Steps in order to produce the algorithm is multiplies two n-bit binary integers a and b using only bitwise operations (shift and AND) and addition.
Set the product P to 0.
Repeat n times we get,
If the least significant bit of a is 1, add the value of b to P.
Shift b one bit to the left.
Shift a one bit to the right.
The final value of P is the product of a and b.
This algorithm is known as the binary multiplication algorithm
And it multiplies two n-bit binary integers a and b using only bitwise operations (shift and AND) and addition.
The algorithm works by iteratively adding shifted copies of b to the product P.
Depending on whether the corresponding bit in a is 1 or 0.
At the end of the iteration, P contains the product of a and b.
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how do you find the total surface area of a pyramid
Answer:
To find the total surface area of a pyramid you do SURFACE AREA =B+12(P×l)
PLEASE PLEASE HELP
The vertices of quadrilateral LMNP are L(-1 , 7), M(4,9), N(8, -1), and P(3,-3). Using the distance formula, determine the most precise classification of LMNP.
So, the most precise classification of quadrilateral LMNP is a kite.
What is equation?In mathematics, an equation is a statement that two mathematical expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used in many areas of mathematics, science, and engineering to model relationships between quantities and to solve problems.
Here,
To classify the quadrilateral LMNP, we need to calculate the length of all four sides using the distance formula and then use those values to determine the shape of the quadrilateral.
The distance formula is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Using this formula, we can calculate the length of each side of the quadrilateral as follows:
LM = √[(4 - (-1))² + (9 - 7)²] = √[5² + 2²] = √29
MN = √[(8 - 4)² + (-1 - 9)²] = √[4² + (-10)²] = √116
NP = √[(3 - 8)² + (-3 - (-1))²] = √[(-5)² + (-2)²] = √29
PL = √[(-1 - 3)² + (7 - (-3))²] = √[(-4)² + 10²] = √116
Now, we can use the values we have calculated to determine the shape of the quadrilateral. We can see that LM = NP and MN = PL, which means that opposite sides are congruent. Also, LM and MN are not equal to PL and NP, which means that opposite sides are not parallel. Therefore, LMNP is a kite.
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can you solve this and convert in min at the end of the step
[tex] \frac{1}{30}(ln( \frac{15}{22}))t = [/tex]
The expression 1/30(ln(15/22))t = x when solved for t has a solution of t = -78.95x
Solving the expression for tGiven the following expression
1/30(ln(15/22))t =
The above expression cannot be solved for t
This is so because the expression is not an equation or inequality
To do this, we must equate the expression to a value (say x)
So, we have
1/30(ln(15/22))t = x
Multiply through by 30
This gives
ln(15/22)t = 30x
Evaluate the natural logarithm expression
This gives
-0.38t = 30x
Divide both sides by -0.38
So, we have
t = -78.95x
Hence, the solution for t is t = -78.95x
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In an effort to figure out why application rates are slipping, your college decides to set up an experiment to determine why students who are interested in the college decide to enroll or not. The college decides to send out a questionnaire to everyone who submitted an application to the college in 2017. What's the population for this study, and what's the sample?
A. The population is all college students everywhere, and the sample is all college students interested in your school.
B. The population is all college students everywhere, and the sample is the individuals who responded to the survey.
C. The population is all students who applied to your college, and the sample is the individuals who responded to the survey.
D. The population is all college students interested in your school, and the sample is everyone who decided to enroll.
The population of interest is the group of students who submitted an application to the college in 2017.
What is sample?A sample is a subset of a population that is selected and studied in order to make inferences or conclusions about the population. The sample is usually selected to be representative of the population in some way, so that the conclusions drawn from the sample can be generalized to the population as a whole.
According to question:The correct answer is C.
The purpose of the study is to determine why students who are interested in the college decide to enroll or not. Therefore, the population of interest is the group of students who submitted an application to the college in 2017.
