Construct triangle PQR in which angle Q = 30 deg , angle R=60^ and PQ + QR + RP = 10cm
Answers
We can see here that in order to construct a triangle PQR in which angle Q = 30°, angle R=60° and PQ + QR + RP = 10cm, here is a guide:
Draw a line segment AB = 10 cm.Construct angle 30° at point A and angle 60° at point B.Draw angle bisectors to angles A and B.Make sure these angle bisectors intersect at point P.Draw perpendicular bisector to line segment AP.Let this bisector meet AB at Q.Then draw perpendicular bisector to line segment BP.Let this bisector meet AB at R.Join PQ and PR.PQR is the required triangle.What is a triangle?A triangle is a geometric shape that is defined as a three-sided polygon, where each side is a line segment connecting two of the vertices, or corners, of the triangle. The interior angles of a triangle always add up to 180 degrees.
Triangles can be classified into different types based on their side lengths and angles, such as equilateral triangles with three equal sides and three equal angles, isosceles triangles with two equal sides and two equal angles, and scalene triangles with no equal sides or angles.
Triangles are used in many areas of mathematics and science, including geometry, trigonometry, and physics.
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Related Questions
find the slope of a line parallel to the line whose equation is 5x - 6y = 30. fully simplify your answer 
Answers
By answering the presented questiοn, we may cοnclude that Since a line equatiοn parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.
What is equatiοn?When twο expressiοns are equal, a mathematical equatiοn is a statement stating that equality. Twο sides are jοined by the algebraic symbοl (=), and tοgether they make up an equatiοn. Fοr instance, the claim that "2x + 3 = 9" means that "2x plus 3" equals the number "9" is made in this argument. Finding the value(s) οf the variable(s) necessary fοr the equatiοn tο be true is the gοal οf sοlving equatiοns.
There are variοus types οf equatiοns, including regular and nοnlinear οnes with οne οr mοre elements. "x² + 2x - 3 = 0" is an equatiοn that raises the variable x tο the secοnd pοwer. Mathematical disciplines like algebra, calculus, and geοmetry all make use οf lines.
the given equatiοn:
[tex]$\begin{array}{c}{{5x-6y=30}}\\ {{-6y=-5x+30}}\\ {{y=(5/6)x-5}}\end{array}$[/tex]
Sο the slοpe οf the given line is 5/6.
Since a line parallel tο this οne will have the same slοpe, the slοpe οf the parallel line is alsο 5/6.
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Two cars, one going due east at the rate of 90 km/hr and the other going to south at the rate of 60 km/hr are traveling toward the intersection of two roads. At what rate the two cars approaching each other at the instant when the first car is 0.2 km and the second car is 0.15 km from the intersection ?
Answers
The two cars are approaching each other at a rate of 36 km/hr at the given instant.
We can solve this problem by using the Pythagorean theorem and differentiating with respect to time. Let's call the distance of the first car from the intersection "x" and the distance of the second car from the intersection "y". We want to find the rate at which the two cars are approaching each other, which we'll call "r".
At any moment, the distance between the two cars is the hypotenuse of a right triangle with legs x and y, so we can use the Pythagorean theorem
r^2 = x^2 + y^2
To find the rates of change of x and y, we differentiate both sides of this equation with respect to time
2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)
Simplifying and plugging in the given values
dr/dt = (x(dx/dt) + y(dy/dt)) / r
dr/dt = (0.2 x 90 + 0.15 x (-60)) / sqrt((0.2)^2 + (0.15)^2)
dr/dt = (18 - 9) / sqrt(0.04 + 0.0225)
dr/dt = 9 / sqrt(0.0625)
dr/dt ≈ 36 km/hr
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How do you compute the sum of squared errors
Answers
Answer:
Relating SSE to Other Statistical Data
Variance = SSE/n, if you are calculating the variance of a full population.Variance = SSE/(n-1), if you are calculating the variance of a sample set of data.
a) find the probability the chosen person is a woman
b) find the probability the chosen person favors pink or purple
c) if the chosen person favors turquoise, what is the probability this person is a man?
Answers
The probability that the person chosen is a woman is 0.51.
The probability that the person chosen favors pink or purple is 0.67.
The probability that a person that favors turquoise is a man is 0.66.
What are the probabilities?Probability is the odds that a random event would occur. The odds that the event occurs has a probability value that lies between 0 and 1. The more likely it is that the event would happen, the closer the probability value would be to 1.
The probability that the person chosen is a woman = number of women / total number of people = 152 / 300 = 0.51.
