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kolezko [41]
3 years ago
12

Consider the following statement. ∀a ∈ Z, (a − 1) a is not an integer. (a) Select the correct negation for this statement. For e

very integer a, a − 1 a is an integer. There is an integer a such that a − 1 a is not an integer. For every integer a, a − 1 a is not an integer. There is an integer a such that a − 1 a is an integer. (b) Is the given statement true or false? If the statement is true, enter TRUE; if the statement is false, enter a value of a that could be used as part of a counterexample that justifies its falseness.
Mathematics
1 answer:
Marta_Voda [28]3 years ago
8 0

Answer:

a) There is an integer a such that  \frac{a-1}{a} is  an integer

b) False

Step-by-step explanation:

Statement : ∀a ∈ Z,    (a − 1) a is not an integer

A) The correct negation will be :

There is an integer a such that  \frac{a-1}{a} is  an integer

B) The Given statement is FALSE because

when we assume the value of a = 1

( a - 1 ) / a = (1 - 1 ) / 1 = 0   ;  which is an integer

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a cell phone company has a basic monthly plan of $40plus $0.45 for many minutes ised over 700. John was charged a total of $48.1
jonny [76]
Cost of month plan = $40

Cost of minutes used = $0.45 after 700 minutes

Total cost = $48.10

Let x be the total minutes used
Total cost = 40 + 0.45(x - 700)

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Form the equation and solve x
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40 + 0.45(x - 700) = 48.10
40 + 0.45x - 315 = 48.10
0.45x - 275 = 48.10
0.45x = 48.10 + 275
0.45x = 323.10
x = 323.10 ÷ 0.45
x = 718

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Answer: John had used 718 mins this month
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8 0
3 years ago
For an experiment comparing two treatment conditions, an independent-measures design would obtain ____ score(s) for each subject
mrs_skeptik [129]

The score(s) that will be obtained respectively in an independent-measures design and repeated-measures design are; 1 and 2

<h3>How to interpret Experiments?</h3>

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P and W are twice-differentiable functions with P(7)=2(W(7)). The line y=9+2.5(x-7) is tangent to the graph of P at x=7. The lin
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Using the product rule, we have

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m'(7) = 7W'(7) + W(7)

The equation of the tangent line to <em>W(x)</em> at <em>x</em> = 7 has all the information we need to determine <em>m'</em> (7).

When <em>x</em> = 7, the tangent line intersects with the graph of <em>W(x)</em>, and

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