According to a driver, the South Boro Police issue 60 speeding penalties on average each day. These numbers display the daily average number of speeding fines issued over a randomly chosen 30-day period. At alpha = 0.05, there is not enough data to disprove the motorists' assertion.
Traditional Method:
H0: μ = 60
H1: μ ≠ 60
n = 30
Sample mean = 58.9
Standard Deviation = 13.42
t-statistic = -1.85
Number of Degrees of Freedom = 30 - 1 = 29
α = 0.05
Critical t-value = ±2.045
Since -1.85 does not lie in the rejection region, we fail to reject the null hypothesis.
Therefore, there is not enough evidence to reject the motorists claim at alpha = 0.05.
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13. So far, two-thirds of the seniors bought prom
tickets. If they need a minimum of 250 people
to attend in order to keep the venue, how
many students must be in the senior class to
ensure they sold enough tickets? Please write out the equation
Answer:
[tex]\dfrac{2}{3}x \geq 250[/tex]
Step-by-step explanation:
Let x be the number of students in the senior class.
If two-thirds of the seniors bought prom tickets and a minimum number of 250 tickets needs to be sold, the inequality that models this scenario is:
[tex]\boxed{\dfrac{2}{3}x \geq 250}[/tex]
Solving the inequality:
[tex]\implies \dfrac{2}{3}x \geq 250[/tex]
[tex]\implies 2x \geq 250 \cdot 3[/tex]
[tex]\implies 2x \geq 750[/tex]
[tex]\implies x \geq 750 \div 2[/tex]
[tex]\implies x \geq 375[/tex]
Therefore, there must be at least 375 students in the senior class to ensure they sold enough tickets to keep the venue.
Joe Jan wants to receive $22,000 each year for the next 22 years. Assume a 6% interest rate compounded annually. How much must Joe invest today? (Round your answer to the nearest cent.)
If Joe deposits $264,954.31 today then he will reach his goal
Define Present Value
Finding the appropriate quantity of money to deposit today in order to ensure a specific amount of future payments is one objective of financial analysis. The target payment amount, the quantity and frequency of payments, and the interest rate all influence the present value, which is the value in today's dollars.
Given,
Joe want to receive each month = $22,000
Interest rate = 6%
number of payment = 22 years
We know, the formula of present value is
Present value = pmt * (1 - (1/ (1+r)ⁿ) ) / r
pmt = $22,000
r = 0.06
n = 22 years
Now, plug in the values
Present value = $22,000( 1 - (1/(1+0.06)²² ) / 0.06
=$22,000( 1 - (1/(1+0.06)²² ) / 0.06
≈ $264,954.311
Hence, If Joe deposits $264,954.31 today then he will reach his goal.
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Please help me find the answer to this question
-------------------------------------------------------------------------------------------------------------
Answer: The top right table
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{y = 30 - 3x}[/tex]
Find: [tex]\textsf{Match the table of values with the equation}[/tex]
Solution: First we must understand what form our equation is in and what each of the numbers represent. This form is known as the slope intercept form which is formatted as y = mx + b. Our equation is slightly re-ordered but we can change that by converting it to y = -3x + 30 where m is equal to -3 and b is equal to 30. Let us know talk about what m and b are. M is the slope of the equation or also known as the rise/run or the change in y over the change in x. B is the y-intercept which is basically the value of y when x is equal to 0. In this case, our b is equal to 30.
Looking at the tables we can see what the value of y when x is equal to 0 for each table. The only table that matches up stating that y is equal to 30 when x is 0 is the top right table.
You do not have to go any further but if you want to confirm that the slope is as expected we can do the following: [tex]\frac{y_2\ -\ y_1}{x_2\ -\ x_1}[/tex].
