Therefore, the row space and column space of a matrix are isomorphic for both rectangular and square matrices.
(a) The row space of a matrix is isomorphic to the column space of its transpose.
(b) The row space of a matrix is isomorphic to its column space.
(a) The row space of a matrix is isomorphic to the column space of its transpose.
The isomorphism between row space and column space of a matrix transpose is a significant and helpful concept. The row space of a matrix A is the subspace that is spanned by the rows of A. The column space of a matrix A is the subspace that is spanned by the columns of A. The row space of A is equivalent to the column space of A transpose. The statement is denoted mathematically as row(A) ≅ col(A^T).
(b) The row space of a matrix is isomorphic to its column space.
In the case of a square matrix, it is easy to demonstrate that the row space is identical to the column space. Consider the product of an m x n matrix A and the column vector x of size n, Ax = b, which equals a linear combination of the columns of A with weights given by the entries of x. The solution b lies in the column space of A. Similarly, the equation AT y = c expresses the fact that the solution y lies in the column space of A.
Know more about row space of a matrix here:
https://brainly.com/question/30332493
#SPJ11
Assume that a sample is used to estimate a population proportion μ. Find the margin of error M.E. that corresponds to a sample of size 10 with a mean of 33.7 and a standard deviation of 13.3 at a confidence level of 95%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = _________ Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
The margin of error for a 95% confidence level is 8.2.
How to find the margin of error?The margin of error (ME) is determined using the formula:
ME= z ∗ σ/√n
where:
z is the z-score for the desired confidence level
σ is the population standard deviation
n is the sample size
For a 95% confidence level, the z-score is 1.96. Thus, we have:
z = 1.96
σ = 13.3
n = 10
Substituting these values into the formula, we have:
ME = 1.96 ∗ 13.3/√10
ME = 8.2
Learn more about margin of error on:
brainly.com/question/31876031
#SPJ4
use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.)
The inverse Laplace transform of X(s) = [tex]1/s^7[/tex] is f(t) =[tex]t^6.[/tex]
To locate the inverse Laplace rework of X(s) =[tex]1/(s^7[/tex]), we are able to use algebraic manipulation and the inverse Laplace transform assets said in Theorem 7.2.1, which permits us to discover the original characteristic while given its Laplace rework.
Using the assets of the Laplace transform, we will rewrite the given expression as:
X(s) = [tex]x^-1(1/s^7) = (1/s^7)[/tex]
We need to locate the feature f(t) such that its Laplace transform is X(s) = [tex]1/s^7[/tex]. By making use of Theorem 7.2.1, we understand that the inverse Laplace remodels of X(s) will give us f(t).
Now, we need to find a characteristic f(t) that has a Laplace transform [tex]1/s^7[/tex]. By examining the Laplace transform a desk or the usage of regarded formulas, we will decide that the Laplace remodel of [tex]t^n[/tex](wherein n is a high-quality integer) is given by means of[tex]n!/s^(n+1).[/tex]
In our case, we're looking for a function whose Laplace remodel is[tex]1/s^7.[/tex]Comparing this with the Laplace transform formulation cited earlier, we see that the exponent within the denominator of sought to be [tex]8 ^(7+1).[/tex]
Hence, f(t) must be t^6 (given that 6+1 = 7), and its Laplace remodel maybe [tex]6!/s^7 = 720/s^7.[/tex]
Therefore, the inverse Laplace transform of X(s) = [tex]1/s^7 is f(t) = t^6.[/tex]
In precis, by applying algebraic manipulation and making use of the inverse Laplace rework assets, we determined that the inverse Laplace transform of [tex]1/s^7 is f(t) = t^6[/tex]. This approach that a unique feature corresponding to the given Laplace rework is [tex]t^6.[/tex].
To know more about Inverse Laplace transformation,
https://brainly.com/question/27753787
#SPJ4
Please help AND SHOW WORK!!!!
