The dilated points are:
W': (-1, 2)
X': (2.5, 0)
Y': (-0.5, -2).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.
Given:
Triangle WXY with vertices W(-4, 8), X (10, 0), and Y(-2, -8).
And the scale factor is 1/4.
So, the image points are,
W': (-4/4, 8/4) = (-1, 2)
X': (10/4, 0/4) = (2.5, 0)
Y': (-2/4, -8/4) = (-0.5, -2)
Hence, the image points are given above.
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A GP surgery is recording the waiting time of its patients and produces the
cumulative frequency graph shown below.
100
Cumulative frequency
80
60
40
20
0
5
10
15
Waiting time (mins)
20
25
a) How many patients waited for more
than 20 minutes?
b) Find the median waiting time.
17
patients
minutes
The number of patients that waited for more than 20 minutes is 74
The median waiting time is 17
How to determine the number of patientsFrom the question, we have the following parameters that can be used in our computation:
The graph
Where
x = Waiting time
y = Cumulative frequency
This means that
y = Number of patients that waited x or more time
From the graph, we have
(x, y = (20, 74)
So, the number of patients is 74
The median waiting timeFrom the question, we have the following parameters that can be used in our computation:
Maximum CF = 100
Divide by 2 to calculate the median
Median = 100/2
Evaluate
Median = 50
From the graph, we have
(x, y = (50, 17)
So, the median is 17
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Calculate the volume of this cylinder, giving your answer to 1 decimal point
The volume of the cylinder is approximately 1413.7 cubic centimeters.
The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height or length of the cylinder.
Since the base of the cylinder has a diameter of 9cm, the radius is half of that, or r = 4.5cm.
The length of the cylinder is given as 20cm.
Therefore, the volume of the cylinder is:
V = πr²h
= π(4.5)²(20)
= 1413.72 cubic centimeters (rounded to 1 decimal place)
Thus, the volume of the cylinder is approximately 1413.7 cubic centimeters.
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Complete question:
Calculate the volume of this cylinder. give your answer to 1 decimal place. Base is 9cm. Length is 20cm.
688588478685758486759+2345678909876545355=
Answer:
6.9x10^20
Step-by-step explanation:
688588478685758486759+2345678909876545355=
6.90934158E20
What is the answer to this equation (5+12i)+(7-5i)
The answer to the equation (5+12i) + (7-5i) is found to be 12-7i.
The provided equation is a simple algebraic relation between two complex numbers.
The given complex numbers are 5+12i and 7-5i.
We have to add these two complex numbers.
We will add the real part of the complex number to the real part and complex part of one complex number to the complex part of the complex number.
Sum of number = (5+12i) + (7-5i)
Sum of number = 12-7i
The sum of the two complex numbers is also complex number that has a real part has 12 and the imaginary or the complex part as -7.
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k
m
(x-30)°
y
n
(x+50)
Find the values of x and y that make k || j and
m || n.
x=
y =
0
The value of variables x and y are,
⇒ x = 80°
⇒ y = 130°
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Since, A parallelogram is forming here,
Then, Opposite angels are going to be equal.
Thus, We get;
⇒ y = (x + 50)°
Now, As you know that sum of all angles of a quadrilateral equals 360°
Hence, We get;
2 {(x + 50) + (x - 30)} = 360°
(x + 50) + (x - 30) = 180°
2x + 20 = 180
2x = 160
x = 80°
So, We get;
⇒ y = (x+50)
= 80 +50
= 130°
And,
⇒ x = 80°
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Help please it's urgent
Write a general formula to describe the following variation: F is directly proportional to the square of d, and F = 40 when d = 5.
40 = 5k
F = 8d
F = 1.6*d^2
F = kd
The required formula that describes the given variation is F = 1.6d².
What is the general formula to describe the given variation?The general formula to describe the variation that F is directly proportional to the square of d is F = kd²,
where k is a constant of proportionality.
To determine the value of k, we can use the given information that F = 40 when d = 5:
40 = k(5)²
40 = 25k
k = 40/25
k = 1.6
Substituting this value of k into the general formula, we get:
F = 1.6d²
Therefore, the formula that describes the variation is F = 1.6d².
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simplify
1/2 - 1/4 + 1/8
five times a number is 120
Answer: The Number is 24.
Step-by-step explanation:
1) Set unknown number to a variable (I'm going to do x).
2) Set up equation: 5x = 120.
3) Simplify by dividing both sides by 5: 5x/5 = 120/5 = 24.
What is the growth factor of 2% decreased
The growth factor of a 2% decrease is 0.98.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The growth factor of 2% decreased.
This means,
100% - 2%
= 98%
= 98/100
= 0.98
Thus,
0.98 is the growth factor of a 2% decrease.
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Translate the following sentence into an equation: "The product of 3 and x increased by 7 equals 25 ."
I hate math why is this necessary
Answer:
3
Step-by-step explanation:
Slope = rise/ run = change in y / change in x = 3 / 1 = 3
this is VERY necessary in all of the engineering and physics worlds of which you have yet to be acquainted...... these fields enable you to have a smart phone, a car, a bank account, a computer , rockets etc.
Which statement describes the relationship between −2 and −4? Responses −2 is located to the left of −4 on a horizontal number line because −2>−4. negative 2 is located to the left of negative 4 on a horizontal number line because negative 2 is greater than negative 4. −2 is located to the left of −4 on a horizontal number line because −2<−4. negative 2 is located to the left of negative 4 on a horizontal number line because −2<−4. −2 is located to the right of −4 on a horizontal number line because −2>−4. negative 2 is located to the right of negative 4 on a horizontal number line because negative 2 is greater than negative 4. −2 is located to the right of −4 on a horizontal number line because −2<−4. negative 2 is located to the right of negative 4 on a horizontal number line because −2<−4.
−2 is located to the right of −4 on a horizontal number line because −2>−4. Therefore, option C is the correct answer.
What is number line?A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.
Given that, -2 and -4 is located on number line.
Negative integers on the number line located left to zero.
If the greater integer with negative sign and go farther on left of 0 on number line, the value of integers decreases.
Therefore, option C is the correct answer.
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Use these formulas to help you complete the problems below. State the formula you are using. Set up an equation or show work. Solve.
If a polygon can be divided into 5 triangles when the diagonals are drawn from one of its vertices, how many sides does the polygon have?
The number of sides the polygon have 9.
What is Vertices?A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.
Given:
We have a polygon can be divided into 5 triangles when the diagonals are drawn from one of its vertices.
As, we know the number of triangles in a polygon is = n−2
where n is the number of sides (or vertices)
So, the number of sides the polygon have
n= 5+ 2
n = 7 sides
Thus, the polygon is Heptagon.
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The price of Stock A at 9 A.M. was $13.52. Since then, the price has been increasing at the rate of $0.05 each hour. At noon the price of Stock B was $14.27. It begins to decrease at the rate of $0.14 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
The number of hours that the prices of the two stocks be the same will be 4 hours.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
Let 'x' be the number of hours and 'y' be the price of stocks. Then the equations are written as,
y = 13.52 + 0.05x ...1
y = 14.27 - 0.14x ...2
From equations 1 and 2, then we have
13.52 + 0.05x = 14.27 - 0.14x
0.14x + 0.05x = 14.27 - 13.52
0.19x = 0.75
x = 3.947 ≈ 4 hours
The number of hours that the prices of the two stocks be the same will be 4 hours.
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Consider the function f(x) = (x - 3)^2
a. How could you restrict the domain of f(x) so that its inverse will be a function?
b. Graph f(x) with its restricted domain and then graph its inverse on the same set of axes.
c. Find the equation of the inverse of f(x) with its restricted domain.
Answer:
Step-by-step explanation:
a) As the function is a quadratic you could restrict the domain by taking only values either side of the line x = 3. This means the domain will be
a) 3<x<∞
Or
b) -∞<x<3
b) the graph is attached below.
c) The equation of the inverse of f(x) can be found by switching x and y:
X = (y-3)²
√x = y - 3
y = √x + 3
However this takes in positive and negative values of the square root function. So in order to restrict this, we can take the positive square root only.
Thus y = +√x + 3
Write a general formula to describe the following variation: F is directly proportional to the square of d, and F = 40 when d = 5.
Answers:
40 = 5k
F = 8d
F = 1.6*d^2
F = kd
A general formula to describe is F = 1.6×d² will be correct answer.
What in math is a proportional?A relationship is considered proportional if the ratio remains constant. For instance, the average number of apples produced per tree is a measure of proportionality, and the number of trees in an orchard is inversely related to the number of apples produced in a harvest. When two quantities are proportionate with one another, then expand and contract at the same pace, keeping the relationship constant.
Finding the general formula we obtain:
F=kd²
40=k×5²
k=1.6
so, F =1.6×d².
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according to the table, what is the probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work? give your answer as a fraction in simplest form.
The probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work is 2/3, in simplest form.
The table shows the information about the gym membership and lunch habits of 100 physical therapists.
Given that a physical therapist brings their lunch to work, we can use the information in the table to calculate the probability that they do not use the gym membership. To do this, we'll use the formula:
P(not using gym membership | brings lunch) = P(not using gym membership and brings lunch) / P(brings lunch)
We can use the information in the table to find the values of P(not using gym membership and brings lunch) and P(brings lunch).
P(not using gym membership and brings lunch) = 40/100 = 2/5
P(brings lunch) = 60/100 = 3/5
So, the probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work is:
P(not using gym membership | brings lunch) = P(not using gym membership and brings lunch) / P(brings lunch) = (2/5) / (3/5) = 2/3
Therefore, the probability that a randomly chosen physical therapist does not use the gym membership given that they bring their lunch to work is 2/3, in simplest form.
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a statistics professor finds that when he schedules an office hour for student help, an average of students arrive. find the probability that in a randomly selected office hour, the number of student arrivals is
The probability of 3 students arriving at a randomly selected office hour is 0.27(27%). This can be calculated by using the Poisson distribution equation which is P(x)=e^(-λ)*(λ^x/x!).
In the above equation, λ is equal to the average number of arrivals which is 3.3. Plugging these values into the equation gives us P(3)= e^(-3.3)*(3.3^3/3!) = 0.27, this means that the probability of 3 students arriving in randomly selected office hours is 0.27.The Poisson distribution is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space. It is commonly used in engineering, economics, and other fields.
This equation is especially useful in situations like this one where the arrival rate is known and the probability of a certain number of arrivals needs to be determined.
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A statistics professor finds that when she schedules an office hour for student help, an average of 3.3 students arrive. Find the probability that in a randomly selected office hour, the number of student arrivals is 3.
the diagram below shows the graph of y=x^2+2x-3 for the domain -4 2. use the graph to determine the scale used on the x- axis, the value of y for which x= 1.5, the values of x for which y=0 and the range of values of y, giving your answer in the form a
Answer:
no sisiejdirjr diendieje jdisjeidi
Answer:
awnser is b
Step-by-step explanation:
eg 2023 ........................................
solve the following pair of simultaneous equation graphically
X+2y=3,2x-y=7
Answer:
(x, y) = (3.4, -0.2)
Step-by-step explanation:
You want a graphical solution for the system of equations ...
x +2y = 32x -y = 7GraphThe graph and solution are shown in the attachment. A graphing calculator is a nice bit of useful technology for this. The solution is ...
(x, y) = (3.4, -0.2)
The first line has x-intercept 3 and y-intercept 1.5.
The second line has y-intercept -7 and slope 2. It crosses the x-axis at x=3.5, so will cross the first line in the 4th quadrant.
What is the volume of the solid figure?
Enter your answer in the box
Volume of the composite shape is = 114 ft³
What is volume of composite shape?Volume is a measure of three-dimensional space.
A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes as well.
Now, According to the question:
The shape above shows two cuboid joined together.
Volume of the base cuboid = lbh
= 6×3×1 = 18ft³
Volume of the second cuboid = lbh
= 4×3×8 = 96 ft³
Volume of the composite shape = 18ft³ + 96ft³
= 114 ft³
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Juan the trainer offers two solo workout plans: Plan A and Plan B. Each client does either one or the other (not both). Juan trained on Wednesday and Thursday last week. The table below shows the number of Plan A and Plan B clients Juan trained each day and the total time (in hours) he trained.
Wednesday Thursday
Number of
Plan A workouts
Number of
Plan B workouts
Total time
(in hours)
Let be the length (in hours) of each Plan A workout.
Let be the length (in hours) of each Plan B workout.
(a) Write a system of equations that could be used to find the length (in hours) of each type of workout.
(b) How long (in hours) was each type of workout?
A system of equations that could be used to find the length (in hours) of each type of workout
7a + 9b = 12
5a + 3b = 6
Solve this system of equations by multiplying both sides of one of the equation so that when the equations are added or subtracted there will only be one variable.
-I will multiply both sides of the 2nd equation by -3
-3*(5a + 3b) = 6*-3
-15a - 9b = -18
-Now I will get rid of the variable b by adding the two equations together.
7a + 9b = 12
+ -15a - 9b = -18
-8a = -6
a = -6/-8
a= 3/4 (45 minutes)
-Now plug 3/4 into one of the original equations as a to solve for b.
-I will use the 2nd original equation.
5a + 3b = 6
5(3/4) + 3b = 6
15/4 + 3b = 6
3b = 9/4
b = 9/12 = 3/4 (45 minutes)
Both workout plans last the same amount of time.
Plan A lasts 45 minutes.
Plan B lasts 45 minutes.
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A circle has a diameter of 26 feet what is the circumference
Use 3.14 for pie and do not round your answer be sure to include the correct unit in it in your answer
The circumference of a circle with a diameter of 26 feet is approximately 81.64 feet.
What is the circumference?
The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center. A meridian is any great circle passing through a point designated as a pole.
The formula for the circumference of a circle is 2 * π * r, where r is the radius of the circle.
To find the circumference, we first need to find the radius of the circle.
The diameter of the circle is 26 feet, so the radius can be calculated by dividing the diameter by 2:
r = 26 feet / 2 = 13 feet
Now that we know the radius, we can find the circumference:
C = 2 * π * r = 2 * 3.14 * 13 = 81.64 feet
Therefore, the circumference of a circle with a diameter of 26 feet is approximately 81.64 feet.
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Say you have a 92% in a class and you do 2 assignments and they are both worth 50% of your grade. And you get a 2/5 on one of them and a 5/5 on the other. Whats the resulting grade?
Answer:
70%
Step-by-step explanation:
Find the gradient of the line that passes through (3, 7) and (1, 10).
Answer:
-1.5
Step-by-step explanation:
The gradient of a line can be found using the formula:
gradient = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
So for the line that passes through (3, 7) and (1, 10), the gradient can be found as:
gradient = (10 - 7) / (1 - 3)
gradient = 3 / -2
gradient = -1.5
So the gradient of the line that passes through (3, 7) and (1, 10) is -1.5.
Shawn's retirement party will cost $6 if he invitês 3 guests. If there are 8 guests, how much
will Shawn's retirement party cost? Assume the relationship is directly proportional.
Step-by-step explanation:
Shawns party will cost $16 if there are 8 guest
The accompanying histogram shows the life expectancies at birth for 190 countries as collected by an international health agency. a) Which would you expect to be larger: the median or the mean? Explain briefly. b) Which would you report: the median or the mean? Explain briefly.
What is the azimuth of an object that is ten degrees south of east?
Answer:
Step-by-step explanation:
135°
Quite commonly, azimuths or compass bearings are stated in a system in which either north or south can be the zero, and the angle may be measured clockwise or anticlockwise from the zero.
Classify each ordered pair as a solution or not a solution of the inequality y
a inequality y <2/7 x − 5.
The ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is y<2/7x-5.
Here,
Put (x, y)=(21, 0) in the given inequality, we get
0<2/7(21)-5
0<1
So, it is solution
Put (x, y)=(6, -4) in the given inequality, we get
-4<2/7(6)-5
-4<12/7-5
-4<1.7-5
-4<-3.3
So, it is solution
Put (x, y)=(0, -5) in the given inequality, we get
-5<2/7(0)-5
-5<-5
Which is not true, it is not a solution
Put (x, y)=(7, -3) in the given inequality, we get
-3<2/7(7)-5
-3<-3
Which is not true, it is not a solution
Therefore, the ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.
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The taj Mahal in India is a square about 95.4 on each side.What is the area of the taj mahal?
The area of the Taj Mahal is 9092.16 square meters (97,890.56 square feet).
What is area of a square?The quantity of square units required to completely cover a square is known as the area of a square. The territory that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. The measurement is made using square units, with square meters serving as the standard unit.
The Taj Mahal has an area of 9092.16 square meters (97,890.56 square feet). We utilise the formula for calculating the area of a square, which is length x width. The Taj Mahal's length and width are both 95.4 metres, therefore we just multiply these two values together. 9092.16 square meters = 95.4 × 95.4 square meters (97,890.56 square feet). This is the Taj Mahal's area.
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