The Sides of triangle when only the angles of triangles are given can be found by using the Law Of Sines .
What is Law Of Sines ?
The Law Of Sines states that the ratio of sides of a triangle and their respective Sine angles are equivalent to each other. The other names by which the law of sines is known are Sine Law, Sine Rule and Sine Formula.
The Sine Law is used to find unknown side of an oblique triangle. The oblique triangle is defined as a triangle that is not a right triangle.
Let a , b and c be the sides of a triangle ABC , and A , B and C be the angles .
So , by Sine Law : [tex]\frac{a}{SinA}=\frac{b}{SinB}=\frac{c}{SinC}[/tex] ;
Therefore , The Law Of Sines help in finding the sides of triangle that has only angles .
Learn more about Law Of Sines here
https://brainly.com/question/29077238
#SPJ4
There are 20 gloves in a drawer: 5 pairs of black gloves, 3 pairs of brown,
and 2 pairs of gray. You select the gloves in the dark and can check them
only after a selection has been made. What is the smallest number of gloves
you need to select to guarantee getting the following?
(a) At least one matching pair
(b) At least one matching pair of each color
The number of gloves selected for each cases is 11 and 19 gloves respectively.
How is selection done?
In mathematics, most of the times selection is done using permutation and combination.
Putting things or numbers in order is known as a permutation.
Combinations are a means to choose items or numbers from a collection of items or groups of items without regard to their order.
Given,
Total black gloves = 5 left hand+ 5 right hand
Total brown gloves = 3 left hand + 3 right hand
Total gray gloves = 2 left hand + 2 right hand
Now to find the least number of gloves for the given conditions, we start with the worst condition.
a) To get at least one matching pair, we first consider no matching pair, which is (5 +3+2) gloves of only left only or right only hand of each colour.
Now to make one pair, we need to select only one glove of the opposite hand of any colour.
Therefore to get atleast one matching pair, smallest number of gloves to be selected = 5 + 3 + 2 + 1 = 11 gloves
b) In this case also we start with worst case.
For no matching pair of each colour we have to take 10 black gloves, 6 brown gloves and 2 gray gloves of any one hand.
Therefore to get matching pair of each colour, we have to take one more gray glove.
Therefore to get atleast one matching pair of each colour, smallest number of gloves to be selected = 10 + 6 + 2 + 1 = 19 gloves.
To learn more about selection by permutation and combination, follow the link.
https://brainly.com/question/4658834
#SPJ4
A school is selling cookies as a fundraiser. Each box contains 10 cookies. Each student can sell 17 boxes of cookies. How many cookies can 11 students sell
11 students could sell 1870 cookies.
Explain about the expressions?A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.
Combining numbers, variables, and operators to represent something's value is known as a mathematical expression. Setting two expressions equal to one another creates an equation, a mathematical statement.
An expression is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in certain ways. Language phrases can comprise actions on their own, but they do not make up complete sentences.
= 10 X 17
= 170 X 11
= 1870
To learn more about expressions refer to:
https://brainly.com/question/1859113
#SPJ4
Sangeeta divide R 40000 between her two daughterRimmy and Simmi in the ratio 3:5 Find the hare of each daughter
share of rimmy and simmi is rs15000 and rs25000.
this question is of ratio and proportion, and the solution is as follows,
total amount = rs 40000
Rimmy and Simmi in the ratio = 3:5
sum of shares= 3+ 5 = 8.
so,
share of Rimmy is = 3/8 X 40000
= 120000/8
= 15000
share of simmi is = 5/8 X 40000
= 200000/8
= 25000
so the share of rimmy and simmi is rs15000 and rs25000.
Learn more about ratios here :-
https://brainly.com/question/13419413
#SPJ4
A rare Pokemon trading card deck you have been wanting to buy costs 4500. You have earned 2485 from helping your mom in her online selling business. If you can save 155 weekly from your allowance, how many weeks would it take for your funds to reach 4500
It will take 13 weeks to gather funds that sum up to $4500.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given: I have $2485 and I save $155 weekly
Thus amount left to be gathered is $4500-$2485=2015
If I save $155 weekly then we get = $2015/$155
=13 weeks
Hence, It will take 13 weeks to gather funds that sum up to $4500.
