The function f(x) = (1/2)x^2 + 3x - 5 has a minimum value
Classifying the function as min or maxTo determine whether the function f(x) = (1/2)x^2 + 3x - 5 has a minimum or maximum value, we can use the fact that the vertex of a quadratic function represents the minimum or maximum point of the function.
To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively.
In this case, a = 1/2 and b = 3, so we have:
x = -b/2a = -(3)/(2(1/2)) = -3
To find the corresponding y-coordinate, we can substitute x = -3 into the function:
f(-3) = (1/2)(-3)^2 + 3(-3) - 5 = -9.5
Since the coefficient of the quadratic term is positive, we know that the parabola opens upward and the vertex represents a minimum value.
Therefore, the minimum value of the function is -9.5, which occurs at x = -3.
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Can anyone help me??
1. The coordinates of the vertices of the preimage in the first column of the table are; (2, 2), (-1, 2) (-1, 1) (-2, 1) (-2, -2) (1, -2) (1, -1) (2, -1).
2. The scale factor for the dilation is 3
3. The coordinates for the image are, (6,6) (-3, 6) (-3, 3) (-6, 3)(-6, -6) (3, -6) (3, -3)(6, -3)
4. The sketch has been attached below;
5. The dilation multiplies the length of line segments by the scale factor.
6. The dilation did not affect the angle measures. The angles in the image are the same as the angles in the preimage.
How to calculate the scale factor of the image?
To calculate the scale factor for the dilation, we look at what has been provided (x, y) → (3x, 3y)
x =1 x2 = 3
1 multiplied by what will give us 3
1×? = 3
1/1 = 3/1 = 3
If we multiply 3 to every vertices of the preimage, we will find the coordinated of the image.
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Answer:
S = 2π(10^2) + 2π(10)(3)
= (200 + 60)π = 260π cm^2
So 250 cm^2 is not a reasonable answer for the surface area of this cylinder.
Does the infinite geometric series diverge or converge?
1/5 + 1/10 + 1/20 +1/40 + …
Answer:
the answer is C
Step-by-step explanation:
the answer is C it converges
what is the mean absolute deviation of 8,2,7,8,6,10,2,1,10,6
Answer:
The mean absolute deviation of 8,2,7,8,6,10,2,1,10,6 is 2.24.
To calculate the mean absolute deviation, we first need to find the mean of the data set. The mean is the sum of all the values in the data set divided by the number of values. In this case, the mean is 7.
Once we have the mean, we can find the mean absolute deviation by finding the absolute value of the difference between each value in the data set and the mean. For example, the absolute value of the difference between 8 and 7 is 1. We then add up all of the absolute values and divide by the number of values in the data set. In this case, the mean absolute deviation is 2.24.
Here is the formula for the mean absolute deviation:
```
MAD = (|x1 - μ| + |x2 - μ| + ... + |xn - μ|) / n
```
Where:
* MAD is the mean absolute deviation
* x1, x2, ..., xn are the values in the data set
* μ is the mean of the data set
* n is the number of values in the data set
Step-by-step explanation:
S=4lw +2wh s=92 l=9 w=2
Answer:
h=5
Step-by-step explanation:
Substituting in 92 for s,
92=4lw+2wh
Substituting in 9 for l,
92=4(9)(w)+2wh
Substituting 2 for w,
92=4(9)(2)+2(2)(h)
Simplifying by multiplying terms
92=72+4h
Subtract 72 on both sides
20=4h
Divide by 4 on both sides
5=h
Factor the expression. x^2-12x-45
Answer:
(x + 3)(x - 15)
Step-by-step explanation:
To factor the expression x^2 - 12x - 45, we need to find two numbers that multiply to -45 and add to -12. Let's use the method of decomposition to find these two numbers:
x^2 - 12x - 45
We need to find two numbers that multiply to -45 and add to -12. Let's try -15 and 3:
x^2 - 12x - 45 = x^2 - 15x + 3x - 45
Now we can group the first two terms and the last two terms:
x^2 - 15x + 3x - 45 = x(x - 15) + 3(x - 15)
We can see that both terms have a common factor of (x - 15), so we can factor this out:
x(x - 15) + 3(x - 15) = (x + 3)(x - 15)
Therefore, the expression x^2 - 12x - 45 can be factored as (x + 3)(x - 15).
