The distance is 3.21 +/- 0.04 mm using the first three measurements, and 3.16 +/- 0.08 mm using the entire set of ten measurements.
What is deviation ?
Deviation is a measure of how much a set of values differs from a certain value, typically the mean (average) of the set. There are two types of deviation ,
The absolute deviation is the difference between each value and the mean.
The standard deviation is the square root of the average of the squared absolute deviations.
The mean distance = (3.27 + 3.23 + 3.15) / 3 = 3.21 mm
The standard deviation = sqrt(((3.27 - 3.21)^2 + (3.23 - 3.21)^2 + (3.15 - 3.21)^2) / 2) = 0.04 mm
So, using the first three measurements, we can report the distance as 3.21 +/- 0.04 mm
To report the distance and uncertainty using the entire set of ten measurements, we can calculate the mean and standard deviation of the ten measurements.
The mean distance = (3.27 + 3.23 + 3.15 + 3.16 + 3.28 + 3.14 + 3.16 + 3.12 + 3.32 + 1.46) / 10 = 3.16 mm
The standard deviation = sqrt(((3.27 - 3.16)^2 + (3.23 - 3.16)^2 + (3.15 - 3.16)^2 + (3.16 - 3.16)^2 + (3.28 - 3.16)^2 + (3.14 - 3.16)^2 + (3.16 - 3.16)^2 + (3.12 - 3.16)^2 + (3.32 - 3.16)^2 + (1.46 - 3.16)^2) / 9) = 0.08 mm.
The distance is 3.21 +/- 0.04 mm using the first three measurements, and 3.16 +/- 0.08 mm using the entire set of ten measurements.
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Nicole measured a line to be 10.9 inches long. If the actual length of the line is 10.2 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer: 6.9%
Step-by-step explanation:
Substituting into the percent error formula,
[tex]\frac{|10.9-10.2|}{10.2} \times 100 \approx 6.9\%[/tex]
seniors at a certain high school took a survey regarding future plans. all plan to attend college some time; however, 77% plan to go to college immediately following high school. of those who plan to attend college immediately following high school, 17% plan to major in math. of those who do not plan to attend college immediately following high school, 11% plan to major in math. what is the probability that a randomly chosen senior does not plan to attend college immediately following high school and plans to major in math.
The probability that a randomly chosen senior does not plan to attend college right away and majors in math is 12.5%.
Step 1: Calculate the probability of not attending college immediately after high school:
100% - 77%
= 23%
Step 2: Calculate the probability of majoring in math among those who do not attend college right away: 11%
Step 3: Calculate the probability of not attending college right away and majoring in math:
11% / 23%
= 0.125
The probability of a randomly chosen senior not attending college immediately following high school and majoring in math can be calculated by first determining the probability of not attending college right away. This can be done by subtracting the percentage of seniors who plan to attend college immediately from 100%. This yields 23%. Then, the probability of majoring in math among those who do not attend college right away can be determined by taking the percentage of those who plan to major in math among this group, which is 11%. Lastly, the overall probability of not attending college right away and majoring in math can be calculated by taking the probability of majoring in math among those who do not attend college right away and dividing it by the probability of not attending college right away. This yields 11% / 23%, or 0.125.
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A town has three roads that form an obtuse triangle. James wants to set up a refreshment stand so that the shortest distance from his stand to each road is the same for all three roads. Where should he set up the refreshment stand?
A. on the centroid
B. on the circimcenter
C. on the incenter
D. on the median
James should set up the refreshment stand on the incentre of the obtuse triangle.
The incentre of a triangle is defined as the intersection between the angle bisectors of a triangle. The inradius is the line segments from the incenter of the triangle to each of the three sides of the triangle which are all equal.
The inradius is defined as the radius of an inscribed circle in the triangle. Therefore, the required shortest equal distance from his stand to each road so that the stand is at the same distance for all three roads is on the incentre.
