Answer:
If the angle between two unit vectors u and v is 3.14/3, then using the law of cosines, ||u + v||^2 = 2 + 2cos(3.14/3) = 2 + 2(0.5) = 3. Hence ||u + v|| = sqrt(3).
To find the value of k such that the system has a unique solution, no solution, or an infinite number of solutions, we can use the determinant of the coefficient matrix. If the determinant is nonzero, then the system has a unique solution. If the determinant is zero and the system of equations is inconsistent, then the system has no solution. If the determinant is zero and the system of equations is consistent, then the system has an infinite number of solutions. In this case, the determinant of the coefficient matrix is zero, which implies that the system has an infinite number of solutions.
The eigen values and eigen vectors of the matrix can be found by solving the characteristic equation, which is obtained by det(A - λI) = 0, where A is the matrix and I is the identity matrix.
For the matrix
2 1 -1
3 2 -3
3 1 -2
the characteristic equation is
(2 - λ)(3 - λ) - 3 = 0
which gives us λ = 1 and λ = 3 as the eigen values.
The corresponding eigen vectors can be found by solving the system of equations (A - λI)x = 0, where x is the eigen vector.
For λ = 1, the eigen vector is (1, -1, 1).
For λ = 3, the eigen vector is (-1, 2, 1).
If f(x) is a polynomial of degree 4 with roots 1, 2, 3, 4 and leading coefficient 1, and g(x) is a polynomial of degree 4 with roots 1, 1/2, 1/3, 1/4 and leading coefficient 1, then the limit of 1/f(x)/g(x) as x approaches infinity does not exist. This can be seen by noting that f(x) and g(x) both grow without bound as x grows without bound, so the ratio of the two polynomials also grows without bound.
1. What is the approximate volume of the sugar container? Show your work. (2 points)
2. What is the approximate height of the rice container? Show your work. (2 points)
3. Compare the heights of the sugar container and the rice container. Next, compare their volumes. How many times as large is the volume of the rice container compared to the volume of the sugar container? Explain your answer. (2 points)
4. In the formula V = Bh, B is the area of the base. Use this formula to calculate the volume of the flour container. (2 points)
5. Compare the volumes of the containers. Which container has the greatest volume? Which has the smallest volume? (2 points)
PLS HELP I WILL GIVE BRAINLIST
The greatest volume and smallest volume container is of rice and flour.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
Given;
Sugar container radius and height is 2.5in and 8.5inch
Rice container radius and volume is 2.5in and 235.3inch^3
Sugar container area of base and height is 12.26in and 4inch
Now,
1. volume= pi*r*r*h
=3.14*2.5*2.5*8.5
=166.8125
2. volume= pi*r*r*h
235.3=3.14*2.5*2.5*h
h=11.98in
3. volume= base*h
=12.26*4
=49.04in^3
Therefore, the volume of flour container is 49.04in^3.
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The fact that 1 liter = 1.057 quarts can be written as the conversion factor
The conversion factor of litre to quarts is 1 litre = 1.057 quarts and its meaning is discussed below.
What is a conversion factor?
A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. The correct conversion factor to convert minutes to hours is 60 minutes = 1 hour.
The metric unit of a volume known as the litre is mostly used to measure liquids.
An English measurement of volume equal to the one-quarter gallon is the quart. There are now three different types of quarts in use: the liquid quart, dry quart, and imperial quart of the British imperial system.
The standard value of converting liquid to quarts is 1 litre = 1.057 quarts.
This means that volume of 1 litre of a substance is equivalent to the volume of 1.057 quarts of the same substance.
Therefore the conversion factor of litre to quarts is 1 litre = 1.057 quarts.
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8-642
A
O
B
B
6
#2
E
2465
C4
2
D
B
6 8
Mr. Paulsen challenges Olivia and Angelica to move figure ABCDE onto figure
A'B'C'DE" using a series of two different transformations. They give two different
answers.
Answer the questions to investigate ways to transform ABCDE.
1. Olivia finds a combination of two different transformations that moves ABCDE
onto A'B'C'DE". What is one way she might have done this? (3 points)
Olivia could have used a translation and a rotation to move ABCDE onto A'B'C'DE".
