In order to dilate a line segment by 1/ 2, every coordinate point of the end point of the line segment is multiplied by the scale factor ½.
Dilation refers to a process of changing the size of an object or shape by either increasing or decreasing its dimensions by some scaling factors. It is a type of transformation, which is used to resize the object, making the objects larger or smaller. This transformation produces an image that is the same in shape as the original but there is a difference in the size. A dilation should either stretch or shrink the original shape and is expressed by the term “scale factor.”
When a dilation creates a larger image, it is called enlargement and when a dilation creates a smaller image, it is called reduction. If the scale factor is 1/2, every coordinate point of the original segment line is multiplied by the scale factor 1/2.
Learn more about Dilation:
https://brainly.com/question/10253650
#SPJ4
Which of the following is not a measure of variability of a data set?
a.
variance
b.
standard deviation
c.
median
d.
coefficient of variation
e.
Range
Median is not a measure of variability of a data set.
A collection of data is known as a data set (or dataset). In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable.
The data set includes values for each of the variables, such as the object's height and weight, for each set member. Data sets can also be made up of a group of files or documents.
The information supplied in a public open data repository is measured in the open data discipline using data sets. Over one million data sets are collected through the European portal.
To learn about Dataset :
https://brainly.com/question/17290441
#SPJ4
Evaluate the expression if b=3 and c=1/3.
3c / (2b²)
After evaluation we get the above expression 1/18
What is mathematical expression?It is the mathematical statement that expresses the method of a mathematical operation in a symbolic way. An expression is developed based on two or more terms along with operator. The terms are variables and numbers. In a word, an expression is either combination of numbers, operators or numbers, variables, operators.
How to evaluate the above expression?we are given an expression
3c/ (2b²)
the value of b and c are also given, b= 3 and c = 1/3
The expression is written in fractional form that has 2 numbers and 2 variables. The number are 2 and 3, variables are c and b
The numerator 3c and the denominator 2b²
if we put the value of b and c
(3×1/3) / (2×9) =1/18
hence the result 1/18
To know more about mathematical expression visit:
https://brainly.com/question/29176690
#SPJ1
How do you solve for y varies inversely as x?
The relationship between y and x can be equation as y = k/x, where k is a constant that does not change.
The equation y varies inversely as x means that as the value of x increases, the value of y decreases, and vice versa. To solve for y, we can use the general equation y = k/x, where k is a constant. This equation states that the value of y is directly proportional to the reciprocal of x.
1. Start by understanding that when two variables are inversely proportional, they follow the equation
y = k/x.
2. The constant, k, is a number that will remain the same throughout the equation.
3. For example, if y varies inversely as x, and
y = 2 when x = 4, then k = 8.
4. Therefore, the equation
y = k/x becomes y = 8/x.
5. To solve for y when x = 5, substitute x = 5 into the equation and solve: y = 8/5
= 1.6.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
Let u=1nx and v=1ny. Write y^3x^5 in terms of u and v
The expression y³x⁵ in terms of u and v is [tex]e^{3u} e^{5v}[/tex]
what is the natural logarithm?The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x. The equation being [tex]e^{\ln x}=x[/tex]
Given here, the polynomial expression y³x⁵ where [tex]{\ln x}=u[/tex] and [tex]{\ln y}=v[/tex] thus, [tex]e^{v} =y[/tex] and [tex]e^{u} =x[/tex]
∴ , y³x⁵=[tex]e^{3u}e^{5v}[/tex]
Hence, The expression y³x⁵ in terms of u and v is [tex]e^{3u} e^{5v}[/tex]
Learn more about natural logarithms here:
https://brainly.com/question/30085872
#SPJ1
Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 400 minus quantity y minus 110 end quantity squared over 2304 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? round your answer to the nearest whole number.
The width of the cooling tower at the base of the structure as calculated from the data is 40 meters.
The equation which is given is ,
x²/400 -(y-90)²/1600=1
To calculate the width,
Cooling tower width =2√400
=2×20
=40 meters
Therefore the width is 40 meters.
A cooling tower is a type of heat removal device which uses water to remove waste heat from a process and discharge it into the atmosphere.
Similarly, an industrial cooling tower works by removing heat from water by evaporating little percentage of the water that is recirculated through the unit. When warm water and cooler air mingle, the latent heat of vaporization is released, causing the water to cool.
