We start by expressing the circumference and the size of the slice in terms of the pizza's radius. By setting the pizza slice to be the largest (having an angle of 2π at the centre), we find the radius and hence the diameter of the pizza.
Explanation:The question falls into the area of Circle Geometry. Let's say the radius of the pizza is r inches, the length of the crust is a, and the length of the two straight edges of the pizza slice (each of which is a radius of the circle) are both r.
According to the problem, the perimeter of the pizza slice is given as 36 inches. This sums up the two radii and the length of the crust (a). Therefore, 2r + a = 36.
We know that the crust's length is a fraction of the total circumference of the circle. The whole circle's perimeter is 2πr.
Assuming the angle at the center of the pizza slice is θ (in radians), we have a = θr. θ will be a fraction of 2π depending on the size of the slice.
Substituting θr for a in the equation 2r + a = 36, we get 2r + θr = 36. To get the largest slice, θ has to be as large as possible, 2π.
Replace θ with 2π, we have 2r + 2πr = 36. Solve for r and we find that r = 36/(2+2π). That gives the radius of the pizza. Multiply r by 2 will give us the diameter of the pizza.
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What is an a priori proposition? an a posteriori proposition?
Final answer:
An a priori proposition is knowledge known through reason alone, such as mathematical truths, while an a posteriori proposition requires empirical experience, like knowledge of a physical location.
Explanation:
An a priori proposition is a type of knowledge or statement that is known to be true independently of experience. It relies on reason or logical deduction rather than empirical evidence. For example, mathematical truths, such as the statement "The square root of 9 is 3," are considered a priori because they can be known through reason alone. In contrast, an a posteriori proposition is one that requires experience or sensory input to be known. Empirical knowledge, like knowing the best route to a location, is typically a posteriori because it is based on observations from the world around us.
The foundational philosophical debate revolves around the nature of these propositions, with some philosophers questioning whether any knowledge is genuinely a priori or if all understanding comes from some form of experience. However, in many cases, a priori knowledge is associated with necessity, certainty, and independence from experience, while a posteriori knowledge is empirical and grounded in sense perception.
which of the fallowing is a factor? EXPLAIN:
Which expression is equivalent to 14a + 8?
14(a + 4)
7(7a + 1)
2(7a + 4)
14(a + 1)
The solution is Option C.
The value of the equation A = 14a + 8 can be simplified to A = 2 ( 7a + 4 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 14a + 8 be equation (1)
Now , the equation (1) can be simplified as
Taking the common term as 2 in the equation , we get
A = 2 ( 7a + 4 )
The 2 is taken as common term , and the multiples are the values 7a and 4
So ,
The value of A = 2 ( 7a + 4 )
A = 2 ( 7a ) + 2 ( 4 )
The value of A = 14a + 8
Therefore , the value of A is 2 ( 7a + 4 )
Hence ,
The value of the equation A = 14a + 8 can be simplified to A = 2 ( 7a + 4 )
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Baruka has gallon of milk left in the 1/2 fridge. How many 5/64 gallon (10-ounce) servings of milk does she have left? Show your work
Baruka has [tex]\( \frac{32}{64} \)[/tex] gallons left. [tex]\( \frac{32}{5} \) servings of \( \frac{5}{64} \)[/tex] gallons; she has 6 servings.
To find out how many [tex]\( \frac{5}{64} \)[/tex] gallon servings of milk Baruka has left, we need to first convert the amount of milk she has in gallons to the same unit as [tex]\( \frac{5}{64} \)[/tex] gallons.
Since [tex]\( 1 \)[/tex] gallon is equivalent to [tex]\( \frac{64}{64} \)[/tex] gallons, and she has [tex]\( \frac{1}{2} \)[/tex] gallon left, she has [tex]\( \frac{1}{2} \times \frac{64}{64} = \frac{32}{64} \)[/tex] gallons left.
Now, we can find out how many [tex]\( \frac{5}{64} \)[/tex] gallon servings are in [tex]\( \frac{32}{64} \)[/tex] gallons:
[tex]\[ \frac{\frac{32}{64}}{\frac{5}{64}} = \frac{32}{5} \][/tex]
Now, we divide [tex]\( 32 \) by \( 5 \)[/tex] to find the number of servings:
[tex]\[ \frac{32}{5} = 6.4 \][/tex]
So, Baruka has [tex]\( 6.4 \)[/tex] servings of [tex]\( \frac{5}{64} \)[/tex] gallon servings of milk left. However, since she can't have a fraction of a serving, she has [tex]\( 6 \)[/tex] servings left.
please help im really dumb lol
Let n be a natural number such that the remainder of the division of 4294 by n is 10, and the remainder of the division of 3521 by n is 11. what is n?