Plug in the values and simplify
[tex]\frac{48\ -\ 30}{-6\ -\ 0}[/tex][tex]\frac{18}{-6}[/tex][tex]-3[/tex]Therefore, we can confirm that the slope matches up with the given equation as well. So, the final answer would be that the top right table would correspond to the equation y = 30 - 3x.
what is 12/7Q minus 1/21Q=Q-2/3
The given equation is solved to obtain Q = -1/21.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given equation is as below,
12/7Q - 1/21Q = Q - 2/3
It can be simplified as follows,
12/7Q - 1/21Q = Q - 2/3
=> 12/7Q - 1/21Q - Q = -2/3
=> (36 - 1 - 21)Q = -2/3
=> 14Q = -2/3
=> Q = -1/21
Hence, the solution of the given equation is -1/21.
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Draw a quick picture to find the product of 3×800
Answer:
daymn
it's gonna be okay
Combine the methods of row reduction and cofactor expansion to compute the determinants in Exercises 11-14.
By combining the methods of row reduction and cofactor expansion the determinant of the given matrix is 1 .
In the question ,
it is given that ,
the matrix is [tex]\left[\begin{array}{ccc}0&4&1\\5&-3&0\\2&3&1\end{array}\right][/tex]
we need to compute the determinant using the row reduction that means using the row values [0 4 1 ] to find the determinant .
using the row [0 4 1] , the signs on the values on the first row will be +0, -4 and +1
the by applying the cofactor expansion , determinant will be equal to
= 0 -4[5×1 - 0] + 1[5×3 + 3×2]
= -4(5) + (15 + 6)
= -20 + 21
= 1
Therefore , the determinant is 1 .
The given question is incomplete , the complete question is
Combine the methods of row reduction and cofactor expansion to compute the determinant of the matrix [tex]\left[\begin{array}{ccc}0&4&1\\5&-3&0\\2&3&1\end{array}\right][/tex] .
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two cards are drawn without replacement from an ordinary deck. find the probability that the second is a club, given that the first is not a club
The probability that the second is a club, given that the first is not a club is 0.1911
According to the question,
We have a ordinary deck
An ordinary deck contain 52 cards
Number of club an ordinary have = 13
Let the first event of not getting a club at first draw be "A"
and "B" for getting a club at second draw
P( not getting a club) = P(A) = 1 - P(getting a club)
=> 1 - 13/52
=> 39/52
Now , We are drawing card without replacement
Number of cards we have after first draw = 51
P(getting a club) = P(B) = 13 / 51
The probability that the second is a club, given that the first is not a club
P(A).P(A)=> 39/52 . 13/51
=> 507/2652
=> 0.1911
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All of the Pythagorean Identities are related. Describe how to manipulate the equations to get from sin^2t +cos^2t = 1 to the other forms.
[tex]1 + cot^{2}2t = csc^{2}2t[/tex] can be manipulated from [tex]sin^{2}2t +cos^{2}2t =1[/tex]
What is Pythagorean Identity?
An identity, in mathematics, is an equation that is true for all possible values.(It is always true regardless of the values that are substituted into the equation.)
A trigonometric identity is an equation that involves trigonometric functions and is true for every single value substituted for the variable (assuming both sides are "defined" for that value) You will find that trigonometric identities are especially useful for simplifying trigonometric expressions.
The most common trigonometric identities are those involving the Pythagorean Theorem.
When studying the unit circle (radius of 1), it was observed that a point on the unit circle (a vertex of the right triangle) can be represented by the coordinates (cos 2t, sin 2t ).
