation:

Exponential distribution:

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

f(x) = \lambda e^{-\lambda x}

In which \lambda 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^{-\lambda x}

Either it lasts more 5 years or less, or it survives more than 5 years. The sum of the probabilities of these events is decimal 1. So

P(X \leq 5) + P(X > 5) = 1

In all 3 cases, we want P(X > 5). So

P(X > 5) = 1 - P(X \leq 5)

In which

P(X \leq 5) = 1 - e^{-5\lambda}

(a) lambda=.5

P(X \leq 5) = 1 - e^{-5*0.5} = 0.9179

P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9179 = 0.0821

(b) lambda=0.9

P(X \leq 5) = 1 - e^{-5*0.9} = 0.9889

P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9889 = 0.0111

(c) lambda=1.1

P(X \leq 5) = 1 - e^{-5*1.1} = 0.9959

P(X > 5) = 1 - P(X \leq 5) = 1 - 0.9959 = 0.0041

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