Hence, the correct option is C.
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Five friends are standing in a line. Cliff is standing directly behind Danny, and there are two people between Cliff and Mark. Mark is standing somewhere behind Eric, but somewhere in front of Tom. Which of the five friends is fourth in line
Among the five friends Eric, Mark, Tom, Danny, and Cliff the fourth in line is Danny.
Given the information, we can make the following deductions:
Cliff is standing directly behind Danny.There are two people Cliff and Mark.Mark is standing somewhere behind Eric, but somewhere in front of Tom.From these deductions, we can conclude that Mark is fourth in line.Eric is the first one in line.
Cliff is standing directly behind Danny, so he is the fifth one in line.
Mark is somewhere behind Eric and Tom, but there are two people between Cliff and Mark, so it's Tom is the third one in line.
As we know that Mark is somewhere behind Eric and somewhere in front of Tom, Mark is the second one in line.
The five friends standing sequence will be - Eric, Mark, Tom, Danny, and Cliff.
Hence, the Fourth one in line is Danny.
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which expression can you use to find the number of ways to choose 5 cards from a 52-card deck? how many ways can you choose the 5 cards?
The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52!/(47! * 5!).
The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52 choose 5, which is equal to 52!/(47! * 5!), where the exclamation point indicates the factorial function. This is known as the binomial coefficient, and it represents the number of ways to choose a certain number of items from a larger set. In this case, the binomial coefficient is used to find the number of ways to choose 5 cards from a deck of 52 cards.
The order of the cards is irrelevant in card games like poker. A five-card draw of 1,2,7,9, K is equivalent to a draw of K,7,9,1,2. What counts is the fundamental overall group.
Order is irrelevant, therefore we utilize a combination (instead of a permutation)
We will substitute n = 52 and r = 5 into the nCr combination formula, which is n C r = (n!)/(r!*(n-r)!)
so we obtain:
n C r = r!*(n-r)!/(n!)
52 C 5 = (52!)/(5!*(52-5)!)
52 C 5 = (52!)/((52-5)!*5!)
The complete question is:-
Which expression can you use to find the number of ways to choose 5 cards from a 52-card deck?
a) (52-5)! / 52!5!
b) 52! / (52-5)!
c) 52! / (52-5)!5!
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toddler triplets whose names are red, green and blue each have a coat whose colour is given by their name, but they aren't clear on which coat belongs to which of them. when they go out, red chooses a coat at random among the three coats, green chooses a coat at random among the remaining two coats and blue is left to take the remaining coat. how many ways are there for exactly one of the toddler triplets to end up with their coat? help
The number of ways in which exactly one of the toddler triplets to end up with their coat is given as follows:
3.
What is a sample space?A sample space is a set that contains all possible outcomes in the context of an experiment.
The cardinality of the sample space in this problem, considering the Fundamental Counting Theorem, is obtained as follows:
N = 3 x 2 x 1
N = 6.
(the first chosen has 3 possible options, the second has two and the third has one).
The six possible outcomes are given as follows, considering the order Red - Green - Blue:
Red - Green - Blue. (all end with theirs).Red - Blue - Green (one, the red, end with theirs).Green - Red - Blue (one, the blue, end with theirs).Blue - Red - Green (none end with theirs).Green - Blue - Red. (none end with theirs).Blue - Green - Red. (one, the green, end with theirs).Hence there are three outcomes for exactly one of the toddler triplets to end up with their coat.
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beth and her friends are watching an ice hockey game, so beth decides to buy 4 cups of hot chocolate to share. she figures she'll spend at least $14 on the hot chocolate in all. let x represent how much beth expects each cup of hot chocolate to cost. which inequality describes the problem?
The inequality that describes the problem is: x*4 >= $14.
This inequality can be read as: "the cost of 4 cups of hot chocolate (x) multiplied by 4 is greater than or equal to $14."
