The new average salary of the people on the bus is $84,44,96,111.11 and the median salary will not change and will remain same.
Given, we know that average salary of the 9 people on the bus is $65,000.
Formula for Average = sum of salary of all people/ the number of people.
Let us say average salary of first 8 people is 'S'. Given, salary of the 9th guy on the bus is $120,000 Now, we can write it like this :
⇒$65,000 = (S + $120,000)/9
⇒585,000 = S + $120,000
⇒S = $465,000
Therefore, average salary of 8 people is $465,000 after the 9th guy gets off. Now Bill Gates enters the bus with a salary of $7,600,000,000. New average salary :
⇒ (S + $7,600,000,000) / 9
⇒$84,44,96,111.11
Median will not change since, The median of a set of numbers is the number in the middle when you list them in order. For example, the median of {1, 3, 6, 9, 13} is 6. If you replace the highest number with a different number, the median will not change. In this example, {1, 3, 6, 9, 100} still has a median of 6.
Therefore, the new average yearly income of the people on the bus along with Bill Gates is $84,44,96,111.1111.
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Describe the transformation of f(x)=cos x to g(x)=cos (x+pi/4)
I'll give brainliest
Question 3 Benda is taking about buying a house for $249.000 The table below shows the projected value of two different houses for three years Number of years 1 2 3 House 1 (value in dollars) 253.960 259 059 60 264 240 79 House 2 (value in dollars) 256 000 263.000 270.000 Part A: What type of function Inear or exponential can be used to describe the value of each of the houses after a fixed number of years? Explain your (2) Part B: Wibe one function for each house to describe the value of the house fix) in dollars, after x years (4 points) Part C: Belinda wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in t
please I need help I will give alot of points
Answer:
Part A:
To determine whether a linear or exponential function can be used to describe the value of each house after a fixed number of years, we need to examine the change in the value of the houses over time. If the change is constant, a linear function can be used. If the change is proportional to the current value, an exponential function can be used.
Looking at the data in the table, we can see that the value of House 1 is increasing by a relatively constant amount each year, whereas the value of House 2 is increasing by a proportional amount. Therefore, a linear function can be used to describe the value of House 1, and an exponential function can be used to describe the value of House 2.
Part B:
For House 1, we can use the formula y = mx + b, where y is the value of the house in dollars, x is the number of years, m is the slope or rate of increase, and b is the initial value. Using the data from the table, we can find the slope and initial value:
m = (264240.79 - 253960) / 2 = 5140.395
b = 253960
So the function to describe the value of House 1 after x years is:
y = 5140.395x + 253960
For House 2, we can use the formula y = ab^x, where y is the value of the house in dollars, x is the number of years, a is the initial value, and b is the growth factor. Using the data from the table, we can find the initial value and growth factor:
a = 256000
b = (270000 / 256000)^(1/3) = 1.02905
So the function to describe the value of House 2 after x years is:
y = 256000(1.02905)^x
Part C:
To determine which house will have the greatest value in 45 years, we can plug in x = 45 into the functions we found in Part B and compare the results. Using a calculator, we get:
House 1: y = 5140.395(45) + 253960 = 472 339.25
House 2: y = 256000(1.02905)^45 = 798 825.85
Therefore, House 2 will have a significantly higher value after 45 years.
Step-by-step explanation:
4. What is the connection between exponential function and geometric sequence.
5. Define Moore's law. How Moore's law is associated with exponential function.
1. The connection between exponential functions and geometric sequences is that the terms of a geometric sequence are generated by repeatedly multiplying the previous term by a constant ratio, which can be expressed using an exponential function.
2. Moore's Law is associated with the exponential function because it describes a growth pattern that is exponential in nature.
1. If the first term of a geometric sequence is denoted by a_0 and the common ratio is denoted by r, then the nth term can be calculated using the formula a_n = a_0 * r^(n-1), which is equivalent to the exponential function f(n) = a_0 * r^n. Conversely, if we have an exponential function f(n) = a * r^n, then the sequence of its values for n = 1, 2, 3, ... forms a geometric sequence with first term a and common ratio r.
