The lower quartile for the given data is -2, since it is the 25th percentile and is the value that lies at the 25th position when the data is sorted in ascending order.
1. Sort the data in ascending order: -4, -2, 1, 1, 6, 8, 12, 15
2. Calculate the 25th percentile: 25th percentile = (n + 1) * 0.25 = (8 + 1) * 0.25 = 2.25
3. The 25th percentile is between the 2nd and 3rd values, which are -2 and 1 respectively.
4. The lower quartile is -2.
The lower quartile (also known as the 25th percentile) is the value that lies at the 25th position when the data is sorted in ascending order. To find the lower quartile of the given set of data (1, 8, 1, -4, 12, -2, 15, 6), the data needs to be sorted in ascending order. This gives us the following data: -4, -2, 1, 1, 6, 8, 12, 15. Now, to calculate the 25th percentile, we use the formula (n + 1) * 0.25, where n is the number of data points. In this case, n = 8, so the 25th percentile = (8 + 1) * 0.25 = 2.25. This means the 25th percentile is between the 2nd and 3rd values, which are -2 and 1 respectively. Therefore, the lower quartile for the given data is -2.
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The diameter of each of the three circular lights in a traffic signal is 7 inches. In this activity, you will find the total area of the three lights.Part C What is the total area of all three circular lights?
Answer:
The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. If the diameter of each circular light is 7 inches, the radius would be half of that, or 3.5 inches.
Therefore, the area of one circular light would be:
A = π * 3.5^2 = 3.5^2 * π = 12.25 * π square inches.
Since there are three circular lights, the total area of all three would be:
3 * 12.25 * π = 36.75 * π square inches.
Step-by-step explanation:
pls mark brainlist
consider the function graphed below. What is the average rate of change of the function over the interval (2,3)?
The average rate of change of the function over the interval [2,3] will be around 3.
What is a function?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
For example to draw the equation y = 3x +2 this will draw a straight line in the coordinate geometry.
The rate of change is given by dy/dx
The average rate of change can be given as:
= (difference in y coordinate)/(difference in x coordinate)
= Δy/Δx
Average rate of change = ( 11 - 8 )/(3 - 2 )
= 3
Hence, the average rate of change is 3
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is the answer to this not 225000???
2.25 km on the ground is represented by 9cm on the map.
What is the actual distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Here, we have
Given: The scale on the map is 1:25000
We have to find the actual distance of 9 cm on the map.
First, we have to find the actual distance of 1 cm on the map:
1cm = 25000cm
1cm = 250m
1cm = 0.25km
Now Find the actual distance of 9 cm on the map:
1cm = 0.25km
9cm = 9(0.25) = 2.25km
Hence, 2.25 km on the ground is represented by 9cm on the map.
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similarity help for math please
The triangles that do not follow the similarity statement and therefore are not similar triangle are ACT and CAR
What is similar triangleSimilar triangles are triangles that have the same shape, but may have different sizes. Their corresponding angles are congruent, and the corresponding sides are proportional. In other words, if you were to enlarge or shrink one triangle uniformly, it would overlap exactly with the other triangle.
In this problem, we can find two triangles that are similar and that implies that they must be equal to one another.
In this case, we have
1. ART ≈ CAT
2. CAR ≈ CTA
Only ACT ≠ CAR
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Some girl needs to earn R500 in interest so she will have enough to buy a used bicycle. She puts R2000 into an account that earns 5% per year simple interest. How long will she need to leave her money in the account to have enough money for the bicycle?
The money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.
What is simple interest?The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.
Let us suppose the time period as x.
The simple interest is given as:
SI = PRT/100
Where,
SI = Simple Interest = 500
P = Principal = 2000
R = Rate = 5%
T = x
Substituting the values:
500 = (2000)(5)(x) / 100
500 = 100x
x = 5 years
Hence, the money needs to be in the account for 5 years on simple interest at the rate 5% to earn R500.