We know that Beth expects to spend at least $14 on the hot chocolate in total, and she's buying 4 cups, so we can set up the inequality with the number of cups and the minimum amount she wants to spend.
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
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Digital genius manufactures a cell phone charging pad that can fully charge any cell phone that is placed on it in 15 minutes. the analytics department determined that at a price of $103.00 each, the demand would be 6 thousand pads, and at $53.00 each, the demand would be 16 thousand pads. based on the assumption that a linear relationship exists between price and demand, the price-demand equation is given by where x is the number of thousands of pads in demand. at what price point should they sell the pads to have a demand of 14 thousand pads?
At $63 price point should they sell the pads to have a demand of 14 thousand pads.
p(x) = -5x + 133
Substitute x with 14,
p(14) = -5(14) + 133
= -70 + 133
= 63.
The chance of an event happening given that another event has already occurred (via assumption, supposition, statement, or evidence) is known as conditional probability in the field of probability theory. [1] This particular approach depends on event B happening in some way connected to another event A. In this case, a conditional probability analysis with respect to event B is possible.
The probability of A under the condition B is typically expressed as P(A|B)[2] or PB if the event of interest is A and the event B is known to have occurred or is assumed to have done so (A). This can alternatively be thought of as the percentage of possibility that B and A will collide.
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what is the answer to 2/3 + 1/3 + 5/3?
Answer:
8/3
Step-by-step explanation:
Find an equation of the tangent to the curve at the given point by both eliminating the parameter and without eliminating the parameter. x = tan(θ), y = sec(θ), (1,√2)
The equation of the tangent to the curve x=tan(θ) and y=sec(θ) at the point (1,√2) can be found by both eliminating the parameter and without eliminating the parameter.
Find an equation of the tangent to the curve?Eliminating the parameter: y = x + √2Without eliminating the parameter: dy/dθ = sec(θ) + tan(θ) × csc(θ); y = sec(θ) + tan(θ) × (x - tan(θ)).Without eliminating the parameter:The equation of the tangent line at (1,√2) is given by y = (sec(θ)cos(θ))x - (sec^2(θ)) + √2, where θ is the parameter.This is derived from the slope of the tangent line, which is equal to the derivative of the function at the given point, or sec(θ)cos(θ).By eliminating the parameter:The equation of the tangent line at (1,√2) is y = x + (1/√2). This equation is derived from the slope of the tangent line, which is equal to the derivative of the function at the given point.Since the derivative of x = tan(θ) and y = sec(θ) is sec(θ)cos(θ), by setting θ = π/4, we get sec(π/4)cos(π/4) = 1/√2. Therefore, the equation of the tangent line is y = x + (1/√2).To learn more about tangent line approximation refer to:
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Fill the tables of values for the equation y=2-x
A system of equations is shown below. y = 3x + 4 y = 7x – 2 What is the solution to the system?
The solution to the system of equations is x = 3/2 and y = 11/2.
What is the linear equation?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b
We are given two equations:
y = 3x + 4
y = 7x – 2
We can set the two equations equal to each other and solve for x:
3x + 4 = 7x - 2
Subtracting 3x from both sides:
4 = 4x - 2
Adding 2 to both sides:
6 = 4x
Dividing both sides by 4:
x = 3/2
Now we can substitute this value of x back into either of the original equations to find the corresponding value of y. Using the first equation:
y = 3(3/2) + 4 = 9/2 + 4 = 11/2
Therefore, the solution to the system of equations is x = 3/2 and y = 11/2.
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2) Three trucks can carry 240 bags of cement. How many bags of cement can seven trucks carry?
Answer: 560
Step-by-step explanation:
240 / 3 = 80 x 7 = 560
Using your equation from Question 2*, predict the average pulse rate in beats per minute of an animal that weighs 640 kilograms. You can also estimate the weight of the animal using the graph and the line of best fit (extend the line and x-axis farther).
