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3 years ago

Prove that the inequality (a+1)·(a+1)>(a−1)·(a−1) is not true for some values of a.

Mathematics

1 answer:

Effectus [21]3 years ago

7 0

Explanation:

Consider the case a = -1. Then the expression becomes ...

(-1+1)(-1+1) > (-1-1)(-1-1) . . . . test case

0·0 > (-2)(-2) . . . . . simplified a bit

0 > 4 . . . . . . . . NOT TRUE

_____

If we subtract the right side from both sides, the inequality becomes ...

(a+1)(a+1) -(a-1)(a-1) > 0

a² +2a +1 -(a² -2a +1) > 0

4a > 0

a > 0

The inequality is only true for positive values of "a". For a ≤ 0, the inequality will not be true.

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Use compatible number to find two estimates that the quotient is between 1,624 divided by 3

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The correct answer is 541.2 to be exact

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3 years ago

The dot plot represents the length of practice time in minutes for the math competition. Explain how the outlier of the data aff

lidiya [134]

Using statistical concepts, it is found that:

The mean practice time decreases because of the outlier.

The median practice time does not change because of the outlier.

The range increases because of the oulier.

<h3>What are the mean, the median and the range of a data-set?</h3>

The mean is the sum of all observations divided by the number of observations.

The median is the middle value, the value that separates the upper 50% from the bottom 50%.

The range is the difference between the largest value and the smallest.

From their concepts above, we have that the mean and the range are influenced by outliers.

In this problem, the outlier is at the low end, of 15, hence:

The mean practice time decreases because of the outlier.

The median practice time does not change because of the outlier.

The range increases because of the oulier.

More can be learned about statistical concepts at brainly.com/question/24732674

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2 years ago

What are interger coordinates

nordsb [41]

Answer:

Integer coordinates are pairs of integers that are used to determine points in a grid, relative to a special point called the origin. The origin has coordinates (0,0). Any other point in the grid has a pair of coordinates (x,y).

Step-by-step explanation:

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3 years ago

Read 2 more answers

Given the figure below, find the values of x and z.

slava [35]

Answer:

x = 5 z = 94

Step-by-step explanation:

12x + 26 = 86

12x = 60

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360 - 172 = 188

z = 188 : 2 = 94

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3 years ago

Imagine you have a pair of six-sided dice. What's the

Ksivusya [100]

Answer:

The probability of rolling a seven or rolling an even number as the sum of the two dice is $\frac{2}{3}$

Step-by-step explanation:

Given : Imagine you have a pair of six-sided dice.

To find : What's the probability of rolling a seven or rolling an even number as the sum of the two dice?

Solution :

Rolling a pair of six-sided dice,

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Rolling a seven as the sum of the two dice are (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

Rolling an even number as the sum of the two dice are (1,1),(1,3),(1, 5),(2, 2),(2, 4),(2, 6) ,(3, 1),(3, 3),(3, 5),(4, 2),(4, 4),(4, 6),(5, 1),(5, 3),(5, 5),(6, 2),(6, 4),(6, 6).

Favorable outcome of rolling a seven or rolling an even number as the sum of the two dice are (1,6),(2,5),(3,4),(4,3),(5,2),(6,1), (1,1),(1,3),(1, 5),(2, 2),(2, 4),(2, 6) ,(3, 1),(3, 3),(3, 5),(4, 2),(4, 4),(4, 6),(5, 1),(5, 3),(5, 5),(6, 2),(6, 4),(6, 6) - 24

The probability is given by,

$\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total outcome}}$

$\text{Probability}=\frac{24}{36}$

$\text{Probability}=\frac{2}{3}$

Therefore, the probability of rolling a seven or rolling an even number as the sum of the two dice is $\frac{2}{3}$

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3 years ago