3x^(3)-6x^(2)+15x-30
Answer:
(x - 2)(3x^2 + 5)
Step-by-step explanation:
All four terms here have 3 as a factor. Factor out 3:
3x^(3)-6x^(2)+15x-30 => 3(x^3 - 2x^2 + 5x - 10)
The last two terms can be rewritten as 5(x - 2). The first two terms can be rewritten as 3x^2(x - 2). So (x - 2) is a factor of 3(x^3 - 2x^2 + 5x - 10). We get:
3x^2(x - 2) + 5(x - 2) = (x - 2)(3x^2 + 5)
pls help i'll give u a brainlyy
Answer: -633
Explanation:
formula is a0= a1 + (n-1)d
a0 is what ur tryig to find
a1 = -14
n= 60
d = -11
Answer:
-674Step-by-step explanation:
As,
There is always a gap of -11 in all the proceedings
Hence,
- 14 -11 = -25
-14 -(11 ×2) = -36
So,
60th term
-14 -(11 × 60) = -674 (Ans)
Find the compound interest paid at the end of 11 years and 33 months when a sum of ₹20000 is invested at a rate of 6% per annum compounded annually?
DONT ADD LINKS PLEASE ANSWER CORRECTLY AND FAST, PLEASE I WILL MARK YOU BRAINLIEST FOR CORRECT ANSWER
Answer:
The total would be 36,600.
Step-by-step explanation:
First you will convert 33 months into years which is 2 years and 10 months.
You will then add the 2 years and the 11 years together which gets you 13 so now you have a total of 13 years and 10 months. (this information will be used later)
Now we will start by multiplying the 20000 by 16% and we should get a total of 1200. That means the interest is 1200 per year so lets first take our 13 years and multiply it by the 1200 (13x1200). You should have 15600 as an answer (save this number for later) since we have 10 months were going to take that 1200 and divide it into 12 month meaning the monthly interest should be 100 per month since we have 10 months we will multiply 100 by 10 and get 1000. Now lets bring back that 15600 and add the additional 1000 to it, our answer should be 16,600, and then we add the original 20000 to the 16600 and your final answer should be 36600.
Pew research reported in 2013 that 15% of American adults do not use the internet or e-mail. They report a margin of error of 2.3 percentage points. The meaning of that margin of error is: A) If they repeatedly sampled from the population, and constructed a confidence interval for each estimate, about 2.3% of those intervals would capture the proportion of American adults who don't use the internet or e-mail. B) They estimate that 2.3% of those surveyed answered incorrectly. C) There is a 2.3% probability that their estimate is incorrect. D) They are pretty sure that the poll result differs from the actual percentage of American adults who don't use the internet or e-mail by 2.3% or less.
Answer:
B) They estimate that 2.3% of those surveyed answered incorrectly
Step-by-step explanation:
hope it helps you dude
sum of -10°C,24°C,-12°C,8°C,-1°C
Answer:
9°C
Step-by-step explanation:
Group the terms and get [tex]24+8-1-10-12[/tex]
Then simplify to get [tex]32-23[/tex]
Subtract and you get 9
So the answer is 9°C.
Hope this helps!
Marlene went shopping and bought a bunch of candy for her swim team. She bought packs of Skittles for $1.50 each and packs of M&Ms for $2 each. She spent a total of $39 and bought 24 items. How many of each item did she buy?
Answer:
18 Skittles
6 M&Ms
Step-by-step explanation:
Set up an equation:
Variable x = number of skittles
Variable y = number of M&Ms
1.50x + 2y = 39
x + y = 24
In the second equation, isolate a variable:
x = 24 - y
Substitute the value of x for 24 - y in the first equation:
1.50(24 - y) + 2y = 39
Use distributive property
36 - 1.5y + 2y = 39
Combine like terms
36 + 0.5y = 39
Isolate variable y:
0.5y = 3
y = 6
Substitute the value of y for 6 in the second equation:
x + 6 = 24
Isolate variable x:
x = 18
Plug these values into any equation of your choice to see if these values are correct (I'll do both equations just to prove it):
1.50(18) + 2(6) = 39
27 + 12 = 39
39 = 39
Correct
x + y = 24
18 + 6 = 24
24 = 24
Correct
***I WILL GIVE BRAINIEST TO THE CORRECT ANSWER**
Translate the description as an algebraic expression:
double the product of 15 and k
Answer:
2•15k
Step-by-step explanation:
Answer:
2(15k)
Step-by-step explanation:
PLZZ GIVE BRAINLIEST
kelly deposits $3,000 at a rate of 5.2ompounded quarterly. with no additional deposits or withdrawals, what is the account balance after 10 years?
