What is a natural number and what is a whole number? Explain..
Answers
Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity and are also used for counting purpose. It does not include zero. In fact, 1,2,3,4,5,6,7,8,9…., are also called counting numbers excluding zero, fractions, decimals and negative numbers.
The whole numbers are the numbers 0, 1, 2, 3, 4, and so on (the natural numbers and zero). Negative numbers are not considered "whole numbers." All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.
Natural numbers are also all numbers 1, 2, 3,4.. and so on. They are the numbers you usually count and they will continue on into infinity. Whole numbers are all natural numbers including 0. 0, 1, 2, 3, 4… Integers include all whole numbers and their negative counterpart, -4, -3, -2, -1, 0,1, 2, 3, 4,…
So in all these words, this means that natural numbers are all the numbers not including 0 and negative and whole numbers are all the numbers including 0 and negative.
Related Questions
How is 7.54÷4= 1.88
I got 1.88 with the remainder of 2
Answers
Answer:
I got 1.885 for the answer.
Maybe they wanted it rounded to just 2 decimal places.
Step-by-step explanation:
Answer:
7 .54/4=1.88
Step-by-step explanation:
In division we will see the relationship between the dividend, divisor, quotient and remainder. The number which we divide is called the dividend. The number by which we divide is called the divisor. The result obtained is called the quotient. The number left over is called the remainder.
please hurry.-. and if u can give all answers to the lesson
Answers
100:10 = 10 is the mean age I guess?
For a standard normal distribution,Find P(-1.21 < Z< 2.26)
Answers
Answer:
The range of z-score is given below as
\(P(-1.21Using a graphing calculator, we will have the image be\(\begin{gathered} P(z<-1.21)=0.11314 \\ P(z<2.26)=0.9881 \\ P(-1.21Hence,The final answer is
\(P(-1.21\lt z\lt2.26)=0.8750\)
1:prove that the tangent at the point (1,-2) to the circle x²+y²=5 also touches the circle x²+y²-8x+6y+20=0 .Also find the point of contact.
2:find the length of tangent to the circle
3x²+3y²-7x-6y=12 drawn from (6,-7)
Answers
Circle 1 has center at (0, 0)
The tangent passes through the center and point (1, -2).
Equation of tangent at (1, -2):
x*1 + y*(-2) = 5x - 2y = 5x = 2y + 5If the same line is tangent to circle 2 then they have one common point.
Solve the system:
x = 2y + 5x² + y² - 8x + 6y + 20 = 0Substitute x:
(2y + 5)² + y² - 8(2y + 5) + 6y + 20 = 04y² + 20y + 25 - 16y - 40 + 6y + 20 = 05y² + 10y + 5 = 0y² + 2y + 1 = 0(y + 1)² = 0y + 1 = 0y = -1 ⇒ x = 2(-1) + 5 = -2 + 5 = 3We see only one point of contact, (3, -1), this proves the line is tangent to circle 2 as well.
#2Given circle:
3x² + 3y² - 7x - 6y = 12 and external point (6, -7).Rewrite the equation of the circle as:
3x² + 3y² - 7x - 6y = 12x² + y² - 7/3x - 2y = 4x² - 2*7/6x + 49/36 + y² - 2y + 1 = 4 + 49/36 + 1(x - 7/6)² + (y - 1)² = 229/36The center is (7/6, 1) the radius is √229/36
The length of the tangent t is the leg of the right triangle with another leg r being the radius and the hypotenuse d being the distance between the center and the external point:
t² = d² - r²t² = (6 - 7/6)² + (-7 - 1)² - 229/36t² = 36 - 14 + 49/36 + 64 - 229/36t² = 86 - 180/36t² = 81t = 9Materials and labor for each pet groomed
costs $15. The business also has fixed costs
of $1,000 each month. Define a cost
function for this business.
Answers
Answer:
f(x) = 15x + 1,000
Step-by-step explanation:
y = mx + b
the 15 is the slope or rate and 1000 is the fixed value ( y intercept)
In 2008, more than one million American students gave nearly 20 million service hours to their communities. They made a difference in people's lives and learned some important life lessons in the process. Organizations, including schools, are actively promoting service for all citizens as a way to be involved, help others, and improve themselves.
