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lord [1]
3 years ago
6

Suppose someone tells you that she has a triangle with sides having lengths 2.6, 8.1, and 8.6. Is this a right triangle? Why or

why not? Is there an angle in the triangle larger than 90 degree?
Mathematics
1 answer:
Elodia [21]3 years ago
8 0
First you check for Pythagoras'  Theorem.

Is  8.6² = 8.1²  + 2.6²  ? 
  
8.1²  + 2.6² = 65.61 + 6.76 = 72.37
8.6² =  73.96

8.1²  + 2.6²  ≠ 8.6² 

Since Pythagoras' Theorem is not satisfied it is not a right angled triangle.

The longest side is 8.6,  let's find the angle facing the longest side 8.6.

By cosine formula  CosA =  (b² + c² - a²) / (2bc)

CosA =  (2.6² + 8.1² - 8.6²) / (2*2.6*8.1) = -1.59/42.12 = -0.0377

A = Cos inverse (-0.0377) = 92.1 degrees

So there is  an angle is greater than 90 degrees.
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Which expression are equivalent to the one below? 4^3 * 4^x
nignag [31]

Step-by-step explanation:

=  {4}^{3}  \times  {4}^{x}

=  {4}^{3 + x}

=  {4}^{x + 3}

5 0
2 years ago
A group of freshmen at a local university consider joining the equestrian team. Thirty‑five percent of students choose Western r
lesantik [10]

Answer:

a) Option D) 0.75

b) Option D) 0.3

Step-by-step explanation:

We are given the following in the question:

Percentage of students who choose Western riding = 35%

P(w) = 0.35

Percentage of students who choose dressage= 45%

P(d) = 0.45

Percentage of students who choose jumping = 50%

P(j) = 0.50

Percentage of students who choose both dressage and jumping = 20%

P(d \cap j) = 0.20

Percentage of students who choose Western and dressage = 10%

P(w \cap d) = 0.10

Percentage of students who choose Western and jumping = 0%

P(w \cap j) = 0

Thus, we can say

P(w \cap j \cap d) = 0

Formula:

P(A \cup B) = P(A) + P(B) - P(A \cap B)

a) P(student chooses dressage or jumping)

P(d \cup j) = P(d) + P(j) -p(d \cap j)\\= 0.45 + 0.50-0.20 = 0.75

b) P(student chooses neither dressage nor Western riding)

= 1 - P(d \cup w)\\= 1 - (P(d) + P(w) - P(d \cap w))\\= 1 - (0.45 + 0.35 - 0.10)= 0.3

5 0
3 years ago
John makes a commission of 6% when he sells a house how much is john's commission if he is sells a house for $300,000
Elan Coil [88]

Answer:

18,000

Step-by-step explanation:

6% is 0.06

300,000 * 0.06 = 18,000

5 0
3 years ago
Read 2 more answers
John Calipari, head basketball coach for the 2012 national champion University of Kentucky Wildcats, is the highest paid coach i
MrRissso [65]

Answer:

A) sample mean = $1.36 million

B) standard deviation = $0.9189 million

C) confidence interval = ($1.93 million , $0.79 million)

*since the sample size is very small, the confidence interval is not valid.

Step-by-step explanation:

samples:

  1. $2.7 million
  2. $2.4 million
  3. $2.2 million
  4. $2 million
  5. $1.5 million
  6. $1.5 million
  7. $0.5 million
  8. $0.5 million
  9. $0.2 million
  10. $0.1 million

sample mean = $1.36 million

the standard deviation:

  • $2.7 million - $1.36 million = 1.34² = 1.7956
  • $2.4 million - $1.36 million = 1.04² = 1.0816
  • $2.2 million - $1.36 million = 0.84² = 0.7056
  • $2 million - $1.36 million = 0.64² = 0.4096
  • $1.5 million - $1.36 million = 0.14² = 0.0196
  • $1.5 million - $1.36 million = 0.14² = 0.0196
  • $0.5 million - $1.36 million = -0.86² = 0.7396
  • $0.5 million - $1.36 million = -0.86² = 0.7396
  • $0.2 million - $1.36 million = -1.16² = 1.3456
  • $0.1 million - $1.36 million = -1.26² = 1.5876
  • total $8.444 million / 10 = $0.8444 million

standard deviation = √0.8444 = 0.9189

95% confidence interval = mean +/- 1.96 standard deviations/√n:

$1.36 million + [(1.96 x $0.9189 million)/√10] = $1.36 million + $0.57 million = $1.93 million

$1.36 million - $0.57 million = $0.79 million

7 0
3 years ago
The Cheer Club is making a banner for your school using the design shown. The area of the yellow portion is 1 ft2. The expressio
olga nikolaevna [1]

Answer:

Blue = \frac{8}{9}

Step-by-step explanation:

Given

Yellow = 1ft^2

Blue = 8z^{-1

Required

Evaluate Blue when z = 9

To do this, we simply substitute 9 for z in Blue = 8z^{-1

Blue = 8 * 9^{-1

Convert indices to fraction

Blue = 8 * \frac{1}{9}

Blue = \frac{8}{9}

<em>Hence, the blue section has an area of </em>\frac{8}{9}ft^2<em></em>

3 0
3 years ago
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