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A vending machine is designed to dispense a mean of 7.6 oz of coffee into an 8 oz cup. If the standard deviation of the amount of coffee dispensed is 0.2 oz, and the amount is normally distributed, find the percent of times the machine will dispense from 7.5 oz to 7.9 oz.
The percentage of time that the machine will dispense from 7. 5 oz to 7. 9 oz is 62.47% of the time.
How to find the percentage ?Find the Z-scores for both 7. 5 oz and 7. 9 oz :
Z = ( X - μ ) / σ
For 7. 5 oz :
Z = ( 7.5 - 7.6 ) / 0.2
Z = -0. 1 / 0. 2
Z = -0. 5
For 7.9 oz:
Z = (7. 9 - 7.6 ) / 0.2
Z = 0. 3 / 0. 2
Z = 1. 5
Using the z - values from the table, the percentage of time is:
0.9332 - 0.3085 = 0.6247
= 62. 47 %
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Adam works as an account manager for a local insurance company. He makes $3500 per month, after taxes. He sticks to a strict monthly budget to make sure that he is able to pay for all of his expenses each month. Look at the list below of the items Adam must budget for each month. He gives a specific percentage of his income to each item. Use his monthly income and the percentage of each item to determine how much Adam will need to budget for each expense. 30% for rent/mortgage $ 15% for Insurances $ 12% for food $ 8% for utilities $ 10% for savings $ 5% for fun $ 7% for clothing $ 3% for personal items $ 10% charitable giving $ How much money will Adam have left over after budgeting for each item on the list? $
Answer:
see below
Step-by-step explanation:
Given a $3500 net income per month and a list of budget percentages, you want to know the budget amounts for each item, and the amount left over.
AmountsEach budget amount is the product of the net income and the associated budget percentage. Those products are ...
rent: $1050insurance: $525food: $420utilities: $280savings: $350fun: $175clothing: $245personal: $105charity: $350Left overThe sum of these amounts is $3500, so there will be $0 left over.
__
Additional comment
The list is stored in the variable 'b' by the first line in the calculator. Then these values are multiplied by the net income to get the budget amounts.
Every weekend, Camilla teaches ice skating lessons at a nearby ice rink. She earns $12 for a
30-minute lesson.
Complete the table.
Minutes taught
30
Money earned ($) 12
Graph the data from the table.
60
90 120
Next, using the matching x and y values for each row of the table, we can place a point for each row and connect it to the other points using a line.
what is line ?A line represents a one-dimensional straight figure that can go on forever in both directions in geometry. To separate it from a curved or an angle-filled line, it is frequently referred to as a "straight line." Two points on a line define the line, while every other position on the line may be discovered by tracing the line through the two defined points. A line can be made with a pencils or another non-thick tool, and it can have any width or depth. Shape and figures are described and analysed using lines, which are a basic building block of geometry.
given
Minutes Taught Dollars Earned (30, 12, 60, 24)
90 36
120 48
We may plot the minutes taught on the x-axis and the money made on the y-axis to graph the data from the table.
Next, using the matching x and y values for each row of the table, we can place a point for each row and connect it to the other points using a line.
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2. Although Kevin has money, he is not spending it.
Complex or compound -complex
Answer:
complex
Step-by-step explanation:
The given sentence "Although Kevin has money, he is not spending it." is a complex sentence.
This is because it contains one independent clause, "he is not spending it," which can stand alone as a complete sentence. The other part of the sentence, "Although Kevin has money," is a dependent clause because it cannot stand alone as a complete sentence.
The dependent clause "Although Kevin has money" introduces a contrast or concession to the independent clause that follows it. Therefore, this sentence is an example of a complex sentence that uses a dependent clause to add meaning and complexity to the independent clause.
Each container holds 3 L 456 mL of water. How much water is in 206 identical containers?
Answer:
711 L 936 mL
Step-by-step explanation:
3 L 456 ml times 206=711L 936mL
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Determine if the relationship between x and y is linear or not linear. Explain.
Answer: To determine if the relationship between x and y is linear, we need to graph the data and look for a straight-line pattern.
