The value [tex]\displaystyle \sum^{2007}_{n = 2} F(n)[/tex] is 2016532.
What is an integer?The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. Integer examples include 1, 2, 5, 8, -9, -12, etc. "Z" stands for an integer. The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Integer examples include: -1, -12, 6, and 15.
Zero is not an integer that can be positive or negative. There is no (+ or -) sign on zero, making it a neutral number.
F(2) = 3
We learn that for the majority of the graphs by examining different graphs.
F(n) = n+1
3+4+5+5+7+8+9+9+··········+2008
= (1+2+3+4+5+·····+2008)-3-501
= [tex]\frac{(2008) \times( 2009)}{2} -504[/tex]
= 2016532
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F is inversely proportional to d^2.When F=9, d=5
Work out F
when d=3
Answer:
9
Step-by-step explanation:
Answer:
F is inversely proportional to d^2when F=9,d=
Step-by-step explanation:
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
m Z 2.
In the figure below, m1= 59°. Find m
Answer:
121°
Step-by-step explanation:
These are supplemental angles. a straight angle is 180 degrees.
180 - 59 = 121
Answer: m2=121 degrees
Step-by-step explanation:
m1+m2=180 ==> m1 and m2 are on a straight line. Straight lines measure 180 degrees and are called straight angles. m1 and m2 are supplementary angles, so they add up to 180 degrees.
59+m2=180
59-59+m2=180-59
m2=180-59
m2=121 degrees
Write and expression equivalent to 62.7 - 82.4
Answer: -19.7
Step-by-step explanation:
62.7 - 82.4=
-(82.4-62.7)= -19.7 ==> switch the numbers and negate the expression to get the same answer
In Exercises 26-29, use the following information. You belong to a book club.
Your yearly book budget is $350. Each book in the book club costs $7.
26. Complete the table.
Books Cost (dollars) Amount left (dollars)
1
343
2
336
3
?
4
?
7
14
?
?
27. Write a variable expression for the cost of b books.
28. Write a variable expression for the amount of your budget after b books.
29. How many books will you be able to buy before the $350 is spent?
50 books can be purchased with $ 350.
We have the data:
Books Cost (dollars) Amount left (dollars)
1 343
2 336
3 336 - 7 = 329
4 329 - 7 = 322
7 322 - 21 = 301
14 301 - 49 = 252
Cost of 1 book = $ 7
Cost of b books = 7 × b = 7 b
Amount of budget after b books = 350 - 7 b
We can buy = 350 / 7 = 50 books before spending the entire amount.
Therefore, we get that 50 books can be purchased with $ 350.
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an equilateral triangle has sides of equal length. determine whether the triangle with vertices 1-1, -12, 12, 32, 1-4, 32 is equilateral.
No, the triangle with vertices (-1, -1), (2, 3), (-4, 3) is not equilateral.
What is equilateral triangle?An equilateral triangle is a triangle that has all three sides of equal length, also known as a "regular" triangle.
An equilateral triangle is thus a subset of an isosceles triangle in which all three sides are equal. An equilateral triangle has three equal sides.Now, as per the given question.
The vertices are given as (-1, -1), (2, 3), (-4, 3).
Find the distance between the two corresponding vertices.
First, find distances between (-1, -1), (2, 3) lets say 'c'.
c² = (-1-3)² + (-1-2)²
c² = 4² + 3²
c² = 16 + 9
c² = 25
c = 5
Now, find the distance between (2, 3), (-4, 3), let say it 'd'.
d² = (-4-2)² + (3-3)²
d² = 36
d = 6
Now, find the distance between (-1, -1), (-4, 3) say it 'p'
p² = (-1-(-4 ))² +(-1-3)²
p² = 3² +4²
p² = 25
p = 5
As, all three distances are not same. Thus, the given vertices does not form equilateral triangle.
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The correct question is-
An equilateral triangle has sides of equal length. Determine whether the triangle with vertices (-1, -1), (2, 3), (-4, 3) is equilateral.
A study was performed with a random sample of 513 bolts produced at one factory. What population would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases?.
The population that would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases is All 513 bolts that were randomly selected.
What sample should be used to generalize the conclusions from a study?Generalizing the conclusions from a study can only be done with a sample that is well-represented. The question here says that all 513 bolts were chosen without bias. This means that a fair conclusion can be reached from the sample.
So, the results that occur from studying the 513 bolts can be sure to produce accurate results. Moreso, the population is large, thus, the population can be used to generalize conclusions.
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2.
Find the sum of the digits of each multiple of 9 below.
Sum of digits
9
1+8=9
9.1 9
9.2=18
9.3=27
9.4 36
9.5=45
9-6=54
9.7=63
9.8=72
9.9 81
The sum of the multiples of 9 till 81 is 405 by arithmetic progression.
We have to sum the multiples of 9 up to 81
= 9 + 18 + … + 45 + …+ 72 + 81
We will use arithmetic progression for this.
we get that:
initial term = a = 9
Common difference = d = 9
n = 9
Sum of terms = n / 2 ( 2 a + ( n - 1) d )
Sum = 9 / 2 (2( 9) + 8 ( 9))
sum = 9 / 2 (18 + 72)
Sum = 9 / 2 ( 90)
Sum = 810 / 2
Sum = 405
Therefore, we get that, the sum of the multiples of 9 till 81 is 405 by arithmetic progression.
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help pls
with step by step explanation
Answer:
give me one second brooo
Explanation:
50 P0!NTS!
Favorite hobby/activity?
mines dirt biking
Answer:
Step-by-step explanation:
Favorite hobby is gaming
Favorite activity is football
100 points !!!!! HELP ME ASAP
Write a piecewise function represented by the graph.
The piecewise function represented by the graph is:
f(x) = -3, x ≤ 0.f(x) = 3 - 3x, x > 0.What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For x to the left of 0, inclusive, the function is constant at y = -3, hence the definition is:
f(x) = -3, x ≤ 0.
For x to the right of 0, with an open interval, the function is linear, with an intercept of 3(when x = 0, y = 3) and a slope of -3(the function fell from y = 3 to y = 0 when x moved from x = 0 to x = 1), hence:
f(x) = 3 - 3x, x > 0.
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Six friends each use a $2-off coupons to buy themselves a movie tickets. They sped be a total of $42. What is the price of one movie ticket without the coupon?
Answer:
Since there are a total of six friends and they each use a $2 off coupon then what you first want to do is multiply:
2 times 6 = 12
Then you want to add:
42 + 12 = 54
So the total that they would have spent without the discount would be $54.
Step-by-step explanation:
Hope it helps! =D
Mr Johnson's plans to fence the triangular section of a backyard for a dog run
!!Figure is not clear!! Formulae is provided below.
To fence the triangular section Mr. Johnson has to find the perimeter of the triangular field.
To find the perimeter of the triangle one has to add the length of all the three sides of the triangle.
Similarly we can also find the perimeter of other plane figures by adding the lengths of all the sides of the figure.
Suppose if the length of the sides of a triangle is a,b and c units.
Then the perimeter of the triangular field will be = (a + b + c) units.
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Two adjacent angles (two angles that share
a common side and vertex) form a straight
angle. One of the angles measures 140°.
What is the measure of the other angle?
The value of the other angle will be 40°.
How to calculate the angle?It should be noted that the value of the angle on a straight line equals to 180°.
In this case, the adjacent angles (two angles that share a common side and vertex) form a straight
angle and one of the angles measures 140°.
The value of the other angle will be:
= 180° - 140°
= 40°
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from 1-4 which are linear and non linear?
Answer properly
Only function 2 represent a linear function.
How to find whether a function is linear or non-linear
Herein we find four cases of functions, of which we are asked to determine if each function is linear or not. A function is linear if and only if the change between every pair of two consecutives values of x and y is the same. Now we proceed to check each case:
Function 1
Δx = - 1 - (- 3) = 2; Δy = 6 - 2 = 4
Δx = 1 - (- 1) = 2; Δy = 18 - 6 = 12
Δx = 3 - 1 = 2; Δy = 54 - 18 = 36
The function is not linear.
Function 2
Δx = 5 - 1 = 4; Δy = - 1 - 1 = - 2
Δx = 9 - 5 = 4; Δy = - 3 - (- 1) = - 2
Δx = 13 - 9 = 4; Δy = - 5 - (- 3) = - 2
The function is linear.
Function 3
Δx = 5 - 4 = 1; Δy = - 10 - (- 5) = - 5
Δx = 6 - 5 = 1; Δy = - 13 - (- 10) = - 3
Δx = 7 - 6 = 1; Δy = - 15 - (- 13) = - 2
The function is not linear.
