Answer:
2x² + 3x - 5
Step-by-step explanation:
(2x + 5)(x - 1)
2x² - 2x + 5x - 5
2x² + 3x - 5
What are the values of t and u?
t = ?°
u= ?°
Find the point on the line 3x + y = 8 that is closest to the point
(−3, 1)
The point on the line 3x + y = 8 that is closest to the point (-3, 1) is (1.8, 2.6).
What is Quadratic Equations?Quadratic equations are equations of the form a x² + b x + c = 0 where a, b and c are real numbers.
Given line is,
3x + y = 8 ⇒ y = -3x + 8
So we have any point (x, -3x + 8).
We have to find a point (x, -3x + 8) such that distance of this point from (-3, 1) is minimum.
Distance between (-3, 1) and (x, -3x + 8) = √[(x - -3)² + (-3x + 8 - 1)²]
= √[(x + 3)² + (-3x + 7)²]
= √(x² + 6x + 9 + 9x² - 42x + 49)
= √(10x² - 36x + 58)
So the distance between (-3, 1) and (x, -3x + 8) is √(10x² - 36x + 58) should be minimum.
We minimize the function f(x) = 10x² - 36x + 58.
A quadratic function represents the equation of a parabola.
Coefficient of x² is positive, so parabola opens upward. So we will be having the minimum value.
Minimum value at the point x = -b / 2a for the quadratic equation a x² + b x + c.
Minimum value is at x = - (-36) / (2 × 10) = 36/20 = 9/5 = 1.8.
To find the y coordinate,
y = -3x + 8 = 2.6
So the required point is (1.8, 2.6).
Hence the point on the line closest to the point (-3, 1) is (1.8, 2.6)
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Kyra is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve large rooms that can hold 8 people, and small rooms that can hold 6 people. Kyra reserved twice as many large rooms as small rooms, which altogether can accommodate 88 guests. Determine the number of small rooms reserved and the number of large rooms reserved.
The number of small rooms reserved is 4.
The number of large rooms reserved is 8.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Small rooms are denoted as S.
Large rooms are denoted as L.
Now,
We will make two equations.
L = 2S _____(1)
8L + 6S = 88 ______(2)
Putting (1) in (2) we get,
8L + 6S = 88
8 x (2S) + 6S = 88
16S + 6S = 88
22S = 88
S = 88/22
S = 8/2
S = 4
Now,
Putting S = 4 in (1) we get,
L = 2 x 4
L = 8
Thus,
The number of small rooms and large rooms reserved is 4 and 8.
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determine the 97.5th percentile of the standard normal distribution as a decimal rounded to the nearest hundredth.
40 POINTS
Use the image to determine the type of transformation shown.
Image of polygon ABCD and a second polygon A prime B prime C prime D prime to the right.
Horizontal translation
Vertical translation
Reflection across the y-axis
270° counterclockwise rotation
Reflection across the y-axis is the transformation used to the polygon ABCD.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given that Image of polygon ABCD and a second polygon A prime B prime C prime D prime to the right.
ABCD is the original image and prime B prime C prime D prime is the transformed image.
ABCD rectangle is transformed to A'B'C'D'.
As we observe the diagram, the two rectangles look the same which means the shape remains constant.
The translation is applied to the original image which move to the right side.
A translation is a movement of the graph either horizontally parallel to the x axis or vertically parallel to the y axis.
We can reflect the graph of any function f about the x-axis by graphing y=-f(x) and we can reflect it about the y-axis by graphing y=f(-x).
Hence, Reflection across the y-axis is the transformation used to the polygon ABCD.
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Answer: reflection across the y axis
Step-by-step explanation: I hope that helps :)
let
[tex]A=(\sqrt{2} +\sqrt{3} )(\sqrt{4} +\sqrt{5} )...(\sqrt{2020} +\sqrt{2021} )\\B=(\sqrt{2021} -\sqrt{2020} )(\sqrt{2019} -\sqrt{2018} )...(\sqrt{3} -\sqrt{2} )[/tex]
what is A times B?