If the graph shows a straight-line pattern, then the relationship is linear. If the graph shows a curve or a non-linear pattern, then the relationship is not linear. So it is linear
Step-by-step explanation: can i get brainliest :D
the volume of the indian ocean is about 2.1 X 10^17 cubic meters. How many years would it take for the Narmada River to fill the Indian, assuming it has a water flow of 6.3 X 10^11 cubic meters per year? Answer in scientific notation
Write a word problem to match -2.75>x
A word problem that matches the inequality -2.75 > x is:
John has a balance of $25 in his bank account and wants to withdraw some money and he needs to withdraw at least x dollars, but not more than $2.75.
How to write a word problem to match -2.75>x?A word problem that matches the inequality -2.75 > x is:
John has a balance of $25 in his bank account and wants to withdraw some money. He needs to withdraw at least x dollars, but not more than $2.75.
What is the largest possible value of x that John can withdraw and still have a positive balance in his account?
In this scenario, the variable x represents the amount that John can withdraw from his account, and the inequality -2.75 > x means that x must be less than -2.75 (i.e., negative and greater in magnitude than 2.75)
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PLEASE HELP ME!
LaNiyah uses 2 eggs to make brownies, 3 eggs to make a cake, and 6 eggs to make a soufflé. In all, she has one gross of eggs (that’s 144 eggs). If she only makes brownies and soufflés and she uses all the eggs, write an equation to model the eggs used.
An equation that models the eggs used by LaNiyah is 2b + 6s = 144.
What is an equation?An equation is a mathematical statement that shows that two or more mathematical expressions are equal or equivalent.
Equations contain the equal symbol (=), unlike mathematical expressions that combine variables with numbers, and constants using mathematical operands only.
The number of eggs used to make brownies per unit = 2
The number of eggs used to make cakes per unit = 3
The number of eggs used to make soufflés per unit = 6
The total number of eggs used = 144
Let the total number of brownies made = b
Let the total number of soufflés made = s
Equation:2b + 6s = 144
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A scale drawing of a square has a sidle length of 9 inches. The drawing has a scale of 1 in. : 7 mi. Find the actual permitted and area of the square
Answer: To find the actual perimeter and area of the square, we need to use the scale given in the problem, which is 1 inch on the drawing represents 7 miles in real life.
The side length of the square on the drawing is 9 inches, so in real life, the side length would be:
9 inches x 7 miles/inch = 63 miles
Therefore, the actual perimeter of the square would be:
4 x 63 miles = 252 miles
To find the actual area of the square, we can use the formula:
area = side length x side length
In this case, the side length is 63 miles, so:
area = 63 miles x 63 miles = 3,969 square miles
So the actual perimeter of the square is 252 miles, and the actual area of the square is 3,969 square miles.
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Which equation can be used to solve for x
Answer:
(a) 7(x +3.5x) = 56
Step-by-step explanation:
You want an equation to solve for x, the length of a morning run, if the evening run is 3.5 times as long, and these runs total 56 miles when done every day of the week.
Daily runThe morning run is given as x.
The evening run is 3.5 times as long, so is 3.5x
The total mileage each day is (x +3.5x).
Weekly totalIn 7 days, the mileage will be 7 times the daily mileage. That total is given as 56 miles:
7(x +3.5x) = 56
The Soule's live on a corner lot. Often, children cut across
their lot to save walking distance. The diagram to the right
represents the corner lot. The children's path is
represented by a dashed line. Approximate the walking
distance that is saved by cutting across their property
instead of walking around the lot.
...
The walking distance that is saved by cutting across the lot is
feet.
X
15 feet
x+3
Answer:
The walking distance that is saved by cutting across the lot is approximately 18 feet.
The diagonal of a square is 32 cm. What is the length of one side of the square rounded to the nearest tenth?
The length of the square with a diagonal of 32 cm is 22.6 cm.
What is a square?A square is a plane shape with all sides and angles equal.
To calculate the length of the square from its diagonal, we use Pythagoras formula
Formula:
d² = l²+l².................... Equation 1Where:
d = Diagonal of the squarel = length of the squareFrom the question,
Given:
d = 32 cmSubstitute these values into equation 1 and solve for l
32² = l²+l²1024 = 2l²l² = 1024/2l² = 512l = √512l = 22.6 cmLearn more about square here: https://brainly.com/question/27307830
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the set of five number each of which is divisible by 3
Answer:
{3, 6, 9, 12, 15}
Each of these numbers is divisible by 3
Step-by-step explanation:
A political pollster wants to know what proportion of voters are planning to
vote for the incumbent candidate in an upcoming election. A poll of 150
randomly selected voters is taken from the more than 2,000 voters in the
population, and 78 of those selected plan to vote for the incumbent
candidate.