Learn more about the unitary method here:
https://brainly.com/question/22056199
#SPJ1
Find the numbers. A room is 12 feet longer than it is wide. Half the perimeter of the rectangular floor is 72 feet. Find the length and the width. Use elimination or substitution to solve this problem.
Answer: The width of the room is 36 feet and the length of the room is 48 feet.
Step-by-step explanation:
To solve this problem using elimination, you can set up a system of equations to represent the information given in the problem.
Let w be the width of the room, and let l be the length of the room. We are told that the length of the room is 12 feet longer than its width, so we can set up the equation:
l = w + 12
We are also told that half the perimeter of the rectangular floor is 72 feet. The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
Since half the perimeter is 72 feet, the full perimeter is 2 * 72 = 144 feet. Substituting the equation for the length of the room, we get:
144 = 2 * (w + 12 + w)
Combining like terms and solving for w, we get:
w = 36
Substituting this value back into the equation for the length of the room, we get:
l = 36 + 12 = 48
Therefore, the width of the room is 36 feet and the length of the room is 48 feet.
To solve this problem using substitution, we could start by solving for the width of the room in one of the equations, and then substituting that value into the other equation to solve for the length of the room.
For example, we could solve the equation l = w + 12 for w to get:
w = l - 12
Substituting this expression for w into the equation for the perimeter, we get:
144 = 2 * (l - 12 + l)
Combining like terms and solving for l, we get:
l = 48
Substituting this value back into the equation for the width of the room, we get:
w = 48 - 12 = 36
Therefore, the width of the room is 36 feet and the length of the room is 48 feet.
The question is in the picture
Answer:
For the first line its distributive property
The 2nd is combining like terms
4th is simplifying it
Im not sure about the last one since its just the answer of the problem
Step-by-step explanation:
Tony performs a dilation on Figure R. He uses a scale factor of 4 with a center of dilation at the orgin.
What are the coordinates of the image of vertex P?
The x- coordinate of the vertex P is -4 and the y coordinate is -3. The coordinates of the image of vertex P is thus, (-4, -3).
What are coordinates?Coordinates are numbers describing the position of a point or shape in a line or particular space. We can represent a line or shape in the space between number lines with both positive and negative coordinates.
The vertical axis in the number line is called y-axis and the horizontal axis is called the x- axis. The coordinate of a point is written as (x, y). The x, y represents the numbers on x-axis and y -axis touched at which the point lies in the graph.
For the given vertex P, the vertex lies on the point -4 on x-axis and on -3 in y axis. Hence, the coordinate of P is (-4, -3).
Find more on coordinates:
https://brainly.com/question/27749090
#SPJ1
Can 123 make a triangle?
No, 1, 2, and 3 are not valid side lengths for a triangle. So 1, 2 and 3 cannot make a triangle.
In order for a shape to be a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.
3 + 2 = 5 > 1
3 + 1 = 4 > 2
1 + 2 = 3 not greater than 3
So as 1 + 2 not greater than 3, these set of side lengths does not follow the theorem. Thus a triangle cannot be formed with sides of length 1, 2, and 3.
--The question is incomplete, answering to the question below--
" Can 1, 2 and 3 make the sides of a triangle?"
To know more on triangle inequality theorem
https://brainly.com/question/30195794
#SPJ4
Determine the slope, x-intercept and y-intercept of the line given by the equation 2x+3y=6
Worksheet fun balancing equations
The number of left-handed people in the world is one-tenth the number of right-handed people. The percent of right-handed people is nine times the percent of left-handed people and ambidextrous people combined. What percent of people are ambidextrous
According to question we can say that 1% percent of people are ambidextrous.
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
Let 'x' represent the percentage of left-handed people.
Let y represent the percentage of right-handed people.
