[tex]Let \: the \: two \: points \: be \: \underline{\underline{A( x_{1} ,y_{1})}} \: and \: \underline{\underline{B \: ( x_{2}, y_{2})}}[/tex]
Then ,
[tex]\boxed{d(AB) = \sqrt{ {( x_{2} - x_{1}) }^{2} + {( y_{2} - y_{1}) }^{2} } }\\ [/tex]
where , d(AB) is the distance between the two points A and B.
hope helpful! :)
Answer:
the Distance Between the two points a and b
Step-by-step explanation:
Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
8w + 5?? Please help i'm so DUM
The required value of w in the given expression is 1, as per the given conditions.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
The question seems to be incomplete, assume that the given expression 8w + 5 = 13
So
8w + 5 = 13
simplify
8w = 13 - 5
w = 8 / 8
w = 1
Thus, the required value of w in the given expression is 1, as per the given conditions.
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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 3
2 2
3 10
4 9
5 7
6 3
Determine the probability that a student studied for exactly 4 hours. Round to the nearest hundredth.
0.74
0.35
0.26
0.11
Answer:
0.26
Step-by-step explanation:
There are 1 + 3 + 2 + 10 + 9 + 7 + 3 = 35 total students. Additionally, there are 9 students who work exactly 4 hours. Thus, the probability is 9/35, or 0.26 rounded to the nearest hundredth.
Answer:
26
Step-by-step explanation:
1+3+2+10+9+7+3= 35
35 divided by 4
let a be a 3x2 matrix. suppose we know that u=[2 -3] and v=[4 2] satisfy the equations au = a and av =b. find a solution to x .
The solution to x, when the equations au = a and av =b are satisfied, will be x = [0 0].
Given that u = [2 -3] and v = [4 2] satisfy the equations au = a and av = b, we need to find a solution to the equation ax = b.
Let's express the matrix an as a column vector of its columns: a = [a1 a2]. Now, we have the following equations:
a*u = a
[a1 a2] * [2 -3] = [a1 a2]
This yields two equations:
2a1 - 3a2 = a1
2a1 - 3a2 = a2
Simplifying these equations, we get:
a1 = 3a2 ...(1)
a2 = 2a1 ...(2)
Substituting equation (2) into equation (1), we have:
a1 = 3(2a1)
a1 = 6a1
Solving for a1, we find a1 = 0.
Substituting this value back into equation (2), we have:
a2 = 2(0)
a2 = 0
Therefore, a solution to x is x = [0 0].
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A house has 12 rooms (10 bedroom and 2 living rooms). We want to paint 4 yellow, 5 red and 3 purple. We do not want the living rooms to be the same color. In how many ways this can be done?
Total number of ways to paint rooms is 19,740.
We can solve this problem using the combinatorics. First, we choose the color for the living rooms, which can be done in 3*2 = 6 ways (yellow, red, or purple). Then, we choose the colors for the remaining 10 rooms.
Case 1 : living room is yellow and red
Then remaining colors are 3 yellow, 4 red, 3 purple
number of ways to paint living room = 2
number of ways to pain bedroom = 10!/(3! 4! 3!)
So number of ways = 2 * 10!/(3! 4! 3!) = 8400
Case 2 : living room is yellow and purple
Then remaining colors are 3 yellow, 5 red, 2 purple
So number of ways = 2 * 10!/(3! 5! 2!) = 5040
Case 3 : living room is red and purple
Then remaining colors are 4 yellow, 4 red, 2 purple
So number of ways = 2 * 10!/(4! 4! 2!) = 6300
Total number of ways = 8400 + 5040 + 6300 = 19,740
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is it possible for one of φ∧(ψ ∨θ) and (φ∧ψ)∨(φ∧θ) to be true and the other false?
By examining the truth table, we can determine the two expressions are equivalent and it is possible for one of them to be true and the other false.
Given two Boolean expressions, it is possible for one of them to be true and the other false if they are not equivalent. For example, consider the two expressions: φ ∧ (ψ ∨ θ) and (φ ∧ ψ) ∨ (φ ∧ θ).
It is possible to construct a truth table for these two expressions, which shows all possible combinations of truth values for φ, ψ, and θ, along with the corresponding truth values for the two expressions.
Boolean logic is a branch of mathematical logic that deals with binary operations (i.e., true or false values) and is often used in computer science. One of the basic operations in Boolean logic is the logical conjunction (denoted by ∧), which represents the and operator. For example, if φ and ψ are two propositions, then φ ∧ ψ is true if and only if both φ and ψ are true.
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A geometry student is flying a
kite with 120-ft of string and their
hand 4-ft from the ground. The
angle between the horizontal and the kite is 30°. Find the height of the kite from the ground. Round to the nearest tenth
The height of the kite from the ground is 54ft
How to find the height?Information involves angles of elevation that can be solved using the trigonometric ratios of sine.
The question reads that a geometry student is flying a
kite with 120-ft of string and their
hand 4-ft from the ground
The height is found by sin30 = h+4/120
Making h the subject of the relationship
h+4 = 120 * 0.5
h= 60-4
Therefore the height of the kite is 54ft
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It takes 6 cubic inches of colored sand to fill a plastic cone. How many cubic inches will it take to fill a plastic cylinder with the same base and height as the cone?.
The plastic cylinder will take 18 cubic inches of sand to fill it.
Ratio of volume of a cylinder to the volume of a cone:Let 'r' and 'h' be the radius and height of the both cylinder and cone, then the ratio of the volume of the cylinder to the volume cone can be calculated as given below
=> Volume of cylinder: Volume of cone
=> πr²h : 1/3 πr²h
=> 1: 1/3
=> 3: 1
Ratio of volume of a cylinder to the volume of a cone = 3: 1
which means the volume of the cone is one-third of the volume of the cylinder
Given that
It takes 6 cubic inches of colored sand to fill a plastic cone.
The volume of the cone = 6 cubic inches
It is also given that cylinder has the same base and height as the cone
As we know the volume of the cone is one-third of the volume of the cylinder
Volume of cone = (1/3) × Volume of cylinder
=> Volume of cylinder = 3 × Volume of cone
Volume of the given cylinder = 3 × 6 cubic inches
= 18 cubic inches
Therefore,
The plastic cylinder will take 18 cubic inches of sand to fill it.
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The last time Zach checked, the corn stalks in his back yard were 50 inches tall. Now they are 5.8% taller. How tall are the stalks now?
Answer:
52.9 inches.
Step-by-step explanation:
Let's call the current height of the corn stalks as "h". Then the increase in height will be 0.058 * 50 = 2.9 inches.
So, h = 50 + 2.9 = 52.9 inches.
match the direction fields labeled a through d with the differential equation below. 1. y′=y 2x 2. y′=y−2x 3. y′=1−xy 4. y′=xy y
The solutions that match the given differential equation are a)y=0 and b)y=2x.
The differential equation is a homogeneous linear differential equation with constant coefficients, which can be written in the form of y" + p(x)y' + q(x)y = 0. The general solution to this type of equation is y = c1e^(rx) + c2e^(rx) where r is the root of the characteristic equation r^2 + p(x)r + q(x) = 0.
In this case, the equation is of the form xy'' - y' = 0. By dividing both sides by x, we get y'' - (1/x)y' = 0, which is a homogeneous linear differential equation with constant coefficients. The characteristic equation is r^2 - (1/x)r = 0. The roots of this equation are r1 = 0 and r2 = 1/x.
Therefore, the general solution to this differential equation is y = c1 + c2x.
y=0 is a solution of the differential equation since it satisfies the equation when plugged in.
y=2x is also a solution of the differential equation since it also satisfies the equation when plugged in.
y=2x^2 and y=2 are not solutions of the differential equation because when plugged into the equation they don't satisfy it.
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The diagram shows a circle with centre O.
A, B & C lie on the circumference of this circle.
Given that AC is a diameter of the circle and ∠ACB = 59°, find the size of ∠BAC as highlighted in the diagram.
The required angle ∠BAC is equal to 31
What is the angle sum property of a triangle?The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°
Given here: ∠ACB = 59° and the diameter of the circle as AC
Now since AC is diameter , When two angles are subtended by the same arc, the angle at the centre of a circle is twice the angle at the circumference.
Thus ∠ABC= 1/2 × 180
=90
Thus ∠BAC= 180-90-59
= 31
Hence, The required angle ∠BAC is equal to 31
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Here is part of the menu price list at a takeaway. Chips Peas Rice Pickled onion Fish 45p Sausage 90p Bread roll 25p Samosa £1.20 b) Taha buys one fish, a portion of peas and a pickled onion. lowan buys a portion of rice, a sausage and a bread roll. How much more (in £) does Taha pay than lowan? Optional working Answer: £ £2.70 £1.60 30p 75p
The required money that Taha paid more than lowan is £0.6, as per the given condition.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Taha buys one fish, a portion of peas, and pickled onion.
taha paid = 2.70 + 0.45 + 0.25
= £3.40
Lowan buys a portion of rice, a sausage, and a bread roll.
Total money lowan to pay
= 0.90 + 1.60 + 0.30
= £2.80
Money Taha pays more than lowan = 3.40 - 2.80
= £0.6
Thus, the required, money that Taha paid more than lowan is £0.6, as per the given condition.
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Given the diagram below, solve for x.
The solution for x on the diagram is given as follows:
x = 111.
How to obtain the solution for x?The angle measures in this problem are given as follows:
x and (x - 42)º.
They are on the same side relative to the transversal line, and between the two parallel lines, hence they are classified as consecutive interior angles.
Consecutive interior angles are supplementary, as the sum of their measures is of 180º, hence the value of x is obtained as follows:
x + x - 42 = 180
2x = 222
x = 222/2
x = 111.
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how do I find a probability?
Answer:not sure
Step-by-step explanation:
Answer:
See explanation and examples below.
Step-by-step explanation:
The probability that an event (desired outcome) will occur is the quotient of the number of ways the event can occur (desired outcomes) and the total number of possible outcomes.
For example, consider a die. A die is a 6-faced cube with numbers 1 through 6 on its faces.
The total number of possible outcomes is 6 since it can land with any face with numbers 1 through 6 facing up.
What is the probability if getting a 5?
Here the desired outcome is a 5. There is only one desired outcome since only 1 face has a 5. The total number of possible outcome is 6.
p(5) = 1/6
The probability of getting a 5 is 1/6.
Another example:
A spinner has 4 sections of equal size.
1 section is red.
1 section is blue.
1 section is green.
1 section is yellow.
What is the probability of landing on red?
Desired outcome: landing on red
Number of desired outcomes: 2
Total number of possible outcomes: 4
p(red) = 1/4
Using the same spinner, what is the probability of landing on yellow or green?
Landing on the green section or landing on the yellow section are both desired outcomes, so the number of desired outcomes is 2.
The total number of outcomes is 4.
p(yellow or green) = 2/4 = 1/2
Which angle must be congruent to /BAC ?
Answer: CDB
Step-by-step explanation: Congruent angles are angles that are identical to each other. For a more in-depth explanation, Congruent angles are basically when two angles "have the same shape and size, or if one has the same shape and size as the mirror image of the other". Out of the choices given, CDB is the most identical to BAC. If you rotate CDB with your mind, you'll notice that you get BAC.
the following picture, a hydraulic lift balances two masses. solve for m2 if m1 = 70 kg , and the diameters are d1 = 1.0 m , and d2 = 3.0 m .\
The equation for a hydraulic lift can be used to calculate the force on each mass. F1 = F2
m2 = 210 kg
Using the equation for a hydraulic lift, the force on each mass can be calculated.
F1 = F2
(m1 x g) x (d1/d2) = (m2 x g)
(70 kg x 9.8 m/s2) x (1.0 m/3.0 m) = (m2 x 9.8 m/s2)
210 kg = m2 x 9.8 m/s2
m2 = 210 kg/9.8 m/s2
m2 = 21.43 kg
m2 = 210 kg (rounded up)
The equation for a hydraulic lift can be used to calculate the force on each mass. F1 = F2
(m1 x g) x (d1/d2) = (m2 x g)
Plug in the given values:
(70 kg x 9.8 m/s2) x (1.0 m/3.0 m) = (m2 x 9.8 m/s2)
Solve for m2:
m2 = 210 kg/9.8 m/s2
m2 = 21.43 kg
m2 = 210 kg (rounded up)
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PLEASE HELP ASAP SOLVE WITH EXPLANATION 3
Answer:
3.4 in²
Step-by-step explanation:
Information we must know:
The radius of the circle is 2 inches so the diameter would be 4!The diameter of the square is equal to one side of the squareArea of circle = πr²Area of square = l²1) Find the area of the circle
π × 2² = 12.5663706144We won't round up or down until the last step to get a more accurate answer!2) Find the area of the square around the circle
4² = 163) Subtract!
16 - 12.5663706144 = 3.43362938563.4 in²Have a lovely day :)
Answer:
3.4 in²
Step-by-step explanation:
We can solve for the area of the blue portion of this figure by subtracting the area of the circle (the area that is NOT blue) from the area of the surrounding square.
First, we can solve for the area of the square using arithmetic.
In this problem, the side length is twice the radius ([tex]r[/tex]) of the circle (given as 2 in), since the circle is circumscribed inside the square, meaning that it touches the square at all 4 midpoints of its sides.
[tex]\textrm{side length} = 2r[/tex]
[tex]\textrm{side length} = 2(2 \, \textrm{in})[/tex]
[tex]\textrm{side length} = 4 \, \textrm{in}[/tex]
Now we can solve for the area of the square using the formula:
[tex]\textrm{Area}_\square = \textrm{side length}^2[/tex]
[tex]\textrm{Area}_\square = (4 \, \textrm{in})^2[/tex]
[tex]\textrm{Area}_\square = 16 \, \textrm{in}^2[/tex]
Next, we can solve for the area of the circle using the formula:
[tex]\textrm{Area}_\circ = \pi r^2[/tex]
Remember that the radius of the circle was given as 2 in.
[tex]\textrm{Area}_\circ = \pi (2 \, \textrm{in})^2[/tex]
[tex]\textrm{Area}_\circ = 4\pi \, \textrm{in}^2[/tex]
Finally, we can solve for the area of the blue portion of the figure by subtracting the area of the circle from the area of the square.
[tex]\textrm{Area}_{\textrm{blue}} = A_\square - A_\circ[/tex]
[tex]\textrm{Area}_{\textrm{blue}} = 16 \, \textrm{in}^2 - 4\pi \, \textrm{in}^2[/tex]
If we plug this into a calculator, we approximately get:
3.4 in²
if you have flipped t tails, you need to flip t 1 consecutive heads to win the game. what is the probability to win the game?
The probability of flipping 1 head in a fair coin flip is 0.5. The probability of flipping t heads in a row is [tex]0.5^{t}[/tex]. To win the game, you need to flip t heads after flipping t tails, so the probability of winning the game is ([tex]0.5^{t}[/tex])².
The probability of flipping heads in a fair coin flip is 0.5, meaning that the chance of getting heads on any given flip is 50%. If you have flipped t tails and now need to flip t heads in a row to win the game, then the probability of flipping t heads in a row is [tex]0.5^{t}[/tex].
To win the game, you need to flip t heads after t tails, so the overall probability of winning the game is ([tex]0.5^{t}[/tex])², which is the probability of flipping t heads multiplied by the probability of flipping t tails. In other words, the chance of winning the game is the product of the individual probabilities of each coin flip outcome. The probability of winning the game decreases as the number of heads you need to flip in a row increases.
To simplify the answer, let's assume that you need to flip t=3 heads in a row to win the game after flipping t=3 tails
The probability of flipping one head is 0.5, so the probability of flipping 3 heads in a row is (0.5)³ = 0.125.
The probability of flipping one tail is also 0.5, so the probability of flipping 3 tails in a row is (0.5)³ = 0.125.
The probability of winning the game, which is flipping 3 heads after flipping 3 tails, is (0.125)² = 0.015625.
So, the probability of winning the game is approximately 0.016, or 1.56%.
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we toss a fair die three times. what is the probability that all tosses produce different outcomes?
The probability that all tosses produce different outcomes is 1.666
Probability;
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
Number of toss of dice = 3 times
Number of ways to throw one dice that shows different results = 6 × 5 × 4 × 3 = 360 ways
The total number of throw results = 6³ = 216
Now,
The probability that each throw will result in a different result;
Number of ways / Total number of throws = 360 / 216 = 1.666
The probability that each toss will result in a unique outcome is 1.666
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the___ is measure of a country's total economic output.
Answer:gdp
Step-by-step explanation:gross domestic product
Answer:
GDP => Gross Domestic Product
Step-by-step explanation:
GDP measures the monetary value of final goods and services produced in a country in a given period of time
pencils are sold in boxes of 10
erasers are sold in boxes of 14
a teacher wants to buy the same amount of pencils and erasers. How many of each boxes should she buy
Answer:
7 boxes of pencils and 5 boxes rubbers.
Step-by-step explanation:
Since LCM (10,14) = 70, that means that the minimum number of each you must buy is 70. So it's 7 boxes of pencils ( 10 each ) and 5 boxes of rubbers ( 14 each ).
Which interval in the histogram contains the median guinea pig weight?
The histogram in question is a visual representation of the weights of guinea pigs. It indicates that the median weight is located in the interval between 250 and 300.
This is determined by first looking at the shape of the histogram. The histogram is approximately symmetrical, meaning that the median is going to be located in the middle of the data points. When looking at the intervals listed in the histogram, the interval between 250 and 300 is the middle interval, thus indicating that the median weight falls in this range.
In addition, the peak of the histogram is located in this interval, which further confirms that the median weight falls in the interval between 250 and 300. Overall, the interval between 250 and 300 contains the median guinea pig weight.
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What is the slope of the line?
Answer:
m = 5/4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0, -3) (4, 2)
We see the y increase by 5 and the x increase by 4, so the slope is
m = 5/4
Can someone please help me with this? I’m having a hard time understanding. Part a and part b show work please
Answer:
see bleow
Step-by-step explanation:
supplementary simply means angle 1+ which angle =180
so angle 2 & 4 are supplementary.
if angle 1 = 124, then angle 4 = angle 2 = 180-124 =56
angle 3 = angle 1 =124
A rectangle,l unit long and b unit wide has an area of A square unit where A=lb. the area of a picture is 3•125m and it's width is 1•25m.Find it's length
The length of the picture is 30 meters
How to determine the length of teh pictureFrom the question, we have the following parameters that can be used in our computation:
Area = lb
Also, we have
Area = 3 * 125
Where
Width = 1.25 meters
Substitute the known values in the above equation, so, we have the following representation
3 * 125 = Length * 1.25
Divide both sides by 1.25
Length = 30
Hence, the length is 30 meters
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*URGENT*
Solve the triangle: If it is not possible, say so
Answer:
a
Step-by-step explanation:
reliability is measured as the amount of time the system is running and functioning properly. this includes the system’s hardware and software. What is the correct question for the statement above?
How frequently and how long is the system in use function
A system's reliability can be used to gauge how well it is operating and performing. It considers both the system's software and hardware components. This includes how long the system can function without experiencing any issues, how frequently it bounces back from a crash or failure, and how rapidly it reacts to information or service demands. The frequency and length of any system outages, as well as how quickly and dependably the system recovers from failure, must all be determined in order to assess a system's reliability. The user experience should also be taken into account because people may assess the reliability of a system based on how fast and effectively it answers to their requests. In order to determine a system's reliability with precision,
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The complete question is
reliability is measured as the amount of time the system is running and functioning properly. this includes the system’s hardware and software. What is the correct question for the statement above. How frequently and how long is the system in use function ?
What are the pros and cons of a histogram and a stem and leaf plot?
Histogram is a visual representation of data distribution and a stem and leaf plot provide individual values in a set.
What makes up a histogram and a stem and leaf plot?Pros of a histogram:
It provides a visual representation of the distribution of data, making it easier to understand patterns and trends in the data.It can show the overall shape of the data, including the skewness and the presence of outliers.It can be useful for comparing multiple datasets by plotting them on the same graph.Cons of a histogram:
It can be less precise in representing individual values within a data set compared to other forms of data representation.It can be misleading if the bin width is not chosen properly, as it can hide or emphasize certain features of the data.Pros of a stem-and-leaf plot:
It provides a more detailed representation of individual values within a data set.It is useful for quickly checking the range and distribution of the data.It is relatively simple to construct and interpret.Cons of a stem-and-leaf plot:
It can become cluttered for large data sets, making it difficult to see the overall pattern and distribution.It is less visually appealing compared to other forms of data representation such as histograms and box plots.Learn more on histograms here: https://brainly.com/question/25983327
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Solve the following linear system by elimination
The solution to the system of equation -3x = 2y - 34 and 3y = 13 + 5x is x = 4 and y = 11
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.
Given the equations:
-3x = 2y - 34
multiply the equation by 3:
-9x = 6y - 102
-9x - 6y = -102 (1)
And:
3y = 13 + 5x
multiply the equation by 2:
6y = 26 + 10x
-10x + 6y = 26 (2)
To solve by elimination method, add equation 2 and 1 to get:
-19x = -76
x = 4
Put x = 4 in the equation:
-3x = 2y - 34
-3(4) = 2y - 34
2y = 22
y = 11
The solution to the equation is x = 4 and y = 11
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what is 57.8 divided by 3.4?
Answer: 17
Step-by-step explanation: 3.4 can go into 57.8 seventeen times. 3.4 x 17 is 57.8. Therefore, 57.8 divided by 3.4 is 17.
please if anyone could help me out with this question and a couple of others that would be amazing and i would be so grateful
Check the picture below.
[tex]\cfrac{x}{1225}=\cfrac{2035}{2950}\implies \cfrac{x}{1225}=\cfrac{407}{590}\implies x=\cfrac{(1225)(407)}{590}\implies x=\cfrac{99715}{118}~ft[/tex]
now, we know your strolling speed is 200 ft per minute or 200 ft per 60 seconds, so how long for that distance above?
[tex]\begin{array}{ccll} feet&seconds\\ \cline{1-2} 200&60\\[1em] \frac{99715}{118}&y \end{array}\implies \cfrac{200}{ ~ \frac{99715}{118}~ } =\cfrac{60}{y}\implies \cfrac{200}{1}\cdot \cfrac{118}{99715}=\cfrac{60}{y} \implies \cfrac{4720}{19943}=\cfrac{60}{y} \\\\\\ 4720y=(19943)(60)\implies y=\cfrac{(19943)(60)}{4720}\implies y\approx 254~seconds[/tex]