2. Moore's Law is a prediction made by Gordon Moore, co-founder of Intel, in 1965, that the number of transistors on a microchip would double every 18-24 months, while the cost per transistor would decrease. This has been interpreted to mean that the processing power of computers would double every 18-24 months, leading to exponential growth in computing power and an exponential decrease in the cost of computing.
Moore's Law is associated with the exponential function because it describes a growth pattern that is exponential in nature. The number of transistors on a microchip is growing at an exponential rate, which means that the rate of growth is proportional to the current number of transistors. This can be represented mathematically as an exponential function, such as y = a * e^(kx), where y is the number of transistors, x is time, a is the initial number of transistors, and k is the growth rate.
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a guy wire runs from the top of a cell tower to a metal stake in the ground. rashon places a 6-foot tall pole to support the guy wire. after placing the pole, rashon measures the distance from the stake to the pole to be 4 ft. he then measures the distance from the pole to the tower to be 9 ft. find the length of the guy wire, to the nearest foot.
The length of the guy wire, to the nearest foot is 23 feet.
How to calculate the length of the guy wire?Based on the information provided, we can logically deduce that triangle ABE (ΔABE) is similar to triangle (ΔCDE) and the following parameters about the geometric figures;
CD = 6 ft.DE = 4 ft.BD = 9 ft.Additionally, the corresponding sides of similar triangles are equal;
AB/CD = BE/DE
AB/6 = (9 + 4)/4
AB/6 = 13/4
AB = 19.5 feet.
By applying Pythagorean' theorem, side AE is given by:
AE = √(AB² + BE²)
AE = √(19.5² + 13²)
AE = 23.44 ≈ 23 feet.
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what is 164.8 cm height in feet?
The height of 164.8 centimeter after conversion to feet is equivalent to 5.41 feet .
The various measurements units that are used in measuring the height of an object are , centimeter (cm) , meter (m) , feet , inches .
We have to convert the height of 164.8 cm to feet ;
we know that , 1 centimeter is = 0.0328 feet ;
So , we multiply the units given in centimeter by 0.0328 ,
On multiplying 164.8 cm by 0.0328 ;
We get ;
⇒ 164.8 centimeter = 164.8 × 0.0328 ;
⇒ 164.8 centimeter = 5.40544 feet ≈ 5.41 feet ;
Therefore , 164.8 cm is approximately equal to 5.41 feet .
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When an object is dropped into a liquid, the volume of the displaced liquid is _______ to the volume of the object that is dipped. ( a ) Smaller ( b ) Greater ( c ) Equal ( d ) May be Greater or Smaller
Answer:
C
...................
what is multiplying polynomials calculator?
A multiplying polynomials calculator is a tool used to multiply two or more polynomials together.
A multiplying polynomials calculator is a tool used to multiply two or more polynomials together. It can be helpful for simplifying algebraic expressions, solving equations, and performing various calculations in mathematics and engineering.
The calculator takes the coefficients of each polynomial as input and uses the distributive property to multiply the terms of each polynomial together. It then combines like terms and arranges the result in descending order of degrees. Multiplying polynomials can be a tedious and error-prone process, especially for large polynomials, so using a calculator can save time and reduce the chances of errors. The multiplying polynomials calculator is commonly used by students, teachers, engineers, and anyone working with algebraic expressions.
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Let A be a matrix with linearly independent columns. Which one of these statements must be true? You have only three attempts at this problem. A. The equation Az b always has a solution for all b B. The equation Ab has a solution for all b precisely when it has more rows than columns. O C. There is no easy way to tell if Ax-b has a solution for all b D. The equation Az -b has a solution for all b precisely when it has more columns than rows. OE. The equation Ax -b never has a solution for all b F. The equation Az-b has a solution for all b precisely when it is a square matrix. G. none of the abovePrevious question
If A be a matrix with linearly independent columns, then the statement that must be true is (A) The equation Az=b always has a solution for all b.
Since the columns of A are linearly independent, the matrix A has full column rank, i.e., its column space is the entire space R^n. Here are the implications of this fact for each statement:
A. The equation Az=b always has a solution for all b.
This is true, because for any b in R^n, we can write it as a linear combination of the columns of A, say b=c_1a_1+c_2a_2+...+c_na_n. Then, the solution to Az=b is simply z=[c_1,c_2,...,c_n]^T.