Let z represent the percentage of ambidextrous people.
x = y/100
100x = y
y/100 = 9( x/100 + z/100)
y = 9x + 9Z
10x = 9x + 9z
x = 9z
x+y+z = 100
11x + x/9 = 100
100x/9 = 100
x = 9
z = 1%
To know more about percentage visit:
brainly.com/question/28269290
#SPJ4
A manufactor makes integrated circuits that each have a resistance layer with a target thickness of 200 units. A circuit won't work well if this thickness varies too much from the target value. These thickness measurements are approximately normally distributed with a mean of 200 units and a standard deviation of 12 units. A random sample of 17 measurements is selected for a quality inspection. We can assume that the measurements in the sample are independent. What is the probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value?Choose 1 answer:A) 0.16B) 0.32C) 0.40D) 0.80E) We cannot calculate this probability because the sampling distribution is not normal.
The probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.
What is the Central Limit Theorem?
The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
We can use the Central Limit Theorem to determine that the sampling distribution of the mean thickness of a random sample of size 17 from a population with a mean of 200 units and a standard deviation of 12 units will be approximately normal with a mean of 200 units and a standard deviation of (12 units)/√17 = 2.8 units.
Given that the mean thickness in these 17 measurements x is farther than 3 units away from the target value, we can use the standard normal table to find the probability.
Let's call X = mean thickness,
if X > 203, we have P(X>203) = P(Z> (203-200)/2.8) = P(Z>1.071) = 0.15
if X < 197, we have P(X<197) = P(Z< (197-200)/2.8) = P(Z<-1.071) = 0.15
Hence, the probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.
To learn more about the Central Limit Theorem visit,
https://brainly.com/question/18403552
#SPJ4
How many ways can a president, a vice-president and a secretary be chosen from 11 members of a club assuming that one person cannot hold more than one position
On solving the provided question, we can say that so, we apply permutation P(12,4) = 12!/ 8! = 11880
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of.
so, we apply permutation
P(12,4) = 12!/ 8! = 11880
To know more about permutation visit:
https://brainly.com/question/1216161
#SPJ4
I need to factor completely to get an answer for
n²-10n+24
I need to get factors in parenthesis like (n +/- #) (n +/- #)
I need it before tomorrow
Answer:
(n - 6)(n -4)
Step-by-step explanation:
Find two numbers that add to - 10 and multiply to +24.
In this case, -6 * -4 satisfies these requirements.
What are the 3 steps to solving an equation?
Following are three steps 1. Isolate the variable: First, identify the variable you are trying to solve for and use the other terms in the equation to isolate that variable. This means using inverse operations to move any terms containing the variable to one side of the equation and any terms without the variable to the other side of the equation.
2. Simplify the equation: Once the variable is isolated, use the properties of equality and inverse operations to simplify the equation, if needed.
3. Solve the equation: Finally, use the inverse operations to solve the equation and find the value of the variable.
To know more about equation here
https://brainly.com/question/30187464
#SPJ4
What will be the output of 7 by 2?
The resultant output of the given question is 7 by 2 is 14.
This is because 7 multiplied by 2 is equal to 14
When you multiply two numbers, the result is the product of the two numbers. In this case, 7 multiplied by 2 is equal to 14.
Mathematicians use the process of multiplication to calculate the product of two or more given numbers. It is a fundamental mathematical operation in maths that is frequently utilised in everyday life. When we need to combine groups of similar sizes or values , we utilise multiplication.
Hence the correct answer to the given question is 14 .
To know more about multiplication here
https://brainly.com/question/27646651
#SPJ4
What are the zeros of the quadratic 3(x+4)(x − 12) = 0?
Answer:
-4 and 12 are the zeros of the quadratic.
Step-by-step explanation:
What value does X need to be so (x+4) is 0? -4
What value does X need to be so (x-12) is 0? 12
Identify a method of developing systems that is well-suited to traditional project management tools and technique
The waterfall model has equivalent flexibility to other approaches. suitable for conventional project management tools and methods.
The waterfall model of the software development life cycle is the greatest technique for creating systems.
