ten distinct points are chosen on a circle. a line segment is drawn between every pair of chosen points. how many line segments are drawn?
Answers
Answer:
45
Step-by-step explanation:
You want to know the number of line segments that can be drawn between pairs of points in a group of 10 distinct points.
SolutionFrom the first point, 9 segments can be drawn.
From the second point 8 more segments can be drawn. (The segment to the first point has already been counted.)
From the third point, 7 more segments can be drawn. The total number of segments will be the sum of integers from 1 through 9:
9(10)/2 = 45
45 line segments can be drawn.
__
Additional comment
This is identical to the "handshake" problem: the number of handshakes in a group of 10 people if each shakes hands with all the others.
Related Questions
Rewrite -cot^2x/ 1+ cscx so its not in fraction form.
Answers
Rewriting the given trigonometric form using trigonometric identities by eliminating fraction form gives [tex]-cotx.cosx.(sinx+1)[/tex]
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.
Calculation:We know that,
[tex]cot^{2} x = \frac{cos^{2}x }{sin^{2}x }[/tex]
[tex]1+cscx = (1+\frac{1}{sinx} ) = \frac{sinx+1}{sinx}[/tex]
Rewriting the given trigonometric form using trigonometric identities by eliminating the fraction form gives[tex]-cotx.cosx.(sinx+1)[/tex]
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ANSWER ASAP
L=M-N solve for N
1. N=M - L
2. N= LM
3. N= M + L
4. N= L - M
Answers
Answer:
1) N = M - L
Step-by-step explanation:
Given equation,
→ L = M - N
Now the value of N will be,
→ L = M - N
→ M - N = L
→ -N = L - M
→ N = -L + M
→ [ N = M - L ]
Hence, value of N is M - L.
A company ha net ale of $732400 and cot of good old of $293400. It gro profit equal:
Answers
By subtracting the cost of goods sold form the net sales, the gross profit = $439000.
What is gross profit?Gross profit is a financial measure that represents the difference between a company's net sales and the cost of goods sold. It is a key indicator of a company's profitability and can be used to assess the efficiency of the company's operations.
What is the formula to calculate gross profit?The formula for calculating gross profit is:
Gross profit = net sales - cost of goods sold
Gross profit = net sales - cost of goods sold
Gross profit = $732400 - $293400
Gross profit = $439000
Therefore, the gross profit of the company is $439000.
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a certain statistic dˆ is being used to estimate a population parameter d. the expected value of dˆ is not equal to d. what property does dˆ exhibit?a. The sampling distribution of d hat is normal.b. The sampling distribution of d hat is binomial.c. The sampling distribution of d hat is uniform.d. d hat is unbiased.e. d hat is biased.
Answers
The right answer is: E, according to the Central Limit Theorem for proportionality. The statistic is inaccurate.
In probability theory, the central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
The Central Limit Theorem establishes that for a proportion p in a sample of size n:
The expected value is μ=р
The standard error is s=[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
In this problem, the expected value is different of the expected of μ=р , hence, the statistic is biased, and the correct option is E.
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A family member has two and one fifth yds of ribbon, and you add two thirds yds to it. How much ribbon would you each get if you split the total amount in half?
forty three over fifteen
thirty four over fifteen
forty three over thirty
twenty two over thirty
Answers
Answer:
C) forty three over thirty----------------------------------------------------
Add up the two numbers:
two and one fifth + two thirds = 2 1/5 + 2/3 = 11/5 + 2/3 = Covert mixed number to fraction3*11/(3*5) + 5*2/(5*3) = Common denominator is 3*5 = 1533/15 + 10/15 = Add up fractions43/15 SumSplit this in half:
43/15 : 2 = 43/30This is matching the third option.
is 65% grater or less than 3/ 5
Answers
Answer:
Greater than
Step-by-step explanation:
65% =65/100=6.5/10=3.25/5
Answer 1+13-b
I just built diff
7. 20,000 pounds equals how many us tons? a. 2,000 tons b. 10 tons c. 10,000 tons d. 1 ton
Answers
20,000 pounds equals to 10 US ton.
