It is proved that the difference between squares of consecutive even numbers is always a multiple of 4.
Let's consider two consecutive even numbers.
If n = a positive integer
Then the 1st even number would be = 2n
Let the next consecutive even number = 2(n+1)
The consecutive even numbers would be:
2n, 2(n+1)
The square of each consecutive even number is given by -
(2n)² = 2n ×2n = 4n²
[2(n+1)]² = (2n+2)² =(2n+2)(2n+2)
Expanding, we get,
= 4n² +4n +4n+4
[2(n+1)]² = 4n²+8n+4
To determine if the difference between squares of consecutive even numbers is always a multiple of 4, we would substitute values for ' n ' to find the differences between the squares of each consecutive even number.
Let n = 1, 2, 3
For n= 1,
4n² = 4(1)² = 4×1 = 4
4n²+8n+4 = 4(1)² + 8(1) + 4
= 4+8+4 = 16
Thus, the difference between the squares of consecutive even numbers = 16-4 = 12
For n= 2,
4n² = 4(2)² = 4×4 = 16
4n²+8n+4 = 4(2)² + 8(2) + 4
= 16+16+4 = 36
Thus, the difference between the squares of consecutive even numbers = 36-16 = 20
For n= 3
4n² = 4(3)² = 4×9 = 36
4n²+8n+4 = 4(3)² + 8(3) + 4
= 36+24+4 = 64
Thus, the difference between the squares of consecutive even numbers = 64-36 = 28
Clearly, we can see that 12, 20, and 28 are multiples of 4.
Therefore, the difference between squares of consecutive even numbers is always a multiple of 4.
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This data records the ages of people on a bus to the seaside.
2 4 25 31 3 23 24 26 37 42
60 76 33 24 25 18 20 77 5 13
18 13 15 49 70 48 27 25 24 29
Find the mean age of all the people on the bus, showing your working.
Answer:
29.5 or 30 if rounded
Step-by-step explanation:
Add all of the numbers then divide by how many there is 30
886 divide by 30
= 29.5
Hope this helps!!!
The bird population on an island is declining at a rate of 2. 2% per year. The population was 3500 in the year 2009. Which answer is the best prediction of the population in the year 2014? responses 2730 2730 3062 3062 3132 3132 3423.
The best prediction of the bird population in the year 2014 is 3132.
Explain the term population decline?The population mean could be determined by dividing the number of values with in given data/population by the sum of any and all values in the data/population.A decrease in the number of people in a population is known as a population drop in humans (sometimes referred to as underpopulation, population reduction, or population collapse).The given data is-
2009 : 3,500 populationRate of decline ; 2.2% per year. 100% - 2.2% = 97.8%Difference of the years;
2014 - 2009 = 5 years
Decline = 3,500 * (0.978)^5
Decline = 3,500 * 0.89473
Decline = 3131.57
Thus, the population of the birds in 2014 will be 3,131.57 ≈ 3,132.
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A cloed cylindrical tank of diameter 14 m and height 5 m i made from a heet of metal. How much heet of metal will be required?
Answer:
[tex]528m^{2}[/tex]
Step-by-step explanation:
In order to find out how much sheet of metal is required to cover the cylinder, We find the total surface area
So the Formula to find the total surface area is,
[tex]2\pi r^{2} + 2\pi rh[/tex]
But first we need to find the radius with the formula
[tex]r= \frac{d}{2} \\[/tex]
[tex]r= \frac{14}{2} \\r=7[/tex]
Now we can apply the formula for the total surface area of a cylinder
[tex]2[/tex]x[tex]3.14[/tex]x[tex](7)^{2} +[/tex] [tex]2[/tex]x[tex]3.14[/tex]x[tex]7[/tex]x[tex]5[/tex]
[tex]307.72+[/tex][tex]219.8[/tex]
[tex]528m^{2}[/tex]
Hence the sheet of metal required is [tex]528m^{2}[/tex]
Hope it helps you
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1. A cube with side length 5 centimeters has a density of 3 grams per cubic centimeter.
What is its mass?
Answer: The mass of the cube is 3 grams/cubic centimeter * (5 cubic centimeters) = 15 grams.
Step-by-step explanation:
What is an equation for the line that passes through the points (8,-1) and (5,-1)?
Given:
The line that passes through the points (8,-1) and (5,-1)
To find:
Find the equation.
