Yes, this is true. This phenomenon is known as the Central Limit Theorem and it states that, as the sample size increases, the distribution of the sample mean converges to a normal distribution.
Yes, this is true. According to the Central Limit Theorem, as the sample size increases, the distribution of the sample mean converges to a normal distribution. This means that, when the sample size is large enough, the histogram of sample means will appear to be close to a normal distribution. This is because the mean of a large enough sample size will be close to the population mean, regardless of the shape of the original population distribution.
The Central Limit Theorem also states that the larger the sample size, the more closely the sample distribution will resemble a normal distribution. This is why, when the sample size is large enough, a histogram of sample means will appear to be a normal distribution.
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The market value of Julie’s home is $180,000 of which she still owes $100,000. If she wanted to take out a home equity loan, what is the maximum amount that she can borrow? (Assume that she can borrow up to 80 percent of the market value of the home. )
The amount which she can borrow from the home equity loan is $44,000.
According to the question
According to the following equation:
maximum loan amount = market value of the home * borrowing limit
Julie is able to borrow a maximum amount for a home equity loan.
The maximum loan amount is
$180,000 * 80% = $144,000,
In Julie's situation because the home's market value is $180,000 and the borrowing ceiling is 80%.
Julie can only borrow the $44,000
difference between the maximum loan amount and the remaining debt because she still owes $100,000 on her house.
The difference is calculated as follows: $144,000 - $100,000 = $44,000.
Julie is therefore qualified for a home equity loan of up to $44,000.
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The amount which she can borrow from the home equity loan is $44,000.
According to the question
According to the following equation:
maximum loan amount = market value of the home * borrowing limit
Julie is able to borrow a maximum amount for a home equity loan.
The maximum loan amount is
$180,000 * 80% = $144,000,
In Julie's situation because the home's market value is $180,000 and the borrowing ceiling is 80%.
Julie can only borrow the $44,000
difference between the maximum loan amount and the remaining debt because she still owes $100,000 on her house.
The difference is calculated as follows: $144,000 - $100,000 = $44,000.
Julie is therefore qualified for a home equity loan of up to $44,000.
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we turn over the cards of a well-shuffled standard deck of 52, and we observe the sequence. (a) how many sequences have all cards of the same suit together? (b) how many sequences have all the clubs together?
There are 13! x 4 possible sequences where all cards of the same suit are together, and 13! possible sequences where all the clubs are together.
A standard deck of 52 cards contains 4 suits: spades, hearts, diamonds, and clubs.
(a) To find how many sequences have all cards of the same suit together, we need to find the number of sequences where all the cards of the same suit are together.
There are 4 possible suits, and each suit contains 13 cards.
So, the number of sequences where all the cards of the same suit are together is 13! x 4.
(b) To find how many sequences have all the clubs together, we need to find the number of sequences where all the clubs are together.
There are 13 clubs, and each club card can be placed in any order.
So, the number of sequences where all the clubs are together is 13!
Therefore, there are 13! x 4 possible sequences where all cards of the same suit are together, and 13! possible sequences where all the clubs are together.
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A trapezoid has an area of 100 square units. What scale factor would be
required to dilate the trapezoid to have each area?
a. 6400 square units
b. 900 square units
c. 100 square units
d. 25 square units
e. 4 square units
What is the correct statement for three
The definition that justifies the congruence of angle measures GJH and GJI is given as follows:
Definition of Angle Bisector.
What is the definition of Angle Bisector?A bisection is defined as a segment that splits an angle measure into two equal measures.
Hence an angle bisector means that an angle is divided into two angles of equal measure.
For this problem, we have that segment GJ is the angle bisector of angle G, meaning that the angle measures GJH and GJI are congruent.
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Select all the correct answers.
Which three pairs of side lengths are possible measurements for the triangle?