Based on this sample, which of the following is a 90% confidence interval
for the proportion of all voters who plan to vote for the incumbent
candidate?
Choose 1 answer:
780.067
78±0.080
0.520.067
The confidence interval is 0.52±0.067.(option c)
What is confidence interval?
In statistics, confidence interval means that the probability in which a population parameter will fall between a set of values for a certain proportion of times.
A political pollster wants to know what proportion of voters are planning to
vote for the incumbent candidate in an upcoming election. A poll of 150
randomly selected voters is taken from the more than 2,000 voters in the
population, and 78 of those selected plan to vote for the incumbent
candidate.
The formula for confidence interval(CI) is given by:
CI= p ± z √{p(1-p)/n} ----------------(1)
Here from the given data p= 78/150= 0.52
n= 150
For 90% confidence interval the value of z= 1.645.
Putting all the values in equation (1) we get,
CI= 0.52± 1.645√{(0.52×0.48)/150}
= 0.52±1.645×0.04
= 0.52±0.067
Hence, the confidence interval is 0.52±0.067.
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Find the perimeter of each figure
The hexagon with sides of length 5 inches, 4 inches, 4 inches, 5 inches, 3 inches, and 3 inches has a perimeter of 24 inches.
What is a hexagon?A hexagon is a regular polygon, meaning all sides and angles are equal in size. It is a symmetrical shape, which means it can be divided into two equal halves.
To calculate the perimeter of this hexagon, we must first identify the length of each side.
All sides of the hexagon have a length of either 5 inches, 4 inches, or 3 inches, as there are two sides of each length.
The perimeter of the hexagon is the sum of the length of all its sides. Adding the length of all the sides, we get
5 + 4 + 4 + 5 + 3 + 3 = 24.
Thus, the perimeter of the hexagon is 24 inches.
Hence, the sum of the length of the sides of a hexagon is always greater than the length of any one of its sides.
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A theme park has a ride that is located in a cylinder with a height of 11 yards.The ride goes around the outside of the cylinder, which has a circumference of 513.88 yards. What is the surface area of the cylinder? Estimate to the nearest hundredth, using 3.14. Apply the formula for surface area of a cylinder SA=2B+Ph
Answer:
To calculate the surface area of the cylinder, we need to find the area of the two circular bases and the lateral surface area.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference and r is the radius. We can rearrange this formula to solve for the radius:
r = C/2π = 513.88/(2 x 3.14) = 81.91 yards
The formula for the area of a circle is:
A = πr^2
where A is the area and r is the radius. We can use this formula to find the area of one of the circular bases:
B = πr^2 = 3.14 x 81.91^2 = 21,237.93 square yards
The formula for the lateral surface area of a cylinder is:
P x h
where P is the perimeter of the base and h is the height. We can use the formula for the circumference to find the perimeter of the base:
P = C = 513.88 yards
Now we can calculate the lateral surface area:
L = P x h = 513.88 x 11 = 5,652.68 square yards
Finally, we can use the formula for the surface area of a cylinder:
SA = 2B + L = 2(21,237.93) + 5,652.68 = 48,128.54 square yards
Therefore, the surface area of the cylinder is approximately 48,128.54 square yards when rounded to the nearest hundredth.
use compass and ruler to contruct bisector of the angle
Bisector of the angle is the line that divides the angle into two angles with the same measure. In the image attached, the bisector of the angle is represented by the green line.
Here, we have,
The next steps show you how to construct the bisector of the angle from a ruler and a compass.
Draw an arc using the vertex of the angle (O) as the center;
Mark the points A and B;
Draw an arc using the point (A) as the center;
Draw an arc, with the same radius, using the point (B) as the center. This arc should intersect the arc that you draw in the previous step.
Draw a line connecting the point C to the vertex O.
Finally, you have the bisector of the angle that is represented by the green line.