B. The equation Ab has a solution for all b precisely when it has more rows than columns.
This statement is false. The equation Ab=b is always solvable, regardless of the dimensions of A and b. The solution is simply b expressed in the basis of the column space of A.
C. There is no easy way to tell if Ax-b has a solution for all b.
This statement is also false. Since the columns of A are linearly independent, the equation Ax=b has at most one solution for each b. Therefore, Ax=b has a solution for all b if and only if the columns of A span the entire space R^n. This can be checked by computing the rank of A.
D. The equation Az-b has a solution for all b precisely when it has more columns than rows.
This statement is false. The equation Az=b is always solvable, regardless of the dimensions of A and b, as we have seen in (A).
E. The equation Ax-b never has a solution for all b.
This statement is false. The equation Ax=b has at most one solution for each b, and it is solvable for all b if and only if the columns of A span the entire space R^n, as we have seen in (C).
F. The equation Az-b has a solution for all b precisely when it is a square matrix.
This statement is false. The equation Az=b is always solvable, regardless of whether A is square or not, as we have seen in (A).
Therefore, the only true statement among the given options is (A) The equation Az=b always has a solution for all b.
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Which function is represented by the graph?
A nonlinear function starts at the point (minus 2, minus 1) and also passes through (0, minus 2.4), (2, minus 3), and (7, minus 4)
The option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
As we can see in the picture, we have given a function:
We have a function:
g(x) = 4log(x) + 4
To find x-intercept plug g(x) = 0
0 = 4logx + 4
x = 0.1
(0.1, 0)
The vertical asymptote:
x = 0
The range of a function:
(-∞, ∞)
Thus, the option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.
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when samuel asked to borrow 1000, his dad told him he must pay it back in 6 months and he will be charged 12%. How much interest will samuel have to pay
The simple interest Samuel will have to pay will be 60 Rs.
What exactly is simple interest?
Simple Interest is a simple way for computing interest on a loan or principle amount. Simple interest is a concept that is employed in numerous industries, including banking, finance, and automobiles. When you make a loan payment, the monthly interest is deducted first, followed by the principle amount.
The simple interest formula is as follows:
SI=P*R*T/100
SI stands for simple interest.
P stands for principal.
R is the interest rate (in percentage)
T denotes the length of time (in years)
The following formula is used to compute the total amount:
Amount (A) = Principal (P) x Simple Interest (SI)
Now,
As given principle=1000
rate=12%
time=6 months=1/2 years,
Then interest in 6 months will be = 1000*12*1/2*100
=10*12/2
=10*6
=60
Hence,
The simple interest Samuel will have to pay will be 60 Rs.
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How to make 8 by 10 frame?
The step by step process of making the 8 by 10 frame consists of gather materials, measure the size and cut and screw it.
The first step in making a frame is to gather your materials. You'll need wood or other materials to construct the frame, as well as some tools like a saw and a hammer or nail gun.
To calculate the size of your frame, you'll need to add some extra length and width to the dimensions of your photo.
Once you have your dimensions, you'll need to cut your wood or other materials to size. You'll need four pieces of wood to create the frame - two longer pieces for the sides, and two shorter pieces for the top and bottom.
Next, you'll need to assemble your frame using nails or screws. Make sure the corners are flush and that the frame is square. You can use a carpenter's square to check your angles and make sure everything is aligned correctly.
Finally, you'll need to finish your frame. This could involve painting or staining the wood, adding decorative elements like beads or embellishments, or simply leaving the wood as-is for a more natural look. Once your frame is complete, you can insert your photo or artwork and enjoy your new creation!
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y=3x-4 and y= -1/2x+10
Answer:
x = 4
y = 8
Step-by-step explanation:
If y = 3x - 4 and y = -1/2x + 10, then
3x - 4 = -1/2x + 10
3.5x = 14
x = 14/3.5 = 4
y = 3(4) - 4 = 8
The difference between the high and low temperatures on Sunday was at least 35°F. The low temperature on Sunday was -8°F.