45
B
45
AB=16, AC=16
AB= 6, AC= 6√/2
BC=7√2, AC = 14
AB= 15, BC = 15
OBC=8, AC = 8√3
AB= 11, AC = 22
The possible measurements for the triangle are given as follows:
AB = 6, AC = 6√2.AB = 15, BC = 15.What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For this problem, we have an angle of 45º, which has the same value for sine and cosine, hence:
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Use the given confidence level and sample data to find the margin of error. Assume that the sample is a simple random sample and the population has a normal distribution. Round your answer to one more decimal place than the sample standard deviation.
99% confidence; n=201; /x=276; s=75
The margin of error to be 21.2
How to find the margin of errorThe formula for the margin of error for a simple random sample with a normal population and a known standard deviation is given by:
Margin of Error = z* (s / √n)
Where
z is the z-score that corresponds to the given confidence level. For a 99% confidence level, the z-score is 2.576.
Plugging in the given values, we get:
Margin of Error = 2.576 * (75 / √201) = 2.576 * (75 / 14.1) = 21.15
Rounding to one more decimal place than the sample standard deviation (which is 75), we get the margin of error to be 21.2.
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MWhat is the measure of ∠F?
Answer:
Angle F i= 48 degrees
Step-by-step explanation:
Sum of angles in a triangle= 180°
8x -18+ 6x-4+5x-7= 180
Collect like terms
8x +6x +5x -18 -7-4=180
19x-29=180
19x = 180 +29
19x=209
x=209/19
x= 11
⇒Angle F= 5x-7
= 5(11)-7
= 55-7
=48 degrees
Answer:
48°
Step-by-step explanation:
A/C, 6x - 4 + 8x - 18 + 5x - 7 = 180°
or, 19x - 29 = 180°
or, x = 209 ÷ 19 = 11
So, x equals 11.
Now, Angle F = (5 × x) - 7 = (5 × 11) - 7 = 55 - 7 = 48°
Hence, Angle F measures 48°.
HOPE IT HELPED BUDDY!
(1 point) write the formal negation of ∀x∃y(x > y). your negation must not contain any explicit negation symbols
∃x∀y(x ≤ y) We can write the negation by switching the existential and universal quantifiers, and inverting the inequality sign. The negation is therefore expressed as ∃x∀y(x ≤ y).
The negation of the statement “for all x, there exists a y such that x is greater than y” can be expressed as “there exists an x such that for all y, x is less than or equal to y”. This negation is written as ∃x∀y(x ≤ y). This is done by switching the existential and universal quantifiers, and inverting the inequality sign. By doing so, we can form an expression that is the logical opposite of the original statement, which is necessary in order to negate it.
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1. A recipe requires 1 cup of milk for every 4 cups of flour. Write a linear equation that describes the relationship.
Linear equation for the relationship between flour and milk cups
y = 4x,
where x is number of milk cups
y is number of flour cups
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
A recipe requires 1 cup of milk for every 4 cups of flour.
Ratio between milk(x) and flour(y)
x/y = 1/4
y = 4x
where x number of cups of milk
y is number of cups of flour
Hence, y = 4x is the linear equation that defines the relationship.
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How do you calculate the area of a circle within a circle?
To calculate the area of a circle within a circle, you can use the following formula Area = πr^2 - πr1^2
How do you calculate the area of a circle within a circle?Where,r is the radius of the larger circler1 is the radius of the smaller circlePi, which is roughly equivalent to 3.14159, is a mathematical constant.The area of a circle is given by the formula πr^2, where r is the radius of the circle.In the case of a circle within a circle, the area of the larger circle can be found by using this formula with the radius of the larger circle.The area of the smaller circle can also be found using the same formula, but with the radius of the smaller circle.The difference between the areas of the two circles represents the area of the circle within the circle.To find the area of the circle within the circle, simply subtract the area of the smaller circle from the area of the larger circle.It's important to note that this formula assumes that the smaller circle is fully contained within the larger circle, with no overlap.If there is overlap between the two circles, a different method may need to be used to calculate the area of the circle within the circle.To learn more about area of circle refer:
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A polynomial function f(x) with integer coefficients has a leading coefficient of 7 and a constant term of 2. According to the Rational Root Theorem, which of the following are possible roots of f(x)?
