To solve this problem efficiently, we can follow a simple algorithm: Create an empty list to store the even numbers.
Start from the largest possible even number, which is N rounded down to the nearest even number.
Check if N is even. If not, decrease N by 1 to make it even.
While N is greater than 0, add the current even number to the list and subtract it from N.
If N becomes 0, return the list of even numbers.
If N becomes negative or if the list contains duplicates, return an empty list.
If the current even number is not a valid option, decrease it by 2 and repeat steps 4-7.
This algorithm ensures that we use the largest possible even numbers first, which maximizes the number of even integers in the sum. It terminates when N is divided into a maximal number of positive even integers or when it is not possible to divide N in such a way.
The algorithm has a time complexity of O(N) since we iterate through N/2 even numbers at worst. This complexity is efficient for the given input range of up to 100,000,000.
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Air pressure may be represented as a function of height (in meters) above the surface of the Earth, as shown below. In this function, Po is the air pressure at the surface of the Earth, and h is the height above the surface of the Earth, measured in meters. Which expression best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth
The expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.
Air pressure at an altitude above the surface of the EarthThe air pressure at an altitude of 3,000 meters above the surface of the Earth is calculated as follows;
Po = ρgh
where;
ρ is density of airg is acceleration due to gravityh is the altitudeSubstitute the value of altitude into the equation;
Po = 3,000ρg
Thus, the expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.
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Question 1
Which equation represents the relationship shown in the table
at the right?
Answer:
Step-by-step explanation:
b = a + b table chart what equation represents the relationship between a and b shown in the table .
Please look at the picture, I need help ASAP.
See below for the proof that the areas of the lune and the isosceles triangle are equal
How to prove the areas?The area of the isosceles triangle is:
[tex]A_1 = \frac 12r^2\sin(\theta)[/tex]
Where r represents the radius.
From the figure, we have:
[tex]\theta = 90[/tex]
So, the equation becomes
[tex]A_1 = \frac 12r^2\sin(90)[/tex]
Evaluate
[tex]A_1 = \frac 12r^2[/tex]
Next, we calculate the length (L) of the chord as follows:
[tex]\sin(45) = \frac{\frac 12L}{r}[/tex]
Multiply both sides by r
[tex]r\sin(45) = \frac 12L[/tex]
Multiply by 2
[tex]L = 2r\sin(45)[/tex]
This gives
[tex]L = 2r\times \frac{\sqrt 2}{2}[/tex]
[tex]L = r\sqrt 2[/tex]
The area of the semicircle is then calculated as:
[tex]A_2 = \frac 12 \pi (\frac{L}{2})^2[/tex]
This gives
[tex]A_2 = \frac 12 \pi (\frac{r\sqrt 2}{2})^2[/tex]
Evaluate the square
[tex]A_2 = \frac 12 \pi (\frac{2r^2}{4})[/tex]
Divide
[tex]A_2 = \frac{\pi r^2}{4}[/tex]
Next, calculate the area of the chord using
[tex]A_3 = \frac 12r^2(\theta - \sin(\theta))[/tex]
Recall that:
[tex]\theta = 90[/tex]
Convert to radians
[tex]\theta = \frac{\pi}{2}[/tex]
So, we have:
[tex]A_3 = \frac 12r^2(\frac{\pi}{2} - \sin(\frac{\pi}{2}))[/tex]
This gives
[tex]A_3 = \frac 12r^2(\frac{\pi}{2} - 1)[/tex]
The area of the lune is then calculated as:
[tex]A = A_2 - A_3[/tex]
This gives
[tex]A = \frac{\pi r^2}{4} - \frac 12r^2(\frac{\pi}{2} - 1)[/tex]
Expand
[tex]A = \frac{\pi r^2}{4} - \frac{\pi r^2}{4} + \frac 12r^2[/tex]
Evaluate the difference
[tex]A = \frac 12r^2[/tex]
Recall that the area of the isosceles triangle is
[tex]A_1 = \frac 12r^2[/tex]
By comparison, we have:
[tex]A = A_1 = \frac 12r^2[/tex]
This means that the areas of the lune and the isosceles triangle are equal
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Instructions: Given the coordinates, Complete the translation (x,y)→(x+2,y−2) C(−5,−1) D(−4,3) E(−3,2) F(−2,0)
the translations is,
C(-5,-1) → (-3,-3)
D(-4,3) → (-2,1)
E(-3,2) → (-1,0)
F(-2,0) → (0,-2)
What is Translation ?
The changes in the value of the x and y coordinates is known as translation.