Part A
Select the correct values and symbol to write an inequality that represents the possible high temperatures, t, on Sunday.
t- __ _ __
High temp ≥ Low temp + difference
High temp ≥ -8°F + 35°F
High temp ≥ 27°F
InequalityAn inequality is a relationship between two different quantities or expressions.
An inequality may be expressed by a mathematical sentence that uses the following symbols:
< is less than
> is greater than
≤ is less than or equal to
≥ is greater than or equal to
≠ is not equal to
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plsssssssssssss helpppppppp
Answer:
Option 3: about 14 inches
Step-by-step explanation:
The notebook paper is in the form of a rectangle of length
[tex]l = 11[/tex] inches and width [tex]w = 8.5[/tex] inches
The diagonal of such a rectangle is given by the Pythagorean formula
[tex]d = \sqrt{l^{2} + w^{2}}[/tex]
Substituting the values of [tex]l[/tex] and [tex]w[/tex]:
[tex]d = \sqrt{11^{2} + 8.5^{2}}\\\\d = \sqrt{121 + 72.25}\\\\d = \sqrt{193.25}\\\\d= 13.9014\;inches[/tex]
This corresponds to Option 3: about 14 inches
Find the product of 4 x 3/8
Answer:
1.5
Step-by-step explanation:
Answer: 1.5
Step-by-step explanation:
what is mean arterial pressure formula
The mean arterial pressure formula is MAP = CO x TPR or MAP = (SBP + 2DBP) / 3.
The mean arterial pressure (MAP) formula is:
MAP = CO x TPR
where:
CO is the cardiac output (how much blood is siphoned by the heart each moment)
TPR is the all-out peripheral resistance (the resistance from the bloodstream in the body's veins)
On the other hand, the mean arterial pressure can also be calculated using the following equation:
MAP = (SBP + 2DBP)/3
where:
SBP is the systolic blood pressure (the highest pressure in the arteries when the heart beats)
DBP is the diastolic blood pressure(the lowest pressure in the arteries when the heart is at rest between beats)
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3x+5=50 , can anyone help me solve that ! . Tysm , also its not high school . its middle but wtv
Answer: x=15
Step-by-step explanation:
3x+5=50
3+5=50
Subtract the numbers
3x+5-5=50-5
3x/3=45/5
x=15
how to convert 300000 yen to usd?
300000 yen is approximately equal to 2233.38 USD ( rounded to two decimal places )
The conversion factor to convert yen to USD is 0.0074
1 yen = 0.0074 USD
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The currency in USD = The currency in yen × conversion factor
Substitute the values in the equation
1 yen = 0.0074 USD
300000 = 300000 × 0.0074
Multiply the numbers
= 2233.38 USD ( rounded to two decimal places )
Therefore, 300000 yen is 2233.38 USD
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Y= -128x + 3840
Create a table for the values when x = 0,5,8,10,30
The table of values for y = -128x + 3840 is:
x y
0 3840
5 3200
8 2816
10 2560
30 0
How to create the table of valuesFrom the question, we have the following parameters that can be used in our computation:
Y= -128x + 3840
Then, we have
x = 0,5,8,10,30
To find the values of y, we substitute each value of x into the equation and simplify:
When x = 0, y = -128(0) + 3840 = 3840When x = 5, y = -128(5) + 3840 = 3200When x = 8, y = -128(8) + 3840 = 2816When x = 10, y = -128(10) + 3840 = 2560When x = 30, y = -128(30) + 3840 = 0This means that the above is the table of values for y = -128x + 3840 when x takes on the values 0, 5, 8, 10, and 30
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AC=3x-4 AB=62 BC=x-2 find the x
AC=3x-4 AB=62 BC=x-2, x = 17. This can be solved by using the concept of simplification.
What is straight line?A line is an endlessly long object without breadth, depth, or curvature in geometry. So, despite the fact that they can exist in two, three, or more dimensional environments, lines are one-dimensional things. The term "line" can also refer to a line segment that has two locations that serve as its endpoints in daily life.
The most clear and simple way to calculate depreciation is along a straight line. It is most beneficial when an asset's value declines slowly over time at a pace that is close to constant.