The probability that the person chosen favors pink or purple = (number of people who favor pink / total number of people) + (total number of people that favor purple / total number of people) = (50 /300) + (50 / 300) = 0.67.
The probability that a person that favors turquoise is a man = men who favor turquoise / total number of people who favor turquoise = 79/120 = 0.66
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please help I know its 9:35 PM I Just need help what this question2.1 × 1.6 =
21
10
×
16
10
= tenths × tenths my parents are gonna kill me help
Answers
The value of the expression 2.1 × 1.6 = 3.36.
What are decimals?Decimals are a collection of numbers falling between integers on a number line. They are only an additional mathematical representation of fractions. Decimals allow us to express quantifiable quantities like length, weight, distance, money, etc. with more accuracy. Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are shown to the right of the decimal point.
Given that the expression is: 2.1 × 1.6.
2.1 × 1.6 can be written as:
2.1 × 1.6 = 21/10 × 16/10
Multiply the numerator and denominator:
21/10 × 16/10 = 336/100
Covert the fraction into decimal:
336/100 = 3.36
Hence, the value of the expression 2.1 × 1.6 = 3.36.
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I need help with this
Answers
The line segment AB and CB are perpendicular to each other.
How to determine if a line is perpendicular?Check whether the slopes of the lines are the negative reciprocals of one another to see if they are perpendicular to one another. The steps are as follows:
Using the following formula, get the slope of the first line:slope is equal to (y-change) / (change in x)where the "change in y" refers to the difference between the y-coordinates of two points on the line, and the "change in x" refers to the difference between the x-coordinates of the same two places.Using the same formula, determine the slope of the second lineTake the first slope's negative reciprocal by turning it upside down and altering its sign. For instance, the negative reciprocal of the first line's slope of 2/3 is -3/2.Check if the second slope is equal to the negative reciprocal of the first slope. If it is, then the lines are perpendicular.Learn more about Coordinates here:
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state the third congruence statement that is needed to prove that FGH is congruent to LMN using the ASA congruence therom
Answers
Answer:
a
Step-by-step explanation:
show that if 16 people are seated in a row of 20 chairs, then some group of 4 consecutive chairs must be occupied.
Answers
The process to show that if 16 people are seated in a row of 20 chairs, then some group of 4 consecutive chairs must be occupied is shown below.
We prove this using the Pigeonhole Principle, which states that if n items are placed into m containers, and n > m, then at least one container must contain more than one item.
Let us consider the 16 people seated in a row of 20 chairs. Each person occupies one chair, so there are 20 - 16 = 4 empty chairs in the row.
We assume that empty chairs as containers, and people as items that need to be placed into containers.
Since there are more items (people) than containers (empty chairs), there must be at least one group of 2 or more consecutive empty chairs.
Now, let's consider the complement of this statement: Suppose there are no groups of 4 consecutive chairs that are occupied. Then, each group of 4 consecutive chairs contains at most 3 people.
We partition the row of chairs into groups of 4 consecutive chairs.
So, there are 20 - 3 = 17 such groups. By the statement above, each of these groups contains at most 3 people. Therefore, the total number of people seated in the row is at most 17×3 = 51.
But, we know that there are actually 16 people seated in the row. This is a contradiction, since 51 < 16. Therefore, our assumption that there are no groups of 4 consecutive chairs that are occupied must be false, and we have proved that some group of 4 consecutive chairs must be occupied.
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What is the difference between the questionnaire and an interview?
Answers
Answer: Questionnaire refers to a research instrument, in which a series of question, is typed or printed along with the choice of answers, expected to be marked by the respondents, used for survey or statistical study. It consists of aformalisedd set of questions, in a definite order on a form, which are mailed to the respondents or manually delivered to them for answers. The respondents are supposed to read, comprehend and give their responses, in the space provided.
A ‘Pilot Study’ is advised to be conducted to test the questionnaire before using this method. A pilot survey is nothing but a preliminary study or say rehearsal to know the time, cost, efforts, reliability and so forth involved in it.
The interview is a data collection method wherein a direct, in-depth conversation between interviewer and respondent takes place. It is carried out with a purpose like a survey, research, and the like, where both the two parties participate in the one to one interaction. Under this method, oral-verbal stimuli are presented and replied by way of oral-verbal responses.
It is considered as one of the best methods for collecting data because it allows two way exchange of information, the interviewer gets to know about the respondent, and the respondent learns about the interviewer. There are two types of interview:
Personal Interview: A type of interview, wherein there is a face to face question-answer session between the interviewer and interviewee, is conducted.
Telephonic Interview: This method involves contacting the interviewee and asking questions to them on the telephone itself.
The graph of triangle has coordinates E(1,4) F(-1,1) and G(2,-1). Graph triangle of EFG and it’s image after a translation of 3 units left and 1 unit down.
Answers
Answer:
Step-by-step explanation:1.4 -1, 1 2, -1
Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. y 0 1 2 3 4 ply) 0.60 0.20 0.15 0.03 0.02 (a) Calculate and interpret Hy My = 0.20 (b) In the long run, for what proportion of cartons is the number of broken eggs less than jy? (Round your answer to two decimal places). Enter a number. Does this surprise you? Yes O No 0 + 1 + 2 + 3 + 4 (c) Explain why sy is not equal to = 2.0. 5 This computation of the mean is incorrect because the value in the denominator should equal the maximum y value. This computation of the mean is incorrect because it does not take into account that the number of broken eggs are all equally like O This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when O This computation of the mean is incorrect because it does not take into account the number of partially broken eggs.
Answers
a) The value of Hy = 1.15
b) The proportion of cartons with less than 1.15 broken eggs is 0.60
c) The answer is B)This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like.
(a) Hy = 0.67, which means that on average, there are 0.67 broken eggs per carton.
Hy = (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1
= 0.67
(b) The proportion of cartons with less than 0.67 broken eggs is 0.60 which is probability of 0 broken eggs.. This may be surprising as the probability of having less than 0.67 broken eggs is only 0.60, but this is due to the fact that the distribution is skewed towards higher values.
(c) Hy is not equal to the simple average of 0, 1, 2, 3, and 4 because the distribution is not symmetrical. The probabilities are weighted towards higher values, which increases the mean. Additionally, the value of zero should be included in the calculation, as it represents a possible outcome. Therefore, the correct formula for Hy is (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1 = 0.67.
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--The question is incomplete, answering to the question below--
"Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs.
y 0 1 2 3 4
p(y) 0.60 0.20 0.15 0.03 0.02
(a) Calculate and interpret Hy
(b) In the long run, for what proportion of cartons is the number of broken eggs less than Hy? (Round your answer to two decimal places).
Does this surprise you?
Yes
No
(c) Explain why Hy is not equal to (0 + 1 + 2 + 3 + 4)/5 = 2.0.
A. This computation of the mean is incorrect because the value in the denominator should equal the maximum y value.
B. This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like
C. This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when
D. This computation of the mean is incorrect because it does not take into account the number of partially broken eggs."
Answer the question below: *
Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is
increased by 5 m, the new total area of the garden will be 121 m². Find the length of each side of the original garden.
O 6 meters
O 6.6 meters
O 11 meters
O 16 meters
Answers
Sea "x" la longitud de cada lado del jardín original en metros.
La superficie del jardín original es x^2 m².
Si cada lado del jardín original se aumenta en 5 m, el nuevo lado del jardín será de (x+5) metros, y la nueva superficie será (x+5)^2 m².
Según el problema, la nueva superficie total es de 121 m²:
(x+5)^2 = 121
Tomando la raíz cuadrada en ambos lados:
x+5 = 11
Restando 5 en ambos lados:
x = 6
Por lo tanto, la longitud de cada lado del jardín original es de 6 metros.
Por lo tanto, la respuesta correcta es O 6 metros.
x - the length of each side of the original garden
A = x²
( x + 5 )² = 121 /√
x + 5 = 11, or x + 5 = - 11;
x = 11 - 5
x = 6 ( another solution in negative )
Answer:
A ) 6 m
find the closed formula for 3,6,11,18 by relating them to a well known sequence. assume the first term given is
Answers
The closed formula for this particular sequence is an = n² + 2.
Take note that the odd numbers 3, 5, 7, 9, and 11 are separate consecutive terms. This shows that the first n odd numbers can be added to the initial term, az, to get the nth term. Hence, the following is how we may represent the nth term a = az + 1 + 3 + 5 + ... + (2n-3) (2n-3). We may utilize the formula for the sum of an arithmetic series to make the sum of odd integers simpler that is 1 + 3 + 5 + ... + (2n-3) = n².
As a result, we get a = az + n^2 - 1. In conclusion, the equation for the series (an)n21, where a1 = az and an is the result of adding the first n odd numbers to az, is as a = az + n^2 - 1. We have the following for the given series where a1 = az = 3.
So, the closed formula for this particular sequence is an = n² + 2.
