The Cox-Ross-Rubinstein (CRR) model is a mathematical model used in finance to evaluate the potential future value of an asset or portfolio. The model is based on the concept of a binomial tree.
What is a binomial tree?A binomial tree is a mathematical model used in finance to estimate the probable future value of an asset or portfolio. The notion of a binomial, a mathematical expression with two potential outcomes, forms the foundation of the model. In a binomial tree, the future value of the asset is defined by two potential outcomes at each time step: a "upper" element and a down factor. The underlying variables that affect the asset, such as interest rates and market circumstances, dictate the up and down components. Reflecting This enables investors to assess the advantages and dangers of a possible investment and come to wise judgments.
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Determine if the following functions are increasing or decreasing, and compare their rates of change.
A.
Both functions are increasing and have different rates of change.
B.
Both functions are increasing and have the same rate of change.
C.
Both functions are decreasing and have different rates of change.
D.
Both functions are decreasing and have the same rate of change.
The rate of change of the functions are: I. -3 II. -1/4.
Therefore, C. Both functions are decreasing and have different rates of change.
How to Find the Rate of Change o fa Function?The rate of change of any function can be calculated as = change in y / change in x.
If the rate of change is a negative number, the function is decreasing. If it is a positive number, the function is decreasing:
Rate of change of the line that passes through (3, 3) and (4, 0):
Rate of change = (0 - 3) / (4 - 3)
= -3/1
= -3 [this means the function is decreasing].
Rate of change of the function represented by the table, using two pairs of the table values, (0, -1) and (-4, 0):
Rate of change = (0 -(-1)) / (-4 - 0)
= 1/-4
= -1/4 [this shows the function is decreasing]
Therefore, the answer is: C. Both functions are decreasing and have different rates of change.
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Ahby ate a lot for thankgiving dinner. He decided to go on a long run. He ran 6 mile in 57 minute. How long did it take him to run a mile
It takes Ahby a total of 9.5 minutes to run a mile.
What is a total?
The sum of two or more numbers is known as the total in mathematics. It is the total of the figures added up. When we add two or more numbers, amounts, or items, the total sum is obtained. The sum can also be expressed as the total, aggregate, or tally in this example, where the sum of 3 and 7 is 10.
Solution Explained:
Given in the question,
Total time taken to run 6 miles = 57
So,
Total time taken to run 1 mile = 57/6 = 9.5 minutes
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if you wanted to save $30,000 to buy a new car. instead of focusing on saving the whole amount, you work to earn $1,000 at a time. this makes the process seem more manageable to you because you are using the heuristic. question 1 options: availability subgoaling algorithm mechanical
If you wanted to save $30,000 you need to work 30 times .
Given:
if you wanted to save $30,000 to buy a new car. instead of focusing on saving the whole amount, you work to earn $1,000 at a time. this makes the process seem more manageable to you because you are using the heuristic.
Number of times to work = money to save / at a time money.
= $30000/$1000
= 30000/1000
= 3000/100
= 300/10
= 30 times
Therefore you need to work 30 times to earn $30,000.
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How many combinations of a president, vice-president, secretary, and treasurer can be chosen from a group of 12 students?.
The number of combinations of a president, vice president, secretary and a treasurer can be chosen from a group of 12 students is 11,880.
Given: we have group of 12 students.
we are asked to determine the number of combinations of a president, vice-president, secretary, and treasurer can be chosen from a group of 12 students.
nPr = n!/(n-r)!
12P4 = 12!/(12 - 4)!
12P4 = 12!/8!
9 × 10 × 11 × 12
= 11,880
Hence the number of combinations are 11,880.
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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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A regular polygon ha an interior angle of 157. 5°. Calculate the number of ide of the polygon
The total number of sides of the given polygon is 16.
What is the interior and exterior angle of a regular polygon?
In a regular polygon, all internal angles and exterior angles are equal. The formula for determining the amount of an interior angle is given:
Interior angle of a polygon = sum of interior angles/number of sides
A polygon's exterior angles add up to 360°.
