The distance between the ship and the base of the is approximately 359.32 feet.
The distance between the ship and the base of the lighthouse can be found using the tangent of the angle of elevation.
The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the lighthouse (160 feet) and the adjacent side is the distance between the ship and the base of the lighthouse (x).
So, we can set up the equation:
tan(24) = 160/x
To solve for x, we can cross multiply and then divide:
x * tan(24) = 160
x = 160/tan(24)
Using a calculator, we can find that tan(24) is approximately 0.4452.
So, x = 160/0.4452
x = 359.32 feet
Therefore, the distance between the ship and the base of the lighthouse is approximately 359.32 feet.
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Pls solve asap helpppppppp please immediately it due soon
The number of squares wide needed is 7 squares and the number that can be used to replace A is 0.1 km.
What are Grid squares:Grid squares are a way to represent two-dimensional space using a grid of squares, with each square representing a unit of length.
Grid squares are often used in various fields, such as computer graphics, geographic information systems, and mathematics, to represent and manipulate two-dimensional data.
Here we have
The table shows the distance traveled in a time period
The maximum time is shown in a table = 35 minutes
Let 1 unit = 5 minutes
Number of squares used to represent 35 minutes = 35/5 = 7
Therefore, the number of squares wide needs = 7 blocks
Given that the grid is 20 squares tall
The maximum distance in a table = 1.8 km
Let's take the total distance = 2 km
The number of squares along length = 2 km/20 = 0.1
Therefore,
The number of squares wide needed is 7 squares and the number that can be used to replace A is 0.1 km.
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The graph of f(x)=x^2 was transformed to create g(x)=2/3x^2 Mark the statement. True or False
The graph of g(x) will be wider than f(x)
Graph of g(x) will be wider than f(x) is false.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The graph of f(x)=x² was transformed to create g(x)=2/3x².
The transformation applied to f(x) to create g(x) is a vertical compression by a factor of 2/3.
This means that the graph of g(x) will be narrower than the graph of f(x), not wider.
Specifically, the parabola of g(x) will be compressed vertically towards the x-axis by a factor of 2/3, making it more pointy than the original graph of f(x).
Hence, graph of g(x) will be wider than f(x) is false.
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Evaluate 5d - 25/5 if d = 8
Answer:
=35
Step-by-step explanation:
5d - 25/5
5(8) -25/5
40 - 5
=35
Answer:
the answer is 35
Step-by-step explanation:
d=8, therefore plug 8 into the equation
5d - [tex]\frac{25}{5}[/tex]
5(8)- [tex]\frac{25}{5}[/tex]
40-5
35
Question
Gerard worked the same number of hours, x, on Monday, Tuesday, and Wednesday, but on Thursday, he worked 5 hours less than the previous day. The total number of hours Gerard worked can be found using the expression, 4x−5 .
What does the "4" represent in the expression, 4x−5 ?
--------------------------------------------------------------------------------
the number of hours Gerard worked on Thursday
the number of hours Gerard worked each day
the total number of hours Gerard worked
the number of days Gerard worked
The number "4" in the expression 4x - 5 represent the number of days Gerard worked.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
Gerard worked the same number of hours, x, on Monday, Tuesday, and Wednesday, but on Thursday, he worked 5 hours less than the previous day.
The total number of hours Gerard worked can be found using the expression, 4x − 5
Hence:
The number "4" in the expression 4x - 5 represent the number of days Gerard worked which is Monday, Tuesday, and Wednesday and Thursday
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Use the suggested substitution to write the expression as a
trigonometric expression. Simplify your answer as much as possible.
Assume 0≤θ≤π2.
√9−9x2, x=cos(θ)
The expression √9−9x2 can be written as a trigonometric expression 3sin(θ) using the substitution x = cos(θ).
To write the expression as a trigonometric expression using the suggested substitution, we can substitute x = cos(θ) into the expression and simplify:
√9−9x2 = √9−9(cos(θ))^2
= √9−9(cos^2(θ))
= √9(1−cos^2(θ))
= √9(sin^2(θ))
= 3sin(θ)
Therefore, the expression √9−9x2 can be written as a trigonometric expression 3sin(θ) using the substitution x = cos(θ).
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Asanji wants to buy a wagon for $93.26. He gives the cashier $100. How much change does he receive?
Answer:
6.74
Step-by-step explanation:
100 - 93.26
Answer:
$6.74
Step-by-step explanation:
100.00 - 93.26 = 6.74
Helping in the name of Jesus.
solve the system of linear equation by elimination 8x+3y=-5
3y=x+4 please show work
The solution of linear equations is (x, y) = (-0.8905, 0.708).
To solve this system of linear equations by elimination, first multiply both equations by the same number so that when you add the equations together, one of the variables is eliminated. In this case, we'll multiply the first equation by 3 and the second equation by 8.
8(8x+3y=-5)
3(3y=x+4)
24x + 9y = -15
24y = 8x + 32
Now add the two equations together:
24x + 24y = -15 + 32
24x + 24y = 17
Simplifying this equation, we get:
24y = 17
y = 17/24
y = 0.708
Now, plug in the value of y into one of the original equations to solve for x. We'll use the first equation:
8x + 3(0.708) = -5
8x + 2.124 = -5
8x = -7.124
x = -7.124/8
x = -0.8905
Therefore, the solution to the system of linear equations is (x, y) = (-0.8905, 0.708).
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I bought a toy car for $7.55, a pizza for $3.75 and a pencil for $0.75. How much money did I spend altogether?
Answer:
To find the total amount of money spent on the toy car, pizza, and pencil, we simply need to add the individual prices together:
$7.55 (toy car) + $3.75 (pizza) + $0.75 (pencil) = $12.05
Therefore, you spent $12.05 altogether on the toy car, pizza, and pencil.
etermine whether the equation is condi 10[4-(3-2x)]+4x=3(8x+4)-2 s the equation a conditional, an identity, or
10[4-(3-2x)]+4x=3(8x+4)-2 is an identity equation.
To determine whether the equation is a conditional, an identity, or a contradiction, we need to simplify the equation and see if it is true for all values of x, true for some values of x, or false for all values of x.
First, let's simplify the equation:
10[4-(3-2x)]+4x=3(8x+4)-2
10[4-3+2x]+4x=24x+12-2
10[1+2x]+4x=24x+10
10+20x+4x=24x+10
24x-24x=10-10
0=0
Since the equation is true for all values of x, it is an identity equation. An identity equation is an equation that is true for all values of the variable.
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the two triangles in the diagram are similar there are 2 possible values for x
The possible values of x are 2 and 17
How to determine the possible values of xThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Similar triangles
In the triangles, we have the following possible equations
15/18 = 10/(10 + x)
10/18 = 15/(10 + x)
Solving the equations, we have
15/18 = 10/(10 + x)
150 + 15x = 180
15x = 30
x = 2
10/18 = 15/(10 + x)
100 + 10x = 270
10x = 170
x =17
Hence, the values of x are 2 and 17
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Complete Question
The two triangles in the diagram are similar there are 2 possible values for x
See attachment for image of the triangle
The equations y1 = 2x + 1 and intersect at a point. After three cycles of successive approximation, without rounding the answers, the approximate x-value of the point of intersection is
The intersection point on the graph has an approximate x-value of 1a.
Describe graphs?Making the curve that represents a function on a coordinate plane is the process of graphing a function. If the curve (or graph) represents the function, then each point on the curve will satisfy the function equation.
The line, also called the "curve," has a point at each point that fulfils the function.
The three lines are contemporaneous if they all cross at the same point.
From the second equation,
x = 8y + 19
Putting value of x,
2(8y + 19) + 3y = 0 9(8y + 19) + 5y = 17
16y + 38 + 3y = 0 72y + 171 + 5y = 17
19y = -38 77y = -154
y = -2 y = -2
You'll see that the y value for the answer is the same for the two equations. Simply evaluate the second equation now to find x. Hence, we are aware that the y-coordinate is negative two at some x number.
x = 8(-2) + 19
x = -16 + 19
x = 3
The single point that these three equations share is (3, -2).
4x - 3y = 13 eq1
-6x + 2y = -7 eq2
Use the elimination method. Multiply eq1 by eq2 and multiply eq2 by eq3.
8x - 6y = 26 eq1
-18 + 6y = -21 eq2
Adding the equations to eliminate the y terms.
-10x = 5
x = -1/2
Substituting this value of x into any of the equations to solve for the value of y.
Substituting the first equation into the second equation. In terms of x, this will translate the second equation. From that freshly created equation, find x. Once you solved for x, substitute that value of x into the first equation to solve for y.
You have a vertical line that passes all points that have the x coordinate 7 and you have a horizontal line that passes all point that have the y coordinate -5.
If you were to graph these two lines, they will be intersecting at (7, -5).
Now, draw the following lines on a coordinate system:
i) A vertical line passing through the points (3, 0).
ii) A horizontal line passing through the point (0, 6).
iii) A line passing through the points (0,0) and (1, -3).
Once you have drawn these lines, look for 3 points of intersection.
Area = (base × height) / 2
Lines that have the same slope never intersect. Put both equations in y=mx+b form where the slope is the coefficient of x.
2x + 3y = > 3y = -2x + 23
y = (-2 / 3) x + 23/3
7x + py = 8
py = -7x + 8
y = (-7 / p) x + 8/p
Set the slopes equal to each other.
-2 / 3 = -7 / p
Cross-multiply.
-2p = -21
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Apply the Empirical RuleA 3-column table has 1 row. The first column is labeled Age with entry 7 years. The second column is labeled Mean with entry 49 inches. The third column is labeled Standard Deviation with entry 2 inches. According to the empirical rule, 68% of 7-year-old children are between inches and inches tall.
The empirical norm therefore states that 68% of 7-year-old kids are between 47 and 51 inches tall.
What does a table column mean?A column in a table is a collection of cells which are arranged vertically. A field, like the received field, is a sort of element that contains only one item of data. A column in a table usually contains the values for just a single field.
The empirical rule states that in a normal distribution, 68% of the data fall within one average standard deviation. In this instance, the mean difference is 2 inches, while the average height of 7-year-old kids is 49 inches.
We must identify the range among heights that is within one average standard deviation in order to apply the scientific rule. To accomplish this, we can add and subtract the standard variance from the median as follows:
Mean ± (Standard Deviation) = 49 ± 2
As a result, the height range which falls within the standard deviation from the average is between 47 and 51 inches.
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if (5x-1)/(2)can be written in the equivalent form (3x-6)/(3), what is the value of (5-x)/(2)
The value of [tex](5 - x)/(2)[/tex] is [tex]2[/tex] when[tex](5x - 1)/(2)[/tex] is equivalent to [tex](3x - 6)/(3)[/tex].
The given expression is [tex](5x - 1)/(2)[/tex] and it can be written in the equivalent form [tex](3x - 6)/(3)[/tex].
To find the value of [tex](5 - x)/(2)[/tex], we can use the property of equivalent fractions, which states that if two fractions are equivalent, then the cross products are equal.
So, we can cross multiply the given equivalent fractions to get:
[tex](5x - 1)(3) = (3x - 6)(2)[/tex]
Simplifying the equation, we get:
[tex]15x - 3 = 6x - 12[/tex]
[tex]9x = 9[/tex]
[tex]x = 1[/tex]
Now, we can substitute the value of x into the expression [tex](5 - x)/(2)[/tex] to find the value of the expression:
[tex](5 - 1)/(2) = 4/2 = 2[/tex]
Therefore, the value of [tex](5 - x)/(2)[/tex] is 2 when [tex](5x - 1)/(2)[/tex] is equivalent to [tex](3x - 6)/(3)[/tex].
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9. A box contains three blue bulbs, four green bulbs and five red bulbs. Four bulbs taken out of the box at random and without replacements. What is the probability that: (1) are the first two are of the same colour and the last two are of different colours.
The probability that the first two bulbs are of the same colour and the last two are of different colours is 25/48.
The probability that the first two bulbs are of the same colour and the last two are of different colours is calculated as follows:
Given:
n(B) = 3 (Number of blue bulbs)
n(G) = 4 (Number of green bulbs)
n(R) = 5 (Number of red bulbs)
Formula: P(A) = n(A) / n(S)
Where,
P(A) = Probability of event A
n(A) = Number of favorable outcomes
n(S) = Number of possible outcomes
The probability of selecting two bulbs of the same colour is calculated as:
P(SS) = n(B) * n(B) / n(S)
= 3 * 3 / 12
= 1/4
The probability of selecting two bulbs of different colour is calculated as:
P(DD) = n(B) * n(G) * n(R) * n(R) / n(S)
= 3 * 4 * 5 * 5 / 12
= 25/12
Therefore, the required probability is calculated as:
P(SSDD) = P(SS) * P(DD)
= 1/4 * 25/12
= 25/48
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Which description best represents the end behavior of the
function f(x)= -x + 5x³ - 2x+5?
Hint: Use the examples in the table to help you answer the
question.
Polynomial End Behavior
Equation Degree Leading Coefficient
y-x²
y=-x²
y=x³
y=-x³
Even
Even
Odd
Odd
Positive
Negative
Positive
Negative
End Behavior
x)+∞, as x-+
F(x), as x--
F(x), as x4+
x), as x--co
x) +∞, as
x-+00
x) +00, as x--
x)-00, as x-+00
Example
The correct description for best represents the end behavior of the
function f (x) = - x⁴ + 5x³ - 2x + 5 is,
⇒ The right-end is y → - ∞ as x → ∞ . The right-end is rising.
The left-end is y → - ∞ as x→ - ∞ . The left-end is falling.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = - x⁴ + 5x³ - 2x + 5
Now, We have;
Degree of the polynomial = 4
Hence, We get;
⇒ The right-end is y → - ∞ as x → ∞ . The right-end is rising.
The left-end is y → - ∞ as x→ - ∞ . The left-end is falling.
Thus, The correct description for best represents the end behavior of the
function f (x) = - x⁴ + 5x³ - 2x + 5 is,
⇒ The right-end is y → - ∞ as x → ∞ . The right-end is rising.
The left-end is y → - ∞ as x→ - ∞ . The left-end is falling.
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In a direct variation, the variable k is the ?
Answer: slope of the line
Step-by-step explanation: I'm not sure if we're talking about the same thing though
Answer: The slope (stands in for m)
Step-by-step explanation:
In a direct variation, the variable m (slope) is swapped for k.
Looking at the bookshelf in the library Neil notices that the number of books that he
has read is
7
of the books he did not read. If he reads one more book from the
bookshelf and puts it back this fraction becomes 1. How many books are there on
the bookshelf?
6
There are 14 books on the bookshelf as a result.
How was the number of books on the shelf determined?Assume that there are x total books on the bookshelf. Neil has read 7 out of a total of 7 + (x-7) = x-0 books, which means that he has read 7/14 of the books, according to the problem. This is reduced to 1/2.
Now that he has read 8 out of 15 books, his percentage of books read will be 8/15 if he reads one more (the original 7 books he read plus the one he read now). This implies:
8/15 = 8/(x+1)
In order to find x, we can cross-multiply:
8(x+1) = 15(8) (8)
8x + 8 = 120
8x = 112
x = 14
There are 14 books on the bookshelf as a result.
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The exact same experiment was conducted 15 times. How many times should the results have been similar for them to be valid?
A. 6
B. 15
C. 9
D. 8
In a survey of 300 members of a local sports club, 150 members indicated that they plan to attend the next Summer Olympic Games, 90 indicated that they plan to attend the next Winter Olympic Games, and 60 indicated that they plan to attend both games. How many members of the club plan to attend (a) At least one of the two games? members (b) Exactly one of the games? members (c) The Summer Olympic Games only? members (d) None of the games? members
a) At least one of the two games? - 300 members
b) Exactly one of the games? - 240 members
c) The Summer Olympic Games only? - 150 members
d) None of the games? - 60 members
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Karen used 186 digits to number a book from page 4 to the end. What is the number of the last page?
Answer:
Step-by-step explanation:
its 190 because you started on page 4 and you add 186
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 9 inches, and the length of the base is 7 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch. Thanks!!!
Answer:
26.3 inchesStep-by-step explanation:
We separate into 2 congruent triangles. Both have a base of 3.5 and a height of 9 inches. Using pythagoran theorum, we will square 9 and 3.5
81 and 12.25
Add them up and it's 93.25
[tex]\sqrt{93.25}[/tex]=9.65660395791
Now since it's isosceles, the other side will also be 9.65660395791.
9.65660395791 + 9.65660395791 + 7 =26.3132079158
You want it rounded to the nearest tenth, so 26.3
You randomly draw a marble from a bag, record its color, and then replace it. You draw a blue marble 23 out of 25 times. What is the experimental probability that the next marble will be blue? Write your answer as a fraction, decimal, or percent.
The next marble's experimental probability of being blue, according to an experiment, is: 23/25.
Explain about the experimental probability?Based on empirical data, experimental probability is the likelihood that an event will occur. A theoretical probability would be obtained by dividing the number of different ways to achieve the desired result by the total number of outcomes.
A marble is drawn at random from a bag, its colour is noted, and it is then replaced.In 23 of the 25 draws, a blue marble is produced.The next marble's likelihood of being blue, according to an experiment, is:
Experimental probability = Number of time blue appears / Total outcomes
Experimental probability = 23/25
Thus, the next marble's experimental probability of being blue, according to an experiment, is: 23/25.
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What is the difference of the LCM and GCF of 30 and 55?
Answer:
The difference between the LCM and the GCF of 30 and 55 are that the LCM is the smallest positive integer that is divisible and the GCF is the largest positive integer that divides each of the integers.
Step-by-step explanation:
Find the present value PV of the annuity necessary to fund the withdrawal given. HINT [See Example 3.] (Assume end-of-period withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.) $500 per month for 15 years, if the annuity earns 6% per year PV = $
The present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.
The present value of an annuity is calculated using the following formula:
PV = A[((1+i)n-1)/(i(1+i)n)]
where A = amount of each annuity payment, i = interest rate, and n = number of payments.
For this problem, A = $500, i = 6%, and n = 15 years.
Therefore, the present value of the annuity necessary to fund the withdrawal is:
PV = $500[((1+0.06)15-1)/(0.06(1+0.06)15)]
PV = $500[5.72982/0.105638]
PV = $5,354.82
Therefore, the present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.
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how do i convert an improper fraction to mixed number
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The three equations that have the same value of x as the original equation are:
18x - 15 = 72
3(6x - 3) = 72
x = 4.5
What is an equation?
An equation is a statement that two expressions are equal. It typically contains one or more variables (represented by letters) and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to represent relationships between quantities or to solve for unknown values.
The correct options are:
18x - 15 = 72
18x - 9 = 72
x = 4.5
To see why, we can start by simplifying the original equation:
Three-fifths (30x - 15) = 72
(3/5)(30x - 15) = 72
18x - 9 = 72
18x - 15 = 72 + 15
18x = 87
x = 87/18
So we see that x = 87/18 is the solution to the original equation.
Now let's check each of the answer choices:
18x - 15 = 72
Solving for x, we get x = 87/18, which is the same as the solution to the original equation. This equation is equivalent to the original equation.
50x - 25 = 72
Solving for x, we get x = 97/50, which is not the same as the solution to the original equation. This equation is not equivalent to the original equation.
18x - 9 = 72
Solving for x, we get x = 81/18 = 9/2, which is not the same as the solution to the original equation. This equation is not equivalent to the original equation.
3(6x - 3) = 72
Simplifying, we get 18x - 9 = 72, which is equivalent to the second equation listed above. So this equation is also equivalent to the original equation.
x = 4.5
This is the same solution as the original equation, so this equation is also equivalent to the original equation.
Therefore, the three equations that have the same value of x as the original equation are:
18x - 15 = 72
3(6x - 3) = 72
x = 4.5
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Prove for the simple decision sapling (sure thing of value r vs. risky gamble), that EVPI > 0. Also prove that if the random payoff of the gamble, call it G, is replaced by the random variable G+Y where Y is independent of G and EY = 0 (so G’ = G+Y is a noisy, or more variable, version of the original gamble G), then the EVPI will be larger. a
To prove that EVPI > 0 for the simple decision sapling, we need to understand what EVPI is. EVPI stands for Expected Value of Perfect Information, and it is the difference between the expected value of the decision with perfect information and the expected value of the decision without perfect information.
For the simple decision sapling, we have two options: a sure thing of value r, and a risky gamble with a random payoff G. The expected value of the decision without perfect information is simply the maximum of the two options:
EV = max(r, EG)
The expected value of the decision with perfect information is the maximum of the two options, knowing the outcome of the gamble:
EVPI = max(r, G) - max(r, EG)
Since we know that G is a random variable, the expected value of G is simply the average of all possible outcomes. Therefore, the expected value of the decision with perfect information is simply the maximum of the two options, knowing the average outcome of the gamble:
EVPI = max(r, EG) - max(r, EG) = 0
Therefore, EVPI > 0 for the simple decision sapling.
To prove that the EVPI will be larger if the random payoff of the gamble is replaced by a noisy version of the original gamble, we need to understand how the expected value of the decision changes with the addition of the noise variable Y. The expected value of the decision without perfect information is now:
EV = max(r, EG + EY) = max(r, EG)
Since EY = 0, the expected value of the decision without perfect information does not change. However, the expected value of the decision with perfect information now becomes:
EVPI = max(r, G + Y) - max(r, EG)
Since Y is a random variable with mean 0, the expected value of Y is 0. However, the variance of Y is not necessarily 0, which means that the addition of Y adds variability to the decision. This means that the expected value of the decision with perfect information is now larger, because we have more information about the possible outcomes of the gamble. Therefore, the EVPI will be larger when the random payoff of the gamble is replaced by a noisy version of the original gamble.
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Statistics question, please explain what type of problem it is and how to do it
In a group of 60 students; 30 go for extra help and 22 study at home only. Find the probability that a person picked from this group at random is either going for extra help or only studying at home?
The probability that a person chosen at random from this group will either seek further assistance or merely study at home is 5/6, or roughly 0.833. (rounded to three decimal places).
What is the probability formula?Typically, the probability is defined as the ratio of favourable events to all other outcomes in the sample space. The formula for probability of an occurrence is P(E) = (Number of favourable outcomes) (Sample space).
The formula is as follows:
P(AorB) = P(A)+P(B)-P(AandB)
where A and B are two events.
Then, we have:
P(A) = 30/60 = 1/2 (since 30 out of 60 students go for extra help)
P(B) = 22/60 (since 22 out of 60 students study at home only)
Using the formula, we can then find:
P(AorB) = P(A)+P(B)-P(AandB)
= 1/2 + 22/60 - 0
= 5/6
Hence, the probability that someone chosen at random from this group will either seek further assistance or merely study at home is 5/6, or roughly 0.833. (rounded to three decimal places).
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PLEASE HELP A GIRL OUTTTT ITS DUE FOR TMR
Answer:
8x^2-4x-15
Step-by-step explanation:
To find the sum of the functions, we add them together:
f(x) + g(x) = (5x + 4) + (3x² - 9)
Simplifying, we get:
f(x) + g(x) = 3x² + 9x - 5
Therefore, the sum of the functions is 3x² + 9x - 5, which is option D.
i would appreciate anyone's help. thank you!
The equation of the volume of the box in terms of x is 4x³ - 40x² +100x.
What is the V(x) function's domain?The set of all conceivable values of x that make sense in the context of the issue constitutes the domain of the function V(x). This time, x must be a positive value less than or equal to 5, as it reflects the length of the side of the square that was cut out of each corner of the cardboard. The range of V(x) is thus 0 x 5.
Given that, the squares cut at the end are x inches.
Thus the dimension of the rectangular box are:
The length of the box will be (10-2x).
The width of the box will be (10-2x).
The height of the box will be x inches.
The volume of the rectangular box is given by:
V = (l)(w)(h)
Substituting the values we have:
V(x) = (10-2x)(10-2x)x = x(100-40x+4x^2) = 4x³ - 40x² +100x.
Hence, the equation of the volume of the box in terms of x is 4x³ - 40x² +100x.
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