Before a theorem is proven, it is known as a proposition. This term indicates that the statement is proposed to be true and is pending proof.
Explanation:A theorem called before it is proven is known as a proposition. A proposition is a statement that is proposed to be true and is awaiting proof or disproof. In contrast, a postulate is a statement that is assumed to be true without proof for the purposes of reasoning in mathematics or science, whereas a contradiction refers to a statement that is always false. A tautology is a statement that is true by necessity or by virtue of its logical form.
Final answer:
A theorem before it is proven is known as a proposition. Propositions are statements considered in mathematics and philosophy for investigation and proof. Other terms like postulate, contradiction, and tautology have different distinct meanings in logic.
Explanation:
Before a theorem is proven, it is known as a proposition. A proposition is a statement that proposes an idea, which can be either true or false, but has not yet been proven to be true. In mathematics and philosophy, this term is used to describe concepts that are considered and investigated for proof. Once a proposition is proven conclusively, it becomes a theorem. Other options like postulate, contradiction, and tautology have different meanings within mathematical logic and reasoning.
The initial number of views for a reader board was 25. The number of views is growing exponentially at a rate of 18% per week. What is the number of views expected to be four weeks from now? Round to the nearest whole number Enter your answer in the box.
This is an exponential growth problem. Let's write the equation for exponential growth.
[tex]P=P_{0} (1+r)^{n}[/tex]
Where,
P is the final amount[tex]P_{0}[/tex] is the initial amountr is the rate at which increasingn is the timeFrom the problem, we know initial number of views, [tex]P_{0}[/tex], is 25. Rate of increase, r, is 0.18. Time, n, is 4 weeks. Plugging in these values in the equation and solving for P will give us the number of views expected in four weeks time.
[tex]P=(25)(1+0.18)^{4}\\=(25)(1.18)^{4}\\=48.47[/tex]
Rounding to nearest whole number, it is 48.
ANSWER: 48
how do i determine if the equation is always, never, or sometimes true
Algebraic terms are separated by ______.
Choose all that apply.
1)=
2)+
3)x
4)÷
5)-
In algebra, terms are separated by addition (+), subtraction (-), multiplication (x), and division (÷) symbols. The equals (=) sign is used to show equality, not to separate terms.
Explanation:In the realm of mathematics, particularly in algebra, algebraic terms are separated by addition (+), subtraction (-), multiplication (x), and division (÷) symbols. These operations are the main components that allow us to manipulate and solve algebraic expressions and equations. For example, in the expression 3x - 2y + 5z, the terms (3x, 2y, 5z) are separated by subtraction (-) and addition (+) symbols. Please note that the equals (=) sign does not separate terms; rather, it is used to show the equality between two mathematical expressions.
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Final answer:
Algebraic terms are separated by plus (+) and minus (-) signs, which denote addition or subtraction between terms in an expression.
Explanation:
Algebraic terms are separated by plus (+) and minus (-) signs.
These signs denote addition or subtraction between terms in an algebraic expression.
While the multiplication sign (x) and division sign (÷) indicate operations between terms, they do not separate independent terms within an expression.
For instance, in the expression 2x + 3y - 5z, the plus and minus signs separate the terms 2x, 3y, and 5z.
Find Dxy using the rules for finding derivatives.
=(5x^2−8)(9x^2−3x+5)
Please complete z2+9z-90=(z-6)(z+?) ...?
Answer:
Answer would be 15.
Step-by-step explanation:
We have to complete the expression given as
[tex]z^{2}+9z-90=(z-6)(z+?))[/tex]
We will try to factorize the expression given in the left side.
[tex]z^{2}+9z-90=z^{2}+15z-6z-90[/tex]
= z(z+15)-6(z-15)
=[tex](z-6)(z-15)[/tex]
Now we will compare this factorized form with the right side of the expression.
(z-6) (z-15) (= (z-6) (z+?)
We find question mark is 15.
Therefore, the answer is 15.
Celeste is making fruit baskets for her service club to take to a local hospital. the directions say to fill the boxes using 5 apples for every 6 oranges. celeste is filling her baskets with 2 apples every 3 oranges.
Celeste is making fruit baskets for her service club, and she is not following the specific ratio but using a similar ratio of apples to oranges in her baskets.
Explanation:Celeste is making fruit baskets for her service club, and the directions say to fill the boxes using 5 apples for every 6 oranges. However, Celeste is filling her baskets with 2 apples for every 3 oranges. To determine if Celeste is following the directions, we can compare the ratio of apples to oranges in her baskets with the ratio specified in the directions.