Service is helping other people and being active in your community. For example, one group of teens planted a community garden with their friends. They grow a variety of vegetables. The garden requires regular care. The teens donate the produce to a local soup kitchen. Workers there use the produce to help feed people in the community. By tending the garden and donating their produce, the teens are actively helping make life a bit better for others in their community.
Service is valuable in ways that cannot be measured in dollars. People volunteer or serve others without expecting money or gifts in return. Service is not about earning money. It is not just collecting money to give to a group. It is about action and contributing to the common good. The people who serve as well as those who receive help benefit in many ways that are more important than money or gifts. For example, a soup kitchen provides essential food to people who may otherwise go hungry. The soup kitchen is extremely valuable for those struggling to get enough to eat. Those serving learn about compassion and how helping others can improve life for all.
Millions of Americans are making society better for themselves and for others. They are participating citizens in their community, raising up those who are less fortunate. In return, they become better people who can understand the perspectives and needs of others, which are invaluable and important qualities of good citizens.
Which sentence best represents the main idea of paragraph three, the second body paragraph?
Group of answer choices
(Answers)
Service is valuable in ways that cannot be measured in dollars.
It is about action and contributing to the common good.
Workers there use the produce to help feed people in the community.
The soup kitchen is extremely valuable for those struggling to get enough to eat.
Answers
Answer:
A
Step-by-step explanation:
As the first sentence states, Service is valuable in ways that cannot be measured in dollars, and goes on to explain how that is.
help!!! Don’t I don’t understand this
Answers
Answer:
B, C, D
Step-by-step explanation:
plit a convex octagon given by the list of vertices v1, v2, v3, v4, v5, v6, v7, v8 into a set of triangles and give the vertices that make up each triangle.
Answers
A convex octagon can be split into a set of triangles by connecting its vertices in a way that each vertex is connected to its neighboring vertices.
There are several ways to split a convex octagon into triangles, but a common approach is to use the ear clipping algorithm, which involves finding triangles that have their vertices on the octagon's perimeter and have no other vertices inside the triangle.
For example, if the vertices of the octagon are given by v1, v2, v3, v4, v5, v6, v7, and v8, then we can split the octagon into the following triangles:
(v1, v2, v3), (v3, v4, v5), (v5, v6, v7), (v7, v8, v1), (v2, v3, v5), (v4, v5, v7),
(v6, v7, v1), and (v8, v1, v3).
Each of these triangles has three vertices that are connected to form a closed polygon, and together they form the entire convex octagon. By splitting the octagon into smaller triangles, it is easier to perform computations, such as finding the area or the normal vectors of the octagon's surface.
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Find the surface area of a water tower that is 40 feet tall and 20 feet across the base
Answers
Answer:
800 ft (Please brainlist me)
Step-by-step explanation:
A = B*W
40 * 20 = 800
Pls help me I’m struggling
Answers
Answer: Peter < 65
Step-by-step explanation: Peter has less than charlie so charlie is more than or/and equal to being solid line underneath or solid line on graph represented by ≥ 65 stays equal to 65 or more which is a correct statement for charlie as charlie cards are increasing at 65 and has 65 and Peter is shown as ≤ 65 but is slightly wrong as we were told in question that 'he has just started collecting' this means it has to be or certainly less than charlie has - Just in diagram is interpreted as a dotted line on graph coordinates represented by < 65 instead IS LESS THAN 65 would be correct way to interprete inequality of Peters relationship value to that of charlie given amount
Find the volume 8 feet 10 feet 8 ft
Answers
Answer:
640 ft^3solution,
\(volume = length \times width \times height \\ \: \: \: \: \: \: \: \: \: = 8 \times 10 \times 8 \\ \: \: \: \: = 640 \: {ft}^{3} \)
Hope this helps...
Good luck on your assignment..
Find the unit rate 28 miles in 7 minutes is how many miles
per minute
Answers
Answer:
4 miles per minute
Step-by-step explanation:
Answer:
4 miles per minuteStep-by-step explanation:
28 miles = 4 miles per minute
7 min
yoo if you passed algebra one help me with these questions please should be pretty easy u dont have to explain or anything.
