The probability of rolling a 4 on a single throw of a fair 6-sided die is 1/6, since there is only one way to roll a 4 and there are 6 equally likely outcomes in total.
The probability of rolling an even number on a single throw of a fair 6-sided die is 3/6, or 1/2, since there are three even numbers (2, 4, and 6) out of six possible outcomes.
To find the probability of rolling a 4 or an even number on a single throw, we can add the probabilities of these two events:
P(4 or even) = P(4) + P(even) - P(4 and even)
where P(4 and even) is the probability of rolling a 4 and an even number on the same throw. Since there is only one outcome (rolling a 4), which is not even, this probability is 0.
Therefore:
P(4 or even) = P(4) + P(even) - P(4 and even)
= 1/6 + 1/2 - 0
= 2/3
So the probability of rolling a 4 or an even number on a single throw of a 6-sided die is 2/3.
If the die is thrown 2 times, the probability of rolling a 4 or an even number on both throws is the product of the probabilities of rolling a 4 or an even number on each throw:
P(4 or even on both throws) = P(4 or even) × P(4 or even)
= (2/3) × (2/3)
= 4/9
Therefore, the probability of rolling a 4 or an even number on both throws of a 6-sided die is 4/9.
3
Florence Griffith-Joyner was an Olympic runner who set the women's world records
for the 100- and 200-meter races in 1988. She completed the 100-meter race in
10.49 seconds and the 200-meter race in 21.34 seconds. How much faster did
Florence run in the 100-meter race than in the 200-meter race, in meters per second?
A 10.85
B 0.1085
C 0.0016
D 0.16
Florence was 0.16 m/s faster in the 100-meter race than in the 200-meter race
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
She completed the 100-meter race in 10.49 seconds and the 200-meter race in 21.34 seconds. Hence:
For 100 meters:
Speed = 100 m / 10.49 s = 9.53 m/s
For 200 meters:
Speed = 200 m / 21.34 s = 9.37 m/s
The speed difference = 9.53 m/s - 9.37 m/s = 0.16 m/s
Florence was 0.16 m/s faster
Find out more on equation at: https://brainly.com/question/17145398
#SPJ1
Suppose a city with population 500,000 has been growing at a rate of 4.3% per year. If this rate continues, find the population of this city in 10 years
In the Show Your Work box, must have the following:
- 1 pt- Formula used
- 1 pt- Variables and what they stand for
- 3 pts- Full solving process
Answer:
t = time in years
p(t) = population at time t
[tex]p(t) = 500000( {1.043}^{t} )[/tex]
[tex]p(10) = 500000( {1.043}^{10}) = 761751 [/tex]
The scale of this blueprint of an art gallery is 1 in 48 ft. find the actual lengths of the following walls.
The calculated values of the actual lengths of the walls are AB = 144 ft, CD = 288 ft, EF = 528 ft and EF = 240 ft
Finding the actual lengths of the walls.From the question, we have the following parameters that can be used in our computation:
Scale of blueprint = 1 in : 48 ft
This means that
Scale = 48 ft/1in
Calculating the actual lengths of the walls, we have
AB = 3in * 48 ft/1in
AB = 144 ft
CD = 6in * 48 ft/1in
CD = 288 ft
EF = 11in * 48 ft/1in
EF = 528 ft
FG = 5in * 48 ft/1in
EF = 240 ft
Hence, the actual lengths of the walls are AB = 144 ft, CD = 288 ft, EF = 528 ft and EF = 240 ft
Read more about scale drawings at
https://brainly.com/question/29229124
#SPJ1
I do not understand how to round to whole number
The given fraction can be converted into whole number as
16/5 +52/9 =9
99/7 -15/2=7
13/8+ 27/5=7
41/4-26/15=9
27/10+44/9=8
How can the fraction be converted to whole number?We can see that all the expression was given as a fraction the to convert to whole number we will need to solve them by performing the neccessary addition as well as substraction operations then it will converted to whole number.
16/5 +52/9
=404/45.
=8.977
=9
99/7 -15/2=
= 93/14
=6.643
7
13/8+ 27/5
= 281/40
=7.025
7
41/4-26/15
=511/60
=8.52
=9
27/10+44/9
= 683/90
=7.59
=8
Learn more about fraction at:
https://brainly.com/question/78672
#SPJ1
PLEASE HELP BRO PLEASEEEE
The likelihood that a milkshake chosen at random will be a sloppy, thin, flavourless mess is 0.62.