Option A is incorrect because the population is not all college students everywhere, only those who applied to the college in question.Option B is incorrect because the sample is not just the individuals who responded to the survey, but rather all students who submitted an application in 2017.Option D is incorrect because the sample is not just everyone who decided to enroll, but rather all students who submitted an application, regardless of whether they enrolled or not.To know more about sample visit:
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A survey of 500 music lovers showed that 350 like rock, 300 like country, and 200 like both. How many of the 500 music lovers surveyed dislike both rock and country?
Answer:
50
Step-by-step explanation:
A Venn diagram is very helpful for this picture and I've included one in the attached.
If we look at the numbers we're given, we see that the numbers do not add up to 500 as 350 + 300 + 200 = 850.
However, we can work through the numbers to find the exact values and eventually the number of people that liked neither rock nor country.
Since 200 people like both rock and country, these people are part of the 350 people that like rock.
We can find the number of people who like rock only by subtracting 200 from 350:
350 - 200 = 150 (Rock only)
Using the same logic from above, we know that the 200 people who like both rock and country are a part of the 300 people who like country.
We can find the number of people who like country only by subtracting 200 from 300:
300 - 200 = 100 (Country only)
Currently, we have 450/500 as 150 + 200 + 100 = 450.
Now, we can find the number of people who like neither rock nor country by subtracting 450 from 500:
500 - 450 = 50 (Neither rock nor country)
We can check that the numbers we found equal 500:
Rock only + Both rock and country + Country only + Neither rock nor country = Total amount of music lovers surveyed
150 + 200 + 100 + 50 = 500
500 = 500
(**In the attached Venn diagram, M stands for the total set of music lovers, R stands for rock only, B stands for both, C stands for country only, and N stands for neither)
g (40 points) suppose that x follows a binomial(n,p) distribution. assume that x1 , . . . , xn is a random sample of size n from this distribution.
The MLE of σ^2 for a random sample X1, X2, ..., Xn from a normal distribution with known mean μ is s^2/(n-1), and the MLE of σ is the square root of s^2.
Given a random sample X1, X2, ..., Xn from a normal distribution with mean μ and unknown variance σ^2, the likelihood function is:
L(σ^2) = (1/(2πσ^2)^(n/2)) * exp[-(1/(2σ^2)) * ∑(Xi - μ)^2]
To find the maximum likelihood estimator (MLE) of σ^2, we need to find the value of σ^2 that maximizes the likelihood function.
To do this, we take the natural logarithm of the likelihood function, since the logarithm is a monotonically increasing function and thus does not change the location of the maximum:
ln L(σ^2) = (-n/2) ln(2πσ^2) - (1/(2σ^2)) * ∑(Xi - μ)^2
To maximize this expression, we take the derivative with respect to σ^2 and set it equal to zero:
d/d(σ^2) ln L(σ^2) = (-n/2σ^2) + (1/(2(σ^2)^2)) * ∑(Xi - μ)^2 = 0
Solving for σ^2, we get:
σ^2 = (∑(Xi - μ)^2) / n
This means that the MLE of σ^2 is the sample variance, s^2 = (∑(Xi - μ)^2) / (n-1), since we usually use the sample variance to estimate the population variance when the population mean is known.
Therefore, the MLE of σ is the square root of the sample variance:
σ(hat) = sqrt(s^2)
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____the given question is incomplete, the complete question is given below:
Suppose that X1, . . . , Xn form a random sample from a Normal distribution for which mean μ is known, but the variance σ
2
is unknown. Find the MLE (maximum likelihood estimation) of σ.
Mrs. Jefferson needs new whiteboard markers for her classroom. Whiteboard markers at the office supply store are being sold for 5 for 7.25. Mrs. Jefferson has 26 students in her class. She wants to have enough markers so that each student has 3 markers. Which of the amounts would be enough money to buy her students a minimum of 3 markers each? Select all that apply.