To learn more about width
brainly.com/question/25855344
#SPJ4
The width of the cooling tower at the base of the structure is 16 meters.
x = 16 meters
x^2/400 - (y - 110)^2/2304 = 1
x^2/400 = (y - 110)^2/2304 + 1
400x^2 = 2304(y - 110)^2 + 2304
400x^2 = 2304y^2 - 514240y + 2574304
x^2 = 514240y/400 - 2574304/400 = 514.6y - 6435.76
x = √(514.6y - 6435.76)
For y = 0, x = 16 meters
Therefore, the width of the cooling tower at the base of the structure is 16 meters (rounded to the nearest whole number).The width of the cooling tower at the base of the structure is 16 meters.
learn more about width here
brainly.com/question/25855344
#SPJ4
HELP PLEASE FAST !!
Order the numbers from least (top) to greatest (bottom) PICTURE ATTACHED!!
Answer:
-9
-4
1
|-2|
|-3|
|-5|
|-6|
Step-by-step explanation:
| |
This symbol means whatever number inside of it turns to positive
Answer:
-9
-4
1
|-2|
|-3|
|-5|
|-6|
Ms. Mayer's class has 8 students who are 5 feet or taller. That is 25% of the total number of students in her class. What is the total number of students in Ms. Mayer's class?
The total number of children in Ms. Mayer's class is 32.
What is Percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:
Percentage = (value / total value) * 100%
Let Total number of student = X
Therefore;
25% of X = 8
(25/100)X = 8
Therefore;
X = 8 / (25/100)
X = 800/25
X = 32
Find out more on Percentage at: brainly.com/question/24304697
#SPJ1
Order the rational numbers from least to greatest
-3.11,-3.1,-3.01
Answer: -3.11, -3.1, -3.01
Explanation:
We are comparing:
-3.11
-3.10
-3.01
-3.11 < -3.10 < -3.01
On Monday, jack rode 4 miles on a bike. On Tuesday, he rode 4 times more than he did Monday. On Wednesday, he rode an additional 5 miles.
How many miles has jack ridden so far this week?
Answer:
She has ridden 25 miles this week
Step-by-step explanation:
She rode 4 miles on monday to start off the week. Then she rode 4 times the amount he did on Monday, so multiply 4x4. Then he rode 5 more miles so add 5 and receive the answer of 25 miles.
Equation:
1. Write Equation: 4+(4x4)+5=
2. Solve for parenthesis: 4+16+5=
3. Solve: 4+16+5=25
-Hope this helped & Happy New Years
Based on data collected by the National Center for Health Statistics and made available to the public, an estimate of the percentage of adults who at some point in their life have been told they have hypertension is 23.53%. If we select a simple random sample of 20 US adults and assume that the probability that each has been told that he or she has hypertension is 0.20, find the probability that the number of people in the sample who have been told that they have hypertension will be (a) exactly three (b) at least three (c) at most five (d) between six and ten, inclusive
The answer is (a) exactly three. The probability of selecting exactly three adults out of a sample of 20 who have been told that they have hypertension is calculated using the Binomial Distribution. The probability can be calculated using the formula:
P(X=3) = (20C3) * (0.20^3) * (0.80^17) = 0.1504The probability of selecting at least three adults out of a sample of 20 who have been told that they have hypertension is calculated using the Cumulative Binomial Distribution. The probability can be calculated using the formula:
P(X>=3) = 1 - P(X<3) = 1 - P(X<=2) = 1 - (20C0) * (0.20^0) * (0.80^20) - (20C1) * (0.20^1) * (0.80^19) - (20C2) * (0.20^2) * (0.80^18) = 0.9991The probability of selecting at most five adults out of a sample of 20 who have been told that they have hypertension is calculated using the formula:
P(6<=X<=10) = P(X<=10) - P(XLearn more about probabilities of patients with hypertension:
https://brainly.com/question/22595986
#SPJ4
Points A,B, and C are collinear Point B is between A and C. Solve for x
The required values of x in the collinear points A, B and C are -3, 1, -12 and 12
What are collinear points?Points that lie on the same line are called collinear points.
Given that, Points A, B, and C are collinear point B is between A and C.