Define probabilityThe possibility or chance of an event occurring is measured by probability. It is a number between 0 and 1, where 0 denotes that the occurrence is impossible and 1 denotes that it is unavoidable. By dividing the number of favourable outcomes by the total number of potential outcomes, the probability of an occurrence is determined.
a. The milkshake will most likely turn out to be a watery, thin, flavourless mess (2, 4, 7).
The likelihood that a milkshake chosen at random would be a sloppy, thin, flavourless mess is equal to the final result of the milkshake will be a watery, thin, flavourless mess.
=2+4+7/21
=13/21
=0.62
b. No association can be removed from this table. We are unable to forecast the result of any event since the overall number of events is random.
To know more about outcomes, visit:
https://brainly.com/question/28740329
#SPJ1
PLEASE HELP!!!
A cylinder has a height of 15 inches. A similar cylinder has a height of 20 inches.
What is the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder?
Enter your answer by filling in the boxes.
The ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder is 4:3, or 4/3.
How do you find the ratio of the surface area of the larger cylinder to the the smaller cylinder?To find the ratio of the surface areas of the two similar cylinders, we need to consider the ratio of their corresponding dimensions. Since the two cylinders are similar, their radii are proportional to their heights. Let's denote the height of the smaller cylinder as h1, the height of the larger cylinder as h2, the radius of the smaller cylinder as r1, and the radius of the larger cylinder as r2.
Given:
h1 = 15 inches
h2 = 20 inches
The ratio of the heights is:
h2 / h1 = 20 / 15 = 4 / 3
Since the cylinders are similar, the ratio of their radii is the same as the ratio of their heights:
r2 / r1 = 4 / 3
Find more exercise on The ratio of a surface area;
https://brainly.com/question/29449175
#SPJ1
-2√48 simplified is:
-8√3.
-4√3.
No solution.
None of these choices are correct.
Answer:
-8√3
Step-by-step explanation:
[tex] - 2 \sqrt{48} \\ = - 2 \sqrt{16 \times 3} \\ = - 2 \sqrt{16} \times \sqrt{3} \\ = - 2 \times 4\sqrt{3} \\ = - 8 \sqrt{3} [/tex]
I need help pleaseee
The result of the row 1 multiplication by 1/4 is determined as [¹/₂ 0 ].
What is the result of the row multiplication?The resultant of the row multiplication in the surd is calculated by applying the following method;
row 1 in the given surds = [2 0]
To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;
[2 0] x 1/4 = 1/4(2 0)
= [¹/₂ 0 ]
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that 2, and 0 by 1/4.
Learn more about row multiplication here: https://brainly.com/question/31531585
#SPJ1
Suppose that the functions q and r are defined as follows.
Answer:
Step-by-step explanation:
Given:
q(x) = -3x+4
r(x) = -4x
(r₀q)(4) => r(q(4)) solve for q(4) first
q(4) = -3(4)+4 > substitute 4 in for x
q(4) = -12 +4
q(4) = -8 > now substitute this into r(q(4))
r(-8) = -4(-8) > substitute -8 in for x
r(-8) = 32
(r₀q)(4) = 32
(q₀r)(4) => q(r(4)) solve for r(4) first
r(4) = -4(4) > substitute 4 for x
r(4) =-16 > substitute this into q(x)
q(-16) = -3(-16)+4
q(-16) = 48 +4
q(-16) = 52
(q₀r)(4) = 52
Let S be a collection of subset of {2000, 2001, 2002, …, 2020} such that intersection of any two sets in S is nonempty. What is the maximum cardinality of S?
The maximum cardinality of S is 20.
How to find the maximum cardinality ?To increase the number of subsets within S, our goal must be to find as many non-empty subset intersections as possible. This is achieved by constructing subsets that possess only one shared element. In this particular case, any two sets contained in the collection will include the element 2000 in their intersection causing it to become a valid subset.
Now, we shall investigate whether an additional subset can be added to S. If an extension exists without including 2000, its intersection with the previous 20 subsets would negligibly have no common elements and would hence not be regarded as a valid subset for addition into S.