Explanation:
We know, the equation of the line passes through the two points,
y−y1 =y2 −y1 x2 −x1 (x−x1 ) Here,(x1 ,y1 )=(8,−1) and (x2 ,y2 )=(5,−1) y−(−1)=−1−(−1) 5−8 (x−8) y+1=0 −3 (x−8) y+1=0 y=−1 18. Which table represents a non-proportional relationship between x and y? X 1 3 7 15 Y -4 -12 -28 -60 X 1 4 7 10 Y 7. 5 30 52. 5 75 X -17 -5 2 10 Y 93. 5 27. 5 -11 -55 X -5 -1 1 8 Y 11 -1 -7 -28 10 X -5 -1 1 8 Y 7. 5 30 52. 5 75 y 11 - 1 -7 -28
Option D) is the correct answer. This is a non-proportional relationship.
A) -4 / 1 = -4
-12/3 = -4
-28/7 =-4
-60 /15 = -4
In this relationship, the value of y / x is constant. So, this is a proportional relationship.
B) 7.5 /1 =7.5
30/4 = 7.5
52.5/7 = 7.5
75/10 = 7.5
In this relationship, the value of y / x is constant. So, this is a proportional relationship.
C) 93.5 / -17 = -5.5
27.5/ -5 = 5.5
-11 / 2 = -5.5
-55 /10 = -5.5
In this relationship, the value of y / x is constant. So, this is a proportional relationship.
D) 7.5 / 5 =1.5
30 / -1 = -30
52.5 / 1 = 52.5
75/ 8 = 9.375
In this relationship, the value of y / x is not constant. So, this is a non-proportional relationship.
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The correct question is :
Which table represents a non-proportional relationship between x and y? A)X 1 3 7 15 Y -4 -12 -28 -60 B)X 1 4 7 10 Y 7. 5 30 52. 5 75 C)X -17 -5 2 10 Y 93. 5 27. 5 -11 -55 D) X -5 -1 1 8 Y 7. 5 30 52. 5 75
What is 6 divided by 2 (1+2)
Answer: 9
Step-by-step explanation:
6 / 2 ( 1+2)
We divided first
3 ( 1 +2)
Then we do the 1+2 second because they have ( )
3 (3)
Then we times them and get 9
a family consumes 4 litres of oil in 16 days how much old will be consumed in 200 days
Find the equation of the line, given the following information:
Passes through (-9,3) and is perpendicular to y =1/2x+6.
Answer:
y = -2x - 15
Step-by-step explanation:
We are given 2 pieces of information: (1) a point our line passes through, and (2) a line it is perpendicular to. The only thing we need from (2) is the slope.
We know that perpendicular lines have opposite signs and are inverses (denominator and numerator switched). So our line must have a slope of
m = -2
Using our equation for a line: y = mx+b, our line so far is
(I) y = -2x + b
Let's use the point we have (-9,3) and substitute what we know into equation (I) to find b.
x = -9
y = 3
(I) (3) = -2(-9) + b
3 = 18+b
b= -15
Now we have m and b so we can write the equation of our line:
y = -2x - 15
A credit card ha an APR of 28. 53%, and it billing cycle i 31 day long. What i the credit card' periodic interet rate?
By dividing the annual percentage rate (APR) by the number of billing cycles per year, the periodic interest rate = 73.89%
What is periodic interest rate?The periodic interest rate is the interest rate that is applied to your credit card balance on a periodic basis, usually on a monthly or daily basis. It is calculated by dividing the annual percentage rate (APR) by the number of billing cycles in a year.
What is the formula to calculate periodic interest rate?The periodic interest rate would be calculated as follows:
Periodic interest rate = APR / number of billing cycles per year
Periodic interest rate = APR / number of billing cycles per year
Since the billing cycle is 31 days long, there are approximately 12/31 = 0.387096774 billing cycles per year. Therefore, the periodic interest rate would be:
Periodic interest rate = 28.53% / 0.387096774 = 73.89%
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Please help me on this someone.
Ariel is correct, the statement is false and the equation has no solutions.
Is Ariel correct or not?Ariel says that the given linear equation has no solutions, so we need to check that.
The linear equation is:
3y - 12 = 3*(y + 1)
If we expand the right side we will get:
3y - 12 = 3y + 3
Now we can subtract 3y in both sides, then we will get:
3y - 12 - 3y = 3y + 3 - 3y
-12 = 3
That is a false equation, thus there are no values of y such that the equation is true, then we don't have any solutions.
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2. What is the x-coordinate of the image of point (2,-5) after reflection in the
line y=x?
