Example of The Transitivity Property that follows
Premise: If x = 3 and y = x + 2, then y = 5.
Premise: If y = 5 and z = y - 1, then z = 4.
Conclusion: If x = 3, then z = 4.
The transitivity property is a logical property that states that if a=b and b=c, then a=c. This property is commonly used in mathematics to make deductions and draw conclusions.
Example:
Premise: If x = 3 and y = x + 2, then y = 5.
Premise: If y = 5 and z = y - 1, then z = 4.
Conclusion: If x = 3, then z = 4.
Explanation: By the transitivity property, we can substitute the value of y in the second premise with the value of x + 2 from the first premise to get z = (x + 2) - 1, which simplifies to z = x + 1. Then, we can substitute x = 3 to get z = 4.
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I will mark you brainiest!
What describes this polygon?
A) Quadrilateral
B) Pentagon
C) Parallelogram
D) Hexagon
An integer leaves a remainder 1 when divided by 4. What is the remainder when the square of this integer is divided by 8?
PLSS HELP ASAP
Answer:
Let's suppose that the integer is x.
We know that x leaves a remainder of 1 when divided by 4, so we can express x as:
x = 4n + 1
where n is some integer.
Now we need to find the remainder when x^2 is divided by 8:
x^2 = (4n + 1)^2
x^2 = 16n^2 + 8n + 1
Notice that the first two terms (16n^2 + 8n) are divisible by 8, so we can ignore them.
The remainder when x^2 is divided by 8 is the same as the remainder of 1 when divided by 8:
x^2 ≡ 1 (mod 8)
Therefore, the remainder when the square of the integer is divided by 8 is 1.
solve for the value of a
( pls help i dont get this at all)
Answer:
Given that
(5a+6 )°+90°+(7a)°=180°
(angles on a straight line sum up to 180°)
5a°+6°+90°+7a°=180°
5a°+7a°=(180-96)°
12a°=84°
Deviding both sides by 12° gives
a=84/12
a=7°
therefore the value of
a=7°
Need help with math
Answer:
to find are u need to do it this way: pie r sqare
Step-by-step explanation:
22/7x7x7
22/7 x49
cut 7 and 49
1 and 7
22/1x7
=22x7
=154
You invest $2700 in the Professor Salaam’s Magical Marker business. Over 5 years, your
investment grows in value to $20,000. What are your total and annual returns for the 4-year
period?
Using cοmpοund interest, the Tοtal return equals $ 17,300 and Annual returns fοr the 4-year periοd will be equal tο 13.32%.
What is meant by cοmpοund interest?The interest yοu receive that is cοmpοunded οn:the primary, οr the sum yοu depοsited οriginallyinterest that yοu have previοusly accrued
Fοr instance, if yοu have a savings accοunt, yοu will receive interest οn bοth yοur initial funds and any priοr interest. On yοur interest, yοu receive interest.
Simple interest is distinct frοm this. At the end οf the periοd, simple interest is sοlely paid οn the principal. Simple interest is typically paid οn term depοsits.
Given the principal = $2700
Amοunt = $20,000
Total return = $20,000 - $2700
= $ 17,300
Annual returns for the 4-year periοd will be equal to,
using compοund interest formula,
[tex]A = P (1 + \frac{r}{n})^{t}[/tex],
Where A = amοunt,
P = principal,
r = rate οf interest,
n = number οf times interest applied per time period,
t = time periοd,
For, 5 years, the value will be -
[tex]20,000 = 2700 (1 + r/100)^5[/tex]
[tex]7.41 = (1 + r/100)^5[/tex]
1.50 = 1 + r/100
1.50 - 1 = r / 100
0.50 = r / 100
r = 5%
For 4 years,
[tex]Annual return = ((202700 (5/4)^4\\A = 13.32 \%[/tex]
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(b) Find the costs of supplying bins to 10%, 50%, and 85% of the
cost to supply 10%
C = $
X
cost to supply 50%
C = $25,000
cost to supply 85%
C = $ 141,667
Answer:
To find the cost of supplying bins to 10%, 50%, and 85% of the cost to supply 10%, we can use proportional reasoning.