As a result, a total of 20 subsets represent maximum cardinality for set S per these conditions.
Find out more on maximum cardinality at https://brainly.com/question/30701593
#SPJ1
What is deviance? Identify the term and provide an overview. Think of a time when you or a
friend used informal negative sanctions. To what act of deviance were you or your friend
responding? Did this reaction help maintain social control? Is it possible to function as a society
without the threat of physical violence to keep people under control? Why or why not?
Deviance is a term used in sociology to describe behavior that violates social norms or expectations. It refers to any behavior that is considered outside of the established rules and expectations of a society or culture.
What are informal negative sanctions?Informal negative sanctions are the social disapproval or punishment that people receive for violating social norms. An example of informal negative sanctions could be a group of friends ostracizing another friend for breaking a social rule, such as not showing up to a planned event.
In terms of the act of deviance, it could be anything from breaking a minor social norm to committing a serious crime. The reaction of informal negative sanctions is often an attempt to maintain social control by encouraging conformity to the established norms of the group or society.
While physical violence is not necessary to maintain social control, the threat of punishment is an important part of any functioning society. People follow the rules and norms of society because they know that if they do not, there will be consequences. However, it is important to note that violence and punishment should not be the only means of social control. Positive reinforcement, such as rewards for good behavior, can also be an effective way of encouraging conformity to social norms.
In summary, deviance refers to behavior that violates social norms, and informal negative sanctions are a way of enforcing social norms. The threat of physical violence is not necessary to maintain social control, but consequences for deviant behavior are essential for any functioning society.
to know more about deviance
brainly.com/question/16022748
#SPJ1
Find the missing side lengths. Leave your answers as radicals in simplest form.
The value of missing side lengths are,
m = 4/√3
h = 2 / √3
We have to given that;
A triangle is shown in figure.
Now, We can formulate;
sin 60° = 2 / m
√3/2 = 2 / m
m = 4/√3
cos 60° = h / m
1/2 = h / (4/√3)
1/2 = √3h / 4
2 = √3h
h = 2 / √3
Thus, The value of missing side lengths are,
m = 4/√3
h = 2 / √3
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ1
The distance from Hans house to Priyas house is 4/5 kilometer. Han has walked 3/4 of the way already. How many kilometers has he walked?
Han has walked 3/5 km.
What is distance?Distance is the length of space between two reference points. It is a scalar quantity, and it is measured in meters.
In the given question, we have that;
distance from Han's house to Priya's house = 4/5 km
Han has walked 3/4 of the way already.
Thus,
distance walked by Han = 3/4 of 4/5
= 3/4 x 4/5
= 12/ 20
= 3/ 5
distance walked by Han is 3/5 km.
Learn more about distance at https://brainly.com/question/28745428
#SPJ1
A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 2 tables is $25.
The cost of each chair and table is $2.5 and $8.75 respectively.
Given that the total cost to rent 3 chairs and 2 tables is $25 and total cost to rent 5 chairs and 6 tables is $65.
We need to find the cost of each chair and table,
Let the cost of each chair and table be x and y respectively,
3x+2y = 25.......(i)
5x+6y = 65.........(ii)
Multiply the equation (i) by 3 and subtract ii from i,
9x+6y = 75 - (5x+6y = 65)
4x = 10
x = 2.5
Put x = 2.5 in any equation to find the value of y,
3(2.5)+2y = 25
2y = 17.5
y = 8.75
Hence, the cost of each chair and table is $2.5 and $8.75 respectively.
Learn more about linear algebra click;
https://brainly.com/question/1952076
#SPJ1
100 POINTS!!!
Question
Step-by-step explanation:
A.
Sequence 2:
25-2×5=15
25-2×6=13
25-2×7=11
25-2×8=9
25-2×9=7
Ordered pairs :
(13,15)
(16,13)
(19,11)
(21,9)
(24,7)
B.
Sequence1 :
The rule is 3x+2 for x starts by 1, so:
3×1+2=5
3×2+2=8
3×3+2=11
3×4+2=14
3×5+2=17
Sequence2
The rule is 2x+3 forx starts by 6, so :
2×6+3=15
2×7+3=17
2×8+3=19
2×9+3=21
2×10+3=23
Ordered pairs
(5,15)
(8,17)
(11,19)
(14,21)
(17,23)
A music app has a shuffle play function.