Calculation:
The given points are C(-5,-1), E(-4,3), F(-3,2), F(-2,0).
according to the question (x,y)→(x+2,y-2)
this means x coordinate changes by addition of 2
And the y coordinate changes by subtraction of 2
Addition and Subtraction in the Coordinates,
C(-5,-1) → (-5+2,-1-2) → (-3,-3)
D(-4,3) → (-4+2,3-2) → (-2,1)
E(-3,2) → (-3+2,2-2) → (-1,0)
F(-2,0) → (-2+2,0-2) → (0,-2)
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PLEASE ANSWER QUICKLY
Answer:
9
Step-by-step explanation:
See the attached image.
PLEASE HELP WILL GIVE YOU ALL MY POINTS In the picture, t || s, mz1 = 10x + 2, and mz2 = 12x - 22. Find the measure of angle 2.
Answer:
[tex]\huge\boxed{\sf < 2 = 122\°}[/tex]
Step-by-step explanation:
From the figure,
∠1 = ∠2 (Alternate angles are equal)We know that:
∠1 = 10x + 2∠2 = 12x - 22So,
10x + 2 = 12x - 22Add 22 to both sides
10x + 2 + 22 = 12x
10x + 24 = 12x
Subtract 10x to both sides
24 = 12x - 10x
24 = 2x
Divide 2 to both sides
12 = x
OR
x = 12Given that,
∠2 = 12x - 22
Put x = 12
∠2 = 12(12) - 22
∠2 = 144 - 22
∠2 = 122°[tex]\rule[225]{225}{2}[/tex]
Answer: 122°
Step-by-step explanation:
∠1 an ∠2 are alternate interior angles, which are angles that are inside both parentheses and are on alternate sides of the transversal. The Alternate Interior Angles Theorem states that if two lines are parallel and cut by a transversal, then the alternate interior angles formed are congruent.
Since the lines are parallel as given in the question, ∠1 and ∠2 are of equal measure. We can solve for ∠2 by first solving for x, then plugging it in ∠2's measure.
[tex]10x+2=12x-22[/tex]
[tex]-2x=-24[/tex]
[tex]x=12[/tex]
Putting x in the expression 12x-22, we get
[tex]12(12)-22\\144-22\\122[/tex]
Hence, the value of ∠2 is 122°.
Please help me bef9yer9h
Answer:
y = -6x + 7.5
Explanation:
To find perpendicular bisector equation:
Given points: B(-2, 1), C(4, 2)
First find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\sf slope: \dfrac{2-1}{4-(-2)} } = \dfrac{1}{6}[/tex]
Then the perpendicular slope will be negatively inverse.
[tex]\sf perpendicular \ slope \ (m) : -(\dfrac{1}{6} )^{-1} = -6[/tex]
Then find the mid point coordinates between BC:
[tex](x_m, y_m)= \sf (\dfrac{x_1 + x_2}{2} , \dfrac{y_2 + y_1}{2} )[/tex]
[tex](x_m, y_m) = \sf (\dfrac{-2 + 4}{2} , \dfrac{1 + 2}{2} )[/tex]
[tex](x_m, y_m) = \sf ( 1 , 1.5 )[/tex]
Then find equation:
y - yₘ = m(x - xₘ)
y - 1.5 = -6(x - 1)
y = -6x + 6 + 1.5
y = -6x + 7.5
The answer is y = -6x + 15/2.
First, find the slope of BC.
m = Δy/Δx
m = 2 - 1 / 4 - (-2)
m = 1/6
Hence, the slope of the perpendicular bisector will be the negative reciprocal of the given line.
m' = - (1/ [1/6])
m' = -6
Now, find the midpoint of BC.
M = (-2 + 4 / 2, 2 + 1 / 2)
M = (1, 3/2)
Now, we can find the equation of the perpendicular bisector using the point slope form of equation.
y - y₁ = m (x - x₁)
y - 3/2 = -6 (x - 1)
y - 3/2 = -6x + 6
y = -6x + 15/2
. In your rectangular backyard, you know the width of the yard is three less than four times the length. If the perimeter of your yard is 24 yards, what is the width?
The width of the rectangular backyard is 9 yards.
How to find the width of the rectangle?The width of the yard is three less than four times the length.
