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3 years ago

Find two consecutive even integers such that the sum of the larger and three times the smaller is 234

Mathematics

1 answer:

viva [34]3 years ago

7 0

Represent even numbers as "2n" since each is a multiple of 2.

Represent odd numbers as "2n+1" since each is one more than an even.

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Your problem:

smaller # : 2n

larger #: 2n+2

-------------------

EQUATION:

2n+2 + 3(2n) = 234

8n = 232

n = 29

---------

smaller = 2*29 = 58

larger = 2n+2 = 60

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When plotting points on the coordinate plane below, which point would lie on the x-axis?

nordsb [41]

If you plot the points you can easily find the answer. (X,Y) The x-axis is the horizontal line and the y-axis is the vertical line.

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3 years ago

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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.

5 0

3 years ago

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enyata [817]

Answer:

addition prop of equality

Step-by-step explanation:

youre welcome

4 0

3 years ago

In AABC, mZA=x, mZB = 2x +2, and

AnnyKZ [126]

Answer:

x = 29

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180

x + 2x + 2 + 3x + 4 = 180, that is

6x + 6 = 180 ( subtract 6 from both sides )

6x = 174 ( divide both sides by 6 )

x = 29

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3 years ago

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Sales prices of baseball cards from the 1960s are known topossess a skewed-right distribution with a mean sale price of $5.25and

Serga [27]

Answer:

c. Skewed-right with a mean of $5.25 and a standard error of$0.28

Step-by-step explanation:

As we have given that Sales prices of baseball cards have a right-skewed distribution with a mean $5.25 and a standard deviation is $2.80.

Now, We know that if standard deviation = σ

then, standard error = $\frac{\sigma}{\sqrt{n}}$

As, we have standard deviation = $2.80

then standard error will be $\frac{2.80}{\sqrt{100}}$

⇒ Standard error = $0.28

Hence, Option (c) is the correct option.

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3 years ago