This function allows songs to be played in a random order without repeat.
Gabriella puts songs A, B and C on shuffle play.
List all the possible orders of songs A, B and C.
One has been done for you.
ABC,
Answer:ABC(Done for you)
ACB
BAC
BCA
CAB
CBA
Step-by-step explanation:
Which of the following explains why this inequality is true?
7 3/8 × 4/5 < 7 3/8
The answers I have to choose from are:
A. When 7 3/8 is multiplied by a number greater than 1, the product is more than 7 3/8
B. When 7 3/8 is multiplied by a number greater than 1, the product is less than 7 3/8
C. When 7 3/8 is multiplied by a number less than 1, the product is more than 7 3/8
D. When 7 3/8 is multiplied by a number less than 1, the product is less than 7 3/8.
The correct option is B: The result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.
Explain about the term mixed fractions:Once kids have a firm grasp on right fractions, they are exposed to mixed numbers and improper fractions.
Divide the numerator and denominator to create a mixed fractions from an incorrect fraction. The solution to this problem is the whole number portion; the leftover portion is the numerator; its denominator stays the same.
We can convert the two fractions to decimal form in order to compare them.
7.375 is equivalent to 7 3/8, and
4/5 is equivalent to 0.8.
7.375 multiplied by 0.8 results in:
7.375 × 0.8 = 5.9
Since the result is 5.9, which is less than 7.375, it follows that 7 3/8 multiplied by 4/5 is less than 7 3/8.
Thus, the result of multiplying 7 3/8 by a number larger than 1 is less than 7 3/8.
Know more about the term mixed fractions:
https://brainly.com/question/1055953
#SPJ1
25 Points! Multiple choice algebra question. Photo attached. Thank you!
a math teacher gave her class two test 70% of the class passed both tests and 80% of the class passed the first test what percent of those who passed the first test also passed the second test this statement is an example of supplementary probability true or false
87.5% of those who passed the first test also passed the second test.
The given statement in the question is an example of conditional probability rather than supplementary probability. Therefore, the statement is false.
We are given the following information:
- 70% of the class passed both tests.
- 80% of the class passed the first test.
We want to find the percentage of those who passed the first test and also passed the second test.
To do this, we will use the concept of conditional probability.
Let A be the event of passing the first test, and B be the event of passing the second test.
We are asked to find the conditional probability P(B|A), which is the probability of passing the second test given that the student has passed the first test.
Using the formula for conditional probability, we have:
P(B|A) = P(A ∩ B) / P(A)
We know that P(A ∩ B) = 0.7 (since 70% of the class passed both tests) and P(A) = 0.8 (since 80% of the class passed the first test).
Now, we can calculate P(B|A):
P(B|A) = 0.7 / 0.8 = 0.875.
For similar question on conditional probability.
https://brainly.com/question/10739947
#SPJ11
A bag contains 605 red, 342 blue, 518 green, and 535 yellow tokens. A token is selected at random and then replaced.this is performed 2,000 times
The probability of randomly selecting a red token would be 0. 30.
How to find the probability ?First, we know that the experiment was done 2, 000 times;
605 + 342 + 518 + 535 = 2000
The probability that a red token is randomly selected is therefore:
= Red token / Total times
= 605 / 2, 000
= 0. 3025
In fractions, we can make this:
= 605 / 2, 000
= 121 / 400
This is closest to the fraction 3 / 10 which is 0. 30.
Find out more on probability at https://brainly.com/question/24583998
#SPJ1
solve the following system of equations algebraically for all values of x and y
The values of x, y, and z based on the system of equations will be (-2,4,7).