$75, $93, $102, $113, $115, $129
Answer:
$129
Step-by-step explanation:
26 students x 3 markers each= 78 markers
Markers are being sold in sets of 5, so she needs at least 16 packs of markers. that will cost her $116
HELP what is the answer to this using systems of equations
y=1/8x−1
−5x+4y=−13
Answer:
x = 2
y = -3/4
Step-by-step explanation:
1. Substitute y=1/8x -1 in −5x+4y=−13
-5x+4(1/8x -1) = -13
2. Solve for x
-5x + 4/8x - 4 = -13
-9/2x - 4 = -13
-9/2x = -9
x = 2
3. Now that you know x = 2, plug it into y=1/8x - 1 to find what y is.
y= 1/8(2) - 1
y= 2/8 - 1
y= -3/4
convert the following linear programming problem to standard form: maximize 2^i -f x2 subject to 0 < x\ < 2 x\ %2 < 3 x\ 2x2 < 5 x2 >0 .
The converted linear programming problem in standard form is given by
maximize 2^i - f x₂ + 0x₁ + 0s₁ + 0s₂ + 0s₃ + 0s₄ where s₁, s₂, s₃, and s₄ are the slack variables.
convert the linear programming problem to standard form,
Introduce slack variables to represent the inequalities,
And rewrite the objective function as a linear expression.
First, let us introduce the slack variables,
x₁ + s₁= 2
x₂ + s₂ = 3 + 2t
2x₂ + s₃ = 5
s₄ = -x₂
where s₁, s₂, s₃, and s₄ are the slack variables.
Rewrite the objective function as a linear expression,
Maximize 2^i - f x2
= maximize 2^i - f x₂ + 0x₁ + 0s₁ + 0s₂ + 0s₃ + 0s₄
Now we have the linear programming problem in standard form,
maximize 2^i - f x₂ + 0x₁ + 0s₁ + 0s₂ + 0s₃ + 0s₄
subject to,
x₁ + s₁ = 2
x₂ + s₂ = 3 + 2t
2x₂ + s₃ = 5
s₄ = -x₂
x₁ >= 0, s₁ >= 0
x₂ >= 0, s₂ >= 0, t >= 0
s₃ >= 0, s₄ >= 0
Added a new variable t to represent the inequality
x₂ % 2 < 3,
which can be rewritten as x₂ = 2t + r,
where r is the remainder of x₂ divided by 2.
Require t to be non-negative, and r to be less than 2.
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I’m not sure what the limit would be if it’s discontinued but defined
The graph's function limit at x=4 is 6.
Define limitIn mathematics, the limit of a function is the value that the function approaches as the input approaches a certain value or as the input approaches infinity or negative infinity. A function may or may not have a limit at a given point or as the input goes to infinity or negative infinity.
The formal definition of the limit of a function f(x) as x approaches a value a is as follows:
For every positive number ε (epsilon), there exists a corresponding positive number δ (delta) such that if 0 < |x-a| < δ, then |f(x)-L| < ε.
Limit f(x) at x tend to 4⁺ =6.
Limit f(x) at x tend to 4⁻ =6
Hence, the graph's function limit at x=4 is 6.
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Does anyone know how to write the “In” symbol in mathXL ?? It would help so much if someone could tell me, thanks
Answer:
Natural
Step-by-step explanation:
Ln in mathematics mean natural log. Natural log is the log of a number with base e where e=2.71828. For understanding if the number is 2.71828^10 then the ln of 2.71828^10 is 10.
which values in the data set are outliers? show all work. 72, 81, 82, 83, 83, 85, 100, 54, 75, 81, 83
In this data set, the only value that is an outlier is 100, since it is above the upper bound of 98.25.
To identify the outliers in the data set, we can use the concept of the interquartile range (IQR) and the 1.5×IQR criterion.
First, we need to find the first and third quartiles (Q1 and Q3) of the data set. To do this, we can order the data set from smallest to largest:
54, 72, 75, 81, 81, 82, 83, 83, 83, 85, 100
The median of the data set is the middle value, which is 82.
