translate (x , y) ( x - 5, y - 3); reflect over the line x = 0 ( the x- axis); rotate 180 defgrees clockwise about the orgin
Answers
The vertices of the image of triangle ABC after the transformations are given as follows:
A'(4,-2), B'(4,2), C'(0,-1).
How to obtain the vertices of the image of triangle ABC?The vertices of triangle ABC are given as follows:
A(1,1), B(1,5), C(5,2).
The first transformation is the translation defined as follows:
(x,y) -> (x - 5, y - 3).
Hence the translated vertices are given as follows:
A'(-4, -2), B'(-4, 2), C'(0, -1).
The second transformation is the reflection over the x-axis, hence the rule is:
(x,y) -> (x, -y).
Then the vertices of the translated and reflected triangle are given as follows:
A'(-4, 2), B'(-4,-2), C'(0,1).
The final transformation is the rotation of 180º clockwise around the origin, for which the rule is of:
(x,y) -> (-x,-y).
Then the vertices of the image, after all the transformations, are given as follows:
A'(4,-2), B'(4,2), C'(0,-1).
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Related Questions
What’s 3(4x + 6) + 7x
Answers
Required
Question 1- Which parallelogram has an area of 60 square units? *
A
12
15
10
C
15
15
12
B
10
10.2
6
D
6
6
10
Show your reasoning
Answers
Answer:
To find the area of a parallelogram, we can use the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we are given that the area is 60 square units, so we can use this information to find the value of b and h for each of the options given.
Option A: 12 15 10
In this option, we can see that the base is 12 units and the height is 15 units, so we can plug these values into the formula to find the area: A = 12 * 15 = 180 square units. This is much larger than the given area of 60 square units, so option A cannot be correct.
Option B: 10 10.2 6
In this option, we can see that the base is 10 units and the height is 6 units, so we can plug these values into the formula to find the area: A = 10 * 6 = 60 square units. This matches the given area of 60 square units, so option B could be correct.
Option C: 15 15 12
In this option, we can see that the base is 15 units and the height is 12 units, so we can plug these values into the formula to find the area: A = 15 * 12 = 180 square units. This is much larger than the given area of 60 square units, so option C cannot be correct.
Option D: 6 6 10
In this option, we can see that the base is 6 units and the height is 10 units, so we can plug these values into the formula to find the area: A = 6 * 10 = 60 square units. This matches the given area of 60 square units, so option D could be correct.
Therefore, the correct answer is either option B or option D.
What is the slope of ½?
Answers
The slope of ½ is 0. A line with a zero slope is neither rising nor falling when seen from left to right or the other way around. Simply put, the slope of a horizontal line is zero.
y=m x + b, where m is the slope and b is the y-intercept, is the slope-intercept form.
where y= 0 and
y = m x + b
The slope is 0 when expressed in the slope-intercept form, or m = 0.
A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
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Given: BD and AC bisect each other.
Prove: AB
CD.
Note: quadrilateral properties are not permitted in this proof.
Step
1
try
Statement
BD and AC bisect each other
Type of Statement
A
Reason
Given
B
Answers
The proof of AB ≅ CD is given below.
What is triangle?
Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.
Given: BD and AC bisect each other.
So, AE = AC and BE = ED
Consider the triangles ΔAEB and , ΔECD
Given,
AE = EC ...S
BE = ED ....S
Here, lines BC and AD intersects at point E, so
m ∠AEB = m ∠DEC ....A
Therefore, from SAS congruency,
ΔAEB ≅ ΔECD
Hence, AB ≅ CD
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A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?
22 feet
26 feet
33 feet
44 feet
136 degrees
Answers
Answer:
Step-by-step explanation:
So if one bit of the length, is half the size of the other bit then we can make the following equation, for x being the length of rope:
x + 2x = 66
3x = 66
x = 22
That is the length, of the smaller one (half the big one), so 2x = 44. Hence d) is your answer.
Hope I helped!
for the transition matrix P = [0.9 0.1 0.3 0.7], solve the equation SP = S to find the stationary matrix S and the limiting matrix P.
Answers
The limiting matrix is [tex]\bar{P}[/tex]=[tex]\left[\begin{array}{ccc}0.75&0.25\\0.75&0.25\\\end{array}\right][/tex].
