A technique called simple random sampling involves choosing a random group of individuals from a predetermined population.
What is Simple random sampling?A selection of participants from a population is chosen at random by the researcher using simple random sampling, a sort of probability sampling.
Every person in the population has the same chance of being chosen.
Then, data are gathered from as much of this randomly selected subgroup as possible.
A straightforward random sample, where each participant has an equal chance of being selected, selects a small, random portion of the entire population to represent the entire data set.
Using techniques like lotteries or random draws, researchers can generate a straightforward random sample.
Therefore, a technique called simple random sampling involves choosing a random group of individuals from a predetermined population.
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sketch the solution to each system of inequalities.
y<=-x-2
y>=-5x+2
Answer:
Where you see the colors overlap is the answer.
Step-by-step explanation:
Desmos is a free graphing calculator.
mona wants to buy pens each pens costs 3.50 she can only buy 3 pens with the money she has which of these could be the money she has
a. rs 11
b. rs 10
c. rs 14
d. rs 9
Answer:
a. 11
Step-by-step explanation:
Mona wants to buy pens each pens costs 3.50 she can only buy 3 pens with the money she has which of these could be the money she has:
a. 11
b. 10
c. 14
d. 9
3.5 * 3 = 10.5 cost
She has 11.
10 post hole that are 3 feet deep and 1 foot across with a pipe down the center that is 3 inches in diameter
The total volume of all 10 holes and pipes is about 24.135 cubic feet.
What is Volume?Generally, To calculate the volume of the holes, you can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
In this case, the radius of the hole is 0.5 feet (since the hole is 1 foot across and the diameter of the pipe is 3 inches, which is 0.25 feet), and the height is 3 feet. Plugging these values into the formula, we get:
Volume = π * 0.5^2 * 3 = 0.785 * 3 = 2.355 cubic feet
So each hole has a volume of about 2.355 cubic feet. To find the total volume of all 10 holes, you can simply multiply this number by 10:
Total volume = 2.355 * 10 = 23.55 cubic feet
This is the volume of the holes themselves, not including the volume of the pipes. To find the volume of the pipes, you can use the same formula, but with the radius of the pipe (which is 1.5 inches, or 0.125 feet) and the length of the pipe (which is 3 feet).
Volume = π * 0.125^2 * 3 = 0.0195 * 3 = 0.0585 cubic feet
So the volume of one pipe is about 0.0585 cubic feet. To find the total volume of all 10 pipes, you can multiply this number by 10:
Total volume = 0.0585 * 10 = 0.585 cubic feet
23.55 + 0.585 = 24.135 cubic feet.
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CQ not found
Which decimal is equivalent to 2/27
Answer:
0.07407407
Step-by-step explanation:
divide 2 by 27
Answer:
0.0740
Step-by-step explanation:
just divide 2 by 27
in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens. give a 95% confidence interval for percent of american adults who believe in aliens.
The American adults who believes in alien as per given 95% of confidence interval and the given sample surveyed is in the range of
( 0.657 , 0.783 ).
As given in the question,
Number of American adults surveyed (sample size) 'n' = 200
Percentage of people who believes in aliens 'p'= 72%
= 0.72
Percentage of people who don't believes in aliens ' 1 - p' = 1 - 72%
= 28%
= 0.28
95% Confidence interval that represents percent of people believes in aliens
Z - score of 95% confidence interval = ± 1.96
Margin of error = (z-score)√p ( 1- p) /n
= ( 1.96)√(0.72 × 0.28)/ 200
= 1.96 ( 0.032)
= 0.06272
= 0.063
Lower limit = p - Margin of error
= 0.72 - 0.063
= 0.657
Upper limit = p + Margin of error
= 0.72 + 0.063
= 0.783
Therefore, for the given 95% confidence interval and sample size the Americans who believes in alien are in range of ( 0.657 , 0.783 ).
