Answer:
C.
Step-by-step explanation:
The point S=(8,7) is the center of the circle O. Through the point M=(-5,-2) is drawn a secant k, whose distance from the point S is equal to 5, and a tangent l to the circle O. The secant k intersects the circle O in the points B and C. Point A is the common point of tangent l and circle O, and segment AC is the diameter of this circle.
Determine the equation of the circle O.
The equation for the circle O, given the diameter, the secant K and the common point of tangent I, is:
(x - 8)² + (y - 7)² = 15²
(x - 8)² + (y - 7)² = 225
How to find the equation of the circle ?To determine the equation of the circle O with center S(8, 7) and point M(-5, -2) on the secant k, we first need to find the radius of the circle.
Given that the distance from point S to secant k is 5, we can use the Pythagorean theorem to find the length of MA, which is equal to the radius of the circle.
MA² + AS² = MS²
MA² + 5² = MS²
Calculate the distance between points M and S:
MS = √((8 - (-5))² + (7 - (-2))²) = √(13² + 9²) = √(169 + 81) = √250
Now we can find the length of MA:
MA² + 5² = 250
MA² = 250 - 25 = 225
MA = √225 = 15
The equation of a circle with center (h, k) and radius r is given by:
(x - h)² + (y - k)² = r²
Using the given center S(8, 7) and radius 15, the equation of the circle O is:
(x - 8)² + (y - 7)² = 15²
(x - 8)² + (y - 7)² = 225
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Acellus
Acellus
Length of Arcs
Find the length of AB. Leave
your answer in terms of π.
27
A
20° AB =[?]T
B
l'o
The length of arc-AB = 3π
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
Given circle;
arc-AB (θ) = 20° and radius, r = 27
We know the formula,
length of arc = (θ/360°) × 2πr
after putting the values,
length of arc-AB = (20°/360°) × 2π × 27
length of arc-AB = (1/18) × 54π = 3π
Therefore, the length of arc-AB = 3π
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The length of arc-AB = 3π. The Circle identities are a collection of trigonometric fundamental identities that relate to the six trigonometric properties of an angle in a right-angled triangle.
How do I find the length of an arc?The central angle and sector area are required to compute arc length without radius: Divide the value by the central angle in radians after multiplying the area by two. Calculate the square root of this fraction. To get the arc length, multiply this root by the centre angle once more. The arc length is shown to be identical to the radius length. Radians are the ratio constant between an arc length and a radius length.
Given circle;
arc-AB (θ) = 20° and
radius, r = 27
The length of an arc,
length of arc = (θ/360°) × 2πr
after substituting the values,
length of arc-AB = (20°/360°) × 2π × 27
Simplify the above equation,
length of arc-AB = (1/18) × 54π = 3π
Therefore, the length of arc-AB = 3π
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Divide: (x2 – 3x – 33) = (x + 4)
Answer:
x2-3x-33=x+4
<=> x2-3x-x-33-4=0
<=> x2-4x-37=0
<=> x=2 + square root(41) or 2- square root(41)
A rectangle has an area of
72 square centimeters. The width of the rectangle is 8 centimeters.
Answer:
[tex]\boxed{\bf length=9\; cm}[/tex]Step-by-step explanation:
Given:-
Area = 72
width = 8
Area = length × width
[tex]\bf 72=length \times 8[/tex]
Divide 72 / 8:-
[tex]\bf length=9\; cm[/tex]
If you're asking to find the length, this's your answer.
____________________________
Hope this's what you're looking for!
what is 6 of 1/4, can someone please give me an answer.
The value of the operation 6 of 1/4 is 3/2
What are fractions?Fractions are simply described as part of a whole number, element or variable.
There are different types of fractions in mathematics. They include;
Mixed fractionsProper fractionsImproper fractionsSimple fractionsComplex fractionsSome examples of simple fractions are; 1/2 , 2/3
Some examples of mixed fractions are; 2 1/3, 4 1/2
Some examples of improper fractions are; 3/2, 4/3
From the information given, we have that;
6 of 1/4,
'of' in this sense means multiplication, then, we get;
6 × 1/4
Multiply the values
6/4
Divide
3/2
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In the given Fig. PQR is a triangle, right angled at Q. If XY || QR, PQ = 6 cm, PY = 4 cm and PX : XQ = 1 : 2. Calculate the lengths of PR and QR.
Basic Proportionality Theorem (BPT): If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points then the other two sides are divided in the same ratio. This is also known as Thales theorem.