The account balance after 10 years will be approximately $5,259.99.
The balance in Kelly's account after 10 years can be determined using the formula for compound interest which is given as:
A = [tex]P(1 + r/n)^{nt}[/tex]
Where, A is the balance after time t, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.
Using this formula and substituting the given values, we get:
A = [tex]3000(1 + 0.052/4)^{4 \times 10}[/tex]
= [tex]3000(1.0125)^{40}[/tex] ≈ $5,259.99
Therefore, the account balance after 10 years will be approximately $5,259.99.
Learn more about account balance https://brainly.com/question/28699225
#SPJ11
A test for divisibility by 11 is to see if the digits taken in order and alternately added and subtracted produce a number which is divisible by 11. Consider 5-digit numbers of the form "abcde'. Show that "abcde' will be divisible by 11 if and only if a - b+c-d+e is divisible by 11.
An test for divisibility that a 5-digit number "abcde" will be divisible by 11 if and only if "a - b + c - d + e" is divisible by 11.
To show that a 5-digit number "abcde" is divisible by 11 if and only if "a - b + c - d + e" is divisible by 11, the concept of modular arithmetic.
The 5-digit number "abcde" as a sum of its digits multiplied by their respective place values:
"abcde" = a × 10000 + b × 1000 + c × 100 + d × 10 + e
Then express "a - b + c - d + e" in terms of the digits:
a - b + c - d + e = a × (10,000 mod 11) - b × (1,000 mod 11) + c × (100 mod 11) - d × (10 mod 11) + e
examine the patterns of the modulos:
10,000 mod 11 = 1
1,000 mod 11 = 10
100 mod 11 = 1
10 mod 11 = 10
Substituting these values back into the expression,
a - b + c - d + e = a × 1 - b ×10 + c × 1 - d × 10 + e
Simplifying further:
a - b + c - d + e = a - b + c - d + e
observe that the expression "a - b + c - d + e" is equivalent to the original 5-digit number "abcde." This means that if "abcde" is divisible by 11, then "a - b + c - d + e" will also be divisible by 11.
Conversely, if "a - b + c - d + e" is divisible by 11, it implies that the expression and the 5-digit number "abcde" have the same remainder when divided by 11. Since they are equivalent, "abcde" must also be divisible by 11.
To know more about divisibility here
https://brainly.com/question/2684764
#SPJ4
What is the value of g^-1(7)? PLEASE HELP!!! I’ll give brainliest!!
Answer: g-7
Step-by-step explanation:
Answer:
Step-by-step explanation:
5 is the correct answer
I finally started watching my hero academia, its really good but i HATEEE the season long competition thing!! its annoying! same with naruto, u watch an episode thinking ur gonna at least finish the round he is in but nOOOOoOOO
Answer:
same
Step-by-step explanation:
Ajar contains 5 red and 3 purple jelly beans. How many ways can 4 jelly beans be picked so that at least 2 are red? 11 15 10 6
There are 10 ways to pick 4 jelly beans from a jar containing 5 red and 3 purple jelly beans, ensuring at least 2 are red.
To calculate the number of ways, we consider the cases where we choose exactly 2 red jelly beans, 3 red jelly beans, or all 4 red jelly beans.
Case 1: Choosing 2 red jelly beans - There are 5 red jelly beans to choose from, and we need to select 2. This can be done in [tex]5C2 = 10[/tex] ways.
Case 2: Choosing 3 red jelly beans - There are 5 red jelly beans to choose from, and we need to select 3. This can be done in [tex]5C3 = 10[/tex] ways.
Case 3: Choosing all 4 red jelly beans - There are 5 red jelly beans, and we need to select 4. This can be done in [tex]5C4 = 5[/tex] ways.
Adding up the possibilities from all three cases, we get 10 + 10 + 5 = 25 ways. However, we need to subtract the case where we select all 4 purple jelly beans, which is only 1 way. Therefore, the final number of ways is 25 - 1 = 24 ways.