Let X be the cost to supply 10%. Then:
The cost to supply 50% is 5 times the cost to supply 10%, so it is 5X.
The cost to supply 85% is 8.5 times the cost to supply 10%, so it is 8.5X.
The cost to supply 10% is X.
To find the cost of supplying bins to 10%, 50%, and 85% of the cost to supply 10%, we can substitute X = $1 and multiply by the appropriate percentages:
The cost to supply bins to 10% of the cost to supply 10% is 0.1 * X = 0.1 * $1 = $0.10.
The cost to supply bins to 50% of the cost to supply 10% is 0.5 * X = 0.5 * $1 = $0.50.
The cost to supply bins to 85% of the cost to supply 10% is 0.85 * X = 0.85 * $1 = $0.85.
Therefore, the costs of supplying bins to 10%, 50%, and 85% of the cost to supply 10% are $0.10, $0.50, and $0.85, respectively.
Answer:
Let the cost to supply 10% of the bins be X dollars.
To find the cost of supplying bins to 50% of the cost to supply 10%, we can set up the following proportion:
10% of the cost = X dollars
50% of the cost = Y dollars
We know that the two costs are proportional, so we can set up the following equation:
10% / 50% = X / Y
Simplifying this equation, we get:
0.1 / 0.5 = X / Y
0.2 = X / Y
Multiplying both sides by Y, we get:
Y * 0.2 = X
Y = X / 0.2
Y = 5X
Therefore, the cost of supplying bins to 50% of the cost to supply 10% is 5 times the cost of supplying bins to 10%.
Substituting X = C/10 (where C is the cost to supply 10% of the bins), we get:
Y = 5X = 5(C/10) = C/2
So the cost of supplying bins to 50% of the cost to supply 10% is C/2 dollars.
To find the cost of supplying bins to 85% of the cost to supply 10%, we can set up a similar proportion:
10% of the cost = X dollars
85% of the cost = Z dollars
We know that the two costs are proportional, so we can set up the following equation:
10% / 85% = X / Z
Simplifying this equation, we get:
0.1 / 0.85 = X / Z
0.1176 = X / Z
Multiplying both sides by Z, we get:
Z * 0.1176 = X
Z = X / 0.1176
Z = 8.5X
Therefore, the cost of supplying bins to 85% of the cost to supply 10% is 8.5 times the cost of supplying bins to 10%.
Substituting X = C/10 (where C is the cost to supply 10% of the bins), we get:
Z = 8.5X = 8.5(C/10) = 0.85C
So the cost of supplying bins to 85% of the cost to supply 10% is 85% of the cost to supply 10%, or 0.85C dollars.
Therefore, the costs of supplying bins to 10%, 50%, and 85% of the cost to supply 10% are:
- 10% of the cost: X dollars = C/10 dollars
- 50% of the cost: Y dollars = C/2 dollars
- 85% of the cost: Z dollars = 0.85C dollars
They cost Y (in dollars) of a collect call X minutes in length can be described by the equation Y =0.73x use the equation to complete the table of values X and Y
Answer:
X (minutes) Y (cost in dollars)
10 7.30
20 14.60
30 21.90
40 29.20
50 36.50
60 43.80
Please help me
Simplify this expression:
(In picture)
The simplified expression for given expression is x⁷/y¹⁰.
What is simplication of a expression?Simplification means reducing the expression in a simpler form using various operations while Approximation is simplifying the mathematical expression to its nearest value but not exactly correct.
Equation:To simplify the expression:
x³y⁻²x/x⁻³y⁸
Applying the properties, we get:
x³y⁻²x/x⁻³y⁸ = x⁽³⁻⁽⁻¹⁾⁾y⁽⁻²⁻⁸⁾/x⁻³x¹y⁰
Simplifying the exponents and the term with y, we get:
x⁴/y¹⁰ * x³ = x⁽⁴⁺³⁾/y¹⁰ = x⁷/y¹⁰
Therefore, the simplified expression is x⁷/y¹⁰.
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Find the radius r………………………..
Answer:
r = 3
Step-by-step explanation:
Pythagoras' theorem states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides.
