Answers
hope this helped
Related Questions
Please help with 1 & 2
Answers
I urge you to perform the division using the synthetic division method:
________________
-4 / 1 3 -6 -6 8
-4 4 8 -8
-----------------------
1 -1 -2 2 0
Note that there is no remainder. When this is the case, the divisor (here, that's -4) is a root of the given polynomial, and the value of that polynomial, g(-4), is 0.
If the remainder were not 0, then the remainder represents the value of the polynomial for that particular divisor. For example, if x = -3, the remainder is -28. We'd write that as g(-3) = -28.
But here, g(-4) = 0.
WORTH 20 POINTS
Which functions are equivalent to f(x)= 4√162? Check all that apply
A)f(x)= 162 x/4
B)f(x)=(3 4√2)x
C)f(x)=9 4√2 x
D)f(x)=162 4/x
E)f(x)=[3 (2 1/4)]x
Answers
The options that are equivalent to the given function are;
Option A
Option B
Option E
The correct options are;
A) f(x) = [tex]162^{x/4}[/tex]
B) f(x) = (3∜2[tex])^{x}[/tex]
C) f(x) = [tex]9\sqrt[4]{2^{x} }[/tex]
D) f(x) = [tex]162^{4/x}[/tex]
E) f(x) = [tex](3(2^{1/4}))^{x}[/tex]
We are given the function; f(x) = [tex](\sqrt[4]{162})^{x}[/tex]
Now, when we have something like; [tex]\sqrt[b]{2}^{a}[/tex]
This expression can also be expressed as; [tex]2^{a/b}[/tex]
Therefore our function can also be expressed as; f(x) = [tex]162^{x/4}[/tex]
Option A; This is correct because it is equal to our function gotten
Option B; f(x) = (3∜2[tex])^{x}[/tex]
From earlier, we will have; (3 × [tex]2^{1/4}[/tex][tex])^{x}[/tex]
Now, 3 can also be expressed as [tex]81^{1/4}[/tex]
Thus, we now have;
([tex]81^{1/4}[/tex] × [tex]2^{1/4}[/tex][tex])^{x}[/tex]
Factorizing out the 1/4 exponent gives;
(81 × 2[tex])^{x/4}[/tex]
⇒ = [tex]162^{x/4}[/tex]
This is same with our function and it is correct
Option C; f(x) = (9∜2[tex])^{x}[/tex]
This is similar to our equation in option B which was correct but the difference here is 9 instead of 3 and clearly this option is not correct.
Option D; f(x) = [tex]162^{4/x}[/tex]
This is not the same with our function and so it is wrong
Option E; f(x) = [tex](3(2^{1/4}))^{x}[/tex]
As seen in option B;
3 can also be expressed as [tex]81^{1/4}[/tex]
Thus, we now have;
;([tex]81^{1/4}[/tex] × [tex]2^{1/4}[/tex][tex])^{x}[/tex]
Factorizing out the 1/4 exponent gives;
(81 × 2[tex])^{x/4}[/tex]
⇒ = [tex]162^{x/4}[/tex]
This is same with our function and it is correct
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Match the pairs of equations that represent concentric circles. Tiles
Answers
(x - a)^2 + (y - b)^2 = r^2 where the center of circle is at (a, b)
Concentric circles wil all have the same values for a and b.
Define a method pyramidvolume with double parameters baselength, basewidth, and pyramidheight, that returns as a double the volume of a pyramid with a rectangular base. relevant geometry equations: volume = base area x height x 1/3 base area = base length x base width. (watch out for integer division).
Answers
A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. if the fencing costs $16 per linear foot to install and the farmer is not willing to spend more than $8000, find the dimensions for the plot that would enclose the most area.
Answers
Answer:
100 feet by 250 feet or 25,000 sq. feet
Explanation:
Okie-dokie - here we go:
So, think about it, and maybe sketch this out as you are going. You have a barn, so make a little square on a paper with a big x on it. The top side is the north facing wall that you don't need any fence along. The side that will be on the left is the side that will be half the cost since your neighbor is splitting it with you. So lets think about the other two sides first:
Keep in mind that the barn wall will not grow with the size of the area you are making, so the "vertical" sides on the left and right will get longer but the "horizontal" fence at the top of the area will always be as wide as the barn. This isn't very helpful in finding the area or even the perimeter, but is helpful to keep in mind visually.