Given:
[tex]\angle Q= 90^\circ , XY \ || \ QR, PQ = 6 \ \text{cm}, PY = 4 \ \text{cm} \ \text{and} \ PX : XQ = 1 : 2[/tex]
Since, [tex]XY \ || \ QR[/tex],
[tex]PX/XQ = PY/YR[/tex]
[ By Thales theorem (BPT)]
[tex]\dfrac{1}{2} = PY/YR[/tex] [tex][PX : XQ = 1 : 2][/tex]
[tex]\dfrac{1}{2} = 4 /(PR - PY)[/tex]
[tex][YR= PR - PY][/tex]
[tex]\dfrac{1}{2} = 4 /(PR - 4)[/tex]
[tex]PR - 4 = 2 \times 4[/tex]
[tex]PR - 4 = 8[/tex]
[tex]PR = 8 +4[/tex]
[tex]PR = 12 \ \text{cm}[/tex]
In right [tex]\Delta PQR[/tex],
[tex]PR^2 = PQ^2 + QR^2[/tex]
[ By Pythagoras theorem]
[tex]12^2 = 6^2 + QR^2[/tex] [tex][\text{Given} : PQ= 6 \ \text{cm}][/tex]
[tex]144 = 36 + QR^2[/tex]
[tex]144 - 36 + QR^2[/tex]
[tex]108= QR^2[/tex]
[tex]QR =\sqrt{108} =\sqrt{3\times36} = 6\sqrt{3} \ \text{cm}[/tex]
Hence, the lengths of PR and QR is 12 cm and [tex]6\sqrt{3}[/tex] cm.
A fair die is tossed three times - Find the probability that a prime even number Showed twice.
Answer:
Step-by-step explanation:
Total no. of possible outcomes = 6 (1,2,3,4,5,6,)
As given we have only one prime even no. from the above given set, that is 2.
Let's call this event A.
Total no. of favourable outcomes =P(A)= 1
Therefore the probability is P(A)= 1/6
what is the value of b
Answer:
b=46
Step-by-step explanation:
First we know that the sum of all three angles is 180. So that gives us the equation 2b+88=180, then we can solve.
2b=180-88
2b=92
b=46
So that means b=46!
As you may know, a straight line = 180°
Since we already have 88° as one of the values, we can simply subtract that from 180.
180 - 88 = 92
Next, divide 92 by 2
92 ÷ 2 = 46
With that being said, we can conclude that the value of B is 46.
You can double check this by adding all of the values together: 46 + 46 + 88 = 180
the worlds population hit 8 billion in 2022. suppose the population increases exponentially with doubling time of 60 years. what population can we expect in the year 2100. Answer in billions
Therefore, we can expect the world population to be around 17.6 billion in the year 2100 if it continues to increase exponentially with a doubling time of 60 years.
What is decimal place?A decimal place is a position in a number that is to the right of the decimal point. It represents a fractional part of the number. For example, in the number 3.14159, the digit "1" is in the tenths place, the digit "4" is in the hundredths place, the digit "1" is in the thousandths place, and so on. Each place value to the right of the decimal point represents a power of 10 that is negative, such as tenths, hundredths, thousandths, ten-thousandths, and so on. The number of decimal places determines the degree of precision in the number.
by the question.
To determine the population in the year 2100, we need to calculate how many times the population will double between 2022 and 2100, which is 78 years.
78 years divided by 60 years is approximately 1.3, which means that the population will double 1.3 times between 2022 and 2100.
2 to the power of 1.3 is approximately 2.2, which means that the population in 2100 will be 2.2 times the population in 2022.
So, the population in 2100 will be:
8 billion x 2.2 = 17.6 billion (rounded to one decimal place)
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Find the value of x.
13)
(2x+8)
62°
14)
rights serve d.-1-M a de
(x-4) (2x+1)
Infinite Geometry
In the given right angle, the required value of x is 10° respectively.
What is the right angle?Right-angled shapes can be any polygon, ranging from triangles to figures with numerous sides.
Right-angled shapes like squares and rectangles have exactly 4 right angles that add up to 360 degrees.
Right angles can also be found in other shapes like trapezoids, pentagons, and hexagons.
An angle with a measure of exactly 90 degrees (or /2) is referred to as a right angle.
The proper angles are frequently demonstrated in everyday life. For instance, the edges of the cardboard or the corner of a book.
So, we know that the given angles together make a right angle as:
2x + 8 + 62 = 90
Then, solve for x as follows:
2x + 8 + 62 = 90
2x + 70 = 90
2x = 90 - 70
2x = 20
x = 20/2
x = 10
Therefore, in the given right angle, the required value of x is 10° respectively.