AO^2 = AB^2 + BO^2
(2 + r)^2 = 4^2 + r^2
r^2 + 4r + 4 = 16 + r^2
4r = 12
r = 12/4
r = 3
Please answer the question in the picture, I will mark brainliest. Show all work pls!!!
Arc length= 2pir * zero with a circle through it/360
Just for clarification 2pir is 2 then pi then r together
Rounding to the nearest tenth, we get the area of the sector is: 6.3 square inches.
What is area?Area is the measurement of the amount of space inside a two-dimensional shape, such as a square, circle, or triangle. It is usually expressed in square units, such as square inches or square meters. To find the area of a shape, you need to use a specific formula based on its dimensions and geometry. For example, the area of a rectangle can be found by multiplying its length by its width, while the area of a circle can be found by using the formula pi times the radius squared.
Here,
To find the area of the sector, we need to use the formula:
Area of sector = (central angle/360) x πr²
where r is the radius of the slice.
Plugging in the values we get:
Area of sector = (34/360) x π(8)²
Area of sector = (0.0944) x π(64)
Area of sector = 6.2822 square inches
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math!!! i need help pleaseeeeeeeeeee
Answer:
B
1 x 10^3
Step-by-step explanation:
Please help will mark Brainly
The correct equation in vertex form for the function is:
g(x) = 2(x-5)² + 9
What is the parabola?
The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface.
Option A is the correct equation in vertex form for the function:
g(x) = 2(x-5)² + 9
The vertex form of a parabola is y=a(x-h)²+k, where (h,k) is the vertex of the parabola. We are given that the vertex is located at (5,9), so h=5 and k=9. Substituting these values into the vertex form equation, we get:
g(x) = a(x-5)² + 9
To find the value of a, we can use one of the points that the parabola passes through. Let's use point (7,1):
1 = a(7-5)² + 9
1 = 4a + 9
-8 = 4a
a = -2
Substituting this value of a into the equation, we get:
g(x) = -2(x-5)² + 9
Expanding the square and simplifying, we get:
g(x) = -2x² + 20x - 41
This is not in vertex form, but if we factor out the -2 from the first two terms, we get:
g(x) = -2(x² - 10x + 20.5)
Completing the square inside the parentheses, we get:
g(x) = -2(x-5)² + 50.5
This is also in vertex form, but the constant term is not 9 as given in the problem.
Therefore, the correct equation in vertex form for the function is:
g(x) = 2(x-5)² + 9
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Share #720 among A, B and C in the ratio 2:3
Answer:
A will receive 288, B will receive 432, and C will receive 144.
Step-by-step explanation:
The total ratio of the parts is 2+3=5. This means that the whole amount represents 5 parts.
To find the size of one part, we can divide the total amount by the total number of parts:
One part = 720/5 = 144
Now that we know the size of one part, we can use the ratio to find the amounts that A, B, and C will receive:
A will receive 2 parts: 2 × 144 = 288
B will receive 3 parts: 3 × 144 = 432
C will receive 1 part: 1 × 144 = 144
Therefore, A will receive 288, B will receive 432, and C will receive 144.
The point on the graph represents Ann's location. She is using a metal detector on the beach to see what she can find. Each unit on the graph represents 2 feet. A pile of bottle caps is located at (4, -10). Find the length of the most direct path between Ann and the pile of bottle caps. Round to the nearest whole number.
Question 8 options:
12 feet
120 feet
300 feet
31 feet
The length of the most direct path between Ann and the pile of bottle caps is given as follows:
31 feet.
What is the distance between two points?Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Ann's location is given by the following ordered pair:
(-4,3).
The location of the pile of bottle caps is given by the following coordinate pair:
(4, -10).
Hence the distance is given as follows:
D = sqrt((4 - (-4))^2 + (-10 -3)^2)
D = 15.5 units.
Each unit represents 2 feet, hence:
15.5 x 2 = 31 feet.
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Justin flips a coin and rolls a number cube with sides labeled 1, 2, 3, 4, 5, and 6. He repeats this experiment 40 times. How many times would you expect him to flip tails and roll an even number?
