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1 year ago

Convert the degree measurement to radians. Express answer as multiple of π: 126°A. 5π/8B. 7π/10C. 6π/9D. 3π/5

Mathematics

1 answer:

malfutka [58]1 year ago

8 0

Answer:

Explanations:

To convert angles from degrees to radians, multiply the angle by π/180

For angle 126°, the equivalent measurement in radian is:

$\begin{gathered} 126\text{ }\times\frac{\pi}{180} \\ \frac{126\pi}{180} \end{gathered}$

Reduce to the lowest term by dividing the numerator and denominator by 18:

$\begin{gathered} \frac{126\pi\div18}{180\div18} \\ \frac{7\pi}{10} \end{gathered}$

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A group of college students were asked about their TV watching habits. Of those surveyed, 28 students watch The Walking Dead, 19

rusak2 [61]

Answer:

39 of the students surveyed watched at least one of the shows.

Step-by-step explanation:

We can solve this question building the Venn's Diagram of these sets.

I am going to say that:

A are those who watch The Walking Dead.

B are those who watch The Blacklist.

C are those who watch Game of Thrones.

We have that:

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

In which a are those who only watch The Walking Dead, $A \cap B$ are those who watch The Walking Dead and The Blacklist, but not Game of Thrones, $A \cap C$ are those who watch The Walking Dead and Game of Thrones, but not The Blacklist, and $A \cap B \cap C$ are those who watch all three of these shows.

By the same logic, we also have that:

$B = b + (A \cap B) + (B \cap C) + (A \cap B \cap C)$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

How many students surveyed watched at least one of the shows?

This is

$T = a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

We have to find these values, starting from the intersection of A, B and C.

8 students who watch all three shows.

This means that

$A \cap B \cap C = 8$

10 watch The Blacklist and Game of Thrones.

This also includes those who watch all three shows. So

$(B \cap C) + (A \cap B \cap C) = 10$

$(B \cap C) = 2$

14 watch The Walking Dead and Game of Thrones

This also includes those who watch all three shows. So

$(A \cap C) + (A \cap B \cap C) = 14$

$(A \cap C) = 6$

16 watch The Walking Dead and The Blacklist

This also includes those who watch all three shows. So

$(A \cap B) + (A \cap B \cap C) = 16$

$(A \cap B) = 8$

24 watch Game of Thrones.

This means that $C = 24$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

$24 = c + 6 + 2 + 8$

$c = 8$

19 watch The Blacklist

This means that $B = 19$

$B = b + (A \cap B) + (B \cap C) + (A \cap B \cap C)$

$19 = b + 8 + 2 + 8$

$b = 1$

28 students watch The Walking Dead

This means that $A = 28$

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

$28 = a + 8 + 6 + 8$

$a = 6$

Finally

$T = a + b + c + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

$T = 6 + 1 + 8 + 8 + 6 + 2 + 8$

$T = 39$

39 of the students surveyed watched at least one of the shows.

5 0

3 years ago

PLZ HELP ME!!

devlian [24]

Hey! I JUST took the k12 TOD quiz for this and the answer is 55!

7 0

3 years ago

How many times does four go into 127

vfiekz [6]

31 times the full decimal is 31.75

8 0

3 years ago

Read 2 more answers

H(x) = 3x + 2; Find h(-5)

Setler [38]

Answer:

h(-5) = -13

Step-by-step explanation:

h(x) = 3x + 2

Let x = -5

h(-5) = 3(-5) +2

= -15 +2

= -13

6 0

3 years ago

Read 2 more answers

Now that you have converted a terminating decimal number into a fraction, try converting a repeating decimal number into a fract

Tom [10]

The first step is to assign the decimal number to a variable.

For the repeating fraction 0.111_1, this would look like
.. x = 0.111_1 . . . . . . . . . . where we use an underscore to identify the following digit(s) as repeating

The next step is to multiply that value by 10 to a power equal to the number of repeating digits. If there is one repeating digit (as here), then you want (10^1)x = 10x.
.. 10x = 1.111_1

The third step is to subtract x from this.
.. 10x -x = 1.111_1 -0.111_1 = 1
.. 9x = 1

And the final step is to divide by the coefficient of x.
.. x = 1/9 . . . . . . this is the value of the repeating decimal fraction.

_____
Here's one that's a little more complicated. It is done the same way.
.. x = 3.254545_45
.. 100x = 325.454545_45
.. 100x -x = 99x = 322.2
.. x = 322.2/99 = 3222/990 = 179/55

3 0

4 years ago