This includes the following elements:
1. The requirements phase, which takes into account the needs needed to build the product
2. The product's design is created
3. The programmers who wrote the code to put the product into action built the product.
4. The product is examined and all flaws are fixed to ensure that it responds correctly to inputs.
5. The systems are periodically maintained to ensure continued operation and proper output
To know more about the waterfall model, refer to this link:
https://brainly.com/question/13439438
#SPJ4
A lost tourist arrives at a point with 2 roads A and B. Road A leads to the city and takes either 4 or 8 hours, depending on traffic, with equal probability. Road B brings him to the city after 7 hours on average. Since there are no signs on the road, the tourist chooses a road with equal probability; what is the expected time until the tourist arrives to the city
The expected time until the tourist arrives in the city is 4.75 hours.
The expected time until the tourist arrives at the city can be calculated by using the formula for the expected value:
Expected value = (probability of outcome 1) x (value of outcome 1) + (probability of outcome 2) x (value of outcome 2) + ...
In this case, there are two possible outcomes: the tourist takes road A or road B.
If the tourist takes road A, the expected time until he arrives in the city is the average of the two possible travel times (4 hours and 8 hours). The probability of this outcome is 0.5 (the tourist has an equal chance of choosing either road). So, the expected value for this outcome is (0.5) x (4 + 8)/2 = 6 hours.
If the tourist takes road B, the expected time until he arrives in the city is 7 hours. The probability of this outcome is also 0.5. So, the expected value for this outcome is (0.5) x 7 = 3.5 hours.
To find the overall expected time until the tourist arrives in the city, we add up the expected values for each outcome:
Expected time = (0.5) x 6 + (0.5) x 3.5 = 4.75 hours
So the expected time until the tourist arrives in the city is 4.75 hours.
To learn more about the probability, visit:
brainly.com/question/30034780
#SPJ4
Get the standard form and slope-intercept form
1. y -2 = 2/3 (x - 1)
2. y + 4 = - 4/5 (x+3)
Answer:
1. y-2=2/3(x-1) slope: y=2/3x+4/3 standard: 2x-3y=-4
Step-by-step explanation:
Kayla had 20 candie. Kayla have 1/5 of the candie to her iter. Of the amount left , he gave 3/8 of her friend. How many candie doe Kayla have left for herelf ?
The candies left for Kyla were 10 based on the amount given to her sister and friend from total 20 candies.
Firstly we will calculate the remaining candies from twenty after giving to her sister. Next calculation will be the final answer representing candies left for Kyla herself.
Remaining candies = total number of candies - 1/5×total candies
Keep the values in formula
Remaining candies = 20 - 1/5×20
Remaining candies = 20 - 4
Remaining candies = 16
Total candies for Kyla = remaining candies - 3/8×remaining candies
Candies for Kyla = 16 - 3/8×16
Candies for Kyla = 16 - 3×2
Candies for Kyla = 16 - 6
Candies for Kyla = 10
Thus, Kyla received 10 candies.
Learn more about fraction -
https://brainly.com/question/1622425
#SPJ4
What is the slope and y-intercept of this linear equation y 3x 5?
The slope of the line is 3 and the y-intercept is -5.
The slope of a line is the coefficient of the x term (in this case, 3). To calculate the y-intercept, we can plug in x = 0 and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5. Therefore, the slope is 3 and the y-intercept is -5.
The slope of a linear equation is found by looking at the coefficient of the x term. In this case, the coefficient of the x term is 3, so the slope of the line is 3. To find the y-intercept, we can plug in x = 0 into the equation and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5, so the y-intercept is -5. Therefore, the slope of the line is 3 and the y-intercept is -5. This equation is therefore a linear equation with a slope of 3 and a y-intercept of -5.
Learn more about slope here
https://brainly.com/question/3605446
#SPJ4
Mike is saving money for a new bike that costs $180.00
If represents the amount of money he has saved so far, which expression represents the amount of money,in dollars, he still needs to save?
A
180+m180+m180+m
B
180−m180-m180−m
C
180×m180\times m180×m
D
180÷m180\div m180÷m
Answer: B
Step-by-step explanation:
B) 180−m180-m180−m
Please answer quick! The question is in a file down below.
