The first 4 terms of the sequence represented by the expression 3n + 5
is 8, 11, 14 and 17.
Sequence:
In mathematics, an array is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same element can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position. The concept of series can be generalized as a family of indices, defined in terms of any set of indices.
According to the Question:
Given, aₙ = (3n+5).
First four terms can be obtained by putting n=1,2,3,4
a 1=(3×1+5) = 8
a 2 =(3×2+5) = 11
a 3 =(3×3+5) = 14
a 4 =(3×4+5) = 17
First 4 terms in the sequence are 8, 11, 14, 17.
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In data analytics, a _____ refers to all possible data values in a certain dataset
In data analytics, a population refers to all possible data values in a certain dataset.
What is data analytics?Data analytics is a set of procedures and processes for examining datasets in order to draw conclusions from the information they contain, often aided by specialized systems and software. Organizations use data analytics to aid decision-making, increase efficiency, and evaluate outcomes.
The population and sample are two concepts in statistics. The population and sample are two concepts in statistics. The population is the entire set of objects or individuals being studied, while the sample is a subset of the population that is chosen for analysis. The sample is a subset of the population, chosen at random or according to some other criteria in order to represent the population as a whole.
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Triangle ABC has coordinates A(4,1), B(5,9),and C (2,7). If the triangle is translated 7 units to left, what are the coordinates of B'?
Answer:
(-2,9)
Step-by-step explanation:
when moving it 5 units left on the x axis it would be 5-7
So in turn you would be given (-2,9)
Because the y stays the same you would still have (?,9)
I NEED HELPP PLEASEEEEEEEE
The slope between the points (-3, 0) and (0, -1) is -1/3.
What is slope?The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.
Let us consider the first two points (-3, 0) and (0, -1).
The slope of the line is given as:
m = (y2 - y1) / (x2 - x1)
Substituting the values we have:
m = (-1 - 0) / (0 - (-3)) = -1/3
Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.
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in how many ways can a class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer and a secretary g
The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040
A class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer, and a secretary in the following way:Step-by-step explanation:The number of ways that a class of 40 students can choose a committee consisting of a president, vice president, treasurer, and a secretary can be found by using the permutation formula.If we assume that the positions of the committee members are different, the number of ways can be calculated as follows:The number of ways of selecting the president from 40 students is 40.The number of ways of selecting the vice president from the remaining 39 students is 39.The number of ways of selecting the treasurer from the remaining 38 students is 38.The number of ways of selecting the secretary from the remaining 37 students is 37.The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040Thus, secretary.
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Each of these measures is rounded to nearest whole: a=5cm and b=3cm Calculate the upper bound of a +b
The upper bound of a + b can be found by adding the upper bounds of a and b.
For a = 5cm, the nearest whole number is 5. The upper bound would be the midpoint between 5 and 6, which is 5.5.
For b = 3cm, the nearest whole number is 3. The upper bound would be the midpoint between 3 and 4, which is 3.5.
So the upper bound of a + b is:
5.5 + 3.5 = 9
Therefore, the upper bound of a + b is 9cm.
Ryan buys some jumpers to sell on a stall. He spends £190 buying 80 jumpers. He sells 50% of the jumpers for £12 each. He then puts the rest of the jumpers on a Buy one get one half price offer. He manages to sell half the remaining jumpers using this offer. How much profit does Ryan make?
Ryan makes a profit of £240. the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.
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a rectangular swimming pool 50 ft long, 30 ft wide, and 8 ft deep is filled with water to a depth of 6 ft. use an integral to find the work required to pump all the water out over the top. (take as the density of water lb/ft. )
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
We have,
To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.
First, let's calculate the weight of the water in the pool.
The weight of an object is given by the formula:
Weight = mass x gravitational acceleration
Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.
The volume of the pool is given by the formula:
Volume = length x width x depth
Volume = 50 ft x 30 ft x 6 ft = 9000 ft³
Now, let's calculate the weight of the water:
Weight = density x volume x gravitational acceleration
Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb
To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.
The work required to pump the water out is given by the formula:
Work = weight x height
Work = 290,400 lb x 8 ft = 2,323,200 ft-lb
Therefore,
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
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Operación de vectores
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Step-by-step explanation:
Find the interest refund on a 35-month loan with interest of $2,802 if the loan is paid in full with 13 months remaining.
