The sum of the first 4 terms of the binomial expansion of (0.9 + 0.081)³ is approximately 0.9441.
What is binomial expansion?The binomial expansion formula is given by:
[tex](a + b)^n = nC_0 \times a^n \times b^0 + nC_1 \times a^{(n-1)} \times b^1 + nC_2 \times a^{(n-2)} \times b^2 + ... + nC_n \times a^0 \times b^n[/tex]
where nCk is the binomial coefficient, which is equal to n! / (k! * (n-k)!) for k = 0, 1, 2, ..., n.
Here, we have a = 0.9 and b = 0.081, and we want to find the sum of the first 4 terms, which means we need to find:
(0.9 + 0.081)⁰ + (0.9 + 0.081)¹ + (0.9 + 0.081)² + (0.9 + 0.081)³
Using the binomial expansion formula with n = 3, we get:
(0.9 + 0.081)³ = 3C0 x 0.9³ x 0.081^0 + 3C1 x 0.9² x 0.081¹ + 3C2 x 0.9¹ x 0.081² + 3C3 x 0.9⁰ x 0.081³
Simplifying each term, we get:
1 x 0.729 x 1 + 3 x 0.81 x 0.081 + 3 x 0.9 x 0.006561 + 1 x 0.000531441
= 0.729 + 0.19683 + 0.0177117 + 0.000531441
= 0.944076141
Therefore, the sum of the first 4 terms of the binomial expansion of (0.9 + 0.081)³ is approximately 0.9441 (rounded to 4 decimal places).
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Slect all that apply
The rational numbers in this problem are given by these following options:
A, B, C, D, E, G, I, K, L, O.
What are rational and irrational numbers?Rational numbers are the whole numbers plus decimals that can be represented by fractions, involving both positive and negative numbers.
The set of irrational numbers is composed by numbers that cannot be represented by fractions, such as non-exact roots, which are non-terminating and non-repeating decimal numbers.
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A unit of an abstract mathematical system subject to the laws of arithmetic is?
Units are a natural number, a natural number that are negative, or zero. The number zero and any number generated by adding one to it repeatedly. A single integer or the product of two integers (division by zero excluded).
What exactly are integers?
In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.
The number zero and any number generated by adding one to it repeatedly. A single integer or the product of two integers (division by zero excluded).A natural number, a negative of a natural number, or zero is a unit of an abstract mathematical system according to the principles of arithmetic.
e.g. 1,2,0, 0+1, 0+2+3, 8, 8/2=4, -8/2=-4 etc. all are units of an abstract mathematical system subject to the laws of arithmetic.
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Let X be a random variable whose distribution is Normal, with a mean of 100 and a standard deviation of 10. The proportion of observations above 115 is equal to the proportion below what value? Use the fact that the normal distribution is symmetric about the mean.
The value for which the proportion of observations below it is equal to the proportion of observations above 115 is 85.
The normal distribution, also known as the Gaussian distribution or the bell curve, is a continuous probability distribution that describes the distribution of many real-world phenomena such as height, weight, IQ scores, and financial returns. It is a symmetric distribution with a bell-shaped curve that is centered on the mean and characterized by its mean and standard deviation.
Since the normal distribution is symmetric about the mean, the proportion of observations above 115 is equal to the proportion of observations below 100 - (115 - 100) = 85.
So, the value for which the proportion of observations below it is equal to the proportion of observations above 115 is 85.
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3.8m² of concrete is made into the shape of a cylinder.
The base has radius 0.5 metres.
Work out the height of the cylinder.
0.5 m
(2 Marks)
Answer:
4.84 m
Step-by-step explanation:
V = πr²h
h = V/πr² = (3.8 m³) / π(0.5m)² = 4.84 m
the mean is an inappropriate measure of central tendency when the distribution is severely skewed because
The mean is sensitive to outliers and will not accurately represent the center of the data if the distribution is significantly skewed.