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simplify the following:
Answer:
[tex]\dfrac{\left(12x-56\right)x}{\left(x-4\right)\left(-x^2+20x-32\right)}[/tex]
Step-by-step explanation:
Simplify
[tex]\dfrac{\dfrac{16}{x-2}-\dfrac{4}{x-4}}{\dfrac{16}{x}-\dfrac{x-4}{x-2}}[/tex]
The first-level numerator is
[tex]\dfrac{16}{x-4}-\dfrac{4}{x-2}\\\\\\= \dfrac{16(x-4) - 4(x - 2)}{(x-2)(x-4)}\\\\\\= \dfrac{16x -64 - 4x + 8}{(x-2)(x-4)}\\\\\\= \dfrac{12x -56}{(x-2)(x-4)}[/tex]
The first-level denominator is
[tex]\dfrac{16}{x}-\dfrac{x-4}{x-2}\\\\\\= \dfrac{16(x-2) - x(x-4)}{x(x-2)}\\\\\\\\= \dfrac{16x - 32 -x^2 +4x}{x(x-2)}[/tex]
[tex]= \dfrac{-x^2+20x-32}{x\left(x-2\right)}[/tex]
Therefore
[tex]\dfrac{\dfrac{16}{x-2}-\dfrac{4}{x-4}}{\dfrac{16}{x}-\dfrac{x-4}{x-2}}\\\\\\= \dfrac{12x -56}{(x-2)(x-4)} \div\dfrac{-x^2+20x-32}{x\left(x-2\right)} \\\\\\[/tex]
Use the fraction rule: [tex]\dfrac{a}{b} \div \dfrac{d}{c} = \dfrac{a}{b} \cdot \dfrac{d}{c}[/tex]
[tex]= \dfrac{12x -56}{(x-2)(x-4)} \cdot \dfrac{x(x-2)}{-x^2 +20x -32}}[/tex]
The (x-2) term cancels out resulting in:
[tex]\dfrac{\left(12x-56\right)x}{\left(x-4\right)\left(-x^2+20x-32\right)}[/tex]
Find the horizontal asymptotes and vertical asymptotes of the function [tex]k(x)= \frac{3x^{2} }{(x+1)(x-4)}[/tex]
the vertical asymptotes are x = -1 and x = 4, and there is no horizontal asymptote.
what is vertical asymptotes ?
Vertical asymptotes are vertical lines on a graph where a function approaches infinity or negative infinity as the input (x) approaches a certain value. In other words, vertical asymptotes occur when the denominator of a function becomes zero and the function is undefined at that point
In the given question,
To find the horizontal and vertical asymptotes of the function f(x) = 3x²/[(x+1)(x-4)], we need to analyze the behavior of the function as x approaches infinity or negative infinity and as x approaches the vertical asymptotes (if any).
Vertical asymptotes occur at the values of x that make the denominator of the fraction equal to zero. In this case, we have vertical asymptotes at x = -1 and x = 4.
To find the horizontal asymptote, we need to divide the leading term of the numerator by the leading term of the denominator when x approaches infinity or negative infinity. Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. However, we can use long division or synthetic division to write the function in the form of a polynomial plus a proper fraction:
f(x) = 3x²/[(x+1)(x-4)] = (3x + 15)/(x² - 3x - 4)
As x approaches infinity or negative infinity, the fraction approaches the value of 3/1 (the ratio of the leading terms of the numerator and denominator), but there is no horizontal asymptote.
Therefore, the vertical asymptotes are x = -1 and x = 4, and there is no horizontal asymptote.
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Kyle is buying gifts for Megan's birthday and needs to stay in budget
Cake = half his money + 36.50
Decorations = half of what he had left + 36.50
Sweets = half of what he had left + 18.25
Now he is out of money, what did he start with?
Answer: Let's start by using algebra to represent the problem.
Let X be the amount of money that Kyle started with.
Then we can create the following equations:
Cake = 0.5X + 36.50Decorations = 0.5(X - Cake) + 36.50Sweets = 0.5(X - Cake - Decorations) + 18.25
And we know that he's out of money, so:
Cake + Decorations + Sweets = XWe can use substitution to solve for X.
Substitute the first equation into the second equation to get:
Decorations = 0.5(X - (0.5X + 36.50)) + 36.50Decorations = 0.25X + 9.25
Substitute the first two equations into the third equation to get:
Sweets = 0.5(X - (0.5X + 36.50) - (0.25X + 9.25)) + 18.25Sweets = 0.25X + 4.75
Substitute all three equations into the fourth equation to get:
(0.5X + 36.50) + (0.25X + 9.25) + (0.25X + 4.75) = X
Simplify and solve for X:
1X + 50.50 = X50.50 = 0.5XX = 101
Therefore, Kyle started with $101.
Compare these distributions.
Both distributions of exam scores are and there are clear outlier(s) in each distribution of exam scores.
The center of the distribution of exam scores earned by students who completed homework is the center of the distribution of exam scores earned by students who did not complete homework.
The variability in scores of those who completed homework is that of the students who did not complete homework.
The comparison data is shown below.
Based on the information provided, we can infer that:
Both distributions have outliers.The center of the distribution of exam scores is the same for both groups, meaning that the average score of students who completed homework is the same as the average score of students who did not complete homework.The variability (spread) of exam scores of those who completed homework is the same as the variability of exam scores of those who did not complete homework.Without more information about the specific data and the context of the study, it is difficult to make further comparisons or draw any conclusions about the relationship between completing homework and exam scores. However, it is interesting to note that completing homework did not seem to have an impact on the average exam score or the variability of exam scores.
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There is a straight road between town 4 and town B of length 130 km. Maxi travels from town 4 to town B. Pippa travels from town B to town A. Both travel at a constant speed of 40 km/h. Maxi leaves 30 minutes before Pippa. Work out how far from town A they will be when they pass each other
The distance from town A that they will be, when they will pass each other is 44 4/9 .
How can the distance be calculated?It should be noted that time traveled in each segment is constant, which implies that in this case the average speed can be regarded as the simple mean of speeds. An in the case whereby the distance traveled in each segment is constant, average speed can be described to be the reciprocal of simple mean .
This can be expressed mathematically as
Average speed = Reciprocal [ 1/40 & 1/50].
Average speed = Reciprocal of (1/40 + 1/50)/2
= Reciprocal of [(5+4)/400]
= 44 4/9 .
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A plane is flying at a speed of 320 miles per hour on a bearing of N65°E. Its ground speed is 390 miles per hour and its true course, given by the direction angle of the ground speed vector, is 30°. Find the speed, in miles per hour, and the direction angle, in degrees, of the wind.
The speed in miles per hour is 111.2 and the direction angle in degrees is 260.2.
We are given the speed of a plane on a bearing of N [tex]75^\circ[/tex] E and its ground speed. We have to find its speed in miles per hour and the direction angle in degrees. We will apply the formula of projection for both the x-axis and y-axis.
As we know, projection, R = V + W
Now, the x-axis projection will be R cos[tex]15^\circ[/tex] according to the angle given to us. Therefore, R cos [tex]15^\circ[/tex] = V cos[tex]30^\circ[/tex] + [tex]W_{x}[/tex]
The y-axis projection,
R sin [tex]15^\circ[/tex] = V sin [tex]30^\circ[/tex] + [tex]W_{y}[/tex]
From here, now we will find [tex]W_{x}{[/tex] and [tex]W_{y}[/tex]
[tex]W_{x}{[/tex] = 330 cos[tex]15^\circ[/tex] - 390 cos[tex]30^\circ[/tex]
[tex]W_{x}[/tex] = -19 miles/hour
[tex]W_{y}[/tex] = 330 sin[tex]15^\circ[/tex] - 390 sin[tex]30^\circ[/tex]
[tex]W_{y}{[/tex] = -109.6 miles per hour
Now, W = [tex]\sqrt{(W_{x})^{2} + (W_{y})^{2{}}[/tex]
W = [tex]\sqrt{(-19.0)^{2} + (-109.6})^{2{}}[/tex]
W = 111.2 miles/hour
Now, we will find the angle with the help of tan θ.
tan θ = [tex]\frac{W_{y}}{W_{x}}[/tex]
tan θ = [tex]\frac{-109.6}{-19.0}[/tex]
θ = [tex]tan ^{-1} (\frac{109.6}{19.0})[/tex]
θ = 260.[tex]2^\circ[/tex]
Therefore, the speed in miles per hour is 111.2 and the direction angle in degrees is 260.2.
To learn more about projection;
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