The first hiker is 2 miles east and 1 mile north of the starting point, so the position can be represented by the coordinate pair (2, 1).
What is the Pythagorean theorem in plain English?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.
The second hiker is 2 miles west and 3 miles south of the starting point, so the position can be represented by the coordinate pair (-2, -3).
The Pythagorean theorem can be used to calculate the separation between the two points:
d = √((2 - (-2))² + (1 - (-3))² ) = √((2 + 2)² + (1 + 3)²) = √(4² + 4²) = √(16 + 16) = √32
So, the two hikers are approximately 5.66 miles apart.
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What are all the factors of the number 16
Answer: 1,2,4,8,16
Step-by-step explanation: All of the factors of a number multiply to equal a certain number.
Question 3: Solve each of the following equations using completing the square
Write each answer in simplified surd form
(a) x² + 4x-3=0
The value of x is 0.645 and x= 4.645.
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x² + 4x-3=0
Now, using Completing the Square method we have to half the coefficient of x and add and subtract the square.
then, x² + 4x-3=0
x² + 4x-3 + 2² - 2² =0
x² + 4x + 2² -3 - 2² =0
(x+ 2)² - 7 = 0
(x+ 2)² = 7
x+ 2= ±2.645
x= 0.645 and x= 4.645
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the following are two points in a data set, find the euclidean distance between them. (1.0, 6.1) and (3.3, 8.7) round your answer to 1 decimal place.
The Euclidean distance between (1.0, 6.1) and (3.3, 8.7) is 3.48, rounded to 1 decimal place.
The Euclidean distance formula is used to calculate the distance between two points in a two-dimensional plane. The formula for Euclidean distance between two points (x1, y1) and (x2, y2) is given by:
[tex]d = √(x2-x1)2 + (y2-y1)2[/tex]
For our two points, (1.0, 6.1) and (3.3, 8.7), the Euclidean distance is:
[tex]d = √(3.3-1.0)2 + (8.7-6.1)2 \\ = √(2.3)2 + (2.6)2 \\ = √5.29 + 6.76 \\ = √12.05 \\ = 3.48[/tex]
Therefore, the Euclidean distance between (1.0, 6.1) and (3.3, 8.7) is 3.48, rounded to 1 decimal place.
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Which transformations have been performed on the
graph of 0.2^3√x +3 +4
The graph of f(x) = x^(-1/3) underwent three transformation to give 0.2^3√(x +3) + 4 which are horizontal shift, vertical scaling and vertical shift
What are the transformation of the graphThe graph of f(x) = x^(-1/3) has undergone the following transformations to give 0.2^3√(x +3) + 4:
Horizontal Shift: The graph has been shifted to the right by 3 units. This is because x has been replaced with x + 3 in the equation.
Vertical Scaling: The graph has been scaled by 0.2^3 in the vertical direction. This is because f(x) has been multiplied by 0.2^3.
Vertical Shift: The graph has been shifted upward by 4 units. This is because f(x) has been added by 4 in the equation.
In summary, the transformations performed on the graph of f(x) = x^(-1/3) to give 0.2^3√(x +3) + 4 are a horizontal shift of 3 units to the right, a vertical scaling by 0.2^3, and a vertical shift of 4 units upward.
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QUESTION 7 A family moved to Orlando, FL and bought a home. They paid $350,000 for their house. In their neighborhood the mean price of a home is $375,000 with a standard deviation of $7,500. Calculate the z-score for the price of their home and indicate if the price they paid for their home usual or unusual. Choose one • 10 points The z-score is 3.333 and it is usual The z-score is -3.333 and it is usual The z-score is 3.333 and it is unusual The z-score is -3.333 and it is unusual
Step-by-step explanation:
The z-score for the price of the family's home can be calculated as follows:
z = (350,000 - 375,000) / 7,500 = -3.333
A negative z-score indicates that the value is below the mean. Therefore, the price the family paid for their home is lower than the average price of homes in their neighborhood, so it can be considered unusual.
So, the answer is: The z-score is -3.333 and it is unusual.
using the following data on the observations 10, 13, 4, and 20, confirm that the complete linkage distance between the cluster containing {10, 13} and the cluster containing {4, 20} is 2.577 units as displayed in the dendrogram.
According to the dendrogram, the complete linkage distance between the cluster containing {10, 13} and the cluster containing {4, 20} is 2.577 units.
A dendrogram is a type of diagram that is used to represent the structure of a set of objects, where the objects are linked together in a hierarchy.
Now, let's take a closer look at the dendrogram that displays the complete linkage distance between the cluster containing {10, 13} and the cluster containing {4, 20}.
In this case, the maximum distance is
=> 20 - 4 = 16 units.