Answer:
1
Step-by-step explanation:
A)
[tex]( \sqrt{3 } - \sqrt{2} )( \sqrt{3} + \sqrt{2} )( \sqrt{5 } - \sqrt{4} )( \sqrt{5} + \sqrt{4} )....[/tex]
using difference of two squares
[tex]( \sqrt{a} + \sqrt{b} )(\sqrt{a} - \sqrt{b} ) = a - b[/tex]
we can rewrite the A) to 1×1×1×1.... so the answer would be 1
Joyce wants to survey a simple random sample of 10 people from members of a gym.
Which of the following sampling methods are not examples of simple random sampling?
Select all that apply.
Select the first 10 people from alist of members
Ask 10 members in the gym on a Monday morning
Use a random number generator to select 10 members from a list
Select 10 members' names from a box without looking.
Select every 20th person from a list of members until she has 10 .
Ask all members of the gym
The sampling methods here that are not examples of simple random sampling are;
A) Select the first 10 people from a list of members.
B) Ask 10 members in the gym on a Monday morning
E) Select every 20th person from a list of members until she has 10 .
F) Ask all members of the gym
What is the importance of simple random sampling?A simple random sample is defined as a randomly selected subset of a particular population. In this method of sampling, it will be noticed that each member of the population has an exactly equal chance of being selected.
The importance of simple random sampling is that it removes every form of bias as every member has an equal chance of being selected. Thus, it will give a good representation of what we want to research.
A) Select the first 10 people from a list of members; This is not simple random sampling because it is not random but specific.
B) This is not random because it is specific which is just a monday morning and we don't have an idea of the type of people that come on the other days.
C) Use a random number generator to select 10 members from a list; This is simple random sampling because a random number generator is used.
D) Select 10 members' names from a box without looking; This is random because all members have an equal chance of being selected.
E) Select every 20th person from a list of members until she has 10; This is not random as all members don't have an equal chance of being selected.
F) Ask all members of the gym; This is not random selection.
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To estimate the number of bass in a lake, a biologist catches and tags 32 bass. Several weeks later, the biologist catches a new sample of 55 bass and finds that 5 are tagged. How many bass are in the lake.
The career placement office at a large university tracks the number of job applications graduating seniors complete before getting their first job. Data on college graduates suggests that most will send out a large number of applications before getting their first job. Which one of the following histograms best represents the distribution of job applications for graduating seniors?
a.Histogram III
b.Histogram II
c.Histogram IV
d.Histogram I
The histogram that best represents the distribution of job applications for graduating seniors is given as follows:
a. Histogram III.
How to identify the correct histogram?An histogram shows the number of times that each observation appears in a data-set.
Data on college graduates suggests that most will send out a large number of applications before getting their first job, hence the left bins on the histogram should have small numbers, while the right bins on the histogram should have greater numbers.
The only histogram that follows this pattern is Histogram III, hence option A gives the histogram that best represents the distribution of job applications for graduating seniors.
Missing InformationThe histograms are given by the image shown at the end of the answer.
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Help me solve I will give you 15 points the answer is 720m3
Answer:
Step-by-step explanation:
You split it up into two 3-D triangles.
One of them has a volume of ((6*(5+5))/2)*8 = (60/2)*8=240
For the other one, you are missing a side on the 2-D face, so in order to apply pythagorean's theorem you need to split it into two more triangles. You know that 13^2=5^2+x^2 169-25=x^2 144=x^2 x=12
now that you know the missing side of the triangle you can recombine them. The volume of the remaining 3-D triangle is (((5+5)*12)/2)*8 = 60*8=480
480+240=720 meters cubed
If a share of a stock jumped from $9 to $25, what was the percent increase of this stock (rounded to the
nearest tenth)?
Answer: 177.8
Step-by-step explanation: To find the percent increase, we have to use this formula:
New value-old value/ old value x 100
So, following this formula, we would do 25-9, which, is 16, divided by 9. That would be 1.777... So now let's round that to 1.78, so 1.78 x 100 = 177.8. I hope this helped.