Answer: $1,071.54
Step-by-step explanation:
To find the interest refund, first we need to calculate the total interest charged on the loan. We can do this by multiplying the monthly interest by the number of months in the loan:
Monthly interest = Total interest / Number of months
Monthly interest = $2,802 / 35
Monthly interest = $80.06
Total interest charged on the loan = Monthly interest x Number of months
Total interest charged on the loan = $80.06 x 35
Total interest charged on the loan = $2,802.10
Now we need to calculate the interest that would have been charged for the remaining 13 months of the loan:
Interest for remaining 13 months = Monthly interest x Remaining months
Interest for remaining 13 months = $80.06 x 13
Interest for remaining 13 months = $1,040.78
Finally, we can find the interest refund by subtracting the interest for the remaining 13 months from the total interest charged on the loan:
Interest refund = Total interest charged - Interest for remaining months
Interest refund = $2,802.10 - $1,040.78
Interest refund = $1,074.32
Therefore, the interest refund on the loan is $1,074.30.
I need some help with this
Answer:
12
Step-by-step explanation:
i think its right
HELP PLS combine the like terms 3x+5-x+3+4x
Answer:
3x, 4x | 5, 3
Step-by-step explanation:
The equation y = 8x represents the
relationship between the amount of
time Shanay takes to weave thread
into fabric and the number of rows.
How long will it take Shanay to weave
72 rows of fabric at this constant rate?
write the equation in standard form for the circle with center (5,0) passing through (5, 9/2)
The equation in standard form for the circle with center (5,0) passing through (5, 9/2) is 4x² + 4y² - 40x + 19 = 0
Calculating the equation of the circleGiven that
Center = (5, 0)
Point on the circle = (5. 9/2)
The equation of a circle can be expressed as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
Radius = r
So, we have
(x - 5)² + (y - 0)² = r²
Calculating the radius, we have
(5 - 5)² + (9/2 - 0)² = r²
Evaluate
r = 9/2
So, we have
(x - 5)² + (y - 0)² = (9/2)²
Expand
x² - 10x + 25 + y² = 81/4
Multiply through by 4
4x² - 40x + 100 + 4y² = 81
So, we have
4x² + 4y² - 40x + 19 = 0
Hence, the equation is 4x² + 4y² - 40x + 19 = 0
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parabola a and parabola b both have the x-axis as the directrix. parabola a has its focus at (3,2) and parabola b has its focus at (5,4). select all true statements.
a. parabola A is wider than parabola B
b. parabola B is wider than parabola A
c. the parabolas have the same line of symmetry
d. the line of symmetry of parabola A is to the right of that of parabola B
e. the line of symmetry of parabola B is to the right of that of parabola A
In the following question, among the given options, Option (b) "Parabola B is wider than Parabola A" and option (d) "The line of symmetry of Parabola A is to the left of that of Parabola B" are the true statements.
The following statements are true about the parabolas: c. the parabolas have the same line of symmetry, and d. the line of symmetry of parabola A is to the right of that of parabola B.
Parabola A and Parabola B have the x-axis as the directrix, with the focus of Parabola A at (3,2) and the focus of Parabola B at (5,4). As the focus of Parabola A is to the left of the focus of Parabola B, the line of symmetry for Parabola A is to the right of the line of symmetry of Parabola B.
Parabola A and Parabola B may have different widths, depending on their equation, but this cannot be determined from the information given.
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The radius of a circle is 8 meters. What is the circle's circumference?
Use 3.14 for л.
Answer:
circumference=50.24
Step-by-step explanation:
c=2x3.14xr
c=2x3.14x(8)
c=50.24
I NEED YOUR HELP ASAP!!
To create a modified box plot for a data set, determine the outliers of the data set and the smallest and largest numbers in the data set that are not outliers. Next, determine the median of the first half of the data set, the median of the entire data set, and the median of the second half of the data set.
What are the values that are needed to create a modified box plot for this data set?
19, 15, 22, 35, 16, 22, 4, 22, 24, 16, 17, 21
Enter your answers in the blanks in order from least to greatest.
Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.
Give a short note on Median?
In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.
The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.
To create a modified box plot, we need the following values:
The smallest number in the data set that is not an outlier: 15
The median of the first half of the data set: 17
The median of the entire data set: 20.5
The median of the second half of the data set: 22
The largest number in the data set that is not an outlier: 35
So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.