You are the farmer. You have $8,000 , and you are a stickler, so no more than that. You can go under by a bit, but no more than that limit. So see how many linear feet of fence you can buy at $16 per foot.
8000 ÷ 16 = 500. You can get 500 feet out of this amount of money. But you can get more on the fence you are sharing with your neighbor, since it is half the price. Don't think about that for now.
Let's set a width for the barn. I'm going to say the barn is 100 feet wide, so the top part of the fence will be 100 feet long. That is 400 feet left to build. If you were paying full price for both sides, that would be 200 feet on each side. However, you have a discount on the left fence, so you can stretch each side out another 1/2 the distance because he is splitting the cost of that fence with you. In other words:
two 200 foot sides = $6400 at full price
one 200 foot side = $3200
Find how much the neighbor is paying for:
3200 ÷ 2 = 1600.
So you only paying for 1 and a half sides, or:
1600 + 3200 = $4800 for 300 feet.
You now have an extra 1600 to spend, which is another 100 feet. Split this between your two sides, so now each side is 250 feet long.
But your neighbor is paying for half of that 50 feet you just added, so:
50 • 16 = $800
So he pays for $400, giving you another $400 to buy fence with.
If you understand what is happening, I'm just going to keep going mathematically without explanations:
$400 ÷ $16 = 25 feet
25 feet ÷ 2 = 12.5 feet (250 + 12.5 = 262.5 feet)
12.5 • $16 = $200 ÷ 2 = $100
$100 ÷ $16 = 6.25 feet
6.25 ÷ 2 = 3.125 (262.5 + 3.125 = 265.625 feet)
3.125 • $16 = $50 ÷ 2 = $25
$25 ÷ $16 = 1.5625 feet
1.5625 ÷ 2 = .78125 (265.625 + .78125 = 266.40625 feet)
And so on, this could keep going until you run out of money, but you'd really be milking it. Plus, let's say that you can only buy full linear feet, and not fractions, then you would stop at 250 feet per side. Which is:
100 feet + 250 feet + (250 feet – 125 feet) = 475 feet
475 feet • $16 = $7600 Under the limit! But you do have $400, which you could keep adding to your sides, or maybe your width is longer. Either way, find the area of 100 feet by 250 feet:
A = l • w
A = 250 • 100 = 25,000 sq. feet
A 90% confidence interval for a population mean is (65, 77). the population distribution is approximately normal and the population standard deviation is unknown. this confidence interval is based on a simple random sample of 25 observations. calculate the sample mean, the margin of error, and the sample standard deviation.
Answers
The sample mean is at the midpoint of the lower and the upper values of the confidence interval.
Thus, the sample mean is given by:
(77 + 65) / 2 = 71
Therefore, the sample mean is 71.
Part 2:
The margin of error is the distance between the upper and the lower confidence interval values from the sample mean.
Thus, margin of error is given by 77 - 71 = 71 - 65 = 6.
Therefore, margin of error is 6.
Part 3:
The margin of error is given by
[tex]ME= t_{\alpha/2}\left(\frac{s}{\sqrt{n}}\right) [/tex]
where [tex]t_{\alpha/2}[/tex] is the value of the t-distribution given the degree of freedom; s is the sample standard deviation and n is the sample size.
Since the sample size is 25, the degree of freedom is 25 - 1 = 24.
[tex] \frac{\alpha}{2} = \frac{(1-0.9)}{2} = \frac{0.1}{2} =0.05[/tex]
From the t-distrbution table, we have:
[tex]t_{\alpha/2}=1.710882[/tex]
Thus, margin of error is given by:
[tex]6=1.710882\left( \frac{s}{\sqrt{25}} \right) \\ \\ \Rightarrow\left( \frac{s}{\sqrt{25}} \right)= \frac{6}{1.710882} \\ \\ \Rightarrow\frac{s}{5}=3.506963 \\ \\ \Rightarrow s=5(3.506963)=\bold{17.53}[/tex]
The sample mean for the given 90% confidence interval (65, 77) is 71. The margin of error is 6. The sample standard deviation cannot be specifically calculated without the t-value, but presuming a common t-value for such datasets (1.96), it approximates to 3.072.
Explanation:The subject at hand pertains to confidence intervals and basic statistics calculations. Given a 90% confidence interval of (65, 77), we can find the sample mean by adding the two limits and dividing by 2. So (65 + 77) / 2 equals 71.
The margin of error for the confidence interval is calculated by subtracting the sample mean from the upper limit. That gives us 77 - 71 equals 6.
Unfortunately, without knowing the value of the t-statistic, we can't calculate the sample standard deviation, as it's calculated via the formula: standard deviation = margin of error / (t-value/sqrt(sample size)). But, usually, for a sample size of 25 observations and a 90% confidence level, the t-value is about 1.96. Using that assumed t-value, the standard deviation calculation gives us 6/(1.96/sqrt(25)) equals approximately 3.072.
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The quotient of-54 and 9, subtracted from 8 times a number, is-18
Answers
_____________________________________
Explanation:
_____________________________________
Let "x" be the "unknown number" for which we are to solve.
8x − (-54/9) = -18 ; Solve for "x" ;
→ 8x − (-6) = - 18 ;
→ 8x + 6 = - 18 ;
Subtract "6" from each side of the equation:
→ 8x + 6 − 6 = - 18 − 6 ;
to get: 8x = -24 ;
Divide EACH SIDE of the equation by "8" ; to isolate "x" on one side of the equation ; & to solve for "x" ;
8x / 8 = -24 / 8 ;
to get: x = -3 .
________________________________
The number is: " -3 " .
________________________________
Write a unit test for addinventory(). call redsweater.addinventory() with parameter sweatershipment. print the shown error if the subsequent quantity is incorrect. sample output for failed unit test given initial quantity is 10 and sweatershipment is 50: beginning tests. unit test failed: addinventory() tests complete. note: unit test failed is preceded by 3 spaces.
Answers
A unit test for the function addInventory() can be written in JavaScript using Jest. The test checks that the quantity of red sweaters increases correctly after calling addInventory(). If the test fails, an error message will be shown.
Explanation:Based on the information given, you can create a unit test in many programming languages. Here we are going to illustrate with JavaScript and use the Jest testing framework.
Firstly, let's name the unit test file as redSweater.test.js. In this file, we call the addInventory() of the redSweater object with sweaterShipment as parameter. Note that addInventory() is a method that increases the quantity of red sweaters in inventory by a certain amount provided by sweaterShipment.
Here is a sample unit test for your needs:
const redSweater = require('./redSweater'); // path to your redSweater.js file
test('addInventory() unit test', () => {
let initialQty = 10;
redSweater.qty = initialQty;
let shipmentQty = 50;
redSweater.addInventory(shipmentQty);
expect(redSweater.qty).toBe(initialQty + shipmentQty);
});
This script tests that the quantity of red sweaters increases correctly after calling the addInventory() method. If the quantity is not correct after the method call, the test will fail and show an error message.
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Given the expression −10p2q + 7p3q − 5q, do the following as instructed below: A: Write the polynomial in descending order. B: Classify the polynomial by the number of terms. C: State the degree of the polynomial.
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-10p²q + 7p³q - 5q
(A) Writing this polynomial in descending order, we properly looked the exponent of the first variable and arrange it from highest to least.
7p³q - 10p²q - 5q
(B) There are three terms in the polynomial given above. Hence, the given is TRINOMIAL.
(C) The degree of the polynomial is 4 since it is the highest exponent of the term in the given.
Pin Numbers A student loan administrator distributes pin numbers to its debtors. Each pin consists of two letters followed by three numbers. (Assume repetition is allowed, and order is important.) (a) How many different pin numbers are there? (b) What is the probability a pin number selected at random ends in 000? (c) What is the probability a pin number selected at random begins with AA?
Puppies of the Dow Refer to Problems 41 and 43. (a) If five stocks from the Dogs of the Dow list are randomly selected, what is the probability all five will be Puppies of the Dow? (b) If five stocks from the Dogs of the Dow list are randomly selected, what is the probability exactly three will be Puppies of the Dow? (c) If five stocks from the Dogs of the Dow list are randomly selected, what is the probability at least two will be Puppies of the Dow?
40. Hockey There are 15 teams in the Eastern Conference of the National Hockey League for the 2009–2010 season, divided
Answers
I will just answer the problem about Pin numbers because the other questions lack other given values.
a. How many different pin numbers are there?
There are 26 letters in total and 10 numbers in total (including zero), therefore the total number of different pin numbers are:
Total possible = 26 * 26 * 10 * 10 * 10
Total possible = 676,000 different pins
b. What is the probability a pin number selected at random ends in 000
The total possible numbers with ending of 0 0 0 is:
Possible numbers = 26 * 26 * 1 * 1 *1
Possible numbers = 676
Therefore the probability is:
Probability = 676 / 676,000
Probability = 0.001 = 0.10%
c. What is the probability a pin number selected at random begins with AA?
The total possible numbers starting with A A is:
Possible numbers = 1 * 1 * 10 * 10 * 10
Possible numbers = 1000
Therefore the probability is:
Probability = 1000 / 676,000
Probability = 1.48 x 10^-3 = 0.148%
Given: 2x + 11 = 15 Prove: x = 2 Statements Reason 1. 2x + 11 = 15 1. Given 2. 2x = 4 2. 3. x = 2 3. Division Property of Equalit
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2x + 11 - 11 = 15 - 11 ⇒ Subtracting 11 from both sides, this is the Property of Equality
2x = 4 ⇒ Carried on from the previous line of working out
2x ÷ 2 = 4 ÷ 2 ⇒ Divide both sides by 2, this is the property of division equality
x = 2 ⇒ Proved as required
Find all the real square roots of 0.0625.
-0.25 and 0.25
-0.025 and 0.025
0.25
-0.025
Answers
0.0625
0.25 * 0.25
Square root is a 2nd root which is even so there can be negative solutions.
Sqrt(0.0625) = 0.25 or -0.25
The real square roots of 0.0625 are -0.25 and 0.25, as both of these numbers squared equal 0.0625.
Explanation:The student has asked to find all the real square roots of 0.0625. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we're looking for a number which, when squared, equals 0.0625.
To find this, we can recognize that the square root of 0.0625 could be thought of in fraction form as the square root of 625/10000, which simplifies to the square root of 625 divided by the square root of 10000. This reduces to 25/100 because 625 is a perfect square (25 * 25) and 10000 is also a perfect square (100 * 100). Therefore, the principal square root of 0.0625 is 0.25.
However, since every positive number has two square roots, one positive and one negative, and because the square of both -0.25 and 0.25 gives 0.0625, we conclude that the real square roots of 0.0625 are -0.25 and 0.25.
PLEASE HELP
Nestor is building a new swimming pool for $11,000. He makes a $1,000 down payment and the builder gives him an add-on loan, charging him an annual interest rate of 7.7%. If he takes a 6-year loan, what will Nestor's monthly payments be?
Answers
-$1,000
_______
$10,000 * 7.7% = $700
$700/6 = $116.70
Nestor's monthly payment will be roughly about $116.70
®PLEASE MARK AS BRAINLIEST TO HELP ME MOVE TO THE NEXT RANK LEVEL®
please help me with this
Answers
I'll do the first chart as an example.
The equation is n + 6.
So taking the first number, 4, you can just put it in as n,
or 4 + 6.
Then the output would be 10.
Then 8 + 6 = 14
12 + 6 = 18
16 + 6 = 22
20 + 6 = 26
24 + 6 = 30
And you can complete the rest of the charts by doing this.
Hope this helped :D
Select all numbers that are irrational.
π
1.33
√196
√20
Answers
There are two kinds of real numbers in mathematics, one is rational number and other is irrational number. Out of given options, π and √20 are irrational number. Therefore option A, D are correct option
What is irrational number?Real numbers that can not be written in the form of fraction is called irrational number. Real number that can be written in form of fraction is called rational number.
In option (1) π is an irrational number as it contains infinite decimals when we divide 22 by 7
In option (2) 1.33 is a fixed number so it can be written in fractions so this number is rational number
In option (3) √196, it is square root of 14 so it can be written in fraction so it is rational number.