Using the definitional formula, compute Ss, variance and the standard deviation for the following population of scores. Scores: 1, 8, 0, 4,2 SS 40 variance 10 standard deviation 3.16
Ss, variance and the standard deviation for the population of scores is 2.83 and 8 respectively
What is standard deviation and variance?
Standard deviation is a measure of the distribution of statistical data, whereas variance is a measure of how data points differ from the mean. The fundamental distinction between the two is that although the variance is expressed in squared units, the standard deviation is expressed in the same units as the data's mean.
Given,
SS = 40
Variance = 10
Standard Deviation = 3.16
Using Population Variance Formula :
= [tex]\frac{1}{n}[/tex]∑( x-xbar)² where i is 1
For the complete solution see the attachment of table
sum ( x - x bar)² = 40
so, variance = 40/5
= 8
standard deviation = [tex]\sqrt{8}[/tex]
= 2.83
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A-Level Cambridge
PURE MATHEMATICS - PI
CH1 COORDINATES GEOMETRY
1-(9709-S 2012-Paper 1/2-Q4) COORDINATES GEOMETRY
[6]
The point A has coordinates (-1, -5) and the point B has coordinates (7, 1). The perpendicular
bisector of AB meets the x-axis at C and the y-axis at D. Calculate the length of CD.
ШОә
Answer:
either 8.6 or 9. check if it's correct?
7² + 5² = 74
square root 74 = 8.6
At a local print shop, 18 copies can be made for $6. At this rate, how how many copies could be made for $28? Fill out the table of equivalent ratios until you have found the value of x. Copies Dollars 18 18 6 6 x x 28 28 It would cost $28 to make copies.
Answer:
84 copies
Step-by-step explanation:
18 copies: $6 ==> 18:6
18:6 ==> 18/6 = 3
18 copies: $6 = 3 copies: $1 ==> common ratio of copies to cost
3 copies: $1 =
(3 copies: $1)*28 = ==> multiply by 28 to get the number of copies for $28
3*28 copies: $28 = 84 copies: $28
Answer: 84 copies
Answer:
(18 copies for $6 = x copies for $28)
18:6 = x:28
6x = 18(28)
6x = 504
x = 84 copies
Copies | Dollars
18 | $6
84 | $28
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Leslie wants to invest $3,800.00 in a savings account that pays 4.8% simple interest.
How many years will it take for this investment to triple in value? Round your answer to the nearest tenth of a year.
It will take _______ years for this investment to triple in value.
Answer:
It will take 41.7 years for this investment to triple in value.
Step-by-step explanation:
Here is the formula for simple interest
[tex]A=P(1+rt)[/tex]
Lets solve for [tex]t[/tex].
Divide both sides by [tex]P[/tex].
[tex]\frac{A}{P}=rt+1[/tex]
Subtract 1 from both sides.
[tex]\frac{A}{P}-1=rt[/tex]
Divide both sides by [tex]r[/tex].
[tex]\frac{\frac{A}{P}-1}{r} =t[/tex]
To write [tex]-1[/tex] as a fraction with a common denominator, multiply by [tex]\frac{P}{P}[/tex] .
[tex]\frac{\frac{A}{P}-1*\frac{P}{P}}{r} =t[/tex]
[tex]\frac{\frac{A}{P}*\frac{-P}{P}}{r} =t[/tex]
Combine the numerators over the common denominator.
[tex]\frac{\frac{A-P}{P} }{r} =t[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]t=\frac{A-P}{Pr}[/tex]
We are given
[tex]P=3800\\r=0.048[/tex]
We need to find what amount is triple his money.
[tex]3800*3=11400[/tex]
[tex]A=11400[/tex]
Substitute our numbers into the equation for [tex]t[/tex].
[tex]t=\frac{11400-3800}{3800*0.048}[/tex]
Factor 3800 out of 11400.
[tex]t=\frac{3800*3-3800}{3800*0.048}[/tex]
Factor 3800 out of −3800.
[tex]t=\frac{3800*3-3800*-1}{3800*0.048}[/tex]
Factor 3800 out of [tex]3800*3-3800*-1[/tex].
[tex]t=\frac{3800*(3-1)}{3800*0.048}[/tex]
Cancel the common factor of 3800.