1) Find the domain of the function f ( x ) = 3 ( 3 ) x - 1
options: a. ( 0, ∞ ) b. ( − ∞, ∞ ) c. ( − ∞, 0 ) d. ( 0, 10 )
2) What is the range of the function f ( x ) = 2 x.
options: a.( 0, ∞ )b.( − ∞, 0 )c.( − ∞, ∞ )d.( − ∞, 1 ]
3) What is the range of the function f ( x ) = 2 x.
options: a. ( 0, ∞ ) b. ( − ∞, 0 ) c. ( − ∞, ∞ ) d. ( − ∞, 1 ]
4) What is the domain of the function f ( x ) = 2 x.
options: a. ( 0, ∞ ) b. ( − ∞, 0 ] c. ( − ∞, 0 ) d. ( − ∞, ∞ )
5) What is the range of the function f ( x ) = 2 x − 2.
options: a. [ 1, 5 ] b. ( − ∞, 0 ) c. ( − ∞, ∞ ) d. ( 0, ∞ )
6) What is the domain of the function f ( x ) = -2 x
options: a. ( − ∞, 0 ) b. [ − 1, 5 ] c. ( − ∞, ∞ ) d. ( 0, ∞ )
7) Find the range of the function f ( x ) = -.5 ( 3 ) x-1
options: a. ( 1, ∞ ) b. ( − ∞, 0) c. ( − ∞, ∞ ) d. ( − ∞, -1 )
thanks :)
Answers
See below for the domain and the range of the functions.
How to determine the domain and the range?As a general rule, all linear functions have a domain and a range of all set of real numbers i.e. (−∞, ∞)
The functions (2), (3), (4), (5) and (6) are linear functions.
So, their domain and range are (−∞,∞)
For function (1), we have:
f(x) = 3(3)^x - 1
The above is an exponential function.
The domain of an exponential function is all set of real numbers i.e. (−∞, ∞)
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Solve the equation log(base 2)(x) + log(base 4)(x+1) = 3.
Answers
We can use the logarithmic identity log_a(b) + log_a(c) = log_a(bc) to simplify the left side of the equation:
log_2(x) + log_4(x+1) = log_2(x) + log_2((x+1)^(1/2))
Using the rule log_a(b^c) = c*log_a(b), we can simplify further:
log_2(x) + log_2((x+1)^(1/2)) = log_2(x(x+1)^(1/2))
Now we can rewrite the equation as:
log_2(x(x+1)^(1/2)) = 3
Using the rule log_a(b^c) = c*log_a(b), we can rewrite this as:
x(x+1)^(1/2) = 2^3
Squaring both sides, we get:
x^2 + x - 8 = 0
This is a quadratic equation that can be solved using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 1, and c = -8. Plugging in these values, we get:
x = (-1 ± sqrt(1^2 - 4(1)(-8))) / 2(1)
x = (-1 ± sqrt(33)) / 2
x ≈ -2.54 or x ≈ 3.54
However, we must check our solutions to make sure they are valid. Plugging in x = -2.54 to the original equation results in an invalid logarithm, so this solution is extraneous. Plugging in x = 3.54 yields:
log_2(3.54) + log_4(4.54) = 3
0.847 + 0.847 = 3
So x = 3.54 is the valid solution to the equation.
Find the product of the roots of the equation
xl-5x - 36 = 0
Answers
Answer:
Step-by-step explanation:
Hello, I assume that you mean
\(x^2-5x-36\)
The product is -36.
\(x_1 \text{ and } x_2 \text{ are the two roots, we can write}\\\\(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2\)
So in this example, it means that the sum is 5 and the product is -36.
Thank you
How do I know if a function is quadratic, exponential, or logarithmic?
Answers
Answer:
Exponential function
Explanation:
Linear - the output of linear function are always directly proportional to the input. it forms a straight line in the graph.
\(f(x)\propto x\)The output increases at a constant rate.
Quadratic - the quadratic function forms a 'U' or 'n' shaped graph.
the output rises almost exponentially then reduces at some point.
That means the value of f(x) increases then later decrease on the table.
Exponential - The value of exponential function increases shapely or decreases sharply.
f(x) increases sharpely as x increases, OR it decreases sharply as x increases.
Logarithmic - it is just like an inverse of the exponential function, the value of f(x) increases very slowly as x increase, Or it decreases slowly as the value of x increases.