Only the Fahrenheit one plz
A box contains marbles of five different colors: red, green, blue, yellow, and purple. there is an equal number of each color. assign probabilities to each color in the sample space. (give your answers as fractions.)
To assign probabilities to each color in the sample space of marbles in a box, you need to determine the total number of marbles and the number of marbles of each color. Assuming there is an equal number of each color, the probability of drawing each color is 1/5.
Explanation:To assign probabilities to each color in the sample space, we need to determine the total number of marbles and the number of marbles of each color. Since there is an equal number of each color, let's assume there are n marbles of each color.
The total number of marbles is 5n. The probability of drawing a red marble is n/5n = 1/5. Similarly, the probability of drawing a green marble is n/5n = 1/5, the probability of drawing a blue marble is n/5n = 1/5, the probability of drawing a yellow marble is n/5n = 1/5, and the probability of drawing a purple marble is n/5n = 1/5.
What is the simplified form of the expression k^3(K^7/5)^-5
Find the nth term of the follwing sequences 7,13,19,25
What percentage is 1022.40 of 1420 and how do i solve
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing current measure 0.8 amps and 0.55 amps find the measure of the third outgoing current
The measure of the third outgoing current will be 0.5 amperes.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing currents measure 0.8 amps and 0.55 amps.
Then the measure of the third outgoing current will be
We know that the sum of the incoming current will be equal to the sum of the outgoing current at a junction.
Let the incoming current be I₁, I₂, and I₃. And the outgoing current is I₄, I₅, and I₆. Then we have
I₁ + I₂ + I₃ = I₄ + I₅ + I₆
0.7 + 0.68 + 0.47 = 0.8 + 0.55 + I₆
1.85 = 1.35 + I₆
I₆ = 0.5
Thus, the measure of the third outgoing current will be 0.5 amperes.
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John is 3 years older than jim. jim is 4 years less than twice david's age. how old are the three boys if their ages add up to 35?
Jan has a 12 ounce milkshake four ounces in the milkshake are vanilla and the rest is chocolate what are two equivalent fraction of the milkshake is vanilla
Answer:
In this item, we are given that out of 12 ounces of ingredients comprising the milkshake, there are 4 ounces vanilla. Expressing this into fraction will give us an answer of 4/12. This fraction can be one of the answers. Since we are asked for two fractions, we can simplify 4/12 such that we get an equivalent fraction that is equal to 2/6. Hence, the answers to this question are 4/12 and 2/6...
hope it helps
We can solve for x using a technique called successive approximations. step 1: if we assume that x is very small compared to 0.100 (such that 0.100 x ≈ 0.100) then our first approximation of x (let\'s call it x1) can be calculated as
Supposed that we are given the equation:
7.20 x 10^-5 = x(0.100+x)^2
So assuming that x is very small so that:
0.100 + x ~ 0.100
and calling it x1, so:
7.20 x 10^-5 = x1 (0.100)^2
Then we simply solve for x1:
x1 = 7.20 x 10^-5 / (0.100)^2
x1 = 7.20 x 10^-3
Final answer:
Successive approximations involve iterative guesses to find a solution, Newton's Method refines initial guesses using derivatives, and the Intermediate Value Theorem guarantees a solution in a given interval.
Explanation:
Successive Approximations: When solving for x using successive approximations, we make iterative guesses, refining our estimation with each step. The method involves making an initial guess, then refining it until a sufficiently accurate solution is obtained.
Newton's Method: Newton's method is a numerical technique used to find roots of a function. It involves making an initial guess and then iteratively improving upon it by using the function's derivative.
Intermediate Value Theorem: The intermediate value theorem states that a continuous function that takes on values of opposite signs at two points must have at least one root within that interval.
Which of the following numbers is not part of the solution to x ≤ -2?