Pound is the name of a type of currency. It was used in many different countries both in the past and at the present time. The Latin expression libra pond, in which pond is an adverb meaning "by weight" and libra is a noun meaning "pound," is where the English term "pound" comes from. US Mass is measured in tons, which is one ton. In the United States, where it is frequently used, it is referred to as a common ton.Value conversion from Pound to US Ton
Add the value and the conversion ratio together.
1 pound = 0.0005 US ton
20,000 pounds worth
20,000 pounds × value of one US ton
20,000 × 0.0005
10 tons
Therefore, 20,000 pounds equals to 10 US ton.
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The ratio of red marble to blue marble in a bag i 3:4. If there are 42 marble in the bag how many of the marble are red
Answers
The ratio of red marble to blue marble in a bag is 3:4. If there are 42 marble in the bag,There would be 30 red marbles in the bag.
Red and blue marbles are distributed in a 3:4 ratio.This means that for every 4 blue marbles, there are 3 red marbles.
If we divide 42 (the total number of marbles in the bag) by 4, we get 10.5. This tells us that if there are 4 blue marbles, there are 10.5 red marbles. We can't have a fraction of a marble, so we round down to 10.
Since for every 4 blue marbles there are 3 red marbles, if there are 10 blue marbles, there must be 10 x 3 = 30 red marbles.
Therefore, there are 30 red marbles in the bag.
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Can someone please help me with this problem?
Answers
Answer: 18/9 if not it's something along that-
Step-by-step explanation:
7^2 = 49 so like 49-31 equals 18 and the denominator 3^2 = 9 , so if it's not 18/9 then it's like 1/2 or something bc 9 + 9 is 18 yk-
what is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations? (round your answer to three decimal places.)
Answers
0.003 is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations
To calculate the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations.The mean is the expected number of calls involving a fax transmission, while the standard deviation is the measure of variability in the distribution. We then use this information to calculate the probability of exceeding the expected number by more than 2 standard deviations, which can be done using the z-score formula. The z-score for values more than 2 standard deviations away from the mean is 2.33, which corresponds to a probability of 0.003. Thus, the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations is 0.003.
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Julia decided to pend 5 1/4 hour exerciing over the weekend. She pent 3 1/3 hour exerciing on Saturday. How much longer doe he need to pend exerciing on Sunday in order to reach her goal?
Answers
Julia needs to spend 1.92 hours exercising on Sunday in order to reach her goal.
The number of hours Julia needs to spend exercising on Sunday can be calculated as follows;
Total number of hours to spend exercising = 5 1/4 = 21/4 = 5.25 hours
Total number of hours spent exercising on Saturday = 3 1/3 = 10/3 = 3.33 hours
Now the number of hours she needs to spend exercising on Sunday can be determined by subtraction as follows;
Hours on Sunday = Total hours - Hours on Saturday
Hours on Sunday = 5.25 hours - 3.33 hours
Hours on Sunday = 1.92 Hours
Thus the number of hours she needs to spend exercising on Sunday is calculated to be 1.92 hours.
Although a part of your question is incorrect, you might be referring to this question:
Julia decided to spend 5 1/4 hours exercising over the weekend. She spent 3 1/3 hours exercising on Saturday. How much longer doe he need to spend exercising on Sunday in order to reach her goal?
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What is the equation of the line that passes through the point (8, 6) and has a slope
of o?
Answers
Answer:
y=6
Step-by-step explanation:
The equation of a line in slope-intercept form is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis. In this case, we are given that the line passes through the point (8, 6) and has a slope of 0, so we can plug these values into the equation to find the equation of the line.