The mean is a measure of central tendency that is calculated by adding up all values in a dataset and dividing by the number of values. It is often used as a measure of average since it takes into account all values in the dataset. However, it is an inappropriate measure of central tendency when the data distribution is severely skewed. A skewed distribution is one in which the data is not distributed evenly around the mean, and the data is either concentrated in the lower or higher end of the range. Since the mean is sensitive to outliers, it will be greatly affected by these values and not accurately represent the center of the data. In this case, it is more appropriate to use the median as a measure of central tendency since it is not affected by outliers. The median is the middle value of a dataset when the data is sorted from smallest to largest and is a better representation of the true center of the data in a skewed distribution.
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show that the cosine rule shown below can be solved can be rearranged to give..
Using trigonometry, solving the provided question, we can say that here, [tex]2ab cos A = \frac{b^{2} + c^{2} - a^{2}}{2bc}[/tex] and [tex]\theta = 37[/tex]
What is Trigonometry?The relationship between triangle side lengths and angles is examined in the branch of mathematics known as trigonometry. The application of geometry in astronomical study gave rise to the area's first appearance in the Hellenistic era, roughly in the third century BC. Exact approaches mathematics focuses on certain trigonometric functions and how they could be applied to calculations. In trigonometry, there are six well-known trigonometric functions. They are known by their various names and acronyms: sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly of right triangles. The features of all geometric figures are studied in geometry.
where the sides b and c are forced together, trapping the angle A in (1). There are three options if you wish to rearrange the formula. You can get the answer for B, C, or A.
Reverse the cosine rule provided:
[tex]A^{2} = b^{2} + c^{2}- 2abcos A[/tex]
[tex]2ab cos A = \frac{b^{2} + c^{2} - a^{2}}{2bc}[/tex]
Replace A = θ with a = 17, b = 14, and c = 26,
then simplify:
[tex]Cos \theta = \frac{14^{20} + 26^{2} - 17^{2}}{2\times 14 \times 26}[/tex]
[tex]Cos \theta = \frac{583}{728}[/tex]
[tex]\theta = cos^{-1}(\frac{583}{728})[/tex]
[tex]\theta = 37[/tex]°
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Complete question -
Solve 4x - 5 = 19.
O A. x=8
O B. x=6
O C. x=3.5
O D. x=10
Which of the following is not true of slope of the least-squared regression line?The square of the slope equals the fraction of the variation in the response variable that is explained by the explanatory variable, it is unit less.
The slope of the least-squares regression line is not directly related to the fraction of the variation in the response variable that is explained by the explanatory variable.
The slope of the least-squares regression line is a numerical measure of the rate of change in the response variable for a unit change in the explanatory variable. It does not directly relate to the fraction of the variation in the response variable that is explained by the explanatory variable. This is because the fraction of the variation in the response variable that is explained is determined by the correlation coefficient, which is a measure of how well the regression line fits the data. The slope of the least-squares regression line is unitless, meaning it does not have any specific unit such as meters, seconds, or degrees. The slope of the least-squares regression line is simply a numerical measure of the rate of change in the response variable per unit change in the explanatory variable. This is different from the fraction of the variation in the response variable explained by the explanatory variable, which is determined by the correlation coefficient.
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What is 40,753 in expanded form
Answer:
40,000 + 700 + 50 + 3
Step-by-step explanation:
Expanded form requires you to separate the numbers in power of ten
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Enter the missing numbers in the boxes to complete the table of equivalent ratios.
Time (min) Distance (km)
6
6 18
24
15
Answer:
Time (min) Distance (km)
6 9
12 18
24 36
15 45
Step-by-step explanation:
The table shows equivalent ratios between time in minutes and distance in kilometers. An equivalent ratio means that the ratio of time to distance stays the same, even though the numbers themselves change.
For example, in the first row, the ratio of time to distance is 6 minutes to 9 kilometers. In the second row, the ratio of time to distance is 12 minutes to 18 kilometers. Despite the change in numbers, the ratio of time to distance remains the same. This is why these ratios are considered equivalent.
Can someone help answer this equation
Answer:
0.707106781187
Step-by-step explanation:
I recommend using the website desmos
An oil change at instant auto service is regularly $35. Mr.oliver has a coupon for 25% off.He wants to know the sales price of an oil change
Answer:
$26.25
Step-by-step explanation:
25% of 35 can be found by multiplying .25 x 35 to get 8.75
the coupon will reduce the regular price of $35 by 8.75 to produce the new price of $26.25
The total cost of producing a type of tractor is given by C(x)=11000−60x+0.1x2 C ( x ) = 11000 − 60 x + 0.1 x 2 , where x is the number of tractors produced. How many tractors should be produced to incur minimum cost?