-2
-2.45
-8
-1.76
Answer:
i think it is -1.76
So here's the question
"Melissa knitted a scarf with 9 1/5
yards of red yarn. She used another 3 11/25 yards of blue yarn to finish knitting. How much more red than blue yarn did Melissa use?"
I need help solving it, and it is subtraction, right?
a tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an inital speed of 120 feet per second. What is the maximum height, in feet, the ball will attain?
A major stadium has 45,000 seats. If baseball fans have bought 5/8 of the seats for the next game, how many seats are available?
if 5/8 were bought then 3/8 are still available ( 5/8 +3/8 = 1)
45000 * 3/8 = 135000/8 = 16,875 seats are still available
Find the total amount due on a simple-interest loan if the principal is $3000 with a rate of 5% for 10 years.
Final answer:
The total amount due on the simple-interest loan is $4500.
Explanation:
To find the total amount due on a simple-interest loan, we can use the formula:
Total Amount = Principal + (Principal x Rate x Time)
Given that the Principal is $3000, the Rate is 5%, and the Time is 10 years, we can substitute these values into the formula to calculate the total amount:
Total Amount = $3000 + ($3000 x 0.05 x 10)Total Amount = $3000 + $1500Total Amount = $4500Therefore, the total amount due on the loan is $4500.
A car travels down a highway at 45 m/s. An observer stands 200 m from the highway.
How fast is the distance from the observer to the car increasing when the car passes in front of the observer?
How fast is the distance increasing 40 s later?
whats the answer for 5x+14=k
Drag a statement or reason to each box to complete this proof. If 4x+5=17 , then x=3 .
The answer fam is........
Statement Reason
1) 4x + 5 = 17 Given
2) 4x + 5 - 5 = 17 - 5 Subtraction property of equality
3) 4x = 12 Simplifying
4) 4x/4 = 12/4 Division property of equality
5) x = 3 Simplifying
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Answer:
Here it is!
Step-by-step explanation:
you work for a dress maker and your boss sends you to the fabric store to buy blue fabric she tells you to buy the best deal what's is the best deal
20 yards for $30.00
40 yards for $45.00
50 yards for $70.00
65 yards for $85.00
Use the normal approximation to find the indicated probability. the sample size is n, the population proportion of successes is p, and x is the number of successes in the sample. n = 86, p = 0.68: p(54 x 61) 9)
mrs. ellis wants to tile a rectangular room that is 16 feet long and 12 feet wide with square tiles. each square floor is 2 feet. the tiles cost $0.84 per tile. what is the cost to tile the room not including labor?
Mrs. Ellis would need 48 tiles to cover the area of her room. The cost of a single tile is $0.84, so the total cost to tile the room not including labor would be $40.32.
Explanation:To determine the cost to tile the room, we first need to figure out how many tiles Mrs.Ellis needs. We know that each tile covers an area of 2ft * 2ft, which is 4 square feet. Now, we must find out the area of the room by multiplying the length by the width (16ft * 12ft), resulting in 192 square feet. To find out how many tiles are needed, we can divide the total area of the room by the area of one tile (192ft² / 4ft² = 48). Therefore, Mrs. Ellis needs 48 tiles to cover the entire room. Since each tile costs $0.84, the total cost would be 48 * $0.84 = $40.32. Thus, the cost to tile the room excluding labor charges is $40.32.
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60 bricklayers began a 16-day project to build a castle. After five days, five of the bricklayers quit the job. If they work the same amount each day, how many extra day(s) (beyond the original estimate of 16) will the remaining bricklayers need?
Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = x3 + x − 9, [0, 2]
The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm. What is the approximate difference between m∠C and m∠A?
Answer
Difference between m∠C and m∠A= 44.76
Step-by-step explanation:
The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm.
Hypotenuse AC = 13 cm
So angle B is right angle = 90 degrees
AC is the hypotenuse
BC is the adjacent side for C
cos (c)= adjacent side / hypotenuse
C= cos^-1(BC/AC)
[tex]C= cos^{-1}(\frac{5}{13})= 67.38[/tex]
angle B is a right angle= 90 degree
Angle C= 67.38 degrees
Sum of angles in a triangle is 180°
A + B +C = 180
A + 90 + 67.38 = 180
A= 180 - 90 - 67.38=22.62
Difference between m∠C and m∠A= 67.38 - 22.62=44.76
Francis gets 6 paychecks in 12 weeks how many paychecks does she get in 52 weeks