To learn more about possibilities
Click here brainly.com/question/31135280
#SPJ11
Find an equation of the sphere that passes through the point (7.3.-1) and has center (5, 8, 5).
The equation of the sphere passing through the point (7, 3, -1) with center (5, 8, 5) is:
(x - 5)^2 + (y - 8)^2 + (z - 5)^2 = 65.
To find the equation of the sphere passing through the point (7, 3, -1) with center (5, 8, 5), we can use the general equation for a sphere in three-dimensional space. The equation of a sphere with center (h, k, l) and radius r is given by:
(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2.
Using the given center (5, 8, 5), we have:
(x - 5)^2 + (y - 8)^2 + (z - 5)^2 = r^2.
Since the sphere passes through the point (7, 3, -1), we can substitute these values into the equation:
(7 - 5)^2 + (3 - 8)^2 + (-1 - 5)^2 = r^2.
Simplifying the equation gives us:
4 + 25 + 36 = r^2.
65 = r^2.
Therefore, the equation of the sphere passing through the point (7, 3, -1) with center (5, 8, 5) is:
(x - 5)^2 + (y - 8)^2 + (z - 5)^2 = 65.
Know more about Sphere here:
https://brainly.com/question/22849345
#SPJ11
Is (2,0) a solution for the equation -3+9y=-6
Answer:
[tex]y=-\frac{1}{3}[/tex]
Step-by-step explanation:
- 3 + 9y = - 6
- 3 + 3 + 9y = - 6 + 3
9y = - 3
9y ÷ 9 = - 3 ÷ 9
[tex]y=- \frac{1}{3}[/tex]
is 12, -15, -18, -21 arithmetic
Determine the area of a circle whose radius is 15 feet. Use pie=3.14
Answer:
Down below
Step-by-step explanation:
[tex]A=\pi r^2\\A=3.14*(15)^2\\A=3.14*225\\A=706.5[/tex]
use the inner product u, v = 2u1v1 u2v2 in r2 and the gram-schmidt orthonormalization process to transform {(2, 1), (−2, −5)} into an orthonormal basis.
The orthonormal basis for (2, 1), (2, 5) is therefore u1, u2 = (2/5, 1/5), (2/5, -1/5) because u2 = v2_orth/||v2_orth|| = (2/5, -1/5).
In R2, the internal result of the two vectors u and v is as follows: The Gram-Schmidt procedure can be used to request the transformation of (2, 1), (2, 5) into an orthonormal premise. u, v = 2u1v1 + u2v2. An orthonormal premise is made by changing over a bunch of directly free vectors utilizing the Gram-Schmidt process. Our set's principal vector, v1 = (2, 1), should serve as our starting point.
We standardize v1 to obtain our first orthonormal premise vector: We must locate the second vector in our set, v2 = (-2, -5), and we can orthogonalize v2 by deducting its projection from u1: u1 = v1/||v1|| = (2/5, 1/5) proj_u1(v2) = (v2 u1)u1 = (- 8/5, - 4/5)v2_orth = v2 - proj_u1(v2) = (6, - 21/5)Our second orthonormal premise vector is acquired by normalizing v2_orth: The orthonormal reason for (2, 1), (2, 5) is subsequently u1, u2 = (2/5, 1/5), (2/5, - 1/5) in light of the fact that u2 = v2_orth/||v2_orth|| = (2/5, - 1/5).
To know more about orthonormal refer to
https://brainly.com/question/31992754
#SPJ11
The question is in the photo above plz answer
Answer:
surface area of cuboid=2(lb+bh+hl)
surface area of cuboid=2(12×5+5×2+2×12 )
surface area of cuboid=188in²
Tue diameter of a bike is 27 inches if the wheel makes 15 complete rotations how far does the bike travel?
Answer:
1271.7 inches
Step-by-step explanation:
Given
[tex]d = 27in[/tex]
[tex]Rotations = 15[/tex]
Required
The total distance moved
First, we calculate the circumference of the wheel
[tex]c = \pi *d[/tex]
[tex]c = 3.14 * 27[/tex]
[tex]c = 84.78[/tex]
This represents the distance traveled in one complete rotation.
So, in 15 rotations.