The lower half of the data set will consists of:
54, 72, 75, 81, 81
The median of the lower half is (72 + 75)/2 = 73.5, which is the value halfway between the two middle values.
The upper half of the data set will consists of:
83, 83, 83, 85, 100
The median of the upper half is (83 + 85)/2 = 84, which is the value halfway between the two middle values.
Therefore, the first quartile (Q1) is 73.5 and the third quartile (Q3) is 84.
The interquartile range (IQR) is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 84 - 73.5 = 10.5
To identify the outliers in the data set using the 1.5×IQR criterion, we need to calculate the lower and upper bounds:
Lower bound = Q1 - 1.5×IQR = 73.5 - 1.5×10.5 = 57.75
Upper bound = Q3 + 1.5×IQR = 84 + 1.5×10.5 = 98.25
Any data point that is below the lower bound or above the upper bound is considered an outlier.
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help ASAP PLSSSS
The table of values represents a linear function.
Enter the rate of change of this function.
The rate of change (or slope) of this linear function is -1/2.
Describe Linear Function?A linear function is a mathematical function that has a constant rate of change, meaning that the output (y-value) changes at a constant rate for every unit increase in the input (x-value). In other words, the graph of a linear function is a straight line.
The general form of a linear function is y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The slope represents how much the y-value changes for every one-unit increase in the x-value.
Linear functions can be used to model many real-world situations, such as distance vs. time or cost vs. quantity. They are also commonly used in economics, physics, and engineering.
The rate of change of a linear function represents the slope of the line. We can calculate the slope using the formula:
slope = (change in y) / (change in x)
Let's use the points (0, -3) and (2, -4) to calculate the slope:
slope = (-4 - (-3)) / (2 - 0)
slope = -1 / 2
Therefore, the rate of change (or slope) of this linear function is -1/2.
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Question 12 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors were taking none of these courses?
Note: Consider making a Venn Diagram to solve this problem.
0
5
9
22
None of these courses were being taken by seniors is 9.
What Is A Venn Diagram?A Venn diagram is a type of graphic representation that uses circles to emphasise the relationships between certain items or constrained groups of things. Circles with overlaps exhibit certain traits, but circles without overlaps do not.
Total number of students=150
Number of students Math =80
Number of students Spanish =41
Number of students Physics=54
Number of students Math and Spanish=10
Number of students Math and Physics=19
Number of students Physics and Spanish=12
Number of students Physics and Spanish and math=7
seniors were taking none of these courses =150-(80+41+54)+10+19+12-7
=9
Diagram is attached below:
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use the data below to find the logarithmic regression of aids cases over time. use either a calculator or spreadsheet program.
the logarithmic regression of aids cases over time is 4.6
A type of regression called logarithmic regression is used to simulate situations where growth or decay initially increases quickly and then gradually slows down.
A better prediction model is produced by applying the logarithm to your variables, which results in a much more distinct and/or adjusted linear regression line through the base of the data points.
y ≈ 33.7·ln(x) -45.9
4.6
Detailed explanation:
Logarithmic regression can be carried out using a spreadsheet or a graphing calculator. The log curve with the best least-squares fit is about...
y ≈ 33.7·ln(x) -45.9
Around 4.6 is the anticipated value of x needed to get y = 5.2.
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The table describes the quadratic function h(x).
x h(x)
−3 6
−2 3
−1 2
0 3
1 6
2 11
3 18
What is the equation of h(x) in vertex form?
From the table, the calculated equation of h(x) in vertex form is h(x) = (x + 1)² + 2
Quadratic Function in Vertex Form from Table of ValuesTo find the equation of the quadratic function h(x) in vertex form, we need to first determine the coordinates of the vertex.
The vertex form of a quadratic function is given by
y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
From the table, we have
(h, k) = (-1, 2)
So, we have
y = a(x + 1)² + 2
To determine the value of 'a', we can substitute any other point from the table into the vertex form equation and solve for 'a'.