The X coordinate of the image is (-5,2)
What is meant by coordinate ?A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
The coordinates of one point in the coordinate system are included in an ordered pair. An ordered pair of the form of a point's name is (x, y). The x-coordinate is represented by the first integer, and the y-coordinate by the second. You must place a dot at the coordinates of the ordered pair in order to graph a point.
Given
The coordinates for x and y change when you consider the line y=x. The end product is (-5,2)
Because (-5,2) its reflection means x coordinate will y coordinate and y coordinate will x coordinate so the coordinate be (-5,2)
The complete question is : Find the coordinates of the image of point (2,-5) after a reflection in the line y=x
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Pleaseeee helpppp meeeee
Answer:
A. 1/4
Step-by-step explanation:
Gradient = y2-y1/x2-x1
=(2-1)/(8-4)
=1/4
A once thriving company in teaneck had its monthly profits, in thousands of dollars, modeled by the equation? f(t) = t^2 9/ 1t^2 2 where t is in months after june 1st, 2002. estimate the company's profits on june 1st, 2002. estimate the company's profits many years into the future
The company's profits on June 1, 2002 is $4500 and the company's profits many years into the future is $1000 per month.
The equation f(t) = (t^2 + 9) / (t^2+2) provides the monthly profits, in thousands of dollar, where t refers to months after June 1, 2002.
The company’s profit on June 1, 2002 using the equation is when t = 0 months
f(0) = (0^2 + 9) / (0^2+2) = 9/2 = 4.5 or $4500.
The company’s profit on many years into the future using the equation is given by:
Limit(t→∞)((t^2+9)/(t^2+2))= Limit(t→∞)(2t/2t)=1
Hence the monthly profit is $1,000.
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What is the missing number?
Answer:
42
Step-by-step explanation:
You want to know the missing denominator in the equation ...
2/35 = 1/30 +1/x
SolutionSubtract 1/30 from both sides and simplify.
2/35 -1/30 = 1/x
(2·30 -1·35)/(35·30) = 1/x
25/(35·30) = 1/x
1/(7·6) = 1/42 = 1/x
The missing denominator is 42.
what is the answer too 1/14 x 9
Answer:
1/14×9=1×9/14and is equal to 9/14
Help me I don’t know
AU is 20 degrees and ∠QPA is 35 degrees and ∠ARU is 40 degrees are the unknown measures.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle.
In the given triangle A is the incenter for triangle PQR.
By observing figure, AR is angle bisector of angle URK.
So, ∠ARU = ∠ARK = 40 degree
Since, incenter point is equidistant from the sides of a triangle.
AT = AU = AK = 20
Since, PA is angle bisector of angle QPU.
So, ∠QPA = ∠UPA
3x + 2 = 4x - 9
Subtract 3x and add 2 on both sides of equation.
4x - 3x = 9 + 2
x = 11
Now plug in x value in ∠QPA=3(11)+2
=33+2=35 degrees.
Hence, Measures ∠ARU is 40 degrees, AU is 20 degrees and ∠QPA is 35 degrees.
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PLEASE HELP!!!!!! IT IS URGENT!!!
how to do question no 9 b?
Answer:
4 records sold on Wednesday, 32 records sold on Thursday!
Step-by-step explanation:
To do 9b, you need to set up our own equation!
Let's use W to represent records sold on Wednesday and T to represent records sold on Thursday.
It said 36 total records were sold on Wednesday and Thursday. This can be represented with the following equation ...
W + T = 36
It also tell us that on Thursday (T), 8 times the number of records sold on Wednesday were sold on Thursday. In equation form, this looks like ...
T = 8 × W
Now, let's use all this info to solve!
Let's first solve the equation W + T = 36
But, we need values! We have one! We know what T equals!
Let's plug in T
T = 8 × W
W + ( 8 × W ) = 36
Solve
W + 8W = 36
9W = 36
W = 4
4 records were sold on Wednesday!
Let's plug in W in our T equation to see how many records were sold on Thursday.
T = 8 × W
T = 8 × 4
T = 32
32 records were sold on Thursday!
Wednesday can be represented with HALF A CIRCLE
and Thursday can we represented with FOUR CIRCLES
A three-column table i given. Part A C D
Part 14 28 63
Whole 20 40 B
What i the value of B in the table?
60
75
80
90
B in the table has a proportional value of 90.