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A furniture maker buys foam rubber x times per year. The delivery charge is a flat rate of $400 dollars per purchase regardless of how much is bought. The annual cost of storage is figured as $10,000/x, because the more frequent the purchase, the less it costs for storage. The annual cost is: C = 400x+10,000/x
A. Graph the function.
B. Find the number of purchases per year that minimizes the annual cost of delivery and storage.
Answer:
Should be B
Step-by-step explanation:
suppose there are 6 roads connecting town a to town b and 4 roads connecting town b to town c. in how many ways can a person travel from a to c via b?
Number of ways can a person travels from A to C via B = 24 ways
How it can be calculated that a person can travel in no. of ways?
To calculate the likelihood of an event occurring, we will apply the equation number of favourable outcomes divided by total number of outcomes. We sometimes need to apply a permutation to calculate the overall number of outcomes. A permutation is a method for calculating the number of events that occur when order is important.
Given,
Connection of roads from a = 6
Connection of roads from a = 4
Number of roads from a to b =6
Number of roads from b to c =4
Number of ways can a person travels from a to c via b
= 6*4
= 24 ways
The number of ways a person can go from A to C via B is 24.
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At the start of 2014, Jim's house was worth £240,000.
The value of the house increased by 5% every year.
Work out the value of his house at the start of 2017.
Answer: $146,410
Step-by-step explanation:
Compare √18 and 23/5 using >, <, or =.
23/5<√18
23/5 = √18
√18 > 23/5
√18<23/5
Answer: Thus, sqrt 18 < 23/5
Step-by-step explanation:
23/5=4.6
4.6x4.6=21.16
18<21.16
Graph the line that has a slope of
1
6
and includes the point (0,0).
Hence, the line having the slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex] is [tex]y=\frac{x}{5}+c[/tex].
What is the slope of line?
The slope is always estimated by determining the ratio of the “vertical change” to the “horizontal change” between any two different points on a line.
Here given thaat the line that has a slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex].
Then,
[tex]y=mx+c\\\\y=\frac{x}{5}+c\\\\x=0,y=0\\\\0=0+c\\\\c=0[/tex]
Thus,
[tex]y=\frac{x}{5}+c\\\\c=0[/tex]
Hence, the line having the slope of [tex]\frac{1}{6}[/tex] which includes the point [tex](0,0)[/tex] is [tex]y=\frac{x}{5}+c[/tex].
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Diana arrives late at the theater for a play.
Her ticket entitles her to sit anywhere in Circle
G. She had hoped to sit in Seat D, which she
thought would give her the widest viewing
angle of the stage. But Seat D is taken, as
are all the other nearby seats in Circle G. The
seating chart for the theater is shown.
Identify two other spots where Diana can sit
that will give her the same viewing angle she
would have had in Seat D. Explain how you
know how your points would provide the
same viewing angle, and support your claim
by showing the viewing angles on the
drawing.
We have to set ∠AMN equal to ∠D.
What are angles?
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.
Label the rows (A nearest the screen, through G at back) and the seat numbers (starting with 1 on the far left of the diagram) and count towards the right.
The seat is not equal to 1 and will align to point D.
Viewing angle is in terms of another angle
Set ∠AMN equal to ∠D.
Hence, we have to set ∠AMN equal to ∠D.
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Suppose your parents agree to pay you
one cent today, two cents tomorrow (the first day after today), four cents the next day (second day after today), and so forth. Each time they double the amount they pay you. Write an equation expressing amount paid in terms of number of days after today. What kind of function is this? How much will they pay you the 30th day? Surprising?! Show that the amount paid today (0 days after today) agrees with the definition of zero exponents.
They will pay You $5368709.12 on the 30th day
What does the term "compound interest" mean?
Compound interest is when you receive interest on both your interest income and your savings.
You start with a one cent.
You have $0.01 x 2 the following day.
You have $0.01 x 2 x 2 the following day.
and so forth
You will have $0.01 x 2^n-1 on day n.
This means that on the 30th day, you have $0.01 x 2^29 = $5 368 709.12.
That is compound interest at work! It equates to daily payments of 100% interest. It immediately soars to inconceivable heights with even a penny as your initial investment!