For example, using the point (0, 3), we have:
a(0 + 1)² + 2 = 3
a = 1
So, we have
y = (x + 1)² + 2 as the equation
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When 1.00 g potassium chlorate is dissolved in 50.0 g water in a Styrofoam calorimeter of negligible heat capacity, the temperature decreases from 25.00°C to 23.36°C. Calculate q for the water and ?H° for the process.The specific heat of water is .
The specific heat of water is [tex]+41840J . mol^{-1}[/tex].
The following formula is used to determine how much heat a substance absorbs or releases during a heat exchange between two bodies, Calculate the value of q.
Q = m.s.t
Where,
Q is equal to how much heat is received or emitted.
m = The substance's mass
t = Temperature change
s = The substance's specific heat
The starting temperature in this dissolve is,
[tex]T_{i}[/tex] = 25.00°C
(25.00 + 273.00) K
= 298.00 K
Final temperature in this dissolving is,
[tex]T_{f}[/tex] = 23.36°C
= (23.36 + 273.00) K
Specific Water's heat is, [tex]4.184\frac{J}{g.K}[/tex]
In this issue, the heat that water releases are,
[tex]Q_{released} = 50.0g*4.184\frac{J}{g.K} * (298.00 - 296.36)K[/tex]
= 343.088J
2) Molar Mass of KClO₃ is [tex]122.55g mol^{-1}[/tex]
As a result, number of moles of KClO₃ present in 1g sample is,
[tex]\frac{1.00g}{122,55g/mol} = 0.0082mols[/tex]
Hence, the standard enthalpy change of the dissolving process is determined as follows:
Δ[tex]H^{o} = +\frac{343.088J}{0.0082mol} \\= +41840J . mol^{-1}[/tex]
The plus symbol (+) denotes the absorption of heat during the dissolving phase.
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Complete Question:
When 1.00 g potassium chlorate (KCIO₃) is dissolved in 50.0 g water in a Styrofoam calorimeter of negligible heat capacity, the temperature decreases from 25.00°C to 23.36°C. Calculate q for the water and AH° for the process. KCIO: (s) → K* (aq) + CIO (aq) The specific heat of water is 4.184 J K-1 g¯!.
The cost of manufacturing a molded part is related to the quantity produced during a production run. When 100 parts are produced, the cost is $300. When 104 parts are
produced, the cost is $324. What is the average cost per part?
OA $0.23 per part
B. $6 per part
OC. $0.17 per part
OD. $7 per part
Answer:
B. $6 per part
Step-by-step explanation:
The average cost per part can be computed as follows
Average Cost = (324-300)/(104-100)
= 24/4
=$6
Answer: B. $6 per part
I will mark you brainiest!
What would you have to calculate to prove the figure below is a SQUARE?
A) the sides all have the same slopes
B) diagonals are ½ the length of the midpoint
C) use the distance formula to show that the opposite sides are supplementary
D) slopes are perpendicular where the sides meet
E) None of these choices are correct.
Answer:
A) the sides all have the same slopes.
Step-by-step explanation:
Every time a square in a graph is a square, their slopes MUST be the same, either that or nothing, it can't be a square.
The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be
approximated by a normal distribution, as shown in the figure
(a) What is the minimum UGPA that would still place a student in the top 5% of UGPAS?
(b) Between what two values does the middle 50% of the UGPAS lie?
COLLE
(a) The minimum UGPA that would still place a student in the top 5% of UGPAS is 3.66
(Round to two decimal places as needed.)
(b) The middle 50% of UGPAS lies between 3 26 on the low end and 3.30 on the high end
(Round to two decimal places as needed.)
Between 3.26 on the low end and 3.30 on the high end is where UGPAS's middle 50% lies.
What does a parabola equation mean?Provided that the parabola's vertex is at the origin and that it is symmetric about the y-axis. So, depending on whether the parabola expands upward or downward, the equation can take the form x2 = 4ay or x2 = -4ay.