What is proportion?A percentage is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province. The population percentage is marked by the letter p, whereas the sample proportion is denoted by the letter p. Thus, p=0.43 if 43% of individuals visiting a business make a purchase before leaving.
Here,
Part 14 28 63
Whole 20 40 B
14/20=63/B
B=63*20/14
B=90
The value of B in the table is 90 by proportion.
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a ship leaves a harbor. it travels 35 miles due east and then adjusts its course 40 degrees northward. after traveling 45 miles in that direction, how far is the ship from its point of departure?
a ship leaves a harbor. it travels 35 miles due east and then adjusts its course 40 degrees northward. after traveling 45 miles in that direction,The distance from the ship's point of departure is approximately 59.9 miles.
To determine the distance from the ship's point of departure, we must first break down the distance traveled into x and y components. Initially, the ship traveled 35 miles due east, which can be represented as 35 miles on the x-axis. When the ship adjusted its course 40 degrees northward, it traveled 45 miles in that direction. This can be represented as 45 miles in the y direction, forming a triangle with the origin (point of departure). Using the Pythagorean theorem, we can calculate the hypotenuse of the triangle, which is equal to the distance from the point of departure. The hypotenuse of the triangle is equal to the square root of (35^2 + 45^2), which is equal to approximately 59.9 miles. Therefore, the distance from the ship's point of departure is approximately 59.9 miles.
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the questions are on the picture
Answer:
(i) x = 17 cm
(ii) 360 cm²
(iii) 14400 cm³
(iv) 4000 cm²
Step-by-step explanation:
You want the slant side length, end area, volume, and total surface area of an isosceles trapezoidal prism with end bases 16 cm and 32 cm and end height 15 cm. The length of the prism is 40 cm.
(i) Slant sideThe slant side of the base is the hypotenuse of a right triangle that has legs of 15 cm and (32 -16)/2 = 8 cm. You recognize these numbers as belonging to the {8, 15, 17} Pythagorean triple, so you know the slant side is 17 cm.
If you don't recognize that triple, you can figure the side length as ...
x = √(15² +8²) = √(225 +64) = √289
x = 17 . . . centimeters
(ii) End areaThe area of the end trapezoid is given by ...
A = 1/2(b1 +b2)h = 1/2(32 +16)(15) = 360 . . . cm²
The area of the end surface is 360 cm².
(iii) VolumeThe volume of the prism is given by ...
V = Bh
where B is the area of the base, and h is the length between bases.
V = (360 cm²)(40 cm) = 14400 cm³
The volume of the prism is 14400 cubic centimeters.
(iv) Surface areaThe total surface area is the sum of the areas of the two bases and the lateral area. The lateral area is the product of the perimeter of the base and the length of the prism.
total area = 2 · base area + lateral area
total area = 2 · 360 cm² + (32 + 17 + 16 + 17 cm)(40 cm)
total area = 720 cm² + 3280 cm² = 4000 cm²
The total surface area of the prism is 4000 square centimeters.
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Julia just lit a new candle and then let it burn all the way down to nothing. The candle burned at a rate of 0.75 inches per hour and its initial length was 9 inches. Write an equation for L, L, in terms of t,t, representing the length of the candle remaining unburned, in inches, tt hours after the candle was lit
Which of the following is the solutionsto | x +11|< 17?
OA. x< 6 and x < -28
OB. x< 6 orx>-28
OC. x<6
OD. x< 6 and x > -28
Answer:
OB
Step-by-step explanation:
|x+11|<17
x+11<17
x<17-11
x<6
-(x+11)<17
-x-11<17
-x<17+11
-x<28\×(-)
x>-28
Identify the measure of angle x please show work Bc I have too
Answer:
79°
Step-by-step explanation:
Angles on a line add to [tex]180^{\circ}[/tex].
[tex]28+x+73=180 \\ \\ 101+x=180 \\ \\ x=79[/tex]
All of the points in the picture of on the same line (Points are: (5,13) (c,10) (2,4)
A. Find the Slope of the line and explain/show your reasoning.
B. Write an equation for the line.
C. What is the value of c? Explain or show your reasoning
Sorry for weird format wouldve uploaded a picture of it but it wasn't working
The slope of the line is 3, equation of the line is y = 3x-2 and value of c is 4
What is a slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
Given that, All the given points are on the same line and the points are: (5,13) (c,10) (2,4)
Finding the slope;
We know slope of a line passing through two points = (y₂-y₁)/(x₂-x₁)
so, considering the points (5,13) and (2,4)
= (4-13)/(2-5) = 3
Therefore, the slope of the line is 3
Finding the equation,
We know the general equation of a line is given by, y = mx+b,
Where m is slope and b is y intercept.