How to solve the equationx + 3y + 5z = 45
6x - 3y + 2z = - 10
------------------------add
7x + 7z = 35
6x - 3y + 2z = -10
-2x + 3y + 8z = 72
----------------------add
4x + 10z = 62
7x + 7z = 35....multiply by 4
4x + 10z = 62...multiply by -7
---------------------
28x + 28z = 140 (result of multiplying by 4)
-28x - 70z = - 434 (result of multiplying by -7)
--------------------add
- 42z = - 294
z = -294/-42
z = 7
4x + 10z = 62
4x + 10(7) = 62
4x + 70 = 62
4x = 62 - 70
4x = - 8
x = -8/4
x = -2
x + 3y + 5z = 45
-2 + 3y + 5(7) = 45
-2 + 3y + 35 = 45
3y + 33 = 45
3y = 45 - 33
3y = 12
y = 12/3
y = 4
Learn more about equations on
https://brainly.com/question/2972832
#SPJ1
Solve the following system of equations algebraically for all values of x,y and z
x+3y+5z=45
6x-3y+2z=-10
-2x+3y+8z=72
Solve for the missing angle measurements for angles a, b, c, and d
Note that the angle measurements are given as follows:
A = 145° (Sum of angles on a straight line.
B = 35° Opposite angles
C = 145° Opposite angels
D) = 35° supplementary angels.
What is the explanation of the above statements?a) Note that Sum of angles on a straight line=180° and are therefore supplementary
b) All opposite angle are equal, since ∠b is opposite to 35°, then ∠b = 35°
c) 145° is also opposite to ∠c
d) when two angles are supplementary, it means that they sum up to 180°
Learn more about angle measurements;
https://brainly.com/question/31186705
#SPJ1
Full Question:
Solve for the missing angle measurements for angles a, b, c, and d
See the attached imge
Which roman symbol is neither repeated nor added or subtracted?
Answer:
symbols V
The symbols V L and D are not written to the left of a symbol that has greater value
Pete has an anvil used for metal working, he models the base as two trapeziums the anvil applied of 834 newton's
The pressure using Pete's model based on the information will be 2.79 N/cm³
What is a trapezium?A trapezium (often known as a trapezoid in some parts of the world) is a four-sided figure with at least one set of parallel lines. These two lines are often referred to as the bases, and the other sides as its legs.
Isosceles Trapezium is a type of trapezium has its legs of equal length, and its base angles possessing an equivalent measure..
Pete has an anvil used for metal working, he models the base as two trapeziums the anvil applied of 834 newton's
The pressure using Pete's model based on the information will be:
= 834 / 299.25
= 2.79 N/cm³
Learn more about trapezium on
https://brainly.com/question/1410008
#SPJ1
Answer:
1.54
Step-by-step explanation:
Trapezium=
12+24=36
36 x (length) 15 = 540cm^2
Pressure= force/area
832/540 = 1.54N/cm^2
The architect stands 6 feet from a climbing frame looking up at the top of the frame at an angle of 63.43
The value of the height of the entire climbing frame is 11.99 feet
How to determine the valueTo determine the value, we need to know the different trigonometric identities.
These identities are;
tangentcotangentcosecantsecantcosinesineFrom the information given, we have that;
In the triangle, the parameters are;
Hypotenuse is the distance between the architect and frame
The angle is 63.43
Adjacent is 6 feet
Using the tangent identity, we have;
tan 63.43 = h/6
cross multiply, we get;
h = tan (63. 43) × 6
Find the tangent value and substitute, we have;
h = 1. 99 × 6
Multiply the values, we have;
h = 11. 99 feet
Then, the height of the entire climbing frame is 11. 99 feet
Learn about trigonometric identities at: https://brainly.com/question/7331447
#SPJ1
Complete question:
'The architect stands 6 feet from climbing frame, looking up at the top of the frame at an angle of 63.43" It is 5 and half feet from ground to the architect's eyes: The vertical distance from eye level to the top of the climbing frame is feet: The height of the entire climbing frame is feet:'
What is it?????????!!!!!!!!!
From the attached graph the solution set is (3, 3) for the inequalities
The first inequality is y < -(2/3)x + 5.
We can graph this by plotting the y-intercept of 5 and then using the slope of -2/3 to find additional points.
We then draw a dashed line through these points to indicate that the points on the line are not included in the solution set.
Since the inequality is y <, we shade the region below the line.
The second inequality is y ≥ (4/3)x - 1.
We can graph this by plotting the y-intercept of -1 and then using the slope of 4/3 to find additional points.
We then draw a solid line through these points to indicate that the points on the line are included in the solution set.
Since the inequality is y ≥, we shade the region above the line.
