There are mainly 6 methods used to solve a linear equation depending on the complexity and form of the equation.
A linear equation is represented as the equation of first order or variable having power 1 and can be written in the general form of Ax+By+C= 0, where A, B, and C are real numbers. And its simplest form is y= mx+b, where m is the slope or ratio of change in y and change in x, and b is the y-intercept. The following are the methods used to solve the linear equation:
1. Graphical Method.
2. Elimination Method.
3. Substitution Method.
4. Cross Multiplication Method.
5. Matrix Method.
6. Determinants Method
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if r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to ?
a. 3 (6)-1/2(6) +1
b. (6)/ 2(6)+1
c. 36-1/26+1
d. (6)-1/(6)+1
If the expression [tex]r(x) = 3x - 1[/tex] and the expression [tex]s(x) = 2x + 1[/tex] , then the expression equivalent to [tex]\frac{r}{s} (6)[/tex] is (a) [tex]\frac{3(6)-1}{2(6) +1}[/tex] .
What are Algebraic Expression ?
The algebraic Expression are defined as the expressions that are written with the combination of variables and constants joined by mathematical operators , For Example : [tex]3x+7[/tex] .
Here the two expressions are given as [tex]r(x) = 3x - 1[/tex] and [tex]s(x) = 2x + 1[/tex] ;
we have to find equivalent expression for [tex]\frac{r}{s} (6)[/tex] ;
By the Division Property of Algebraic Expression ;
it can be written as : [tex]\frac{r(6)}{s(6)}[/tex] ;
So , Substituting [tex]x=6[/tex] , in r(x) ,
we get ; [tex]r(6) = 3(6) - 1[/tex] , ......equation(1)
On Substituting [tex]x=6[/tex] , in s(x) ,
we get ; [tex]s(6) = 2(6)+1[/tex] , ....equation(2) ;
Substituting the values of r(6) and s(6) from equation(1) and equation(2) in [tex]\frac{r(6)}{s(6)}[/tex] ;
we get ;
⇒ [tex]\frac{r(6)}{s(6)} = \frac{3(6)-1}{2(6) +1}[/tex] ;
Therefore , the expression equivalent to [tex]\frac{r}{s} (6)[/tex] is [tex]\frac{3(6)-1}{2(6) +1}[/tex] .
The given question is incomplete , the complete question is
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to r/s(6) ?
(a) [tex]\frac{3(6)-1}{2(6) +1}[/tex]
(b) [tex]\frac{(6)}{2(6)+1}[/tex]
(c) [tex]\frac{36-1}{26+1}[/tex]
(d) [tex]\frac{(6)-1}{(6)+1}[/tex]
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in general (whether events are disjoint or not), what is the formula for finding p(ab)? 3.) explain the difference between the addition rule for disjoint events and the general addition rule. 4.) what is meant by joint probability? 5.) what is meant by conditional probability?
The Formula is p(A and B) = p(A) * p(B|A)
1) In general, the formula for finding the probability of the intersection of two events, A and B, is:
p(A and B) = p(A) * p(B|A)
This is also known as the conditional probability formula, where p(B|A) is the probability of event B occurring given that event A has already occurred.
2) The addition rule for disjoint events is:
p(A or B) = p(A) + p(B)
This rule applies when events A and B are disjoint, meaning they cannot occur at the same time. In other words, the two events have no common outcomes.
The general addition rule, on the other hand, is:
p(A or B) = p(A) + p(B) - p(A and B)
This rule applies when events A and B are not disjoint, meaning they can occur at the same time. In this case, we need to subtract the probability of the intersection of A and B, as we have double-counted the outcomes that are common to both events.
3) Joint probability refers to the probability of two or more events occurring together, also known as the probability of the intersection of the events. It is the probability of multiple events occurring at the same time.
4) Conditional probability refers to the probability of an event occurring, given that another event has already occurred. It is the probability of an event A happening, given that event B has already happened. The conditional probability of A given B is represented as P(A|B).
5) Conditional probability is the probability of an event occurring given that another event has already occurred. It is a way to express how likely an event is given that another event has already occurred. It is represented as P(A|B) where A and B are events, it is the probability of event A happening given that event B has already happened.
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A line passes through the point (5, -3) and has a slope of -3. Write an equation in .point-slope form for this line.