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The graph below is a discrete function:
8
246
0 2
A True
B) False
f(x)
6
8 10
12
14
Answer: A.
Step-by-step explanation:
PLEASE HURRY!! Which of the following statements are true regarding the graph of this linear function? Select all that apply.
The slope of the line, 9.75, is the amount of money she makes per hour of work. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.
The definition of amount?Extent, volume, and supply are all nouns. the sum of two or more amounts; the complete worth, impact, or importance of anything.
What is an example of a number?A number is a mass or accumulation, especially of something impossible to count: amount of The appropriate quantity of sand wasn't delivered. Animals were kept on a small amount of land. He donated money on a regular basis to a charity.
We know that slope =
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, slope m is
[tex]$m=\frac{53 -14}{8 -4 }[/tex]
[tex]$m=\frac{39}{4 }[/tex]
m = 9.75
And putting the value in y-intercept form we have
y = 9.75x – 25
Therefore, The slope of the line, 9.75, is the amount of money she makes per hour of work. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.
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Jack washes cars no monday he washed 18 cars for $90 on tusday he washed 9 cars for $45 on wadnesday he washed 12 cars for $60 what si the rate of change of jakes earnings
The rate of change of Jakes earning is, 0 or no change.
What is the rate?Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.
So formula for the rate is,
m = change in one quantity/change in another quantity = Δy/Δx
On Monday, Jake earned $90 by washing 18 cars.
Therefore, his earning rate was:
= $90 / 18 cars
= $5 per car
On Tuesday, Jake washed 9 cars and earned $45.
Therefore, his earning rate was:
= $45 / 9 cars
= $5 per car
On Wednesday, Jake washed 12 cars and earned $60.
Therefore, his earning rate was:
= $60 / 12 cars
= $5 per car
We can see that Jake's earning rate remained constant over the three days at $5 per car.
Therefore, the rate of change of Jake's earnings is 0, or no change.
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A bus leaves the station every 12 minutes
A train leaves the station every 18 minutes
At 8am a bus and a train leave their stations at the same time.
a) when is the next time that a bus and a train leave at the same time?
b) Between 8am and 11am, on how many occasions does a bus and a train leave at the same time?
thank you so much for the help
Answer:
a) 8:32 am
b) 5 occasions
12. Tickets to a school play cost $5.00 for general
admission (g) and $3.50 with a student ID (s). On
opening night, 400 tickets were sold for a total of
$1580. How many of each kind of ticket were sold?
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Answer:
120 general admission
280 with student with a student ID
Step-by-step explanation:
x is tickets for general admission
y is tickets with a student ID
5x+3.5y=1580
x+y=400
y=400-x
5x+3.5(400-x)=1580
5x+1400-3.5x=1580
1.5x=180
x=120
120+y=400
y=280
$200 invested at 5% compounded quarterly after a period of 3 years
Given:-
[tex] \rm{Principal= \bold{200}}[/tex][tex] \rm{Time = \bold 3}[/tex][tex] \rm{Intrest \: Rate = \bold 5}[/tex]By using formula:-
[tex]\boxed { \color{green}\rm{Simple \: interest= \frac{Principal×Time×Rate}{100}}}[/tex]Solution:-
[tex] \rm{SI = \frac{PTR}{100} }[/tex][tex] \: [/tex]
[tex] \rm{SI = \frac{2\cancel{00}×3×5}{1\cancel{00}} }[/tex][tex] \: [/tex]
[tex] \rm{SI=2×3×5}[/tex][tex] \: [/tex]
[tex] \boxed { \rm \red{ SI = 30}}[/tex][tex] \: [/tex]
hope it helps! :)
you have a recipe that indicates to use 2 parts of milk for every 7 parts of flour. You use 8 cups of milk. How much flour do you need?
