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3 years ago

The shorter leg of a 30°-60°-90° triangle is 6. What is the length of the other leg?

Mathematics

2 answers:

VLD [36.1K]3 years ago

3 0

The length of the other leg is 12, I think, but I'm not sure. Sorry if it's wrong.

Rina8888 [55]3 years ago

3 0

Answer:

$x=6\sqrt{3}$ units.

Step-by-step explanation:

It is given that shorter leg of a 30°-60°-90° triangle is 6.

In a triangle larger interior angle has larger opposite side and vice versa.

The length of shortest leg is 6 units it means it is opposite to the angle 30°.

Let the length of second leg be x.

In a right angle triangle,

$\tan \theta =\dfrac{\text{Opposite}}{\text{Adjacent}}$

$\tan (30^\circ) =\dfrac{6}{x}}$

$\dfrac{1}{\sqrt{3}}=\dfrac{6}{x}}$

On cross multiplication, we get

$x=6\sqrt{3}$

Hence, the length of the other leg is $x=6\sqrt{3}$ units.

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Given the following winning percentages of the teams in a league (for a single year) compute the within-season standard deviatio

Masja [62]

Answer:

(b) 0.251

Step-by-step explanation:

1. Standard deviation equation:

$SD=\sqrt{\frac{\sum\limits^N_i {(x_{i}-X)^{2} } }{N} }$

Where X is the mean of the data, and N the amount of data. Then, N=5

2. Estimate the Mean:

$X=\frac{0.750+0.750+0.200+0.600+0.200}{5}=\frac{2.5}{5}=0.5\\$

3. Caclulate Standard deviation:

$SD=\sqrt{\frac{{(0.750-0.500)^{2}+(0.750-0.500)^{2}+(0.200-0.500)^{2}+(0.600-0.500)^{2}+(0.200-0.500)^{2} } }{5} }$

$SD=\sqrt{\frac{0.315}{5} }=\sqrt{0.063}\\SD=0.251$

7 0

3 years ago

Please help asap i’m stupid

nevsk [136]

Answer:

Step-by-step explanation:

Say that arc JL going through M is arc E and JL going the other way is arc D

For the angle formed by two tangents, K=(1/2)(E-D)

64=E-D

Furthermore, angle K and central angle JCL (facing toward K) are supplementary, so 180-K=JCL=180-32=148

Thus, as the angles around angle C add up to 360, angle JCL (facing toward M) is 360-148=32+180=212

E is then 212

64=212-D

212-64=D=148

Thus, as JML is an inscribed angle, M=1/2(D)=1/2(148)=74

3 0

3 years ago

John takes out a personal loan for $5,000 at an annual interest rate 7.5%, compounded monthly. He plans to pay off the loan (inc

myrzilka [38]

Answer:

155.53

Step-by-step explanation:

I know where this question is from hahaha

6 0

3 years ago

An employer uses the linear regression equation y = 0.18 x + 320.22 to predict the weekly salary, y, of an employee who sells x

Nata [24]

Answer:

Option C is correct.

Alex earned about $60 more than Joaquin did.

Step-by-step explanation:

The linear regression equation

y = 0.18 x + 320.22

is used to predict the weekly salary, y, of an employee who sells x dollars worth of merchandise.

Joaquin sold $1500 worth of goods. Meaning that x for that week for Joaquin is 1500.

Joaquin' s salary for that week is then given as

y = 0.18x + 320.22

y = 0.18(1500) + 320.22 = 590.22

Hence, Joaquin's salary for that week = $590.22

Alex earns $650 that week. Meaning that y for Alex in that week = 650

y = 0.18x + 320.22

650 = 0.18x + 320.22

0.18x = 650 - 320.22 = 329.78

x = (329.78/0.18) = 1832.1

Hence, Alex sold goods worth $1832.1 that week.

Joaquin sold goods worth $1500

Joaquin earned $590.22

Alex sold goods worth $1832.1

Alex earned $650

From this calculation, it is evident that 'Alex earned about $60 more than Joaquin did' is the correct option as $650 is about $60 more than $590.22

Hope this Helps!!!

7 0

3 years ago

Read 2 more answers

Jake can cut and split a cord of firewood in 9 fewer hours than Dwight can. When they work together, it takes them 6 hours. How

Luba_88 [7]

Answer:

18 hours for Dwight, 9 hours for Jake

Step-by-step explanation:

If J is the time it takes for Jake working alone, and D is the time it takes for Dwight working alone, then:

J = D − 9

Working together, Jake's speed plus Dwight's speed equals 1 cord per 6 hours.

1 / J + 1 / D = 1 / 6

Solve the system of equations by substituting for J:

1 / (D − 9) + 1 / D = 1 / 6

Multiply both sides by D − 9.

1 + (D − 9) / D = (D − 9) / 6

Multiply both sides by D:

D + D − 9 = D (D − 9) / 6

Simplify and solve:

2D − 9 = (D² − 9D) / 6

12D − 54 = D² − 9D

0 = D² − 21D + 54

0 = (D − 3) (D − 18)

D = 3 or 18

Since J = D − 9, D must be greater than 9. So D = 18 and J = 9.

That means it takes Dwight 18 hours working alone, and it takes Jake 9 hours working alone.

3 0

3 years ago