We will use here segment addition postulate, to solve each part.
The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC.
1) AB = x+15, BC = x+13 and AC = 22
x+15+x+13 = 22
2x = 22-28
2x = -6
x = -3
2) BC = 2x-2, AC = 3x-3 and AB = 4
3x-3-(2x-2) = 4
3x-3-2x+2 = 4
5x = 5
x = 1
3) BC = x+28, AB = 2x+28 and AC = 12
x+20+2x+28 = 12
3x+48 = 12
3x = -36
x = -12
4) BC = x-8, AB = 9 and AC = 2x-11
x-8+9 = 2x-11
x+1 = 2x-11
x = 12
Hence, the values of x are -3, 1, -12 and 12
For more references on collinear points, click;
https://brainly.com/question/1593959
#SPJ2
someone please help asap!!!
Answer:
y = -4x + 1
Step-by-step explanation:
We find the equation of a line passing through two given points using the generalized slope-intercept which is
y = mx + b
m is the slope(gradient) of the line and b is the y-intercept i.e. the y-value where it crosses the y-axis. This is nothing but the value of y when x 0
Start by finding the slope first
Slope, m = (y2-y1)/(x2-x1)
Taking(x1, y1) as (-1, 5) and (x2, y2) as (2, -7)
we get
y2 - y1 = -7 -5 = -12
x2 - x1 = 2 - (-1) = 1 2 + 1 = 3
m = -12/3 = -4
Equation would be
y = -4x + b
To find b, choose a known value for x and its corresponding y value and solve for b
Let's take (-1, 5)
Subbing this into the equation gives
5 = (-4)(-1) + b
5 = 4 + b
or b = 1
So the equation of the line in slope-intercept form is
y = -4x + 1
I am so confused on this question and do not understand how to do the topic.I need help so bad.What I need help with is like how do I get the answer on the right.
The distance that the cyclist would ride in 8 seconds is; 97.6 yards
How to find the linear equation from a table?The general form of the equation of a line in slope intercept form is;
y = mx + b
where;
m is slope
b is y-intercept
Now, from the function table, we are given the coordinates;
(2, 24.4), (3, 36.6), (5, 61), (6, 73.2)
Now, we can find the slope from the formula;
m = (y₂ - y₁)/(x₂ - x₁)
m = (36.6 - 24.4)/(3 - 2)
m = 12.2
At x = 0, we have;
12.2 = (24.4 - y)/(2 - 0)
2(12.2) = 24.4 - y
y = 24.4 - 24.4
y = 0
Thus, the equation is; y = 12.2x
Thus, at 8 seconds, we have;
y = 12.2(8)
y = 97.6 yards
Read more about Linear Equation at; https://brainly.com/question/28732353
#SPJ1
the area of a rectangular pool is 7980m^2. if the width if the pool is 84m what is its length?
Answer:
95 m would be the answer.
Decrease £19064.67 by 19.5%
Give your answer rounded to 2 DP.
Answer:
£ 15347.06
Step-by-step explanation:
Percentage:First find 19.5% of 19064.67.
Decreased amount = percentage of decrease * total amount
= 19.5% * 19064.67
= 0.195 * 19064.67
= £ 3717.61
Amount after decrease = 19064.67 - 3717.61
= £ 15347.06
Solve for m.
m+ < 1/4 < -1 2/5
O
0 m < -1 13/20
Om < -1 3/20
0 m > -1 3/20
O m > -1 13/20
The solution of the inequality m + 1/4 < -[tex]1\frac{2}{5}[/tex] is m < [tex]-1\frac {13}{20}[/tex].
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
We have the inequality expression,
m + 1/4 < -[tex]1\frac{2}{5}[/tex]
Simplifying,
m + 1/4 < -7/5
Subtracting 1/4,
m < -7/5 - 1/4
m < (-28-5)/20
m < -33/20
m < [tex]-1\frac {13}{20}[/tex]
Therefore, the solution is m < [tex]-1\frac {13}{20}[/tex].
To learn more about the inequality;
brainly.com/question/28823603
#SPJ1
A line passes through the point (-4, 3) and has a slope of -2.
Write an equation in point-slope form for this line.
Answer:
i agree
Step-by-step explanation:
A line passes through the point (-4, 3) and has a slope of -2 will be y = - 2x - 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is - 2. Then the equation of the line is given as,
y = - 2x + c
The equation passes through the point (-4, 3). Then the value of 'c' is given as,
3 = - 2(-4) + c
3 = 8 + c
c = - 5
The equation of the line is given as,
y = - 2x - 5
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
Why is it called secant line?
Secant line is the name given to any line that intersects a circle at two or more points. This line is called "secant" because it comes from the Latin word secare, which means to cut.
In mathematics, the secant line is used as a tool for finding the length of an arc, area of a sector, and other geometric measurements. The secant line is also used in calculus to calculate derivatives and integrals of functions.
The secant line is formed by two points on a circle’s circumference, and its slope is determined by those points. Its slope is calculated by the difference between the two points divided by the product of the radius of the circle and the angle made by the two points.
Learn more about Secant Line here:
https://brainly.com/question/16310158
#SPJ4
Find the algebraic representation of the reflection below.
The algebraic representation of the reflection in the image is the one in option A.
(x, y) → (-x, y)
What is the algebraic representation of the reflection?Here we have an image with two moons, such that one is the reflection of the other.
Notice that the reflection is across the vertical axis (it is the y-axis). So the y-values don't change after the reflection, only the x-values change.
So we will have a change of sign on the x-value, then the reflection must be written as:
(x, y) → (-x, y)
In this way we can conclude that the correct option is A.
Learn more about reflections by reading:
https://brainly.com/question/4289712
#SPJ1
2x-0.4=1+1.8x solve for X
Answer:
x=7
Step-by-step explanation:
2x-0.4=1+1.8x
Subtract 1.8x from both sides
0.2x-0.4=1
Add 0.4 to both sides of the equation
0.2x=1.4
Divide both sides by 0.2
x=7
kyle practices the piano trombone and violin. he dedicates one fourth of this practice time to piano, four ninths of his time to the trombone, and rest of his time to the violin. what fraction of kyle's practice time is spent playing the violin?
Answer:
Step-by-step explanation:
1/4 + 4/9 + n= total amount of time spent on all of the instruments.
1/4 + 4/9=
9/36 + 16/36= 25/36 (time on piano and trombone)
36/36- 25/36= 11/36- total time spent on violin
Please help as fast as you can
I think the answer is D (Day) ...........
Help aspp please thank you!!!
Answer:
YES ITS A DIRECT VARIATION
Step-by-step explanation:
explanation in the picture
A bag contains 222 red marbles, 333 green marbles, and 444 blue marbles. If we choose a marble, then another marble without putting the first one back in the bag, what is the probability that the first marble will be green and the second will be red?
There is a 7.4% probability that the first marble will be green and the second will be red.
To calculate the probability, you will need to use the following formula:
P(A and B) = P(A) x P(B).
In this case, P(A) is the probability of picking a green marble on the first pick and P(B) is the probability of picking a red marble on the second pick. Using this formula,
we get P(A and B) = 333/999 x 222/998 = 0.074,
which is the probability of picking a green marble on the first pick and a red marble on the second pick.
So, there is a 7.4% chance of this happening.
To learn more about probability, click here:
https://brainly.com/question/24756209
#SPJ4
solve 0 =3 x + 4 - x
Answer:
x = -2
Step-by-step explanation:
Combine like terms
0 = 2x + 4
-4 = 2x
-2 = x
Need this solved! precal please help if you can Thx
Answer:
[tex]f(-1)=-11\\f(0)=16\\f(2)=22[/tex]
Step-by-step explanation:
[tex]\displaystyle f(-1)=3(-1)-8=-3-8=-11\\f(0)=3(0)+16=16\\f(2)=3(2)+16=6+16=22[/tex]
Look at the figure below. The area of the rectangle is 200 in².
What is the radius of the semicircle?
Answer:
r≈11 m or 1/2πr2 /=fraction
Step-by-step explanation:
too many fractions to put but yeah have fun with answer though i'm 1 hour late
The radius of the semicircle given in the given figure is 10in.
What is a semicircle?A semicircle is a half circle created by splitting a circle into two equal parts. It is created when a line pierces the circle's center and touches its two ends. The diameter of the circle is the name given to this line.
In the given figure, A semicircle is drawn on the base of the rectangle.
Since the Area of the rectangle is 200 inches square and the height of the rectangle is 10 inches.
Thus, the Base of the semicircle = 200/10 = 20in.
Since the Base of the rectangle is equal to the diameter of the semicircle that is 10.
Therefore, the semicircle's radius in the provided illustration is 10 inches.
Learn more about semicircles here:
https://brainly.com/question/29140521
#SPJ1
Complete question:
The probability that both of two tossed coins will come down heads (or tails) is: 1/4 x 1/2 or 1/8 1/2 x 1/2 or 1/4 1/4 x 1/4 or 1/16.
Answer:
B
Step-by-step explanation:
The probability that both the two tossed coins will come down heads (or tails) is 1/2 x 1/2 or 1/4.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
To calculate the probability of two independent events happening at the same time, you multiply their individual probabilities.
In this case, the two events are the two coin tosses coming up heads (or tails).
The probability of the first coin coming up heads (or tails) is 1/2, and the probability of the second coin coming up heads (or tails) is also 1/2, so the probability of both of them coming up heads (or tails) is (1/2) x (1/2) = 1/4.
Hence, the correct answer would be an option (B).
Learn more about probability here:
brainly.com/question/11234923
#SPJ2
How many solutions exist for the given equation 12x 1 3 4x 1 2?
There are existing infinite solutions for the given equation 12s + 1 = 3 ( 4s + 1) - 2.
Solving the equation,
12s + 1 = 3 ( 4s + 1) - 2
12s + 1 = 12s + 3 -2
12s + 1 equals to (=) 12s + 1
Bringing constant to one side of the equation and variables to the other side of the equation so that equation could be solved
+ 12s - 12s = + 1 - 1
0 = 0
This shows that the given equation has infinite solutions because after solving it gives a solution where both sides are equal.
"
Complete question:
How many solutions exist for the given equation 2s + 1 = 3 ( 4s + 1) - 2?
"
You can learn more about infinite solution at
https://brainly.com/question/14648711
#SPJ4
Let E be the region enclosed by the paraboloids z = x² + y2 and z = 2 – x2 - y2. Then SSS Vox2 + y2 DV = E 21 1 2-22 (A) S S S rdz dr do 0 0 -2 21 1 2-r2 (B) I ſ T 12 dz dr de 0 0 2 1 -r (C) SS S rdz dr do 0_0_12 (A) Sj rdz dr do 0 0 72 21 1 2-22 (B) į jį r2 dz dr do 0 0 72 1 1 2,2 (C) S S S rdz dr de 00 p2 1 1 2–,2 (D) ſi s 12 dz dr do 00 p2 21 1 -2 (E) IS S rdz.dr do 0 0 2-2
Let E be the region enclosed by the paraboloids z = x² + y² and z = 2 – x² - y² , then ∫∫∫(√x² + y²)dV is equals to the [tex]∫^{\pi}₀∫^{1} ₀∫^{2 - {r}^{2}} ᵣ₂ r² dz dr dθ ,[/tex].
We have two equations of paraboloids are z = x² + y² and z = 2 – x² - y² . Let E be the region enclosed by the (1) and (2). We have to determine the value of volume integral ∫∫∫(√x² + y²)dV in polar form. Now, change the Cartesian co-ordinates (i.e., x and y) into polar coordinates ( i.e., r and θ ). In polar coordinates, x = r cosθ ; y = r sinθ then, x² + y² = (r cosθ)² + (r sinθ)²
= r²cos²θ + r²sin²θ = r²(sin²θ + cos²θ)
= r² or √x² + y² = √r² = r
Plugging the value in curve equation,
z = x² + y² = r² and z = 2 – x² - y² = 2 - r²
i.e., z varies from r² to 2 - r²
and θ varies from 0 to π ( see in graph) and r varied from 0 to 1. Also, dxdy = r dr dθ. So, the triple integral or volume integral in polar coordinates is
[tex]∫^{\pi}₀∫^{1} ₀∫^{2 - {r}^{2}} ᵣ₂ r² dz dr dθ ,[/tex]
Hence, we get the required expression in polar coordinates.
To learn more about triple integral , refer
https://brainly.com/question/14179438
#SPJ4