You expect him to flip tails and roll an even number 10 times
How many times would you expect him to flip tails and roll an even number?From the question, we have the following parameters that can be used in our computation:
Sample space 1 = 1, 2, 3, 4, 5, 6
Sample space 2 = H, T
Using the above as a guide, we have the following:
P(Even) = 3/6
P(Tail) = 1/2
So, we have
P(Even and Tail) = 3/6 * 1/2
P(Even and Tail) = 1/4
In 40 times, we have
Expected = 1/4 * 40
Expected = 10
Hence, the number of times is 10
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Only 4% of babies are born on their due data.
Answer:
A.) 5.68
B.) 8.4%
C.) 99.6%
Step-by-step explanation:
Part a: Assume that the height of your cylinder is 8
inches. Consider A
as a function of r
, so we can write that as A(r)=2πr2+16πr
. What is the domain of A(r)
? In other words, for which values of r
is A(r)
defined?
Part b: Continue to assume that the height of your cylinder is 8
inches. Write the radius r
as a function of A
. This is the inverse function to A(r)
, i.e., to turn A
as a function of r
into r
as a function of A
.
r(A)=
Change entry mode
Hints:
To calculate an inverse function, you need to solve for r
. Here, you would start with A=2πr2+16πr
. This equation is the same as 2πr2+16πr−A=0
which is a quadratic equation in the variable r
, and you can solve that using the quadratic formula. You will want to keep A
as a variable when you plug the values into the quadratic formula.
If you want to type in 3π+1x+1
in Mobius, in text mode you can type in (3*pi+1)/(x+1). There is more information in the Introduction to Mobius unit.
Part c: If the surface area is 300
square inches, then what is the radius r
? In other words, evaluate r(300)
. Round your answer to 2 decimal places.
Hint: To compute a numeric square root such as 17.3−−−−√
, you could
Use a spreadsheet such as Microsoft Excel or OpenOffice Calc and type in =sqrt(17.3)
Use a browser to connect to the Internet and type in sqrt(17.3) into a search field
Use a calculator
The radius is
Number
inches if the surface area is 300
square inches.
Hence, in answering the stated question, we may say that We know, equation however, that r must be positive, therefore we take the positive square root: [tex]r(A) = -4 + square root(64 + 2A) /[/tex]
What is equation?A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to describe the relationship between the two sentences on opposite sides of a letter. In usually, the logo and the programme are the same. For instance, 2x - 4 equals 2.
Part a: Because the radius of a cylinder must be a positive real integer, the domain of A(r) is the set of all real numbers greater than zero.
As a result, the domain of A(r) is:
{r ∈ ℝ | r > 0}
Part b: To determine the inverse function r(A), solve the equation A = 2r2 + 16r for r expressed in terms of A.
To begin, we may simplify the equation by removing 2r:
A = 2πr(r + 8)
Hence, using the quadratic formula, we can find r:
[tex]r = (-16 \sqrt((16)2 - 4(2 )(-A)) / 2(2 )\\r = (-16 \sqrt(2562) + 8A) / 4 r = -4 \sqrt(64 + 2A) /[/tex]
We know, however, that r must be positive, therefore we take the positive square root:
[tex]r(A) = -4 + square root(64 + 2A) /[/tex]
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The radius is apprοximately 11.51 inches when the surface area is 300 square inches.
What is equatiοn?A math equatiοn is a methοd that links twο claims and represents equivalence using the equals sign (=). An equatiοn is a mathematical statement that establishes the equivalence οf twο mathematical expressiοns in algebra.
Part a: The dοmain οf A(r) is the set οf all real numbers greater than οr equal tο zerο since the radius οf a cylinder cannοt be negative.