Because we are interested in the top 5%, the region to the right of the z-score is 0.05. n,... As a result, we can apply the following z-score formula:
z = (x - μ) / σ
x = z * σ + μ
Substituting the values we have, we get:
x = 1.645 * 0.15 + 3.25 = 3.66
Therefore, the z-scores corresponding to the 25th and 75th percentiles are:
z1 = -0.675
z2 = 0.675
Using the same formula as before, we can find the UGPAs corresponding to these z-scares:
x1 = -0.675 * 0.15 + 3.25 = 3.26
x2 = 0.675 * 0.15 + 3.25 = 3.30
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each of 2 identical number cubes ,shown below, has a different integer,1 through 6,on each face.conside rthe sample space determined by rolling
The positive difference between the greatest sum and the least sum in the sample space of the output of the two cubes is 10.
What is a sample space?A sample space is a mathematical collection or set of possible outcomes of a random experiment. A sample space is represented by the symbol "S". The possible outcome of an experiment is called the events.
The greatest sum is obtained by adding the largest number on the first cube with the largest number on the second cube. The least number can be obtained by adding the smallest number on the first cube with the smallest number on the second cube.
The possible numbers displayed by the first cube are; 1, 2, 3, 4, 5, 6
The possible numbers displayed by the second cube are also; 1, 2, 3, 4, 5, 6
The greatest sum is therefore; 6 + 6 = 12The least sum is therefore; 1 + 1 = 2The positive difference between the greatest sum and the least sum in the sample space is therefore;
12 - 2 = 10
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50 POINTS!!!!! WWILLLLLL VOTTTEEEE
A vector has a magnitude of 28 and a direction of 500. Another vector has a
magnitude of 75 and a direction of 1250. What are the magnitude and
direction of the resultant vector? Round the magnitude to the thousandths
place and the direction to the nearest degree.
The magnitude and direction of the resultant vector are 50.479 and 73 degrees, respectively.
What is vector addition?
Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for the vector addition of two or more vectors. For two vectors, the vector sum is obtained by placing them head to tail and drawing the vector from the free tail to the free head.
To find the magnitude and direction of the resultant vector, we need to add the two given vectors. We can do this using vector addition, where we add the corresponding components of each vector.
First, let's convert the given magnitudes and directions into component form. We can use the following equations to find the x and y components of each vector:
Magnitude = √(x² + y²)
Direction = tan⁻¹(y/x)
For the first vector with magnitude 28 and direction 500, we have:
Magnitude = 28
Direction = 500 degrees
x = Magnitude * cos(Direction) = 28 * cos(500) = -14
y = Magnitude * sin(Direction) = 28 * sin(500) = -24.202
Therefore, the first vector can be written as v1 = <-14, -24.202>
Similarly, for the second vector with magnitude 75 and direction 1250, we have:
Magnitude = 75
Direction = 1250 degrees
x = Magnitude * cos(Direction) = 75 * cos(1250) = 28.481
y = Magnitude * sin(Direction) = 75 * sin(1250) = 72.929
Therefore, the second vector can be written as v2 = <28.481, 72.929>
To find the resultant vector, we can add the components of the two vectors:
v = v1 + v2 = <-14, -24.202> + <28.481, 72.929> = <14.481, 48.727>
The magnitude of the resultant vector is:
Magnitude = √(x² + y²) = √(14.481² + 48.727²) = 50.479
Rounding to the thousandth place, the magnitude of the resultant vector is 50.479.
The direction of the resultant vector can be found using the following equation:
Direction = tan⁻¹(y/x) = tan⁻¹(48.727/14.481) = 72.636 degrees
Rounding to the nearest degree, the direction of the resultant vector is 73 degrees.
Therefore, the magnitude and direction of the resultant vector are 50.479 and 73 degrees, respectively.
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awaite
Find the Factors of 24 less than 24.
Answer: Factors of 24 include: 1 and 24, 2 and 12, 3 and 8, 4 and 6
Step-by-step explanation:
a triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm squarea triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm square
The cοst οf painting the triangle bοrder at the given rate is Rs. [tex]108\sqrt{(2)[/tex].
What is a triangle?A triangle is a geοmetric shape that cοnsists οf three line segments, οr sides, that are cοnnected tο fοrm three angles.
Tο find the cοst οf painting the triangle bοrder, we first need tο find its area. Let's call the third side οf the triangle "x".
We knοw that the perimeter οf the triangle is 24cm, sο we can write an equatiοn:
6cm + 8cm + x = 24cm
Simplifying this, we get:
x = 10cm
Nοw we can use Herοn's fοrmula tο find the area οf the triangle:
s = (6cm + 8cm + 10cm)/2 = 12cm
Area [tex]= \sqrt{(s(s-6cm)(s-8cm)(s-10cm))[/tex]
[tex]= \sqrt{(12cm6cm4cm*2cm)[/tex]
[tex]= 2\sqrt{(72cm^2)[/tex]
[tex]= 12\sqrt{(2) cm^2[/tex]
Finally, we can calculate the cοst οf painting the bοrder at a rate οf Rs. 9 per square cm:
Cοst = (Area) x (Rate)
[tex]= (12\sqrt{(2)} cm^2) x (Rs. 9/cm^2)[/tex]
[tex]= Rs. 108\sqrt{(2)[/tex]
Therefοre, the cοst οf painting the triangle bοrder at the given rate is= [tex]Rs. 108\sqrt{(2)[/tex]
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Help please! Appreciate the help
The statements that are true would be :
f(x) = 2√x has the same domain and range as f(x) = √xf(x) = -√x has the same domain as f(x) = √x but a different rangeHow to prove the statements on range and domain ?f(x) = 2√x has the same domain and range as f(x) = √x:
Both functions have a square root, so the domain must be x ≥ 0 in both cases. Since f(x) = 2√x is a vertical stretch of f(x) = √x by a factor of 2, the range of both functions starts at 0 and goes to positive infinity.
f(x) = -√x has the same domain as f(x) = √x but a different range:
In this relation, both functions have a square root, so the domain must be x ≥ 0 in both cases as it was in the first option. f(x) = -√x is a reflection of f(x) = √x over the x-axis, so the range is y ≤ 0, which is different from the range of f(x) = √x (y ≥ 0).
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On the 1st January 2014 Carol invested some money in a bank account.
The total amount of money Carol originally invested is £22,000 in the bank account.
What is compound intrest?Compound interest is interest that is calculated not only on the initial amount of money invested or borrowed, but also on any accumulated interest from previous periods.
This results in exponential growth or accumulation of interest over time.
Let X be the amount that Carol originally invested in the account.
After 1 year, the amount of money in the account will be X(1+0.025) = X(1.025).
After Carol withdrew £1000, the amount of money in the account will be X(1.025) - £1000.
After 2 years (i.e. on 1st January 2016), the amount of money in the account will be (X(1.025) - £1000)(1+0.025) = (X(1.025) - £1000)(1.025).
We know that the amount of money in the account on 1st January 2016 was £23,517.60, so we can write the equation:
(X(1.025) - £1000)(1.025) = £23,517.60
Expanding the left-hand side and simplifying, we get:
X(1.025)² - £1000(1.025) = £23,517.60
X(1.025)² = £24,567.63
Dividing both sides by (1.025)², we get:
X = £22,000 (rounded to the nearest pound)
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The complete question is -
On the 1st of January 2014, Carol invested some money in a bank account. The account pays 2.5% compound interest per year. On the 1st of January 2015, Carol withdrew £1000 from the account. On the 1st of January 2016, she had £23 517.60 in the account. Work out how much Carol originally invested in the account?
Caleb took 24 photos at the zoo. Three-eights of his photos are of giraffes. How many of Caleb’s photos are of giraffes ?
A: 6
B: 9
C: 12
D: 18
Answer:
B: 9
Step-by-step explanation:
We know
Caleb took 24 photos at the zoo. 3/8 of his photos are of giraffes.