Given that,
AC=3x-4
AB=62
BC=x-2
As we can clearly see in line AB:
AC+BC= AB
=>(3x-4)+(x-2)= 62
=>4x -6 = 62
=>4x = 62+6
=>4x = 68
=>x = 68/4
=>x= 17
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The complete question is as follows:
if 2 distinct numbers are chosen from the set below at random, what is the probabilityt that their sum will be greater than 100?
( 1, 5, 10, 100 )
Answer:0.50
Step-by-step explanation:
{1 , 5 , 10 , 100)
Two numbers can be chosen from the above set of four numbers in 4C2 ways.
4C2 = 4!/(2!*2!) = (4*3*2!)/)2*2!) = 12/2 = 6
Two numbers can be chosen from the above set of four numbers in 6 ways.
The pair of numbers which give a sum greater than 100 is (1,100) , (5,100) , (10,100).
3 pairs out of 6 total pairs will give a sum greater than 100.
P(sum > 100) = 3/6 = 1/2 = 0.50
P(sum > 100) = 0.50
0.50
Determine the equation of the ellipse with center (6, -6), a vertex at (13, -6), and a co-vertex at (6, 0).
The equation of the ellipse is equal to (x - 6)² / 49 + (y + 6)² / 36 = 1.
How to derive of the equation of an ellipse
In this problem we must derive the equation of an ellipse based on information about the center, a vertex and a co-vertex thereof. The vertex represents the end of the major semiaxis that lies on the curve and co-vertex is the end of the minor semiaxis that lies on the curve. The major semiaxis is parallel with x-axis and the minor semiaxis is parallel with y-axis.
The standard form of the ellipse is shown below:
(x - h)² / a² + (y - k)² / b² = 1
Where:
(h, k) - Center of the ellipsea - Length of the major semiaxis.b - Length of the minor semiaxis.Now we proceed to derive the equation of the ellipse:
Major semiaxis:
A = (13, - 6) - (6, - 6)
A = (7, 0)
a = 7
Minor semiaxis:
B = (6, 0) - (6, - 6)
B = (0, 6)
b = 6
Equation of the elipse:
(x - 6)² / 49 + (y + 6)² / 36 = 1
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(Please help!!) Leslie creates designer bracelets with gemstones. Her most recent order included a total of 6 bracelets. It takes 12 stones to make one bracelet.
Write and solve an equation that represents how many stones were used for the order.
6s = 12; s = 2 stones
s + 6 = 12; s = 6 stones
s − 6 = 12; s = 18 stones
s divided by 12 equals 6; s = 72 stones
Leslie used a total of 128 stones for the order.
What is an arithmetic operation?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics.
It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
The correct equation that represents how many stones were used for the order is:
total number of stones = number of bracelets x stones per bracelet
Let's use "s" to represent the total number of stones Leslie used for the order:
s = 8 x 16
s = 128
Hence, Leslie used a total of 128 stones for the order.
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what is rhombus angle sum
Answer:
360 degrees
Step-by-step explanation:
I remember learning this in Math class. The rhombus angle sum will make 360 degrees.
each dot in the following dot plot represents the number of players at one table in bev's bingo hall. a dot plot has a horizontal axis labeled number of players marked by 8 equidistant tick marks numbered from 0 to 7. dots are plotted above the following: 0, 1; 1, 2; 3, 3; 4, 1; 5, 1; 7, 1. a dot plot has a horizontal axis labeled number of players marked by 8 equidistant tick marks numbered from 0 to 7. dots are plotted above the following: 0, 1; 1, 2; 3, 3; 4, 1; 5, 1; 7, 1. find the interquartile range (iqr) of the data in the dot plot. players
Answer:
Step-by-step explanation:
each dot in the following dot plot represents the number of players at one table in bev's bingo hall. a dot plot has a horizontal axis labeled number of players marked by 8 equidistant tick marks numbered from 0 to 7. dots are plotted above the following: 0, 1; 1, 2; 3, 3; 4, 1; 5, 1; 7, 1. a dot plot has a horizontal axis labeled number of players marked by 8 equidistant tick marks numbered from 0 to 7. dots are plotted above the following: 0, 1; 1, 2; 3, 3; 4, 1; 5, 1; 7, 1. find the interquartile range (iqr) of the data in the dot plot. players
The interquartile range (IQR) of the data in the dot plot is 3.5 players.