The estimate of the average pulse rate in beats per minute of an animal that weighs 640 kilograms is given as follows:
29.6 beats per minute.
How to obtain the equation for the regression line?The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.
(this is because there are multiple types of regression, such as logistic, exponential and quadratic regression).
The points for this problem are given as follows:
(3, 130), (28,75), (56, 75), (192, 95), (362,48), (465, 66), (521, 34).
Inserting these points into a calculator, the regression equation is given as follows:
y = -0.11x + 100.
Hence, for a weight of x = 640 kg, the estimate of the average heart rate is given as follows:
y = -0.11(640) + 100
y = 29.6 beats per minute.
Missing InformationThe table is given by the image presented at the end of the answer.
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1. the very first step in verifying a statement about a product is represented by the c in claim. what does the letter c stand for?
Note that the very first step in verifying a statement about a product is represented by the acronym C.L.A.I.M. The first letter "C" stands for Claim.
What do the other letters stand for?L - Logic: Examining the logic of the claim to see if it is reasonable and if the evidence offered supports the assertion.
A - Attribution: Identifying the source of the assertion and assessing its reliability.
I - Investigation: Research and evidence collecting to support or reject the allegation.
M - Measurement: Evaluating the quality and quantity of evidence obtained and assessing whether or not it supports the claim being made.
Following the CLAIM technique allows one to assess the correctness and validity of a claim and make an educated judgment about the product or service in issue.
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Use quadratic regression to find a
function that fits the following points.
(-1, 21) (3, 45) (4, 81)
The function that fits the points (-1, 21) (3, 45) (4, 81) is 6x²-6x+9.
Quadratic Regression is a method according to which we can make an equation of a quadratic curve from given no. of x and y data points
Quadratic Regression Equation(y) = a + b x + c x^2
The formula for its coefficients is,
c = { [ Σ x2 y * Σ xx ] - [Σ xy * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }
b = { [ Σ xy * Σ x2x2 ] - [Σ x2y * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }
a = [ Σ y / n ] - { b * [ Σ x / n ] } - { a * [ Σ x 2 / n ] }
Where,
Σ x x = [ Σ x 2 ] - [ ( Σ x )2 / n ]
Σ x y = [ Σ x y ] - [ ( Σ x * Σ y ) / n ]
Σ x x2 = [ Σ x 3 ] - [ ( Σ x 2 * Σ x ) / n ]
Σ x2 y = [ Σ x 2 y] - [ ( Σ x 2 * Σ y ) / n ]
Σ x2 x2 = [ Σ x 4 ] - [ ( Σ x 2 )2 / n ]
x and y are the Variables.
a, b, and c is the Coefficients of the Quadratic Equation
n = Number of Values or Elements
Σ x= Sum of First Scores
Σ y = Sum of Second Scores
Σ x2 = Sum of the square of the First Scores
Σ x 3 = Sum of Cube of First Scores
Σ x 4 = Sum of Power Four of First Scores
Σ xy= Sum of the Product of First and Second Scores
Σ x2y = Sum of Square of First Scores and Second Scores
when we input the points (-1,21),(3,45),(4,81)
we get the equation 6x²-6x+9
which looks like this (The image has been attached),
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This table shows some of the values of x and y that satisfy the equation y=acos0+b, find the value of y when x = 45
Answer: [tex]4\sqrt{2}+1[/tex]
Step-by-step explanation:
[tex]x=0 \implies y=a+b \implies a+b=9\\\\x=30 \implies \frac{\sqrt{3}}{2}a+b=1+4\sqrt{3}\\\\\implies \frac{\sqrt{3}}{2}a-a=4\sqrt{3}-8\\\\a=\frac{4\sqrt{3}-8}{\frac{\sqrt{3}}{2}-1}=\frac{8\sqrt{3}-16}{\sqrt{3}-2}=8\\\\\implies b=9-8=1\\\\\therefore y=8\cos x^{\circ}+1\\\\x=45 \implies y=8\left(\frac{\sqrt{2}}{2} \right)+1=4\sqrt{2}+1[/tex]
A plane is heading in a direction of 045° and changes course in a clockwise direction to 135°. The angle through which the plane turns is A) 45° B) 90° C) 135° D) 180°
The angle through which the plane turns is B; 90 degrees clockwise
How to determine the angle of turn?When determining the angle of turn, it is important to consider the direction of rotation (in this case, clockwise) and the starting and ending points (in this case, South East to North).