Work Shown:
y - y1 = m(x - x1)
y - (-3) = -3(x - 5)
y + 3 = -3(x - 5)
Explanation:
The variable m refers to the slope. The point (x1,y1) is on the line. We do not distribute the -3 through to the terms in (x-5), nor do we isolate y, since your teacher wants this in point-slope form.
a college student organization wants to start a nightclub for students under the age of 21. to assess support for this proposal, they will select an srs of students and ask each respondent if he or she would patronize this type of establishment. they expect that about 70% of the student body would respond favorably. what sample size is required to obtain a 90% confidence interval with an approximate margin of error of 0.04? show your work.
On solving the provided question we can say that at confidence Level = 90%, we have sample size = 423
what is sample size?The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number. The sample size influences two statistical characteristics: 1) The precision of our estimates; 2) The ability of research to produce inferences. The results of random tests are the samples. When sampling a random variable, a particular value is chosen from a range of potential values. A sample is this specific value. The random variable's probability distribution determines the possible values and their probabilities.
Confidence Level = 90%
E = 0.04
Corresponding to 90%
confidence level role=="1654454884514" Z = 1.645
formula
n= p(1 - p)(0Z/E)
n = 0.50(1 - 0.50)(1.645/0.04)
= 422.816 = 423
so, sample size = 423
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A television station claims that the amount of advertising per hour of broadcast time has an average of 17 minutes and a standard deviation equal to 2.3 minutes. You watch the station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 5 minutes. Calculate the z-score for this amount of advertising time.
The z-score for this amount of advertising time will be -5.217.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
A TV slot guarantees how much promotion each hour of transmission time has a normal of 17 minutes and a standard deviation equivalent to 2.3 minutes.
The amount of advertising time is equal to 5 minutes. Then the z-score is calculated as,
z = (5 - 17) / 2.3
z = -12/ 2.3
z = -5.217
The z-score for this amount of advertising time will be -5.217.
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the altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 9.5 centimeters and the area is 100 square centimeters?
So, the base of the triangle is decreasing at the rate of 1.6 cm/min.
Given that:
The altitude of is increasing at a rate of 1 centimeters/minute, which means;
dh/dt = 1 cm/min
The area of the triangle is increasing at a rate of 4 square centimeters/minute;
dA/dt = 4 cm2/min
When A = 100 cm2, h = 10 cm
We know that, area of a triangle is given by:
A = 1/2 × b × h
b = 20 cm
Let us differentiate both sides with respect to time:
dA/dt = 1/2 [b dh/dt + h db/dt]
Substituting the values
2 = 1/2 [20 × 1 + 10 × db/dt]
By further simplification, we get
4 = 20 + 10 db/dt
db/dt = -1.6 cm/min
Therefore, the base of the triangle is decreasing at the rate of 1.6 cm/min.
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A cereal box has dimensions of 12 inches, 7~
4
inches, and 2 inches. A pastry box
has dimensions of 3.
} inches, 3.
¿ inches, and 2¾ inches, Whatis the difference
in volume, in cubic inches, between the two boxes?
Answer:
To find the volume of the cereal box, we multiply the length, width, and height:
12 inches * 7 and 3/4 inches * 2 inches = 96 inches * 7.75 inches * 2 inches = 1458 cubic inches
To find the volume of the pastry box, we multiply the length, width, and height:
3 and 2/3 inches * 3 and 1/2 inches * 2 and 1/3 inches = 3.666 inches * 3.5 inches * 2.333 inches = 25.158 cubic inches
To find the difference in volume between the two boxes, we subtract the volume of the pastry box from the volume of the cereal box:
1458 cubic inches - 25.158 cubic inches = 1432.842 cubic inches
So the difference in volume between the two boxes is 1432.842 cubic inches.
Answer:1432.842 cubic inches
Step-by-step explanation:
13) Complete the proof. Given: A RST, RT > ST Prove: measure of angle RST > measure of angle R
Proof: Since RT > ST, there exists a point Q on RT, where QT is the same length as ST. By the Isosceles Triangle Theorem, angle 2 is congruent to angle 3, and by definition of congruent angles, the measure of angle 2 = the measure of angle 3.
Answer:
To prove that the measure of angle RST is greater than the measure of angle R, we can use the following steps:
By the definition of a triangle, angle RST is supplementary to angles R, S and T.
Since RT > ST, we can conclude that angle R is less than angle S.
Since angle RST is supplementary to angles R and S, the measure of angle RST is greater than the measure of angle R.