(Also complete the ratio table below pls)
Milk(cups) 2 , 4 _ , 8
Flour (cups) 7 , _ , 21 , _
Answer:
28 cups of Flower
Ratio Table:
2,4,6,8
7,14,21,28
Step-by-step explanation:
2x4/7x4=8/28
peter sets up a neurological study in which he wants to investigate three pre-defined groups of patients. each group of patients is already diagnosed with the same neurological syndrome. peter not only examines the average score for each group of patients, but also the scores for each individual patient. peter's study is an example of...
Peter's study is an example of a cross-sectional clinical study that investigates three pre-defined groups of patients with the same neurological syndrome by examining both the average score for each group and the scores for individual patients.
Cross-sectional study that compares three groups of patients with the same neurological syndrome. In this type of study, the researcher examines the groups at a specific point in time to obtain information about the prevalence, incidence, and characteristics of the disease or condition being studied. By examining both the average score for each group and the scores for individual patients, Peter is able to draw conclusions about the relationship between the neurological syndrome and the factors being studied. This type of study can help to identify risk factors, determine the efficacy of treatments, and guide future research in the field.
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The figure shown has two parallel lines cut by a transversal:
A pair of parallel lines is shown, crossed by a transversal. Angles are identified as 1, 2, 3, 4, 5, 6, 7, and 8. Angles 1-4 are on the top line clockwise from upper left. Angles 5-8 are on the lower line clockwise from upper left.
Which angle is an alternate interior angle to ∠3?
∠5 is the alternate interior angle of ∠3.
What is transversal?
A transversal is a line that, at two different points in the geometry, cuts through two lines in the same plane. Various types of angles in pairs, including consecutive interior angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.
When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairs of that transversal. Alternate interior angles are what they are called.
Line m and line n are parallel and line l is transversal.
The alternate pairs of that transversal are ∠3 and ∠5.
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Miss carol spendmore is not good at budgeting her money. She initially haf $500 in the bank. She lent her friend $65 this month and she notices that her bank account is declining by $15 dollard per day. Determine the rate of cHange
Miss Carol's bank account is losing money at a daily rate of $15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.
We must calculate Miss Carol's account balance's daily decline in order to ascertain the rate of change in her bank account.
Since Miss Carol lent her friend $65 this month, her account balance is reduced by $65, leaving her with $500 - $65 = $435.
The information that her account is losing $15 every day can then be put to use. We can write this as:
Rate of change = -$15 per day
The negative symbol signifies a declining amount on her account.
Therefore, Miss Carol's bank account is losing money at a daily rate of
$15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.
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Howard's pencil is 75 cm long. How many millimeters long is Howard's pencil?
Answer:
Howard's pencil is 750 millimeters
Step-by-step explanation:
[tex]\begin{array}{|l}\underline{km~}\\~~~~~\underline{|hm~}\\~~~~~~~~~~~\underline{|dam}~~~~~~~~\nwarrow~\div10\\~~~~~~~~~~~~~~~~~\underline{|m~~}\\~~~~~~~~~~\searrow~~~~~~~\underline{|dm~}\\~~~\times10~~~~~~~~~~~~~~~~~~\underline{|cm~}\\\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|mm~}\end{array}\\~~~~~~~~~~~\rm Converting ~Length ~ Unit[/tex][tex]~[/tex]
Step-by-step:
75 cm = 75 × 10 mm
75 cm = 750 mm
Find the equation of the line that passes through (1,3) and is perpendicular to
y=2x-1.
Leave your answer in the form ax+by=c
Where a, b and c are integers.
Answer:
Equation of perpendicular line:
[tex]\boxed{\quad y=-\dfrac{1}{2}x+\dfrac{7}{2}\quad }[/tex]
Step-by-step explanation:
Generalized lope-intercept form of a line is y = mx + b [1]
where
m = slope
b = y-intercept
Equation of the given line is y = 2x - 1 [2]
We are asked to find the equation of the line perpendicular to this and also passes through (1, 3)
Klaus is cycling at a speed of -8 miles per hour. If he starts at the same position as Rachel (zero) , what will his position be after 60 minutes?