From the given data;
The value of f(x) on the table increases sharply with an increase in x,
So, it is an Exponential function
An airplane has an airspeed of 528 mi/hr bearing 25° west of north. Which of the following vectors best describes the path of the airplane? O v= 528 cos(155°)i + 528 sin(1550); O v = 25 cos(528°)i + 25 sin(528°); O None of these O v = 528 cos(25°)i + 528 sin(259); O v = 528 cos(115°)i + 528 sin(115)
Answers
An airplane has an airspeed of 528 mi/hr bearing 25⁰ west of north. The path can be described as a vector v = (528 cos 115⁰) i + (528 sin 115⁰) j
Suppose we have a vector with magnitude v and angle α with the positive x-axis, then the vector can be expressed as its component as:
vx = v cos α
vy = v sin α
or
v = vx i + vy j
v = (v cos α) i + (v sin α) j
In the given problem, the magnitude is 528, while the angle is:
α = 25⁰ west of north = 25⁰ + 90⁰ = 115⁰
Hence,
vx = 528 cos 115⁰
vy = 528 sin 115⁰
v = (528 cos 115⁰) i + (528 sin 115⁰) j
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A to D is an example of _____________?
A. reflection across the line y = 1
B. reflection across the line y = x
C. y-axis symmetry
D. x-axis symmetry
Answers
Answer:
D
Step-by-step explanation:
A and D are both equidistant from the x- axis, that is
A is 3 units above the x- axis and D is 3 units below the x- axis
then the x- axis is the line of symmetry
Find the perimeter of the triangle.
Answers
9514 1404 393
Answer:
84 in
Step-by-step explanation:
The Pythagorean theorem is used to find the length 'b'.
b^2 +12^2 = 37^2
b = √(37^2 -12^2) = √1225 = 35
Then the perimeter is the sum of side lengths:
P = a + b + c = 12 + 35 + 37
P = 84 . . . inches
Answer:
in triangle
b=√(37²-12²)=35
perimeter of the triangle.=sum of all side
=37+12+35=84in
Here are the heights (in inches) of 12 students in a seminar. 71, 67, 62, 60, 70, 64, 68, 72, 58, 63, 60, 66 What is the percentage of these students who are shorter than 65 inches? 1% X 5
Answers
25% of the students in the seminar are shorter than 65 inches.
To find the percentage of students who are shorter than 65 inches, we first need to find the number of students whose height is less than 65 inches:
There are three students who are shorter than 65 inches: 62, 60, and 58.
Therefore, the percentage of students who are shorter than 65 inches is:
(3 students / 12 students) × 100% = 25%
Note that the value given for 1% × 5 does not appear to be relevant to this question, and is not necessary for the calculation of the percentage of students who are shorter than 65 inches.
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What is the range of the function graphed below?
A. Y>-1
B X< -1
C X>-1
D Y< -1
LOOK AT THE GRAPH.
Answers
Answer:
Option A
Step-by-step explanation:
Range of a function is defined by the set of y-values (output values).
From the given graph,
Y-values of the exponential function given in the graph vary from y = -1 to y = ∞ (excluding both the points)
Therefore, Range of the given exponential function will be y > -1
Option A will be the correct option.
Diane, Sam, and Boris served a total of 54 orders Monday at the school cafeteria. Diane served 6 fewer orders than Sam. Boris served 2 times as
many orders as Sam. How many orders did they each serve?
Number of orders Diane served:
Number of orders Sam served:
Number of orders Boris served:
Answers
Answer:
Let's denote:
- The number of orders Diane served as `D`
- The number of orders Sam served as `S`
- The number of orders Boris served as `B`
From the problem, we know:
1. `D + S + B = 54` (the total number of orders they served)
2. `D = S - 6` (Diane served 6 fewer orders than Sam)
3. `B = 2S` (Boris served 2 times as many orders as Sam)
We can substitute equations 2 and 3 into equation 1 to solve for the variables:
Substitute `D` and `B` in equation 1:
`(S - 6) + S + 2S = 54`
Combine like terms:
`4S - 6 = 54`
Add 6 to both sides:
`4S = 60`
Divide by 4:
`S = 15`
Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:
`D = S - 6 = 15 - 6 = 9`
`B = 2S = 2 * 15 = 30`
So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.
using excel lookup functions, add new fields to the invoice data by bringing in information from the other data sheets
Answers
To pull values from another worksheet, we need to follow these steps:
Select cell C3 and click on it.