Answer:
perimeter= 9+9π cm
area= 40.5-10.125π cm²
Step-by-step explanation:
area of the square =9x9=81cm²
area of the two semicircles which have the same diameter =area of one circle
= (9÷2)²π =(81÷4)π
area of the whole shaded part = 81- (81÷4)π cm²
the area of each shaded part= (81-(81÷4)π)÷2
= 40.5-10.125π cm²
circumference of 2 semicircles= circumference of 1 circle = 2πr = 2x9xπ= 18π cm
then are perimeter of the whole shaded part = 18π+9+9= 18+18π cm
perimeter of each shaded part = (18+18π)÷2=
9+9π cm
The Jackson family is planning a weekend vacation. They plan to rent a car from the ABC Car Rental Company. Let m represent the number of miles the family will drive. Let c represent the cost for renting a car. Write an equation that shows what the cost for renting a car will be.
Weekend Special: $40 + $0. 10 per mile
An equation that shows what the cost of renting a car will be: C=R+mc.
Let the rental cost = R
consider m to be the number of miles driven= m
let c be the cost per mile
And C is the total cost of renting;
Then C = R+mc
the given equation $40 + $0. 10 per mile
Now, in the above equation consider:
R =$40 ( the rental cost)
c = $0.10 ( the cost per mile)
The total cost is C = $40+$0.10m
Ex:
if m is known assume m=1000 miles
Then the total cost C = $40+($0.10/mile)(1000miles)
then C = $40+$100=$140
To know more about the equation of cost of renting:
https://brainly.com/question/16404189
#SPJ4
simpelest form of the ratio 2 weeks to 30 days
Answer:
7:15 ,2 weeks=14 days and 30 days divide by 2 = 7 and 15 put them to a ratio and you'll get 7:15.
Please help asap!!!
Rotation of PQRS by 90 degree.
What does a math transformation mean?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location. What are the four mathematical transformations?
In how many ways Transformations can be divided?Translation, rotation, reflection, and enlargement. You must be able to carry out each transformation and recognize which ones have already been done.
To know more about geometric figure visit:-
brainly.com/question/11266123
#SPJ1
The average monthly salary of 10 male staffs and 5 female staffs of a manufacturing company are Rs. 20,000 and Rs. 18,000 respectively. Find the average monthly salary of all staffs taken together.
The average monthly salary of all the staff is going to be 19,333.34 ₹.
Average is the value obtained by dividing the sum total of a set of figures by the number of figures. In this question, we have to find the average monthly salary of all the staff taken together,
So the sum total of the set of figures here will be (20,000 × no. of males + 18,000 × no. of males) ₹ and the number of figures here will be no. of males + no. of females. It's given that
No. of males=10
No. of females=5
So, the total no. of figures = 15
Sum total of set of figures = (20,000 × 10 + 18,000 × 5 )₹ and the average will be
=(20,000 × 10 + 18,000 × 5) ₹/15
=(200,000+90,000)/15₹
=290,000/15 ₹
=19,333.34 ₹
Learn more about Averages on
https://brainly.com/question/24057012?referrer=searchResults
#SPJ4
How many solutions will the following system have? 4x+y=13 1/2}y=-2x+5
Step-by-step explanation:
I have to assume the equations are
4x + y = 13
(1/2)y = -2x + 5
let's bring both of them into a "y = ..." form :
y = -4x + 13
y = -4x + 10
now we see that both equations are lines with the same slope but different y-intersect.
so, they are parallel but not identical.
therefore, there are 0 solutions. the lines will never intersect and have no point in common.
HELP ASAP PLSS 50 POINTS!!!
Answer:
Missing part is ∠BAC and ∠DPFStep-by-step explanation:
ASA requires that both triangles have two angles and the included side to be congruent.
We have one side and an adjacent angle and need the second angle adjacent to the marked side to be congruent as well
It is the ∠BAC of ΔABC and ∠DPF of ΔPDF or simply ∠A and ∠P.