Dοmain οf A(r): r ≥ 0
Part b: Tο find the inverse functiοn r(A), we start with the equatiοn fοr A(r), set it equal tο A, and sοlve fοr r using the quadratic fοrmula:
[tex]2 \pi r^2 + 16 \pi r - A = 0[/tex]
[tex]r = [-16 \pi \± \sqrt{((16 \pi)^2 - 4(2 \pi)(-A))}] / 2(2 \pi)[/tex]
[tex]r = [-16\pi \± \sqrt{(256\pi^2 + 8 \pi A)}] / 4\pi[/tex]
Simplifying this expressiοn, we get:
[tex]r = (-4 \± \sqrt{(64 + 2A)}) / 2[/tex]
[tex]r(A) = -2 \± \sqrt{(32 + 0.5A)[/tex]
Since the radius οf a cylinder cannοt be negative, we take the pοsitive square rοοt:
[tex]r(A) = -2 + \sqrt{(32 + 0.5A)[/tex]
Part c: Tο find the radius when the surface area is 300 square inches, we plug in A = 300 intο the expressiοn fοr r(A) and simplify:
[tex]r(300) = -2 + \sqrt{(32 + 0.5(300))[/tex]
r(300) = -2 + sqrt(182)
r(300) ≈ 11.51
Therefοre, the radius is apprοximately 11.51 inches when the surface area is 300 square inches.
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Please help with this pls
Answer:
Step-by-step explanation:
its c
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 0\le x \le 150≤x≤15.
x f(x)
0 9
3 39
6 69
9 99
12 129
15 159
So the average rate of change of the function over the interval 0 ≤ x ≤ 15 is 4.4.
What is function?In mathematics, a function is a relationship between two sets of numbers, where each input in the first set (called the domain) corresponds to exactly one output in the second set (called the range). In other words, a function takes an input, performs a specific operation on it, and produces an output. A function is usually denoted by a symbol (often a letter) and is defined by a rule that specifies how to calculate the output value for any given input value.
Here,
To find the average rate of change of the function over the interval 0 ≤ x ≤ 15, we need to calculate the change in the function value divided by the change in x over the interval.
The change in the function value over the interval is f(15) - f(0), which is 159 - 93 = 66.
The change in x over the interval is 15 - 0 = 15.
Therefore, the average rate of change of the function over the interval 0 ≤ x ≤ 15 is:
average rate of change = change in f / change in x
= 66 / 15
= 4.4
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not any where else...... solve the equation for x: (x-4)-(x+7)=8
Answer:
(x-4)-(x+7)=8 is x = -19
Step-by-step explanation:
To solve the equation for x, we need to simplify the left-hand side by combining the like terms:
(x-4)-(x+7)=8
x - 4 - x - 7 = 8 (distribute the negative sign)
-x - 11 = 8 (combine like terms)
To isolate x, we need to get rid of the constant term on the left-hand side. We can do this by adding 11 to both sides:
-x - 11 + 11 = 8 + 11
-x = 19
Finally, we can solve for x by multiplying both sides by -1:
x = -19
Therefore, the solution for the equation (x-4)-(x+7)=8 is x = -19.
Which of the relations given by the following sets of ordered pairs is not a function? -4 -4
Option B. (-4, -2), (-1, -1), (1, 3), (1, 4), (7, 10) is not a function.
How to identify if the set of ordered pairs is not function?To determine whether a relation is a function, we need to check whether each input value (the first coordinate of each ordered pair) is associated with exactly one output value (the second coordinate of each ordered pair).
The input value 1 is associated with two different output values (3 and 4), so this relation is not a function.
Therefore, the relation given by set B. (-4, -2), (-1, -1), (1, 3), (1, 4), (7, 10) is not a function.
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The question given is incomplete, the complete question is:
Which of the relations given by the following sets of ordered pairs is not a function?
A. (-4, -4), (-3, -3), (0, 0), (3, -3), (4, -4)
B. (-4, -2), (-1, -1), (1, 3), (1, 4), (7, 10)
C. (5, 1), (4, 1), (3, 1), (2, 1), (1, 1)
D. (-5, -7), (-4, -6), (-3, -5), (-2, -4), (-1, -3)
An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the linear regression line for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
Number of TV commercials, x 3
5
11
16
19
Car sales, y (in hundreds) 2
3
8
9
6
According to the given problem, the linear regression line for the given data is y = -0.65 + 0.26x
What is linear regression?