[tex]Total = 15 * 84.78[/tex]
[tex]Total = 1271.7[/tex]
Let X be a normal random variable with a mean of 0.33 and a standard deviation of 2.69.
a)Calculate the corresponding standardized value (z) for the point x = 4.1. Give your answer to 2 decimal places.
z =
b)The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable is:
less than or equal to z
equal to z
greater than or equal to z
a) the corresponding standardized value (z) for x = 4.1 is approximately 1.39.
b) The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable is less than or equal to z.
a) To calculate the standardized value (z) for the point x = 4.1, we can use the formula:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
In this case, x = 4.1, μ = 0.33, and σ = 2.69. Plugging these values into the formula:
z = (4.1 - 0.33) / 2.69
z ≈ 1.39
So, the corresponding standardized value (z) for x = 4.1 is approximately 1.39.
b) The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable is less than or equal to z.
Visit here to learn more about standard normal probability brainly.com/question/31226766
#SPJ11
HELPPPP PLZ BEST ANSWER GET BRAINLIEST
Please help.
Indices and Standard Form question
Answer:
A= 4.5×10^11
B= 3.5×10^3
Step-by-step explanation:
A
(5×10^3)= 5000
(9×10^7)=90000000
multiply both of them
=450000000000 or 4.5×10^11
B
(7×10^5)=700000
(2×10^2)=200
700000÷200
3500 or 3.5×10^3
A sample of two items is selected without replacement from a batch. Describe the ordered sample space for the following batch:
(a)The batch contains 3 defective items and 10 good times.Hint: suppose we denote defective item by ‘d’ and good item as ‘g’, so one possible outcome could be "dg".
(b)The batch contains the items {a, b, c, d}.
For both scenarios, a sample is selected without replacement from a batch of items. In the first scenario, the batch contains 3 defective items ('d') and 10 good items ('g'). The ordered sample space consists of all possible ordered pairs of items: {dd, dg, gd, gg}. In the second scenario, the batch contains the items {a, b, c, d}. The ordered sample space also consists of all possible ordered pairs of items: {aa, ab, ac, ad, ba, bb, bc, bd, ca, cb, cc, cd, da, db, dc, dd}.
In the first scenario, the ordered sample space is derived by considering all possible combinations of the two items selected from the batch. Since the selection is done without replacement, the first item can be either defective ('d') or good ('g'). For each case, the second item can also be defective or good, depending on what was chosen as the first item. Therefore, the ordered sample space consists of four possibilities: dd, dg, gd, and gg.
In the second scenario, the batch consists of four distinct items: a, b, c, and d. Again, the ordered sample space is obtained by considering all possible combinations of the two items selected without replacement. Since there are four items, there are 16 possible combinations. Each combination is represented by an ordered pair of the selected items, such as aa, ab, ac, and so on.
To know more about ordered sample space, click here: brainly.com/question/29189463
#SPJ11
what is 25/x 15/30 can you please help
Answer:
x = 50.... 25/50 = 15/30 or 1/2 = 1/2
Step-by-step explanation:
25/x = 15/30
consider the cross multiply
25 * 30 = 15 * x
750 = 15x
divide both sides with 15 to make the co-efficient of x, 1.
x = 50
Answer:
5×15/6
5×5/2
25/2
12.2 is your answer ☺️☺️☺️. If I'm right so,
Please mark me as brainliest. thanks!!!
If the true means of the k populations are equal in an ANOVA model, then MSTR/MSE should be: a. more than 1.00 b. close to 1.00 c. close to 0.00 d. close to -1.00 e. a negative value between 0 and - 1 f. not enough information to make a decision
The correct answer is b. close to 1.00. Ratio close to 1.00 indicates that the between-group variation is similar to the within-group variation.
In an ANOVA (Analysis of Variance) model, MSTR refers to the mean square treatment (or between-group variation), while MSE refers to the mean square error (or within-group variation).
If the true means of the k populations are equal, it means that the between-group variation is similar to the within-group variation, and there is no significant difference between the group means.
In this scenario, we would expect the MSTR/MSE ratio to be close to 1.00 (answer b). A ratio close to 1.00 indicates that the between-group variation is similar to the within-group variation, supporting the assumption that the true means of the populations are equal.
Therefore, the correct answer is b. close to 1.00.