The number of tractors that should be produced to incur the minimum cost will be 300.
What are the maxima and minima of a function?For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.
The maximum and minimum value of the function is at f'(x) = 0.
The function is given below.
C(x) = 11000 − 60x + 0.1x²
Differentiate the function with respect to x, then we have
C'(x) = 0
(d/dx)(11000 − 60x + 0.1x²) = 0
− 60 + 0.2x = 0
0.2x = 60
x = 300
The number of tractors that should be produced to incur the minimum cost will be 300.
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Solve for x
12 + x = 15
Answer: x = 3
Step-by-step explanation: just isolate the variable x
So subtract 12 on both sides of the equation and you are left with x is equal to 3
Hope this helped
Solve using elimination. 3x - 2y = 10 3x - y = 17
The first step is to rewrite the equations in standard form by subtracting the constant from each side.
What is standard form ?Standard form is a type of numerical notation used to express large numbers in a concise form. It is based on powers of 10, which means each place value of a number is multiplied by a power of 10. Standard form is typically used in scientific and mathematical applications, and it is also known as scientific notation. To write a number in standard form, the number is written as a coefficient, followed by the base of 10, raised to an exponent.
3x - 2y = 10 becomes 3x - 2y - 10 = 0
3x - y = 17 becomes 3x - y - 17 = 0
Let's multiply the first equation by 2 and the second equation by 3.
2(3x - 2y - 10) = 0
3(3x - y - 17) = 0
6x - 4y - 20 = 0
9x - 3y - 51 = 0
The next step is to add the two equations together.
6x - 4y - 20 + 9x - 3y - 51 = 0
15x - 7y - 71 = 0
The last step is to solve for the variable.
15x - 7y = 71
15x = 71 + 7y
x = (71 + 7y)/15
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Problem Statement: Create a function named tclip that determines the intersection of a line (solution of a given linear equation) with a clipping triangleT having vertices(0,0),(1,0)and(0,1).The function declaration should have the form function [count, list] =tclip(a,b,c)where the line in question is ordinarily the solution set of the linear equation ax+by=c.The value of the variable count returned should be −2 if the equation ax+by=c has no solutions(e.g.0x+0y=1). −1if the equation ax+by=c is solved by all values of x and y(0x+0y=0)0 if the solutions of ax+by=c do not intersectT(e.g.0x+1y=7)1 if the solutions of ax+by=cintersect T in one point (e.g.1x+1y=0)2 if the solutions of ax+by=c intersect T in more than one point(e.g.∣x−1y=0)The variable 1.st, which reports the distinct endpoints of the intersection, should be a2x0 empty array (empty list of 2-vectors) if count is−2,−1 or 0, 2×1 array (a single column vector)-the unique point of intersection-if count is 12×2 array (list of two column vectors)-the endpoints of the intersection- if count is 2.
The equation that determines the intersection of line with a clipping triangle is ax + by + c = 0 [1]. The solution has been obtained by using functions.
What is a function?
A function is described as a relationship between a group of inputs with one output each. A function is, to put it simply, a relationship between inputs in which each input is connected to exactly one output. Every function has a domain and a codomain, or range. A function is typically represented by the notation f(x), where x represents the input. A function is typically shown as y = f(x).
The equation ax + by + c = 0 [1] represents the line in question. A list of pairs of coordinates for each intersection point and the number of intersections (count) should be returned by the function (list).
A list of items can be sent to the function count list, which will return the total number of objects in the list. The function returns the number of objects in the specified list after accepting an array or list of objects.
Hence, the equation that determines the intersection of line with a clipping triangle is ax + by + c = 0 [1].
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The 149 heights of males from a data set of body measurements vary from a low of 154 cm to a high of 196.9 cm. Use the range rule of thumb to estimate the standard deviations and compare the result to the standard deviation of 8.04 cm calculated using the 149 heights. What does the result suggest about the accuracy of estimates of s found using the range rule of thumb? Assume the estimate is accurate if it is within 1.4 cm.