This can be written as measure of angle RST = measure of angle R + measure of angle S > measure of angle R
So, we've proven that if RT > ST in triangle RST, then measure of angle RST > measure of angle R.
Proof by contradiction could also be used to prove that if RT > ST in triangle RST, then measure of angle RST > measure of angle R.
Assume that the measure of angle RST <= measure of angle R. By the triangle inequality theorem, we know that RT + ST > R. But we are given that RT > ST, so RT + ST > RT > R which is a contradiction. Therefore, measure of angle RST must be greater than measure of angle R.
steve and elsie are camping in the desert, but have decided to part ways. steve heads north, at 7 am, and walks steadily at 3 miles per hour. elsie sleeps in, and starts walking west at 3.5 miles per hour starting at 10 am. when will the distance between them be 35 miles? (round your answer to the nearest minute.)
At 2.57 hours distance between them is 35 miles
(2t)2 + (2.5(t - 2))2 = 302
4t2 + (2.5t - 5)2 = 900
4t2 + 6.25t2 - 25t + 25 = 900
2.25t2 - 25t - 875 = 0
Let t (hours) be the amount of time Elsie needs to travel in order to reach a distance of 35 miles. Steve travels t + 2 miles to the north in the time it takes him since he is 2 hours early.
Solve for t, then add to 7:00 for your time.
which will give you 2.57 hours.
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The correct question will be
Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 7 AM, and walks steadily at 3 miles per hour. Elsie sleeps in and starts walking west at 2.5 miles per hour starting at 9 AM.
When will the distance between them be 35 miles?
Shawndra said that it is not possible to draw a trapezoid that is a rectangle, but it is possible to draw a square that is a rectangle. Marcella said that it is possible. Who is correct
Marcella is correct. A square is a type of rectangle.
A rectangle is a four-sided plane figure with four right angles. A trapezoid is a four-sided plane figure with one pair of parallel sides. Thus, it is not possible to draw a trapezoid that is also a rectangle. However, a square is a four-sided plane figure with four equal sides and all four right angles, making it a type of rectangle. Therefore, it is possible to draw a square that is a rectangle.
A rectangle is a four-sided plane figure with four right angles. A trapezoid is a four-sided plane figure with one pair of parallel sides.
Marcella is correct. A square is a type of rectangle.
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act math scores are approximately normally distributed, with a mean of 21 and a standard deviation of 5.4. if eli decides to take the act exam, what would he need to score in order to be in the 85th percentile?
In order to be in the 85th percentile Eli would need to score 26.62.
What is called percentile?In statistics, a score below which a certain percentage of scores (k) in a frequency distribution falls is known as a k-th percentile, whereas a score at or below which a given percentage falls is known as a k-th centile.
Given that act math scores are approximately normally distributed,
mean (μ) = 21 and a standard deviation (σ) = 5.4
percentile P(X>x) = 85 =0.85
P(z<x) = 0.85
z = 1.04
y the formula
z = (x - μ)/ σ
⇒ 1.04 = (x - 21)/5.4
⇒ 1.04*5.4 = x - 21
⇒ 5.616 = x - 21
⇒ x = 5.616 + 21
⇒ x = 26.62
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What is the difference between X1 and x1? O X1 is a random variable, and X1 is a specific numerical value. a. X1 is a random variable, and X1 is a specific numerical value. b. There is no difference. c. They are both random variables. d. There is no difference. e. They are both specific numerical values.
The main difference between X1 and x1 is that X1 is a random variable and x1 is a specific numerical value.
In mathematics, variables are often used to represent different values, and the difference between uppercase and lowercase letters is often used to distinguish between different types of variables. X1 is a random variable, which represents a value that can take on different values depending on the outcome of an experiment or a probability distribution. x1, on the other hand, is a specific numerical value, which represents a fixed value that is known or can be determined. In short, X1 refers to a variable whose value is uncertain and x1 refers to a specific value of that variable.
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what is the sum of the measures of the interior angles, in degrees, of a decagon (10-sided polygon) ?
The sum of the measures of the interior angles, in degrees, of a decagon (10-sided polygon) is 1440°
A polygon having ten sides (or a ten-sided polygon) is called a decagon or ten-gon, in geometry. Also, it has ten vertices and ten angles.
The summation of the interior angles of a polygon is ( n - 2 ) x 180 where n is the number of sides.