Next, we need to normalize the distance by dividing it by the square root of the number of data points in the two clusters. In this case, there are 4 data points in total, so the normalized distance is
=> 16 / √4 = 4.
Finally, we can use the formula for the complete linkage distance, which is given by
D = √2 * (1 - x),
where x is the normalized distance. Plugging in our values, we get
D = √2 * (1 - 4) = √2 * -3 = -2.236 units.
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Pls help Im so confused
Answer:
57 ft
Step-by-step explanation:
Solution Given:
BC =40ft it also known as a.
<C=55°
<B=90°
<C=180-90-55=35°
height of the building =? also known as c
we have
law of sines
[tex]\frac{Sin A}{a} =\frac{Sin B}{b}=\frac{Sin C}{c}[/tex]
By inserting value[tex]\frac{Sin 35}{40} =\frac{Sin 55}{c}[/tex]
you can take any two what you want
doing criss cross multiplication
Sin 35*c=Sin55*40
we get
c=sin55 * 40 /Sin35
c=AB=57.12 ft in nearest 10 it is 57 ft
5x+3y=-7 6x-7y=-8. Substitution method
The solution of the system is X = -73/53 and Y = -2/53.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
System of equations,
5X + 3Y = -7 {equation 1}
6X - 7Y = -8 {equation 2}
From equation 1,
Y = (-7-5X)/3
Substituting the value to the equation 2,
6X - 7{(-7-5X)/3} = -8
18X + 49 + 35X = -24
53X = -24 - 49
53 X = -73
X = -73/53
And Y = -2/53
Therefore, X = -73/53 and Y = -2/53.
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Which set of ordered pairs (x, y) could represent a linear function?
A = {(-8,8), (-4,5), (0, 2), (5, -1)}
B = {(-1, -2), (2,1), (5,4), (8,7)}
C = {(-2,8), (1,5), (4,2), (6, -1)}
D = {(-1,0), (1, 1), (7,5), (9,6)}
The ordered pairs that represent the linear function is Option A, B and C.
What is linear function?A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph. If the function has more variables, they should all be constants or known variables in order for the function to continue to function as a linear function.
To determine which ordered pairs represent a linear function we use the equation of slope.
The slope is given as:
m = (y2 - y1) / (x2 - x1)
Option A:
m = (5 - 8) / (-4 + 8) = -3 / 4
m = (2 - 5) / (0 + 4) = -3/ 4
The slopes between the consecutive points are same hence option A represents a linear equation.
Similarly, for option B:
m = (1 + 2) / (2 + 1) = 1
m = (4 - 1) / (5 - 2) = 1
Option B is correct.
Option C:
m = (5 - 8) / (1 + 2) = -3 / 3 = -1
m = (2 - 5)/ (4 - 1) = -1
Option C is correct.
Option D:
m = (1- 0)/ (1 + 1) = 1/2
m = (5 - 1) / (7 - 1) = 4 / 6 = 2/3
Option D is incorrect.
Hence, the ordered pairs that represent the linear function is Option A, B and C.
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3
How many full 4 3/4in. sheets can be cut from 22 1/8in. stock?
3
The 22 1/8in stock can be cut into full sheets of length 4 3/4in.
The number of sheets that can be cut from 22 1/8 inches would be 4 25/38
How to solve for the divisionTo solve this, I would first have to convert the values to decimals
4 3/4in = 4.75 inches
22 1/8 = 22.125
To get the full length that can be cut from the 22.125, we would have to divide. That is;
22.125 / 4.75
= 4.657
4 25/38
The number of full sheet that can be cut from this would be 4 25/38
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A coroner arrives at a murder scene at 11p.m. She finds the temperature of the body to be 85.7 degrees F. She waits one hour, takes the temperature again, and finds it to be 81.2 degrees F. She notes that the room temperature is 70 degrees F. Assuming that the temperature of the body was 98.6 degrees F when the murder occurred, when was the murder committed?
Answer:
f
Step-by-step explanation:
hvggggggggghgvggjjjj
To prove that there is a unique element x such that P(x) is true is the same as showing which of these statements is true?a) 3xAy(P (y) ↔ x = y)b) 3x(P(x) & Ay( y =/ x --> notP(y)))c) 3x(P(x) & Ay(P(y) --> x = y))
The statement that proves that there is a unique element x such that P(x) is true is: c) 3x(P(x) & Ay(P(y) --> x = y)).
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms.
Here,
In this statement, the quantifier "3x" says that for every element x, and the condition "P(x)" says that x satisfies a certain property. The statement "Ay(P(y) --> x = y)" says that for every other element y, if y also satisfies the property, then it must be equal to x. Hence, if there is a unique element x such that P(x) is true, then this statement is true.
Option (a) says that for every element y, P(y) is equivalent to y = x, but this statement alone does not imply that there is only one element that satisfies P(x).
