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2 years ago

13

Using Colored Counters, where yellow counters are positive and red counters are negative, model 5 (use 7 chips)

1 answer:

vova2212 [387]2 years ago

8 0

Answer:

Step-by-step explanation:

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Prove the following statements: (a) For every integer x, if x is even, then for every integer y, xy is even. (b) For every integ

Murrr4er [49]

Answer and Step-by-step explanation:

(a) Given that x and y is even, we want to prove that xy is also even.

For x and y to be even, x and y have to be a multiple of 2. Let x = 2k and y = 2p where k and p are real numbers. xy = 2k x 2p = 4kp = 2(2kp). The product is a multiple of 2, this means the number is also even. Hence xy is even when x and y are even.

(b) in reality, if an odd number multiplies and odd number, the result is also an odd number. Therefore, the question is wrong. I assume they wanted to ask for the proof that the product is also odd. If that's the case, then this is the proof:

Given that x and y are odd, we want to prove that xy is odd. For x and y to be odd, they have to be multiples of 2 with 1 added to it. Therefore, suppose x = 2k + 1 and y = 2p + 1 then xy = (2k + 1)(2p + 1) = 4kp + 2k + 2p + 1 = 2(kp + k + p) + 1. Let kp + k + p = q, then we have 2q + 1 which is also odd.

(c) Given that x is odd we want to prove that 3x is also odd. Firstly, we've proven above that xy is odd if x and y are odd. 3 is an odd number and we are told that x is odd. Therefore it follows from the second proof that 3x is also odd.

3 0

3 years ago

Can someone help me please

m_a_m_a [10]

Answer:

d

Step-by-step explanation:

5.53eqbhabsfnbhjvfwj

4 0

3 years ago

masha68 [24]

Answer:

Step-by-step explanation:

Volume of the figure = Base area * height

Base area:

Base area = area of trpezium + area of triangle

<u />

<u>Trapezium:</u>

a, b area the length of parallel sides and h is the height of trapezium.

a = 8 m ; b = 5 m & h = 3 m

$\boxed{ \text{ Area of trapezium = $\dfrac{(a +b)*h}{2} $}}$

$=\dfrac{(8+5)*3}{2}\\\\\\=\dfrac{13*3}{2}\\\\\\= \dfrac{39}{2}\\\\\\= 19.5 \ m^{2}$

<u>Triangle:</u>

height = 4 m & base = 8 m

$\boxed{\text{Area of triangle =$\dfrac{1}{2}*base*height$}}$

$=\dfrac{1}{2}*8*4\\\\\\= 4*4\\\\= 16 \ m^{2}$

Base area = 19.5 + 16

= 35.5 m²

Volume of the figure = Base area * height

= 35.5 * 14

= 497 m³

8 0

3 years ago

At an outpatient mental health clinic, appointment cancellations occur at a mean rate of 1.5 per day on a typical Wednesday. Let

Kamila [148]

Answer:

a) Cancellations are independent and similar to arrivals.

b) 22.31% probability that no cancellations will occur on a particular Wednesday

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

Mean rate of 1.5 per day on a typical Wednesday.

This means that $\mu = 1.5$

(a) Justify the use of the Poisson model.

Each wednesday is independent of each other, and each wednesday has the same mean number of cancellations.

So the answer is:

Cancellations are independent and similar to arrivals.

(b) What is the probability that no cancellations will occur on a particular Wednesday

This is P(X = 0).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-1.5}*(1.5)^{0}}{(0)!} = 0.2231$

22.31% probability that no cancellations will occur on a particular Wednesday

5 0

3 years ago

What is the decrease of a right angle pls help i suck at math NVM ITS 90

Nookie1986 [14]

Answer: 90 degrees

Step-by-step explanation:

7 0

2 years ago