[tex]t=\frac{3-1}{0.048}[/tex]
Simplify.
[tex]t=\frac{2}{0.048}[/tex]
[tex]t=41.666[/tex]
Merry Christmas!
What is one fifth of twenty more than half
of 80?
(A) 8
(B) 10
(C) 12
(D) 13
Answer:
(C) 12
Step-by-step explanation:
To solve this problem, we can use the following steps:
Find half of 80: 80/2 = 40
Add 20 to half of 80: 40 + 20 = 60
Find one fifth of the result: 60/5 = 12
Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.
Answer:
(C) 12
Step-by-step explanation:
What is one fifth of twenty more than half of 80
0.5 × 80 = 40
What is one fifth of twenty more than half of 80
40 + 20 = 60
What is one fifth of twenty more than half of 80
1/5 × 60 = 60/5 = 12
What sides are similar to this triangle with the side dimensions of 6cm, 12cm, and 15cm?
Answer: Pythagorean triplets.
Step-by-step explanation:
not sure but this is the triangle that helps at all.
lf mike is 13 and leslie is 7 how old will leslie be when mike is 24?
in a -page manuscript, there are randomly distributed misprints. find the mean number of misprints per page. round the answer to one decimal place as needed.
The mean number of misprints per page on manuscript is 0.5 and If a page is selected then the probability that it has 3 misprints is 0.0126..
What is Poisson probability distribution ?The Poisson distribution is a theoretical discrete probability, also known as the Poisson distribution probability mass function. It is used to find the probability that independent events occur at regular time intervals and have a constant average rate. λ is the Poisson rate parameter, the expected average number of events over a given time interval.
Using the Poisson distribution formula:
P(X = x) = (e-λ (λˣ) )/x!
where λ is mean number or poisson rate parameter ; x = 0, 1, 2, 3...
e is the Euler's number(e = 2.718)
We have given that,
Total number of Manuscript Pages = 400
total misprinted pages = 200
let X be random variable that the page is misprinted .
Mean number, λ = 200/400 = 0.5
the probability that it has 3 misprints, P(X= 3) = (e⁻⁰·⁵ (0.5)³ )/3!
= e⁻⁰·⁵ ( 0.125 )/6 =0.075816/6 = 0.0126
Hence, the required probability is 0.0126..
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Complete question:
Misprints on Manuscript Pages In a 400-page manuscript, there are 200 randomly distributed misprints Part 1 of 2 Find the mean number of misprints per page. Round the answer to one decimal place as needed. If a page is selected, find the probability that it has 3 misprints.
Select <, >, or = to make the expression true.
Answer:
the answer is < explanation at the step by step
Step-by-step explanation:
Do the Basic equation
2.18 x 10 - 6= 15.8
4.36 x 10 - 7= 36.6
Determine if the following equation has one, none, or many solutions.
2(2x+-1)=4x-4
Answer: no solutions
Step-by-step explanation:
a. Use the points (1, 226.9) and (4, 275.2) to write an equation for the line of fit in slope-intercept form, where x is the number of years since 2010 and y is the median price in thousands of dollars. what will be the approximate price by 2025?
The Equation of line is y= 16.1x + 210. 8.
The approximate price by 2025 is 452.3.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
The points are (1, 226.9) and (4, 275.2).
So, Slope for line
m = ( 275.2- 226.9)/( 4-1)
m = 48.3/ 3
m= 16.1
Now, using the slope- intercept form
y= mx+ b
y = 16.1x + b
Now, x= 1 and y= 226.9
By, y = 16.1 + x
226.9 = 16.1(1)+ b
b= 210.8
So, the equation of line is y= 16.1x + 210. 8
Now, x is the number of years since 2010 and by 2025
x= 2025 - 2010 = 15
Then, the approximate price by 2025
y= 16.1(15) + 210.8
y= 452.3
Hence, the approximate price by 2025 is 452.3.
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Find X,Y,Z Please Help!!!
The values of the angles x, y, z are x=56°, y=124°, z=56°
What is meant by an angle?In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.
