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
skad [1K]
3 years ago
15

Given that tan theta = square root of 3 over 4, and 0 < theta < pi over 2, what is the exact value of cot theta?

Mathematics
1 answer:
Natali5045456 [20]3 years ago
5 0

Answer:

\frac{4\sqrt{3} }{3}

Step-by-step explanation:

4sqrt3/3

You might be interested in
Someone please answer
Doss [256]

Answer:

59.6

Step-by-step explanation:

7 0
3 years ago
. upper left chamber is enlarged, the risk of heart problems is increased. The paper "Left Atrial Size Increases with Body Mass
Sonbull [250]

Answer:

Part 1

(a) 0.28434

(b) 0.43441

(c) 29.9 mm

Part 2

(a) 0.97722

Step-by-step explanation:

There are two questions here. We'll break them into two.

Part 1.

This is a normal distribution problem healthy children having the size of their left atrial diameters normally distributed with

Mean = μ = 26.4 mm

Standard deviation = σ = 4.2 mm

a) proportion of healthy children have left atrial diameters less than 24 mm

P(x < 24)

We first normalize/standardize 24 mm

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (24 - 26.4)/4.2 = -0.57

The required probability

P(x < 24) = P(z < -0.57)

We'll use data from the normal probability table for these probabilities

P(x < 24) = P(z < -0.57) = 0.28434

b) proportion of healthy children have left atrial diameters between 25 and 30 mm

P(25 < x < 30)

We first normalize/standardize 25 mm and 30 mm

For 25 mm

z = (x - μ)/σ = (25 - 26.4)/4.2 = -0.33

For 30 mm

z = (x - μ)/σ = (30 - 26.4)/4.2 = 0.86

The required probability

P(25 < x < 30) = P(-0.33 < z < 0.86)

We'll use data from the normal probability table for these probabilities

P(25 < x < 30) = P(-0.33 < z < 0.86)

= P(z < 0.86) - P(z < -0.33)

= 0.80511 - 0.37070 = 0.43441

c) For healthy children, what is the value for which only about 20% have a larger left atrial diameter.

Let the value be x' and its z-score be z'

P(x > x') = P(z > z') = 20% = 0.20

P(z > z') = 1 - P(z ≤ z') = 0.20

P(z ≤ z') = 0.80

Using normal distribution tables

z' = 0.842

z' = (x' - μ)/σ

0.842 = (x' - 26.4)/4.2

x' = 29.9364 = 29.9 mm

Part 2

Population mean = μ = 65 mm

Population Standard deviation = σ = 5 mm

The central limit theory explains that the sampling distribution extracted from this distribution will approximate a normal distribution with

Sample mean = Population mean

¯x = μₓ = μ = 65 mm

Standard deviation of the distribution of sample means = σₓ = (σ/√n)

where n = Sample size = 100

σₓ = (5/√100) = 0.5 mm

So, probability that the sample mean distance ¯x for these 100 will be between 64 and 67 mm = P(64 < x < 67)

We first normalize/standardize 64 mm and 67 mm

For 64 mm

z = (x - μ)/σ = (64 - 65)/0.5 = -2.00

For 67 mm

z = (x - μ)/σ = (67 - 65)/0.5 = 4.00

The required probability

P(64 < x < 67) = P(-2.00 < z < 4.00)

We'll use data from the normal probability table for these probabilities

P(64 < x < 67) = P(-2.00 < z < 4.00)

= P(z < 4.00) - P(z < -2.00)

= 0.99997 - 0.02275 = 0.97722

Hope this Helps!!!

7 0
3 years ago
Two lines, C and D, are represented by the following equations:
guapka [62]

Answer:

(−2, 3), because both lines pass through this point

Step-by-step explanation:

The meaning of "solution to the system of equations" is that both lines intersect at the solution point. That is, they both pass through that point.

8 0
3 years ago
Read 2 more answers
-4 1/5+3 2/3+ -1 2/5
Paul [167]

Answer:

-1.9

Step-by-step explanation:

I rounded it to the tenth

8 0
3 years ago
Read 2 more answers
21. Name an angle that is adjacent to O ZDGB<br> O ZEGC<br> O ZEGF<br> O ZCGB<br> O ZFGA<br> O ZEGT<br> O ZDGE
olga2289 [7]

Answer:

the answer is D hope this helps you

6 0
2 years ago
Other questions:
  • Use the picture to answer the question. Angle ABC is rotated 50° around point D . What is the measure of angle A'B'C' ?
    14·2 answers
  • Evaluate −6 − (−4).<br> −10<br> −2<br> 24<br> 2
    8·2 answers
  • 9-(6+3)= what is the answer ​
    9·2 answers
  • A local grocery store charges for oranges based on weight as shown in the graph below. Find the price (dollars per kilogram) of
    15·2 answers
  • Please help me with this problem. image attached.
    15·1 answer
  • 16,321,407.23 to the nearest tenth
    13·1 answer
  • Find two decimals that are equivalent to (4x10)+(7x1/100). Write decimals in the box
    5·1 answer
  • 4+5<img src="https://tex.z-dn.net/?f=4%2B5%5Cfrac%7Bx%7D%7By%7D%203x%5E%7B2%7D%20-%203x%5E%7B2%7D" id="TexFormula1" title="4+5\f
    8·2 answers
  • HEEEEEEEEEEELLLLLLLLLLPPPPPPP!!!!!!!!! QUICK!!!!!!
    14·1 answer
  • A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 deg
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!