Learn more about variation here
https://brainly.com/question/13998680
#SPJ11
The table below gives a record of variations of the values of y with the values of x. Draw a scatter plot for the data.
x
0.4
1.2
2.0
3.1
4.5
5.7
7.1
8.4
9.3
9.8
y
7.8
7.1
6.8
6.0
5.2
4.3
3.4
2.3
1.1
0.5
a.
On a graph, points are at (2, 6.9), (9.3, 1.2), (9.8, 0).
c.
On a graph, points are at (0.4, 7.8), (3.1, 6.0), and (9.8, 0.5).
b.
On a graph, points are at (2, 7), (9.3, 1.2), (9.8, 1.5).
d.
On a graph, points are at (1.2, 7.2), (9.3, 1.2), (9.8, 0.2).
Please select the best answer from the choices provided
A
B
C
D
Answer: taake this link, it has all the answers
Step-by-step explanation: https://quizlet.com/183183758/statistical-studies-scatterplots-practiceamdm-flash-cards/
The best option for the points on the graph is points are at (0.4, 7.8), (3.1, 6.0), and (9.8, 0.5).
What are co ordinate axis?In two-dimensional Cartesian geometry, two intersecting straight lines are used as reference lines. In three-dimensional Cartesian geometry, three straight lines with a common point are the intersections of the three coordinate reference planes.
Estimation of the coordinates from the graph:From the attached file of scatter plot for the data, it is clear that the for every value of x there is a suitable value of y which was given in the question.
Considering x values and plot the y vale on the graph.
For x = 0.4; y = 7.8
For x = 3.1; y = 6.0
and for x = 9.8; y = 0.5
To know more about the Cartesian system, here
https://brainly.com/question/4726772
#SPJ2
The volume of a cylinder can be determined using the formula V=πr2h, where r and h represent the radius and height of the cylinder, respectively. A volume of paint expressed as (8x3 + 31x2 + 32x)π and a volume of paint expressed as (10x3 + 17x2)π are poured into a paint can in the shape of a cylinder. Determine possible expressions for the radius of the can and the depth of the paint in the can.
Answer:
Possible expressions for the radius of the can and the depth of the paint in the can are [tex]r = \sqrt{9\cdot x^{2}+24\cdot x+16}[/tex] and [tex]h = 2\cdot x[/tex], respectively.
Step-by-step explanation:
Let be the initial volumes of the initial cans represented by these expressions:
[tex]V_{1} = (8\cdot x^{3}+31\cdot x^{2}+32\cdot x)\cdot \pi[/tex] (1)
[tex]V_{2} = (10\cdot x^{3}+17\cdot x^{2})\cdot \pi[/tex] (2)
The resulting volume of the paint can is the sum of the two functions:
[tex]V_{3} = (18\cdot x^{3}+48\cdot x^{2}+32\cdot x)\cdot \pi[/tex] (3)
Then, we proceed to factor the polynomial:
[tex]V_{3} = 2\cdot (9\cdot x^{2}+24\cdot x +16)\cdot x \cdot \pi[/tex]
[tex]V_{3} = \pi\cdot (9\cdot x^{2}+24\cdot x + 16)\cdot (2\cdot x)[/tex] (3b)
By direct comparison with the volume formula for the cylinder we have the following expressions:
[tex]r^{2} = 9\cdot x^{2}+24\cdot x + 16[/tex]
[tex]r = \sqrt{9\cdot x^{2}+24\cdot x+16}[/tex]
[tex]h = 2\cdot x[/tex]
Possible expressions for the radius of the can and the depth of the paint in the can are [tex]r = \sqrt{9\cdot x^{2}+24\cdot x+16}[/tex] and [tex]h = 2\cdot x[/tex], respectively.
The number of calories of a food item varies directly with the size of the portion. If a 2-inch slice of a certain delicacy contains 170 calories, how many calories are in a 3-inch slice?
Answer:
A 3-inch slice of the food item contains 255 calories.
Step-by-step explanation:
Set calories per inch slice as variable x.
2x = 170
x = 85 cal
Since each inch slice of the food item contains 85 calories, a 3-inch slice would contain:
3x = 3(85) = 255 cal