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Shkiper50 [21]
3 years ago
7

provide a counterexample (specific values of a,b, etc. which make the statement false) for each of the following statements. Ass

ume that a,b,c,d ∊ ℤ for all statements. 1. If a I bc, then a I b or a I c. 2. If ab I cd , then a I b and c I d. 3. If a I b^2 , then a I b.
Mathematics
1 answer:
ivolga24 [154]3 years ago
8 0

Answer:

1. a=3, b = 2, c = 1.

2. a=2, b=3, c=4, d=6.

3. a = 9, b = 3.

Step-by-step explanation:

1.  3 | 21   is a counterexample  because 3 does not divide into  2 or 1.

2. 23 | 46 is a counterexample because 2 does not divide into 3.

3. 9 | 3^2 is a counterexample because 9 does not divide into 3.

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If two lines are parallel to each other. Does that mean they are equal to each other as well?
fomenos

Answer:

No.

Step-by-Step Explanation:

When two lines are parallel, they might or might not be equal. It is not necessary that they should be equal.

See the triangle below in which two lines are parallel to each other.

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3 years ago
Which would be included in a probability model for rolling a cube with faces numbered 1 through 6. Select all that apply.
scoundrel [369]

Answer:

Step-by-step explanation:

8 0
3 years ago
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Solve 10/12 - 3/8 show your solution as an equation​
elena55 [62]

Answer:

11/24

Step-by-step explanation:

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator. Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1. The two fractions now have like denominators so you can subtract the numerators.

This fraction cannot be reduced.

Therefore the answer is 11/24

7 0
3 years ago
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What is six more than twice a number x
natta225 [31]

Answer:

2x + 6

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six more than that would be +6

5 0
3 years ago
I will give lots of points please help
aalyn [17]

Answer:

a)  81π  in³

b)  27  in³

c)  divide the volume of the slice of cake by the volume of the whole cake

d)  10.6%

e)  see explanation

Step-by-step explanation:

<h3><u>Part (a)</u></h3>

The cake can be modeled as a <u>cylinder </u>with:

  • diameter = 9 in
  • height = 4 in

\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in

\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}

\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}

<h3><u>Part (b)</u></h3>

\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}

If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.

\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}

<h3><u>Part (c)</u></h3>

The volume of each slice of cake is 27 in³.

The volume of the whole cake is 81π in³.

To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:

\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}

<h3><u>Part (d)</u></h3>

Probability is approximately 10.6%  (see above for calculation)

<h3><u>Part (e)</u></h3>

If the four slices of cake are cut and passed out <em>before </em>anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, <u>until the marble is found</u>.  So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.

3 0
2 years ago
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