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3 years ago

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Which of the following is the quotient of the rational expressions shown below? 2x-3/5x^2 divided by x-5/3x-1

2 answers:

Vikentia [17]3 years ago

7 0

Find the attachment bellow.

First, form the expression.

(2x-3)/(5x²) ÷ (<span>x-5)/(3x-1)

= (2x-3)/(5x</span>²) ×(3x-2)/(x-5)

= ((2x-3)(3x-1))/((5x²)(x-5))

= (6x²-11x+3)/(5x³-25x²)

Kamila [148]3 years ago

6 0

The expression in fraction form will be:

$\frac{ \frac{2x-3}{5 x^{2} } }{ \frac{x-5}{3x-1} }$

The denominator can be multiplied to the numerator by taking its reciprocal as shown below:

$\frac{2x-3}{5 x^{2} } * \frac{3x-1}{x-5} \\ \\ 
= \frac{(2x-3)(3x-1)}{5 x^{2}(x-5) }$

There are no common factors, so the expression can not be simplified any further.

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A new security system needs to be evaluated in the airport. The probability of a person being a security hazard is 4%. At the ch

ivolga24 [154]

Answer:

(a) 0.9412

(b) 0.9996 ≈ 1

Step-by-step explanation:

Denote the events a follows:

$P$ = a person passes the security system

$H$ = a person is a security hazard

Given:

$P (H) = 0.04,\ P(P^{c}|H^{c})=0.02\ and\ P(P|H)=0.01$

Then,

$P(H^{c})=1-P(H)=1-0.04=0.96\\P(P|H^{c})=1-P(P|H)=1-0.02=0.98\\$

(a)

Compute the probability that a person passes the security system using the total probability rule as follows:

The total probability rule states that: $P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})$

The value of P (P) is:

$P(P)=P(P|H)P(H)+P(P|H^{c})P(H^{c})\\=(0.01\times0.04)+(0.98\times0.96)\\=0.9412$

Thus, the probability that a person passes the security system is 0.9412.

(b)

Compute the probability that a person who passes through the system is without any security problems as follows:

$P(H^{c}|P)=\frac{P(P|H^{c})P(H^{c})}{P(P)} \\=\frac{0.98\times0.96}{0.9412} \\=0.9996\\\approx1$

Thus, the probability that a person who passes through the system is without any security problems is approximately 1.

7 0

3 years ago

Circle O has a circumference of 36π cm.

ehidna [41]

Answer:

r = 18 cm

Step-by-step explanation:

The formula for the circumference of a circle is 2πr.

Hence,

2πr = 36π

r = 18 cm

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2 years ago

A 48 fluid ounce container orange juice cost $2.40. 60 fluid ounce container of orange juice cost $3.60. Which is the better buy

Allushta [10]

48 fluid ounce it is $0.40 per fl oz, while the other one is $0.60 per fl oz

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3 years ago

Calculate the constant of proportionality, k, for the given table.

yan [13]

Answer:

k = y/x

Step-by-step explanation:

1/5, 2/10, 3/15 . . . all equal to 1/5 which is what the value of k is; 'k' stands for constant of proportionality

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3 years ago

Is 0.23 or 2.3% greater?

Vaselesa [24]

Answer:

0.23

Step-by-step explanation:

If you convert 0.23 into a percent, it becomes 23%, which is more than 2.3%.

<em>Hope that helps!</em>

<em>-Sabrina</em>

5 0

3 years ago