Hence, from the attached graph the solution set is (3, 3) for the inequalities
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
HELP ASAP!! 15 POINTS!!
Based on the information, we can infer that the correct graph/table is option D.
How to identify the correct table/chart?To identify the correct chart or table, we must identify the information about the data that Emily uses each year. She uses 360GB each year, in this case, to identify the relationship we must divide the amount of data she uses by the number of months she has in a year:
360GB / 12 months = 30 GB/month
In accordance with the above, we must identify the table or graph that represents this relationship. In this case it would be table D because it shows an increasing relationship of 1 month with 30gb, 2 months with 60gb, 3 months with 90gb, 4 months with 120gb, and so on.
Learn more about relationship in: https://brainly.com/question/31248849
#SPJ1
find the taylor polynomial t3(x) for the function f centered at the number a. f(x) = cos(x), a = pi/2
The Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.
How do we calculate?A polynomial is described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:
We get the derivatives :
pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....
f(x) = cos(x)
f'(x) = -sin(x)
f''(x) = -cos(x)
f'''(x) = sin(x)
We the evaluate these derivatives at x = pi/2:
f(pi/2) = cos(pi/2) = 0
f'(pi/2) = -sin(pi/2) = -1
f''(pi/2) = -cos(pi/2) = 0
f'''(pi/2) = sin(pi/2) = 1
We substitute these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:
the Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.
Learn more about Taylor polynomial at:
brainly.com/question/2533683
#SPJ1
What are the period and amplitude of the function?
Answer:
period : π ; amplitude : 2
Step-by-step explanation:
Correct me if I'm wrong!!
Can someone give me the answer to the following 4 trig questions using sum and difference formulas
1. Therefore, the exact value of cos(105°) is (√2 - √6)/4.
2. Therefore, the exact value of sin(75°) is (√6 + √2)/4.
3. Therefore, the exact value of tan(105°) is (√3 + 1)/(3 - √3).
4. Therefore, the exact value of cos(105°)cos(15°) is (2 + 2√3)/8.
What is trigonometry?A branch of mathematics known as trigonometry is concerned with the study of triangles and the correlations between their sides and angles.
It entails computing different triangle measurements and attributes using trigonometric functions including sine, cosine, and tangent.
Trigonometry is an essential component of calculus and other advanced mathematical studies, and it has applications in many disciplines including engineering, physics, navigation, astronomy, and architecture.
1. We can use the formula cos(A + B) = cos(A)cos(B) - sin(A)sin(B) with A = 60° and B = 45°. Then:
cos(105°) = cos(60° + 45°)
= cos(60°)cos(45°) - sin(60°)sin(45°)
= (1/2)(√2/2) - (√3/2)(√2/2)
= (√2 - √6)/4
Therefore, the exact value of cos(105°) is (√2 - √6)/4.
2. We can use the formula sin(A + B) = sin(A)cos(B) + cos(A)sin(B) with A = 45° and B = 30°. Then:
sin(75°) = sin(45° + 30°)
= sin(45°)cos(30°) + cos(45°)sin(30°)
= (√2/2)(√3/2) + (√2/2)(1/2)
= (√6 + √2)/4
Therefore, the exact value of sin(75°) is (√6 + √2)/4.
3. We can use the formula tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)tan(B)) with A = 60° and B = 45°. Then:
tan(105°) = tan(60° + 45°)
= (tan(60°) + tan(45°))/(1 - tan(60°)tan(45°))
= (√3 + 1)/(3 - √3)
Therefore, the exact value of tan(105°) is (√3 + 1)/(3 - √3).
4. We can use the formula cos(A + B) = cos(A)cos(B) - sin(A)sin(B) with A = 60° and B = -45°. Then:
cos(105°)cos(15°) = cos(60° - 45°)cos(15°)
= [cos(60°)cos(-45°) - sin(60°)sin(-45°)]cos(15°)
= [(1/2)(√2/2) - (√3/2)(-√2/2)]cos(15°)
= (√2 + √6)/4 * cos(15°)
= (√2 + √6)/4 * (√6 + √2)/4
= (2 + 2√3)/8
Therefore, the exact value of cos(105°)cos(15°) is (2 + 2√3)/8.
Learn more about trigonometry:
https://brainly.com/question/31347150
#SPJ1