Since the slope of the line is 0, the equation of the line becomes:
y = 0x + b
To find the value of b, we need to plug in the coordinates of the point (8, 6) into the equation and solve for b. This gives us:
6 = 0 * 8 + b
b = 6
Therefore, the equation of the line is given by:
y = 0x + 6
This equation tells us that the y-coordinate of any point on the line is always 6, regardless of the x-coordinate of the point. This means that the line is horizontal and passes through the point (8, 6).
Mia' plant grow at an average rate of 5cm each month. When he bought it, it wa 18 cm tall. Select the function that model the relationhip between y, the height of the plant in cm, and x, the time in month that it grow. A. Y = 18x 5
B. Y = 18 5x
C. Y = x 18
D. Y = 23x
Answers
The function that models the relationship between plant height (y) and growth time (x) is y = 18 + 5x
The linear equation of two variables
The two-variable linear equation is a solving system for a mathematical problem in which there are two case variables.
In the problem, we get the info that the plant's initial height is 18 cm, meaning this value will not change.
We also get information that the height of the plants increases by 5 cm every month, meaning this value will change over time. If x is the growth time (in months), then the increase in height over time can be written mathematically as 5x.
Based on the two statements above, if y is the plant height (in cm) after x months, then mathematically it can be written as:
y = 18 + 5x
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Equation of line passing through the point (1, 2) and perpendicular to the line y = 3x - 1 is A. x+3y+7=0 B. x+3y-7=0 B.x+3y=0 D. x-3y=0
Answers
To find the equation of the line that passes through the point (1, 2) and is perpendicular to the line y=3x-1, we can first find the slope of the line y=3x-1. The slope of this line is 3, so a line perpendicular to it will have a slope of -1/3. We can then use the point-slope form of the line to write the equation of the line that passes through (1,2) and has a slope of -1/3. The point-slap form of a line is given by y-y₁ = m(x-x₁), where (x₁,y₁) is a point on the line and m is the slope of the line. Plugging in the coordinates of the point (1,2) and the slope -1/3, we get the equation y-2 = -1/3(x-1), which simplifies to y-2 = -x/3 + 1/3. Multiplying both sides of the equation by 3 to get rid of the fractions, we get 3y-6 = -x+1. Finally, we can move all the terms to one side of the equation to get the standard form of the line: 3y-x-5 = 0. Therefore, the equation of the line that passes through the point (1, 2) and is perpendicular to the line y = 3x - 1 is x-3y-5=0, so the correct answer is A.
suppose v1,v2,...,vn is a set of vectors each of dimension d. if d < n, what is the maximum number of linearly independent vectors that you can draw from the set? justify your answer
Answers
The dimension is d and d<n. Thus maximum number of linearly independent vectors that can draw from the set V1, V2....Vn is d.
First note that for "any vector space V, basis B of V is maximal linearly independent set in V". That is there is no other any linearly independent set which contains more than |B| number of elements on B. Let us consider this statement as 1. Two or greater vectors are stated to be linearly independent if none of them may be written as a linear mixture of the others. On the contrary, if at the least certainly considered one among them may be written as a linear mixture of the others, then they may be stated to be linearly dependent. Now here dimension is d and d<n. Thus maximum number of linearly independent vectors that can draw from the set V1, V2....Vn is d.
Thus, the maximum number = d
Therefore, statement is true hence proved.
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Latanya needs to order some new supplies for the restaurant where she works. The restaurant needs at least 739 glasses. There are currently 390 glasses. If each set on sale contains 6 glasses, which inequality can be used to determine xx, the minimum number of sets of glasses Latanya should buy?
Answers
The solution to this inequality is x >= 58. This means that Latanya should buy at least 58 sets of glasses in order to have at least 739 glasses.
What is the inequality equation?
Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤, or ≥.
To determine the minimum number of sets of glasses that Latanya should buy, we can set up the following inequality:
x * 6 + 390 >= 739
This inequality states that the number of glasses Latanya has after buying x sets of glasses should be greater than or equal to the minimum number of glasses the restaurant needs.