A hawk flying at 19 m/s at an altitude of 228 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation y = 228 − x^2/57 until it hits the ground, where y is its height above the ground and x is its horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground. Express your answer correct to the nearest tenth of a meter.
The parabolic trajectory of the falling prey can be described by the equation y = 228 – x2/57, where y is the height above the ground and x is the horizontal distance traveled in meters. In this case, the prey was dropped at a height of 228 m and flying at 19 m/s. To calculate the total distance traveled by the prey, we can use the equation for the parabola to solve for x.
We can rearrange the equation y = 228 – x2/57 to solve for x, which gives us[tex]x = √(57*(228 – y))[/tex]. When the prey hits the ground, the height (y) is 0. Plugging this into the equation for x, we can calculate that the total distance traveled by the prey is[tex]x = √(57*(228 - 0)) = √(57*228) = 84.9 m.\\[/tex] Expressing this answer to the nearest tenth of a meter gives us the final answer of 84.9 m.
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The summaries of data from the balance sheet, income statement, and retained earnings statement for two corporations, Walco Corporation, and Gunther Enterprises, are presented below for 2017.
Determine the missing amounts. Assume all changes in stockholders equity are due to changes in retained earnings
Walco Corporation Gunther Enterprise
Beginning of year Total assets $100,000 $159,000
Total liabilities 73,000 $_____ (d)
Total stockholders' equity $_____ (a) 67,500
End of year Total assets $_____ (b) 190,000
Total liabilities 128,000 50,000
Total stockholders' equity 54,000 $_____ (e)
Changes during year in retained earnings Dividends $_____ (c) 4,900
Total revenues 219,000 $_____ (f)
Total expenses 167,000 79,000
The missing amounts for Walco Corporation and Gunther Enterprises assuming all changes in stockholders equity are due to changes in retained earnings are
(a) Walco Corporation Total Stockholders' Equity = $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues = $135,100
A balance sheet is a financial statement that reports a company's assets, liabilities, and stockholder equity on a specific date. Assets are resources a company owns that have monetary value, liabilities are obligations that must be paid in the future, and stockholder equity is the difference between a company's assets and liabilities. To calculate the missing amounts, you need to subtract the beginning of year figures from the end of year figures.
a) Total liabilities + Total stockholders' equity = Total assets
Total liabilities + $54,000 = $100,000
Total liabilities = $46,000
(b) Total assets = Total liabilities + Total stockholders' equity
Total assets = $128,000 + $54,000
Total assets = $182,000
(c) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $219,000 - $167,000 - $4,900
Changes during year in retained earnings = $47,100
The missing values for Gunther Enterprises:
(d) Total liabilities + Total stockholders' equity = Total assets
$67,500 + $(e) = $159,000
$(e) = $91,500
(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $(f) - $79,000 - $4,900
Changes during year in retained earnings = $(f) - $83,900
Using the balance sheet equation, we can find the missing values:
(d) Total liabilities = Total assets - Total stockholders' equity
Total liabilities = $159,000 - $67,500
Total liabilities = $91,500
(e) Total stockholders' equity = Total assets - Total liabilities
Total stockholders' equity = $190,000 - $50,000
Total stockholders' equity = $140,000
(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends
Changes during year in retained earnings = $219,000 - $79,000 - $4,900
Changes during year in retained earnings = $135,100
Therefore, the missing amounts are:
(a) Walco Corporation Total Stockholders' Equity = $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues = $135,100
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The tires on Mavis’ car will have to be replaced when they each have 160 000 km of wear on them. If new tires cost $140.00 each, what is the total cost of the wear on Mavis’ tires for a year in which she drives 25 000 km?
Answer:
If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:
4 tires * 160,000 km = 640,000 km
If Mavis drives 25,000 km in a year, she will need to replace her tires after:
640,000 km ÷ 25,000 km/year = 25.6 years
Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:
$140.00/tire * 4 tires = $560.00
So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.
Step-by-step explanation:
source: trust me bro
What is an equation for the quadratic function represented by the table shown?
Use the following function to find d(0)
d(x)=-x+-3
d(0)=
Answer:
d(0) = -3
Step-by-step explanation:
d(x) = -x + -3 d(0)
d(0) = 0 - 3
d(0) = -3
So, the answer is d(0) = -3
PLEASE HELP!!! WILL MARK BRANLIEST!!!
