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2 years ago

Is 9/81 a rational number? why or why not.

Mathematics

1 answer:

soldi70 [24.7K]2 years ago

4 0

Answer:

9/81=1/9 The fraction 1/9 is a rational number. All rational numbers can be written as a fraction showing the relationship between two integers.

Step-by-step explanation:

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There are 200 students in eleventh grade high school class. There are 40 students in the soccer team and 50 students in the bask

bekas [8.4K]

Answer:

P(A) = 0.2

P(B) = 0.25

P(A&B) = 0.05

P(A|B) = 0.2

P(A|B) = P(A) = 0.2

Step-by-step explanation:

P(A) is the probability that the selected student plays soccer.

Then:

$P(A)=\dfrac{40}{200}=0.2$

P(B) is the probability that the selected student plays basketball.

Then:

$P(B)=\dfrac{50}{200}=0.25$

P(A and B) is the probability that the selected student plays soccer and basketball:

$P(A\&B)=\dfrac{10}{200}=0.05$

P(A|B) is the probability that the student plays soccer given that he plays basketball. In this case, as it is given that he plays basketball only 10 out of 50 plays soccer:

$P(A|B)=\dfrac{P(A\&B)}{P(B)}=\dfrac{10}{50}=0.2$

P(A | B) is equal to P(A), because the proportion of students that play soccer is equal between the total group of students and within the group that plays basketball. We could assume that the probability of a student playing soccer is independent of the event that he plays basketball.

4 0

2 years ago

You found $6.60 on the ground at school, all in nickels, dimes, and quarters. you have twice as many quarters as dimes and 42 co

Veseljchak [2.6K]

Let the number of nickels found be n, the number of dimes be d and the number of quarters be q.

i) "you have twice as many quarters as dimes and 42 coins in all."

means that 2d=q, and n+d+q=42

we can reduce the number of unknowns by substituting q with 2d:

n+d+q=42
n+d+2d=42
n+3d=42

We can write all n, d and q in terms of d as follows:

there are n=42-3d nickels, d dimes and q=2d quarters.

ii) In total there are $6.60 dollars,

1 nickel = 5 cent = $0.05
1 dime = 10 cent = $0.1
1 quarter = 25 cent = $0.25

thus

(42-3d)*0.05 + d*0.1 +2d*0.25= $6.60

2.1 - 0.15d+0.1d+0.5d=6.60

2.1+0.45d=6.6

0.45d=6.6-2.1=4.5

d=4.5/0.45=10

iii)

so, there are 10 dimes, 2d=2*10=20 quarters and 42-3d=42-3*10=12 nickels.

Answer: 10 dimes, 20 quarters, 12 nickels

8 0

2 years ago

Select the correct answer from each drop-down menu. Polygon ABCD goes through a sequence of rigid transformations to form polygo

Viktor [21]

Answer:

The sequence of transformations involved is a reflection across the x axis, followed by a reflection across the y = x line

Step-by-step explanation:

The polygon ABCD is shown in the image attached. The coordinates of the polygon are A(-6, 6), B(-4, 6), C(-4, 4), D(-6, 2), while the polygon A'B'C'D' is at A'(-6, -6), B'(-6, -4), C'(-4, -4), D'(-2, -6)

A transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, dilation and rotation.

If a point O(x, y) is reflected across the x axis, the new coordinate is O'(x, -y).

If a point O(x, y) is reflected across the y = x line, the new coordinate is O'(y, x)

Hence if polygon ABCD is reflected across the x axis, the new coordinates are A*(-6, -6), B*(-4, -6), C*(-4, -4), D*(-6, -2). If a reflection across the y = x line, the new coordinates are A'(-6, -6), B'(-6, -4), C'(-4, -4), D'(-2, -6)

8 0

2 years ago

Which composition of transformations maps figure RSTUV to figure R"S"T"U"V"?

Sergeu [11.5K]

Answer:

option: B is correct

A reflection across line n followed by a 270° rotation about point P.

Step-by-step explanation:

Clearly from the figure we could see that the graph is first reflected across the given line n such that we obtain the figure R'S'T'V'U' and then it is rotated 270° across the point P so that we obtain the figure R"S"T"U"V".

Hence, option B is correct.

( A reflection across line n followed by a 270° rotation about point P )

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2 years ago

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Happy is four times as old as Grumpy. The sum of their age is 100. How old are Happy and<br> Grumpy?

lys-0071 [83]

Answer:

grumpy is 20 happy is 80

Step-by-step explanation:

5 0

1 year ago

Read 2 more answers