We are given that plane is heading in a direction of 045° and changes course in a clockwise direction to 135°.
To Subtract the angles to get the answer
135 - 45 = 90
In terms of compass, 45 degrees is directly pointed at northeast while 135 degrees is pointed directly at southeast. We have zero degrees pointed straight north.
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(WILL GIVE BRAINLIEST!!) Which of the following lengths are Pythagorean Triples? Justify your answers.
10, 24, 26 are the Pythagorean triples. Therefore, option (i), (iii) and (iv) are the correct answers.
What are Pythagorean triples?Pythagorean triples are a²+b² =c² where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.
i) 10, 24, 26
Here, 26²=10²+24²
676=100+576
676=676
So, the given set of numbers are Pythagorean triples
ii) 2, 3, 5
Here, 5²=2²+3²
25≠13
So, the given set of numbers are not Pythagorean triples
iii) 3a, 4a, 5a; where a is any whole number
Here, (5a)²=(3a)²+(4a)²
25a²=9a²+16a²
25a²=25a²
So, the given set of numbers are Pythagorean triples
iv) 7, 24, 25
Here, 25²=24²+7²
625=576+49
625=625
So, the given set of numbers are Pythagorean triples
v) 12, 13, 15
Here, 15²=12²+13²
225=144+169
225≠313
So, the given set of numbers are not Pythagorean triples
Therefore, option (i), (iii) and (iv) are the correct answers.
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If you work 45 minutes a day for 90 days in row and add an additional 20 hours how many hours do you have?
Write an equation for the line that passes through (8, 2) and is parallel to the graph of y = 3/4x + 2.
Answer: do it youself
Step-by-step explanation:
x race to power 4 minus 8x race to power 2 plus 1 equal to zero (Pls can anybody solve this)
Answer:
×⁴-8ײ+1
Explanation:
kaya yan ung sagot ksi hnd mo na sya mai-sosolve kasi mag kaiba ung upper right side nya kaya i coppy molng un^_^..hope its help...
Will give 5 star if correct: eden purchased a home for $156,200. the home appreciates about 4.5% each year. what is the value of the home after 17 years? (5 points)
$275,693.00
$71,406.60
$330,109.46
$166,462.16
The value of the home after 17 years $275,693.00.
The correct option is (A).
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Eden purchased a home for $156,200.
The appreciates percent = 4.5%
So, the appreciates percentage in 17 year
= 4.5 x 17
= 76.5%
Now, the amount increased of home
= 156200 x 76.5%
= $119,493
So, the value of home after 17 year
= 119493 + 156200
= $ 275, 693
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Rebecca is playing a video game that involves planting and cutting down trees. She moves up an energy level for each tree she plants, and she moves down a level for each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.
Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: 1 tree cut
Answer the questions to find out whether Rebecca earned bonus points in the next 3 turns. Use the number line to help you add.
A number line from -5 to 10.