What is meant by transition matrix?Mathematicians frequently refer to "transition matrices" in a variety of situations. The term "change of coordinates matrix" is occasionally used in the context of linear algebra. As an alternative term for a stochastic matrix, or a matrix that describes transitions, it is employed in the theory of Markov chains. Use row operations to try to create the identity matrix to the left while augmenting the matrix of the second basis with the matrix of the first basis. Afterward, the transition matrix will be on the right. Row 1 should be multiplied by 1 as follows: R1=R1 R 1=-R 1 R1=R1.
The given transition matrix is:
P=[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex]
Let S=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9a+0.1b\\0.3a+0.7b\\\end{array}\right][/tex]=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
Here, 0.9a+0.1b=0, 0.3a-0.3b=0
So, a=b
a+b=1
a=b=1/2
S=[tex]\left[\begin{array}{ccc}0.5\\0.5\\\end{array}\right][/tex]
This S is called the stationary matrix
P=[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex]
P=det[tex]\left[\begin{array}{ccc}0.9-\lambda&0.1\\0.3&0.7-\lambda\\\end{array}\right][/tex]=0
λ²-1.6λ+0.6=(λ-1)(λ-0.6)=0
λ₁=1, λ₂=0.6
x=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
Px=λx
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =1[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
0.9a+0.1b=a
a=b
v₁=[tex]\left[\begin{array}{ccc}1\\1\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =0.6[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
0.9a+0.1b=0.6a
b=-3a
v₂=[tex]\left[\begin{array}{ccc}1\\-3\\\end{array}\right][/tex]
V=[tex]\left[\begin{array}{ccc}1&1\\1&-3\\\end{array}\right][/tex]
V⁻¹=(1/4)[tex]\left[\begin{array}{ccc}3&1\\1&-1\\\end{array}\right][/tex]
D=[tex]\left[\begin{array}{ccc}\lambda_{1} &0\\0&\lambda_{2}\\\end{array}\right][/tex]
D=[tex]\left[\begin{array}{ccc}1&0\\0&0.6\\\end{array}\right][/tex]
P=VDV⁻¹
Pⁿ=VDⁿV⁻¹
[tex]\bar{P}[/tex]=[tex]\left[\begin{array}{ccc}0.75&0.25\\0.75&0.25\\\end{array}\right][/tex]
This is the required limit matrix.
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A 20-cm wrench is used to loosen a bolt. The force is applied 0. 20m from the bolt. It takes 100n to loosen the bolt when the force is applied perpendicular to the wrench. How much force would it take if the force was applied at a 30o angle from perpendicular? round-off your answer to the nearest whole number.
Answers
The force that it will take if applied perpendicular at 30° = 58 N
According to the formula of torque = τ and force = F,
τ = r x F x sinθ --- equation 1
Given, F = 100 N , r = 0.2 m (r = radius)
We have to find the force when θ (angle) = 30°
Putting value in equation 1,
τ = 0.2 x 100 x sin (30°)
τ = 10 Nm
Value of torque from here = 10 Nm
Now to calculate the force perpendicular at 30° the equation will change as,
τ = r x F x cosθ --- equation 2
10 = 0.2 x F x cos 30°
Taking τ on the right side and F on left,
F = 10/ (0.2 x cos 30°)
F = 57.73 N
F = 58 N
Therefore, The force that it will take if applied perpendicular at 30° = 58 N
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Melvin plays tennis and swims for a total of 110 minutes every day. He plays tennis for 40 minutes longer than he swims. Part A: Write a pair of linear equations to show the relationship between the number of minutes Melvin plays tennis (x) and the number of minutes he swims (y) every day. Part B: How much time does Melvin spend swimming every day? Show your work. Part C: Is it possible for Melvin to have spent 70 minutes playing tennis if he plays and swims for a total of exactly 110 minutes and plays tennis for 40 minutes longer than he swims? Explain your reasoning.
Answers
The answers to all the subparts using equations are shown:
(A) pair of linear equations: y + 40 = x and x + y = 110
(B) 75 minutes every day of swimming.
(C) The given statement is false as a result.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, (A):
Y indicates the volume of swimming
X denotes the quantity of tennis.
Making two equations now:
y + 40 = x
x + y = 110
(B)
X in the other equation is changed to match the first equation.
Please plug this in:
y + 40 + y = 110
2y = 70
35 minutes of swimming equals Y.
Including: 35
35 + 40 = 75 minutes every day of swimming.
(C)
No, given that equation: 70 + (70 - 40) = 100
This statement is false as a result.