In the directions, the ratio of apples to oranges is 5 apples: 6 oranges, which can be simplified to 5/6. In Celeste's baskets, the ratio of apples to oranges is 2 apples : 3 oranges, or 2/3.
To compare these ratios, we can find the least common multiple (LCM) of the denominators (6 and 3), which is 6. Then, we can convert both ratios to have the same denominator using equivalent fractions:
5/6 * 1/1 = 5/6 and 2/3 * 2/2 = 4/6.
Since 4/6 is less than 5/6, Celeste is not following the directions exactly. However, she is still using a similar ratio of apples to oranges in her baskets.
Determine the sum -46.38 (-24.6)
What is the standard form for y + 5 = 0?
A _______ is a group of people who agree to save their money together and to make loans to each other at a relatively low rate of interest. A. credit union B. mutual fund C. investment firm D. commercial bank
a, 2a, 4a, 8a
If a < 0, which of the four numbers above is the greatest?
A. a
B. 2a
C. 4a
D. 8a
E. It cannot be determined from the information given.
On sunday,sheldon bought 4 and 1 half kg of plant food. he used 1 and 2 thirds kg on his strawberry plants and used 1 fourth kg for his tomato plants. how many kilograms of plant food did sheldon have left write one or more to show how u reached your answer.
Match the given equation with the verbal description of the surface:
A. Cone
B. Elliptic or Circular Paraboloid
C. Plane
D. Half plane
E. Circular Cylinder
F. Sphere
1. r = 4
2. θ = [(π)/3]
3. ρ = 2cos(φ)
4. r = 2cos(θ)
5. ρ = 4
6. r2 + z2 = 16
7. ρcos(φ) = 4
8. φ = [(π)/3]
9. z = r2
Each equation matches with a surface as follows: A. Cone - ρ = 2cos(φ); B. Elliptic or Circular Paraboloid - z = r²; C. Plane - ρcos(φ) = 4; D. Half plane - θ = [(π)/3]; E. Circular Cylinder - r = 2cos(θ); and F. Sphere - r² + z² = 16 or r = 4.
Explanation:In order to match each equation with the verbal description of the surface, it's important to recognize their respective characteristics.
A. Cone matches with 3. ρ = 2cos(φ). This is because this polar equation describes a cone in spherical coordinates, where ρ represents the radius, φ is the angular altitude, and cos(φ) describes the height-to-radius ratio of the cone.B. Elliptic or Circular Paraboloid is linked to 9. z = r². This equation represents a paraboloid in cylindrical coordinates. Here, z elevation varies quadratically with the distance from the z-axis, r.The C. Plane can be matched with 7. ρcos(φ) = 4. In spherical coordinates, if ρcos(φ) equals a constant, a plane is obtained where it cuts the z-axis at that constant.D. Half plane corresponds to 2. θ = [(π)/3]. This polar equation with θ as a constant represents a half plane.The E. Circular Cylinder links to 4. r = 2cos(θ). This equation represents a circular cylinder in cylindrical coordinates.F. Sphere is matched with 6. r² + z² = 16 and 1. r = 4 which represent a sphere in cylindrical and polar coordinates, respectively.Learn more about Surface Equations here:https://brainly.com/question/28482933
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Factor of 3x^2 - 6x 3
Rock musician Donny West is paid 15% on his CD sales and tour video sales. Last year, he sold one million CDs and $550000 videos. The CDs were sold to the music store for $5 each. The videos were sold to the music store for $6 each.
a.) What was the total amount of CD sales?
b.) What was the total amount of video sales?
c.) What was the combined total of CD and video sales?
d.) How much did he receive in royalties last year?
How would you explain the relationship between an exponential function and a logarithmic function to an English major you are tutoring in math? Can you give me a real life example of it?
Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay.
The logarithmic function [tex]\bold{y=log_ax}[/tex] is defined to be equivalent to the exponential equation x = ay.
Real life example:
Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity)
Three of the most common applications of exponential and logarithmic functions have to do with interest earned on an investment, population growth, and carbon dating.
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A(n) ______ is a letter or symbol that represents some unknown value.
A. term
B. equation
C. variable
D. expression
Answer:
It is a variable
Step-by-step explanation:
A variable is a characteristic, number, or quantity that increases or decreases over time or takes different values in different situations. Hope this helps.