What is distance?Distance in numerical measurement of how far apart to 16 places in point are in space age is often measured in unit like came miles with as for free system also can be conceptualized in the term of time as Indian distance between two points in the time.
A translation would involve shifting the figure ABCDE along some axis by a certain distance, while a rotation would involve rotating the figure ABCDE around a fixed point. By combining the two transformations, Olivia could move ABCDE onto A'B'C'DE".
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you need to divide the number of cars by the number of people to calculate cars per person on day one. Which formula can you type in Cell D92 to do this?
This formula divides the number of cars in Cell C92 by the average number of people in Cell B92, and calculates the cars per person on day one.
This formula divides the number of cars in Cell C92 by the number of people in Cell B92, and calculates the cars per person on day one. By typing =C92/B92, you can easily calculate the number of cars per person in a single cell. This formula can be used for any data set, and will always give an accurate result. It is an effective way to compare the ratio of cars to people in a given situation, and to compare the results to other data sets. The formula is also simple to use and understand, which makes it a powerful tool for quickly analyzing data. It is a useful tool for making decisions, as it allows you to assess the ratio of cars to people quickly and accurately.
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A classic counting problem is to determine the number of different ways that the letters of "recommend " can be arranged.
The number of different ways that the letters of "recommend" can be arranged is 90720.
What is arrangement?
Generally speaking, an arrangement of objects is just a collection of them. A combination (order is ignored) or permutation is used to determine the number of "arrangements" of the components (order is significant). An arrangement is a group of hyperplanes that divides a space into cells.
If there are n different objects in the system then the number of different ways of arrangement of n objects is n!
If the repetition of the objects are allowed in the system the number of different ways of arrangement is -
n! / (no. of repetition of object 1)! .... (no. of repetition of object r)!
Total number of letters in the word "recommend is 9.
The number of different ways of arangement of the 9 letters is 91
The repetition of letter "e" is 2 and repetition of letter "m" is 2.
The number of different ways that the letters of "recommend" can be arranged is -
9! / 2! × 2!
(9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (2 × 1) × (2 × 1)
(9 × 8 × 7 × 6 × 5 × 3 × 2 × 1)
90720
Therefore, the number of different ways is 90720.
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What is the quotient of 2 3/4 divided by 4 1/2
The quotient of 2 3/4 divided by 4 1/2 is approximately 0.622222222.
What do you mean by Quotient?The outcome of dividing two numbers is referred to mathematically as the quotient. It is the amount produced when a numerator is divided by a denominator.
For example, consider the expression "10 ÷ 2". 10 is the numerator, and 2 is the denominator. The quotient of this expression is 5. This has the following notation in mathematics:
10 ÷ 2 = 5
The quotient can also be a fraction, in which case it represents a ratio of two numbers. For instance, the fraction representation of the equation "5 2" is as follows:
5 ÷ 2 = 5/2
In this case, the quotient represents the ratio of 5 to 2.
The quotient is an important concept in mathematics, as it is used in many areas, including arithmetic, algebra, and calculus. It is used to solve problems involving division and ratios, and it is a basic building block for more advanced mathematical concepts.
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Points X, Y, and Z are on the sides QR , PR, and PQ respectively, of right triangle PQR such that PZXY is a square. If PQ=1 and PR=1, then what is the side length of the square?
Answer:
Step-by-step explanation:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Triangles PQR and ZQX are similar!
Square side => a
XZ / (PQ - PZ) = PR / PQ
a / (12 - a) = 8 / 12
a = 4.8
The side length of the square PZXY is sqrt(2).
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side².
We have,
Since triangle PQR is a right triangle, we can use the Pythagorean theorem to find the length of QR:
QR² = PQ² + PR²
QR² = 1² + 1²
QR² = 2
QR = √2
Since PZXY is a square, its sides are equal in length.
Let's denote the length of one side of the square as s.
Then, we can write:
PR = PX + RX
1 = s + QY
Since QY = PZ = s and PX = QX = QR - QY = sqrt(2) - s,
we can substitute these values into the equation for PR to get:
1 = s + (√2 - s)
1 = √2
Therefore,
The side length of the square PZXY is √2.