Therefore, the answers to all the subparts using equations are shown:
(A) pair of linear equations: y + 40 = x and x + y = 110
(B) 75 minutes every day of swimming.
(C) The given statement is false as a result.
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phil dunphy, a real estate agent, is considering whether he should list an unusual $774,395 house for sale. if he lists it, he will need to spend $5,747 in advertising, staging, and fresh cookies. the current owner has given phil 6 months to sell the house. if he sells it, he will receive a commission of $16,870. if he is unable to sell the house, he will lose the listing and his expenses. phil estimates the probability of selling this house in 6 months to be 49%. what is the expected profit on this listing?
Answers
The required expected profit on this listing with 49% probability in 6 months.
What is Probability?A probability is a number that mirrors the opportunity or probability that a specific occasion will happen. Probabilities can be communicated as extents that reach from 0 to 1, and they can likewise be communicated as rates going from 0% to 100 percent.
According to question:We have,
he will need to spend $5,747 in advertising, staging, and fresh cookies.he will receive a commission of $16,870 on selling.Then, there is 49% chances in 6 months = 49% of $16,870
⇒ $8266.3
And 51% of expenditure = 51%of $5,747
⇒ $29.3
So, required profit = $8266.3 - $29.3 = $8237
Thus, required profit is $8237.
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see attached please thank you
Answers
After solving for the angles, the resultant answers are as follows:
(A) ∠L = 55°
(B) ∠LMN = 62°
What are angles?When two consecutive lines or rays intersect at a single endpoint, an angle is created.
The vertex of an angle is the point where two points come together.
The Latin word "angulus," which means "corner," is from which the term "angle" originates.
The intersection of two planes also creates angles.
We refer to these as geometric angles.
So, according to the given diagram:
KMN = LMN + 118
180 = LMN + 118
LMN = 180 - 118
LMN = 62°
Now,
6x - 9 + 4x + 7 + 62 = 180
10x + 60 = 180
10x = 180 - 60
10x = 120
x = 120/10
x = 12
Then,
∠L = 4x + 7
∠L = 4*12 + 7
∠L = 55°
Therefore, after solving for the angles, the resultant answers are as follows:
(A) ∠L = 55°
(B) ∠LMN = 62°
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PLS HELP ME WITH THE QUESTION
Answers
Answer: 175
Step-by-step explanation: So the formula for finding the area of a rhombus is A= 1/2 d1+d2. So, we multiply 14 x 25 to get 350, then we divide by 2, and get 175! I hoped this helped you solve your problem :)
What is limit of a function in maths?
Answers
The limit of a function is a value of the function as the input of the function gets closer to some number.
We know that, a limit is a value toward which an expression converges as variable approaches certain values.
The limit of a function at m point is nothing but the value that the function approaches as its argument(variable) approaches m.
When a function is said to have a limit L at point p if it is possible to make the function arbitrarily close to L by choosing values to point p.
It is a value of the function as the input of the function gets closer to some number.
Therefore, the limit of a function is nothing but a value of the function as the input of the function gets closer to some number.
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PLEASE HELP QUICKLY
MEJEJEJDNE
Answers
a rectangular swimming pool has the same depth everywhere. the combined surface area of the floor of the pool and the four sides is $4800$ square feet. what is the maximum volume of the swimming pool in cubic feet?
Answers
the maximum volume of the swimming pool in cubic feet = 29744[tex]ft^{3}[/tex]
volume:A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder or a sphere.
Different shapes have different volumes. In 3D geometry, we have studied the various shapes and solids such as cubes, cuboids, cylinders, cones, etc., that are defined in three dimensions. For all these shapes, we are going to learn to find the volume.
Unit of Volume:
Volume of a solid is measured in cubic units. For example, if dimensions are given in meters, then the volume will be in cubic meters. This is the standard unit of volume in the International System of Units (SI). Similarly, other units of volume are cubic centimeters, cubic feet, cubic inches, etc.
given that
the combined surface area of the floor of the pool and the four sides is $4800$ square feet.
each side (there are 4) = 4 x w x w
and the bottom w x w
total surface area 5 w^2 = 4800
w = depth = 30.984 ft
volume= 30.984^3 = 29744.89[tex]ft^{3}[/tex]
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in october, marshal drove 217 miles ,which was 62% of the distance he drove in september. How far in miles did marshal drive in september?
Answers
Answer:
350 miles
Step-by-step explanation:
62 : 100 = 217 : x
x = 217 · 100 / 62
x = 21 700 / 62
x = 350
please anyone help me with this question i need it ASAP!! all it’s asking is to Write the equation of a line perpendicular to y=2x-4 and
goes through the point (4,-1). please anyone help meee!!
Answers
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x - 4 ← is in slope- intercept form
with slope m = 2
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (4, - 1 ) into the partial equation
- 1 = - 2 + c ⇒ c = - 1 + 2 = 1
y = - [tex]\frac{1}{2}[/tex] x + 1 ← equation of perpendicular line
You are bending a strip of metal into an isosceles triangle for a sculpture. The strip of metal is 28 inches long. The first bend is made 10 inches from one end. Describe two ways you could complete the triangle.
Answers
Answer:
2 ways below
Step-by-step explanation:
To complete the triangle, you would need to bend the other end of the strip of metal so that it is also 10 inches from the first bend. One way to do this would be to measure 10 inches from the first bend and mark the spot, then use a bending tool to carefully bend the metal at the mark.
Another way would be to hold the metal strip against a ruler or measuring tape, aligning the first bend with the 10-inch mark, then use the bending tool to make the second bend at the 20-inch mark. In either case, the resulting triangle would have two equal sides that are 10 inches long, and a base that is 8 inches long.
-3/4 x 4/3 x -3/7
Just need the answer. Need by next Friday. 30 points for whoever answered.
Answers
Answer:-3/4x=-3x/4
4/3x -3/7 = 4x/3 - 3x
Step-by-step explanation:
24 3/5 +4^3x(8 1/5 -2)
Answers
Answer: i believe it is 123/5 + 1984x/5
Step-by-step explanation:
Question 3
Answer choices:
A) copy an angle
B) copy a segment
C) construct a perpendicular line to a point not on the line
D) bisect an angle
Answers
"Copy an angle" construction has been performed.
What is an angle?
Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.
Observe that angles BAC and TSR are same.
This means, construction is done to copy the angle BAC.
So, "copy an angle" construction has been performed.
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The diameter of a circle is 4 feet. What is the circle's circumference?
Answers
Answer: Your answer will be 12.57.
Step-by-step explanation:
Using the formulas
C=2 x π x r
d=2 x r
Solving for C.
C = πd = π·4 ≈ 12.56637
In 2005, the total waste generated in a certain country was 8.618 x 10^8 pounds. Also in 2005, the country's population was 2.76 x 10 ^5 people. Determine the garbage per capita (per person) in that
country in the year 2005.
(use scientific notation to answer this question)
Answers
Answer:
To determine the garbage per capita, we need to divide the total waste generated by the population. In 2005, the total waste generated was 8.618 x 10^8 pounds and the population was 2.76 x 10^5 people, so the garbage per capita in that country in 2005 was 3.12 pounds per person. This can be calculated as follows:
8.618 x 10^8 pounds / 2.76 x 10^5 people = 3.12 pounds/person
Alternatively, we can rewrite the population in scientific notation to make the calculation easier:
8.618 x 10^8 pounds / (2.76 x 10^5) people = 8.618 x 10^8 pounds / (2.76 x 10^3 x 10^2) people
Now we can cancel out the common factors of 10^2 from the numerator and denominator to get the final result:
8.618 x 10^8 pounds / (2.76 x 10^3 x 10^2) people = 8.618 x 10^8 pounds / (2.76 x 10^3) people
= 8.618 x 10^5 pounds / (2.76) people
= 3.12 pounds/person
This shows that in 2005, the garbage per capita in that country was 3.12 pounds per person.
f(d) = 0.0071d³ - 0.090d² + 0.48d,
where d is the diameter of the diamond.
Find the domain of the function in the
context of the situation. (Lesson 4-1)
A. The domain is all real numbers.
B. The domain is {dl d > 0).
C. The domain is {dl d < 0).
D. The domain is (dld > 0.48).
Answers
On a certain hot summer's day, 354 people used the public swimming pool. The daily prices are $1.50 for children and $2.25 for adults. The receipts for admission totaled $548.25. How many children and how many adults swam at the public pool that day?
Answers
The number of children and adults that swam at the public pool is
331 and 23.
What is an equation?An equation is a mathematical statement of two expressions connected by an equal sign.
Example:
2x + 5 = 9 is an equation.
We have,
The total number of people = 354.