Answer:
The point z = 3+4i is plotted as a blue dot, and the two square roots are plotted as a red dot and a green dot. The magnitudes of z and its square roots are shown by the radii of the circles centered at the origin.
Step-by-step explanation:
qrt(z) = +/- sqrt(r) * [cos(theta/2) + i sin(theta/2)]
where r = |z| = magnitude of z and theta = arg(z) = argument of z.
Calculate the magnitude of z:
|r| = sqrt((3)^2 + (4)^2) = 5
And the argument of z:
theta = arctan(4/3) = 0.93 radians
Now, find the two square roots of z:
sqrt(z) = +/- sqrt(5) * [cos(0.93/2) + i sin(0.93/2)]
= +/- 1.58 * [cos(0.47) + i sin(0.47)]
= +/- 1.58 * [0.89 + i*0.46]
Using a calculator, simplify this expression to:
sqrt(z) = +/- 1.41 + i1.41 or +/- 0.2 + i2.8
A straw that is 15cm long leans against the inside of a glass. The diameter of a glass is
5cm, and has a height of 8cm. How far past the edge of the glass would the straw extend?
Round your answer to the nearest tenth.
The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.
Does someone mind helping me with this problem? Thank you!
the answer to the problem that you need to is 1024
Martina made $60 for 5 hours of work. At the same rate, how many hours would she have to work to make $204 ?
Answer:
WELL 17
Step-by-step explanation:
60 DIVED BY 5 IS 12
SO 12 DIVIDED BY 204 IS 17 SOOOOOO 17 IS THE ANS
a
49⁰
Find the measure of a.
127⁰
72⁰
Answer:
112°
Step-by-step explanation:
Finding the unknown angle in a quadrilateral:
Sum of all angles of a quadrilateral = 360
a + 49 + 72 + 127 = 360
a + 248 = 360
a = 360 - 248
a = 112°
if (20x+10) and (10x+50) are altenative interior angle then find x
Answer:
x = 4
Step-by-step explanation:
Alternative interior angles means these angles are equal in magnitude and sign
[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]
Find the value of x.
Answer:
x=1.9
Step-by-step explanation:
[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]
[tex]11x=21.16[/tex]
[tex]X=1.9[/tex]
What are the zeros of the function? Set the function = 0, factor, and use the zero-product property. Show your steps!
f(x) = x² + 7x – 60
(100 POINTS AND BRAINLIEST)
The zeroes of the function are -12 and 5.
What is meant by Zeros of the function?Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.
According to the question:
To find the zeros of the function
f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.
So we start with the equation:
x² + 7x - 60 = 0
Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:
x² + 7x - 60 = (x + 12)(x - 5) = 0
Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:
x + 12 = 0 or x - 5 = 0
Solving for x, we get:
x = -12 or x = 5
The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.
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What is result of following operation(4623. 56)10+ (110011. 11)2whare (110011. 11(2 mean that 110011. 11as a number express in base 2
The given numbers are in decimal and binary system and the final result of the given operation is [tex](4675.31)_{10}[/tex].
A binary integer (base-2) is converted to an equivalent decimal number using the binary to decimal conversion formula. (base-10). In mathematics, integers are expressed using a number system. It is a method to display numerical data. The four various numeral systems are as follows:
System of Binary Numbers (Base-2)
system of octal numbers (Base-8)
System of Decimal Numbers (Base-10)
System of Hexadecimal Numbers (Base-16).
We are the two numbers:-
[tex](4623.56)_{10} , (110011.11)_{2}[/tex]
these are in decimal and binary system respectively.
now, we will express them in same system ( here we choose decimal system).
[tex](110011.11)_{2} = (2^{5} + 2^{4} + 0 + 0 + 2^{1} + 2^{0} + 2^{-1} + 2^{-2} )_{10} \\= (2^{5}+2^{4}+0*2^{4}+0*2^{3}+2^{1}+2^{0}+2^{-1}+2^{-2})_{10} \\= (32+16+2+1+0.5+0.25)_{10} \\= (51.75)_{10}[/tex]
Now, addition is done below:-
4623.56+51.75= 4675.31.
hence, the final result of the given operation= [tex](4675.31)_{10}[/tex]
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