The sum of interior angles = (10 - 2) x 180
The sum of interior angles = 1440º
Therefore the measure of each angle is
10 angles = 1440
1 angle = 1440 ÷ 10 = 144º
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Find the area of shaded figure, use units squared
Answer:
43.5 square units
Step-by-step explanation:
You want to know the area of shading in a 12 by 7 rectangle with a white right triangle of side length 9 removed.
Triangle areaThe area of the white triangle is ...
A = 1/2bh
A = 1/2(9)(9) = 40.5 . . . . square units
Rectangle areaThe area of the rectangle is ...
A = LW
A = (12)(7) = 84 . . . . square units
Shaded areaThe shaded area is the area of the rectangle that is not included in the triangle.
Shaded area = 84 -40.5 = 43.5 . . . . square units
__
Additional comment
The given figure cannot actually be constructed. The triangle is too large to be inscribed in the rectangle. An inscribed right triangle can have a side length between 7 and √74 ≈ 8.6.
now using the right side of each slice as the height, sketch in 4 rectangles on your graph. find the area of these rectangles and add them up. this is your second approximation of the area under the curve, and hence ln(2). what is your answer (as a decimal with at least four digits of precision)? is this an over-estimate or an under-estimate
The area of the resulting two-dimensional cross-section of the pyramid geometry will be 5 square inches.
What is Geometry?
It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
What is an area in math definition
Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares
A slice is made parallel to the base of a right rectangular pyramid, as shown.
Then the area of the resulting two-dimensional cross-section will be
Area = 2 in × 2.5 in
Area = 5 in²
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Masha is three times as old as Pete. Their age difference is
10 years. How old is Pete?
Pete is
years old.
Answer:
Pete is 5
Step-by-step explanation:
Let Pete's age be x
Therefore Masha is 3x
since their age difference is 10,
3x - x = 10
2x = 10
x = 5
check:
3x = 15
x = 5
15 - 5 = 10
HELP Someone please help me ASAP
Answer: 67 degrees
Step-by-step explanation: If you add two angles together, this is actually equal to the second angle because it has to be if you pay attention to the complementary angles.
a carnival game offers a 100 cash prize for anyone whjo can break a balloon by throwing a dart at it. find the expected winnings
a carnival game offers a 100 cash prize for anyone whjo can break a balloon by throwing a dart at it. then The expected number of darts you'll throw is 3.44 darts .
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Expected = ∑ value * probability
= $1*0.01 + 2.(0.09) + 3(0.081) + 4(0.0729)
= 3.44
Thus, 3.44 darts .
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3/5 + 5/7 = ____
6/12 + 9/12 ____
1/4 + 4/4 = ____
2/3 + 5/3 = ____
(fractions please explain step by step how u got your answer)
The answers are 46/35 ,5/4, 5/4, 7/3
What is a fraction in math?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given here: 3/5 + 5/7 = 46/35
6/12 + 9/12=5/4
1/4 + 4/4 = 5/4
2/3 + 5/3 = 7/3
Hence, The answers are 46/35 ,5/4, 5/4, 7/3
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A bottle holds 850 cL of water. How many liters does the pitcher hold?
Answer:
8.5
Step-by-step explanation:
850/100
Answer:
[tex]8.5l[/tex]
Step-by-step explanation:
1cl = 10ml
850cl = 8500ml
1000ml= 1l
8500ml= 8.5l
given the function defined in the table below,find the average rate of change,in simplest form,of the function over the interval 12
Answer: The average rate of change over the interval 12 < x < 30 is -4/3
Step-by-step explanation:
The average rate of change over an interval is defined as the change in the output (f(x)) divided by the change in the input (x) over that interval. In this case, the interval is 12 < x < 30. To find the average rate of change, we need to evaluate the function at the endpoints of the interval and subtract the value at the start point from the value at the end point, and divide that by the change in x.
Given the table:
f(30) = 16 and f(12) = 40
The average rate of change over the interval 12 < x < 30 is:
(f(30) - f(12)) / (30 - 12) = (16 - 40) / 18 = -24/18 = -4/3
So the average rate of change over the interval 12 < x < 30 is -4/3
It's worth noting that this is only the average rate of change, and the function may have different rates of change at different points within the interval 12 < x < 30.
what is the value of the expression (x-3y)2, when x =4 and y= -3
Answer: 26
Step-by-step explanation:
Simplify
2x-6y
Plug in numbers
2(4)-6(-3)
Answer:
26
Step-by-step explanation:
We want to find the value of the following expression:
[tex](x-3y)2[/tex]
We are given the following variable values:
[tex]x=4[/tex]
[tex]y=-3[/tex]
Start by simplifying the given expression with the distributive property:
[tex]2x-6y[/tex]
Now, plug in the provided variable values:
[tex]2(4)-6(-3)[/tex]
Simplify:
[tex]8+18[/tex]
Finally, add to get the simplified expression:
[tex]26[/tex]
In BINGO, a card is filled by marking the middle square as WILD and placing 24 other numbers in the remaining 24 squares.
Specifically, a card is made by placing 5 numbers from the set 1-15 in the first column, 5 numbers from 16-30 in the second column, 4 numbers 31-45 in the third column (skipping the WILD square in the middle), 5 numbers from 46-60 in the fourth column and 5 numbers from 61-75 in the last column.
One possible BINGO card is:
To play BINGO, someone names numbers, chosen at random, and players mark those numbers on their cards. A player wins when he marks 5 in a row, horizontally, vertically, or diagonally.
How many distinct possibilities are there for the values in the diagonal going from top left to the bottom right of a BINGO card, in order?
To find the number of distinct possibilities for the values in the diagonal going from the top left to the bottom right of a BINGO card, we need to look at the values in each of the five squares that make up the diagonal.
How is this calculated?In the first column, there are 5 possible values (1-15), in the second column, there are 4 possible values (16-30), in the third column there are no possible values because the middle square is WILD, in the fourth column there are 4 possible values (46-60) and in the fifth column there are 5 possible values (61-75).
We need to find the total number of possible combinations of these values. To find the total number of combinations, we can use the formula for combination:
C(n, k) = n! / (k! (n-k)!)
where n is the number of items to choose from and k is the number of items to choose.
In this case, we have 5 items to choose from in the first column, 4 items in the second column, 0 items in the third column, 4 items in the fourth column and 5 items in the fifth column. So we have:
C(5, 1) * C(4, 1) * C(0, 0) * C(4, 1) * C(5, 1) = 5 * 4 * 1 * 4 * 5 = 400
There are 400 distinct possibilities for the values in the diagonal going from top left to the bottom right of a BINGO card.
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Graph the image of the given triangle after the transformation with the rule (x, y)→(−x, y).
Select the "Polygon" button from the toolbar to plot your triangle. You may use the "Move" button to move the triangle after it is created.
A graph of the image of the triangle with vertices (4, 7), (3, 4), and (8, 2) after a transformation with the rule (x, y) → (−x, y) is shown in the image attached below.
What is a reflection?In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By applying a reflection over the y-axis to the coordinates of this triangle the image coordinates include the following:
(x, y) → (-x, y)
Coordinate A = (4, 7) → Coordinate A' = (-(4), 7) = (-4, 7).
Coordinate B = (3, 4) → Coordinate B' = (-(3), 4) = (-3, 4).
Coordinate C = (8, 2) → Coordinate C' = (-(8), 2) = (-8, 2).
Next, we would use an online graphing calculator to plot the coordinates of the image as shown in the image attached below.
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junior secondary Use elimination method to solve the following simultaneous equations: 10m-7n=26
7m+7n=42
Using Elimination method the simultaneous equations is -16/3.
How can a three-step elimination equation be solved?Elimination is a mathematical technique that can be used to solve a system of three equations with three variables.
In standard form, without any fractions or decimals, write all the equations. Decide which one of the three variables you want to eliminate, then pick any two of the equations to do so.
The term "simultaneous equations" refers to two or more algebraic equations that share the same unknown variables and have the same answer. This suggests that the simultaneous equations have a single, solvable problem. For instance, 2x - 4y = 4, 5x + 8y = 3, are instances of simultaneous equations.
10m-7n=26
- 7m+7n=42
3m = -16
m = -16/3
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Evaluate the line integral, where
C
is the given curve.
∫ xyds,C:x2,y=2t,0≤t≤2
C
According to the given information the line integral is 8(1+125[tex]\sqrt{110}[/tex]) / 15 .
What distinguishes a line integral from a definite integral?
Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.
[tex]\int\limits_c {xy} \, ds[/tex], C : x = t^2 , y = 2t, 0 ≤ t ≤ 3
x' = 2t , y' = 2
ds = [tex]\sqrt{(x')^2 + (y')^2}[/tex]
[tex]\sqrt{4(t)^2 + 4}[/tex]
[tex]\int\limits C {xy} \, ds[/tex] = [tex]\int\limits^3_0 {2.2t.2\sqrt{1+t^2}} \, dt[/tex]
t = tanθ
dt = (1+[tex]tan^{2}[/tex]θ)dθ = ([tex]sec^{2}[/tex]θ)dθ
= [tex]\int\limits^3_0 {4t^3\sqrt{1+t^2} } \, dt[/tex]
= 8(1+125[tex]\sqrt{110}[/tex]) / 15
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In the figure below, which term best describes point W?
A. Incenter
B. Centroid
C. Orthocenter
D. Circumcenter
Orthocenter is the best term to describes point R in the triangle UVW.
What is orthocenter?
" Orthocenter is defined as intersecting point of the altitudes of the sides of the acute angle triangle."
According to the given figure,
In triangle UVW,
Ray VR perpendicular to UW
Ray UR perpendicular to VW
Ray WR perpendicular to UV
Altitudes of side ( UV , VW, and WU) of triangle UVW intersect at
point R.
As per the definition of orthocenter , point R represents orthocenter.
Hence, orthocenter is the best term to describes point R in the triangle UVW.
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A survey conducted in a college intro stats class during Autumn 2013 asked students about the number of credit hours they were taking that quarter. The number of credit hours for a random sample of 16 student is: a) Find the 5-number summary for these data. b) Sketch a boxplot for these data. c) Describe the shape, center and spread. d) Are there any outliers
a) To find the 5-number summary for these data, we need to find the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values.
Minimum: the smallest value in the data set
Q1: the value that separates the lowest 25% of the data from the rest
Median: the middle value of the data set (when the data is arranged in numerical order)
Q3: the value that separates the highest 25% of the data from the rest
Maximum: the largest value in the data set
b) To sketch a boxplot, we can represent the data using a box that goes from the Q1 to Q3, with a line (the median) in the middle. Whiskers extend from either end of the box to the minimum and maximum values, with any observations outside of the whiskers represented as dots (outliers).
c) The shape of the data is not specified in the problem statement. However, it can be described as skewed, symmetric or normal. The center of the data can be described as the mean or median, and the spread can be described as the range or interquartile range.
d) It is not possible to determine if there are any outliers without the data set.
Please note that the data is not provided, so the above steps are theoretical.
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Isabelle was curious if sample maximum was an unbiased estimator of population maximum. She started with a large normally distributed population of test scores whose maximum was 999999 points. She then took a random sample of 666 tests and calculated the maximum of the sample. She replaced those tests and repeated this process for a total of 404040 trials. Her results are summarized in the dotplot below, where each dot represents the maximum score from a sample of 666 tests.
Isabelle concluded that the sample maximum is an unbiased estimator of the population maximum.
What is value?Value is a term used to describe the worth of something. It can refer to monetary value, but it can also be used to describe the worth of intangible things such as relationships, ideas, and experiences. Value creates an understanding between two parties, as each may have a different opinion on what something is worth. It can be seen as an exchange or trade of something that both parties consider to be of equal or greater value.
This conclusion is supported by the high number of samples that had a maximum value of 999999. The dotplot shows that the sample maximum was 999999 in over 95% of the trials. The other samples had maximum values that were lower, but still close to the true maximum of 999999. This indicates that the sample maximum did not systematically overestimate or underestimate the population maximum.
The sample maximum was also consistent across the different trials, with the majority of the samples having a maximum value near 999999. This consistency indicates that the sample maximum is a reliable estimator of the population maximum. While there is always a chance that the sample maximum may deviate from the population maximum, the results suggest that the sample maximum is unbiased and reliable for estimating the population maximum.
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Graph the following:
a) y= 2(x-7)^2 -3 using 5 points
b) y= -(x+5)(x+1) using 3 points
A graph of this system of equations with the data points is shown in the image attached below.
How to graph this system of linear equations?In this scenario, we would use an online graphing calculator to plot the given system of equations by using five (5) points and three (3) points respectively;
y = 2(x - 7)^2 - 3 ........equation 1.
y = -(x + 5)(x + 1) ........equation 2.
Generally speaking, the solution to any system of equations is the point of intersection of the lines on the graph representing each of them.
In this scenario, the points that are located on the line of the graph of this equation y = 2(x - 7)^2 - 3 include the following:
Ordered pair (5, 5).
Ordered pair (10, 15).
Ordered pair (7, -3).
Ordered pair (5.775, 0).
Ordered pair (8.225, 0).
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