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A rectangular field is 0.4 m longer than it is wide. If its length is 6m find its Perimeter.. When the breadth of the rectangle is reduced by 0.5m. the length is increased such that the perimeter is increased by 1/4 of its Original What is the Change in the length of the rectangle ?
PLS HELP EMERGENCY I NEED U
Answer:
1. sin∠EDA is equal to sin∠EBC
2. sin∠CEB is not equal to sin∠EBC
3. cos∠BEC is equal to sin∠EBC
4. cos∠ADE is not equal to sin∠EBC
5. sin(90 - m∠EBC) is not equal to sin∠EBC
6. cos(90 - m∠EDA) is equal to sin∠EBC
Step-by-step explanation:
From inspection of the given diagram, ∠EAD = ∠ECB = 90°.
According to the vertical angles theorem, ∠BEC = ∠DEA.
According to AA similarity theorem, ΔADE ~ ΔCBE
Therefore, ∠EDA = ∠EBC.
This means that:
sin∠EDA is equal to sin∠EBCsin∠CEB is not equal to sin∠EBC[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Since cos∠BEC = CE/BE and sin∠EBC = CE/BE then:
cos∠BEC is equal to sin∠EBC.As ∠BEC ≠ ∠ADE then:
cos∠ADE is not equal to sin∠EBC.As sin(90° - x) = cos(x) then sin(90 - m∠EBC) = cos∠EBC.
As cos∠EBC ≠ sin∠EBC then:
sin(90 - m∠EBC) is not equal to sin∠EBCAs cos(90° - x) = sin(x) then cos(90 - m∠EDA) = sin∠EDA.
As sin∠EDA = sin∠EBC then cos(90 - m∠EDA) = sin∠EBC.
Hence:
cos(90 - m∠EDA) is equal to sin∠EBC.vector a has a magnitude 5.00 and points in a direction 60.0degrees clockwise from the negative y axis. what are the x and y components of vector a.
A is directed along negative X and Y axes respectively having magnitudes 3.214 and 3.83 units respectively.
A vector is an object that, as we all know, possesses both magnitude and direction. We must determine a vector's length in order to determine its magnitude. Vector quantities include things like velocity, displacement, force, momentum, etc. However, scalar quantities like as speed, mass, distance, volume, temperature, etc. exist. In contrast to vectors, which
have both magnitude and direction, scalars only have magnitude.
Magnitude of vector A = |A| = 5 units
We know, the negative Y-axis is an angle of 270° counterclockwise with a positive X-axis.
θ = Angle of vector A with positive X-axis = (270° - 40°) = 230°
So, x component of vector A = Ax = |A| * cos 230° = |A| * cos (180° + 50°) = |A| * (- cos 50°) = 5 * (-0.6428) = -3.214
And, y component of vector A = Ay = |A| * sin 230° = |A| * sin (180° + 50°) = |A| * (- sin 50°) = 5 * (-0.766) = -3.83
Since Ax and Ay both are negative relative to positive X and Y axes respectively; so, the x and y components of vector A are directed along negative X and Y axes respectively having magnitudes 3.214 and 3.83 units respectively.
the complete question is -
Vector img has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis.What are the x and y components of vector img .
A)Ax = 3.83 and Ay = 3.21
B)Ax = 3.83 and Ay = -3.21
C)Ax = -3.21 and Ay = -3.83
D)Ax = -3.21 and Ay = 3.83
E)Ax = 4.29 and Ay = 2.16
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Question 10
A diagram has circles such that the area represents the populations of various
countries in the world. The circle for United States has a radius of 4.2 cm and the circle
for India has a radius of 8.7 cm. If 4% of the world's population is in United States, what
percentage of the world's population is in India? Round to the nearest percent.
Answer:
17%
Step-by-step explanation:
area represents the populations
United States has a radius of 4.2 cm and
India has a radius of 8.7 cm.
If 4% of the world's population is in United States,
what percentage of the world's population is in India
US π r² = π*4.2²
India π r² = π*8.7²
so india/US = 4.29
so india = 4.29 *4% = 17%
What are the constants in this expression?
