Answer:
y = 36
Step-by-step explanation:
For proving two parallel lines in a triangle, we will take the proportionality of their sides, such that
\(\frac{28}{14} = \frac{y}{18}\)
Cross- Multiplying
18 × 28 = y × 14
14y = 504
Dividing both sides by 14
y = 36
So, y = 36 would prove that Segment OP is parallel to segmant LN
Answer:
y = 36
Step-by-step explanation:
If OP were parallel to LN then OP divides the sides proportionally, thus
\(\frac{MP}{PN}\) = \(\frac{MO}{OL}\) , substitute values
\(\frac{y}{18}\) = \(\frac{28}{14}\) = 2 ( multiply both sides by 18 )
y = 36
What year was math invented?
Answer:
Around 3000 BC
Answer:
It is difficult to pinpoint a specific year or time period in which math was "invented," as math is a fundamental aspect of human thought and has likely been present in some form since ancient times.
The study of mathematics has a long and rich history, dating back to ancient civilizations in Mesopotamia, Egypt, Greece, and India. These early societies developed mathematical concepts and techniques to aid in practical tasks such as measuring land, calculating the volume of objects, and tracking the movement of celestial bodies.
As human civilizations developed and advanced, so too did the study of mathematics. Over time, new mathematical concepts and techniques were developed and refined, leading to the development of more advanced branches of mathematics such as algebra, geometry, trigonometry, and calculus.
In summary, math has a long and complex history, and it is difficult to pinpoint a specific year or time period in which it was "invented." It has likely been present in some form since ancient times and has evolved and developed over the course of human history.
Step-by-step explanation:
SELF EXPLANATORY
the heights of adult women in the us are roughly normally distributed with mean 64.5 inches and standard deviation 2.5 inches. approximately, what is the probability that a randomly selected us adult woman is shorter than 69.5 inches?
The approximate probability that a randomly selected US adult woman is shorter than 69.5 inches is 0.9772 or about 97.72%.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.
We are given that the height of adult women in the US follows a normal distribution with a mean of 64.5 inches and a standard deviation of 2.5 inches.
We need to find the probability that a randomly selected US adult woman is shorter than 69.5 inches.
To find this probability, we need to calculate the z-score first:
z = (x - mu) / sigma
where x is the height we want to find the probability for, mu is the mean, and sigma is the standard deviation.
Substituting the values, we get:
z = (69.5 - 64.5) / 2.5 = 2
Using a standard normal distribution table or calculator, we find that the probability of a z-score of 2 or less is 0.9772.
Therefore, the approximate probability that a randomly selected US adult woman is shorter than 69.5 inches is 0.9772 or about 97.72%.
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A square piece of plastic has sides that are 18 centimetres long. What is the piece of plastic's area?
Answer:
324 \(cm^{2}\)
Step-by-step explanation:
Area is the length multiplied by width. In the case of a square, both sides are the same so it would simply be 18 x 18 or \(18^{2}\) which equals 324, but make sure to adds units, \(cm^{2}\). Hope this helps
Is Circumcentre and centroid of a triangle same?
Answer:
no, they are different in their different ways
Need help ASAP for math thank youu
Answer:
X is 6
Step-by-step explanation:
The reson X is 6 is that if you removed the 3 and layed the side with x it would be alittle bit smaller than 5 making it 6.
a positive number is 7 times another number if 3 is added to both the numbers then one of the new number becomes 5 by 2 times the other new number what are the numbers
Answer:
7 and 1
Step-by-step explanation:
Let the numbers be a and b.
A positive number is 7 times another number:
a = 7bIf 3 is added to both the numbers then one of the new number becomes 5 by 2 times the other new number:
a+3 = 5/2 × (b +3)To solve this we substitute a with 7b in the second equation:
7b + 3 = 5/2 × (b +3) ⇒ multiplying both sides by 214b + 6 = 5b + 15 ⇒ collecting like terms14b - 5b = 15 - 69b = 9b = 1 ⇒ solved for bThen, finding a:
a= 7ba=7*1a= 7 ⇒ solved for aSo the numbers are 7 and 1
AB is a diameter in a circle whose centre is the origin where A =(2,0) then B=
Answer:
(-2,0)
Step-by-step explanation:
Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order.
y dA, D is bounded by y = x − 6; x = y2
D
The value of the double integral using the easier order, ydA bounded by y = x − 6; x = y² is 125/12.
