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2 years ago

10

3) Jacob has 4 granola bars. He cuts them into pieces that are 1/3 of a bar each. After he cuts the 4 bars, how many pieces does

Jacob have?

1 answer:

klio [65]2 years ago

5 0

Answer:

12

Step-by-step explanation:

if each bar is cut into 3 pieces, then we multiply 4 by 3 to get 12.

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Find the smallest relation containing the relation {(1, 2), (1, 4), (3, 3), (4, 1)} that is:

professor190 [17]

Answer:

Remember, if B is a set, R is a relation in B and a is related with b (aRb or (a,b))

1. R is reflexive if for each element a∈B, aRa.

2. R is symmetric if satisfies that if aRb then bRa.

3. R is transitive if satisfies that if aRb and bRc then aRc.

Then, our set B is $\{1,2,3,4\}$ .

a) We need to find a relation R reflexive and transitive that contain the relation $R1=\{(1, 2), (1, 4), (3, 3), (4, 1)\}$

Then, we need:

1. That 1R1, 2R2, 3R3, 4R4 to the relation be reflexive and,

2. Observe that

1R4 and 4R1, then 1 must be related with itself.
4R1 and 1R4, then 4 must be related with itself.
4R1 and 1R2, then 4 must be related with 2.

Therefore $\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(4,1),(4,2)\}$ is the smallest relation containing the relation R1.

b) We need a new relation symmetric and transitive, then

since 1R2, then 2 must be related with 1.
since 1R4, 4 must be related with 1.

and the analysis for be transitive is the same that we did in a).

Observe that

1R2 and 2R1, then 1 must be related with itself.
4R1 and 1R4, then 4 must be related with itself.
2R1 and 1R4, then 2 must be related with 4.
4R1 and 1R2, then 4 must be related with 2.
2R4 and 4R2, then 2 must be related with itself

Therefore, the smallest relation containing R1 that is symmetric and transitive is

$\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}$

c) We need a new relation reflexive, symmetric and transitive containing R1.

For be reflexive

1 must be related with 1,

2 must be related with 2,

3 must be related with 3,

4 must be related with 4

For be symmetric

since 1R2, 2 must be related with 1,
since 1R4, 4 must be related with 1.

For be transitive

Since 4R1 and 1R2, 4 must be related with 2,
since 2R1 and 1R4, 2 must be related with 4.

Then, the smallest relation reflexive, symmetric and transitive containing R1 is

$\{(1,1),(2,2),(3,3),(4,4),(1,2),(1,4),(2,1),(2,4),(3,3),(4,1),(4,2),(4,4)\}$

5 0

2 years ago

The expected number of typographical errors on any page of a certain magazine is 0.2. What is the probability that a certain pag

zhuklara [117]

Answer:

The probability of 2 or more errors is 0.018.

Step-by-step explanation:

Let <em>X</em> = number of typographical errors on a page of a certain magazine.

The expected number of errors is, <em>λ</em> = 0.2.

The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 0.2.

The probability mass function of <em>X </em>is:

$P(X=x)=\frac{e^{-0.2}0.2^{x}}{x!};\ x=0,1,2,3...$

Compute the probability of 2 or more errors as follows:

P (X ≥ 2) = 1 - P (X < 2)

= 1 - P (X = 0) - P (X = 1)

$=1-\frac{e^{-0.2}0.2^{0}}{0!}-\frac{e^{-0.2}0.2^{1}}{1!}\\=1-0.81873-0.16375\\=0.01752\\\approx0.018$

Thus, the probability of 2 or more errors is 0.018.

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2 years ago

Rena is building a 1:1801:1801, colon, 180 scale model of a real castle. Her model has a rectangular base that is 333 feet wide

liubo4ka [24]

Answer:

388,800 ft^2.

Step-by-step explanation:

Scale = 1 : 180

Actual length, Ls = 180 × 4

= 720 ft

Actual width, Bs = 180 × 3

= 540 ft

Area of a rectangle = Ls × Bs

= 540 × 720

= 388,800 ft^2.

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2 years ago

A car travels 15 kilometers west in 10 minutes. After reaching the destination, the car travels back to the starting point, agai

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Your answer to your question is C

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2 years ago

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B) Find the principal that yields an interest of Rs 2240 at the rate of 10% p.a. in 3

murzikaleks [220]

Answer:

1,500

Step-by-step explanation:

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2 years ago