Cost for children = $1.50
Cost of adults = $2.25
Total amount = $548.25
Now,
Number of children = x
Number of adults = y
Now,
x + y = 354 _____(1)
x = 354 - y ____(2)
1.50x + 2.25y = 548.25 _____(3)
Putting (2) in (3).
1.50 (354 - y) + 2.25y = 548.25
531 - 1.50y + 2.25y = 548.25
0.75y = 548.25 - 531
0.75y = 17.25
y = 17.25/0.75
y = 23
Now,
x = 354 - y
x = 354 - 23
x = 331
Thus,
The number of children is 331.
The number of adults is 23.
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suppose a is a set with m elements and b is a set with n elements. a. how many relations are there from a to b? explain. b. how many functions are there from a to b? explain. c. what fraction of the relations from a to b are functions?
Answers
a)There are [tex]2^m^n[/tex] possible relation
b)Similarly [tex]n^m[/tex]
c)[tex]\frac{n^m}{2^m^n}[/tex]
a)Set A has m elements and set B has n elements
Firstly determine the number of elements A*B by using the multiplication rule
Number of elements[tex]=A*B=m*n=mn[/tex]
For each element, [tex]A*B[/tex] we have two option
First element 2 ways
Second element 2 ways
mn element 2 ways
By using the multiplication rule
[tex]2*2*2......=2^m^n }[/tex]
Then there are [tex]2^m^n[/tex] possible relation
b)Similarly [tex]n^m[/tex]
c)[tex]\frac{n^m}{2^m^n}[/tex]
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What is the equation of the line with slope of 7 and y-intercept equals to 4?
Answers
The equation of a line with slope m and y-intercept is Y = mx + b. (0,b). y = 7x + 4 is the equation of the line with slope of 7 and y-intercept equals to 4?
Since the slope of the line is 7 and the y-intercept is 4, the equation of the line can be written as y = 7x + 4.
The equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept. In mathematics, the slope or gradient of a line is a numerical representation of the line's steepness and direction.
In the equation y = 7x + 4, 7 is the slope of the line and 4 is the y-intercept. This means that the line has a slope of 7 and the y-intercept is 4.
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The bar graph shows the number of reserved campsites at a campground for one week. What percent of the reservations were for Friday or Saturday?
Reservations: Monday=5
Tuesday=3
Wednesday=4
Thursday=7
Friday=26
Saturday=30
Sunday=9
Answers
The percentage of the reservations were for Friday or Saturday is 67%
How to determine the percentage of the reservations were for Friday or Saturday?From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following data values for reservation
Monday = 5Tuesday = 3Wednesday = 4Thursday = 7Friday = 26Saturday = 30Sunday = 9The total number of reservations in the bar chart is then calculated as
Total number of reservations = 5 + 3 + 4 + 7 + 26 + 30 + 9
Evaluate the sum
So, we have the following representation
Total number of reservations = 84
The total number of reservations for Friday or Saturday is then calculated as
Total number for Friday or Saturday = 26 + 30
Evaluate the sum
So, we have the following representation
Total number for Friday or Saturday = 56
The percentage of the reservations were for Friday or Saturday is then calculated as
Percentage = Total number for Friday or Saturday/Total number of reservations
This gives
Percentage = 56/84
Evaluate
Percentage = 67%
Hence, the percentage is 67%
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Someone help Please ASAP
A full pond containing 625 gallons of water begins losing its water at a rate of 20% per week. If the pond now contains 320 gallons of water, how many weeks has it been since the pond was at full capacity?
(Use the digits 0 – 9 to enter a number. Use a decimal point only if necessary.)
Answers
Answer:3
Step-by-step explanation:
if the set alpha is at 0.05 for a two tailed hypothesis test, what is the p value required to reject a null hypothesis
Answers
The required answer is fail to reject a null hypothesis.
What is Null hypothesis?
The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.
Given that:
α = 0.05
then
z0.05 = 1.645
Hence, the rejection region is {z < −1.645}.
Hence, The required answer is fail to reject a null hypothesis.
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pls answer this questions for 15 points
Answers
Answer:
B
Step-by-step explanation:
by plugging in f, you can see that B, is the only correct answer
A fails at values greater than or equal to f = 2
C fails for all values
and D fails for all values
B works for all given values
2(1) + 3 = 5
2(2) + 3 = 7
2(3) + 3 = 3
2(4) + 3 = 11
2(5) + 3 = 13