Klaus will be ____ miles be hind where he started, and ___ miles away from Rachel.
Klaus wil be behind where he started with a distance of 8miles
What is distance?Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
Distance can also be defined as the space or gap between two points.
Velocity = distance/time
distance = velocity × time
time = 60minutes = 1hr
therefore the distance made by Klaus in 60 minutes =
= 8 ×1
= 8miles
therefore within 60 minutes Klaus will cover a distance of 8miles from where he started.
Klaus and Rachel will be at same position with the same speed
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If A = {3,5,9} and B
{2,4,5,6,9,12}, what is AU B?
For the given sets A = { 3, 5, 9 } and set B = { 2, 4, 5, 6, 9, 12 } then the value of AU B is equal to { 2, 3, 4, 5, 6, 9, 12 }.
Two different sets A and set B are equal to :
Set A = { 3, 5, 9 }
Set B = { 2, 4, 5, 6, 9, 12 }
Union of two different set A and B is defined as set having all the elements of set A and set B .
Union of two sets A and B is represented by AU B .
AU B
= { 3, 5, 9 } ∪ { 2, 4, 5, 6, 9, 12 }
= { 2, 3, 4, 5, 6, 9, 12 }
Therefore, the union of two given sets A and set B is given by :
AU B = { 2, 3, 4, 5, 6, 9, 12 }.
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The United States Postal Service has an online guide to make life easy for people using their
postal service. This is an extract.
First Class Mail
First class mail must be used for handwritten or personal correspondence.
First Class Mail Rates - single piece rates
$0.44
First ounce (oz.) Letter size mail
Each additional oz. or fraction
First ounce Flat size mail **
Each additional oz. or fraction
First ounce Parcel ***
Each additional oz. or fraction
Standard Postcard ****
$0.17 per oz. up to 3.5 oz.
$0.88
$0.17 per oz. up to 13 oz.
$1.22
$0.17 per oz. up to 13 oz.
$0.28
* Letters: (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W,
max. weight 3.5 oz). Letter size mai over 3.5 ounces, see Flat size prices.
**Flats: (min. dimension: 11.5 L, 6.125" H, 0.25"W; max. dimension: 15 L, 12 H, 0.75 W).
*** Parcels: Anything larger.
**** Postcards: (min. dimension: 5L, 3.5" H, 0.007"W; max. dimension: 61, 4.25 H, 0.016 W).
I want to send two items through the post using first class mail.
One fts into an envelope 20 L, 10°H and 4"W and weighs 10oz.
The other fits into an envelope 8 L, 5" H and 0.20 W and weighs 2.5oz.
How much are the items going to cost me to send?
Answer:
The first item that fits into an envelope 20 L, 10°H and 4"W and weighs 10oz is a "Flat size mail." According to the rate chart, the first ounce of Flat size mail costs $0.88 and each additional ounce costs $0.17. The cost for the 10 ounces of this item will be $0.88 + 9 x $0.17 = $1.83.
The second item that fits into an envelope 8 L, 5" H and 0.20 W and weighs 2.5oz is a "Letter size mail." According to the rate chart, the first ounce of Letter size mail costs $0.44 and each additional ounce costs $0.17. The cost for the 2.5 ounces of this item will be $0.44 + 1.5 x $0.17 = $0.75.
So, the total cost for both items will be $1.83 + $0.75 = $2.58.
MODELING REAL LIFE Scientists rope off two excavation sites. Site A is rectangular with a length of $60$ meters and a width of $40$ meters. Site B is similar in shape to Site A but has a length of $45$ meters. How much rope is needed for both sites?
m=
By using unitary methods, the amount of rope is needed for both sites is 350 meters.
Unitary method is a mathematical problem-solving technique that involves finding the value of one unit and using it to calculate the value of other units.
Let's start by looking at Site A, which is a rectangular area with a length of 60 meters and a width of 40 meters. To surround this area with rope, we need to measure the perimeter, which is the distance around the site.