Since the legs of the right triangle in the unit circle have the values of sin 2t and cos 2t, the Pythagorean Theorem can be used to obtain [tex]sin^{2}2t +cos^{2}2t =1[/tex]
Given Equation : [tex]sin^{2}2t +cos^{2}2t =1[/tex]
To proof : [tex]1 + cot^{2}2t = csc^{2}2t[/tex]
[tex]1 + cot^{2} \alpha = csc^{2} \alpha [let \alpha =2t] \\\\1 + cot^{2} \alpha = 1 + \frac{cos^{2}\alpha }{sin^{2} \alpha } \\\\1 + cot^{2} \alpha = \frac{sin^{2}\alpha }{sin^{2} \alpha } + \frac{cos^{2}\alpha }{sin^{2} \alpha }\\\\1 + cot^{2} \alpha = \frac{sin^{2}\alpha + cos^{2} \alpha }{sin^{2} \alpha }\\ \\1 + cot^{2} \alpha = \frac{1 }{sin^{2} \alpha } [ since ,sin^{2}\alpha + cos^{2}\alpha = 1]\\\\1 + cot^{2}\alpha = sec^{2} \alpha\\\\or\\1 + cot^{2}2t = sec^{2} 2t[/tex]
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A panda bear at the zoo weighs 162 pounds. A polar bear weighs 6 times as much as the panda bear weighs.
fidn teh are of the shaded region of the circle of radius a if the chord i h units from the center of the circle
Answer:
1027
Step-by-step explanation:
Assume that you want to test the claim that the paired sample data come from population for which the mean difference is Kd = 0. Compute the value of the test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed. Subject Before 168 180 157 132 202 124 190 210 171 After 162 178 145 125 171 126 180 195 163 0 A 0.351 .052 3.156 9.468
The test statistic value for the given sample data with population mean difference is equal to optic C. 3.156.
As given in the question,
Given population mean difference μd = 0
sample size 'n' = 9
Sample data is:
x y [tex]d_{i}[/tex] ( x - y) [tex]( d_{i} - \bar{d} )^{2}[/tex]
168 162 6 15.21
180 178 2 62.41
157 145 12 4.41
132 125 7 8.41
202 171 31 445.21
124 126 -2 141.61
190 180 10 0.01
210 195 15 26.01
171 163 8 3.61
∑[tex]d_{i}[/tex] = 89 ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] = 706.89
[tex]\bar{d}[/tex] = ( 1/ n ) ∑[tex]d_{i}[/tex]
= (1/9) (89)
= 9.889
= 9.9
Standard deviation of the mean difference '[tex]S_{d}[/tex]'
= √[1 / (n - 1)]( ∑ [tex]( d_{i} - \bar{d} )^{2}[/tex] )
= √706.89/ 8
=√88.361
= 9.4
test statistic
t = ( [tex]\bar{d}[/tex] - μd)/ ( [tex]s_{d} /\sqrt{n}[/tex] )
= ( 9.9 - 0) / ( 9.4 / √9)
= 9.9/ 3.133
= 3.156
Therefore, the test statistic value for the given sample data is equal to option C. 3.156
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Consider a square and a regular octagon (an 8
8
-sided figure with sides of equal length). One side of the square is 8
8
feet longer than a side of the octagon, and the two figures have the same perimeter. What are the lengths of the sides of each figure? (Round to two decimal places if necessary.)
Answer:
Sides are 16 ft for the square and 8 ft for the octagon.--------------------------------------------------
Let the side of the square is x and side of the octagon is y.
Set equation for sides:
x = y + 8The perimeter of square is same as the perimeter of the octagon:
4x = 8ySimplify and then substitute:
4x = 8y ⇒ x = 2yy + 8 = 2yy = 8Find x:
x = 8 + 8 x = 16Question 10(Multiple Choice Worth 5 points)
(Proportional Relationships LC)
Does the graph represent a proportional relationship?
graph with a line from 0 comma 0 and going through 25 comma 8
No, it is not proportional because the line does not go through (0, 0).
No, it is not proportional because the graph is curved.
Yes, it is proportional because it is a line that goes through (0, 0).
Yes, it is proportional because the x-axis and y-axis are numbered correctly.
Since the graph has a line from 0 comma 0 and going through 25 comma 8, C. Yes, it is proportional because it is a line that goes through (0, 0).
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
Generally speaking, the graph of any proportional relationship is always characterized by a straight line with the data points starting from the origin (0, 0) and passes through other unique data points on the cartesian coordinate.
By critically observing graph of this proportional relationship (see attachment), we can logically deduce that it starts from the origin (0, 0) and as such, it is proportional.