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27. Solve and graph
-2n-5≥1 or 5n + 7 > 2
28. S
The solution to the inequality expression -2n - 5 ≥ 1 or 5n + 7 > 2 is -1 > n ≥ -3
How to determine the solution to the expression?From the question, we have the following parameters that can be used in our computation:
-2n-5≥1 or 5n + 7 > 2
So, we have
-2n - 5 ≥ 1 or 5n + 7 > 2
Evaluate the like terms
So, we have the following representation
-2n ≥ 6 or 5n > -5
Divide both sides by the coefficient of n
This gives
n ≤ -3 or n > -1
Combine the expression
-1 > n ≥ -3
Hence. the solution is -1 > n ≥ -3
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HELP ANYONE PLEASE IT'S DUE TODAY I WAS STUCK ON THIS QUESTION
A line that goes through (0, 0) and (3.6, 14.4).
Wewant a description of the line that describes the same proportional relationship as the points given in the table:
(x, y) = (3.6, 14.4), (12.2, 48.8), (2.1, 8.4)
What is Proportional relation ?The graph of the relation will be a straight line through points with (x, y) values from the table. A graph of a proportional relation also goes through the point (0, 0).
Of the points listed in the answer choices, only (3.6, 14.4) and (12.2, 48.8) are ones that are given in the table. This eliminates all of the answer choices except the correct one:
A line that goes through (0, 0) and (3.6, 14.4).
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I am very confused on what to do.Can someone help me?
Answer:
739 m²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Equation}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
The given scenario can be modelled as an exponential equation.
Let y be the area the fire covers (in meters squared).
Let x by the time (in hours).
If the fire currently covers an area of 32 m² then the initial value, a, is 32.
If the area covered by the fire increases by 17% each hour, then the growth factor, b, is 1.17 (since an increase of 17% is 117% of the previous amount).
Therefore:
a = 32b = 1.17Substitute the values of a and b into the exponential formula:
[tex]y=32(1.17)^x[/tex]
To find the area that the first covers in 20 hours' time, simply substitute x=20 into the equation:
[tex]\implies y=32(1.17)^{20}[/tex]
[tex]\implies y=32(23.1055991...)[/tex]
[tex]\implies y=739.37917...[/tex]
Therefore, the area the fire will cover in 20 hours' time is 739 m² (nearest 1 m²).
What 2 time 200000= because i dont know the question so can i get some help
Answer:
400000
Step-by-step explanation:
Need help answering this question
The measure of ∠JKM is 145°.
What is exterior angle theorem?The measure of an exterior angle of a triangle is bigger than either of the measures of the distant interior angles, according to the external angle theorem, Proposition 1.16 in Euclid's Elements.
Because the parallel postulate is not required for its proof, this is a fundamental conclusion in absolute geometry. Three of a triangle's corners are its vertices.
Two angles are produced by a triangle's sides (line segments) meeting at its apex (four angles if you consider the sides of the triangle to be lines instead of line segments). An interior angle of the triangle is the only one of these angles that has the third side of the triangle inside of it.
Here it is given that, ∠JLK= 70°
∠LJK = x°
(2x-5)°= 70°+x°
now applying exterior angle theorem,
x=75°
substitute 75 for x in 2x-5 to find m∠JKM.
=2x-5
=2×75-5
=145°
Hence, The measure of ∠JKM is 145°
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B.
5x + 2 = 2x + 14
WITH SOLUTION
i also need it rn-
Answer:
4
Step-by-step explanation:
5x + 2 = 2x + 14
or, 5x - 2x = 14 - 2
or, 3x = 12
or, x = 12/3
.
. . x = 4
In trapezoid ABCD(AB ∥CD), point M∈AD, so that AM:MD=3:5. Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N ,respectively. Find AC:PC.
there are no pictures. Will give brainlest.
a fair coin is flipped nultiple times until it lands on heads if the probability of landing on heads is 50% what is the probability of first landing on heads on the fourth attempt
If a fair coin is flipped several times until it lands on heads and the likelihood of such outcome is 50%, the probability of the coin landing on heads for the first time is 1/8.
what is probability ?There are four primary categories of probability: classical, empirical, subjective, and axiomatic. Since possibility and probability are equivalent, you may define probability as the likelihood that a specific event will occur.
given
A fair coin is repeatedly flipped until it comes up heads.