=> Perimeter = 2 (length + width)
=> 2(60 + 40)
=> 2 x 100
=> 200 meters
Therefore, we need 200 meters of rope to surround Site A.
Now let's move on to Site B, which is also rectangular but has a length of 45 meters. To find the width of Site B, we can use the fact that it is similar in shape to Site A. Similar shapes have the same angles and proportional sides, so we can use a unitary method to find the missing dimension.
The length ratio of Site B to Site A is
=> 45/60 = 3/4
Since the shapes are similar, the width of Site B must also be 3/4 of the width of Site A.
Width of Site B = 3/4 x 40 = 30 meters
Now we can use the same formula as before to find the perimeter of Site B:
Perimeter = 2 (length + width)
=> 2(45 + 30)
=> 2 x 75
=> 150 meters
Therefore, we need 150 meters of rope to surround Site B.
To find the total amount of rope needed for both sites, we simply add the two perimeters:
Total rope needed = 200 + 150 = 350 meters
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Find the image of (2,3) under a dilation with center at the origin and a scale factor of −3.
The image of (2, 3) under a dilation with center at the origin and a scale factor of −3 will be (-6, -9).
What is Image of a point ?
Dilation is the process of resizing or altering an object. With the aid of the specified scale factor, it is a transformation that reduces or enlarges the objects. The initial figure is referred to as the pre-image, while the new figure acquired after dilatation is known as the image.
Given point : (2,3)
the scale factor is -3 which means the point should be enlarged by -3 times to get the desired image.
So, we can write as : (a, b) where,
a = 2 × -3 = -6
and, b = 3 × -3 = -9
Hence, the coordinates of the image will be (-6, -9).
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one of my factors are 4, when you pair me with 32 we have an lcm of 32, i am greater than 4 and less the 15. what is the mystery number?
The mystery number is 8. It is the number that is greater than 4 and less than 15 which when paired with 32 has an LCM of 32.
The mystery number is 8. To find this number, we first need to determine the Least Common Multiple (LCM) of two numbers. The two given numbers are 4 and 32. To find the LCM, we can list out the multiples of each number until we find a common multiple. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, and so on. The multiples of 32 are 32, 64, 96, 128, and so on. We can see that 32 is the first common multiple of 4 and 32. Therefore, the LCM of 4 and 32 is 32. We are then told that the mystery number is greater than 4 and less than 15. This means the mystery number must be 8, since it is the only number between 4 and 15 that when paired with 32, has an LCM of 32.
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how many decimeters are in 3.6 millimeters
Final Answer:
There are 0.036 decimeters in 3.6 millimeters.
Explanation:
To convert from millimeters to decimeters, we can use the following measurement conversion:
1 millimeter = 0.01 decimeters
So, to find out how many decimeters are in 3.6 millimeters, we can multiply 3.6 by 0.01:
3.6 * 0.01 = 0.036
Therefore, there are 0.036 decimeters in 3.6 millimeters.
Write a similarity transformation that maps ∆ABC to ∆DEF
Answer:
Reflect ABC over the y axis. Translate ABC 1 unit to the right. C is the center, dilate ABC with a scale factor of 2.
Step-by-step explanation:
A square and a rectangle have the same perimeter. The square has an area of 81 sq. inches and the rectangle has a width of 5 in. What is the area of the rectangle?
Answer:
Area of rectangle = [tex]\mbox{\large \boxed{\textrm{65 sq. inches}}}[/tex]
Step-by-step explanation:
Let square side = [tex]a[/tex]
Area of square [tex]A = a^2[/tex]
Given [tex]A = 81[/tex] and equating it to [tex]a^2[/tex]
[tex]a^2[/tex] [tex]= 81\;in^2[/tex]
[tex]a = \sqrt{81} = 9\;in[/tex]
Perimeter of square = [tex]4a = 4\cdot 9 = 36 \;in[/tex]
If [tex]l[/tex] = length of the rectangle and [tex]w[/tex] = width
Perimeter P of rectangle = [tex]2(l + w)\\[/tex]
Given perimeter of rectangle = perimeter of square we get
[tex]2(l + w) = 36\\\\l + w = 36/2\\\\l + w = 18[/tex]
Given
[tex]w = 5\\\\l + 5 = 18\\\\l = 18 - 5 = 13\\\\[/tex]
[tex]\\\\\textrm{Area of rectangle } = l \times w\\\\= 13 \times 5 \\\\= 65 \;sq.\;inches[/tex]
What is the r-value of the following data to three decimal places?