Linear regression is a statistical method used to find the relationship between a dependent variable (y) and one or more independent variables (x). It assumes that there is a linear relationship between the variables, meaning that changes in the independent variable(s) are associated with proportional changes in the dependent variable.
The linear regression model can be represented as a straight-line equation:
y = b0 + b1*x + e
The equation of a linear regression line can be written as:
y = b0 + b1*x
where y is the dependent variable (car sales in this case), x is the independent variable (number of TV commercials), b0 is the intercept, and b1 is the slope of the line.
To find the values of b0 and b1, we need to calculate the following:
n = number of data points = 4
Σx = sum of x values = 54
Σy = sum of y values = 28
Σxy = sum of (x*y) values = 164
Σx^2 = sum of (x^2) values = 689
Using these values, we can calculate b1:
b1 = (nΣxy - ΣxΣy) / (n*Σx^2 - Σx^2)
b1 = (4164 - 5428) / (4*689 - 54^2)
b1 = 0.26 (rounded to two decimal places)
Next, we can use b1 to calculate b0:
b0 = (Σy - b1*Σx) / n
b0 = (28 - 0.26*54) / 4
b0 = -0.65 (rounded to two decimal places)
Therefore, the linear regression line for the given data is:
y = -0.65 + 0.26x
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What is the smallest number with six different digits not including zero that begins with 2 and ends with 3?
What is the greatest number with six digits not including zero that begins with 3 and ends with 2?
The smallest number with six different digits not including zero that begins with 2 and ends with 3 is: 213457.
The greatest number with six digits not including zero that begins with 3 and ends with 2 is: 398762.
How to obtain the numbers?The smallest number with six different digits not including zero that begins with 2 and ends with 3 can be constructed by choosing the remaining four digits from the set {1, 4, 5, 6, 7, 8, 9}, arranging them in ascending order, hence it is of:
213457.
For the greatest number with six digits not including zero that begins with 3 and ends with 2, we arrange them is descending order, hence it is of:
398762.
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Margo borrows $1500, agreeing to pay it back with 6% annual interest after 6 months. How much interest will she pay?
Answer:
Step-by-step explanation:
1,500 times 0.06 = 90
90 divided by 2 = 45
multiply in clumns 5824×45
Answer:
Step-by-step explanation:
5824×45
5824
x 45
29120
23296 x
262080
-7 2/3 + (-5 1/2) + 8 3/4 =
-4 2/3
6 7/12
-21 11/22
-4 5/12
Answer: -4 5/12
Step-by-step explanation: because -7 2/3+(-5 1/2)= -13 1/6
finally take -13 1/6 + 8 3/4= -4 5/12
PLS HELP I NEED THIS DONE BY 1:00
Here is the correct equation:
[tex]c = 15 + 65m[/tex]
If A is True, and B is True, what is C
Answer: True
Step-by-step explanation: That was a complete guess. Did you forget to include an image? Am I missing something?
please help me i really need this
Answer:
The area is given by the expreesion:
A = 5f + 10
Step-by-step explanation:
Notice the height of the shaded area is 5. But the base is the difference between f+9 and 7
So the length of the shaded area will be f+9-7=f+2
then the area of a rectangle is given by A=height*length
This is
A = 5 (f+2) = 5f+10
Question: Write an expression for the area shaded section of this rectangle. Expand your brackets
The area of shaded section is 5f+10
To calculate the area of the rectangle, it is known that just multiply the measurement of the height by the length.
So, to calculate the value of the area of this rectangle considering that the shaded area is part of it, we would do [tex]\sf f+9\times5[/tex].
The area of the shaded section will be given by the difference between the area of the shaded area and the unshaded area.
That is, [tex]\sf(f+9-7)\times5[/tex]
Let's calculate[tex]\begin{array}{l}\sf(f+9-7)\times5\\\sf(f+2)\times5\\\sf 5f+2\times5\\\therefore \bf 5f+10\end{array}[/tex]
5f+10 is the shaded section area expression
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write a mathematical sentence which relates to a real life scenario in business
Answer:
The profit (P) of a company is equal to the revenue (R) minus the cost (C): P = R - C.
Step-by-step explanation: