Answer:
First don't forget the [ tex ] [ /tex ] in order to execute the latex code.
Step-by-step explanation:
[tex] \sin A=\frac{5}{\sqrt{89}}sinA= 89 [/tex]
[tex] \cos AcosA [/tex] = [tex] \cos [/tex]
The exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is 8√(89)/89
What are the six trigonometric ratios?Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Given that:
[tex]\sin A=\dfrac{5}{\sqrt{89}}[/tex]
So, from this, we are given the ratio of perpendicular and hypotenuse from the perspective of angle A.
There must be existing a right triangle with same measure of angle A such that:
Perpendicular's length = P = 5 units
and Hypotenuse' length = H = [tex]\sqrt{89}[/tex] units.
Using Pythagoras theorem, we get:
Base' length = B as:
[tex]P^2 + B^2 = H^2\\B = \sqrt{H^2 - P^2}\\\\B = \sqrt{(\sqrt{89})^2 - 5^2}\\\\B = \sqrt{89-25} = \sqrt{64} = 8[/tex]
(took positive root as B is representing length, a non-negative quantity).
Thus, Base is of 8 units length.
Thus, we get:
[tex]\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\cos(A) = \dfrac{B}{H} = \dfrac{8}{\sqrt{89}}[/tex]
Rationalizing, we get:
[tex]\cos(A) = \dfrac{8}{\sqrt{89}} =\dfrac{8}{\sqrt{89}} \times \dfrac{\sqrt{89}}{\sqrt{89}} \\\\\cos(A) = \dfrac{8\sqrt{89}}{89}[/tex]
Thus, the exact value of cosine of angle A for the considered case using a rational denominator in simplest radical form is [tex]\dfrac{8\sqrt{89}}{89}[/tex]
Learn more about Pythagoras theorem here:
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one hundred people were asked about their favorite sport.
Part A
complete the two-way frequency table
Part B which of the following statements is true
Answer:categorical data listed on the left to complete the frequency table. Ways ... 100. B Jenna asked some randomly selected students whether they preferred dogs, cats, or other pets. ... part-time job. The results are shown in the two-way frequency table below. ... Two hundred students were asked about their favorite sport.
Step-by-step explanation:
A two-way table is a useful way to organize data that can be categorized by two variables. Suppose the school board asked 125 households if they would support a tax ... Make a table of the joint and marginal relative frequencies. ... The table shows the results of a survey of 100 randomly selected people entering an.
Soccer - Male; 19 Female; 31
Basketball - Male; 21 Female; 29
Total - Male; 40 Female; 60
What is a two-way frequency table?A two-way or contingency table is a statistical table that shows the observed number or frequency for two variables, the rows indicating one category and the columns indicating the other category.
Given, one hundred people were asked about their favorite sport.
Since the Total number of humans is 50
And female who likes Soccer is 31
Thus, Male who likes Soccer = 50 - 31 = 19
Since the Total number of humans is 50
And female who likes Basketball is 29
Thus, Male who likes Basketball = 50 - 29 = 21
So,
Total males = 21 + 19 = 40
Total number of female = 29 + 31 = 60
about the two-way frequency table.False More males were surveyed than females. (since total male-to-female ratio is 2/3)
True More females like soccer.
True An equal number of people like soccer and basketball.
False Twice as many females as males like basketball.
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Complete question:
One hundred people were asked about their favorite sports.
A) Complete the two-way frequency table.
B) Indicate whether each of the following statements is "T"-True or "F"-False about the two-way frequency table.
__________________ More males were surveyed than females.
__________________ More females like soccer.
___________________ An equal number of people like soccer and basketball.
____________________ Twice as many females as males like basketball.
Find the Interquartile Range (IQR) of the following set of
data. (Round to the nearest whole number.)
$75, $69, $82, $90, $75, $73, $108, $79, $80
HELP ASAP PLEASE
Answer:
39
Step-by-step explanation:
put them in order least to greatest, then subtract 108-69=39
what is the first page in a geography book?
Answer:
uh i think its a uhhh carrotttt
Step-by-step explanation:
Tom made $273 for 13 hours of work.
At the same rate, how many hours would he have to work to make $105?
Answer:
5 hours
Step-by-step explanation:
$272 = 13h
/273 /273
$1= 0.4.......
*105 *105
105= 5
Answer:
5
Step-by-step explanation:
Gina is four years younger
than twice David's age. Gina
is 18. How old is David?
Answer:
44
Step-by-step explanation:
Gina is four years younger so
18+4=22
since its twice davids age
22×2=44
please help will mark brainliest for right answer!
-thanks <3
Answer:
The answer is B
Step-by-step explanation:
6. Alain, Betina, Coley, and Dimitri are artists. One is a potter, u painter, one a pianist, and one a songwriter. Alain, and Coley saw the pianist perform. Betina and Coley have modeled for the puinter. The writer wrote a song about Alain and Dimitri. Bettinn is the potter. Who is the songwriter?
Answer:
discriminatory laws influence the way we think about others in our
society
Step-by-step explanation:
can someone please help
find the slope/rate of change on graph
a. 1/3
b. 3
c. 30
d. 10
Answer:
m
Step-by-step explanation:
Hi I am in desperate need of a "tutor" If anyone is decent at Algebra II, any little help is welcomed! Please respond to this and I will message you on here. I will explain my situation through there
I am honestly in a really tight spot in school and I really need some assistance with my work, thanks :)
Answer:
Step-by-step explanation:
Hi,
I am quite good at maths and will be happy to help you, not just in Algebra, but any other topics in maths
Henry rolls a standard six-sided die, numbered from 1 to 6. Which word or phrase describes the probability that he will roll a multiple of 2?
A certain bile
B unlikely
C an equal chance or 50-50 impossible
D impossible
Answer:
certain
Step-by-step explanation:
Jai rolls a standard six-sided die, numbered from 1 to 6. Which word or phrase describes the probability that he will roll a number between 1 and 6 (including 1 and 6)?
There are 6 possible outcomes for rolling a die numbered from 1 to 6: {1, 2, 3, 4, 5, 6}.
Within that set of outcomes, there are 6 possible ways of rolling a number between 1 and 6 (including 1 and 6): {1, 2, 3, 4, 5, 6}.
6 out of 6 is 1. When something will occur all the time, we say it is certain.
what is the formula for finding area in a triangle
Answer:
Base times Height divided by 2 or 1/2b*h
Step-by-step explanation:
Answer:
multiply the base times the height and then divide your answer by two or A=1/2bh were b=base and h=height
Step-by-step explanation:
What is the GCF of 36 and 68?
Answer:
4
Step-by-step explanation:
Answer:
The greatest common factor of 36 and 68 is 4
Step-by-step explanation:
36÷4=9
68÷4=17
A recipe calls for 1 1/2 c chopped dates, 3/4 c water, 1 1/2 c sugar, 1/2 c chopped nuts, 2/3 c butter, and 3 c flour to be mixed together in a bowl. When these ingredients are combined, how many cups will there be altogether?
Answer:
7 9/12
Step-by-step explanation:
1 1/2 + 3/4 + 1 1/2 + 1/2 + 2/3 + 3 =
add together with pairs
3 + 3 1/2 + 1 5/12
add again
6 1/2 + 1 3/12
7 9/12
(I think it's right not 100% percent sure but 95%)
anyways hope this helped :))
*WILL MARK BRAINLIEST*
given the inequality 4x-y<=k-6, there is a minimum value of k in order for the point (5,0) to be part of a solution. what is the minimum value?
Answer:
26
Step-by-step explanation:
since the question asks for a value of k where the point (5, 0) is part of a solution, plug 5 into the x value and 0 into the y value:
4x-y<=k-6
4(5)-0<=k-6
20-0<=k-6
20<=k-6
26<=k
In this case, k can be equal to any number that is greater than or equal to 26 for the point (5, 0) to be a solution, but the question asks for the minimum value of k, meaning the smallest value. since the question asks for the smallest value, the answer we're looking for is 26.
lmk if this is wrong, hope it helps!!
On a field trip to the farm, students counted a combined total of 27 sheep
and cows. There are 15 more sheep than cows. If s represents the number
of sheep and c represents the number of cows, which system of equations
correctly represents this situation
Answer:
s = c + 15
s + c = 27
substitute for s:
(c + 15) + c = 27
2c = 12
c = 6
s = 21
The system of equation which correctly represents the situation is s + c = 27 and s - c = 15.
What does a System of Linear Equations define?Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.
System of linear equations involve two or more linear equations.
Given that,
Combined total of sheep and cows = 27
Number of sheep = Number of cows + 15
Let s represents the number of sheep and c represents the number of cows.
s + c = 27
s = c + 15 ⇒ s - c = 15
Hence the system of equation is s + c = 27 and s - c = 15.
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the measure of an angle is 49 what is the measure of its complementary angle
Answer:
the complementary angle is 41°
Step-by-step explanation:
49+41=90
Probability mathematic
Answer:
1/9
Step-by-step explanation:
Probability = Expected outcome/Total outcome
From the given pi chart,
Total outcome = 360degrees (since the total angle in a circle is 360 degrees)
Since we to find the probability of scoring a 5, we can see that the angle when he scores a 5 is 40degrees, hence;
Expected outcome = 40degrees
Pr(scoring a 5) = 40/360
Pr(scoring a 5) = 1/9
Hence the probability of scoring a 5 is 1/9
Answer:
1/9
Step-by-step explanation:
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
Divide the number of events by the number of possible outcomes.
Alex drives at an average speed that is 2/5 of the average speed that Roy's train travels. Alex takes 30 minutes to travel 50 km in her car. Roy travels for 1 hour and 20 minutes on his train. How far does Roy travel to 2 dp (decimal places)?
Answer: 333.33km
Step-by-step explanation:
Average speed is calculated as:
= Distance / Time
Since Alex takes 30 minutes to travel 50 km in her car, Alex average speed will be:
= 50km / 30minutes
= 50km / 0.5hour
= 100km/hour
Since Alex drives at an average speed that is 2/5 of the average speed that Roy's train travels. Roy's average speed will be:
= 100 ÷ 2/5
= 100 × 5/2
= 250km/hour
Since Roy travels for 1 hour and 20 minutes on his train, his distance travelled will be:
= Speed × Time
= 250 × 1 hour 20 minutes
= 250 × 1 20/60
= 250 × 1 1/3
= 250 × 4/3
= 1000/3
= 333.33km
Roy travels 333.33km
can someone please help me out on this
PLZ HELP ITS DUE NOW NO LINKS
Answer:
show the options
Step-by-step explanation:
Brainliest?
Find the GCF of the two numbers, and rewrite the sum of the two numbers using the distributive property. 3 + 15 A) 1(3 + 5) B) 1(3 × 5) C) 3(1 + 5) D) 3(1 × 5)
Answer:
GCF of the numbers is 3 and it can be written as 3(1+5)
Step-by-step explanation:
Given the expression 3+15
First we need to find their factors
3 = 3×1
15 = 3×5
Since 3 is common to both factors, hence the GCF is 3
Factorize
3+15
= (3×1)+(3×5)
Factoring 3 out
= 3(1+5)
Hence the GCF of the numbers is 3 and it can be written as 3(1+5)
Kayla rolls two fair number cubes each numbered 1 through 6. She needs to roll a sum of 9 or more to win a game. She rolls the number cubes one at a time. She rolls a 5 with the first number cube.
What is the probability that Kayla will win the game?
Answer:
1/6
Step-by-step explanation:
Starting with 2 cubes that have 6 numbers total for each one, so 2 cubes will have 12 numbers total, and the probability of number 5 is 2/12 (because each cube has a number 5, so two cubes will have 2, and fraction for it will be 2/12). After simplification, the final result is 1/6.
What is the value of r in the following diagram.
9
6
Answer:
r = 3.75
Step-by-step explanation:
Using Pythagoras' identity in the right triangle ABC
AC² = BC² + AB²
(r + 6)² = r² + 9²
r² + 12r + 36 = r² + 81 ( subtract r² from both sides )
12r + 36 = 81 ( subtract 36 from both sides )
12r = 45 ( divide both sides by 12 )
r = 3.75
The cost of 6 CDs are $12, $13, $20, $20, $12.50 and $18.50. What is the range?
Please with steps urgent
There you go. I think that's how it's done. Hope it's useful.
PLSSS HELP EASYY MATH HELPPP
How many of each different 2-D shapes do you see?
OMG HELP PLS IM PANICKING OMG OMG I GOT A F IN MATH AND I ONLY HAVE 1 DAY TO CHANGE MY GRADE BECAUSE TOMORROW IS THE FINAL REPORT CARD RESULTS AND I DONT WANNA FAIL PLS HELP-
Answer:
1.
7 x 30 is equal to 3 tens-
9 x 200 is equal to 2 hundreds-
2 x 5,000 is equal to 5 thousands-
6 x 7,000 is equal to 7 thousands-
Step-by-step explanation:
30/10 = 3
200/100 = 2
5,000/1,000 = 5
7,000/1,000 = 7
I love you it's gonna be okay :)
HELP HELP ASAP PLEASE
Answer:
15
Step-by-step explanation:
Pythagorean Theorem
This is volume of spheres.
Can anyone give me this step by step?
Due tonight..
Answer:
Step-by-step explanation:
4/3(pi)(r)^3
4/3(pi)(0.8m)^3 (converted the cm to m)
then you can simplify it based on wither the answer is in Number*pi or just a number.
Hope this helps!
Suppose that the breaking strength of a rope (in pounds) is normally distributed, with a mean of 100 pounds and a standard deviation of 17. What is the probability that a certain rope will break before being subjected to 130 pounds?
Answer:
0.961
Step-by-step explanation:
To answer this, find the area under the standard normal curve to the left of 130 pounds:
Using the function normalcdf( on a TI calculator, we get:
normalcdf(-1000, 130, 100, 17) = 0.961