Given, each interior angle of a regular polygon = 157.5°
Then, each exterior angle of a regular polygon = 180° - 157.5° = 22.5°
the sum of the exterior angles of any n-gon = 360°
So, the total number of sides = 360°/22.5° = 16 sides
Hence, the total number of sides of the polygon is 16.
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The length of time Y necessary to complete a key operation in the construction of houses has an exponential distribution with mean 10 hours. The formula C = 100 + 40Y + 3Y 2 relates the cost C of completing this operation to the square of the time to completion. Find the mean and variance of C.
The mean and variance of C are 200 & 1960000 respectively.
What are the mean and variance?
The mean is the average of a set of numbers, whereas the variance is the average degree to which each number deviates from the mean.
y ~ Exponential with mean of 10 hours
P. d. f of y,
[tex]f_{y} (y) = { \left \{ {{\frac{1}{10}e^{\frac{-y}{10} } } \atop {0}} \right.\\\left {{y > 0} \atop { 0 \ otherwise}} \right.[/tex]
[tex]f_{y} (y) = \int\limits^{\infty}_{-\infty} {y^{k} f_{y} (y)} \, dy[/tex]
[tex]f_{y} (y) = \int\limits^{\infty}_{0} {y^{k} \frac{1}{10} . e^{-\frac{y}{10} } \, dy[/tex]
[tex]=\frac{1}{10} \int\limits^{\infty}_{0} {y^{k+1} . e^{-\frac{y}{10} } \, dy[/tex]
[tex]= \frac{10^{k+1} }{10} \ \Gamma(k+1)[/tex] ---------(1)
E(Y³) = 10³ Γ(3+1) [putting k = 3 in (1)]
= 10³ Γ(4)
= 10³ 3! ..........[Γ(n) = (n-1)!]
= 6000
E(Y⁴) = 10⁴ Γ(4+1) [putting k = 4 in (1)]
= 10⁴ Γ(5)
= 10⁴ 4! ..........[Γ(n) = (n-1)!]
= 240000
C = 100 + 40Y + 3Y²
Mean of C,
E(C) = E(100 + 40Y + 3Y²)
E(C) = 100 + 40E(Y) + 3E(Y²)
E(Y) = 10 .......[Given]
E(Y²) = 10² Γ(2+1) [putting k = 2 in (1)]
= 10² Γ(3)
= 10² 2!
= 200
E(C) = 100 + 40(10) + 3(200)
E(C) = 1100
The variance of C,
Var(C) = Var[100 + 40Y + 3Y²]
= 1600var(Y) + 9(Y²)
= 1600[E(Y²) - E²(Y)] + 9[E(Y⁴) - E²(Y⁴)]
= 1600[200 -(10)²] + 9[240000 - (200)²]
= 1960000
Hence, the mean and variance of C are 200 & 1960000 respectively.
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Data Set: {(-3, 4), (-2, 3), (-1, 3), (0, 7), (1, 5), (2, 6), (3, 1)}
1. The regression line is: y =
2. Based on the regression line, we would expect the value of response
variable to be
x when the explanatory variable is 0.
4. If x= -3.5, the ŷ =
extrapolation +
3. For each increase of 1 in of the explanatory variable, we can expect a(n)
decreasex of
x in the response variable.
5. The correlation coefficient is r =
x -
hundredth.)
x x
Check
x. This is an example of
x. (Round to the nearest
1.Regression line is given by:
y = 4.14 - 0.04 x
2. When explanatory variable is 0, y = 4.14
3.For each increase of 1 in explanatory variable, there can be a decrease of 0.04 in response variable.
4. The value of y is 4.28
5. The value of r is -0.04
What is regression line?
A regression line is a line that in statistics best depicts the behavior of a set of data. It is, in other words, a line that best fits the trend of the data at hand.
Simple linear regression results:
Dependent Variable: Y
Independent Variable: X
Y = 4.1428571 - 0.035714286 X
Sample size: 7
From above equation:
1. Regression line is given by:
y = 4.14 - 0.04 x
2. When explanatory variable is 0, y = 4.14
3. For each increase of 1 in explanatory variable, there can be a decrease of 0.04 in response variable.
4. when x = -3.5:
substitute this into the equation of regression line
y = 4.14 - 0.04*(-3.5) = 4.28
It is an example of extrapolation
5. r = -0.04
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Is the leading coefficient of the polynomial function negative or positive?.
Greater inputs only result in the leading term becoming more and more positive if the leading coefficient is positive. The graph will incline rightward. Larger inputs will simply make the leading term more and more negative if the leading coefficient is negative. The rightward descent of the graph is planned.
The coefficient of the leading term is the leading coefficient in a polynomial. Because of the negative leading coefficient, the graph slants to the right. To ascertain the behavior, consider the function's degree and the sign of the leading coefficient.
The term with the largest power of x is the leading term in a polynomial. As an illustration, the leading word in 7+x3x2 is 3x2. A polynomial's leading coefficient is the coefficient of the leading term. The leading coefficient in the aforementioned illustration is 3.
The numbers placed in front of the variable with the largest exponent are known as leading coefficients. They can be whole numbers, fractions, or decimals, as well as positive, negative, real, or imaginary, just like regular coefficients.
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What is the point slope formula for Y y1 MX x1?.
The point slope formula is [tex]y-y_1=m(x-x_1)[/tex].
The point slope form is used to calculate the equation of a straight line that is inclined to the x-axis at a certain angle and passes through a particular point.
When we know the slope of a line and a point on it, we may use the point slope formula.
Point Slope Formula:
[tex]y-y_1=m(x-x_1)[/tex]
where,
(x, y) is a point on the line at random (which should be kept as variables while applying the formula).
(x1, y1) is the line's fixed point.
slope of the line is 'm'.
Thus, the point slope formula is [tex]y-y_1=m(x-x_1)[/tex].
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4 3 ​ (2 3 4 2 )=start fraction, 3, divided by, 4, end fraction, left parenthesis, 2, cubed, plus, 4, squared, right parenthesis, equals
Using PEMDAS rule , we can evaluate the provide expression . The required result is thirteen that's the value is L= 13.
PEMDAS order of operations: The order of operations is a rule that tells the correct sequence of steps for evaluating a given mathematical expression. We can remember the order using "PEMDAS" where
P --> Parentheses
E --> Exponents (2⁵ is 2 raised to the power of 5)
M------> Multiplication and
D---->Division (from left to right)
A--->Addition
S--->Subtraction (from left to right).
We have given that
3/4 ( 2³ + 4² )
let given expresion equal to L i.e
L = 3/4 ( 2³ + 4² )
Now, we have to solve it
Using "PEMDAS" rule ,
L = 3/4 ( 2³ + 4²)
= 3/4 ( 8 + 4²)
= 3/4 ( 8 + 16 )
= 3/4 ( 24)
= 3/4 ×24
= 24×3/4
= 72/4
L = 1 3
Hence, the given expresion is equal to 13 .
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What is the surface area of a cube that has an edge of 7 cm.
Answer: Your answer should be 294 cm2.
Answer:
294 cm²
Step-by-step explanation:
A cube has 6 congruent square faces. The surface area is the sum of the area of the 6 faces.
area of one face = 7 × 7 = 49 cm²
surface area = 6 × 49 = 294 cm²
ow many ways are there for six ce majors and ten cs majors to stand in a line so that no two ce majors stand next to each other?
The number of ways for six ce majors and ten cs majors to stand in a line so that no two ce majors stand next to each other are 462.
We need to maintain one condition that no two ce majors stand next to each other.
So, what we can do firstly we allow ten cs majors to stand in a line as there are no restrictions on cs majors.
Total number of ways by which ten cs majors can stand=10!=3628800
Now, when 10 cs majors stand in a line then we have 11 spaces.
Now, we need to choose such space for 6 ce majors so that no two ce majors stand next to each other.
So, it is equivalent to choose 6 spaces from 11 spaces which is given by [tex]^1^1C_6[/tex] ways =(11!)/(6!×5!)=11×2×3×8×7=462ways.
Hence, total number of ways are 462.
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Find the x-intercepts of the graph. (Enter your answers as a comma-separated list. Use n as an integer constant.) y = sin πx/6 + 1
the x-intercepts of the given graph are 12n - 3 where n is 0,±1,±2...
What is equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
The given straight line is y = sin πx/6 + 1
To find the x-intercepts we have to y=0 in the function.
So the equation become, 0 = sin πx/6 + 1
sin πx/6 = - 1
πx/6=nπ+(−1) n ( -π/2)
x = 12n - 3
So, the x-intercepts of the given graph are
12n - 3 where n is 0,±1,±2...
Hence the x-intercepts of the given graph are 12n - 3 where n is 0,±1,±2...
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1. If f(x) = x + 3 and g(x) = x² + 2x - 3, find [gxf](x).
If the function f(x) [tex]=[/tex] x [tex]+[/tex] 3 and g(x) = x² + 2x - 3, then the value of the composite function [gof](x) is = x² + 8x + 12 .
In the question ,
it is given that
the function f(x) is [tex]=[/tex] x [tex]+[/tex] 3
and the function g(x) is [tex]=[/tex] x² [tex]+[/tex] 2x - 3 ,
we have to find the value of composite function , (gof)(x)
(gof)(x) = g(f(x))
substituting the value of f(x) = x + 3,
we get ,
g(f(x) = g(x + 3)
Substituting the (x+3) in place of x in the function g(x) , we get
= (x+3)² + 2(x+3) - 3
= x² + 6x + 9 + 2x + 6 - 3
= x² [tex]+[/tex] 8x [tex]+[/tex] 9 + 3
= x² [tex]+[/tex] 8x + 12
Therefore , If the function f(x) = x + 3 and g(x) = x² + 2x - 3, then the value of the composite function [gof](x) is = x² + 8x + 12 .
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I will mark brainliest for help
Answer:
Step-by-step explanation:
78
What is the step by step equation for
Answer:
First, know that [tex]csc(x)=\frac{1}{sin(x)}[/tex]:
[tex]\frac{1}{sin^{2}(x)} *cos^{2}(x)=\frac{cos^{2}(x)}{sin^{2}(x)}[/tex]
Remember that cos²(x) + sin²(x) = 1, so cos²(x) = 1 - sin²(x):
[tex]\frac{cos^{2}(x)}{sin^{2}(x)} =\frac{1-sin^{2}(x)}{sin^{2}(x)} =\frac{1}{sin^{2}(x)} -\frac{sin^{2}(x)}{sin^{2}(x)} =csc^{2}(x)-1[/tex]
Step-by-step explanation:
this might be the answer
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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What is the median of the data 17 2 7?.
Median for the given data 17, 2 ,7 is 12.
What is median?
The median is that the value that’s precisely within the middle of a dataset once it's ordered. It’s a live of central tendency that separates the bottom 50% from the very best 50% of values.
Main body :
First of all to find the median data should be arranged in ascending order.
Aranging data in ascending order
2, 5 , 7 , 7 , 8 , 8 , 10 , 10 , 14 , 15 , 17 , 18 , 24 , 27 , 28 , 48
Now there are even number of terms i. e 16
So,
M1 = n / 2 and M2 = ( n / 2 ) + 1
= 16 / 2 = 8 + 1
= 8th term = 9th term
M1 = 10 M2 = 14
Median, M = ( M1 + M2 ) / 2
= ( 10 + 14 ) / 2
= 24 / 2
= 12
Hence median of observation is 12.
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What are the steps for using a compass and straightedge to construct the bisector of angle A?.
The steps to construct the bisector of angle A are- draw an arc across both rays of the angle. From each arc, draw another pair of arcs that intersect each other. Draw a line to the intersection point to form the angle bisector.
Detailed steps to construct the bisector of angle A using compass are:
1. Give name to the intersection of the arcs in the interior of the angle as point M.
2. Without changing the width of the compass, place the point of the compass at point O and draw another arc in the interior of the angle.
3. Place the point of the compass on point N and again draw an arc in the interior of the angle.
4. Use the straight ruler to draw a line.
5. Place the point of the compass at point A and draw an arc that intersects the sides of ∠A. Label the points of intersection as points N and O.
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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.
a baseball team plays in a stadium that holds 53,000 spectators. with ticket prices at $10, the average attendance had been 27,000. when ticket prices were lowered to $8, the average attendance rose to 33,000.
(a) find the demand function (price p as a function of attendance x), assuming it to be linear.
(b) how should ticket prices be set to maximize revenue?
(a) The demand function assuming it is linear is P(x) = -x/3000 + 19 .
(b) The ticket price to maximize the revenue should be $9.5 .
In the question ,
it is given that ,
the number of spectators that baseball stadium can hold = 53000
the ticket price = $10
the average attendance = 27000 ,
when ticket price lowered to $8 , average attendance rose to 33000 .
So , the points are represented as
for $10 the attendance is 27000 ,
for $8 the attendance is 33000 ,
the points are (27000 , 10) and (33000 , 8) .
the slope = (change in price)/(change in attendance )
= (8-10)/(33000 - 27000)
= -2/6000
= -1/3000
So ,the equation is
(y - 10) = (-1/3000)(x - 27000)
y - 10 = -x/3000 + 27000/3000
y - 10 = -x/3000 + 9
y = -x/3000 + 19
the demand function is P(x) = -x/3000 + 19 ,
the revenue function , R(x) is x.P(x)
R(x) = x.P(x)
So , R(x) = x(-x/3000 + 19)
= -x²/3000 + 19x
to maximize the revenue function , we differentiate with respect to "x" ,
we get ,
R'(x) = 19 - 2x/3000
= 19 - x/1500
for critical value , R'(x) = 0 ,
w get ,
19 - x/1500 = 0
x/1500 = 19
x = 28500
again Differentiating R′(x) with respect to x,
R″(x) = -1/1500 < 0
So , for 28500 spectators, the revenue will be maximum .
the ticket price for 28500 spectators will be ,
P(28500) = 19 - 28500/3000
= 19 - 9.5
= 9.5
Therefore , (a) The demand function assuming it is linear is P(x) = -x/3000 + 19 .
(b) The ticket price to maximize the revenue should be $9.5 .
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a hat contains tags numbered 1, 2, 3, 4, 5, 6. two tags are selected. show the sample space and then compare the probability that the number on the second tag exceeds the number on the first tag when (a) the first tag is not replaced before the second tag is drawn and (b) the first tag is replaced before the second tag is drawn g
The probability that the number on the second tag exceeds the number on the first tag is 0.5
A hat contains tags numbered 1, 2, 3, 4, 5, 6. two tags are selected.
The complete sample space is 6 x 6 = 36
the probability that the number on the second tag exceeds the number on the first tag...Let this event be L
when (a) the first tag is not replaced before the second tag is drawn
If the 1st tag is 1,
Then P(L) = 1/6 x 5/5
If the 1st tag is 2,
Then P(L) = 4/5 x 1/6
If the 1st tag is 3,
Then P(L) = 3/5 x 1/6
If the 1st tag is 4,
Then P(L) = 2/5 x 1/6
If the 1st tag is 5,
Then P(L) = 1/5 x 1/6
If the 1st tag is 6,
Then P(L) = 0/5 x 1/6 = 0
P(L) = 5/30 + 4/30 + 3/30 + 2/30 + 1/30
The probability that the number on the second tag exceeds the number on the first tag = (15/30) = 1/2 = 0.5
Therefore, the probability that the number on the second tag exceeds the number on the first tag is 0.5
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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
Nico wants to use a horizontal number line to compare 134 and 1. 5. He is unsure how to do it and asks you for help. How would you explain the process?.
The number line we can see that 1.5 is less than 1.75.
Mark two points 1.75 and 1.5 on number line and make a number line from -1 to 2 where each point is 0.25 units away
Then compare 1.75 and 1.5 on number line
Given :
Nico wants to use a horizontal number line to compare 1 3/4 and 1.5
Lets write the fraction in decimal form to compare and mark it on number line [tex]1\frac{3}{4}[/tex] = 1.75
Now mark two points 1.75 and 1.5 on number line
Make a number line from -1 to 2 where each point is 0.25 units away
Mark a number line that are 0.25 units away using below numbers
-1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2
On the number line ,
1.5 comes first
1.75 is next to 1.5
From this number line we can see that 1.5 is less than 1.75.
1.5 < [tex]1\frac{3}{4}[/tex]
Hence the answer is the number line we can see that 1.5 is less than 1.75.
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Dos números que suman 54 pero tienen una diferencia de 30
Answer:
12 y 42
Step-by-step explanation:
Let x and y represent the two numbers:
(1) x+y=54 and (2) x-y=30
Solve for x:
x-y=30
x=30-y
Substitute into equation (1):
(30-y)+y=54
2y+30=54
2y=24
y=12
Substitute into equation (2):
x-12=30
x=42
you are 1 of 999,999 peopl e asked. you get to keep whatever 6-digit dollar amount you want as long as no one else chooses it. what do you choose?
you get to keep whatever 6-digit dollar amount you want as long as no one else chooses it is $809,417
you choose a random number, but don't want to make it start with 9 as everyone will be picking nine as the first digit. So instead go with the next best, 8. Then making the next digit 0 since people would be unlikely to have the second number as 0, trying to max out their money while also picking the lowest first number. Then have the rest of the digits be random to maximize the odds of no one happening to select it.
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Find the distance from the point (0, –4) to the line x+5y=10
By the way, I am in high school geometry so maybe you're supposed to use the distance formula and perpendicular bisector? I am still so confused, please help!
The distance from (0, -4) to the line x + 5y = 10 is approximately 6 units.
How to Find the Distance From a Point to a Line?To find the distance from a point to a given line, recall the following:
Slope (m) in a given equation, y = mx + b is represented as m.Slopes of perpendicular lines are negative reciprocalsThe distance formula used for finding the distance between two points is: d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].Step 1: Find the slope of the line, x + 5y = 10:
Rewrite the equation, x + 5y = 10 as y = mx + b, to find the value of the slope (m)
5y = -x + 10
y = -x/5 + 10/5
y = -1/5x + 2
The slope (m) = -1/5.
Step 2: Find an equation of the perpendicular line to the line x + 5y = 10 that passes through the point (0, -4):
Slope (m) = 5 [negative reciprocal of -1/5]
y-intercept (b) = -4
Substitute m = 5 and b = -4 into y = mx + b:
Equation of the line: y = 5x - 4
Step 3: Find the point of intersection of the lines y = 5x - 4 and y = -1/5x + 2:
Therefore, the lines intersect when 5x - 4 = -1/5x + 2
5x - 4 = -1/5x + 2
5x + x/5 = 4 + 2
26x/5 = 6
26x = 30
x = 30/26
x ≈ 1.2
Substitute x = 1.2 into y = 5x - 4:
y = 5(1.2) - 4
y = 2
Point of intersection is: (1.2, 2)
Step 4: Find the distance between (0, -4) and (1.2, 2) using the distance formula:
d = √[(1.2 − 0)² + (2−(−4))²]
d = √[(1.2)² + (6)²]
d = √37.44
d ≈ 6 (nearest whole number)
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What kind of triangle do you have if it has an obtuse angle which measures more than 90 degrees but less than 180 degrees?.
If a triangle has an obtuse angle which measures more than 90 degrees but less than 180 degrees it is an obtuse angled triangle.
When one of the vertex angles of a triangle is greater than 90°, it is called an obtuse angle triangle
An obtuse triangle can either be an isosceles or a scalene triangle but not an equilateral triangle.
In an obtuse angle triangle, the sum of the squares of the two sides is always less than the square of the longest side.
Therefore, if a triangle has an obtuse angle which measures more than 90 degrees but less than 180 degrees it is an obtuse angled triangle.
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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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