In option (4) √20 is an irrational number as on finding its square root there will be infinite decimals so it cannot be written in form of fraction
Therefore π and √20 are irrational number. Therefore option A, D are correct option
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A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue)
a.9
b.4/3
c 1/4
d. 3/4
Answers
To find the probability of not drawing a blue marble from the bag, one must divide the number of non-blue marbles by the total number of marbles, resulting in a probability of 3/4
The question asks to find the probability of not drawing a blue marble from a bag that contains 8 red marbles, 3 blue marbles, and 1 green marble. The total number of marbles is 8 + 3 + 1 = 12. The probability of not drawing a blue marble (P(not blue)) is the number of marbles that are not blue divided by the total number of marbles. This is (8 red + 1 green) / 12 total marbles. Calculated, the probability is 9/12, which simplifies to 3/4
Select the correct rate of change and y -intercept for the linear function that contains the points (4, 6) and (5, 3). Question 1 options: The rate of change is 3, and the y -intercept is –6. The rate of change is –3, and the y -intercept is 18. The rate of change is −1/3 and the y intercept is 7 1/3 The rate of change is 1/3 and the y intercept is 4 2/3
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What is the average speed of an object that travels 50 miles in 2 hours?
Answers
just divide by 2
50 miles
------------ = 25 mph
2 hours
The graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.
Which equation describes g(x)?
g(x)=|x+4|g(x)=|x|−4g(x)=|x−4|g(x)=−4|x|
Answers
Answer:
Option D
Step-by-step explanation:
The given function is
[tex]f(x)=4|x|[/tex]
It is given that the graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.
If a figure reflected across x-axis, then the rule of reflection is
[tex](x,y)\rightarrow (x,-y)[/tex]
Using the above rule, if the given function reflected across x-axis, then g(x)=-f(x).
[tex]g(x)=-(4|x|)[/tex]
[tex]g(x)=-4|x|[/tex]
The equation g(x)=-4|x| describes g(x).
Therefore, the correct option is D.
numbers in order from least to greatest. -5.25, 1.002, -5.09
Answers
-5.25, -5.09, 1.002
hopes this help please mark me as brainliest. :)
volume of a cube measuring 4 yd on each edge
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10-6+(6×8)-8? what would be the answer?
Answers
You would do 6*8 first, which is 48
Then do...
10-6=4+48=52-8=44
So the answer is 44
I hope this helped!!
if 8 pens and 7 pencils cost $3.37 while 5 pens and 11 pencils cost $3.10, how much does each pen and pencil cost?
Answers
8a+7b=3.37; 5a+11b=3.10.
To eliminate a variable multiply the first eqn by 5 and the second by 8:
40a+35b=16.85, 40a+88b=24.80.
Subtract these equations: 53b=7.95, b=$0.15. So 5a=3.10-1.65=$1.45, a=$0.29.
Pens are $0.29 each and pencils $0.15.
Answer with Step-by-step explanation:
Let x be the cost of 1 pen and y be the cost of 1 pencil
8 pens and 7 pencils cost $3.37 while 5 pens and 11 pencils cost $3.10
8x+7y= 3.37 -----------------(1)
and 5x+11y= 3.10 -----------------(2)
equation (1)×5-equation(2)×8
5(8x+7y)-8(5x+11y)=3.37×5-3.10×8
40x+35y-40x-88y= -7.95
-53y = -7.95
y= 0.15
Putting y=0.15 in equation (1), we get
8x+7×0.15=3.37
8x+1.05=3.37
8x=2.32
x=0.29
Hence, Cost of 1 pen=$ 0.29
Cost of 1 pencil= $ 0.15
A certain product has a unit price of 9.5 cents per ounce. The product sells in bottles of 14 ounces and is priced at $1.30.
As compared to the unit price, the $1.30 price of the 14-ounce bottle _____.
is too low
is too high
is correct
can't be determined
Answers
Answer: the answer is too low i really hope this hepls
Step-by-step explanation:
one shelf in the greenhouse holds 467 plants how many plants can 6 shelves hold?
Answers
Which of the following describes the zeroes of the graph of f(x) = 3x6 + 30x5 + 75x4?
Answers
The zeros are:
[tex]x = 0 \: \: or \: \: x = - 5[/tex]
with multiplicity of 4 and 2 respectively.
EXPLANATION
The given function is
[tex]f(x) =3 {x}^{6} + 30 {x}^{5} + 75 {x}^{4} [/tex]
We want to find
[tex]3 {x}^{6} + 30 {x}^{5} + 75 {x}^{4} = 0 [/tex]
We can find the zeros of this function by factorizing the greatest common factor to obtain,
[tex]3 {x}^{4} ( {x}^{2} + 10x + 25) = 0[/tex]
The expression in the bracket can be rewritten as,
[tex]3 {x}^{4} ( {x}^{2} + 2(5)x + {5}^{2} ) = 0[/tex]
We can see clearly that, the expression in the bracket is a perfect square that can be factored as,
[tex]3 {x}^{4} ( x+ 5)^2 = 0[/tex]
This implies that,
[tex]3 {x}^{4} = 0[/tex]
or
[tex](x + 5) ^{2} = 0[/tex]
This gives,
[tex] {x}^{4} = 0 \: \: or \: \: x + 5 = 0[/tex]
This finally gives,
[tex]x = 0 \: \: or \: \: x = - 5[/tex]
Answer:
–5 with multiplicity 2 and 0 with multiplicity 4
Step-by-step explanation:
I just got it wrong on edge 2020
The graph of a line passes through the points (0, -2) and (6, 0). What is the equation of the line?
Answers
[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-2)=\cfrac{1}{3}(x-0) \\\\\\ y+2=\cfrac{1}{3}x\implies y=\cfrac{1}{3}x-2[/tex]
Answer:
y = 1/3x - 2
Step-by-step explanation:
Jessie has a piece of wood that is 8 feet long. He needs to cut pieces that are 7/8 of a foot long. How many pieces will he be able to make?
Answers
8 * 8/7 =
64/7 =
9.14.....so he can cut 9 full pieces
Answer:
9 full pieces.
Step-by-step explanation:
In order to solve this we have to divide the total feets of wood that Jessie has, by the size of the pieces that Jessie needs:
[tex]\frac{8}{\frac{7}{8} }\\\frac{\frac{8}{1} }{\frac{7}{8} }\\\frac{8*8}{7*1}\\\frac{64}{7} =9.14[/tex]
Since Jessie will be able to cut 9.14 pieces of wood, he will have only 9 full pieces, so the total amount of pieces that he would be able to cut will be 9.
in a certain chemical, the ratio of zinc to copper is 4 of 13. a jar of the chemical contains 338 grams of copper. how many grams of zinc does it contain?
Answers
They tell you that you have 338 grams of copper.
4 X
--- ---
13 338
Cross multiple would be 4(338) = 13x
Simplify
1352 = 13x
104=x
104 grams of zinc
All of the following have the same unit price except _____.
2 for $5.08
5 for $12.70
1/2 for $1.27 2
2 1/2 for $6.25
Answers
Answer:
2 1/2 for $6.25
Step-by-step explanation:
Hello
the unit price is the price that you pay for a unit of product, you must find each unit price and compare
the unit price is given by
[tex]Unit\ price = \frac{amount\ paid}{number\ of\ products} \\[/tex]
Step 1
find each unit price
1).2 for $5.08
[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 5.08}{2}\\\\Unit\ price =2.54[/tex]
unit price =2.54 $
2).5 for $12.70
[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 12.7}{5}\\\\Unit\ price =2.54[/tex]
unit price =2.54 $
3) 1/2 for $1.27 2
[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 1.27}{0.5}\\\\Unit\ price =2.54[/tex]
unit price =2.54 $
4) 2 1/2 for $6.25
[tex]Unit\ price = \frac{amount paid}{number of products} \\Unit\ price = \frac{ 6.25}{2.5}\\\\Unit\ price =2.5[/tex]
unit price =2.5 $
Step 2
define
Now, we can define that the unit price of 2 1/2 for $6.25 is different to the others.
2.5 ≠ 2.54
Have a great day