Therefore,
w = 4l - 3
Perimeter of a rectangle = 2l + 2w
where
l = length
w = width
Hence,
24 = 2l + 2(4l - 3)
24 = 2l + 8l - 6
24 = 10l - 6
24 + 6 = 10l
30 = 10l
l = 30 / 10
l = 3 yards
Hence,
w = 4(3) - 3
w = 12 - 3
w = 9 yards
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Consider the volume of the region shown below, which shows a right circular cone with a top radius of 3 cm and height 9cm
Answer:
84.82 cm
Step-by-step explanation:
Volume of a cone: [tex]\frac{1}{3} \pi r^2h[/tex]
[tex]\frac{1}{3} \pi r^2h\\\\\\\\= \frac{1}{3}\pi (3)^2(9)\\\\= \frac{1}{3}\pi(9)(9)\\\\\\\= \frac{1}{3} \pi (81)\\\\= 27\pi \\[/tex]
≈ 84.82 cm
Given that DRWH is a parallelogram, determine the values of x and y.
Answer:
the opposite sides of the parallelogram are equal.
so DR = HW mean : 2 y + 2 = 3 y - 9
3y - 2y = 9+2
y = 11
RW = y+4 = 11+4 = 15
DH = RW
so, 3 x + 6 = 15
3x = 15-6 = 9
x = 3
Find the volume of this sphere.
Answer:
4ft^3
Step-by-step explanation:
1.333333*3*1^3=4
To start finding the volume of this sphere, we get the following data:
π = 3r = 2 ft²To find the volume we apply the following formula:
[tex]\boldsymbol{\sf{V= \dfrac{3}{4}\pi r^{2} }}[/tex], wherev = volumeπ = pir = radiusWe substitute our data in the formula and solve:
Substituting values into the equation
[tex]\boldsymbol{\sf{V=\dfrac{3}{4}*3*(2 \ ft)^{3} }}[/tex]Calculate exponent cubed
[tex]\boldsymbol{\sf{V=\dfrac{3}{4}*3*8 \ ft^{3} }}[/tex]Multiplying
[tex]\boxed{\boldsymbol{\sf{V=32 \ ft^{3} }}}[/tex]Therefore, the volume of the sphere is 32 ft³.
PLEASE HELP IM SERIOUSLY STUCK ON THIS
The purchase price of the new car if the sales tax is $3500 is $50000
Direct variationLet the amount of sales tax be A and the purchase price be p
If the amount of sales tax is directly proportional to the purchase price, this is expressed as:
S = kp
If S = $1750 and p = $25000, the;
k = S/p
k = 1750/25000
k = 175/2500
If the sales tax is $3500, the purchase price will be given as:
S = kp
3500 = 175/2500 p
175p = 3500*2500
175p = 8750000
p = 8750000/175
p = 50000
Hence the purchase price of the new car if the sales tax is $3500 is $50000
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Which graph represents the solution to x<6?
Lines b and c are parallel. What is the measure of angle 6
The measure of ∠6 is 54 degrees.
How to find the angles in a parallel lines?When parallel lines are cut by a transversal, angle relationship are formed. Therefore,
∠6 = 5x + 9 (vertically opposite angles)
∠6 = ∠2
Hence,
∠2 + 13x + 9 = 180
5x + 9 + 13x + 9 = 180
18x = 162
x = 162 / 18
x = 9
Hence,
∠6 = 5(9) + 9 54°
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For each of the following distance matrices of graphs, identify the diameter, radius and center. Assume the graphs vertices are the numbers 1 through
For each of the following distance matrices of graph, the
The diameter = 3The radius of the graph is given as 2What is the diameter of the graph?This is used to refer to the fact that there would be a maximum distance that exists between the pair of vertices.
What is the radius of the graphThis used to refer to the minimum eccentricities of the vertices
What is the center of the graph?This is used to show all of the vertices that have minimum eccentricities.
How to solve the matrixWe have
e 1 = 3
e 2 = 3
e3 = 2
e4 = 3
e 5 = 3
e 6 = 3
e 7 = 3
e8 = 2
e 9 = 3
e 10 = 2
Then the the diameter = maximum eccentricity = 3
The radius = minimum eccentricity = 2
center = [3, 8,10]
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1. What is the domain and range of the
graph shown?
-10 S
2799
-24
Answer:
D: (-∞,∞)
R: (0,∞)
Step-by-step explanation:
This is a parabola, so the domain of this function is always:
D:(-∞,∞)
The y-values of this parabola do not go any lower than 0, and it goes upwards in the positive y-direction. So, the range for this function is:
R:(0,∞)
The picnic breakfast cost $12. Jasmine left a tip that was 15 percent of the
cost of the meal. How much money was the tip that Jasmine left?