Therefore , the solution of the given problem of standard deviation comes out to be the range rule of thumb is only an approximation and does not take into account the shape of the distribution .
The standard deviation is defined.Variance is a measure of variation used in statistics. To calculate the average variance between the data and the mean, use the algorithm below. In opposition to other numerical measures of variability, it incorporates all data points into calculations by comparing each data point's value to the mean. Among the differences are unintentional errors, irrational expectations, and changing market or economic conditions.
Here,
According to the range rule of thumb, the range of the data set is roughly four times the standard deviation. Therefore, we can estimate the standard deviation by dividing the range by 4:
range = 196.9 - 154 = 42.9
estimated standard deviation = range / 4 = 10.725
Comparing this estimate to the actual standard deviation of 8.04 cm calculated using the 149 heights, we see that the estimate is off by about 2.685 cm.
This suggests that the estimate obtained using the range rule of thumb is not very accurate in this case, as it is outside the 1.4 cm threshold for accuracy.
This is not surprising, as the range rule of thumb is only an approximation and does not take into account the shape of the distribution or the sample size.
Therefore , the solution of the given problem of standard deviation comes out to be the range rule of thumb is only an approximation and does not take into account the shape of the distribution or the sample size.
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n is a whole number. Prove that (n+8)(2n+6) is always an even number.
Answer:
Any odd number multiplied by an even number will make an even number.
What is (-3,2),(4,-3) and (-5,-4) rotated 90° counterclockwise
The coordinates after the rotation of 90° will be (-2, -3), (3, 4), and (4, -5) respectively.
What is geometry rotation?Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.
Precession, nutation, and intrinsic rotation are the names of these rotations.
Shapes can be rotated by being moved around a fixed point (clockwise or anticlockwise, and by a certain number of degrees).
Although the shape will remain precisely the same, its location within the room will shift.
So, we have:
(-3,2),(4,-3) and (-5,-4)
Now, the graph then as follows.
Now, rotate them to 90°.
(Refer to the graph attached below)
Then, the coordinates after 90° rotation will be:
(-3,2) = (-2, -3)
(4,-3) = (3, 4)
(-5,-4) = (4, -5)
Therefore, the coordinates after the rotation of 90° will be (-2, -3), (3, 4), and (4, -5) respectively.
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when some population elements are excluded from the process of selecting the sample
Specific individuals in a population are unfairly left out of a study, which is known as exclusion bias. When researchers design a study that inadequately represents specific segments of the community, undercoverage bias emerges.
when a sample is unrepresentative of the population as a whole?When a sample is not chosen that accurately represents the full population of data, a statistical error known as sampling error arises. As a result, the sample's findings do not accurately reflect the outcomes that the complete population would produce.
What is the procedure for choosing a sample from the population called as?When a sample is chosen from a population based on the idea of randomization, this practise is known as probability sampling.
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At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 44
The probability of not ordering nonalcoholic beverages is 66.
What is the probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of samples
Given that at a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 44%.
The probability of not ordering the beverages will be:-
P = 100% - 44%
P = 66%
Therefore, the probability of not ordering nonalcoholic beverages is 66.
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the city of alexandria has a high temperature of 18 degrees and a low temperature of -5 degrees on the same day. by how many degrees did the high temperature exceed the low temperature?
Hi there, here's your answer:
Highest temperature = 18 degrees
Least temperature = -5 degrees
The difference between the two is 18 - (-5) = 18 + 5 = 23 degrees
Hope it helps!
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Answer:
rational number, 2/9, 22/100=11/50, rational, no fraction equivalent, perfect square, non-perfect square
Step-by-step explanation:
For what value of ‘K’ will the following pair of linear equations are inconsistent 3x+ 4y=1 and (2k-1) x+(k-1)y=2k+1
Answer: k=(1/5)
Step-by-step explanation:
Let x represent the number of water bottles and y represent
the number of pairs of socks that Malia buys.
Use the graph to determine if Malia can buy 75 water bottles
and 100 pairs of socks. Explain.
Malia can't buy 75 water bottles and 100 pairs of socks because it is not a solution to the system.
System of Inequalities:
The term "system of inequalities" refers to a collection of two or more disparities in one or more variables. When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems of inequalities are used.
Now in the given question,
Here we have a graph of inequalities, and we just need to see if the pair (75, 100) is a solution.
The solutions of the system are all the points in the intersection of the two shaded areas (in this case are all the points in the green area)
Now, clearly the point (75, 100) is not a solution
Even if you evaluate that in the first inequality:
x + y ≥ 200
we get:
75 + 100 ≥ 200
175 ≥ 200
which is false.
So no, Malia can't buy 75 water bottles and 100 pairs of socks.
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Simply the expression 9(1-4n)
Answer: 9 - 36n
Step-by-step explanation: So, first you multiply 9 by 1 and 9 by 4n, which gives you 9 - 36n.
Answer:
n=1/4
Step-by-step explanation:
9(1-4n)
Distribute the 9 to create the equation 9-36n.
Now set it equal to zero.
9-36n = 0
Add 36n to both sides to get 9 = 36n
Now divide by sides by 36 to get 9/36 = n
Now simplify your fraction 9/36 = 1/4 so 1/4=n
HELP PLEASE ITS DUE TMR
Answer:
[tex]-6[/tex]
Step-by-step explanation:
[tex]-5.f(-2) - 3g(7)[/tex]
The values of [tex]f(-2)[/tex] and [tex]g(7)[/tex] have to be read and deduced from the respective [tex]f(x)[/tex] and [tex]g(x)[/tex] graphs
[tex]f(-2)[/tex]:
For x = [tex]-2[/tex], draw a straight vertical line connecting x = [tex]-2[/tex] and the blue [tex]f(x)[/tex] graph. It can be observed that the the blue [tex]f(x)[/tex] graph is touching the x-axis at x = [tex]-2[/tex]. Therefore, the corresponding y [or [tex]f(x)[/tex]] value is 0.
[tex]g(7)[/tex]:
For x = 7, draw a straight vertical line connecting x = 7 and the red dashed [tex]g(x)[/tex] graph. Then (from this meeting point) draw a straight horizontal line that touches the y-axis. It can be observed that the corresponding y [or [tex]g(x)[/tex]] value is 2
Now substitute the deduced values in the expression:
[tex]-5.[/tex](0) [tex]-3.[/tex](2) = [tex]0 - 6[/tex]
= [tex]-6[/tex]
Use the parabola tool to graph the quadratic function f(x)=x2+10x+24. Graph the parabola by first plotting its vertex and then plotting a second point on the parabola
By using tool, graph of the quadratic function f (x) = x² + 10x + 24 is shown in figure.
And, Vertex = (- 5, - 1)
A point on graph = (- 6, 0)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The quadratic function is,
⇒ f (x) = x² + 10x + 24
Now, By using tool we can draw the quadratic function f (x) = x² + 10x + 24 is shown in figure.
And, By figure of the quadratic function f (x) = x² + 10x + 24, we get;
Vertex = (- 5, - 1)
A point on graph = (- 6, 0)
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Answer:
(-5, -1) & (-6, 0)
Step-by-step explanation:
Just finished the test and this was correct. Hope this was helpful!!
The sugar content of orange juice is decreased from 6% to 4%. How much percent does the sugar content decrease?
Answer:
33.33%
Step-by-step explanation:
amount of sugar at first 6x
now 4x
difference 2x,(6x-4x)
"ratio=2/6"
change in percentage:2/6×100%=33.33%
ana opened a bank account with $1000 that earns interest, compounded continuously, at an annual rate of r
After 1 year of time period, Ana would have $1051.7 in her account, including interest.
Ana opened a bank account with $1000 that earns interest, compounded continuously, at an annual rate of r. To calculate the amount of money in the account after t years, we can use the formula:
[tex]A = P * e^{(rt)}[/tex]
where A is the amount in the account after t years, P is the initial deposit (in this case, $1000), r is the annual interest rate, and e is the mathematical constant approximately equal to 2.718.
For example, if the interest rate is 5% (r = 0.05), after 1 year, the amount in the account would be:
[tex]A = \$1000 * e^{(0.05 * 1)} = \$1000 * 1.0517[/tex]
[tex]A = \$1051.7[/tex]
So, after 1 year, Ana would have $1051.7 in her account, including interest. The higher the interest rate and the longer the time period, the more money Ana would have in her account due to the compounding effect.
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