To find the interquartile range (IQR) of the data in the dot plot, we need to determine the values of the first quartile (Q1) and the third quartile (Q3).
The quartiles divide a dataset into four equal parts, where Q1 represents the 25th percentile and Q3 represents the 75th percentile.
Given the data points from the dot plot:
0, 1; 1, 2; 3, 3; 4, 1; 5, 1; 7, 1
First, arrange the data in ascending order:
0, 1, 1, 1, 3, 4, 5, 7
Next, find the median (Q2), which is the middle value of the data:
Median (Q2) = (3 + 4) / 2 = 3.5
Since there are 8 data points, we can calculate the position of Q1 and Q3 as follows:
Q1 position = (1/4) * (8 + 1) = 2.25
Q3 position = (3/4) * (8 + 1) = 6.75
Q1 is between the 2nd and 3rd data points: Q1 ≈ (1 + 1) / 2 = 1
Q3 is between the 6th and 7th data points: Q3 ≈ (4 + 5) / 2 = 4.5
Finally, calculate the IQR:
IQR = Q3 - Q1 = 4.5 - 1 = 3.5
So, the interquartile range (IQR) of the data in the dot plot is 3.5 players.
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a radioactive substance has a decay rate of 0.044 per hour. how many grams of a 100 gram sample will remain radioactive after 2 hours? round the answer to the nearest tenth of a gram, and do not include the unit in your answer. if necessary, include a leading 0 with any decimals less than 1. for example, 0.4 instead of .4. note: the formula for radioactive substance is w
91.6 grams of a 100 gram sample will remain radioactive after 2 hours. The solution has been obtained by using the concept of radioactive decay.
What is Radioactive decay?
Radioactive decay is the spontaneous destruction of an atomic nucleus in a radioactive substance that causes the emission of radiation from the nucleus. A parent nuclide in a radioactive process is one that decays, and a daughter nuclide is one that is created in the radioactive process.
We are given that a radioactive substance has a decay rate of 0.044 per hour.
Using the radioactive decay formula,
N(t) = N₀ [tex]e^{-kt}[/tex]
Initially, N = 100
k = 0.044
t = 2
So,
⇒N(t) = 100 * e⁽⁻⁰°⁰⁴⁴ ˣ ²⁾
⇒N(t) = 91.5761
⇒N(t) = 91.6
Hence, 91.6 grams of a 100 gram sample will remain radioactive after 2 hours.
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how many sundays in a year
Usually there are 52 Sundays in a year approximately.
There are a total of 52 weeks in a year if we take a rough estimate.
Every week has one sunday in it. So, going by this logic, each year will have about 52 sundays in it.
Now, one thing that we should notice here is that is not certain that there will be definitely 52 sundays. This number of 52 can increase also by a number of one or two because it is possible that the year might not starting from sunday. Because when we do 365/7 we get 52.14 so, this decimal place might include one or two Sundays in it.
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3^8 x 2^3 divided by 3^5
Answer:
216
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how to convert 2.4m to feet?
2.4 meter is approximately equal to 7.8740 feet ( rounded to four decimal places )
To convert 2.4 meter to feet, we can use the following formula:
1 meter = 3.28084 feet
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The length in feet = conversion factor × The length in meter
Substitute the values in the equation
2.4 m = 3.28084 × 2.4
Multiply the numbers
= 7.8740 feet ( rounded to four decimal places )
Therefore, 2.4 m is 7.8740 feet.
Learn more about conversion factor here
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The annual rate of growth in population of a certain city is 8%. If its present population is 1,96,830 then what was the population three years ago?
Answer: The population three years ago was 156250.
Step-by-step explanation:
Let 3 years ago, the population of a city = P
Rate of growth (R) = 8% p.a.
Present population (P) = 1,96,830.
Therefore,
[tex]A=P(1+R100)n[/tex]
P = A÷(1 + 8/100)³
196830 ÷ (1+2/25)³
=156250.
3 years ago, the population of the city = 156250.