To solve for x, we can subtract 390 from both sides of the inequality to get:
x * 6 >= 739 - 390
x * 6 >= 349
x >= 349/6
x >= 58.16
x >= 58
Hence, The solution to this inequality is x >= 58. This means that Latanya should buy at least 58 sets of glasses in order to have at least 739 glasses.
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For the function defined by f (x) = startfraction 12 over x squared endfraction, what is the constant of proportionality? a. 120 c. 12 b. Undefined d. 1200.
Answers
The correct option c. 12, is the constant of proportionality.
Define the term constant of proportionality?The ratio between two quantities that are directly proportional is the constant of proportionality.
When two quantities grow and shrink at the same rate, they are directly proportional. When y and x are two values that really are directly proportional to one another, the proportionality constant k is defined as k=y/x.For the stated question-
f (x) = startfraction 12 over x squared endfraction
Rewrite the function as;
f(x)=12/x^2,
Constant of proportionality = 12 (only fixed term in the function)
Thus, the constant of proportionality for the function f(x)=12/x^2, is found as 12.
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Why is it even? There is 3 arrays in total.
Answers
Answer: welp what is inside of the arrays
Step-by-step explanation:
Casho has a points card for a movie theater. She receives 55 rewards points just for signing up. She earns 2.5 points for each visit to the movie theater. She needs at least 90 points for a free movie ticket. Use the drop-down menu below to write an inequality representing v, the number of visits she needs to make in order to get a free movie ticket.
Answers
Answer: She need 14 visits to reach 90 points
Step-by-step explanation:
Let y be the number of points and v be the number of visits
We will have an equation
y= 2.5v + 55
Now we want to find the number of visits she needs to reach 90 points; we put 90 in the y.
90 = 2.5v +55
Subtracted 55 from both sides
35 = 2.5v
Divided both sides by 2.5
v= 14 visits
So she need 14 visits to reach 90 points
The point F( – 4, – 1) i rotated 270° counterclockwie around the origin. What are the coordinate of the reulting point, F'?
Answers
The point F( – 4, – 1) i rotated 270° counterclockwie around the origin. then The coordinates of the point F' is (-1 ,4 )
Given that the point J(-2,1) is rotated about 270° about the origin.
Coordinates of the resulting point F':
Since, we know that, when rotating a point 270° counterclockwise about the origin, the point (x,y) becomes (y,-x) which means we switch the places of x and y coordinates and make x as negative.
Therefore, the transformation is given by
(x ,y) -> ( y , -x)
Using the above transformation, we have,
(-4 ,-1) ⇒ ( -1 , -(-4)) ⇒ (-1 , 4)
Therefore, the resulting point of the coordinates of the point F' is (-1 ,4)
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A landscaper has 6 pounds of seed available. He uses of a pound of grass seed for each acre he plants. Determine how many whole acres can be planted with the available seed.
Answers
Answer: Only 1 pound.
Step-by-step explanation: It saying it Infront of ya as it said "1 pound fills each acre each".
A model rocket is launched with an initial upward velocity of 35 m/s. The rocket's height h (in meters) after t seconds is given by the followi
h=35t-5t
Find all values of 1 for which the rocket's height is 12 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
h
-ground
t= seconds
Dor
X
S
Answers
Answer:
The possible values of t for which the rocket's height is 12 meters are approximately 1.1 or -1.1.
Step-by-step explanation:
The height of the rocket after t seconds is given by the equationh = 35t - 5t^2.To find the values of t for which the rocket's height is 12 meters, we can set the height equal to 12 and solve for t
12 = 35t - 5t^2
t = (-b ± √(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation. In this case, a = -5, b = 35, and c = -12.Plugging these values into the quadratic formula, we gett = (35 ± √(35^2 - 4(-5)(-12))) / 2(-5)
t = (35 ± √(35^2 + 240)) / -10
t = (35 ± √575) / -10
This gives us two possible values fort = (35 + √575) / -10 = (35 + 24) / -10 = 11/10 = 1.1
t = (35 - √575) / -10 = (35 - 24) / -10 = -11/10 = -1.1
Therefore, the rocket's height is 12 meters when t is approximately 1.1 or -1.1.The rocket's height is 12 meters at time t = 0.4 seconds.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
A model rocket is launched with an initial upward velocity of 35 m/s.