Function 4
Δx = 1 - (- 2) = 3; Δy = 5 - 4 = 1
Δx = 4 - 1 = 3; Δy = 6 - 5 = 1
Δx = 7 - 4 = 3; Δy = 1 - 6 = - 5
The function is not linear.
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
a bunch of gas money
Step-by-step explanation:
Answer:
Increased towing capacity
Step-by-step explanation:
?
11. Which expression has the least value?
B √81 - √25
C √64 + √25
D √64 - 31
Answer:D
Step-by-step explanation:
√81 - √25 = 9 - 5 = 4
√64 + √25 = 8 + 5 = 13
√64 - 31 = 8 - 31 = -23
24. Which of the following real numbers has the greatest value? 13.09, 135, √169, 13.1
Answer:
135
Step-by-step explanation:
135 > 13.1 > 13.09 > √169 (√169 = 13)
I hope I could help ^^
The base of a triangle with the height of 7 units is represented by the formula b=2/7a. the base of the triangle is less than 10. write and solve an inequality that represents the possible area a if the triangle.
The inequality that represents the possible area of the triangle is 2/7a < 10
The solution to the inequality is a < 35
Solving linear inequalitiesFrom the question, we are to write and solve an inequality that represents the possible area, a, of the triangle
From the given information,
The base of the triangle is given by
b = 2/7a
Also, from the given information,
The base of the triangle is less than 10
That is,
b < 10
Then,
we can write that
2/7a < 10
This is the inequality that represents the possible area of the triangle
Now, solve the inequality
2/7a < 10
Multiply both sides of the equation by 7/2
7/2× 2/7a < 7/2× 10
a < 7 × 5
a < 35
Hence, the inequality that represents the possible area of the triangle is 2/7a < 10
The solution to the inequality is a < 35
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call a positive real number special if it has a decimal representation that consists entirely of digits $0$ and $7$. for example, $\frac{700}{99}
The smallest n such that 1 can be written as a sum of n
special numbers is 8.
What is a number?A number is a mathematical concept that is used for counting, measuring, and labeling. The natural numbers 1, 2, 3, 4, and so forth are the original examples. Number terms in language can be used to represent numbers. More commonly, individual numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five. Basic numerals are frequently arranged in a numeral system, which is an ordered manner to represent any number, as only a very small number of symbols can be learned. The most widely used numeral system is the Hindu-Arabic numeral system, which enables the depiction of any number using a combination of 10 basic numerical symbols, or "digits."
Calculations:
Suppose 1 = x1 + x2 + · · · + xn where x1, x2, . . . , xn are special and
n ≤ 9. For k = 1, 2, 3, . . . , let ak be the number of elements of {x1, x2, . . . , xn}whose kth decimal digit is 7. Then
1 =7a1}/10 +7a2/10 +7a3/10 + ... ,
which yields
1/7 = 0.142857 =a1 /10 +a2/[tex]10^{2}[/tex] +a3/[tex]10^{3}[/tex] + ... ,
Hence a1 = 1, a2 = 4, a3 = 2, a4 = 8, etc. In particular, this implies that n ≥ 8. On
the other hand,
x1 = 0.700, x2 = x3 = 0.07, x4 = x5 = 0.077777, and x6 = x7 = x8 = 0.000777
are 8 special numbers whose sum is
(700700+2(70707)+2(77777)+3(777))/{999999} =1
Thus the smallest n is 8.
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A storage bin is built as a rectangular prism with a closed top. The length is
3.5 feet, the width is 2 feet, and the height is 2.5 feet.
What is the amount of material needed to make the box?
A. 34.5 ft²
B. 41.5 ft2
C. 36.5 ft2
D. 17.5 ft2
SUBMIT
Answer:
D
Step-by-step explanation:
Area equal LxWxH
2x2.5x3.5=17+5
The amount of material needed to make the box is 41.5 ft².
What is surface area?The surface area of a figure is the number of unit squares it takes to cover the entire surface without gaps or overlaps. If a three-dimensional figure has flat sides, the sides are called faces. The surface area is the total of the areas of the faces.
Given that, a rectangular storage box is to be made with length is 3.5 feet, the width is 2 feet, and the height is 2.5 feet.
For finding the same, we will find the surface area of the box,
Surface area of the box = 2(length·width + width·height + height·length)
Therefore,
SA = 2(3.5x2+2x2.5+3.5x2.5)
SA = 2 x 20.75
SA = 41.5
Hence, the amount of material needed to make the box is 41.5 ft².
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PLEASE HELP WITH HOMEWORK
Supplementary angles have a sum of 180°
Therefore, we can add the expressions for Angles A and B and set their sum equal to 180.
( 7x - 15 ) + ( 2x - 3 ) = 180
Now we can combine like terms and use inverse operations to find the value of x:
( 7x - 15 ) + ( 2x - 3 ) = 180
9x - 18 = 180
9x - 18 + 18 = 180 + 18
9x = 198
9x/9 = 198/9
x = 22
Then Angle A will have a measure of 7x - 15 or 7• 22 -15 = 154 - 15 = 139°
m∠A = 139°
The measure of Angle b will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°
m∠ B = 41°
NOTE: 139 + 41 = 180
The velocity-time graph for a cycle is shown.
Velocity (m/s)
Time (seconds)
a) Work out the distance travelled on the cycle in the first 14 seconds.
b) Work out the acceleration in the first 4 seconds.
The answers to both the subparts are as follows:
(A) In the first 14 seconds, the cycle traveled 96 meters.(B) The acceleration is 2m/s² for the first 4 seconds.What is velocity?Velocity is the direction at which an object is moving and serves as a measure of the rate at which its position is changing as seen from a specific point of view and as measured by a specific unit of time (for example, 60 km/h northbound). In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a fundamental idea.A physical vector quantity called velocity must have both a magnitude and a direction in order to be defined. Speed, a coherent derived unit whose quantity is measured in the SI (metric system) as meters per second (m/s), is the scalar absolute value (magnitude) of velocity.So, the cycle's velocity-time graph:
The area under the curve will therefore be the distance traveled.A trapezium is formed in the 0–14 second period.With sides that are 14 and 10 in parallel.While there is an 8-mile gap between them.Now,
Area = (1/2)(14 + 10) * 8 = 24 * 4 = 96 So, the distance traveled is 96 meters.Then,
(A) The cycle covered 96 meters in the first 14 seconds.(B) Acceleration in the first four seconds is equal to ((8-0)/(4-0)) = 8/4 = 2 m/s².Therefore, the answer to both the subparts are as follows:
(A) In the first 14 seconds, the cycle traveled 96 meters.(B) The acceleration is 2m/s² for the first 4 seconds.Know more about velocity here:
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If the intquantity and decprice variables contain the numbers 3 and 15.75, respectively, the condition if intquantity > 0 andalso intquantity < 10 orelse decprice > 20 will evaluate to ____.
The correct option is c. True.
If the intquantity and decprice variables contain the numbers 3 and 15.75, respectively, the condition if intquantity > 0 and also intquantity < 10 or else decprice > 20 will evaluate to "True."
What is C++?C++ is an object-oriented programming (OOP) language that many consider to be the best for developing large-scale applications.
C++ is a subset of the C programming language. Java is a programming language that is similar to C++ but is optimized for the dispersion of program objects over a such as the Internet.
Now, as per the question, construct a program in C++.
#include <iostream>
using namespace std;
int main()
{
int intQuantity = 3;
int decPrice = 15.75;
if (intQuantity >0 && intQuantity <10 || decPrice>20){
cout<<"True";
}
else{
cout<<"False";
}
return 0;
}
Because the condition if (intQuantity >0 && intQuantity 10 || decPrice >20) evaluates to true, the output from in this program will be "True." The reason for this is that in programming, the Logical Or (| |) evaluates to true when either or both conditions are met.
Although the condition decPrice>20 is false in the question, the very first condition intQuantity >0 && intQuantity 10 is true, so the OR evaluates to true.
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The complete question is -
If the intQuantity and decPrice variables contain the numbers 3 and 15.75, respectively, the condition If intQuantity > 0 And Also intQuantity < 10 OrElse decPrice > 20 will evaluate to ____.
a.No
b.Yes
c.True
d.False
leo drew a line that is perpendicular to the line shown on the grid and passes through point f g. which of the follwoing is the equation of leos lins
The equation of Leo's line is given by: 3 (y - G) = ( F - x)
What is the equation of a line to the curve?A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Given: An equation of a line on a grid, about which another line is perpendicularly.
To find: Equation of the perpendicular line.
Finding:
Firstly, we will find the equation of the given line.As we can see, the given line passes through (1,1) and (2,4), in the general equation of the line: [tex]y-y_0=m(x-x_0)[/tex],=> m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{4-1}{2-1}=\frac{3}{1} = 3[/tex]
The equation of the line becomes: [tex]y-y_0=3(x-x_0)[/tex]
2. Since the line passes through (1,1), the final equation of the line can be given by:
=> y - 1 = 3 ( x - 1)
=> y = 3x - 3 + 1
=> y = 3x - 2
Now, for the equation of the perpendicular line:The slope of the line will be given by:=> m' = -1/m
=> m' = -1/3
The equation of the perpendicular line will now be: [tex]y-y_0=\frac{-1}{3}(x-x_0)[/tex]=> [tex]3(y-y_0)=(x_0-x)[/tex]
2. Since the perpendicular line passes through the point (F,G), the equation of the line will be: 3 (y - G) = ( F - x).
Hence, The equation of Leo's line is given by: 3 (y - G) = ( F - x).
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In a store opening promotion, Fred advertises T-shirts: "Buy 4 get 1 free." If the cost of 1 T-shirt is $15.97, what is the discount rate, as a percent?
The discount rate, as a percent is 20%
How to determine the discount rate, as a percent? The given parameters are:
Cost of 1 T-shirt = $15.97
Also, we have
4 purchases gives 1 free item
So, the discount rate is
Discount = 1/(1 + 4) * 100%
Evaluate the sum
Discount = 1/5 * 100%
Evaluate the product
Discount = 20%
Hence, the discount rate, as a percent is 20%
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if one rectangular lot with 1350' of frontage contains 25 acres, how many acres would the lot next to it contain if it has a 900' frontage and is the same width as the first lot? select one: a. 1.67 acres b. 16.67 acres c. 26.00 acres d. 14.67 acres
The correct option is b. 16.67 acres would the lot next to it contain if it has a 900' frontage and is the same width as the first rectangular lot.
What do you mean by a rectangle's area?The quantity of space occupied by a flat surface with a specific shape is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.). The quantity of unit squares that can fit inside a rectangle called its area. Blackboards, painting canvases, laptop monitors, and other flat surfaces are a few instances of rectangular shapes.
Area of a Rectangle = (Length × Breadth) square units.
We know that the Area = Length × Width.
For first lot:
43,560 (sq. ft. in acre) × 25 acres = 1,089,000 sq. ft.
We know that 1,089,000 sq. ft. = Width × 1,350 (length). Therefore width =1,089,000 / 1,350 = 806.67.
From the problem the lots were of the same width.
In second lot: Area =806.67 (width) × 900( length)= 726,000 sq. ft. Therefore:
⇒726,000 (area) / 43,560 = 16.67 acres.
The correct answer is: b. 16.67 acres
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jason says you can solve an inequality by replacing the inequality sign with an equal sign and putting it back in after solving the equation. do you agree?
Jason is incorrect, because inequality signs change when we multiply/divide by negative numbers, and we need to follow the signs to make sure we use the correct one.
Is Jason correct whit his claim?Well, Jason says that you can solve an inequality by replacing the sign by an equal sign, solve the equation as you already have done a thousand times, and then put the inequality sign again.
Now, this is clearly incorrect, because inequalities have a really nice property. If you multiply or divide both sides of the inequality by a negative number, then the "direction" of the sign changes.
This means that if we have an inequality like:
-2x > 10
And we divide both sides by -2, we should get:
x < 10/-2
x < -5
Where the direction of the sign changed.
If you did what Jason said, the direction of that sign would not have changed, and thus, you would have got an incorrect solution for the inequality.
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Martha McKenzie sells advertising for a local TV station. She earns 15 % on the fi rst $5,000 in sales, 25 % on the next $1,000, and 30 % on all sales over $6,000. If she were to sell $15,000-worth of advertising, what would her commission be? Help!!!
$3,400
$3,500
$3,600
$3,700
Using proportions, her commission would be of $3,700.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Her commissions are divided as follows:
15% of the first $5,000.25% of the next $1,000.30% of the final $9,000(15000 - 6000).Hence the total commission is:
0.15 x 5000 + 0.25 x 1000 + 0.3 x 9000 = $3,700.
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Calculate the volume of each of the rectangular prisms below.
Answer:its 180 cm
Step-by-step explanation: