There are 100, 4-digit positive integers that are divisible by 5 between 1000 and 9999.
Define the term divisibility by 5?A integer is divisible by 5 if it ends with 0 or 5. 35, 790, and 55, for instance, are also all divisible by 5.
There are [0, 2, 4, 6, and 8] things in all.Only one digit should be present because it is the only one that makes the integer divisible by five.There still are 1 methods for filling a position, making a total of 1.A location can be filled in five different ways, hence there are five different methods to fill it.Since all of the numbers in the specified sets can be used to fill the hundreds position, all integers can be used there.There are five different approaches to fill this hundreds place as a result.A set number of even numbers can be used to fill thousands of spots with four different numbers.The very next step is to apply the idea of factorial to determine how many even integers that really are divisible by five may be combined to create a 4-digit number.We then multiply all the computed ways to fill in the corresponding spaces (4 x 5 x 5 x 1 = 100).
Therefore, there are 100 potential 4-digit positive integers.
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For this linear regression model, r2= 0.90. What does this mean?
A) The maximum long jump was around 90 inches.
B) Each year the winning long jump distance increased by 90%.
C) 90% of the variation in long jump distances is explained by the regression line.
D) The data ends around 1990
C) 90% of the variation in long jump distances is explained by the regression line.
(The number r2 gives the proportion of the variation in the long jump explained by the change in years.)
The given linear regression model means that 90% of the variation in long jump distances is explained by the regression line. (Option C)
Linear regression refers to a basic and commonly used form of predictive analysis. It is used to determine the relationship between two quantitative variables. It is used to determine the strength of the relationship between two variables and the value of the dependent variable at a certain value of the independent variable. Regression models describe the relationship between variables by fitting a line to the observed data. Linear regression models use a straight line, while logistic and nonlinear regression models use a curved line. The regression model illustrates how a dependent variable changes as the independent variable(s) change. The given linear regression model r2= 0.90, where r2 gives the proportion of the variation in the long jump explained by the change in years, the model means that 90% of the variation in long jump distances is explained by the regression line.
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Express 650 m as a fraction of 1 km.
Answer:
1km= 1000m
[tex]\frac{650}{1000}[/tex]
=[tex]\frac{13}{20}[/tex] (simplified)
I don’t understand my math test. please help!! :)
Answer:
4 ) {2,3}
5) {0,1,2,3,4,5}
6) { }
it is always necessary for an agent to disclose the identity of the principal to any third person with whom he is contracting; else the contract becomes void.
The statement is false. It is always necessary for an agent to disclose the identity of the principal to any third person with whom he is contracting; else the contract becomes void.
Given that,
Any third party with whom an agent enters into a contract must always be informed of the identity of the principal; otherwise, the contract is null and void.
By speaking to the third party or carrying out an approved act, the principle reveals his or her identify and existence.
If the principle's identity is unknown and the third party has learned enough details to guess it, the principal is deemed to have been disclosed. The principal is in this case responsible to the third party; the agent is not. Contracts or other agreements between agents and third parties are regarded as agreements between the main and the third party.
Despite the fact that the agent is not a party to the contract, in the event that the principal breaches it, the agent is not personally liable for any damages that follow from the breach.
So, the statement is false.
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X + 3 + 7 (X-5) Step by step
Answer: 8x - 32
Step-by-step explanation: x + 3 + 7(x - 5)
x + 3 - 35
which gives you 8x - 32
A political researcher takes a survey of 300 randomly selected registered voters in atlanta, and each person was asked who they plan on voting for in the 2020 mayoral election. 101 said they plan on voting for candidate a, 184 said they plan on voting for candidate b, and 15 were unsure or plan to vote for another candidate. In question 8, the political researcher estimated p, the population proportion of all registered voters in atlanta who plan to vote for candidate a, with a 95% confidence interval. The researcher now wants to estimate p with a margin of error of 3%. What is the minimum sample size needed?.
The minimum sample size would be 953.
What is the confidence interval?
A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used.
The given sample space is n = 300.
x = 101 plan to vote
P = x/n = 101/300 = 0.3367
95% confidence = [tex]P\pm Z_\frac{\alpha}{2}=1.96[/tex]
Confidence Interval:
[tex]CI=P\pm Z_\frac{\alpha}{2}\sqrt{\frac{P(1-P)}{n}}\\\\CI=0.3367\pm 1.96 \times \sqrt{\frac{0.3367(1-0.3367)}{300}}\\\\CI=(0.2832, 0,3902)[/tex]
Margin of error = 3%
The margin of Error = [tex]Z_\frac{\alpha}{2}\sqrt{\frac{P(1-P)}{n}}[/tex]
[tex]3 \% = P\pm Z_\frac{\alpha}{2}\sqrt{\frac{P(1-P)}{n}}[/tex]
[tex]\frac{1}{\sqrt{n}}=\frac{0.03}{1.96\sqrt{(0.3367)(1-0.3367)}}\\\\\sqrt{n} = 30.875\\\\n = 953[/tex]
Hence the minimum sample size = 953.
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Which expression
O 5√10+4√10
O 5 10+4 10
O 5√10+410
O 510+4 10
DONE
equals
93/10 ?
The expression that equals 9×10^(1/3) is 5×10^(1/3) + 4×10^(1/3).
We are given a number. The number is a multiplication between an integer and another number having an exponent. The number is given below.
N = 9×10^(1/3)
We are given four expressions in the options. We need to find the expression that is equal to the given number. We will follow the rules of the exponents.
The first expression is 5×10^(1/2) + 4×10^(1/2). The sum is 9×10^(1/2).
The second expression is 5×10^(1/3) + 4×10^(1/3). The sum is 9×10^(1/3).
The third expression is 5×10^(1/2) + 4×10^(1/3). The terms can't be simplified.
The fourth expression is 5×10^(1/3) + 4×10^(1/2). The terms can't be simplified.
Hence, the expression that equals the given number is the second expression.
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The rate of acceleration due to gravity i 9. 8 meter / econd2, How fat i that in mile per econd2?
According to the conversion factor where 1 meter is equal to 0.000621371 miles, we find out that the rate of acceleration due to gravity upon conversion is equal to [tex]0.0060894358 miles/second^{2}[/tex].
It is given to us that -
The rate of acceleration due to gravity is [tex]9.8 meter/second^{2}[/tex]
We have to find out the rate of acceleration in [tex]miles/second^{2}[/tex]
We know the conversion factor between meter and miles is -
[tex]1 meter = 0.000621371 miles[/tex]
So, the given rate of acceleration due to gravity can be written as -
[tex]9.8 meter/second^{2}\\= 9.8 * 0.000621371 miles/second^{2}\\= 0.0060894358 miles/second^{2}[/tex]
Thus, using the conversion factor from meter to miles, we find out that the rate of acceleration due to gravity is equal to [tex]0.0060894358 miles/second^{2}[/tex].
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The length l of a rectangle is decreasing at the rate of 2 cm/sec while the width w is increasing at the rate of 2 cm/sec. When l = 12 cm and w = 5 cm, find the rates of change of (a) the area, (b) the perimeter, and (c) the lengths of the diagonals of the rectangle. Which of these quantities are decreasing, and which are increasing?
Using Area and perimeter formulae of rectangle,
a) the rate of change of Area is 14 cm²/sec
b) the rate of change of perimeter is zero.
c) length of diagonal is 13 cm
We have given that
length (l) is decreasing at the rate of 2 cm/min
and the width (w) is increasing at the rate of
2cm/min,
⇒ dl/dt = −2 cm/min and dw/dt = 2cm/sse
Thus the perimeter (P) of a rectangle is,
P=2(l+w) ---(1)
differentiating above equation with respect to time (t) we get,
dp/dt = 2(dl/dt + dw/dt )
=> dp/dt = 2( -2 + 2 ) = 0
=> P = constant
Hence, there is no change in perimeter of rectangle.
(b)Now, it is given that length (l) is decreasing at the rate of 2 cm/min
and the width (w) is increasing at the rate of 2 cm/min,
Thus the area (A) of a rectangle is, A= l× w
=> dA/dt = l ×dw/dt + w×dl/dt (used differentaion
we have l = 12 cm and w = 5 cm
=> dA/dt = 12 (2) + 5(-2)
=> dA/dt = 24 - 10 = 14
Hence, the area is increasing at the rate of
14 cm²/min.
c) length of diagonal = √(12)² + (5)² = √144+25
=> length of diagonal = √169 = 13 cm
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Nov 22, 9:11:24 AM
An online furniture store sells chairs for $100 each and tables for $350 each. Every
day, the store can ship at most 18 pieces of furniture and must sell no less than
$3200 worth of chairs and tables. If a represents the number of tables sold and y
represents the number of chairs sold, write and solve a system of inequalities
graphically and determine one possible solution.
After solving system of inequalities one possible solution is number of chairs y = 12 and number of tables a = 6.
Given:
An online furniture store sells chairs for $100 each and tables for $350 each. Every day, the store can ship at most 18 pieces of furniture and must sell no less than $3200 worth of chairs and tables.
Using a and y as variables, we get
100y + 350a ≥ 3200
Simplified,
50(2y + 7a) ≥ 3200
2y + 7a ≥ 3200/50
2y + 7a ≥ 64
y + a = 18
a = 18 - y
on solving two equations
2y + 7a = 64
2y + 7(18-y) = 64
2y + 126 - 7y = 64
-5y = 64 - 126
-5y = -62
5y = 62
y ≈ 12 chairs
a = 18 - 12
a = 6 tables.
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five cards are drawn at random and without replacement from an ordinary deck of cards. let x1 and x2 denote, respectively, the number of spades and the number of hearts that appear in the five cards. (a) determine the joint pmf of x1 and x2. (b) find the two marginal pmfs. (c) what is the conditional pmf of x2, given x1
There are (525) possible combinations of 5 cards, and each combination has an equal chance of being drawn.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is .According to our question-
It is simpler to derive this from first principles than to add up the x2 (which will work but is harder).
There are (525) possible combinations of 5 cards, and each combination has an equal chance of being drawn.
The number of combinations that contain x1 spades is what we are looking for.
There are (13x1) ways to select the spade, followed by (395x1) ways to select the other card.
Hence, There are (525) possible combinations of 5 cards, and each combination has an equal chance of being drawn.
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The chorus has 30 members. which expression represents the number of ways a group of 6 members can be chosen to do a special performance? 30 · 6
For this combination can be used , the answer would be 639450 ways
What is combination?
In arithmetic, a combination may be a choice of things from a group that has distinct members, such the order of choice doesn't matter.
Main body:
Given, the total number of members in the chorus are 30.
Also, it is given that 6 members from the chorus have to be
chosen for a special performance.
The number of ways of choosing r people out of given n people
is given by the expression
nCr
= n!/r!(n-r)!
So the number of ways of choosing 6 members out of 30 are
³⁰C₆
= 30!/24!6!
= 639450 ways
But since only the expression to represent the number of ways
was asked not the exact number of ways we can leave the
answer as ³⁰C₆ .
Hence total number of ways is 639450 ways.
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for the following gear train, tooth numbers are n2 = 12, n3 = 16, and n4 = 12. how many teeth must internal gear 5 (ring gear) have if gear 5 is fixed? what is the speed of the arm if shaft a rotates counterclockwise at 320 rev/min?
for the following gear train, tooth numbers are n2 = 12, n3 = 16, and n4 = 12 the speed of the arm is 426.67 rev/min.
What is the speed of rotation?The angular velocity of an item as it rotates around an axis or centre is quantified as the speed of rotation. Usually, it is expressed in terms of degrees, per minute (RPM). The angular velocity of an object is a measure of how rapidly the object rotates around a central point and is connected to the linear velocity of the object around the perimeter of its path of revolution. In physics, the idea of It is used to explain the motion of things ranging from tiny particles to large celestial bodies, and it is an important aspect in understanding object behaviour. for the following gear train, tooth numbers are n2 = 12, n3 = 16, and n4 = 12
How to solve?
n1/n2 = n3/n4. In this case, the gear ratio for the first set of gears (gears 1 and 2) is 12/12 = 1. For the second set of gears (gears 3 and 4), the gear ratio is 16/12 = 4/3.
Since internal gear 5 is fixed, it must have the same number of teeth as gear 1, which is 12. Therefore, the number of teeth on internal gear 5 is 12.
To determine the speed of the arm, we need to use the equation for speed of rotation: speed of rotation = (speed of input shaft) x (gear ratio of gears 3 and 4) = 320 rev/min x (4/3) = 426.67 rev/min.
Therefore, the speed of the arm is 426.67 rev/min.
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What is the diameter of the inscribed circle of the triangle?
The diameter of the inscribed circle of the triangle is
(Type a whole number.)
x+2
2x-7
The value of diameter for the given triangle inscribed in a circle will be 22.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
In our daily life, we always see circular objects for example our bike wheel.
The longest line which can be drawn inside the circle will be the diameter.
As per the given triangle inscribed a circle.
The length x +2 and 2x - 7 will be the radius of the circle and the sides of the triangle will be the tangent of the circle.
x + 2 = 2x - 7
2 = 2x - x - 7
x = 9
Thus, radius = 9 + 2 = 11
Diameter = 11 x 2 = 22 units.
Hence "The value of diameter for the given triangle inscribed in a circle will be 22".
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Suppose you repeatedly play a casino game where your probability of winning on each play is 0.48. You want to find the probability that you will be ahead (more wins than losses) if you play n times. Which of the following is true?
a. The probability of being ahead is greater than 1/10 when n=1000 b. The probability of being ahead is greater than 1/3 when n=50 c. The probability of being ahead is greater than 1/4 when n=250 d. None of the above are true
In the casino game of the given options the probability of being ahead is greater than 1/3 when n = 50 .
Let us calculate the probability using normal distribution for the following options at the various sample .
at n= 250
Sample size , n = 250
Probability of the event of winning each play p = 0.48
Mean = np = 120
standard deviation = σ = √np(1-p) = 7.8994
P(X > 125 ) = P(X > 125.5)
Z=(X - µ ) / σ = (125.5-120)/7.8994)= 0.696
=P(Z >0.696 ) = 0.24
now let us calculate for n= 1000
Probability of the event of winning each play p = 0.48
Mean = np = 480
standard deviation = σ = √np(1-p) = 15.7987
P(X > 500 ) = P(X > 500.5)
Z=(X - µ ) / σ = (500.5-480)/15.7987)= 1.298
=P(Z > 1.298 ) = 0.0972
now let us calculate for n= 50
Probability of the event of winning each play p = 0.48
Mean = np = 24
standard deviation = σ = √np(1-p) = 3.5327
P(X > 25 ) = P(X > 25.5)
Z=(X - µ ) / σ = (25.5-24)/3.5327)= 0.425
=P(Z > 0.425 ) = 0.3356
Therefore the probability of being ahead is greater than 1/3 when n=50 .
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Is 15 a multiple of 3 yes or no?.
Answer:
Yes
Step-by-step explanation:
As long as 3 can multiply into 15, then 15 is a multiple of 3.
Multiples of 3 are: 3,6,9,12,15 and so on.
What number is 20% of 50%?.