The coin is impartial.
On the third try, we need to calculate the likelihood of the first landing being on heads.
We are aware that each flip of a fair coin is independent of the others, and that each effort results in P(H) = P(T) = 0.5.
Required probability is the likelihood that the third attempt's first landing will be on heads.
= Chance of (I two trials result in tail and third result in head)
=P(I head) P(II head) P(III tail) (since each trial is independent)
= ( 1 /2 ) (1/2)(1/2) = (1/8 )
If a fair coin is flipped several times until it lands on heads and the likelihood of such outcome is 50%, the probability of the coin landing on heads for the first time is 1/8.
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Are the polygons similar? If they are, write a similarity statement and give the scale factor.
The image consists of two quadrilaterals PQSN and AGKD. The lengths of the sides PQ = 10, QS = 7.5, SN = 15, NP = 15, AG = 12, GK = 12, KD = 8 and DA = 6. Angle P is congruent to angle K. Angle S is congruent to angle A. Angle N and G are right angles.
A. no
B. yes; POSN ~ KDAG, scale factor: 5 : 4
C. yes; POSN ~ KDAG, scale factor: 4 : 5
The polygons (quadrilaterals) are similar by the congruency of three interior angles and the equal ratios (5 : 4) of a pair of adjacent sides. The correct option is therefore
B. Yes; PQSN ~ AGKD, scale factor; 5 : 4
What are similar polygons?Similar polygons are polygons that have the same interior angle, and proportional dimensions.
The specified parameters indicate that we have;
Polygon PQSN and AGKD are quadrilaterals
Length of sides of polygon PQSN
Length of side PQ = 10, QS = 7.5, SN = 15, NP = 15
Length of sides of polygon AGKD
AG = 12, GK = 12, KD = 8, DA = 6
The measure of the angles are;
∠K ≅∠S
∠S ≅ ∠A
∠N = ∠G = 90°
The angle sum property of a quadrilateral indicates that the measure of the fourth angle of both quadrilateral are congruent
The ratio of two adjacent sides of the quadrilaterals are;
7.5/6 and 10/8
7.5/6 = 1.25
10/8 = 1.25
Therefore;
[tex]\dfrac{7.5}{6} =\dfrac{10}{8} =1.25[/tex]
The ratio of two adjacent sides of the quadrilaterals PQSN and AGKD are therefore the same.
The three interior angles of quadrilateral PQSN are congruent to three interior angles of quadrilateral AGKD, and the ratio of two adjacent sides from each quadrilateral are the same, therefore, quadrilaterals are PQSN is similar to quadrilateral AGKD
The scale factor of dilation from quadrilateral PQSN to AGKD is 7.5 : 6 = 15 : 12 = 5 : 4
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Miles is shopping for a new computer. He finds a computer with an original price of $325. 00 but finds that it is 15% off. After paying a 7% sales tax, how much does miles spend on his new computer?.
Miles has to spend $295.3375 on his new computer.
Sales tax is applied to the price after the discount is applied because discounts are typically provided directly by the retailer and lower both the sales price and the money the retailer receives.
So Original price of Computer is $325.00
Discount with computer is 15% off.
15% of $325 is (325*15)/100 = $48.75.
Price of computer after discount = 325-48.75 =$276.25
Now sales tax will be applied on this price.
7% sales tax = 0.07
amount of sales tax = 276.25*0.07 = 19.3375
Price of Computer after sales tax = 276+19.3375 = 295.3375.