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Simplify: (-6 + 10) + [ 14+ ( -7 ) ]+ (-10)
Answer:
1
Step-by-step explanation:
Bc I have calculator
You wish to conduct your own study to estimate the miles per gallon on a 2007 Ford Taurus. How large a sample would you need to estimate the mean per gallon within 0.5 miles per gallon with 95% confidence if you read in a previous study that the standard deviation of miles per gallon for a 2007 Taurus is 3.21.
The sample required to estimate the mean per gallon within 0.5 miles per gallon with 95% confidence is 158.
Given:
You wish to conduct your own study to estimate the miles per gallon on a 2007 Ford Taurus.
How large a sample would you need to estimate the mean per gallon within 0.5 miles per gallon with 95% confidence = ?
if you read in a previous study that the standard deviation of miles per gallon for a 2007 Taurus is 3.21.
we know that :
z value of 95% is 1.96
Margin of error = E = z × sd/√n
we have:
n = (z×sd/E)²
= 158.33
= 158
Hence we get the sample as 158
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denote the volume of the cylinder as vcyl. if the cylinder has a total length l, write an equation for the volume of the cylinder in terms of r, l and any other constants
The volume of cylinder is denoted as πr²h
The density of a cylinder is determined by its volume, which indicates how much material it can hold or how much can be submerged inside it. The volume of a cylinder can be calculated using the formula r2h, where r denotes the radius of the circular base and h denotes the height of the cylinder. Any substance that can be evenly put into the cylinder, including liquid, may be used as the material. Shape volumes can be seen here.
This article contains a basic explanation of cylinder volume as well as examples with solutions for your convenience. The study of shapes and their characteristics is a key component of geometry in mathematics. Any three-dimensional shape must have both volume and surface area.
Hence, the volume of cylinder is denoted as πr²h
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A rectangular paperboard measuring 20 in long and 12 in wide has a semicircle cut out of it, as shown below. Find the area of the paperboard that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer
The area of the remaining paperboard is 246.91 in²
How to we calculate cut out area?A shape can be cut-out of another shape. For example a circle cut off a rectangle. The area of the remaining part of the shape can be calculated as area of original shape - area of cut-out shape
The area of a rectangle = l×w
= 20×21 = 420in²
a semi circle is the shape cut-out, therefore the area of the semi circle= ½πr²
= ½×3.14× 10.5²= 173.09in²
Therefore the area of the remaining part of the paperboard is 420-173.09= 246.91 in²
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an escalator has a slope of 3/4 after traveling forward 128 feet, the escalator is 96 feet above the floor. Write this word problem in point slope form
The point slope form of the slope of escalator and distance is y-24 = 3/4(x-32).
The general point slope form is given by the equation -
y - y1 = m (x - x1)
Now we are given the slope as 3/4. So, keeping the values of y1 and x1 in the equation. Let us assume the points as (32, 24). As per the points, 32 is x1 and 24 is y1.
y - 24 = 3/4(x - 32)
y - 24 = 3x/4 - 3/4×32
Performing division on Right Hand Side of the equation
y - 24 = 3x/4 - 3×8
y - 24 = 3x/4 - 24
Rewriting the equation
y - 3x/4 = - 24 + 24
Solving the equation on Right Hand Side of the equation
y - 3x/4 = 0
y = 3x/4
Thus, the equation is y - 24 = 3/4(x - 32).
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How to multiple fractions with different denominators?
Please explain step by step to get picked brainliest!!
To multiply fractions with multiple denominators, you have to change the fraction to get the same denominator.
For example, if you have 1/3 * 1/2, you will have to find the least common multiple of 3 and 2, which is 6. Then, multiply the numerator by the same number that you multiplied the denominator to get 6.