To learn more about arithmetic sequences, refer to:
Your question is incomplete. The complete question is:
Find the closed formula for the sequence (an)n21. Assume the first term given is az. an = 3, 6, 11, 18, 27... Hint: Think about the perfect squares.
The number 0 is an element of the set of natural numbers.
OA. True
B. False
SUBI
Answers
it is false. 0 is not a natural number. it is a whole number
What is the slope of the line in the following graph?
Answers
Answer:
1/3
Step-by-step explanation:
using rise over run fron the two dots, we can find 2/6, which simplifies down to 1/3
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch. I need help D:
Please !!!!
Answers
The length of the top of the bookcase should be approximately 25 inches to display the soap carving collection with an area of 300 in².
What is the length of the top of the bookcase?
To find the length of the top of the bookcase (which we'll call "b"), we need to know the area of the collection of soap carvings and the formula for the area of a rectangle:
Area = length x width
We're given the area of the soap carving collection (300 square inches), and we know that the soap carvings will be displayed on top of the bookcase, which is a rectangle.
Let's assume that the width of the bookcase is 1 unit (we can choose any unit we want, as long as we're consistent). Then we can write:
300 = b x 1
Simplifying this equation, we get:
b = 300/1
b = 300
So the length of the top of the bookcase should be 300 inches. However, this assumes that the width of the bookcase is only 1 inch, which is quite narrow.
If we assume a more reasonable width of, say, 12 inches, then we can write:
300 = b x 12
Simplifying this equation, we get:
b = 300/12
b = 25
So the length of the top of the bookcase should be 25 inches (if the width of the bookcase is 12 inches).
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If 5 is increased to 9, the increase is what percentage of the original number
Answers
Answer: It's a 80% increase
Step-by-step explanation:
Each interior angle of a regular polygon is 140 Celcius.How many sides does the polygon have?
Answers
Answer:
9 sides
Step-by-step explanation:
180 - 140 = 40
360 ÷ 40 = 9
I will mark you brainiest!
Given the coordinates shown and given that SU = 10, what are the coordinates of U if STUV is a kite?
A) (10, 18)
B) (0, 28)
C) (18, 28)
Answers
The calculated coordinates of U if STUV is a kite is (10, 18)
Calculating the coordinates of U if STUV is a kite?From the question, we have the following parameters that can be used in our computation:
The figute of a kite
Also, we have
S = (0, 18)
And the distance SU to be
SU = 10
If the quadrilateral STUV is a kite, then the coordinates S and U are on the same horizontal level (according to the figure)
So, we have
U = (0 + 10, 18)
Evaluate
U = (10, 18)
Hence, the coordinates of U if STUV is a kite is (10, 18)
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Please help me anyone please ?!!!?!!
Answers
Answer:
7. 23
8. (3 - 8) x 5
Step-by-step explanation:
I think the second one is right but I know the first one is.
Can you guys help me?
Answers
Answer:
[tex]{ \sf{a = \frac{0.012}{0.633 -0.063 } }} \\ \\ { \sf{a = \frac{0.012}{0.57} }} \\ \\ { \sf{a = 0.021 \: (2 \: s.f)}}[/tex]
If A B C are three matric such that AB=AC such that A=C then A is
Answers
Answer:
invertible
Step-by-step explanation:
If A is invertible then ∣A∣ =0
Segment AE shown has length of sqrt 20. Which segment is closest in length to sqrt 10?
Answers
Segment C has a length of √10, which is the closest to √10 compared to the other segments.
What is Segment?Segment is a customer data platform (CDP) that enables companies to collect, store, and analyze customer data from multiple sources. It helps companies build customer profiles and create personalized experiences for their customers. Segment allows businesses to track website visits, user actions, and other events in real-time, as well as to create custom events and store customer data in a secure and unified data warehouse. With Segment, companies can create powerful customer segmentation, which allows them to target customers with personalized messages and offers. Segment also integrates with various marketing, analytics, and CRM tools to provide a complete picture of customer behavior. It enables companies to build cohesive customer journeys, run campaigns, and optimize their customer experience.
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Complete Question.
Whenever we construct a confidence interval for the population mean, the margin of error includes the standard error of x bar and theA. sampling biasB. nonresponse biasC. z or t value associated with a 95% confidence levelD. desired level of confidence
Answers
The margin of error in a confidence interval for the population mean includes the standard error of the sample mean and the z or t value associated with a certain level of confidence, usually 95% or 99%. Therefore, the correct answer is (C).
Sampling bias and nonresponse bias are potential sources of error in survey or study design and data collection, but they are not directly related to the construction of a confidence interval.