The double integral, indicated by ', is mostly used to calculate the surface area of a two-dimensional figure. By using double integration, we may quickly determine the area of a rectangular region. If we understand simple integration, we can easily tackle double integration difficulties. Hence, first and foremost, we will go over some fundamental integration guidelines.
Given, the double integral ∫∫yA and the region y = x-6 and x = y²
y = x-6
x = y²
y² = y +6
y² - y - 6 = 0
y² - 3y +2y - 6 = 0
(y-3) (y+2) = 0
y = 3 and y = -2
\(\int\int\limits_\triangle {y} \, dA\\ \\\)
= \(\int\limits^3_2 {y(y+6-y^2)} \, dx \\\\\int\limits^3_2 {(y^2+6y-y^3)} \, dx \\\\(\frac{y^3}{3} + 3y^2-\frac{y^4}{4} )_-_2^3\\\\\frac{63}{4} -\frac{16}{3} \\\\\frac{125}{12}\)
The value for the double integral is 125/12.
Integration is an important aspect of calculus, and there are many different forms of integrations, such as basic integration, double integration, and triple integration. We often utilise integral calculus to determine the area and volume on a very big scale that simple formulae or calculations cannot.
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Renee built a toolbox in the shape of a rectangular prism that has a length if 36 inchrd, a width of 20 inches and a height of 18 inches. She will make a similar toolbox for her nephew with dimensions that are 1/4 of the dimensions of her toolbox. What will be the surface area of the toolbox Renee is making for her nephew?
Answer A: 216 sq in
Answer B: 864 square in
Answer C: 202.5 square in
Answer D: 3240 sq in
Answer:
Step-by-step explanation:216
1.a. Saquinavir has a log P value = 0.4. Thus, what problem does saquinavir causes? (2marks)
b. How to overcome the problem mentioned in (a)? (2marks)
c. State the indication and the site of action of saquinavir. (2marks)
Saquinavir’s poor solubility due to its log P value of 0.4 can limit its absorption. Strategies to overcome this include prodrug formation, lipid-based formulations, and nanotechnology-based delivery systems.
a. Saquinavir’s log P value of 0.4 suggests that it has poor solubility in water, which can limit its absorption and bioavailability when administered orally.
b. To overcome the solubility problem, various strategies can be employed, such as formulating saquinavir as a prodrug, using co-solvents or surfactants to enhance its solubility, incorporating it into lipid-based formulations, or utilizing nanotechnology-based delivery systems.
c. Saquinavir is indicated for the treatment of HIV infection. It is a protease inhibitor that acts by inhibiting the HIV-1 protease enzyme, thereby preventing viral replication.
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In rugged terrain, Martin can hike 1/8 Mile in 1/2 hour. At this rate, how far can Martin hike in 1 hour?
A. 5/8 mile
B. 1/16 mile
C. 1/4 mile
D. 1/6 mile
y=-3x+12 find the intercepts of x and y
Answer: x intercept: (4,0) y intercept: (0,12)
Step-by-step explanation:
To find the x intercept, substitute in 0 for y and solve for x. To find the y intercept, substitute in 0 for x and alive for x.
the population of a slowly growing bacterial colony after hours is given by . find the growth rate after 3 hours.
The growth rate of the bacterial colony after 3 hours is 32%, the population of a slowly growing bacterial colony after t hours is given by the function p(t) = 100 + 24t + 2t²
The growth rate of the colony is the rate of change of the population, which is given by the derivative of the function. The derivative of p(t) is p'(t) = 24 + 4t
The growth rate after 3 hours is p'(3) = 24 + 4 * 3 = 32. This means that the population of the colony is increasing by 32% after 3 hours.
The derivative of a function gives the rate of change of the function.The growth rate of a population is the rate of change of the population.The growth rate of a bacterial colony can be calculated by differentiating the function that represents the population of the colony.To know more about derivative click here
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If 80% of the people in a community have Internet access from their homes, find these probabilities for a sample of 10 people.
a. At most 6 have Internet access.
b. Exactly 6 have Internet access.
c. Not more than 6 have Internet access.
d. Which event, a, b, or c, is most likely to occur? Explain why
.
a. The probability that at most 6 people in a sample of 10 have Internet access can be found using the binomial probability formula.
