Given:
[tex]\alpha, \beta, \gamma[/tex] are three interior angles of any triangle.
To prove:
[tex]\cos (\alpha+\beta+\gamma)=-1[/tex]
Solution:
According to the angle sum property of a triangle, the sum of all three interior angle of a triangle is always 180 degrees.
It is given that, [tex]\alpha, \beta, \gamma[/tex] are three interior angles of any triangle.
Using the angle sum property of triangles, we get
[tex]\alpha+\beta+\gamma =180^\circ[/tex] ...(i)
We need to prove,
[tex]\cos (\alpha+\beta+\gamma)=-1[/tex]
Taking LHS, we get
[tex]LHS=\cos (\alpha+\beta+\gamma)[/tex]
[tex]LHS=\cos (180^\circ)[/tex] [Using (i)]
[tex]LHS=-1[/tex]
[tex]LHS=RHS[/tex]
Hence proved.
Find the area of this trapezoid.
A. 240 cm2
B. 288 cm2
C. 312 cm2
D. 336 cm2
Answer:
b. 288cm^2
Step-by-step explanation:
[tex]a = \frac{a + b}{2} h[/tex]
[tex] \frac{15 + 21}{2} (16)[/tex]
[tex]a = 288[/tex]
If Danny randomly picks a jelly bean out of the jar, what is the probability that the jelly bean will be blue or green (find the simplest form)?
Answer:
Amount of jelly beans=50
Amount of blue or green jelly beans=17+10
probability that the jelly bean will be a blue or green one=27/50
HELP ASAP WILL GIVE MOST BRANILIST
find the are of the trapizoind
9514 1404 393
Answer:
7.5 square units
Step-by-step explanation:
The formula for the area of a trapezoid is ...
A = 1/2(b1 +b2)h
where b1 and b2 are the lengths of the parallel bases, and h is the perpendicular distance between them.
Here, the bases are TR = 1 and PA = 4. The height is 3 units, so the area is ...
A = (1/2)(1 +4)(3) = 15/2 = 7.5 . . . . square units
The local weather forecast has been accurate for 24 of the past 30 days. Based on this fact what is the relative frequency probability that the forecast for tomorrow will be accurate
Step-by-step explanation:
the empirical probability is 24/30, or 4/5. this is also the desired probability.
#11. The space occupied by a wooden block is 4cm × 2cm × 2cm=_____cm 3 Which is equivalent to_______mililiters
Conan is moving into a two-bedroom apartment in Valley Oaks. The monthly rent is $2,000. His up-front fees
were a $60 application fee, a $20 credit check fee, first and last month's rent and a broker fee of 14% of a year's
rent.
How much can he expect to pay upfront for this apartment?
4,360
4,080
7,440
5,440
A manufacturing manager reports to the CEO that 5% of products that come off the assembly line are defective. A study is performed to investigate this claim. In a random sample of 250 products that come off the assembly line, 14 are found to be defective. The CEO wants to know if the data provide convincing evidence that the true proportion of defective products differs from 0.05. Are the conditions for inference met?
Yes, the conditions for inference are met.
No, the 10% condition is not met.
No, the Large Counts Condition is not met.
No, the randomness condition is not met.
Answer:Yes, the conditions for inference are met
Step-by-step explanation:
I took the test edge 2020
Answer:Yes, the conditions for inference are met.
Step-by-step explanation:
Please help!! Timed assignment
Arrange the figures in increasing order of their volumes. Use Pi =22/7
Answer:
see the list below
Step-by-step explanation:
did all the formulas for each and I believe the order is from (smallest to biggest)
1. The half sphere or hemisphere (3rd in the picture)
2.The pyramid
3.slanted cone
4.cone
5.slanted cylinder
6.and finally the cylinder
Graph the function defined by the parametric equations x = 2t3 – 3t and y = -2t2 – 1 over the parameter
-2 < t < 2.
9514 1404 393
Answer:
see attached
Step-by-step explanation:
A graphing calculator does this nicely.
Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight-year life. What would be the present value of this loan if it carried an 8.5 percent interest rate?
Answer:
the answer 57.8
85 x 8 x 8.5% = 57.8
Step-by-step explanation:
brainliest pls
9/10 + 3/100 plz hlp in dire need of answer
Answer:
I think it's 93/100
Need answered ASAP GOT A TIMER!
Answer:
2
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
1. You have the following multiplication given in the problem above:
(x/3)(6/x)
2. Multiply the numerators and the denominators:
(x/3)(6/x) = 6x/3x
3. You can simplify the expression. Then, you have:
6x/3x = 2
Answer:
2
Step-by-step explanation:
1) simplify x
x/x = 1
2) simplify 6 with 3
6/3 = 2
3) multiply the two numbers
2*1 = 2
Which number line shows the solution of -3x + 6 > 12
Answer:
x < -2
Step-by-step explanation:
subtract 6 from each side
-3x > 6
divide both sides by -3
x < -2
(with inequalities you must flip the sign if you divide by a negative number)
What is the measure of angle L
Answer:
90-15 and you have your answer
Answer:
75
Step-by-step explanation: it is a right angle so you do 90-15 which is 75 degrees.
if 4^(3x-2)=4^(x+1), then x=
Answer:
x = 3 /2
x=1.5
Step-by-step explanation:
Round the number 246.13687 to the nearest thousandth
Answer:
246.137
Step-by-step explanation:
246.13687 ≈ 246.137 (rounded to the nearest thousandth)
PLS HURRY. WILL MARK BRAINLEST!!!! JWKSNWN PLEASE I NEED IT!!
Answer:
B
Step-by-step explanation:
Mark me brainliest PLZ
49 pt = _ fl oz :DDDDD
Answer:
784
Step-by-step explanation:
each 1 PT = 16 FL Oz
49*16=784
Points H and I are located on the coordinate plane at (-2,8) and (-2, 11).
What is the distance between the two points?
Answer:
3
Step-by-step explanation:
distance required=11-8=3
plzzzzzz help for a brainly
Find the volume of the cone.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi.
Please help asap
Right circular cone
Solve for volume
V≈37.7r (Radius )
2h( Height )
9V=πr2h
3=π·22·93≈37.69911In 1999. Sara and her brother Xzavier got money when their rich uncle died. They
each got the same amount of money. Sara bought some land in the country
because she heard they would be building houses near there some day. She
bought 300 acres of land with all of the money she got from her uncle,
$600,000, in 2000. In 2003 they extended the main highway to go near her land
and she sold 100 acres for $2700 lacre. In 2005 she sold half of the land she had
left for $3600 lacre. In 2007 they started a long-term project to build houses in
the area and built a Lowes, a Food Lion, A Bank of America and a Burger King on
the main street. Finally, in 2010. Sara sold the rest of her land for $400,000. What
was her total profit when she finished selling all of the land?
Answer:
$406,300
Step-by-step explanation:
$2,700 + $3,600 = $6,300
$400,000 + $6,300 = $406,300
Given g(x) = -2 – 5, find g(1).
Answer:
-7
Step-by-step explanation:
There's no "x" in the equation, so there's nothing to plug in. I don't know if you just forgot to type it, but for all numbers, it's gonna equal -7. Even if there was an x, it would still equal -7.
WHATS THE ANSWER? MULTIPLE CHOICE 50 PTS
Answer:
D
Step-by-step explanation:
Seventeen less than p infers that the number is p minus 17. This number is then divided by 8, which requires us to put parenthesis in order to properly divide the number after doing p - 17
Please give brainliest thank you
[tex]\boxed{\underline{\bf \: ANSWER}}[/tex]
The quotient when 17 less than p is divided by 8.
Well, let's first take 17 less than p. That'll be :-
[tex] \sf \: p - 17[/tex]
Note :- 'p' comes first as the question has the words - less than p.
Now, we have the remaining -> 'is divided by 8'.
The equation will become :-
[tex] \sf \:( p - 17) \div 8[/tex]
Note :- We have put the bracket because they have asked the quotient. To form a quotient you need 2 numbers - a divisor & a dividend. Hence, 2 numbers -> (p - 17) & 8.
So, Option D [tex]\boxed{\underline{\bf \: (p-17)÷8}}[/tex] is the correct answer.
________
Hope it helps.
꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂
A system has two identical components, and requires both the components for system success. If one component fails, the other cannot fail while the failed component is being repaired. The component failure rates and repair rates are 0.1 failures/year and 365 repairs/year respectively. If a similar component is carried as a spare with an average installation time of 1 hour, evaluate the probability of failure, frequency of failure and the average down time of the system.
Answer:
Step-by-step explanation:
We are given that:
The failure rate = 0.1 failure/year
i.e. = [tex]\dfrac{0.1}{365\times 24}= 0.00001 \ failure /hour[/tex]
The repair rate = 365 repair/year, if we convert this to repair/hour; we get:
[tex]= \dfrac{365}{365\times 24} \\ \\ = 0.04 \ repair/ hour[/tex]
Time (t) = 1 hour
P(failure) = 1 - R ; if (t=1)
where:
[tex]Reliability (R ) = e^{-\lambda t}(1+ \lambda t) \\ \\ = e^{-0.00001*1}(1+0.00001 *1) \\ \\ \simeq 0.9999[/tex]
P (failure) = 1 - R
= 1 - 0.9999
= 0.0001
≅ 0
The frequency meantime of failure = [tex]\dfrac{1}{\lambda}[/tex]
[tex]\dfrac{1}{0.00001}[/tex]
= 100000
The average downtime of repair for the system = [tex]\dfrac{1}{\mu}[/tex]
[tex]=\dfrac{1}{0.04}[/tex]
= 25
f(x)=3x 2 +6x−18Find f(10)
Answer:
342
Step-by-step explanation:
To find f(10), simply substitute x for 10, resulting in 300+60-18 = 342
find the area of the figure
Answer:
5.5
Step-by-step explanation:
area of triangle: 4.5
area of square: 1
Answer: 5.5in
Step-by-step explanation:
Square is 1
Triangle is 4.5
1+4.5=5.5
AREA IS 5.5
What is the difference between a probability experiment that is a binomial experiment and one that is not a binomial experiment?
Answer:
The binomial distribution has the following properties: The mean of the distribution (μx) is equal to n * P . The variance (σ2x) is n * P * ( 1 - P ).
Step-by-step explanation:
Answer: The binomial experiment is the experiment that will satisfy the 4 conditions, a fixed number of trials. And each trial is independent of the others. There will be 2 outcomes. The probability of each of the outcomes remains constant from each trial. (trial to trial.) Is that your question?
Step-by-step explanation:
83 less than triple m
Answer:
3m-83
Step-by-step explanation:
Okay, so first, you'd like to triple m. This would mean that it would be m+m+m, which is also 3m. Next you have to subtract 83. This would make it 3m-83.
Hope this helped!! :D
If you have any questions, let me know!