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Find X round answer to the nearest integer.
which graph represents the solution of the system of inequalities
2x+6y < 6
x + 3y > 12
The life in hours of a battery is known to be approximately normally distributed with standard deviation σ = 1. 25 hours. A random sample of 10 batteries has a mean life of x =40. 5hours. A. Is there evidence to support the claim that battery life exceeds 40 hours? Use α = 0. 5. B. What is the P-value for the test in part (a)? c. What is the β-error for the test in part (a) if the true mean life is 42 hours? d. What sample size would be required to ensure that β does not exceed 0. 10 if the true mean life is 44 hours? e. Explain how you could answer the question in part (a) by calculating an appropriate confidence bound on life
a)[tex]$z=\frac{40.5-40}{\frac{1.25}{\sqrt{10}}}=1.265$[/tex]
Now we can calculate the p value since we have a right tailed test the p values is given by:
[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]
And since the [tex]$p_v > \alpha$[/tex] we have enough evidence to FAIL to reject the null hypothesis. So then there is not evidence to support the claim that the mean is greater than 40 .
b) [tex]$p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029$[/tex]
c) [tex]$\beta=P\left(Z < 1.645-\frac{2 \sqrt{10}}{1.25}\right)=P(Z < -3.409)=0.000326$[/tex]
d) We want to ensure that the probability of error type II not exceeds 0.1, and for this case we can use the following formula:
[tex]n=\frac{\left(z_\alpha+z_s\right)^2 \sigma^2}{(x-\mu)^2}[/tex]
The true mean for this case is [tex]$\mu=44$[/tex] and we want [tex]$\beta < 0.1$[/tex] so then [tex]$z_{1-0.1}=z_{0.9}=1.29$[/tex] represent the value on the normal standard distribution that accumulates 0.1 of the area on the right tail. And we can replace like this:
[tex]n=\frac{(1.65+1.29)^2 1.25^2}{(44-40)^2}=0.844 \approx 1[/tex]
e) For this case we can calculate a one sided confidence interval given by:
[tex]$\left(-\infty, \bar{x}+z_\alpha \frac{\sigma}{\sqrt{n}}\right)$[/tex]
And if we replace we got:
[tex]$40.5+1.65 \frac{1.25}{\sqrt{10}}=41.152$[/tex]
And the confidence interval would be [tex]$(-\infty, 41.152)$[/tex]
And since 40 is on the confidence interval we don't have enough evidence to reject the null hypothesis on this case.
What is null hypothesis?
In a scientific setting, a hypothesis (plural: hypotheses) is a testable claim about the relationship between two or more variables or a suggested explanation for a phenomenon that has been observed.
Part a
We have the following data given:
n=10 represent the sample size
[tex]$\bar{x}=40.5$[/tex] represent the sample mean
[tex]$\sigma=1.25$[/tex]represent the population deviation.
We want to test the following hypothesis:
Null: [tex]$\mu \leq 40$[/tex]
Alternative: [tex]$\mu > 40$[/tex]
The significance level provided was [tex]$\alpha=0.05$[/tex]
The statistic for this case since we have the population deviation is given by:[tex]z=\frac{\bar{x}-\mu}{\frac{-\mu}{\sqrt{n}}}$[/tex]
If we replace the values given we got:
[tex]$z=\frac{40.5-40}{\frac{1.24}{\sqrt{10}}}=1.265$[/tex]
Now we can calculate the p value since we have a right tailed test the p values is given by:
[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]
And since the [tex]$p_v > \alpha$[/tex] we have enough evidence to FAIL to reject the null hypothesis. So then there is not evidence to support the claim that the mean is greater than 40 .
Part b
The p value on this case is given by:
[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]
Part c
For this case the probability of type II error is defined as the probability of incorrectly retaining the null hypothesis and is defined like this:
[tex]\beta=P\left(Z < z_\alpha-\frac{(x-\mu) \sqrt{n}}{\sigma}\right)[/tex]
Where [tex]$z_\alpha=1.645$[/tex]represent the critical value for the test that accumulates 0.05 of the area on the right tail of the normal standard distribution.