2 y
x−3+²7 - 12/2
X-3+
O1 and -3
O-3 and
O-3 and
2/3
y
2
2
1
3 and 2
Answer: The constants in the expression are -3 and 2.
In the expression:
2 y
x−3+²7 - 12/2
X-3+
The term -3 is a constant and does not change its value regardless of the values of any variables. The term 2/2 can also be simplified to 1, which is another constant. Hence, the constants in the expression are -3 and 2.
Step-by-step explanation:
Which expression represents the phrase shown? "3 added to the quotient of a number divided by 6"
The required expression is n/6 +3
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: The statement " 3 added to the quotient of a number divided by 6
Let the number be n
Dividing the number by 6 we get the quotient as n/6
Again adding 3 to the quotient we get
3+n/6
Hence, The required expression is n/6 + 3
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A linear function is shown on the graph.
a linear function beginning with closed circle at 2 comma 0 and ending with a closed circle at 9 comma 7
What is the domain of the function?
{x | 2 < x < 9}
{x | 2 ≤ x ≤ 9}
{y | 0 < y < 7}
{y | 0 ≤ y ≤ 7}
The domain of the linear function shown in the graph is given as follows:
{x | 2 ≤ x ≤ 9}.
How to obtain the domain of the function?The domain of a function is composed by the set containing all the possible input values for the function, hence it is composed by all the values of x assumed by the function.
The bounds of the domain in this problem are given as follows:
Lower bound: closed at x = 2.Upper bound: closed at x = 9.Hence the correct option regarding the domain of the function is given by the second option.
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Suppose that a particle moving along the x-axis encounters a resisting force that results in an acceleration of a =-=-0.10 V v. Given that x = 0 cm and v = 36 cm/s at time t = 0, find the velocity v and position x as a function of t for t 2 0. v= 2 cm/s Edit C x= 2 cm
The velocity of the particle v as a function of time t is given by v(t) = 36 - 0.10 * t^2 cm/s and the position x as a function of time t is given by x(t) = 36 * t - 0.05 * t^3 cm.
The problem states that at time t = 0, the particle has an initial velocity of v = 36 cm/s and is located at x = 0 cm. The particle is accelerating with a=-0.10 V v. This means that the velocity of the particle is changing by -0.10 V v each second. This can be expressed in terms of the time t as v(t) = 36 - 0.10 * t^2 cm/s. The position of the particle at any time t can be expressed as x(t) = x0 + v0 * t + 1/2 * a * t^2, where x0 is the initial position and v0 is the initial velocity. In this case, x0 = 0 and v0 = 36, so the position of the particle at any time t can be expressed as x(t) = 36 * t - 0.05 * t^3 cm. This means that the particle will move away from the origin (x=0) and its velocity will decrease each second.
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find all $r$ for which the infinite geometric series \[2 6r 18r^2 54r^3 \dotsb\]is defined. enter all possible values of $r,$ as an interval.
All possible values of r for which this infinite geometric series is defined is the interval (-1,1).
The infinite geometric series is given by:
[tex]\[2 6r 18r^2 54r^3 \dotsb\][/tex]
This is a geometric series, so it is defined when the absolute value of the common ratio (r) is less than 1. The common ratio of this series is r, so the series converges when |r| < 1. Mathematically, this can be expressed as follows:
|r| < 1
-1 < r < 1
Therefore, all possible values of r for which this infinite geometric series is defined is the interval (-1,1).
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Solve the following system of equations:
-2x + 5y = −11
4x - 3y = 15
Answer: (x,y)=(3,-1)
Step-by-step explanation:
What equation represents the proportional relationship displayed in the table?
-picture-
Enter your answer by filling in the box to complete the equation.
y = (answer)x
Answer:
y = 5x
Step-by-step explanation:
It can be observed that as ‘x’ increases, ‘y’ also increases.
