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3 years ago

The complement of an angle is one-sixth the measure of the supplement of the angle. What is the measure of the complement angle?

Mathematics

2 answers:

cestrela7 [59]3 years ago

7 0

Answer:

The measure of the complement angle is $18\°$

Step-by-step explanation:

Let

x-----> the angle

we know that

The complement of an angle is equal to $(90-x)\°$

The supplement of an angle is equal to $(180-x)\°$

we have

The complement of an angle is one-sixth the measure of the supplement of the angle

$(90-x)\°=(1/6)(180-x)\°$

solve for x

$(540-6x)\°=(180-x)\°$

$(6x-x)=(540-180)\°$

$(5x)=(360)\°$

$x=72\°$

Find the measure of the complement angle

$(90-x)\°$ ------> $(90-72)=18\°$

Alona [7]3 years ago

6 0

Answer:

18⁰

Step-by-step explanation:

Angle = x

Complement = 90 - x

Supplement = 180 - x

Given:

90 - x = 1/6 × (180 - x)

540 - 6x = 180 - x

5x = 360

x = 72

Complement = 90 - 72 = 18⁰

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stepladder [879]

Answer:

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Step-by-step explanation:

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3 years ago

In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2,..., 36. To play the game, a metal ball is spun a

Oxana [17]

Answer:

$E(X)=-0.0526$

$Sd(X)=5.763$

Step-by-step explanation:

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

The variance of a random variable Var(X) is the expected value of the squared deviation from the mean of X, E(X).

And the standard deviation of a random variable X is just the square root of the variance.

Let X be a random variable which denotes the money you may win or lose on each spin.

In the game of roulette, a wheel consists of 38 slots. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. If the number of the slot the ball falls into matches the number you selected, we win $35; otherwise we lose $1. So we have just one possibility to win and 37 of lose on an individual game.

___________________________

X P(X)

___________________________

35 1/38

-1 37/38

___________________________

In order to calculate the expected value we can use the following formula:

$E(X)=\sum_{i=1}^n X_i P(X_i)$

And if we use the values obtained we got:

$E(X)=(35)*(\frac{1}{38})+(-1)(\frac{37}{38})=-0.0526$

In order to find the standard deviation we need to find first the second moment, given by :

$E(X^2)=\sum_{i=1}^n X^2_i P(X_i)$

And using the formula we got:

$E(X^2)=(35^2)*(\frac{1}{38})+((-1)^2)(\frac{37}{38})=33.211$

Then we can find the variance with the following formula:

$Var(X)=E(X^2)-[E(X)]^2 =33.211-(-0.0526)^2 =33.208$

And then the standard deviation would be given by:

$Sd(X)=\sqrt{Var(X)}=\sqrt{33.208}=5.763$

4 0

3 years ago

Rebecca is a Texas resident and she plans to attend Texas Tech for all 4 years of college. She has a yearly scholarship of $10,0

andrezito [222]

Answer:

To complete the required $m dollars for her college, she needs $(m - 60,000).

Step-by-step explanation:

Suppose Rebecca needs $m to complete her college education,

because she has a yearly scholarship of $10,000, she would have $10,000 × 4 = $40,000 for the four years she would spend in college.

Together with her savings of $20,000, she has $20,000 + $40,000 = $60,000 in total.

Therefore to complete the required $m dollars for her college, she needs $(m - 60,000).

5 0

3 years ago

a new rectangular park is planned.it will be 3/4 kilometer long and have an area of 3/8 square kilometers. how many kilometers w

kakasveta [241]

<em>The word usage in last sentence of the question is not well presented. However, I can understand that you intend to solve for the width of the park</em>

Answer:

$Width = 2\ km$