1/3 * 1/2
LCM = 6
[tex]\frac{1*2}{3*2} *\frac{1*3}{2*3} =\frac{2}{6} *\frac{3}{6}[/tex]
Then, multiply across the numerator
[tex]\frac{2}{3}*\frac{3}{6} =\frac{6}{6}=1[/tex]
I need help with this please help me
According to the figure, the side congruent to line GK is line HL
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSS
Side - Angle - Side = SAS
Angle - Side - Angle = ASA
Angle - Angle - Side = AAS
Hypotenuse and one leg = HL
The problem requires the prove by Angle - Side - Angle = ASA to ensure that the the triangles are congruent
The Angle and sides used for the proof include
< F = < J
FL = JK
< L = < K
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Answer:
A. HL
Step-by-step explanation:
You want to identify the side corresponding to GK in the figure showing congruent triangles.
ASA CongruenceThe larger triangles on the left and right each have an angle marked with one arc, an angle marked with two arcs, and the segment between those angles marked with one hash mark. This identical marking of two angles and the side between them means you can declare the triangles congruent by the ASA (angle-side-angle) congruence postulate.
When we name the triangles in order of the number of marks on the angles (0–2 arcs), we find the congruence statement to be ...
∆HLF ≅ ∆GKJ
Corresponding sidesThe segment of interest is GK, which is identified by the first two letters of its triangle designator in the congruence statement. The corresponding side is identified by the first two letters in the other triangle designator: HL.
∆HLF ≅ ∆GKJ
Side HL is congruent to GK.
__
Additional comment
Like a lot of math, this requires you to match patterns.
For any confidence level C, the value of the sample proportion will always be considered a plausible value for p. (a) True (b) False
For any confidence level C, the value of the sample proportion will always be considered a plausible value for p is a true statement.
For any given confidence level, the sample proportion of a given sample will always be within the range of values that are considered plausible for the population proportion. This range is determined by the confidence interval, which is calculated based on the confidence level C. Thus, the sample proportion will always be considered a plausible value for p.
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Answer please! Will give 5 star. Need explanation
The greatest common factor of the given term is 26.
What is the greatest common factor?
The greatest factor that splits both numbers is said to be the greatest common factor. List the prime factors of each integer before calculating the greatest common factor.
The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF. There are three main methods for calculating GCF: division, multiplication, and prime factorization. You can obtain the necessary reduced form by determining the GCF of the denominator and numerator of a fraction or ratio.
Given, [tex]\frac{52}{78} = \frac{26*2}{26*3}[/tex]
So, the simplest form is [tex]\frac{2}{3}[/tex].
Hence, the greatest common factor is 26.
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Find the 10% trimmed mean of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data.
MLB Batting Averages 0.278 0.285 0.299 0.304 0.306 0.306 0.306 0.308 0.309 0.310 0.313 0.313 0.315 0.317 0.317 0.318 0.322 0.322 0.324 0.326
10% trimmed mean of the given data is xbar20 = 0.3269
In between the mean and the median, the trimmed means have some of the advantages of both without some of the disadvantages.
The 10% trimmed mean is the mean computed by excluding the 10% largest and 10% smallest values from the sample and taking the arithmetic mean of the remaining 80% of the sample (other trimmed means are possible: 5%, 20%, etc.
The 10% trimmed means omits 0.278 and 0.326 and yields
xbar10 = 0.278+ 0.285+0.299 + 0.304 + 0.306+ 0.306+ 0.306+ 0.308 +0.309 +0.310+ 0.313+ 0.313+ 0.315+ 0.317+ 0.317 +0.318+ 0.322+ 0.322+ 0.324+ 0.326 / 20
= 5.885 / 20
= 0.29
xbar = 1.29 and xbar = 1
Trimmed means are examples of robust statistics (resistant to gross error).