It can also be observed that
[tex]\frac{y}{x}[/tex] = the same constant for all four sets of values
k =[tex]\frac{10}{2} = \frac{20}{4} = \frac{30}{6} =\frac{40}{8}[/tex]=5
It can concluded that y is directly proportional to x:
y = kx Where k = constant of proportionality
For these four sets of values:
y = 5x
Four classes are on a field trip. There are 6 tour guides. of studentsCan each tour guide have an equal number
The solution is, each tour guide have an equal number of 8 students.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
there are 12 students in each class.
Four classes are on a field trip.
There are 6 tour guides.
total students = 12*4
= 48
so, each guide have = 48/6
= 8
Hence, The solution is, each tour guide have an equal number of 8 students.
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Is it possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100° ?
Use the given sides and angles to explain why or why not.
Answer:
No
Step-by-step explanation:
An isosceles triangle has two sides of equal length.
All interior angles in an isosceles acute triangle are less than 90°.
Therefore, it is not possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100° as two sides are not of equal length and 100° > 90°.
carry out the following matrix multiplications. for each problem, say what the function represented by each matrix does to the standard basis vectors and what the product of the two matrices would do to these vectors.
The row in the original matrix and the column in the primary matrix must match. Hence, the matrix product has the first matrix's number of rows and the second matrix's number of columns.
A matrix is exactly what?Read an overview of this subject. a collection of numbers lined up in rows or columns to form a flat array is called a matrix. The atoms, or units, of the matrix are the integers.
The matrix theory is what?The study of squares is the main focus of the mathematical field known as matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics.
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Let f(x)=6x2+18x. Answer the following questions. 1. Find the x intercepts of the parabola. Intercepts (separate with commas): x=2. Find the vertex of the parabola. Write the vertex as a point (a,b) where a and b are numbers.
The x-intercept is -3 and the vertex of the parabola is (-1.5, -13.5).
What is vertex?The intersection of two lines, two line segments, or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is known as an angle's vertex.
The x coordinate of the vertex is given as:
x = -b/2a= -18/ 2(6)= - 1.5
The y coordinate of the vertex is given as:
y = f(- 1.5)
f(- 1.5) = 6(- 1.5)² + 18(- 1.5) = 13.5 - 27= -13.5
Hence, the vertex of the parabola is (-1.5, -13.5).
The x intercept is found by substituting the value of y = 0 in the function:
0 = 6x² + 18x
0 = 6x (x + 3)
x + 3 = 0
x = -3
Hence, the x-intercept is -3 and the vertex of the parabola is (-1.5, -13.5).
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When two numbers are added together, the sum is at least 100. One of the numbers is 77. Question 1 PART A Which of these numbers could be the other number? Select all the correct answers. response - correct Responses 15 15 20 20 9 9 41 41 50 50 23 23 25 25 Question 2 PART B Write an inequality to represent the possible values of the other number n . Enter the correct answer in the box.
Answer:
Part A: 23
Part B: n < 77
Step-by-step explanation:
Jimena finances a $4,200 furniture purchase. The store offers 3%
simple interest, and Jimena will pay off the balance in 6 months.
How much simple interest will Jimena pay the store?
Answer: To calculate the simple interest, you can use the formula:
I = Prt
where I is the interest, P is the principal (the amount borrowed), r is the interest rate as a decimal, and t is the time in years.
In this case, P = $4,200, r = 0.03, and t = 6/12 = 0.5 (since the interest is paid over 6 months, which is half of a year). Plugging these values into the formula, we get:
I = Prt = 4,200 * 0.03 * 0.5 = $63
So, Jimena will pay the store $63 in simple interest.
Step-by-step explanation:
PLEASE HELP I DONT UNDERSTAND!
Write the following polynomial in descending powers of the variable and with no missing powers
3x^3 -70
3x^3 -70=?
If we are to write the following polynomial in descending powers of the variable and with no missing powers 3x^3 -70, it would be 3x^3 - 70 + 0x^2 + 0x + 0
What is a Polynomial?A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.
Hence, it can be seen that descending order is basically when the power of a term decreases for each succeeding term. For example, x3 + x2 + x or 2 x4 + 3 x2 + 7 x are arranged in descending order. Descending order is more commonly used.