The possible roots of the polynomial function f(x) is, 2/7
What are polynomials?The polynomials are the algebraic expressions, which have multiple powers.
And based on powers of polynomials, we can categorize polynomials into following categories-
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
A polynomial function f(x) ,
Having a leading coefficient of 7 and a constant term of 2
The possible roots of f(x) = ?
According to the Rational Root Theorem,
Rational zero of polynomial = p/q
p = constant term of the polynomial
q = leading coefficient of the polynomial
Rational Zero = a₀/aₙ
= 2/7
Hence, the rational zero is 2/7
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How do you solve this?
(3^{x-1}*27^x*9^2)/(3^{2x-4)*81^x}
Answer: The expression can be simplified as follows:
(3^{x-1} * 27^x * 9^2) = 3^{x-1 + 2} * 27^x
(3^{2x-4) * 81^x} = 3^{2x-4 + 2x} * 3^{-2x}
Replace in the expression: (3^{x-1 + 2} * 27^x) / (3^{2x-4 + 2x} * 3^{-2x}) = 3^{x-1 + 2 - 2x + 4} * 27^x / 3^4 = 3^3 * 27^x / 81
So the simplified expression is 3^3 * 27^x / 81.
Step-by-step explanation:
Decreasing the sample size, while holding the confidence level the same, will do what tothe width of your confidence interval?a.make it bigger b.make it smaller c.it will stay the same d.cannot be determined from the given information
Decreasing the sample size, while holding the confidence level the same, will make the width of your confidence interval bigger. So option a. is correct.
The width of a confidence interval is a measure of the degree of uncertainty in the estimate of the population parameter. It is determined by the sample size, the confidence level, and the standard deviation of the population.
When the sample size decreases, the standard deviation of the sample estimate increases, making the width of the confidence interval larger. This reflects the increased uncertainty in the estimate of the population parameter.
Therefore, decreasing the sample size while holding the confidence level the same will result in a wider confidence interval.
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Decreasing the sample size, while holding the confidence level the same, will make the width of your confidence interval bigger. So option a. is correct.
The width of a confidence interval is a measure of the degree of uncertainty in the estimate of the population parameter. It is determined by the sample size, the confidence level, and the standard deviation of the population.
When the sample size decreases, the standard deviation of the sample estimate increases, making the width of the confidence interval larger. This reflects the increased uncertainty in the estimate of the population parameter.
Therefore, decreasing the sample size while holding the confidence level the same will result in a wider confidence interval.
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how many degrees are there on both the celsius and kelvin temperature scales, between the normal freezing and boiling points of water?
There are 100 degrees between the normal freezing and boiling points of water.
On the Celsius temperature scale, the difference between the normal freezing point (0°C) and the normal boiling point (100°C) of water is 100°C - 0°C = 100°C.
Celsius, also called centigrade, scale based on 0° for the freezing point of water and 100° for the boiling point of water.On the Kelvin temperature scale, the equivalent temperatures for the normal freezing and boiling points of water are 273.15 K and 373.15 K, respectively. The difference between these two temperatures on the Kelvin scale is 373.15 K - 273.15 K = 100 K.
So, in both Celsius and Kelvin scales, there are 100 degrees between the normal freezing and boiling points of water.
Therefore, there are 100 degrees between the normal freezing and boiling points of water.
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2w + 3 - 3w - 7 which is equivalent
Answer:
-w - 4 is equivalent in the question you gave.
determine the probability of the couple having five children with no children being affected by the disorder.
The probability of a couple having five children with no children being affected by the disorder is given by the formula (1 - 0.0025)⁵.