Given that 80% of the people in the community have Internet access, the probability of an individual having access is 0.8. We can then calculate the probability of having 0, 1, 2, 3, 4, 5, or 6 people with Internet access and sum up these probabilities.
b. The probability that exactly 6 people in a sample of 10 have Internet access can also be calculated using the binomial probability formula. We need to find the probability of having exactly 6 people with Internet access and no more or no fewer.
c. The probability that not more than 6 people in a sample of 10 have Internet access can be calculated by summing up the probabilities of having 0, 1, 2, 3, 4, 5, or 6 people with Internet access. This includes cases where fewer than 6 people have Internet access.
d. The event with the highest probability of occurring among a, b, and c is event c, where not more than 6 people have Internet access.
This is because event c encompasses both event an (at most 6 people have Internet access) and event b (exactly 6 people have Internet access).
Since the probability of not more than 6 people having Internet access includes all the cases in the event a and event b, it is more likely to occur than either of the individual events.
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a teacher wants to arrange 3 copies of introduction to geometry and 4 copies of introduction to number theory on a bookshelf. in how many ways can he do that? (all the copies of each book are identical.)
The total number of ways to arrange 3 copies of introduction to geometry and 4 copies of introduction to number theory on a bookshelf is 35.
A permutation of a set of objects is an ordering of those objects. When some of those objects are identical, the situation is transformed into a problem about permutations with repetition. Problems of this form are quite common in practice; for instance, it may be desirable to find orderings of boys and girls, students of different grades, or cars of certain colors, without a need to distinguish between students of the same grade (or cars of the same color, or people of the same gender).
Total number of copies = 3 +4 = 7
Number of ways to arrange 7 copies together = 7!
However, there are 3 copies of introduction to geometry and 4 copies of introduction to number theory. Thus, all copies of each book are identical.
Now, the total number of ways to arrange 7 copies together
= \(\frac{7!}{3!* 4!}\)
=35
Thus, the total number of ways to arrange 3 copies of introduction to geometry and 4 copies of introduction to number theory on a bookshelf is 35.
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proposals for ______ studies include a methodology section.
Proposals for research studies include a methodology section.
This section is an important component of a research proposal as it outlines the procedures and techniques that will be used to conduct the study. It provides the reader with a detailed description of the research design, the data collection methods, and the data analysis methods that will be employed. The methodology section of a research proposal should be well-structured and clearly written to demonstrate the feasibility and validity of the proposed study.
Here are some key components of a methodology section in a research proposal:
Research design: This section describes the overall approach that will be taken to conduct the research, including the type of study (e.g. experimental, qualitative, quantitative), the sample size and selection method, and the data collection methods that will be used.
Data collection methods: This section outlines the methods that will be used to collect data, including the type of data that will be collected (e.g. surveys, interviews, observations), the instruments or tools that will be used, and the procedures for collecting and storing the data.
Sampling method: This section describes the method that will be used to select the participants for the study, including the criteria for inclusion and exclusion, and the process for obtaining informed consent from participants.
Data analysis methods: This section outlines the methods that will be used to analyze the data, including the statistical methods and software that will be used, and any assumptions or limitations associated with the analysis methods.
Ethics and safeguards: This section discusses any ethical considerations associated with the study, including informed consent, confidentiality, and protection of participants' rights. It should also describe any safeguards that will be put in place to ensure that the data is collected and analyzed in a valid and reliable manner.
By including a well-structured methodology section in a research proposal, researchers can demonstrate their understanding of the research process, and provide a clear and detailed plan for conducting the study. This helps to increase the credibility and feasibility of the proposed study, and can increase the chances of the proposal being approved and funded.
Therefore, Proposals for research studies include a methodology section.
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The cost of a phone is reduced by 20%. The new cost is $70.40. What was the original price?
The original price 1. $ 88.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means)
Given;
The cost of the product was reduced by 20%, leaving $ 70.4 as the final price.
Cost of phone after 80% off= $70.40
So, now we will do a cross-multiplication;
If the percent is 80% =70.40
Let, the original price 100% = x
80x = 70.40. 100
80x = 7040
X = 7040: 80
X = 88
Therefore, the 100 percent value of phone will be $88
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giving 60 point if u do
The percentage error of Bob’s measurement to the nearest tenth of a percent is 3.87%
The percentage error is The difference between the estimated value and the actual value in relation to the actual value is given as a percentage. Analyst use this formula to determine how big is the error in a relation to true value.
Here, given that
The experimental volume of liquid is 18.8 ml, and the actual volume of liquid is 18.1 ml
i.e. exprimental volume=18.8 mL
and, actual volume=18.1 mL
Now, we will calculate the percentage error
So,
percentage error=((Exprimental value-Actual value)/(Actual value))∙100
percntage error=((18.8-18.1))/18.1∙100
percentage error=0.7/18.1∙100
percentage error=0.0387∙100
percentage error=3.87%
Thus,
We got percentage error of 3.87% in measurement
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Tlaloc pumped up 56 balls. He pumped up 5 dodge balls for every 9 other balls.
Answer:
What do you need from this question? Its not asking anything.
Step-by-step explanation:
Joan has a square flower with a side length of 5 meters filled with tulips.There are a total of 365 tulips in the bed.Find the density of tulips for the area of the bed.Round to the nearest tenth if necessary
Density of tulips for the area is ≈ 14.6 tulips per square meter
What is the density of tulips in a square flower bed with a side length of 5 meters and a total of 365 tulips?The area of the square flower bed is given by the formula:
A = \(s^2\)
where s is the length of a side of the square. Substituting s = 5 meters, we get:
A = \(5^2\) = 25 square meters
The density of tulips is defined as the number of tulips per unit area. Therefore, the density of tulips in the flower bed is:
density = number of tulips / area
Substituting the given values, we get:
density = 365 / 25 ≈ 14.6 tulips per square meter
Rounding to the nearest tenth, we get:
density ≈ 14.6 tulips per square meter (rounded to one decimal place)
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A pound of chocolate costs 7 dollars. Milan buys p pounds. Write an equation to represent the total cost c that Milan pays.
Answer:
A pound of chocolate costs 7 dollars. Milan buys p pounds. Write an equation to represent the total cost c that Milan pays.
c = 7xp.
Step-by-step explanation:
Isabella invested \$1300$1300 in an account that pays 4.5% interest compounded annually. assuming no deposits or withdrawals are made, find how much money isabella would have in the account 14 years after her initial investment. round to the nearest tenth (if necessary).
Isabella would have $2970.63 in the account 14 years after her initial investment.
Isabella invested $1300 in an account that pays 4.5% interest compounded annually.
Assuming no deposits or withdrawals are made, find how much money Isabella would have in the account 14 years after her initial investment. Round to the nearest tenth (if necessary).
The formula for calculating the compound interest is given by
A=P(1+r/n)^(nt)
where A is the final amount,P is the initial principal balance,r is the interest rate,n is the number of times the interest is compounded per year,t is the time in years.
Since the interest is compounded annually, n = 1
Let's substitute the given values in the formula.
A = 1300(1 + 0.045/1)^(1 × 14)A = 1300(1.045)^14A = 1300 × 2.2851A = 2970.63
Hence, Isabella would have $2970.63 in the account 14 years after her initial investment.
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how u do the sum pls
Answer:
\({ \tt{x + 36 \degree + 48 \degree = 360 \degree}} \\ { \tt{x = (360 - 48 - 36) \degree}} \\ { \tt{x = 276 \degree}}\)
Determine zα for the following. (Round your answers to two decimal places.)
(a) α = 0.0089
(b) α = 0.09
(c) α = 0.707
Please explain where and how you got the answer.
Thank you.
The value of zα for the following is :
(a) α = 0.0089 is 2.37
(b) α = 0.09 is 1.34
(c) α = 0.707 is -0.545
zα is the inverse function of the standard normal CDF.
(a) Central limit c= 1-α
for α = 0.0089 , c=1-0.0089
∴ c=0.9911
Hence confidence level in percentage= 99.5%
Now, the value of zα will be calculated with the help of an excel sheet function normsinv(c).
∴zα = normsinv(c)
where c is central limit
zα = normsinv(0.9911)
zα =2.37
(b) Central limit c= 1-α
for α = 0.09 , c=1-0.09
∴ c=0.91
Hence confidence level in percentage= 91%
Now, the value of zα will be calculated with the help of an excel sheet function normsinv(c).
∴zα = normsinv(c)
where c is central limit
zα = normsinv(0.91)
zα=1.34
(c) Central limit c= 1-α
for α = 0.707 , c=1-0.707
∴ c=0.293
Hence confidence level in percentage= 29.3%
Now, the value of zα will be calculated with the help of an excel sheet function normsinv(c).
∴zα = normsinv(c)
where c is central limit
zα = normsinv(0.707)
zα= -0.545
Therefore zα value for 0.0089 is 2.37, for 0.09 is 1.34 and for 0.707 it is -0.545.
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Which set represents the range of the function {(-1, -3), (0, 1), (1,5), (3,9)}?
A. {-1, 0, 1, 3}
B. {-3, 1, 5,9)
C. {-3, -1, 0, 1, 3, 5, 9}
D. {12}
Answer:
B
Step-by-step explanation:
Because the range are the y values
The range of the given function is {-3, 1, 5,9}. Therefore, option B is the correct answer.
What is domain and range of the function?The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:
Domain = the set of all x-coordinates = {1, 2, 3, 4}
Range = the set of all y-coordinates = {2, 3}
The solution set of the given function is {(-1, -3), (0, 1), (1,5), (3,9)}.
Range is the set of all y-coordinates
So, the range is {-3, 1, 5, 9}
Therefore, option B is the correct answer.
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______ is terminology that is specific to a particular profession or group. For example, statisticians talk about t-tests, chi-square tests, confidence intervals, and normal distributions.
Answer:
parlanceStep-by-step explanation:
The world parlance represents jargon/terms used by a particular profession or by a group of related experts in a field.
In french parler, means "to speak, hence the word parlance has it root from the french word parler.
it is a noun and it often called a slang or a jargon.
for example in law, lawyers use world/terms like, plaintiff, witness, suspect, jury, etc
The terminology that is specific to a particular profession or group is called; Jargons
We are given examples such as;
T-tests, chi-square tests, confidence intervals being used exclusively by statisticians.
Now, these terms used exclusively by statisticians have a general term they are called which is Jargons.
In conclusion, Jargons is the general name for words or expressions that are used exclusively by a group that are not easy for others to understand.
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Which of the following is not true:
A) All squares are rhombi.
B) All trapeziums are quadrilaterals
C) All rectangles are rhombi
D) All squares are rectangles
E) All rhombi are parallelograms
Answer:
a
Step-by-step explanation:
bc i said so
There are 1942 students at West High School.
Use the information in the table to determine how many students study less than 2 hours each day.
Answer:
68
Step-by-step explanation:
The students who study less than 2 hours are the students who study less than 1 hour and the students who study 1.5 hours.
Less than 1 hours: 0.5%
1 hour: 3%
Total percent less than 2 hours: 3.5%
3.5% of 1942 = 0.035 × 1942 = 67.97
Answer: 68
In circle I, IJ=4 and mJIK∠=90∘ Find the area of shaded sector. Express your answer as a fraction times π.
The area of the shaded sector is 4π square units.
To find the area of the shaded sector, we need to calculate the central angle formed by the sector. In this case, we are given that the angle JIK is 90 degrees, which means it forms a quarter of a full circle.
Since a full circle has 360 degrees, the central angle of the shaded sector is 90 degrees.
Next, we need to determine the radius of the circle. The line segment IJ represents the radius of the circle, and it is given as 4 units.
The formula to calculate the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius of the circle.
Plugging in the values, we have A = (90/360) * π * 4².
Simplifying, A = (1/4) * π * 16.
Further simplifying, A = (1/4) * π * 16.
Canceling out the common factors, A = π * 4.
Hence, the area of the shaded sector is 4π square units.
Therefore, the area of the shaded sector, expressed as a fraction times π, is 4π/1.
In summary, the area of the shaded sector is 4π square units, or 4π/1 when expressed as a fraction times π.
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Solve for x
x/2 = 8/5
x=?
Answer:
x = 3.5 or 16/5 or 3 1/5
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.