1. Using only addition, write an expression that represents Rebecca's score after these three turns. (Remember that she starts at an energy level of 4.). (2 points)
2. What is Rebecca's energy level after Turn 1? (2 points)
3. What is Rebecca's energy level after Turn 2? (3 points)
4. What is Rebecca's energy level after Turn 3? Will she earn bonus points after Turn 3? Explain why or why not. (3 points)
In the video game Rebecca is playing using only addition the expression that represents Rebecca's score after these three turns is
= 4 + (-6) + (8) + (-1)
Rebecca's energy level after Turn 1 = -2
Rebecca's energy level after Turn 2 = 6
Rebecca's energy level after Turn 3 = 7
she will not earn bonusHow to find the expression that represents Rebecca's scoreFollowing the rule of the video game the expression is written in steps below
Rebecca is currently at energy level 4
= 4
Turn 1: 6 trees cut
= 4 + (-6)
= 4 - 6
= -2
Turn 2: 8 trees planted
= 4 + (-6) + (8)
= -2 + 8
= 6
Turn 3: 1 tree cut
= 4 + (-6) + (8) + (-1)
= 6 - 1
= 7
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Please the inverse of this function!!
Answer:
[tex]\frac{5x-3}{4}[/tex]
Step-by-step explanation:
[tex]x=\frac{4y+3}{5} \\ 5x=4y+3\\ 5x-3=4y\\ \frac{5x-3}{4} =y[/tex]
PLEASE HELP !!!
Question : what do the MAD’s indicate about the vegetables weights?
The weights of the tomatoes vary _____ (less or more) than the weights of the cucumbers since the MAD for tomatoes is ____ (less or greater) than the MAD for cucumbers.
The weights of the tomatoes vary less than the weights of the cucumbers since the MAD for tomatoes is less than the MAD for cucumbers.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.
It is the average distance between each data point and the mean.
The weights of the tomatoes vary less than the weights of the cucumbers since the MAD for tomatoes is less than the MAD for cucumbers.
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Answer:
less & less
Explanation: Because thats how u do it
Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?
Answer: It is not possible to determine whether rectangle EFGH is the result of a dilation of rectangle ABCD with a center of dilation at the origin just by looking at the statement provided.
A dilation is a transformation that changes the size of a shape but not its shape or orientation. In a dilation, the center of dilation is a fixed point and all other points move away from or towards it by a scale factor.
The statement provided does not include any information about the scale factor, the coordinates or measurements of the rectangle's vertices or any other information that would allow to determine if EFGH is the result of a dilation of ABCD. The statement only indicates that the center of dilation is at the origin.
In order to determine if rectangle EFGH is the result of a dilation of rectangle ABCD with a center of dilation at the origin, we would need additional information such as the scale factor, the coordinates or measurements of the rectangle's vertices, and the direction of dilation (enlargement or reduction)
It's worth noting that a dilation with center of dilation at origin can be performed only if the shape is symmetric.
Step-by-step explanation:
Which of the following represents 18 = 3 × 6?
A.
18 is 3 times as many as 6
B.
18 is 2 times as many as 9
C.
3 is 6 times as many as 18
D.
6 is 3 times as many as 18
Answer:
A) 18 is 3 times as many as 6----------------------------
Translate each wording to mathematical expression and compare with the given 18 = 3 × 6.
A) 18 is 3 times as many as 6:
18 = 3 × 6, yes same as givenB) 18 is 2 times as many as 9:
18 = 2 × 9, different from the givenC) 3 is 6 times as many as 18:
3 = 6 × 18, wrongD) 6 is 3 times as many as 18:
6 = 3 × 18, wronghe length of a rectangle is 11/5 cm and its breadth is 13/5 cm. What, in sq. cm, is the area of the rectangle?
Answer:
Step-by-step explanation:
The area of a rectangle can be found by multiplying its length and breadth. In this case, the length is 11/5 cm and the breadth is 13/5 cm. Therefore, the area of the rectangle is (11/5 cm)*(13/5 cm) = 143/25 sq. cm = 5.72 sq. cm.
F(x) = 2x² +1
g(x) = 3x - 5
f-g
Answer: The answer is. 2x² - 3x + 6. Step-by-step explanation: f(x) = 2x² + 1. g(x) = 3x - 5. To find f - g(x) subtract g(x) from f(x).
I hope this helps! Have a Wonderful day! <3