The 20% trimmed mean excludes the 2 smallest and 2 largest values in the sample above, and
xbar20 = 0.278+ 0.285+0.299 + 0.304 + 0.306+ 0.306+ 0.306+ 0.308 +0.309 +0.310+ 0.313+ 0.313+ 0.315+ 0.317+ 0.317 +0.318+ 0.322+ 0.322+ 0.324+ 0.326 / 18
xbar20 = 0.3269
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a store is selling laptops with six different operating systems. a company would like to buy 35 of those laptops for their employees. in how many ways can this company buy them?. show all your work step by step to get credit. final answers must be provided in decimal form
On solving the provided question, based on the information, we can say that there are 35 X 6 = 210 ways
What are combinations?Combining means selecting all or part of a set of objects, regardless of the order in which the objects are selected. Suppose we have a set of three characters.
[tex]^nC_{r} = \frac{n!}{r!(n - r)!}[/tex]
ways can this company buy them are - 35 X 6 = 210 ways
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A local theatre sells out for their show. They sell all 500 tickets for a total purse of $7,890.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children's tickets, how many of each type were sold?
Answer:the answer is 8070
Step-by-step explanation:
because it is
4 time the sum of 8 and 1 is divided by six. Make expression and simplity.
Answer:
[tex]\frac{4(8-1)}{6}[/tex]
6
Step-by-step explanation:
[tex]\frac{4(8 + 1) }{6}[/tex]
[tex]\frac{4(9)}{6}[/tex]
[tex]\frac{36}{6}[/tex]
6
Answer:
The expression is:
4(8+1)/6
Simplify:
= 6
Step-by-step explanation:
The expression is:
4(8+1)/6
Simplify:
= 4(9) / 6
= 36/6
= 6
a parameter of the exponential smoothing model that provides the weight given to the most recent time series value in the calculation of the forecast value is known as the group of answer choices
The smoothing constant is the correct option.
What is exponential smoothing?
The exponential window function is a general method for smoothing time series data known as exponential smoothing. Exponential functions are used to assign weights that decrease exponentially over time, as opposed to the simple moving average, which weights previous observations equally.
Forecasts using exponential smoothing are precise.
This method generates reliable and accurate forecasts that anticipate the following period.
Demand projections and actual demand are shown in the forecast. This makes it possible to effectively plan for demand, which leads to accurate inventory levels.
In exponential smoothing, the higher the smoothing constant, the greater is the weight assigned to the values from the most recent period.
Hence, the smoothing constant is the correct option.
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Shirley bought 20.8 pounds of bird seed at a bargain store. She wants to fill her feeder 100 times with an equal amount. How much seed should she put in the feeder each time?
Part A
Which expression represents the problem?
20.8 ÷ 100
20.8 + 100
20.8 × 100
100 ÷ 20.8
Part B
When solving Part A, how is the decimal point moved?
3 places to the right
3 places to the left
2 places to the right
2 places to the left
Part C
How much seed should she put in the feeder each time?
pound(s)
Answer: Part A 20.8 divided Part B 2 places to the left Part C 0.208
Step-by-step explanation:
Part A the question ask each time and when it ask each time it means dividing Part B when dividing you move to the left and their are two 0s and moving the decimal two places to the left would get you 0.208 so, therefor the answer is 0.208
Describe the location of the point that has the following coordinates: negative abscissa, zero ordinatea. between Quadrant III and Quadrant IVb. between Quadrant II and Quadrant IVc. between Quadrant I and Quadrant IVd. between Quadrant II and Quadrant III
The correct location of the point is (d) between Quadrant II and Quadrant III.
We must choose the response that accurately describes the position of the point whose coordinates have a negative abscissa and a zero ordinate.
Any point with a negative abscissa and a zero ordinate on the XY plane in two dimensions can be represented as
Where a > 0, (x, y) = (-a, 0).
Let's plot (-1, 0), (-2, 0), (-3, 0), etc. on the coordinate plane as an example. The corresponding figure illustrates this.
The figure shows that every point of the type (-a, 0) is located on the X-axis' negative side.
The location of the negative X-axis between Quadrants II and III is known. As a result, the supplied point is situated between Quadrants II and III.
the appropriate answer is (d).
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Please help with math ?
Answer:
Step-by-step explanation:
you have to use the vertex