Insert the formula: =VLOOKUP(B3,'Sheet 2'!$ B$3:$C$7,2,0)
Press enter.
Drag the formula down to the other cells in the column by clicking and dragging the little “+” icon at the bottom-right of the cell.
How do I add a LOOKUP field in Excel?
Open Design View on the table. Click a cell in the Field Name column in the first available empty row, and then type a field name for the lookup field. Select Lookup Wizard from the drop-down list by clicking the arrow after clicking in the Data Type column for that row.
To compute values in several columns, the VLOOKUP function may be used in conjunction with other functions like the Sum, Max, or Average. Since this is an array formula, all we need to do to make it function is hit CTRL+SHIFT+ENTER at the conclusion of the formula.
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5. The system 2x - 4y = 6 and 7- y = -3 is independent Replacing 2 - y = -3 with which of these equations would result in an inconsistent system?
Answers
A system is inconsistent when its two equations are contradictory. In this case we have:
\(\mleft\{\begin{aligned}2x-4y=6 \\ x-y=-3\end{aligned}\mright.\)If we replace the second equation by :
\(x-2y=-3\)We get an inconsistent system. Because the first equation and the second one would be contradicting itself. So the correct option is: B
"Our new
training room can seat 150
employees. If 6 tables consisting of 6
chairs are now taken, what
percentage of our new facility's
seating is full?"
Employee: "At this point, we have
used up
of our new seating
capacity."
Answers
The percentage of our new facility's seating is full will be 76%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
The percentage is given as,
Percentage (P) = [Initial value - Final value] / Initial value x 100
Our new training room can seat 150 employees.
If 6 tables consisting of 6 chairs are now taken.
Then the number of occupied seats by tables will be
⇒ 6 x 6
⇒ 36
Then the percentage of our new facility's seating is full will be
P = [(150 - 36) / 150] x 100
P = (114/150) x 100
P = 0.76 x 100
P = 76%
The percentage of our new facility's seating is full will be 76%.
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3.2.PS-9
Question Help
Car Survey In a survey of 2,300 people who owned a certain type of car, 1,265 said they would buy
that type of car again. What percent of the people surveyed were satisfied with the car?
% of the people surveyed were satisfied with the car
Answers
Answer:
what percent of 2300 is 1265 is the question , sooo divide 1265 by 2300. why? b/c 2300 is the total.. so that goes in the denominator and 1256 is our give number so that goes in the numerator of the fraction of those numbers to give us their ratio :) or percentage.. if you understand that.. you're on a good road.
Step-by-step explanation:
1265 / 2300 = .55 or 55% :) a bit more than 1/2 of the people .. which makes total sense b/c 1/2 of 2300 is 1150 right? so 50% of 2300 is 1150
55% :) is the answer
In the diagram a || b. Use the diagram to answer the question. Name the alternate interior angle to <2
Answers
The angle 7 is the alternative interior angle to angle 2.
Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.
They are the angles that are on opposite sides of the transversal and inside the two parallel lines.
Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.
We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.
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PLEASE HELP I WILL GIVE BRAINLIEST
Answers
Answer:
a) the cost for each person is not always the same
b) the train appears to go the same distance every minute
Predicted distance traveled in 10 minutes:
30 km
Question 10 of 10
Given the polynomial function below, find F(-5).
F(x) = x2 - 2x-7
O A. -22
B. 42
O C. 8
D. 28
Answers
Answer:
D. 28
Step-by-step explanation:
We are given the following polynomial function:
\(F(x) = x^2 - 2x - 7\)
Find F(-5).
This is the value of F for which \(x = -5\). So
\(F(-5) = (-5)^2 - 2(-5) - 7 = 25 + 10 - 7 = 28\)
28, which means that the correct answer is given by option D.
The diameter of a circle is 10 ft. Find its area to the nearest tenth.
Answers
Answer:
15.70
Step-by-step explanation:
Answer:
78.5
Step-by-step explanation:
Formula: a = πr², r = d/2
Given: π = 3.14, d = 10
Sub: a = (3.14)r²
Find r.
r = 10/2
r = 5
Sub: a = (3.14)5²
Simplify: a = (3.14)25
Solve: a = 78.5
The answer is 78.5.
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