This formula calculates the probability of a certain event (in this case, having no children affected by the disorder) happening five times in a row. However, this does not give the probability of all five children being unaffected by the disorder.
To find the probability of all five children being unaffected, you would need to multiply the probability of each child being unaffected, which is (1 - 0.0025), five times:
(1 - 0.0025) * (1 - 0.0025) * (1 - 0.0025) * (1 - 0.0025) * (1 - 0.0025) = 0.99609This result is the correct probability of a couple having five children with no children being affected by the disorder.
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True or False : The magnitude of a vector is zero if all of its components are zero.
True , a vector cannot have zero magnitude if one of its components is not zero.
If all of a vector's components are zero, is the vector's magnitude also 0?
A vector's magnitude cannot ever be smaller than any of its components' magnitudes. Only when all of a vector's components are 0 can the vector's magnitude be zero.
Their northward components are also equal, and the eastward component of vector A is equal to the westward component of vector B.
What is the vector's magnitude?
A vector's magnitude, represented by the symbol |v|, is used to determine a vector's length. The distance between the vector's beginning point and endpoint is what this amount essentially represents.
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WILL GIVE BRAINLIEST AND 50 POINTS PLEASE DO MY HOMEWORK BY FEBRUARY 2ND
Answer:
Step-by-step explanation:
For the first question, the combinations of bananas and apples that Elena could buy for exactly $3.50 are:
2 bananas and 2 apples (A)
5 bananas and 1 apple (F)
For the second question, Andre's statement is incorrect. The first type of bus holds 50 people and the second type of bus holds 56 people. In total, 3 of the first type of bus and 3 of the second type of bus can only hold 3 * 50 + 3 * 56 = 318 people. However, there are 280 elementary school students and 40 adults, which is a total of 280 + 40 = 320 people. Hence, Andre's statement is incorrect.
For the third question, the reason why equations A and B are not equivalent is because the variables in Equation B are expressed in a different form than in Equation A. Equation A shows the relationship between the variable x and the constant value 13 and 48, while Equation B only shows the relationship between the variable x and the constant value 35. To determine if they are equivalent, we need to solve both equations for x and compare the solutions. Solving Equation A gives us x = (48 + 13) / -5 = 5.6. Solving Equation B gives us x = 35 / 5 = 7. Since the solutions are different, the equations are not equivalent.
How To Get The Domain And Range From The Graph Of A Function
The input values displayed on the x-axis make up the entirety of a graph's domain. The collection of potential output values that make up the range is represented by the y-axis.
How do you find the range of a graph of a function?All y's potential values are referred to as the function's range. Using the formula y = f, one can determine a function's range (x). If every x value in a relation has exactly one corresponding y value, then it is merely a function.The codomain in relations and functions is the collection of all potential results of the specified relation or function. How to determine a function's domain and range f(x) = 3x2 - 5 The set of input values for f, in which the function is real and defined, is known as the domain of a function. All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.To learn more about values refer to:
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The point given lie on a line. (-1,3) (2,-1)(5,-5) (8,-9) Find the lope of the line
Rise divided by run gives you the slope. A line's rise and run can be used to calculate the slope of a line from its graph. A line's continuous slope is one of its defining characteristics. The slope is (-1,3).
What is meant by slope?The slope is defined as the ratio of the rise, which is the vertical change between two points, to the run, which is the horizontal change between those same two sites.A line's slope is determined by how steeply it slopes from LEFT to RIGHT. Slope is the ratio of a line's rise, or vertical change, to run, or horizontal change. No matter which 2 locations on the line you choose, the slope of a line is always constant (it never changes).A surface (such a road or railroad track) has a 2% slope if it changes elevation by 2 units over a run of 100 units.To learn more about slope refer to:
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? what quantitative rule may be used to determine univariate outliers, and are there situations in which deleting a case/participant may be justified?
The Interquartile Range (IQR) rule is a commonly used quantitative rule to determine univariate outliers and deleting a case may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.
The Interquartile Range (IQR) rule is a commonly used method for identifying outliers in a univariate data set. It is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1). Outliers are considered to be any values that fall outside of the range Q1 - 1.5 * IQR to Q3 + 1.5 * IQR. This range encompasses approximately 75% of the data, with outliers being any values that fall outside of this range.
In some cases, deleting a case or participant may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.
This decision should be made carefully and only after careful consideration of the implications, as removing data can affect the validity of the results and the conclusions that can be drawn from the analysis. In some cases, it may be better to keep the outlier and consider it a potential error or to conduct further analysis to determine if there is a valid reason for the outlier.
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exact shape function of tapered bar element
In FEM, nodal displacement is calculated using the matrix equation shown below: [K] is the global stiffness matrix, [u] is the displacement (solution) vector, and [F] is the vector of forces.
Describe function.A function is something that connects an input to an output.
Then, they are interpolated over entire elements using shape functions, which are essentially polynomials of different orders. Although quadratic shape functions, like a quadratic curve, are becoming common, linear shape functions, like a straight line used to approximate a distance between two locations, are the most fundamental. Even higher order shape functions (like cubic) exist, but they are rarely used in practical settings. The calculation of an element's stress uses Gauss Points rather than nodes. You can look up the GP locations for any given kind of element, but for the purposes of this discussion, let's just talk about singles.
Since [K] is the global stiffness matrix, [u] is the displacement (solution) vector, and [F] is the vector of forces, the matrix equation presented below is used to determine nodal displacement.
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Complete question -
Given the tapered bar/axial element below, determine the exact displacement interpolation function and the associated exact shape functions. Show all intermediate steps.
Can anyone help on this?
Step-by-step explanation:
we need Pythagoras and a little bit of open mind.
Pythagoras is
c² = a² + b²
with c being the Hypotenuse (side opposite of the 90° angle), a and b being the legs.
the incenter means that it is the center point of the inscribed circle (being totally inside the triangle and touching every side at exactly one point).
that means that
GF = GB = GD
but GF we know : 22
so, GB = 22
now we can use the right-angled triangle ABG to find AG :
AG² = AB² + GB²
AG² = 32² + 22² = 1024 + 484 = 1508
AG = sqrt(1508) = sqrt(4×13×29) = 2×sqrt(377) =
= 38.83297568...
what is the least common denominater of 1-8 5-12 and 7-18?
On solving the provided question, we can say that Equivalent Fractions with the LCD 1/8 = 9/72 and 5/12= 30/72
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
LCD = 72
Equivalent Fractions with the LCD
1/8 = 9/72
5/12= 30/72
7/18 = 28/72
Rewriting input as fractions
1/8, 5/12, 7/18
For the denominators (8, 12, 18) the least common multiple (LCM) is 72.
LCM(8, 12, 18)
Therefore, the least common denominator (LCD) is 72.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
1/8 = 1/8 × 9/9 = 9/72
5/12 = 5/12 × 6/6 = 30/72
7/18 = 7/18 × 4/4 = 28/72
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What is the measure of angle W ?
Answer:
Angle W is 100 degrees
---------------------------------
Angle W is the exterior angle of the given triangle.
We know that exterior angle is the sum of remote interior angles.
It gives us:
W = 33 + 67 = 100Select all the abiotic factors.
Group of answer choices
Grass
Parasites
Whale
Mushroom
Mold
Bacteria
Trees
Competition between organisms
Sunlight
Oxygen
Carbon Dioxide
Nitrogen
Clouds
Rain
Desert
Snow
Plastic
Dirt
Rock
The abiotic factors are Sunlight, oxygen, Carbon Dioxide, Nitrogen, Clouds, Rain, Desert, Snow, Plastic, Dirt and Rock
How to determine abiotic factors?Abiotic factors are non-living physical and chemical elements and conditions in the environment that influence the survival and growth of living organisms. The abiotic factors in the given list are:
Sunlight: The light energy from the sun that drives photosynthesis and provides energy to living organisms.
Oxygen: A colorless, odorless, tasteless gas essential for respiration in many organisms.
Carbon Dioxide: A colorless, odorless gas that is produced by respiration, combustion and decay of organic material and is used by plants during photosynthesis.
Nitrogen: An odorless, tasteless gas that makes up a major component of the Earth's atmosphere and is essential for plant growth as a component of amino acids and nucleic acids.
Clouds: A visible mass of water droplets or ice crystals suspended in the atmosphere.
Rain: Precipitation that falls from clouds as water droplets.
Desert: An area characterized by little rainfall and high temperature, often with limited vegetation.
Snow: Precipitation that falls from clouds as ice crystals.
Plastic: A synthetic or semi-synthetic material made from various organic polymers.
Dirt: The naturally occurring material that covers the surface of the earth, made up of organic and inorganic matter.
Rock: A naturally occurring solid composed of one or more minerals.
These are all abiotic factors, while the other items in the list are biotic factors, which are living or once-living elements in the environment.
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find parametric equations for two circles c1 and c2 in space such that ¥c1 and c2 have the same radius; ¥c1 and c2 intersect at the points p(2,1,1) and q(2,1,1) and nowhere else.
The parametric equations for the two circles are
c1(t) = R cos(t) i + R sin(t) (0, 1, 0) + (2, 1, 1),c2(t) = R cos(t) (1, 0, 0) + R sin(t) (0, 1, 1)/√2 + (2, 1, 1).How to find the parametric equationsA general parametric equation for a circle can be given as:
c(t) = R cos(t) i + R sin(t) j + k,
where
R is the radius and (i, j, k) is a unit vector perpendicular to the plane of the circle.We can find two unit vectors perpendicular to the plane containing points p and q:
v1 = (1, 0, 0) and v2 = (0, 1, 1)/sqrt(2)
Thus, the two circles c1 and c2 with radius R and intersecting at p and q can be represented as:
c1(t) = R cos(t) i + R sin(t) (0, 1, 0) + (2, 1, 1),
c2(t) = R cos(t) (1, 0, 0) + R sin(t) (0, 1, 1)/√2 + (2, 1, 1).
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if and is as shown, what is the magnitude of the sum of these two vectors?
The magnitude of sum of the given two vectors is 5 .
Describe a vector.A vector is an entity that possesses both magnitude and direction.
Ordinary quantities that are given with direction are called vectors; in other words, a vector quantity is any magnitude that is given with a direction. Scalar quantities refer to any quantity that is defined without any direction. In physics, vector quantities have a significant impact.
Examples of vectors include displacement, velocity, acceleration, force, and others that show both the direction and the size of a quantity.
Given vectors,
a = i + j
b = 2i + 3 j
sum of the vectors = a+ b
= i+j+2i+3j
= 3i+4j
So,
The magnitude of the sum of given vectors = √ (3 ^2 + 4 ^2 )
= √ (9 + 16 )
= √25
= 5
Therefore, The magnitude of sum of the given two vectors is 5 .
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What is the measure of angle B in this triangle?
Enter your answer in the box.
Answer:
it is probably 70° of the triangle
(FOR 100 POINTS!) MY ANSWER PROBABLY WASNT RIGHT, JUST COMMENT THE CORRECT THING IN SIMPLEST RADICAL FORM.
Answer:
6
Your answer is correct, but since √1 = 1
we can simplify this as 6 · 1 = 6
Step-by-step explanation:
Since the given figure is a square, all four sides are equal.
Each side = 3√2
For a square of side a, the diagonal is given by
d = √(a²+a²) = √(2a²) = a√2
Here we have a = 3√2
So diagonal = x = 3√2 (√2) = 3 · 2 = 6