The rocket's height h (in meters) after t seconds is h=35t-5t
We have to find the time(s) when the rocket's height is 12 meters, we need to solve the equation:
h = 35t - 5t = 30t
We want to find all values of t that make h = 12. So we set h = 12 and solve for t:
12 = 30t
Divide both sides by 30
t = 12/30
t = 0.4
Therefore, the rocket's height is 12 meters at time t = 0.4 seconds.
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-3x² - 4x +8>4
solve inequality and state solution in interval and inequality notation 100 points
Answers
Answer:
Step-by-step explanation:
< 4/7
Samuel and Joyce both bought CDs. Samuel bought 3x CDs and Joyce bought 2x-1 CDs.
¿Drive
mS
amS
Part A: If each CD had a regular price of $18 and a discount of $2, then which expression would show the amount of discount for all of their CDs?
Part B: What is the expression for the COST of their CDs, combined (ignore tax)?
Answers
Step-by-step explanation:
Part A: 3(-2) + 2(-2)
Part B: [3(8) + 2(18) - 1] - [3 + 2(-2)]
Price Discount
Please I need help, please answer the question in the image, please and thank you.
Answers
The rate of change of the given data between 3 and 7 hours is; 19 miles per hour
How to calculate the rate of change?We are told that rate of change is the difference between what the value of the data began at versus the value the data ended at.
Now, the formula for the rate of change between two coordinates (x₁, y₁) and (x₂, y₂) is;
Rate of change = (y₂ - y₁)/(x₂ - x₁)
Now, we are told that we should find the rate of change from 3 to 7 hours and so we first write the coordinates;
(3, 209) and (7, 285)
Thus;
Rate of change = (285 - 209)/(7 - 3)
Rate of change = 76/4
Rate of change = 19 miles per hour
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4. Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest
compounded daily. What is the annual percentage yield?
Answers
The annual percentage yield is 4.835%. Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest compounded daily.
Define annual percentage.An annual percentage rate, or APR, is a figure that expresses the entire cost of borrowing money as a proportion of the loan's principle. An accurate picture of how much it costs to borrow money is intended to be provided by the APR on a loan or credit card.
Given
Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest
compounded daily.
1.048353
The table on page A14 shows the cost per $1.00 (over the course of a year).
$35,000×1.048353=$36,692.36
The sum of the initial principle and the amount per $1.00 is the amount (for a year).
$36,692.36−$35,000=$1,692.36
The difference between the amount (for one year) and the initial principal is the interest (for one year).
$1,692.36÷$35,000
=0.04835
=4.835%
The interest (for a year) divided by the initial principle results in the annual percentage yield.
4.835%
The annual percentage yield is 4.835%. Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest compounded daily.
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Find the 5 times the difference of 22 and 16 added to 5 multiplied by the sum of 10 and 8.
Answers
Answer:
120
Step-by-step explanation:
5(22-16) + 5(10+8)
5(6) + 5(18)
30 + 90
120
sketch the curve with equation x2/3 + y2/3 = 4 and use symmetry to find its length.
Answers
Answer:
Step-by-step explanation:Sketch the curve with equation x^(2/3) + y^(2/3) = 1 and usesymmetry to find its length.
There are 10 finalists in a figure skating competition. How many ways can gold, silver, and bronze medals be awarded?
Answers
Answer:
720
Step-by-step explanation:
[tex]\frac{n!}{(n-r)!}[/tex]
[tex]\frac{10!}{(10-3)!}[/tex]
[tex]\frac{10!}{7!}[/tex]
720
-2x² + 41=0
Solve quadratic formula
Answers
Answer:
Step-by-step explanation: