Answer:
Your answer is 48.16 grams.
Austin needs to pour 48.16 grams of salt.
Here the total amount of salt is 71.26 grams.
But he pours 23.1 grams.
So when we minus 71.26-23.1, it is equal to 48.16 grams.
Therefore, Austin needs to pour 48.16 grams of salt.
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An animal shelter has 8 puppies. If the puppies are 32% of the total dog and cat population, how many dogs and cats are in the animal shelter?
well, the total amount is really "x", which oddly enough is the 100%, but we also know that 32% of that is 8, hmmmm
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 8& 32 \end{array} \implies \cfrac{x}{8}~~=~~\cfrac{100}{32} \\\\\\ \cfrac{ x }{ 8 } ~~=~~ \cfrac{ 25 }{ 8 }\implies 8x=200\implies x=\cfrac{200}{8}\implies x=25[/tex]
There are two investment options:
• Option 1: An initial investment of $5 that increases by 50% every year.
.
• Option 2: An initial investment of $0.01 that doubles every year.
Part A:
Write an equation for each option to model the value A of the account after x years
Part B:
Explain which investment will eventually have the greatest value.
Option 1: An initial investment of $5 that increases by 50% every year
as after 20 years, it amounts to a greater value.
What are arithmetic and geometric sequence?An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference
d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.
In a geometric sequence numbers are written in the same constant ratio(r).
It means every next number is a multiple of a common constant and the previous number.
r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.
The given situations can be modeled as a geometric sequence.
Option A :
a₁ = 5, r = 1.5.
We know Sₙ = a₁(rⁿ - 1)/(r -1).
Sₙ = 5(1.5ⁿ - 1)/(1.5 - 1).
Sₙ = 5(1.5ⁿ - 1)/(0.5).
Let us see for n = 20, 20th year.
S₂₀ = 5(1.5²⁰ - 1)/(0.5).
S₂₀ = 5(3324.25)/(0.5).
S₂₀ = 33242.5.
Option B :
a₁ = 0.01 and r = 2.
Sₙ = 0.01(2ⁿ - 1)/(1).
S₂₀ = 0.01(2²⁰ - 1)/(1).
S₂₀ = 10,485.75
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There is 14 feet of fencing available to enclose a rectangular region. For what
The maximum area is 12.25 square feet
How to determine the maximum areaFrom the question, we have the following parameters that can be used in our computation:
Perimeter = 14 feet
This means that
P = 2(l + w)
So, we have
2(l + w) = 14
Divide by 2
l + w = 7
Make l the subject
l = 7 - w
The area is calculated as
A = lw
So, we have
A = (7 - w)w
Expand
A = 7w - w²
Differentiate and set to 0
7 - 2w = 0
So, we have
w = 3.5
Substitute w = 3.5 in A = (7 - w)w
A = (7 - 3.5) * 3.5
Evaluate
A = 12.25
Hence, the area is 12.25 square feet
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Complete question
There is 14 feet of fencing available to enclose a rectangular region. For what value of area is the area maximum
A local bank charges a $31-per-check overdraft protection fee. On June 5, Lewis has $932.77 in his account. Over
the next few days, the following checks were submitted: June 6, $791.29, $340.50, and $208.35; June 7, $428.61;
and June 8, $113.3. How much will he pay in overdraft fees?
Answer: The total amount of overdraft fees that Lewis will pay is {$1149.28}.
Step-by-step explanation:
To find out how much Lewis will pay in overdraft fees, we need to calculate the total amount of his overdrafts. We can do this by subtracting the sum of his checks from his account balance on June 5. This gives us:
overdraft = 932.77 - (791.29 + 340.50 + 208.35 + 428.61 + 113.3)
= 932.77 - 2082.05
= -1149.28
Since the bank charges a $31-per-check overdraft protection fee, Lewis will have to pay $31 for each check that he overdraws his account. Since he overdraws his account by $1149.28 in total, he will have to pay $31 * (1149.28 / 31) = $1149.28 in overdraft fees.
Therefore, the total amount of overdraft fees that Lewis will pay is {$1149.28}.
*Triangle not drawn to scale*
- Which angle is the biggest based on the sides of the triangles below? Explain your reasoning.
Using Triangle inequality theorem Angle C of triangle CBT will be the biggest angle.
What do you mean by triangle inequality?Triangle inequality. A theorem in Euclidean geometry that states that the sum of any two sides of a triangle is greater than or equal to the third side. In symbol a + b ≥ c. Basically, the theorem states that the shortest distance between two points is a straight line.
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides of it must be greater than or equal to the length of the remaining sides.
In the given triangle CBT , CB = 24 cm BT = 35 cm CT = 30 cm
We know angle opposite to larger side will be greatest therefore, angle C of triangle CBT will be the biggest angle
.
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what is the answer to this 6m+8=4(17+m)
Answer:
m=30
Step-by-step explanation:
An approximate solution to an equation is found using this iterative process.
Xₙ₊₁= (Xₙ)³ - 1 / 4 and x₁= -1
a)
(i) Work out the value of x₂
(ii) Work out the value of x₃
b) Work out the solution to 6 decimal places.
a) The values are given as follows:
i) x1: -0.5.ii) x2: -0.280125.b) The solution of the equation is of: -0.25410169644.
How to obtain the solution to the equation?The equation in this problem is given as follows:
y = (x³ - 1)/4.
The solution is obtained using a iterative solution method, until the difference between previous iterations is less than 10^-6, as the solution is exact to 6 decimal places.
Then the values are given as follows:
x1 = -1 -> attributed.x2 = ((-1)³ - 1)/4 = -0.5.x3 = ((-0.5)³ - 1)/4 = -0.28125.x4 = ((-0.281255)³ - 1)/4 = -0.25556212524.x5 = ((-0.25556212524)³ - 1)/4 = -0.25417281837x6 = ((-0.25417281837)³ - 1)/4 = -0.25410513385x7 = ((-0.25410513385)³ - 1)/4 = -0.25410185521.x8 = ((-0.25410185521)³ - 1)/4 = -0.25410169644. -> difference less than six decimal places.More can be learned about iterative solution methods at https://brainly.com/question/13718918
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Suppose the finishing times for cyclists in a race are normally distributed. If the population standard deviation is 16 minutes, what minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean?
The minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean is 40.
What is the confidence interval?In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter.
We have that to find our α level, that is the subtraction of 1 by the confidence interval divided by 2.
α = (1 - 0.90)/2 = 0.05.
Now, we have to find z in the Ztable as such z has a p-value of 1 - α.
So it is z with a pvalue of 1 - 0.05 = 0.95 = 1.96.
Now, find the margin of error M as such,
M = z×(sigma/√n).
5 = 1.96×(16/√n).
5√n = 31.36.
n = 39.9.
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This question has two parts. First, answer Part A. Then, answer Part B.
Part A
USE EFFICIENT METHODS Determine whether Δ D E F P ≅ ΔP Q R.
D(-7,-3), E(-4,-1), F(-2,-5), P(2,-2), Q(5,-4), R(0,-5)
Find the side lengths of each triangle.
A) D E=√13, P Q=√13, E F=2 √5, Q R=√13, D F=√29, P R=√13
B) D E=√13, P Q=√13, E F=√5, Q R=√26, D F=√29, P R=√13
C) D E=√13, P Q=√13}, E F=2 √5, Q R=√26, D F=2 √29, P R=√13
D) D E=√13}, P Q=√13, E F=2 √5, Q R=√26, D F=√29, P R=√13
The side lengths of each triangle are given as follows:
D. [tex]DE = \sqrt{13}, PQ = \sqrt{13}, EF = 2\sqrt{5}, QR = \sqrt{26}, DF = \sqrt{29}, PR = \sqrt{13}[/tex]
How to obtain the side lengths of each triangle?The side lengths of each triangle are given by the distances between the vertices.
These vertices are in the coordinate plane, hence the distance between them is found using the equation for the distance between two points.
Suppose two points in the coordinate plane with notation given as follows:
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Then the 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]
Thus the side lengths are given as follows:
DE: [tex]\sqrt{3^2 + 2^2} = sqrt{13}[/tex]PQ: [tex]\sqrt{3^2 + 2^2} = sqrt{13}[/tex]EF: [tex]\sqrt{2^2 + 4^2} = \sqrt{20} = 2\sqrt{5}[/tex]QR: [tex]\sqrt{5^2 + 1^2} = \sqrt{26}[/tex]DF: [tex]\sqrt{5^2 + 2^2} = \sqrt{29}[/tex]PR: [tex]\sqrt{2^2 + 3^2} = sqrt{13}[/tex]Meaning that option D is correct.
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The length of a rectangle is twice the width. The area of the rectangle is 80 square inches. What irrational number represents the width of the rectangle?
The square root of 40 is approximately 6.324555320336759. This is the width of the rectangle.
What is a rectangle?
It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral. It occupies area in two-dimensional planner geometry.
The area of a rectangle is given by the formula A = lw,
where A is the area, l is the length, and w is the width.
We are told that the length of the rectangle is twice the width, so we can write the formula as follows:
A = 2w * w
We are also told that the area of the rectangle is 80 square inches, so we can substitute this value into the formula:
80 = 2w * w
We can rearrange this equation to solve for w:
80 = 2w²
w² = 40
The square root of 40 is an irrational number, so the width of the rectangle is an irrational number.
Hence, To express this number in decimal form, the square root of 40 is approximately 6.324555320336759. This is the width of the rectangle.
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A consulting company wants to track the results of its new marketing plan. The media manager recorded the number of views for one of the company’s online videos. The results from the first four weeks are shown in this table.
Write an equation to model the relationship between the number of weeks, x, and then number of views, f(x).
f(x)=a(b)^x
The equation which model the relationship between the weeks and the viewers is;
f(x) = 2160(1.5)ˣ
What is common ratio?The distance between each number in a geometric series is known as the common ratio. The ratio between two consecutive numbers, or a number divided by the number before it in the sequence, is known as the common ratio since it is the same for all numbers or common.
Given that the expression f(x) = abˣ
Here, b is the common ratio.
Now to find the common ratio b;
To check for first and second term, 3240 / 2160 = 1.5
To check for second term and third term, 4860 / 3240 = 1.5
To check for third term and forth term, 7290 / 4860 = 1.5
To check for forth and fifth term, 10935 / 7290 = 1.5
Therefore the common ratio b is 1.5.
now to find a,
let x =0 and f(x) = 2160
Then, 2160 = a (1.5)°
a = 2160
Therefore, the equation which model the relationship between the weeks and the viewers is;
f(x) = 2160(1.5)ˣ
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Solve for a given the following proportion:
4/a-3=2/5
a=
Answer:
first do criss cross the it will be like this : 2(a-3)=4*5 . Now do like as given in the picture.
Box contains 160 fruits. of the total number of fruits in the box 30% are apples. 25% of the remaining fruits in the box pears and the rest of the fruits in the box are oranges. how many oranges are in the box?
Answer: If 30% of the fruits in the box are apples, then 100% - 30% = 70% of the fruits in the box are not apples. Of these non-apple fruits, 25% are pears, so the remaining fruits, 100% - 25% = 75% are oranges. Since 75% of the fruits in the box are oranges, and the total number of fruits in the box is 160, then the number of oranges in the box is 75/100 * 160 = <<75/100*160=120>>120. Answer: \boxed{120}.
if 25% of tolla's sallary is birr 135.75, what is the amount of his full salary?
If 25% of Tolla's salary is Birr 135.75, then the full amount of his salary is 4 times this amount, since 25% is one quarter of the total amount.
Therefore, the full amount of Tolla's salary is 4 * Birr 135.75 = Birr 543.
This is the amount of Tolla's full salary.
LOL
Find the cost of driving Jenna’s car (J) in $/mile when the price of gas is $4.29/gallon
The cost of driving Jenna's car is $0.341/mile
Calculating cost of drivingFrom the question, we are to determine the cost of driving Jenna's car in $/mile
From the given information
The formula used to find Jenna's cost to drive her own car for work is
J = g/22 + 0.146
We are to find the cost of driving when the price of gas, g, is $4.29/gallon
Substitute g = 4.29 in the formula
J = 4.29/22 + 0.146
J = 0.195 + 0.146
J = 0.341
Hence, the cost is $0.341
Here is the complete question:
Recall the formula used to find Jenna's cost to drive her own car for work:
J = g/22 + 0.146
In this formula, J = Cost of driving Jenna's car in $/mile, and g = Cost of gas in $/gallon.
Find the cost of driving Jenna’s car (J) in $/mile when the price of gas is $4.29/gallon
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Stem and leaf plots
And box
Pls help I have no idea what this is
Answer:
13
Step-by-step explanation:
The box plot ends at 13.
Box plots show the average score of the data. It shows the minimum, median and maximum. The line inside the box is the median. The minimum, in this case is 0 and the max is 13.
MULTIPLE CHOICE PRACTICE
9. For the function defined by the equation y=2 x²-10, which of the following represents the output when the input is -3 ?
(1) 6
(3) -10
(2) 8
(4) -28
10. If a function is defined by the equation y=-5 x+1 and the domain is the set {-2,0,2,4\}, which set below represents the range of the function?
(1) {11,12,13,14}
(3) {-10,-1,9,19}
(2) {-19,-9,1,10}
(4) {51,53,55,57}
11. A function is given by the set: {(-6,2),(-4,7),(0,5),(2,-4),(5,2),(7,5)}. Which of the following gives a pair of inputs that have the same output?
(1) -6and -4
(3) -4 and 2
(2) 5 and 7
(4) 0 and 7
Answer:
answer for no.10 is {11,12,13,14}
Step-by-step explanation:
According to question domain and equation is given. At first we have to write equation as f(y)=5x+1 and at the place of y we have to write the given domain respectively then we can get the answers
Find the sum of the arithmetic series where n = 50, a = 9, and t50 = 331.
Solution
Given series is [tex]$5+11+17+\ldots .+95$.[/tex]
Thus,
[tex]$\mathrm{a}=5, \mathrm{~d}=11-5=6,1=95$$$\begin{aligned}& \mathrm{n}=\frac{1-a}{d}+1 \\& =\frac{95-5}{6}+1 \\& =\frac{90}{6}+1=15+1=16\end{aligned}[/tex]
Therefore, [tex]$\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}(\mathrm{a}+1)$$$\begin{aligned}& =\frac{16}{2}(5+95) \\& =8(100) \\& =800\end{aligned}$$[/tex]
What is arithmetic series?
The total of the terms in an arithmetic sequence with a predetermined number of terms is known as an arithmetic series. Here is a straightforward formula for calculating the sum: Formula 1: If the sum of an arithmetic series of terms is represented by S n, then The first and last terms' values, as well as the total number of terms, are needed for this formula.
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Therefore, in area or a circles given by the formula.
A. the circumference, or 2π²
B. the radius, r
C. half the radius, or 1/2 r
D. half the circumference, or s r
Area or a circles given by the formula = radius , r
What is area?
The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
For the circle or area given by the formula is radius ,r.
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The time spent by a customer at a checkout counter has mean 4 minutes and standard deviation 2 minutes.
a. What is the probability that the total time taken by a random sample of 52 customers is less than 180 minutes?
b. Find the 30th percentile of the total time taken by 52 customers.
The probability that the total time taken by a random sample of 52 customers is less than 180 minutes is 0.02%.
μ=Population mean=4
σ=Population standard deviation=2
n=Sample size=50
The sampling distribution of the sum S is roughly normal if the sample size is big (30 or more), according to the central limit theorem.
The central limit theorem tells us that the sampling distribution of the sum S is about normal because the sample size of 50 is at least 30.
The sum S's sample distribution has a mean and standard deviation of n and n, respectively.
The z-score is the value decreased by the mean, divided by the standard deviation
z = ( x -μS ) / √σS
= 150 - 50(4) / √ 50(2)
= 3.54
Using the appendix's normal probability table, get the relevant probability,
P(S < 150 ) = P(Z< -3.54)
= 0.0002
=0.02%
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
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Factorise fully the following:
4x² + 28x³
Answer: 4x^2(7x+1)
Step-by-step explanation: Divide by the common divisible of 4x^2 and you will get your answer/.
Answer:4x^2(1+7x)
Step-by-step explanation:
4x^2(1+7x)
what is the perimeter of a rhombus when the diagonals are 42cm and 40cm
Answer:
Step-by-step explanation:
P = 4 a
a = √p^2 + q^2 / 2
P = 2√p^2 + q^2 = 2 x √42^2 + 40^2 = 116cm
∴ the perimeter of a rhombus when the diagonals are 42cm and 40cm is 116cm
Consider r (x) = StartFraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline EndFraction, where a, b, c, and d are positive integers and b < d. What value does r(x) approach as x approachesInfinity?
0
StartFraction a Over c EndFraction
StartFraction b Over d EndFraction
Infinity
The value of r(x) approaches as x approaches Infinity is; 0
How to find the limit of a function?Limit is defined as the value that a function approaches for the given input value.
We have been given a function;
r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction
We can rewrite this function as;
r(x) = (axᵇ + 8)/(cx^d)
where a, b, c, and d are positive integers and b < d.
We need to find the value of r(x) approach as x approaches Infinity.
This means, we need to find the value of the limit [tex]\lim_{x \to \infty} r(x)[/tex]
Now, we find the value of limit for given function;
[tex]\lim_{x \to \infty} \frac{ax^b + 8 }{cx^d}[/tex]
This simplifies to;
[tex]\lim_{x \to \infty} \frac{8 }{cx^d}[/tex] (since d > b)
Thus;
[tex]\lim_{x \to \infty} r(x) = 0[/tex]
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Consider the interval AC that has been graphed on the number plane. Find the length of interval AC, rounding your answer to two decimal places.
By using the distance formula, the length of the interval AC 10.8, After rounding it will be 11 units.
What is the distance formula?The distance formula is given as:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Give the example of two decimal rounding off.
Here are two examples of rounding off to two decimal places:
12.3456 rounded to two decimal places is 12.35
0.678 rounded to two decimal places is 0.68
Plugging in the coordinates of the two points, we get:
Distance = sqrt((5 - (-1))^2 + (4 - 13)^2)
= sqrt(6^2 + (-9)^2)
= sqrt(36 + 81)
= sqrt(117)
= approximately 10.8
Therefore, the distance between the points (-1,13) and (5,4) is approximately 10.8.
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Adrian Alvarez Munoz
Write Expression from Context $(m x+ b)
Dec 12, 8:15:06 PM
Watch help video
Angel is saving up to buy a new video game. He already has $ 30 and can save an additional $ 8 per week using money from his after school job. How much total money would Angel have after 5 weeks of saving? Also, write an expression that represents the amount of money Angel would have saved in w weeks.
Total savings after 5 weeks:
Total savings after w weeks:
The expression that represents the amount of money Angel would have savings in w weeks is 30+8w
The total amount of money saved after 5 weeks is $70
Which algebraic expression is required for Angel's total savings?
The required algebraic expression considers the amount she has saved already which is $30 and her potential to save $8 per week, for w number of weeksSystems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:Each quantity has a value attached to it, such as the cost of an adult or kid ticket, the number of products in a large box as compared to a small box, etc.Total savings=30+8w
Now by substituting 5 , the number of weeks for w, we can determine total savings after 5 weeks
total savings=30+(8*5)
total savings=30+40
Total savings=$70
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Monique wants to rent online movies. Movies Plus charges a one-time free of $20 plus $5 per movie. Movies-To-Go charges $7 per movie. Write and solve an equation to determine m, the number of movies rented when the cost for Movies Plus and Movies-To-Go is the same.
__; m = __ movies
The number of movies rented when the cost for Movies Plus and Movies-To-Go is the same is 10.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Let the no. of movies be 'm' and the total cost is 'C'
Movies Plus charges a one-time fee of $20 plus $5 per movie
which is, C = 5m + 20.
Movies-To-Go charges $7 per movie
which is, C = 7m.
Now, the number of movies rented when the cost for Movies Plus and Movies-To-Go is the same will be when we equate both equations.
∴ 7m = 5m + 20.
2m = 20.
m = 10.
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find the volume of the Rectangular prism given below the length is is 10 cm the width is 3.2 cm and the height is 1.5 cm
Answer:
44.8
Step-by-step explanation:
Volume = Length * Height * Width
Volume = 10 * 1.5 * 3.2
Volume = 44.8cm
the values f(x) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1. which of the following statements must be true?
The following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.
Given :
the values f ( x ) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1.
Function :
In simple words, a function is a relationship between inputs where each input is related to exactly one output.
Every function has a domain and a co - domain.
x sufficiently close to 1 means x → 1
but x ≠ 1.
so function = [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞
Therefore the following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.
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Which statement correctly describes the relationship between the graph of f(x) and the graph of g(x)=f(x)−4?
Answer:
the range of the graph would move down by 4 units.
Step-by-step explanation:
f(x) is the original/basis equation
g(x) is the translation equation
-4 does not have any x's attached to it, so it would affect the range, or the y of the equation
for example:
f(x) = 2x + 8
if you subtracted 4 from that it would be:
f(x) = 2x - 4, so the range would be affected
What is the surface area of the cube shown below?
Answer:
150 in^2
Step-by-step explanation:
It is a cube...it has six equal sides
the surface area of one side is 5 x 5 = 25 in^2
there are six .... so 6 x 25 = 15o in^2
Edited: should be in^2 not cm^2 as originally posted...wrong units
Answer:
150
Step-by-step explanation:
To find the surface area of a cube, you do 6a^2. That would mean it is 150.