PLEASE HELP IM STUCK
Answer:
The 18th term would be "-70"
Answer:
-70
Step-by-step explanation:
Based on the graph of the general solution to the differential equation dy over dx equals 2 times x minus 2 times y comma which of the following statements is true
Statements is TRUE
Based on the graph of the general solution to the differential equation dy over dx equals 2 times x - 2 times y = dy/dx=2x-2y.
What is general solution to the differential equation?A differential equation's solution is an expression for the dependent variable in terms of one or more independent variables that satisfy the relationship.
The statement which is true is the slopes are all positive in quadrant I.
Given the differential equation is dy/dx=2x-2y
A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.
Given dy/dx=2x-2y
now slope=2x-2y
Along x-axis, y=0. So, slope=2x+0.
Since it depends upon x hence the slope along the y-axis are not horizontal.
Along y-axis, x=0. So, slope -2y+0.
The slope along the x-axis are also not horizontal.
In quadrant I:
x,y≥20
So, dy/dx ≥20
Therefore, the slopes are all positive in quadrant I. In quadrant IV,
x≥0,y≤0
so, dy/dx is not always positive.
The slope are not all positive in quadrant IV:
Therefore, the slope are all positive in quadrant I for the differential equation dy/dx=2x-2y.
General solution to the differential equation =
dy/dx=2x-2y.
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Complete Question:
Based on the graph of the general solution to the differential equation dy over dx equals 2 times x plus y comma which of the following statements is true?
The slopes along the y-axis are horizontal.
The slopes along the x-axis are horizontal.
The slopes are all positive in Quadrant 1.
The slopes are all positive in Quadrant 4.
find the area of the diagram
Answer:
13500 ft²
Step-by-step explanation:
Area of rectangle:We can find the width of the rectangle using Pythagorean theorem.
AD² + DC² = AC²
180² + DC² = 195²
32400 + DC² = 38025
DC² = 38025 - 32400
= 5625
DC = √5625
= 75 ft
length = 75 ft
Width = 180 ft
[tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]
= 75 * 180
= 13500 ft²
An insurance office records the number of claims received each day, X, and built the probability distribution table below using the data collected. Find the mean and the standard deviation of the probability distribution using Excel. Round the mean and standard deviation to two decimal places.
The mean of the data given is 13.4364 and.the standard deviation is 1.788.
How to illustrate the information?It should be noted that the mean is the average of the giving set of numbers. In this situation, the mean is 3.1998.
E(X²) will be:
= (0² × 0.0408) + (1² × 0.1304) .... + (12² × 0.0001)
= 13.4364
Var(X) = 13.4364 - 3.1998²
= 3.198
The standard deviation will be:
= ✓3.198
= 1.788
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can someone please help mee (will give brainliest 20 points!!!)
Given that f(x) = -6x and g(x) = x + 4, multiply the functions (f •g)(x).
Answer:
(f • g)(x) = -6x² - 24x
Step-by-step explanation:
The expression (f • g)(x) can be written in an expanded form, f(x) • g(x).
(f • g)(x) <----- Original expression
f(x) • g(x) <----- Rewritten expression
(- 6 x) • (x + 4) <----- Insert functions
-6x² - 24x <----- Multiply -6x and x, and multiply -6x and 4
Determine an equation that describes the number of bacteria in both the foods when they are mixed.
The equation that describes the number of bacteria in both the foods when they are mixed is; Option C: 35T₂ + 55T + 450
How to simply quadratic Equations?
We are given the equations that describes the number of bacteria in both the foods when they are mixed.
Equation for first bacteria is;
N₁(T) = 15T₂ + 60T + 300
Equation for second Bacteria is;
N₂(T) = 20T² - 5T + 150
The equation that describes the number of bacteria in both the foods when they are mixed is;
N₁(T) + N₂(T) = 15T₂ + 60T + 300 + 20T² - 5T + 150
⇒ 35T₂ + 55T + 450
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Round 5 358 708 to the nearest million
Answer:5 million
Step-by-step explanation: Because 300 thousand is below 500 thousand so if its below 500 thousand it cant round up it rounds down.
A rectangle has a width of 2.45 feet and a length of 6.5 feet. how will the area of the rectangle change if each side is increased by a factor of 5? the area will be one-fifth the original. the area will be startfraction 1 over 25 endfraction the original. the area will be 25 times the original. the area will be 5 times the original.
The area of the new rectangle will be 25 times that of the original
Area of a rectangleA rectangle is a 2D shape that has 4 sides and equal interior angles
If rectangle has a width of 2.45 feet and a length of 6.5 feet, then;
Width = 2.45 feet
Length = 6.5feet
A = 2.45 * 6.5
A = 15.925 square feet
If each side of the rectangle is increased by a factor of 5, hence;
W1 = 5(2.45) = 12.25feet
L1 = 5(6.5) = 32.5 feet
Determine the area of the new rectangle
A = 12.25 * 32.5
A = 398.125 square feet
Ratio of the area
A1/A = 398.125/15.925
A1 = 25A
Hence the area of the new rectangle will be 25 times that of the original
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Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?
(2, 12)
(2, 18)
(2, 7)
(3, 7)
Answer: (2, 18)
Step-by-step explanation:
When x=2, [tex]f(2)=2(3)^{2}=18[/tex].
So, it should pass through (2, 18).
Answer:
(2, 18)
Step-by-step explanation:
i posted this at 1:19 in the morning, good day
Please help and explain
Answer:
D
Step-by-step explanation:
Yep, what you did there is correct!
The expression was: [tex](\frac{5^2}{4} )^4[/tex]
So let's solve this step by step.
First the numerator
[tex](5^2)^4[/tex]
Is the same thing as
[tex]5^8[/tex]
Since the exponents are multiplied.
Next is the denominator
[tex]4^4[/tex]
This can stay the same, since solving it as 4 x 4 x 4 x 4 will only make the fraction more complicated. Also, the answer choices below show that the denominator stays in exponential form.
==> [tex]\frac{5^8}{4^4}[/tex] is our final answer!
So the answer to this question is D. You got the question correct! :)
I hope that helped!!
A rectangular field is to be enclosed by 400m of fencing. Use quadratic to
determine what dimensions will result in the maximum area inside the fence. Show
all your work.
Work:
First it's a rectangle so its area is equal to the product (multiplication) of both sides of the rectangle (dimensions). A = a x b = ab
NOW: knowing the the circumference or perimeter is equal to 400m, we can say that P = 400 = 2(a+b) = 2a + 2b since the given polynom is rectangle. 2a + 2b = 400 <==> 2a = 400 - 2b <==> a = 200 - b.
We gave an expression of a in function of b. Now we can replace the variable a by 200 - b in the first expression of the area.
A = ab = (200-b)b = 200b-b^2 = -b^2 + 200b
A is now a quadratic equation. We note A(b) the epression -b^2 +200b so:
A(b) = -b^2 +200b
We can already see that A is a quadratic equation of the form:
ax^2 + b + c. The a coefficient is negative which will lead to closed parabola when looking from the top. Now we need to find the maximum of the function by using the derivatives:
A(b) = -b^2 +200b <==> A'(b) = -2b + 200b
and -2b + 200b = 0 <==> b = 100;
So the derivative function crosses the x-axis at (100; 0).
So is increasing over ]-∞; 100] and decreasing over [100; ∞[.
We obtain a maxima on (100; x) with A. To find it we need to replace 100 by b in the function A.
A(b) = -b^2 + 200b
<==> A(100) = -100^2 + 200 x 100 = - 10000 + 20000 = 10000
Now let's find a: if b = 100 what equals a ?
We know that ab = 10000 <==> 100a = 10000 <==> a = 100;
And we verify that ab = 100 x 100 = 10000.
The rectangle needs to be a square to reach the maximum area of 10000m^2 or also 0.01 km^2.
Q.E.D.
deeksha made cuboid of size 2 cm x 3 cm x 4 cm. how many such
cuboids will be required to make a cube?
b) in a right triangle pqr,
The number of cuboids of dimension 2 cm x 3 cm x 4 cm, required to make a cube is 9.
Dimensions of the cuboid Deeksha made are given as 2 cm x 3 cm x 4 cm.
Thus, the volume of this cuboid = 2*3*4 cm³ = 24 cm³.
Using the formula for the volume of cuboid as the product of the three sides.
Deeksha wants to make a cube combining some number of these cuboids.
Assuming the side length of the cube to a, the volume of the cube = a³.
Assuming the number of cuboids required to make 1 cube to be n, we can write that a³ = n*(24 cm³).
To make this relation true, we need the right-hand side to be a perfect cube.
Prime factorizing the volume of the cuboid, we get 24 cm³ = 2³ * 3 cm³.
To make it a perfect cube, we need to multiply 3², by it.
Thus, n = 3² = 9.
Thus, the number of cuboids of dimension 2 cm x 3 cm x 4 cm, required to make a cube is 9.
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The provided question is incorrect. The correct question is:
"Deeksha made cuboid of size 2 cm x 3 cm x 4 cm. how many such
cuboids will be required to make a cube?"