The desired level of confidence is a key input for determining the z or t value used in the calculation of the margin of error, but it is not included in the margin of error itself. The correct answer is z or t value associated with a 95% confidence level.
So, the correct option is (C).
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Please answer Full question
Answers
(1) 4y-7z is a binomial.
(2) 8-xy² is a binomial.
(3) ab-a-b can be written as ab - (a + b) which is a binomial.
(4) z²-3z+8 is a trinomial.
What are monomials, binomials and trinomials?In algebra, monomials, binomials, and trinomials are expressions that contain one, two, and three terms, respectively.
A monomial is an algebraic expression with only one term. A monomial can be a number, a variable, or a product of numbers and variables.
A binomial is an algebraic expression with two terms that are connected by a plus or minus sign. For example, 2x + 3y and 4a - 5b are both binomials.
A trinomial is an algebraic expression with three terms that are connected by plus or minus signs.
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Classify into monomials, binomials and trinomials.
(1) 4y-7z
(1) 8-xy²
(v) ab-a-b
(ix) z2-3z+8
Both descriptive statistics (mean, median, mode, and range) and probability (the likelihood that something will happen) can be useful in our academic, professional, and personal lives. • Determine which of the two (descriptive statistics or probability) you find to be the most useful in your life and explain why using two (2) specific examples.
Answers
Descriptive statistics are the most useful in life. Descriptive statistics provide information about a data set and can help to summarize and interpret data. Specifically, I find the mean and median to be the most useful.
What does Descriptive statistics mean?Descriptive statistics involves the use of measures such as the mean, median, mode, and range, as well as graphical representations of the data, such as histograms, box plots, and scatter plots.
The mean is the average of a set of data and is useful for summarizing and interpreting data. For example, when I am studying for a test, I often use the mean of my practice test scores to understand my overall performance.
The median is the middle value of a set of data and is useful for understanding the spread of the data. For example, when I am tracking my monthly expenses, I often use the median to understand how much I am spending each month. By taking the median of my monthly expenses, I can get an idea of which expenses are taking up the most of my budget.
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Without an appointment, the average waiting time in minutes at the doctor's office has the probability density function f(t)=1/38, where 0≤t≤38
Step 1 of 2:
What is the probability that you will wait at least 26 minutes? Enter your answer as an exact expression or rounded to 3 decimal places.
Step 2 of 2:
What is the average waiting time?
Answers
The probability of waiting at least 26 minutes is 0.316. The average waiting time is 19 minutes.
Step 1:
The probability of waiting at least 26 minutes can be calculated by finding the area under the probability density function from 26 to 38:
P(waiting at least 26 minutes) = ∫26^38 (1/38) dt = [t/38] from 26 to 38
= (38/38) - (26/38) = 12/38 = 0.316
So the probability of waiting at least 26 minutes is 0.316 or approximately 0.316 rounded to 3 decimal places.
Step 2:
The average waiting time can be calculated by finding the expected value of the probability density function:
E(waiting time) = ∫0³⁸ t f(t) dt = ∫0³⁸ (t/38) dt
= [(t²)/(238)] from 0 to 38
= (38²)/(238) = 19
Therefore, the average waiting time is 19 minutes.
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Part B
Draw
parallel to
. You can draw
any length and place it anywhere on the coordinate plane, but not on top of
.
Find and record the ratio, n, of the length of
to the length of
. Then, multiply the lengths of
and
by n and record the resulting lengths.
Answers
In a diagram,
Then,
[tex]\dfrac{DE}{BC}=n[/tex]
For example, suppose that n=2; thus,
[tex]DE=2BC\longrightarrow2\times CA[/tex]
We can form a new triangle DEF whose side EF is parallel to CA; therefore,
[tex]\longrightarrow EF=2CA[/tex]
What triangles are similar to triangle ABC?
Answers
Answer:
A right angled triangle is similar to triangle ABC
Step-by-step explanation:
If you tilt the triangle and put it straight, you'll see that angle C is equal to 90°
And if a triangle has one angle of 90° then it is a right angled triangle
Hope you understand :)
Question 6 (2 points)
A wire costs $3 per foot. How much will 18 inches of wire cost?
$1.50
$3.00
$4.50
$9
Answers
Answer:
$4.50
Step-by-step explanation:
There are 12 inches in a foot. 18 inches is 1.5 feet.
1 foot of wire is $3.00 and a half of foot should be $1.50.
1.5 feet of wire should cost $4.50
1.5 ft × $3/ft
= $4.50