Option (b) says that for every element x, if P(x) is true, then there is no other element y that also satisfies P(y) and is not equal to x. However, this statement alone does not imply that there exists an element x that satisfies P(x).
The following assertion establishes that there is a unique element x such that P(x) is true: c) 3x(P(x) & Ay(P(y) --> x = y)).
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Twice one number added to another
number is 18. If the second number is equal
to 12 less than 4 times the first number, find
the two numbers.
First complete the equations below, where x stands for
the first number and y stands for the second number.
2x + y = [?]; y = []x - [ ]
solve for x: [tex]2/3[/tex]x=6
Answer:
x = 9
Step-by-step explanation:
⅔x = 6
3/2 × ⅔x = 3/2×6
½ × 2 = 3×3
x = 9
What is the product of 8.5\times 10^38.5×10 3 and 2.6 \times 10^32.6×10 3 expressed in scientific notation?
Answer:
8.468579573930919e+40
2.768574091477416e 41
Step-by-step explanation:
Rectangle MNOP is similar to rectangle WYXZ.
The scale factor of rectangle MNOP to rectangle WYXZ is 2:3.
What is the length of side WY?
A. 12 inches
B. 9 inches
C. 15 inches
D. 18 inches
Answer:
Option B. 9 inches
Step-by-step explanation:
Given
Rectangle MNOP and Rectangle WYXZ are similar
Scale factor of the two Rectangles = 2:3 or 2/3
MN=6 in
So
MN/WY = 2/3
6/WY = 2/3
WY = 6×3/2
WY = 18/2
WY=9
Therefore length of side WY is 9 inches
At a basketball game, a team made 52 successful shots. They were a combination of 1- and 2-point shots. The team scored 89 points in all. Write and solve a system of equations to find the number of each type of shot.
Answer:
15 1-point shots37 2-point shotsStep-by-step explanation:
You want a system of equations and their solution for the number of shots of each type if the total number is 52 and the points from 1- and 2-point shots total 89.
SetupLet x and y represent the numbers of 1- and 2-point shots, respectively. The problem description tells of two relations:
x + y = 52 . . . . . . . total of shots is 52
x + 2y = 89 . . . . . . total of points is 89
SolutionSubtracting the first equation from the second, we get ...
(x +2y) -(x +y) - (89) -(52)
y = 37
Then the first equation tells us ...
x = 52 -y = 52 -37 = 15
The team made 15 1-point shots and 37 2-point shots.
Mario has a piece of string. He cuts off six-eighths of its length. How much is left?
Answer:
2/8 because if their is 6/8, it's denominator is 8 meaning out of 8 so 8/8 - 6/8 = 2/8 of Mario's Rope.
1) City A and City B have increased growth in population. Write an exponential function to represent the City B’s population, y, based on the number of years that pass, x, after a period of exponential growth.
2) City A and City B have decreased growth in population. Write an exponential function to represent City B’s population, y, based on the number of years that pass, x, after a period of exponential decline.
3) Explain the similarities and differences between your GROWTH equations and your DECAY equations.
Consider the data set shown. How does the outlier affect the mean, median, and mode? 7,11,10,8,10,23,8
The way the outlier affects the mean, median, and mode is:
It does not affect the mode It will increase the mean. It will not affect the medianWhat are the effects of outliers ?The outlier will increase the mean, as it will significantly increase the sum of the values. The presence of an outlier will not affect the median, as it only changes the position of the middle value.
The mode is the value that occurs most frequently in a data set. In this case, the mode will not be affected because the outlier is not the most frequent in the data set and only appears once.
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ANWSER 1 AND 2 PLEASE!!!
1. Carter bought a jet pack, he flew for 17 miles at 2 miles per minute. How long did carter travel on his jet pack?
2. Aniya has just become the world champion of cartwheels. She is able to travel at 0.5 mph doing cartwheels. She went a distance of 0.1 miles. How long did Aniya do cartwheels?
Answer:
The trip took 2.5 hours
Step-by-step explanation:
Answer:
1. 8 minutes and 30seconds
Step-by-step explanation:
Divide 17*2= 8.5
The population of a colony started with 1,120 grows at an annual rate of 4.98%. How much more would you have, at the same time if you used continuous growth, compared to a growth rate when the continuous reaches 3,480?
The number of years its to make 3,480 is approximately 23 years.
What is population growth and population decrease formula?If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.
Given that, the population of a colony started with 1,120 grows at an annual rate of 4.98%.
Here, A =3480
Now, 3480=1,120(1+4.98/100)ⁿ
(1+4.98/100)ⁿ=3480/1,120
(1.0498)ⁿ=3.107
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
n=ln(3.107)/ln(1.0498)
Decimal Form:
n=23.32644715
Therefore, the number of years its to make 3,480 is approximately 23 years.