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To the nearest tenth of a second, how long after the pebble falls will it hit the ground?
s
Answer:
Ask away by typing or recording your messageAdam, Ben and Carly work out the mean of their ages.Adam is 4 years older than the mean. Ben is 1 year younger than the mean.Is Carly older or younger than the mean?By how many years?Let's start by finding the mean of their ages. We can do this by adding their ages and dividing by the number of people: Mean = (Adam's age + Ben's age + Carly's age) / 3 Let's call the mean "M" for now. We can use this to create two equations based on the information given: Adam = M + 4 Ben = M - 1 We can substitute these equations into the mean equation to get: M = (M + 4 + M - 1 + Carly's age) / 3 Simplifying this equation gives us: 3M = 2M + 3 + Carly's age Carly's age = M - 3 So Carly's age is younger than the mean by 3 years.Hey ✋, are you still around? anything else on your mind?To the nearest tenth of a second, how long after the pebble falls will it hit the ground?sTo answer this question, we need to know the height from which the pebble was dropped. We can use the formula: time = sqrt(2 * height / acceleration due to gravity) Assuming the pebble was dropped from a height of 10 meters, and taking the acceleration due to gravity as 9.8 m/s^2, we get: time = sqrt(2 * 10 / 9.8) = 1.43 seconds (to two decimal places) Therefore, the pebble will hit the ground approximately 1.43 seconds after it was dropped.
0 / 350
What would the answer be?
The dilation of the black figure to blue figure is a reduction with a scale factor of 0.5
How to find the scale of dilation?A dilation is defined as a transformation that produces an image that is the same shape as the original, but is a different size.
It can either be an enlargement or a reduction.
An enlargement means a scale factor greater than 1 while a reduction is a scale factor less than 1.
Thus, this dilation is a reduction.
Coordinates of initial figure are:
(-8, 10), (10, 10), (8, -8), (2, -8)
Coordinates of dilated figure are:
(1, -4), (4, -4), (-4, 5), (5, 5)
Thus, it is clear that the scale factor is 0.5
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5 inches is
times as big as 1 inch.
12.7 centimeters is
times as big as 2.54 centimeters.
Answer:
d
Step-by-step explanation:
believe me it's d because it says it in the text above u just have to read it carefully
HELP ASAP
A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 5 and three-fourths centimeters by 4 centimeters by 11 and three-fourths centimeters.
What is the surface area of the prism?
five hundred fifty and one-fourth cm2
four hundred twelve and three-fourths cm2
two hundred seventy-five and one-eighth cm2
one hundred thirty-seven and nine-sixteenths
Hence, the rectangular prism has a surface area of 280 and 1/4 [tex]cm^2[/tex] as the rectangular prism has the measurements .
what is rectangle ?A hexagon having four right angles (90º angles) and opposing sides of equal length is called to as a rectangle. It is a particular kind of rectangle in which every angle is a right angle. A rectangle has parallel opposed sides and diagonals that cut it in half. The length (l) and breadth (w), which have been perpendicular to one another, define a rectangle. A rectangle's area is equal to the product of the its width and length, or lw, and its perimeter is equal to the sum of all of its sides, or 2(l+w). In geometry, math, and daily life, such as in doors, frames, and picture frames, rectangles are frequently occurring forms.
given
The rectangular prism has the following measurements: 5 centimetres by 4 centimetres by 11 and three-quarters centimetres.
The region of each face is thus:
Face 1: 5 3/4 cm x 4 cm equals 23 [tex]cm^2[/tex]
Face 2: 5 and 3/4 inches by 11 and 3/4 inches is 70 and 1/8 centimetres square.
Face 3: 4 cm x 11 3/4 cm equals 47 [tex]cm^2[/tex]
Total surface area = 23 cm2 + 70 eighths of a cm2 + 47 eighths of a [tex]cm^2[/tex] + 23 eighths of a cm2
Surface area total = 280 and 1/4 [tex]cm^2[/tex]
Hence, the rectangular prism has a surface area of 280 and 1/4 [tex]cm^2[/tex] as the rectangular prism has the measurements .
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HELP PLS!!!!!!!!!!!!!!!
find the first three terms of the expansion of the following in acceding power of x ((x +2)/(1+x)*2)
Step-by-step explanation:
((x+2)/(1+x)*2)2x +3*22x+6x+6*2x+12if g(x) = f(1/3x) which statement is true
B. The graph οf functiοn f is stretched hοrizοntally by a scale factοr οf 3 tο create the graph οf functiοn g.
What is linear transfοrmatiοn?A linear transfοrmatiοn is a functiοn that mοves frοm οne vectοr space tο anοther while maintaining the underlying (linear) structure οf each vectοr space.
The rules fοr linear transfοrmatiοns are that
g(x) = a·f(b·(x-c)) +d
stretches the graph vertically by a factοr οf "a" (befοre the shift)
cοmpresses the graph hοrizοntally by a factοr οf "b" (befοre the shift)
shifts it tο the right by amοunt "c"
shifts it up by amοunt "d".
Yοur equatiοn has b=1/3, sο the graph is cοmpressed by a factοr οf 1/3, which is equivalent tο a stretch by a factοr οf 3.
The apprοpriate chοice οf descriptiοn is ...
b) the graph οf g(x) is hοrizοntally stretched by a factοr οf 3
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Complete Question:
Select the correct answer. If , which statement is true? if g(x) = f(1/3x)
A. The graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g.
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
C. The graph of function f is compressed horizontally by a scale factor of to create the graph of function g.
D. The graph of function f is compressed vertically by a scale factor of to create the graph of function g.
how many thirds in 6 2/3
Answer:
20
Step-by-step explanation:
it take 3 ⅓ to make a whole so to makee 6 wholes it would take 18 and 2 more thirds and that would 20 ⅓ in 6 ⅔
Evaluate the expression. Round to the nearest tenth
Answer: 3.
Step-by-step explanation:
1 times 1/5 is 1/5.
1/5+ 2 times 1/5 is 1/5+2/5
1/5+2/5+ 3 times 1/5 is 1/5+2/5+3/5
1/5+2/5+3/5+ 4 times 1/5 is 1/5+2/5+3/5+4/5
1/5+2/5+3/5+4/5+ times 1/5 is 1/5+2/5+3/t+4/5+5/5
1/5+2/5+3/5+4/5+5/5=15/5
15/5=3
Three friends, Nakobe, Mikah, and Ashton, are saving up money to buy microphones for their podcast. The total cost of the microphones is represented by the expression 8x2 − 4x + 9.
The friends have already saved the following amounts:
Nakobe: x2
Mikah: x − 14
Ashton: 2x + 6
Which expression represents the amount of money the friends still need to buy the microphones?
x2 + 3x − 8
x2 + 3x + 26
4x2 + 4x + 9
7x2 − 7x + 17
Answer:
7x^2 - 7x + 17
Step-by-step explanation:
we can subtract what they already have from what they total cost for the microphones:
8x^2 - 4x + 9 - (x^2) - (x - 14) - (2x + 6)
simplify this:
8^2 - 4x + 9 - x^2 - x + 14 - 2x - 6 =
7x^2 - 7x + 17
Find X using Sine law
[tex]\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(x)}{32}=\cfrac{\sin(50^o)}{40}\implies \sin(x)=\cfrac{32\sin(50^o)}{40} \\\\\\ x=\sin^{-1}\left[ \cfrac{32\sin(50^o)}{40} \right]\implies x\approx 37.79^o[/tex]
Make sure your calculator is in Degree mode.
Can you solve this question?
f'(3)=?
Answer:
Step-by-step explanation:
[tex]f(x)=16e^x-ex^e[/tex]
[tex]f'(x)=16e^x-e^2x^{e-1}[/tex]
[tex]f'(3)=16e^3-e^23^{e-1}[/tex]
[tex]f'(3)=e^2(16e-3^{e-1})[/tex]
Two trains leave towns 648 miles apart at the same time and travel toward each other. One train travels 14 mi/h faster than the other. If they
meet in 4 hours, what is the rate of each train?
We can conclude after answering the presented question that Hence the equation slower train's speed is 13.25 miles per hour, while the faster train's speed is 27.25 miles per hour (13.25 + 14).
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
Because we know the two trains are going in the same direction, their relative speed equals the total of their speeds, which is (x + x+14) = 2x + 14.
We also know that the distance between them is shrinking at a pace of 648 miles in 4 hours, or at a rate of 648/4 = 162 miles per hour.
[tex]162 = (2x + 14) x 4 = distance = rate x time\\162 = 8x + 56\\106 = 8x\sx = 13.25\\[/tex]
Hence the slower train's speed is 13.25 miles per hour, while the faster train's speed is 27.25 miles per hour (13.25 + 14).
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A total of 5 identical pencils cost $6.50. What was the price for each individual pencil?
Answer:
Step-by-step explanation:
1.3
just divdve
(4,-3) with undefined slope
Answer:
x = 4
Step-by-step explanation:
assuming you require the equation of the line passing through the given point.
A line with an undefined slope is a vertical line parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (4, - 3 ) with x- coordinate 4 , then
x = 4 ← equation of line
Explain the theory of mathematics
There are number of thesis that are given for mathematics by various professors and scientists at various levels that are being implemented from time to time.