The population of a city increases by 10,000 per year. The starting population is 800,000.
Let P be the ending population.
Which shows an equation for the total population after x years?
if there is 1/3 of a pizza left, and Becky only wants to eat 1/2 of it, how much pizza does she want
The amount of pizza she wants is:
[tex]\dfrac{1}{6}[/tex] of the pizza.
Step-by-step explanation:If there is 1/3 of a pizza left, and Becky only wants to eat 1/2 of it.
Then the amount of pizza she wants is:
1/2 of the amount of the pizza left.
i.e. she wants:
[tex]\dfrac{1}{2}\times \dfrac{1}{3}=\dfrac{1}{6}[/tex]
This means that Becky wants 1/6 parts of the whole pizza.
circle of the radius of 3 an arc of a circle has a central angle of 340 degrees what is the length of the arc
Final answer:
The length of the arc of a circle with a radius of 3 and a central angle of 340 degrees is 17π. This is calculated by converting the angle to radians and finding the proportion of this angle to the full circle's circumference (2πr).
Explanation:
To find the length of the arc of a circle with a radius of 3 and a central angle of 340 degrees, we first need to understand that arc length (Δs) is proportional to the central angle when measured in radians. The circumference (Δ4) of a circle is given by the formula Δ = 2πr. Since there are 360 degrees in a complete circle, which corresponds to 2π radians, we can set up a proportion to solve for the arc length of the 340-degree angle.
The proportion will look like this:
Convert the central angle from degrees to radians by multiplying it by π/180.
340 degrees * π/180 = 340π/180 radians.
Use the ratio of the angle in radians to the entire circle in radians (2π) to find the arc length: Δs = (Angle in radians/2π) * Circumference.
Δs = (340π/180) / (2π) * 2π * 3.
Simplify to find the arc length Δs.
The final step yields the arc length for the given central angle and radius:
Δs = (340/360) * 2π * 3 = (17/18) * 2π * 3.
Therefore, the length of the arc is Δs = 17π.
Find the value of tan 39°. Round to the nearest ten-thousandth.
The value of the given trigonometric ratio tan 39° is approximately 0.8098.
Use the concept of trigonometric ratio defined as:
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are several distinctive trigonometric identities that relate to a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
The given trigonometric ratio is: tan 39°
Since,
[tex]\text{tan }\theta = \dfrac{\text{sin }\theta}{\text{cos }\theta}[/tex]
The value of the sine of 39° is approximately 0.6293.
The value of the cosine of 39° is approximately 0.7771.
Therefore,
tan 39° = 0.6293 / 0.7771
tan 39°≈ 0.8098 (After rounding to four decimal places).
Hence,
The required value tan 39° is approximately 0.8098.
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Find the correct prime factorization of 28/98, and then reduce the fraction to lowest terms. ...?
To reduce the fraction 28/98 to lowest terms, we prime factorize each number, cancel out the common factors, and simplify. The fraction 28/98 simplifies to 1/7.
The correct prime factorization of 28 is 2×2×7 (or 2²×7), and for 98 it's 2×7×7 (or 2×7²). To reduce the fraction 28/98 to lowest terms, we can remove the common factors in the numerator and the denominator.
Since both numerator and denominator have a 2 and a 7, we can replace them with '1'. After simplifying, the remaining factors in the numerator are 1 and the remaining factors in the denominator are 7. Therefore, 28/98 reduced to lowest terms is 1/7.
"Sarah is renting a car for her weekend trip to the mountains. The total cost of the rental, y, as it relates to the number of miles driven, x, is shown in the graph below.
Fill in the blanks so that the functions below, written to represent this situation, are correct. If necessary, the answer in terms of a decimal, rounded to the nearest hundredth.
f(x)= ______x+________"
Answer:
[tex]f(x)=\dfrac{1}{4}x+25[/tex]
Step-by-step explanation:
Clearly from the graph we could see that it passes through two points (0,25) and (20,30) and also as the graph is linear so with the help of these two points we can find the relation between f(x) and x.
We know that the equation of a line passing through two points (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here we have:
y=f(x) , (a,b)=(0,25) and (c,d)=(20,30).
