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2 years ago

A term describing a division of observations into four

Mathematics

1 answer:

topjm [15]2 years ago

3 0

Answer:

The name of this term is a quartile.

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Use the figure below to identify angles and segment lengths

slega [8]

So Angle GEN and FED are vertical angles, which means that their angles are congruent. Therefore, Angle FED is 60°

Angle GEN and DEN are a linear pair, which means that they are supplementary angles (add up to 180). To find Angle DEN, we have to form the equation: 60 + DEN = 180

For this, all you have to do is subtract 60 on both sides, and your answer will be: DEN = 120°

6 0

3 years ago

Read 2 more answers

Divide.<br> 14pq4 7p4q4<br> 8r3<br> 2r

svet-max [94.6K]

Dividing is changed to multiplication by inverting the second fraction. So:

7 0

2 years ago

Find the six trig function values of the angle 240*Show all work, do not use calculator

-BARSIC- [3]

Solution:

Given:

$240^0$

To get sin 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, sin 240 will be negative.

$sin240^0=sin(180+60)$

Using the trigonometric identity;

$sin(x+y)=sinx\text{ }cosy+cosx\text{ }siny$

Hence,

$\begin{gathered} sin(180+60)=sin180cos60+cos180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\ \\ Thus, \\ sin180cos60+cos180sin60=0(\frac{1}{2})+(-1)(\frac{\sqrt{3}}{2}) \\ sin180cos60+cos180sin60=0-\frac{\sqrt{3}}{2} \\ sin180cos60+cos180sin60=-\frac{\sqrt{3}}{2} \\ \\ Hence, \\ sin240^0=-\frac{\sqrt{3}}{2} \end{gathered}$

To get cos 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, cos 240 will be negative.

$cos240^0=cos(180+60)$

Using the trigonometric identity;

$cos(x+y)=cosx\text{ }cosy-sinx\text{ }siny$

Hence,

$\begin{gathered} cos(180+60)=cos180cos60-sin180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\ \\ Thus, \\ cos180cos60-sin180sin60=-1(\frac{1}{2})-0(\frac{\sqrt{3}}{2}) \\ cos180cos60-sin180sin60=-\frac{1}{2}-0 \\ cos180cos60-sin180sin60=-\frac{1}{2} \\ \\ Hence, \\ cos240^0=-\frac{1}{2} \end{gathered}$

To get tan 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, tan 240 will be positive.

$tan240^0=tan(180+60)$

Using the trigonometric identity;

$tan(180+x)=tan\text{ }x$

Hence,

$\begin{gathered} tan(180+60)=tan60 \\ tan60=\sqrt{3} \\ \\ Hence, \\ tan240^0=\sqrt{3} \end{gathered}$

To get cosec 240 degrees:

$\begin{gathered} cosec\text{ }x=\frac{1}{sinx} \\ csc240=\frac{1}{sin240} \\ sin240=-\frac{\sqrt{3}}{2} \\ \\ Hence, \\ csc240=\frac{1}{\frac{-\sqrt{3}}{2}} \\ csc240=-\frac{2}{\sqrt{3}} \\ \\ Rationalizing\text{ the denominator;} \\ csc240=-\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\ \\ Thus, \\ csc240^0=-\frac{2\sqrt{3}}{3} \end{gathered}$

To get sec 240 degrees:

$\begin{gathered} sec\text{ }x=\frac{1}{cosx} \\ sec240=\frac{1}{cos240} \\ cos240=-\frac{1}{2} \\ \\ Hence, \\ sec240=\frac{1}{\frac{-1}{2}} \\ sec240=-2 \\ \\ Thus, \\ sec240^0=-2 \end{gathered}$

To get cot 240 degrees:

$\begin{gathered} cot\text{ }x=\frac{1}{tan\text{ }x} \\ cot240=\frac{1}{tan240} \\ tan240=\sqrt{3} \\ \\ Hence, \\ cot240=\frac{1}{\sqrt{3}} \\ \\ Rationalizing\text{ the denominator;} \\ cot240=\frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\ \\ Thus, \\ cot240^0=\frac{\sqrt{3}}{3} \end{gathered}$

5 0

11 months ago

a bag contains 5 grape tootsie pops and 8 chocolate tootsie pops. if juan pulls a chocolate tootsie pop out of the bag and eats

kipiarov [429]

Answer:

= 5 / 12

Step-by-step explanation:

Probability is an outcome of chance. It is a measure of outcomes of events.

To solve the probability of picking a Tootsie Pop, we must comfortably know the contents of the bag.

Number of GRAPE Tootsie pops = 5

Number of CHOCOLATE Tootsie pops= 8

Total number of Tootsie pops = The sum of both Tootsie pops

Total number = 5 + 8

= 13.

Let's note that tge question said , Juan pulls a chocolate Tootsie Pop and eats. The implication is it has reduced the total number of Tootsie Pops left in the bag.

Therefore:

The probability that the next pop he pulls out will be grape will be

Probability (Grape) = 5 / (13 -1)

= 5 / 12

The probability that the next Pop he pulls out will be a grape = 5/12

4 0

3 years ago

Help please I’ll give you 25 points

Ira Lisetskai [31]

Answer: Choice D) $y = \pm \sqrt{x+5}$

The steps to finding the inverse will have us swap x and y. Afterward, we solve for y

$y = x^2 - 5 \\\\x = y^2 - 5 \\\\x+5 = y^2 \\\\y^2 = x+5 \\\\y = \pm \sqrt{x+5} \\\\$

------------------------------

Extra info:

The inverse relation is not a function because of the plus minus. For instance, plugging x = 4 into $y = \pm \sqrt{x+5}$ leads to y = -3 and y = 3 simultaneously. You would have to apply a domain restriction on $y = x^2-5$ to make it a one-to-one function, to make the inverse a function. One possible domain restriction is $x > 0$ which would lead to the inverse function $y = \sqrt{x+5}$

4 0

3 years ago