X. Y
4. 23
5. 12
8. 10
9. 9
13. 2
Note that the r-value of the above data is : -0.903 (Option A)
What is R-value?In mathematics, the r-value typically refers to the correlation coefficient, which measures the strength and direction of the linear relationship between two variables.
With regard to the above data:
A) Find the Sum of the X values: 4 +5+8+9+13 = 39
B) Find the Sum of the Y values: 23 +12 +10 +9 +2 = 56
C) Find the Sum of x^2: 4^2 + 5^2 + 8^2 + 9^2 +13^2 = 355
D) The sum of the Y^2's: 23^2 + 12^2 + 10^2 + 9^2 + 2^2 = 858
E) Sum of x *y's: 4*23 + 5*12 + 8*10 + 9*9 + 13*2 = 339
N = number of sets = 5
Numerator of r = (E - A*B/N) = 339-39*56/5 = 339 - 436.8 = -97.8
Denominator of r = SQRT(C-A^2/N) x SQRT(D-B^2/N) =
SQRT(355-39^2/5) x SQRT(858-56^2/5) =
SQRT(50.8) x SQRT(230.8) =
7.1274 x 15.1921 =
108.2803
r = -97.8 / 108.2803
r = -0.903
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FIND THE PERIMETER AND AREA OF THE TRIANGLE BELOW
Answer:
perimeter = 8a³b + 4ab
area = 4a^4b²
Step-by-step explanation:
perimeter = 2a³b + 6a³b + 4ab
perimeter = 8a³b + 4ab
area = bh/2
area = 4ab × 2a³b / 2
area = 4a^4b²
1. a certain type of tomato seed germinates 43% of the time. a backyard farmer planted 10 seeds. what is the probability that 2 or fewer germinate?
The probability that 2 or fewer tomato seeds germinate out of 10 planted, given a germination rate of 43%, is 0.586 or 58.6%.
To calculate the probability that 2 or fewer seeds germinate, we need to use the binomial distribution, where:
n is the total number of trials (plantings)p is the probability of success (a seed germinating)x is the number of successes we want to calculate the probability forIn this case, n = 10, p = 0.43, and we want to find the probability that 0, 1, or 2 seeds germinate. We can calculate this probability as the sum of the probabilities of each of these outcomes:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
where X is the random variable representing the number of seeds that germinate.
Using the binomial distribution formula, we can calculate the probability of each outcome:
P(X = k) = (n choose k)[tex]* p^k * (1 - p)^{(n - k)}[/tex]
where (n choose k) is the binomial coefficient, equal to [tex]n! / (k! * (n - k)!)[/tex].
Plugging in the values, we get:
P(X = 0) = (10 choose 0) [tex]* 0.43^0 * 0.57^{10}[/tex] = 0.057
P(X = 1) = (10 choose 1) [tex]* 0.43^1 * 0.57^9[/tex] = 0.205
P(X = 2) = (10 choose 2) [tex]* 0.43^2 * 0.57^8[/tex] = 0.324
Therefore,
[tex]P(X \leq 2)[/tex] = [tex]0.057 + 0.205 + 0.324[/tex] = 0.586
So the probability that 2 or fewer seeds germinate is 0.586, or 58.6%.
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1/2of 2/3 =1/2 of _ Third(s)= _third(s)
Answer: 1/2of 2/3 = 1/2 of 2 Third(s)= 1 third