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Use a net of the square pyramid, if necessary, to find the surface area of the pyramid.
The surface area of the pyramid is 25 + 10h.
What is pyramid?A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.
Given:
A pyramid with the square base.
The side of the base is 5 unit.
So, the surface area of the pyramid,
= base area + 1/2 x perimeter of base x slant height
= (5 x 5) + 1/2 x (4 x 5) + h
= 25 + 10h
Hence, surface area is 25 + 10h.
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Find the future value of the loan. Round your answer to the nearest cent. P= 1250, r= 3.31 t= 2 years==The future value of the loan is $
The future value of the loan is $1,333.86
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
Values are,
P = 1250, r = 3.31 and t = 2 years
Now, We know that;
⇒ Amount = P (1 + r)ⁿ
Substitute all the values we get;
⇒ Future value = 1250 (1 + 3.31/100)²
⇒ Future value = 1250 (1 + 0.033)²
⇒ Future value = 1250 (1.033)²
⇒ Future value = 1250 × 1.067
⇒ Future value = $1,333.86
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Which inverse operations could you use to solve the equation m/4-18= -10? Select two answers.
The inverse operations are (b) and (c)
How to determine the inverse operationsFrom the question, we have the following parameters that can be used in our computation:
m/4-18= -10
Operation 1: Option (B)
Add 18 to both sides of the equation, and then multiply through by 4
Using the above as a guide, we have the following:
m/4 = 8
m = 32
Operation 2: Option (C)
Multiply each side by 4 and then add 72
Using the above as a guide, we have the following:
m - 72 = -40
m = 32
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Solve the inequality for x.
-5x + 20 < 5
A x < 3
B x > 5
C x > -5
D x < -5
E x > 3
Answer: E. x > 3
Step-by-step explanation:
Step 1: Subtract 20 from both sides.
−5x +20 − 20 < 5 − 20
−5x < −15
Step 2: Divide both sides by -5.
−5x/−5 < −15/−5x
x > 3
On a number line, it would look like this:
Linear equation that passes through the points of (3,4) and (0,5)
Answer:
y=-2/6+5
Step-by-step explanation:
Parag Parikh is going to receive Rs. 2,00,000 today (at t=0) as the result of an insurance settlement. In addition, he will receive Rs. 3,50,000 one year from today and Rs. 5,50,000 two years from today. He plans on saving all of this money and investing it for her retirement. If Parag can earn an average of 12% on her investments, how much will he have in his account if he retires 26 years from today (at t=26)?
Answer:
Parag will have Rs. 44,68,802 in his account if he retires 26 years from today. This can be calculated by using the formula A = P (1+r)n, where A is the future value of the investment, P is the present value, r is the interest rate, and n is the number of years until retirement. In this case, P = 10,50,000, r = 12%, and n = 26, so A = 10,50,000 (1+0.12)26 = Rs. 44,68,802.
can someone help me to find other parts to this problem?
The required answer of other parts are 4) 1230, 5) Students = 1230 + 53t, 6) 2025 students.
What is average?In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
According to question:As you have calculated average students in a year is 53.So, we can say students are increasing by 53 each year.
4) in 2003, number of students are 1389 and in three year students increase by 53* 3 = 159
in 2000,
Students = 1389 - 159
= 1230
5) We have 1230 students in 2000, and students will increase by 53 each year.
So, for t years equation will be
Students = 1230 + 53t
6) There is 15 years to come 2015, using our equation;
Students = 1230 + 53t
Students = 1230 + 53(15)
Students = 1230 + 795
= 2025 students.
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Describe the possible echelon forms of the standard matrix for a lineartransformation T where T: R^4 --> R^3 is ontoGive some examples of the echelon forms. The leading entries, denoted , may have any nonzero value; the starred entries, denoted t, may have any value (including zero)
Possible echelon forms for matrix are:
[tex]\left[\begin{array}{ccc}Y&&\\0&Y&\\0&0&Y\\0&0&0\end{array}\right][/tex]
What exactly is a matrix?A collection of integers organised in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics. Matrices have also found usage in computer graphics, where they have been utilised to represent picture rotations and other transformations.
If there are m rows and n columns, the matrix is said to be an “m by n” matrix, written “m × n.” For example,
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right][/tex] its a 2×3 matrix.
The proof of the theorem proves that the columns, say, A and B must be independent.
In the matrix, there is linearity and the trivial solution would be [ 0, 0 , 0 , 0] for the matrix to exist. In other words, all the unknowns must be zero.
This establishes the fact that the matrix T needs to be independent for the matrix function, say T (x) to be one-to-one.
By definition, one-to-one is ker (T) = {0}
Thus, the null space is occupied only by the zero vector.
Note: if there was no linear independence in the vectors, the solution would not be zero in the vector.
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