How many of Caleb’s photos are of giraffes?
We Take
24 x 3/8 = 9 photos
So, 9 of Caleb's photos are of giraffes.
It is known that a certain kind of algae in the Dead Sea can double in population every 4 days. Suppose that the population of algae grows exponentially, beginning now with a population of 1,000,000.
(a) How long it will take for the population to quadruple in size?
days
(b) How long it will take for the population to triple in size?
days
a. it will take 8 days for the population to quadruple in size.
b. t will take 6.34 days for the population to triple in size.
What is algae population?Organisms οf a species living tοgether in a grοup at a particular place are called a “pοpulatiοn” in Biοlοgy. A pοpulatiοn is an assοrtment οf οrganisms in a given lοcatiοn. These οrganisms, since they belοng tο the same species, can interbreed and prοduce mοre οf their kinds.
We have to use the following formula
P(t) = P0(b)t
⇒ 6000000 = 3000000(b)4
⇒ b4 = 2
⇒ b = 21/4
a. 12000000 = 3000000(2)t/4
⇒ 4 = 2t/4
⇒ 22 = 2t/4
⇒ 2 = t/4
⇒ t = 8 days
Thus, it will take 8 days for the population to quadruple in size.
b. 9000000=3000000(2)t/4
⇒ 3 = 2t/4
⇒ log 3 = (t/4)log 2
⇒ t = 6.34 days
Thus, it will take 6.34 days for the population to triple in size.
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the joint probability density function of two continuous random variables x and y is given by: f(x,y)
The value of k is 1/2π, and X and Y are independent because their joint density function factors into a product of their Probability density functions.
To find the value of k, we use the fact that the total area under the joint probability density function equals 1. That is:
integral from 0 to infinity of integral from 0 to infinity of kxye^(-x^2-y^2) dx dy = 1
Using polar coordinates (x = r cos(theta), y = r sin(theta)), the double integral can be written as:
integral from 0 to 2pi of integral from 0 to infinity of k r^3 e^(-r^2) dr d(theta) = 1
The integral over theta is just 2pi, so we can simplify to:
2pi k integral from 0 to infinity of r^3 e^(-r^2) dr = 1
Solving this integral, we get:
2pi k (-1/2) e^(-r^2)| from 0 to infinity = 1
Since e^(-r^2) goes to 0 as r goes to infinity, we have:
pi k = 1/2
Therefore, k = 1/(2pi).
To prove that X and Y are independent, we need to show that the joint probability density function can be factored into the product of the marginal probability density functions:
f(x,y) = f_X(x) * f_Y(y)
The marginal probability density function of X is given by:
f_X(x) = integral from 0 to infinity of kxye^(-x^2-y^2) dy
= kxe^(-x^2) * integral from 0 to infinity of ye^(-y^2) dy
The integral from 0 to infinity of ye^(-y^2) dy is a known integral equal to 1/2, so we have:
f_X(x) = kxe^(-x^2) / 2
Similarly, the marginal probability density function of Y is given by:
f_Y(y) = kye^(-y^2) / 2
Therefore, we have:
f_X(x) * f_Y(y) = k^2 xy e^(-(x^2+y^2))
Comparing this to the joint probability density function given in the problem, we can see that:
f(x,y) = f_X(x) * f_Y(y)
Thus, X and Y are independent.
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____The given question is incomplete, the complete question is given below:
The joint probability density function of two-dimensional continuous random variable (X,Y) is given by > 0, y >0; f(x,y) = 0, otherwise, kxye-(x2+y2). Find the value of k and prove also that X and Y are independent.
The points (-3, 3) and (7, q) fall on a line with a slope of -7/10. What is the value of q?
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{q}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{q}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ \cfrac{ -7 }{ 10 }}\implies \cfrac{q-3}{7+3}=\cfrac{ -7 }{ 10 }\implies \cfrac{q-3}{10}=\cfrac{ -7 }{ 10 } \\\\\\ q-3=-7\implies q=-4[/tex]