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3 months ago

Complete the table of inputs and outputs for the given function g(x)=3-8x.

Mathematics

1 answer:

babunello [11.8K]3 months ago

6 0

Respuesta:

A continuación se detallan las respuestas a sus preguntas.

Explicación paso a paso:

A partir de la pregunta mencionada anteriormente,

g(x) = 3 – 8x

Por lo tanto, podemos completar la tabla presentada en la pregunta de la siguiente manera:

1. Encuentro de x

g(x) = 0

x =?

g(x) = 3 – 8x

0 = 3 – 8x

Unimos términos semejantes

0 – 3 = – 8x

– 3 = – 8x

Dividimos ambos lados por –8

x = – 3 / –8

x = 3/8

2. Encuentro de g(x)

x = 0

g(x) =.?

g(x) = 3 – 8x

g(x) = 3 – 8(0)

g(x) = 3 – 0

g(x) = 3

3. Encuentro de x

g(x) = – 5

x =?

g(x) = 3 – 8x

– 5 = 3 – 8x

Unimos términos semejantes

– 5 – 3 = – 8x

– 8 = – 8x

Dividimos ambos lados por – 8

x = – 8 / – 8

x = 1

4. Encuentro de g(x)

x = 3

g(x) =.?

g(x) = 3 – 8x

g(x) = 3 – 8(3)

g(x) = 3 – 24

g(x) = – 21

Resumen

x >>>>>>>>>>>>>>> g(x)

3/8 >>>>>>>>>>>>> 0

0 >>>>>>>>>>>>>>> 3

1 >>>>>>>>>>>>>>>> – 5

3 >>>>>>>>>>>>>>>> – 21

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A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given b

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Answer:

The amount of ovens that must be produced in a week to earn a $1610 profit is 70.

Step-by-step explanation:

Given:

A small-appliance manufacturer determines the profit P (in dollars) from producing x microwave ovens weekly by the formula:

$P=\frac{1}{10}x(300-x)$

with 0 ≤ x ≤ 200.

The target profit is $1610

So, set P = 1610, then solve for x:

$1610=\frac{1}{10}x(300-x)$

Multiply both sides by 10:

$1610\cdot \:10=\frac{1}{10}x\left(300-x\right)\cdot \:10$

$16100=x\left(300-x\right)$

$16100=300x-x^2$

$-x^2+300x-16100=0$

Next, factor the quadratic:

$(x-70)(x-230)=0$

Solving for x gives:

$x=70,x=230$

Since x=230 is outside the domain 0 ≤ x ≤ 200, we discard it.

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3 months ago

Return to the credit card scenario of Exercise 12 (Section 2.2), and let C be the event that the selected student has an America

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Answer:

A. P = 0.73

B. P(A∩B∩C') = 0.22

C. P(B/A) = 0.5

P(A/B) = 0.75

D. P(A∩B/C) = 0.4

E. P(A∪B/C) = 0.85

Step-by-step explanation:

Denote A as the event of a student having a Visa card, B as the event of holding a MasterCard, and C as the event of owning an American Express card. Additionally, let A' indicate the event of not having a Visa card, B' signify not having a MasterCard, and C denote the event of not possessing an American Express card.

Thus, with the given probabilities, we can determine the following probabilities:

P(A∩B∩C') = P(A∩B) - P(A∩B∩C) = 0.3 - 0.08 = 0.22

Here, P(A∩B∩C') refers to the chance that a student has both a Visa and MasterCard but does not own an American Express, P(A∩B) indicates the probability that a student possesses both a Visa and a MasterCard, and P(A∩B∩C) represents the likelihood that a student has a Visa, MasterCard, and American Express. Similarly, we can find:

P(A∩C∩B') = P(A∩C) - P(A∩B∩C) = 0.15 - 0.08 = 0.07

P(B∩C∩A') = P(B∩C) - P(A∩B∩C) = 0.1 - 0.08 = 0.02

P(A∩B'∩C') = P(A) - P(A∩B∩C') - P(A∩C∩B') - P(A∩B∩C)

= 0.6 - 0.22 - 0.07 - 0.08 = 0.23

P(B∩A'∩C') = P(B) - P(A∩B∩C') - P(B∩C∩A') - P(A∩B∩C)

= 0.4 - 0.22 - 0.02 - 0.08 = 0.08

P(C∩A'∩A') = P(C) - P(A∩C∩B') - P(B∩C∩A') - P(A∩B∩C)

= 0.2 - 0.07 - 0.02 - 0.08 = 0.03

A. The likelihood that the selected student holds at least one of the three card types is calculated as follows:

P = P(A∩B∩C) + P(A∩B∩C') + P(A∩C∩B') + P(B∩C∩A') + P(A∩B'∩C') +

P(B∩A'∩C') + P(C∩A'∩A')

P = 0.08 + 0.22 + 0.07 + 0.02 + 0.23 + 0.08 + 0.03 = 0.73

B. The probability that the chosen student possesses both a Visa and a MasterCard without an American Express card can be represented as P(A∩B∩C') equaling 0.22

C. P(B/A) represents the chance that a student holds a MasterCard provided they have a Visa. This is calculated as:

P(B/A) = P(A∩B)/P(A)

By substituting in the values, we find:

P(B/A) = 0.3/0.6 = 0.5

In a similar manner, P(A/B) represents the probability a student has a Visa given they possess a MasterCard, calculated as:

P(A/B) = P(A∩B)/P(B) = 0.3/0.4 = 0.75

D. For a student with an American Express card, the likelihood they also hold both a Visa and a MasterCard is expressed as P(A∩B/C), calculated as:

P(A∩B/C) = P(A∩B∩C)/P(C) = 0.08/0.2 = 0.4

E. If the student has an American Express card, the probability they possess at least one of the other two card types is denoted as P(A∪B/C), computed as:

P(A∪B/C) = P(A∪B∩C)/P(C)

Where P(A∪B∩C) = P(A∩B∩C)+P(B∩C∩A')+P(A∩C∩B')

Consequently, P(A∪B∩C) equals 0.08 + 0.07 + 0.02 = 0.17

Ultimately, P(A∪B/C) equals:

P(A∪B/C) = 0.17/0.2 =0.85

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2 months ago