Hence the equation of this graph is given as:
[tex]f(x)-25=\dfrac{30-25}{20-0}\times (x-0)\\\\f(x)-25=\dfrac{5}{20}\times x\\\\f(x)-25=\dfrac{1}{4}\times x\\\\f(x)=\dfrac{1}{4}x+25[/tex]
Hence,
[tex]f(x)=\dfrac{1}{4}x+25[/tex]
What is 9/2 as a decimal?
Clark wants to figure out how many pens to order for the office there 48 workers and he needs to order one pen for each worker he knows that for every six people who prefer red door 6 prefer blue how many blue pens should he order
Given that the preference for red and blue pens is equal and that there are 48 workers, Clark should order 24 blue pens for the office.
Explanation:The student is interested in figuring out how many blue pens to order for 48 workers in an office knowing that the preferences for red and blue pens are equal. This means that for every 6 people who prefer red, the same number of people will prefer blue.
To determine the number of blue pens needed, we can use a simple proportion. Since 6 people prefer red and the same number prefer blue, we have a 1:1 ratio of red to blue preferences.
Therefore, the total number of blue pens needed would be half of the total number of workers:
Total workers = 48Number of blue pens = Total workers / 2 = 48 / 2Number of blue pens = 24Find the equation of the tangent line to the curve y = 2sinx at the point (pi/6,1). The equation of this tangent line can be written in the form y = mx+b. Compute m and b
The equation of the tangent line to the curve y = 2sinx at the point (pi/6,1) is y = sqrt(3)x + (1 - sqrt(3)(pi/6)).
Explanation:To find the equation of the tangent line to the curve y = 2sinx at the point (pi/6, 1), we need to find the slope of the curve at that point. The slope of a curve at a point is equal to the derivative of the function at that point.
Taking the derivative of y = 2sinx, we have dy/dx = 2cosx. Evaluating this derivative at x = pi/6, we get dy/dx = 2cos(pi/6) = sqrt(3). Therefore, the slope of the tangent line is sqrt(3).
Now we have the slope and a point on the line, (pi/6, 1). We can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we have y - 1 = sqrt(3)(x - pi/6).
Simplifying this equation, we get y = sqrt(3)x - sqrt(3)(pi/6) + 1. Finally, we can rewrite the equation in the form y = mx + b by simplifying the y-intercept, giving us y = sqrt(3)x + (1 - sqrt(3)(pi/6)).
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The sum of two consecutive integers is at least 46. What is the least possible pair of integers?
Answer
23 and 24.
Explanation
let the first integer be x.
The next integer would be x + 1
Now form the equation
x + (x+1) = 46
x + x + 1 = 46
2x + 1 = 46
2x = 46 - 1
x = 45
x = 22.5 This is not an integer.
Since the question is asking for the least possible integer, unless we use 23 ≅22.5
The first integer been 23, the other one would be (23 + 1) = 24.
The least possible pair would be 23 and 24.
Use parallelogram JKLM to find the length of JK.
Answer:
JK = 6
Step-by-step explanation:
Given: We are given a parallelogram JKLM and ML = 6 units. and m∠K = 109°
We need to find length of JK.
Here we use the properties of parallelogram to find the length of Jk.
In a parallelogram, the opposite sides are parallel and equal in measures.
Therefore, ML = JK
Given: ML = 6
So, 6 = JK
Therefore, the length of JK = 6
factor the common factor out of 8x^3+12x
Kamal bought 7 packs of paper clips for a project. then he bought 8 more packs. there are 25 paper clips in each pack. how many paper clips did he buy?
Answer:
He bought 375 paper clips.
Step-by-step explanation:
Given,
The initial number of packs of paper clips = 7,
Also, the additional number of packs of paper clips = 8,
So, the total number of packs of paper clips = 7 + 8 = 15,
Now, the number of paper clips in each pack = 25,
Hence, the total number of paper clips = number of paper clips in each pack × total packs
= 25 × 15
= 375
three apples and two bananas cost 2.00. four apples and four bananas cost 3.00. what is the cost of one apple?
HELP PLS
a)1
b)0.75
c)0.50
d)0.25
The cost of one apple is 0.5, option C is correct.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let A represents cost of one apple and B represents cost of one banana
Three apples and two bananas cost 2.00
3A+2B=2...(1)
Four apples and four bananas cost 3.00.
4A+4B=3..(2)
Let us multiply equation 1 with 2
6A+4B=4...(3)
Subtract equation 3 from 2
4A+4B-6A-4B=3-4
-2A=-1
A=1/2
A=0.5
Hence, the cost of one apple is 0.5, option C is correct.
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