The true mean on this case is assumed [tex]$\mu=42$[/tex], so then we can replace like this:
[tex]\beta=P\left(Z < 1.645-\frac{2 \sqrt{10}}{1.25}\right)=P(Z < -3.409)=0.000326$$[/tex]
Part d
We want to ensure that the probability of error type II not exceeds 0.1, and for this case we can use the following formula:
[tex]n=\frac{\left(z_\alpha+z_\beta\right)^2 \sigma^2}{(x-\mu)^2}[/tex]
The ture mean for this case is [tex]$\mu=44$[/tex] and we want [tex]$\beta < 0.1$[/tex] so then [tex]$z_{1-0.1}=z_{0.9}=1.29$[/tex] represent the value on the normal standard distribution that accumulates 0.1 of the area on the right tail. And we can replace like this:
[tex]n=\frac{(1.65+1.29)^2 1.25^2}{(44-40)^2}=0.844 \approx 1[/tex]
Part e
For this case we can calculate a one sided confidence interval given by:
[tex]\left(-\infty, \bar{x}+z_\alpha \frac{\sigma}{\sqrt{n}}\right)[/tex]
And if we replace we got:
[tex]40.5+1.65 \frac{1.25}{\sqrt{10}}=41.152[/tex]
And the confidence interval would be [tex]$(-\infty, 41.152)$[/tex]
And since 40 is on the confidence interval we don't have enough evidence to reject the null hypothesis on this case.
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Consider all positive integers that are multiples of 10 and are less than or equal to 200. What fraction of those integers are multiples of 15?.
3/10 will be the proportion of those integers that are multiples of 15. Then, C is the best choice.
Algebra: What Is It?Mathematical branch known as algebra deals with symbols and arithmetic operations on them. These symbols are referred to as variables because they lack fixed values. We frequently observe certain values that change in our day-to-day problems. However, there is a continuing need to depict these shifting values. These values are frequently represented in algebra by symbols, which are known as variables, such as x, y, z, p, or q.
Take into account all positive numbers that are multiples of 10 and have a value lower than or equal to 200.
Let x be the quantity of positive integers that are multiples of 10. The equation then becomes
10x ≤ 200
The value of the x will then be.
x ≤ 20
Below is a list of the numbers.
Set = 20 {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200}
The set that can be divided by 15 is
Set = 6 {30, 6,0 90, 120, 150, 180}
So, the percentage of those integers that are multiples of 15 will be
⇒ 6 / 20
⇒ 3/10
3/10 will be the proportion of those integers that are multiples of 15. Then, C is the best choice.
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solve it HURRY if if u can
Answer:
y= 0.25x
Step-by-step explanation:
First, use the slope formula to calculate the slope.
Second, solve for the y-intercept using the slope and one of the points.
Finally, once you've determined m and b, you can enter them into the slope-intercept form of a line (y = mx + b) to obtain the equation for the line.
a jar contains 10 blue marbles and 11 red marbles. two marbles are drawn without replacement. what is the probability of getting two red marbles?
0.2620 is the probability of getting two red marbles.
What is probability?Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
a jar contains 10 blue marbles and 11 red marbles.
So, there total 21 marbles are present.
Now among 21 marbles, 11 are red marble. So, odds of a red on the first are 11/21
Next, there are 20 marbles are present and 10 are red. So odds of a red on the second is 10/20.
For, probability both are red, just multiply
= (11/21) x (10/20)
= 0.2620.
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Please help me ASAP. I will give brainliest after 2 people comment.
Answer: x= 18
Step-by-step explanation:
9 divided by 6 = 1.5
That is the rate change
So take 12 times 1.5 = 18
x= 18
If you can please give me a Brainliest, thank you!
Answer:
18
Step-by-step explanation:
See attached worksheet.
A scaled figure will have dirrent dimensions, but with the same proportions. The ratio of the two sides in Figure A is 2/1 (Side/Top). That same ratio will apply to Figure B. So we could write:
x/9 = 2
x = 18
Find an equation of the line that has a slope of -1 and a y intercept of 5. Write your answer in the form
y = mx + b.
y =
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+\underset{\underset{\textit{\small b }}{\uparrow }}{5}\implies y=-x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]