The polynomial in descending powers of the variable with no missing powers is:
3x^3 - 70 = 3x^3 - 70 + 0x^2 + 0x^1 + 0x^0
= 3x^3 - 70 + 0x^2 + 0x + 0
Note: The polynomial can also be written as 3x^3 - 70x^0.
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Write the first five terms of the arithmetic sequence with the first term a1=7 and the common difference d=4
Answer:
7, 11, 15, 19, 23
Step-by-step explanation:
Since the common difference is 4 each successive term is 4 more than the previous term
If we let aₙ be the nth term,
a₁ = 7
a₂ = 7 + 4 = 11
a₃ = 11 + 4 = 15
a₄ = 15 + 4 = 19
a₅ = 19 + 4 =23
The first five terms are: 7, 11, 15, 19, 23
We can also use the generalized formula for the nth term:
aₙ = a₁ + d(n - 1)
where a₁ = first term
d = common difference
Plugging in the known values we get
aₙ = 7 + 4(n- 1)
aₙ = 7 + 4n - 4
aₙ = 3 + 4n
Substituting n = 1, 2, 3, 4, 5 into the above equation will yield the same values
Maybe your teacher prefers one of the above approach.
Consider the line 5x-8y=-6.
Find the equation of the line that is parallel to this line and passes through the point (4,-4).
Find the equation of the line that is perpendicular to this line and passes through the point (4, -4).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of parallel line:
Equation of perpendicular line: []
8x 12
5
The equation of the line that is perpendicular to 5x-8y=-6 and passes through (4,-4) is y = (-8/5)x + 16/5.
What are Parallel lines?Parallel lines are two or more lines in a coordinate plane that are equidistant from each other at all coordinates.
The given line can be rewritten in slope-intercept form as y=(5/8)x+(3/4), where the slope is 5/8. So, any parallel line will also have a slope of 5/8.
Using the point-slope form of a line, we can write the equation of the line as:
y - (-4) = (5/8)(x - 4)
Simplifying, we get:
y = (5/8)x - 23/8
Therefore, the equation of the line that is parallel to 5x-8y=-6 and passes through (4,-4) is y = (5/8)x - 23/8.
The slope of the given line is 5/8, so the slope of any line perpendicular to it will be -8/5.
y - (-4) = (-8/5)(x - 4)
Simplifying, we get:
y = (-8/5)x + 16/5
Therefore, the equation of the line that is perpendicular to 5x-8y=-6 and passes through (4,-4) is y = (-8/5)x + 16/5.
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Use Empirical Rule………
Approximately 99.7% of the vehicles travel between 53 miles per hour and 77 miles per hour.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.The mean and the standard deviation for this problem are given as follows:
Mean of 65.Standard deviation of 4.Hence:
65 - 3 x 4 = 53.65 + 3 x 4 = 77.Meaning that the approximate percentage is of 99.7%.
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Can anyone help me? Find m
Answer:
m∠Y = 60°WY = 7 inStep-by-step explanation:
Given triangle WXY with sides WX = 7 in and XY = 7 in and angle X = 60°, you want the measure of angle Y and the length of side WY.
Isosceles triangleThe equal given side measures tell you that their opposite angles (W and Y) have equal values. Those values will be such that the total of all angles is 180°:
W +Y +X = 180°
Y +Y +60° = 180° . . . . . . . . . . . use given values; substitute Y for W
Y = (180° -60°)/2 = 60° . . . . . . . subtract 60°, divide by 2
All of the angles in this triangle have the same measure, so it is an equilateral triangle. All of the sides have the same measure, too.
angle Y = 60°
WY = 7 inches
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Additional comment
It is helpful to recognize that an isosceles triangle with a vertex angle of 60° is an equilateral triangle. That recognition lets you write down the answer with no further work.
-3y + 4 – 2 + 6y
can some one answer this step by step
Answer: Sure! To simplify the expression -3y + 4 - 2 + 6y, we'll follow these steps:
Start by combining like terms:
-3y + 6y = 3y
Next, add the constant terms:
3y + 4 - 2 = 3y + 2
Finally, simplify the expression by substituting the values:
3y + 2 = 3y + 2
So the simplified expression is 3y + 2.
Step-by-step explanation: