1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Delvig [45]
3 years ago
9

Help I will be marking brainliest!!!

Mathematics
1 answer:
Keith_Richards [23]3 years ago
4 0
<h3>Answer:  A.  18*sqrt(3)</h3>

=============================================

Explanation:

We'll need the tangent rule

tan(angle) = opposite/adjacent

tan(R) = TH/HR

tan(30) = TH/54

sqrt(3)/3 = TH/54 ... use the unit circle

54*sqrt(3)/3 = TH .... multiply both sides by 54

(54/3)*sqrt(3) = TH

18*sqrt(3) = TH

TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer

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

An alternative method:

Triangle THR is a 30-60-90 triangle.

Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.

The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.

Now use the pythagorean theorem

a^2 + b^2 = c^2

(TH)^2 + (HR)^2 = (TR)^2

(x)^2 + (54)^2 = (2x)^2

x^2 + 2916 = 4x^2

2916 = 4x^2 - x^2

3x^2 = 2916

x^2 = 2916/3

x^2 = 972

x = sqrt(972)

x = sqrt(324*3)

x = sqrt(324)*sqrt(3)

x = 18*sqrt(3) which is the length of TH.

A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.

You might be interested in
People tend to evaluate the quality of their lives relative to others around them (Frieswijk et al., 2004). In one study, resear
Alborosie

Answer:

Step-by-step explanation:

Hello!

Research.

n=9 frail elderly were interview and compared to a fictitious person who was worse off then the interviewee, a life-satisfaction score was determined for each person.

18, 23, 24, 22, 19, 27, 23, 26, 25

Assuming that the population average score is μ= 20, the researchers think that the elderly in the sample are more or less satisfied than others in the general population.

a. You have the information of one sample, assuming this sample has a normal distribution and each elderly interviewed is independent, then the t-test of choice is a one-sample t-test.

b. and c. If you say that the elderly are "more or less" satisfied than the others, this means that they are either as satisfied as to the general population or not satisfied as to the general population. Symbolically:

H₀: μ = 20

H₁: μ ≠ 20

This is a two-tailed test, meaning, you will have two critical regions.

d.  

α: 0.05

Left critical value: t_{n-1;/\alpha 2} = t_{8; 0.025}= -2.306

Right critical value: t_{n-1;1-\alpha /2} = t_{8;0.975} = 2.306

e.

t_{H_0}= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~t_{n-1}

X[bar]= 23

S= 3

t_{H_0}= \frac{23-20}{\frac{3}{\sqrt{9} } }= 3

f.

Considering that the calculated t-value is greater than the right critical value, the decision is to reject the null hypothesis, so using a significance level of 5% you can conclude that the average life-satisfaction score of the elderly is different than 20.

I hope it helps!

7 0
3 years ago
48 L = ____ ML steps plz
Oliga [24]

Ok there are 48000 mL in 48L.

7 0
3 years ago
Which table represents a function with a slope of 1/2 and a y-intercept of 4
Volgvan

Answer:D

Step-by-step explanation: trust me ima sophomore use this for help y=1/2x+4 then x value change it to the number in the x section then if the y appears just like in the box the y section it’s correct

8 0
2 years ago
What is the value of 12 more than the quiotent of a number of and two decreased by 4 when n is 4
liberstina [14]

Answer:

<h2>10</h2>

Step-by-step explanation:

"12 more than the quiotent of a number n of and two decreased by 4"

\left(\dfrac{n}{2}-4\right)+12

Simplify:

\left(\dfrac{n}{2}-4\right)+12=\dfrac{n}{2}-4+12=\dfrac{n}{2}+8

Put n = 4 to the expresssion:

\dfrac{4}{2}+8=2+8=10

4 0
3 years ago
Which of the
kondor19780726 [428]

The pic is attached.

7 0
3 years ago
Read 2 more answers
Other questions:
  • What type of graph displays information by using a column vertically or horizontally? A) Pictograph B) Scatterplot C) Bar Graph
    12·1 answer
  • 8.235 x 10-4 = ? standard form
    5·2 answers
  • I just want to know if I'm correct on that question.
    10·1 answer
  • Given that cos 0 = and sin 0 = - 15<br> What is the value of tan0?
    14·1 answer
  • Every integer is a whole number
    12·1 answer
  • What is 62.5% of 8<br> A 40<br> B 5<br> C 3<br> D 6.25
    9·2 answers
  • HELP ME I WILL GIVE BRAINLIEST
    7·1 answer
  • Can anyone help me with this???
    7·2 answers
  • 9. If you invest $2000 an account that pays 8 % interest
    7·1 answer
  • 4. Solve for x and y
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!