Answer:
0.10 or 10%
Step-by-step explanation:
Think about it, 20% of 50 = 10
You could also do 0.20 x 0.50 to get 0.10
during january, a sample of 16 days has a sample mean of 48 rooms. this information is used to calculate an interval estimate for the population mean to be from 40 to 56 rooms. what is the level of confidence of this interval? report the level of confidence as a percentage and use 2 decimal places.
We'll use our normal distribution to determine how near this number is to nothing but this value. And by resolving this, we can obtain the mean alpha value. 18 mm .
It is assumed that the people who occupy the rented space are dispersed normally. We can state that the sample mean in January is 48 rooms since a sample of 16 days has a sample mean of 48 rules.The population mean, which is estimated to be between 40 and 56 rolls, is calculated using this data. The maximum will be 56, and a different scenario will be 448 minus Z alpha returning to 24 over square root of 16. It will be close to 40 in this valley. Act Alpha by two will give us 16, 24 over the square of the subsection, and 56 minutes. One minus alpha by two and the second letter of the Z alphabet We'll use our normal distribution to determine how near this number is to nothing but this value. And by resolving this, we can obtain the mean alpha value. 18 mm.
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alan can type a research paper in 6 hours. with the help of steve, the paper can be typed in 4 hours. find how long it would take steve to type the paper alone.
It will take 12 hours to type the research paper by the Steve alone.
What is meant by time and work?Work Done = Time Taken x Rate of Work Work Rate = 1 / Time Taken Time taken = 1 / Rate of work If a piece of work is completed in x days, then the work completed in one day equals 1/x.
The fundamental concept of Time and Work is similar to that of all Arithmetic topics, namely the concept of Proportionality. When the amount of work done is constant, efficiency is inversely proportional to time.
Let x be the amount of hours Steve can spend typing a research paper.
Steve completes 1/x of a research paper per hour.
Alan completed 1/6 of the paper in an hour.
1/4 = amount of paper completed each hour by both of them
1/x + 1/6 = 1/4
Multiply by 12 on the LCD to get 12 + 2x = 3x x = 12 hours.
It will take 12 hours to type the research paper by the Steve alone.
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What are non linear quadratic equations?.
A group of two or more equations containing the same variables but with at least one non-linear equation is a non-linear system of equations.
What is a non-linear equation?
An equation that does not form a straight line is said to be non-linear. It has a variable slope value and resembles a graphed curve. Ax2+by2 = c is a common formula for a non-linear equation.What is a nonlinear equation example?
A nonlinear equation is one in which a term can have a maximum degree of two or more. This is an example of a nonlinear equation because equation 1 has the highest degree of 2, and equation 2 has variables. + 2x + 1 = 0, 3x + 4y = 5,Learn more about non-linear equation
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How do you write 1000 in expanded form?.
The number 1000 can be written in its expanded form as
1000 = 1×10³ + 0×10² + 0×10 + 0
Given, a number 1000
we have to write the given number in its expanded form
so, 1000 can be written in its expanded form as
1000 = 1×10³ + 0×10² + 0×10 + 0
and it is the expanded form of the number 1000
where, the place value of 1 is thousand.
So, the number 1000 can be written in its expanded form as
1000 = 1×10³ + 0×10² + 0×10 + 0
Hence, the number 1000 can be written in its expanded form as
1000 = 1×10³ + 0×10² + 0×10 + 0
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A cat weighs 82 ounces. There are about 28.3 grams in 1.6 ounces. Approximately how many
grams does the cat weigh? Round your answer to the nearest whole gram.
The cat's weight in grams will be 1450 grams.
According to the question,
We have the following information:
A cat weighs 82 ounces. There are about 28.3 grams in 1.6 ounces.
Now, we can easily find the weight of the cat in grams by following the given steps:
1.6 ounces = 28.3 grams
We will find the weight in grams in 1 ounce using division.
1 ounce = 28.3/1.6 grams
Now, the weight of 82 ounces in grams:
82 ounces = (28.3*82)/1.6 grams
82 ounces = 1450.375 grams
After rounding it off to the nearest whole gram, we have 1450 grams.
Hence, the cat's weight in grams will be 1450 grams.
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Caleb went to the grocery tore and purchaed can of oup and frozen dinner. Each can of oup ha 200 mg of odium and each frozen dinner ha 500 mg of odium. Caleb purchaed a total of 15 can of oup and frozen dinner which collectively contain 4500 mg of odium. Determine the number of can of oup purchaed and the number of frozen dinner purchae
Both the number of frozen dinners and the number of can soups that were purchased total 10.
What are the linear equations in two variables?When a, b, and c are all real values and the coefficients of x and y, i.e., a and b, are not equal to zero, the equation is said to be linear in two variables. A few more examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.
What is a linear equation in math?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Let's say that "x" cans of soup and "y" frozen meals were purchased.
We may create the equations based on the above conditions,
x + y = 15 ————(I) (I)
200x + 500y = 4500 ——-(II) (II)
Now, y = 15 - x from (I).
If you change the value of "y" in equation (II), you obtain
200x + 500(15 - x) = 4500
200x + 7500 - 500x = 4500
300x = 3000
x = 3000/300
x = 10
In equation (I), x = 10 results in
y = 5
The result is that 10 cans of soup and 10 frozen dinners were bought.
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can someone help me with this?
The estimate of number of cars with speed more than 85 is 25
How to find the estimate of number of cars with speed more than 85In the table, the frequency shows the number of cars with the range of speeds as in the first column
The number of cars with speed more than 85 will fall in the interval 80 < s ≤ 100, the number with speed more than 85 is 85 < s
The frequency of this interval 80 < s ≤ 100 is 25 and this is the estimate of the number of cars with speed ore than 85
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If x = 71, could the triangles be similar? Explain why or why not.
Answer:
Yes, the yellow triangles are similar.
Step-by-step explanation:
Angle-Angle similarity states that if any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.
If angle x is 71° then both yellow triangles have two angles of equal measure (28° and 71°), which means they are similar triangles.
The angle of depression is 24° from a point 7,224 ft above sea level on the north rim of a certain canyon to a point 5,091 ft above sea level on the south rim. How wide is the canyon at that point?
The width of the canyon, from the point on the north rim of the canyon which is 7,224 feet above sea level to the point on the south rim, which is 5,091 feet above sea level, found using the trigonometric ratios is about 4,790.8 feet
What are the trigonometric ratios?The trigonometric ratios indicate the relationship between the interior angles of a right triangle and two sides of the triangle.
The specified angle of depression from the point 7,224 feet above the sea level on the north rim of the of the canyon to the point 5,091 feet above sea level on the south rim, θ = 24°
The difference in height between the north rim and the south rim = 7,224 feet - 5,091 feet = 2,133 feet
The width of the canyon can therefore be found using trigonometric ratios for tangent of an angle as follows;
In a right triangle, we get;
[tex]tan(\theta) = \dfrac{Opposite \, side \, to \, angle \, \theta}{Adjacent \, side \, to \, angle \, \theta}[/tex]
With regards to the the canyon, and the angle, θ, therefore;
[tex]tan(\theta) = \dfrac{Difference \ in \ height}{Width\ of \ the \ canyon }[/tex]
Plugging in the known values indicates;
[tex]tan(24^{\circ}) = \dfrac{2,133}{Width\ of \ the \ canyon }[/tex]
[tex]Width\ of \ the \ canyon = \dfrac{2,133}{tan(24^{\circ})} \approx 4,790.8[/tex]
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One prominent physician claims that 70% of those with lung cancer are chain smokers. If his assertion is correct, find the probability that of 10 such patients recently admitted to a hospital, fewer than half are chain smokers.
The probaility of non smokers is 0.3
One prominent physician claims that 70% of those with lung cancer are chain smokers
use binomial formula, where probability x successes in n tries where each try has probability p:
P(x successes) = C(n,x) * p^x * (1-p)^(n-x)
n is sample size
p is the probability of success
here n = 10, p = 0.7
a) more than have is P(x = 6) + P(x=7) + P(x = 8) + P(x = 9) + P(x = 10)
b) exactly 4 are heavy-smokes is P(x = 4)
c) probability non-smoker is 1 - 0.7 = 0.3
P(x < 2) = P(x = 0) + P(x = 1), and P = 0.3
Therefore, the probaility of non smokers is 0.3
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Disclaimer,
the question given by you is incomplete,
a similar question is
One prominent physician claims that 70% of those with lung cancer are heavy smokers. If his assertion is correct, find the probability that out of 10 such patients recently admitted to a hospital
(a) more than half are heavy smokers
(b) exactly 4 are heavy smokers
(c) less than 2 are non- smokers
use the distance formula and algebra to find an equation that gives all points (x, y) that are equidistant from the points
An equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4) is 3x + y - 5 = 0.
In the given question, using the distance formula and algebra to find an equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4).
The distance between any two points can be determine using the distance formula which is given by √[x(2)-x(1)]^2+[y(2)-y(1)]^2.
Let point P(x, y) be equal distance from points A(3, 6) and B(- 3, 4).
Since they are equidistant, PA = PB
Hence by applying the distance formula for PA = PB, we get
√(x - 3)^2 + (y - 6)^2 = √(x - (- 3))^2 + (y - 4)^2
√(x - 3)^2 + (y - 6)^2 = √(x + 3)^2 + (y - 4)^2
Taking square on both side, we get
(x - 3)^2 + (y - 6)^2 = (x + 3)^2 + (y - 4)^2
Using the formula (a-b)^2=a^2-2ab+b^2
x^2+ 9 - 6x + y^2 + 36 - 12y = x^2 + 9 + 6x + y^2 + 16 - 8y
Now solving
6x + 6x + 12y - 8y = 36 - 16
12x + 4y = 20
3x + y = 5
3x + y - 5 = 0
Thus, the relation between x and y is given by 3x + y - 5 = 0
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The right question is:
Use the distance formula and algebra to find an equation that gives all points (x, y) that are equidistant from the points (3, 6) and (- 3, 4).
A company orders 19 boxed lunches from a deli for $198. 55. If each boxed lunch costs the same amount, how much do 6 boxed lunches cost?.
The cost of 6 boxed lunches is 62.7
A company orders 19 boxed lunches from a deli for $198. 55.
We need to calculate the price of 6 lunch boxes.
This can be found by using unitary method
Number of lunch boxes = 19
Total price = 198.55
If 19 lunch boxes cost 198.55
Cost of 1 lunch box is 198.55/19
Cost of 1 lunch box is 10.45
Cost of 6 lunch boxes is 10.45 x 6
Cost of 6 lunch boxes is 62.7
Therefore, If a company orders 19 boxed lunches from a deli for $198. 55 the cost of 6 boxed lunches is 62.7
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determine the integer floor of the sum of two floating point numbers. the floor is the truncated float value, i.e. anything after the decimal point is dropped.
return(int(a+b)) is the way to determine the integer floor of the sum of two floating point numbers.
Here is an example program:
int main(void){
double a,b,c;
a=1.001;
b=2.243;
c=a+b;
return(int(c));
}
where, a and b are floating points we need addition of that as an integer which means removing the decimal part.
hence, we use return(int(c)), it is also called as parsing integer.
What is parseInt()?
The function parseInt(int I produces an integer when given a textual representation of a number that is either decimal, binary, octal, or hexadecimal (radix equals 10, 2, 8, or 16 correspondingly).
Example in java program:
public class Test {
public static void main(String args[]) {
int x =Integer.parseInt("9");
double c = Double.parseDouble("5");
int b = Integer.parseInt("444",16);
System.out.println(x);
System.out.println(c);
System.out.println(b);
}
}
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