A theory is nothing but a set of statements which may be based on certain principles that might have been derived by performing some experiments and attaining a proper conclusion. For example, if we say 'the sky is blue'. It means this truth can never be changed irrespective of the situations. This will remain mortal.
Similarly, there are plenty of terms in mathematics such as decimals, percentage, geometry, algebra and more fundamentals. These are existing since ages and have been challenged also. But the theory remains the same. There operas-memoranda remains the same. So various scholars, have given various theories of mathematics.
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Please help!!! WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!!
Golf Skydiving Fishing 100-yard dash
Drag racing
1. Brainstorm: Which of the above sports do you think the graph could represent? Why?
2. Brainstorm: What vocabulary and properties of graphs and functions do you see represented in the graph? How did any of those affect your choice for the sport?
(Photo of graph is added)
I think it could represent the 100-yard dash. The graph represents distance versus time, which is a common way to graphically display motion.
What is graph?A graph is a visual representation of data that displays the relationship between two or more variables. Graphs can be used to illustrate numerical information in a clear and concise way, making it easier to understand and analyze complex sets of data. Graphs can be created using various types of software or by hand, and there are many different types of graphs, including line graphs, bar graphs, scatter plots, pie charts, and more.
Here,
The vertical axis represents the distance, and the horizontal axis represents time. The line on the graph shows how the distance traveled changes with respect to time.
The graph also shows that the runner covers a certain distance in a specific amount of time, which is a fundamental concept in physics. In the case of the 100-yard dash, the graph shows how the runner covers 100 yards in a certain amount of time.
Overall, the graph displays the key characteristics of motion and can be used to analyze and compare the performance of athletes in various sports.
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jaquan ate 5 mangoes , 1//9 was what he pick. How much did he pick?
Q6b. The teenager from the question above rejoins the group and another teenager is picked at random.
What is the probability that the teenager picked at random is male and their favourite hobby is playing video games? You can simplify this fraction if you wish.
Picking a male youngster who enjoys playing video games is more likely if you get a score of (4/10) * (6/10) = 24/100 = 6/25.
what is probability ?Probability is a mathematical concept that expresses the possibility or chance of an event happening. It is stated as a number between 0 and 1, where 0 denotes the impossibility of an event and 1 denotes its certainty. By dividing the number of favorable outcomes by the entire number of possible possibilities, the probability of an event is determined.
given
The odds of selecting a male adolescent at random are x/n, while the odds of selecting a teen whose preferred pastime is playing video games are y/n.
As these two occurrences are separate, the likelihood that both will occur is the product of the probabilities:
The odds of selecting a male teen who enjoys video games are (x/n) * (y/n) = xy/n2.
By dividing the numerator and denominator by the greatest common factor (GCF) of x and y, if one exists, this can be made simpler.
For instance, the probability is simplified as follows if x=4 and y=6, where the GCF is 2:
Picking a male youngster who enjoys playing video games is more likely if you get a score of (4/10) * (6/10) = 24/100 = 6/25.
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PLEASE HELP. tons of points for reward
answer like this…
69)
70)
71)
72)
Step-by-step explanation:
69) If 10 packages of shallots cost $40, then the cost of one package of shallots can be calculated as:
$40 ÷ 10 packages = $4 per package
To find out how many packages of shallots can be purchased with $8, divide the total amount of money by the cost per package:
$8 ÷ $4 per package = 2 packages
Therefore, with $8, you can buy 2 packages of shallots.
70) If three Bosc pears cost $2, we can use a proportion to determine how many pears we can buy for $4:
3 pears / $2 = x pears / $4
Cross-multiplying, we get:
3 pears × $4 = $2 × x pears
Simplifying, we get:
12 = 2x
Dividing both sides by 2, we get:
x = 6
Therefore, with $4, you can buy 6 Bosc pears.
71)If the exchange rate is 11 pounds for every $2, we can use a proportion to determine how many pounds we can get if we exchange $4:
11 pounds / $2 = x pounds / $4
Cross-multiplying, we get:
11 pounds × $4 = $2 × x pounds
Simplifying, we get:
44 = 2x
Dividing both sides by 2, we get:
x = 22
Therefore, if you exchange $4, you can get 22 pounds.
72) If 9 packages of basil cost $27, we can use a proportion to determine how many packages of basil we can buy for $9:
9 packages / $27 = x packages / $9
Cross-multiplying, we get:
9 packages × $9 = $27 × x packages
Simplifying, we get:
81 = 27x
Dividing both sides by 27, we get:
x = 3
Therefore, with $9, you can buy 3 packages of basil.