From the given figure,
∠y=124°
∠x+124°=180°
∠x=180°-124°
∠x=56°
∠x=∠z=56°
Therefore, The values of the angles x, y, z are x=56°, y=124°, z=56°
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An experiment consists of drawing one card from a bridge deck. The sample space contains 52 outcomes, one for each of the 52 cards. Suppose we assign a probability of 1/52 to each of the cards. Find the probability that the following happens.
(a) A king is drawn
(b) The card drawn is a king or a queen.
(c) The card drawn is a diamond.
(d) The card drawn is a black card.
The probability of drawing a king, a king or queen, a diamond, or a black card from a deck of 52 cards is 1/52, 4/52, 13/52, and 26/52, respectively.
(a) The probability that a king is drawn is 1/52, since there is only one king in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a king is 1/52.
(b) The probability that a king or a queen is drawn is 4/52, since there are four kings and queens in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a king or queen is 4/52.
(c) The probability that a diamond is drawn is 13/52, since there are 13 diamonds in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a diamond is 13/52.
(d) The probability that a black card is drawn is 26/52, since there are 26 black cards in the deck and 52 total cards. This means that if we draw one card from the deck, the probability that it will be a black card is 26/52.
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The sum of heart rate readings taken five times for of Kundaval and Kulazhi are 400 and 360 respectively. And their projected deviations are 3,16 and 2.0 respectively. If you were. a doctor, who would you treat immediately?
Answer:
Overall, as a doctor, I would prioritize treating Kundaval immediately due to their higher heart rate and larger projected deviation.
Step-by-step explanation:
As a doctor, I would prioritize treating the patient with the higher heart rate and larger projected deviation. In this case, that would be Kundaval, whose sum of heart rate readings is 400 and whose projected deviation is 3.16.
Heart rate is an important vital sign that reflects the health and function of the cardiovascular system. It is measured in beats per minute (bpm) and can vary based on factors such as age, activity level, and overall health. A high heart rate, especially in combination with a large projected deviation, can be a sign of a potential health problem or underlying condition that requires immediate medical attention.
In contrast, Kulazhi has a lower heart rate and smaller projected deviation, which may indicate that their cardiovascular system is functioning normally. However, it is still important to monitor and track their heart rate over time to ensure that it remains within a healthy range.
If I were a doctor, the immediate patient I would treat is; Kundaval because he has a higher projected deviation and a faster heart rate.
What is the standard deviation?Instead of computation or experimentation, the standard deviation is an abstract concept based on observation.
A metric that is used to express the amount of variation or dispersion in a group of data is the standard deviation, which is also represented by the Greek letter sigma(σ).
To put it another way, it specifies the degree to which the members of a data group differ from the group's average value.
Given
The sum of heart rate readings taken five times for Kundaval is 400
The sum of heart rate readings taken five times for Kulazhi is 360
and their projected deviation are 3.16 and 2.0,
Now, the standard deviation is a measure of how dispersed the data are in relation to the mean, whereas the mean simply refers to the average of a set of given data.
As a result, as a doctor, I would prioritize treating the patient whose heart rate and projected deviation are higher. As a result, we would conclude that Kundaval, with a projected deviation of 3.16 and a sum of 400 heart rate readings, should be treated first.
Therefore, The immediate patient I would treat if I were a doctor is; Kundaval because he has a faster heart rate and a higher projected deviation.
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Replace the loading system acting on
the beam by an equivalent resultant
force and couple moment at point O.
The answers are a) FR = 365 N b) u = 70.8° d and c) (MR)O = 2364 N m (counterclockwise)
What is resultant force?When an object is subject to several forces, the resultant force is the force that alone produces the same acceleration as all those forces.
Given is a figure, we need to find equivalent resultant force and couple moment at point O
Equivalent Resultant Force And Couple Moment At O.