Solving for b, put x = 5, m = 3and y = 13, in the equation
13 = 5x3+c
b = 13-15
b = -2
Therefore, the equation is y = 3x-2
Finding the missing coordinate c,
Since, all the points lies in same line, so slope will be equal in all the points,
Therefore, (10-13)/(c-5) = 3
c-5 = -1
c = 4
Hence, The slope of the line is 3, equation of the line is y = 3x-2 and value of c is 4
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यसको वक्र सतहको क्षेत्रफल पत्ता लगाउनुहोस् । The circumference of base of a cylinder is x cm and height is y cm. Find its curved surface area.
Answer:
Step-by-step explanation:
a box has width $m$, where $m$ is a prime number. if the box has height $m 2$, length $m-1$, and a volume of 140, what is $m$?
The width of the box m = 5 units
The width of the box = m units
Where m is a prime number
Height of the box = m+2 units
The length of the box = m -1 units
The volume of the box = 140 cubic units
The volume of the box = Length × width × height
140 = m × (m+2) × (m-1)
140 = (m^2 + 2m )(m-1)
140 = m^3 - m^2 + 2m^2 - 2m
140 = m^3 + m^2 - 2m
m^3 + m^2 - 2m - 140 = 0
We can split the equation by taking the common term outside
(m-5) (m^2 + 6m + 28) = 0
Therefore, one value of m = 5
5 is a prime number
Therefore, the value of m is 5
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quations: Practice
Question 2 of 5
Select the correct answer.
Which value for x makes the sentence true?
2 + 4 = 7
04
044
0-3
O
8
Answer:
there is no X in the eqn❗Step-by-step explanation:
there is no X in the eqn❗how would i answer it
*what is the reward-to-variability (i.e., sharpe) ratio of the best feasible cal? group of answer choices .4221 .4511 .7639 .4315
The reward-to-variability ratio of the best feasible is 0.4221 that is option a.
The proportion of stocks invested in the optimal risky portfolio can be calculated with the use of following formula:
Portfolio Invested in the Stock = [(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 - (Expected Return of the Bond - Risk Free Rate)*Covariance between Bond and Stock]/[(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 + (Expected Return of the Bond - Risk Free Rate)*(Standard Deviation of Stock)^2 - (Expected Return of Stock - Risk Free Rate + Expected Return of Bond - Risk Free Rate)]*Covariance between Bond and Stock
Portfolio Invested in Bond = 1 - Portfolio Invested in the Stock
Here, Risk Free Rate = 4 and Covariance = 32*24*.1250 = 96
Using these values and other information provided in the question, we get,
Portfolio Invested in the Stock = [(10 - 4)*(24)^2 - (7 - 4)*96]/(10 - 4)*(24)^2 + (7 - 4)*(32)^2 - [(10 - 4 + 7 - 4)]*96 = .5593
Portfolio Invested in Bond = 1-.5593 = .4407
Step 2: Calculate Expected Return and Standard Deviation of the Optimal Risky Portfolio
Expected Return = Portfolio Invested in Stock*Expected Return of Stock Portfolio Invested in Bond*Expected Return of Bond = .5593*10% + .4407*7% = 8.68%
Standard Deviation = [(Portfolio Invested in Stock)^2*(Standard Deviation of Stock)^2 + (Portfolio Invested in Bond)^2*(Standard Deviation of Bond)^2 + 2*(Portfolio Invested in Stock)*(Portfolio Invested in Bond)]^(1/2) = [(.5593)^2*(32)^2 + (.4407)^2*(24)^2 + 2*(.5593)*(.4407)*(96)]^(1/2) = 21.90%
Step 3: Calculate Reward-to-Volatility Ratio
The reward-to-volatility ratio can be calculated with the use of following formula:
Reward-to-Volatility Ratio = (Expected Return of the Portfolio - Risk Free Rate)/Standard Deviation of Portfolio = (8.68 - 4)/21.90 = .4221
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At a bakery 5 bagels and 5 breakfast sandwiches cost $30.00 and 8 bagels and 2 breakfast sandwiches cost $24.00.
Create a graph of the scenario, using x to represent the cost of a bagel and y to represent the cost of a breakfast sandwich.
Select two points on each line to graph the lines.
it equals = kwasia
30-24=6