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4 years ago

If the equation of a parabola is y = 9(x - 2)2 + v, and its vertex is (2, -4), what is the value of v in the equation?

1 answer:

5 0

If the vertex of the parabola is (h,k) the equation of the parabola will be
y = a(x - h)² + k

From the question (h,k) is (2,-4) then the equation of the parabola will be
y = a(x - 2)² + (-4)

Compare the equation
y = a(x - 2)² + (-4)
with
y = 9(x - 2)² + v
The value of a is 9 and the value of v is (-4).

The answer of the question ⇒ the value of v is (-4)

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In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces

nadya68 [22]

Answer:

a) 0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less

b) 0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c) 0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours

d) 86 should have a battery life of at least 9 hours.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

$P(X \leq x) = \frac{x - a}{b-a}$

The probability of being higher than x is:

$P(X > x) = \frac{b - x}{b-a}$

The probability of being between c and d is:

$P(c \leq X \leq d) = \frac{d-c}{b-a}$

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.

This means that $a = 8.5, b = 12$

a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

$P(X \leq x) = \frac{x - a}{b-a}$

$P(X \leq 10) = \frac{10 - 8.5}{12 - 8.5} = 0.4286$

0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less.

b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

$P(X > x) = \frac{b - x}{b-a}$

$P(X > 11) = \frac{12 - 11}{12 - 8.5} = 0.2857$

0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours

c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

$P(c \leq X \leq d) = \frac{d-c}{b-a}$

$P(9.5 \leq X \leq 11.5) = \frac{11.5 - 9.5}{12 - 8.5} = 0.5714$

0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours.

d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

Proportion of iPad Minis with a battery life of at least 9 hours.

$P(X > 11) = \frac{12 - 9}{12 - 8.5} = 0.8571$

Out of 100:

0.8571*100 = 85.71

To the nearest whole number

86 should have a battery life of at least 9 hours.

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3 years ago

A housekeeper had 4/5 of a spray bottle of a cleaning solution. He used 1/8 of the solution in a day.How much of the bottle did

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Answer:

0.1

Step-by-step explanation:

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3 years ago

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Patrick wanted to gather data about the cost of joining a community pool in his area. He plotted the data and determined that th

ohaa [14]

Answer:

The y-intercept is 40. This is the cost of registration ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- Patrick wanted to gather data about the cost of joining a community

pool in his area

- He plotted the data and determined that the average community

pool membership cost consists of a one-time registration fee and

a monthly fee

∴ The cost consists of two parts:

# Part A: one-time registration fee, it is a fixed amount not depend on

any other condition

# Part B: monthly fee, it depends on the number of months

- He modeled that by the equation y = 15 x + 40, where

# y is the cost for the membership

# 15 is the monthly fee

# x is the number of months

# 40 is the one-time registration

- The form of the equation is y = mx + c, where c is the y-intercept

∴ The y-intercept in the equation y = 15 x + 40 is 40

∴ The y-intercept is the one-time registration fee

* The y-intercept is 40. This is the cost of registration

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3 years ago

An angle is double its complement. find the angle and the complement

Alona [7]

Complement means the other angle that will sum up to 90°

So:

x + 2x = 90°
3x = 90
x = 30°

So, it is 30° and 30 * 2°, or 60°

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Calculate the middle number between 1-5 and 7.1

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Answer:

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Step-by-step explanation:

1-5=-4 (7.1+1)-5=3.1

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