+→ (FR)x = ΣFx; (FR)x = 600 cos 60° - 455(12 / 13)
= -120 N = 120 N ←
+ ↑ (FR)y = ΣFy; (FR)y = 455(5/13) - 600 sin 60° = -344.62 N = 344.62 N ↓
As indicated in Fig (attached)
a) FR = √F(R)x²+F(R)y²
= √2120² + 344.62² = 364.91 N = 365 N
And
b) θ = tan-1{(FR)y / (FR)x}
= tan-1 {344.62/120}
= 70.80°
Also,
c) a+(MR)O = ΣMO; (MR)O = 455(12/13)(2) + 600 cos 60° (0.75) + 600 sin 60° (2.5)
= 2364.04 N m
= 2364 N m (counterclockwise)
Hence, The answers are a) FR = 365 N b) u = 70.8° d and c) (MR)O = 2364 N m (counterclockwise)
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The scatter plot below shows the average rent (in dollars per month) for a 1 bedroom apartment in new york city each year between 2000 and 2013. A line was fit to the data model the relationship.
which of these liner equations best describes the given model?
a.y=2/5x+800
b.y=40x+800
c.y=800x+2/5
d.y=800x+40
based on this equation,use this equation to estimate the average rent in 2020.round your answer to the nearest dollar.
Therefore , the solution to the given problem of equation that the estimated rent comes out o be $1600.
Investigate the equation.The equivalent sign connects two expressions to form a mathematical statement known as an equation. An equation is, for instance, 2x - 5 = 15. By solving this equation, we can determine that the value of the variable x is 5.
Here,
In 2020, a one-bedroom apartment in New York City will cost $1600.
The formula for a straight line graph is often y = mx + c, where;
m = gradient
c is the vertical intercept.
With this knowledge, the graph clearly shows that the ideal line of fit for the data plot is y = 40x + 800.
This means that a one bedroom flat in New York City will cost; in the year 2020, which is 20 years after the year 2000;
y = 40(20) + 800 = $1600
Therefore , the solution to the given problem that the estimated rent comes out o be $1600.
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Below is the table of values of a function. Write the output when the input is n.
input 1,4,6,n
output 2,8,12,?
Answer:
Step-by-step explanation:
Though 70% of women with children younger than 18 years participate in the labor force, society still upholds the stay-at-home mother as the traditional model. Some believe that employment distracts mothers from their parenting role, affecting the well-being of children. In the GSS 2014, respondents were asked to indicate their level of agreement to the statement: "A working mother hurts children". Of the 435 male respondents who answered the question, 18% strongly agreed that a working mother does not hurt children. a, What is the 90% confidence interval for this statistic for males? b. Of the 566 respondents who answered the question, 40% strongly agree that a working mother does not hurt children. What is the 90% confidence level for this statistic?
a) The 90% confidence interval for this statistic for males is of: (0.1497, 0.2103).
b) The 90% confidence level for this statistic is of: (0.3661, 0.4339).
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
For males, the parameters are given as follows:
[tex]\pi = 0.18, n = 435[/tex]
Hence the lower bound of the interval is given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 - 1.645\sqrt{\frac{0.18(0.82)}{435}} = 0.1497[/tex]
The upper bound of the interval is of:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.18 + 1.645\sqrt{\frac{0.18(0.82)}{435}} = 0.2103[/tex]
For the statistic, the parameters are given as follows:
[tex]\pi = 0.4, n = 566[/tex]
Hence the lower bound of the interval is given as follows:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.645\sqrt{\frac{0.4(0.6)}{566}} = 0.3661[/tex]
The upper bound of the interval is of:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.645\sqrt{\frac{0.4(0.6)}{566}} = 0.4339[/tex]
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can some one please help me with this question
The measure of the largest exterior angle of the triangle will be 162°.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The exterior angles of the triangle are 3x°, 8x°, and 9x°. Then the measure of the interior angle of the triangle will be 180° - 3x°, 180° - 8x°, and 180° - 9x°.
The sum of the interior angle of the triangle is 180°. Then the equation is given as,
180° - 3x° + 180° - 8x° + 180° - 9x° = 180°
360° - 20x° = 0
x = 18°
Then the measure of the exterior angles of the triangle will be given as,
3x° = 3 × 18° = 54°
8x° = 8 × 18° = 144°
9x° = 9 × 18° = 162°
The measure of the largest exterior angle of the triangle will be 162°.
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https://brainly.com/question/25813512
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