The volume of the spherical segment above the plane is[tex](1/3) *\pi * (r^2 - (r-h)^2) * h[/tex] and the volume of the ring resulting from drilling a hole through the center of a sphere is [tex]\pi * (R^2 - r^2) * R.[/tex].
A sphere of radius "r" is cut by a plane "h" units above the equator. To find the volume of the solid (spherical segment) above the plane, we first need to find the height of the segment, which is (r - h). Then, we can use the formula for the volume of a spherical segment: [tex](1/3) * \pi * (r^2 - (r-h)^2) * h.[/tex]
A manufacturer drills a hole through the center of a metal sphere of radius R. The hole has a radius r. To find the volume of the resulting ring, we can use the formula for the volume of a cylindrical ring: [tex]\pi * (R^2 - r^2) * h[/tex], where h is the height of the ring. Since the hole goes all the way through the sphere, the height of the ring is equal to the radius of the sphere, R. So the volume of the ring is [tex]\pi * (R^2 - r^2) * R[/tex].
In the first problem, the volume of the solid (spherical segment) above the plane is [tex](1/3) * \pi * (r^2 - (r-h)^2) * h[/tex]. In the second problem, the volume of the resulting ring is [tex]\pi * (R^2 - r^2) * R.[/tex]
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Haile Resort opened for business on June 1 with eight air conditioned units. Its trial
balance on August 31 is as follows.
Haile Resort
Trial Balance
August 31, 2022
Debit Credit
Cash Br. 39,200
Prepaid Insurance 9,000
Supplies 5,200
Land 40,000
Buildings 240,000
Equipment 32,000
Accounts Payable Br. 9,000
Unearned Rent Revenue 9,200
Mortgage Payable 100,000
Share Capital—Ordinary 200,000
Retained Earnings 0
Dividends 10,000
Rent Revenue 172,400
Salaries and Wages Expense 89,600
Utilities Expense 18,400
Maintenance and Repairs Expense 7,200
Br.490,600 Br.490,600
Other data:
1. The balance in prepaid insurance is a 1-year premium paid on June 1, 2022.
2. An inventory count on August 31 shows Br.1,300 of supplies on hand.
3. Annual depreciation rates are buildings (4%) and equipment (10%).
4. Unearned rent revenue of Br.7,600 should be recognized as revenue prior
to August 31.
5. Salaries and wages of Br.750 were unpaid at August 31.
6. Rentals of Br.1,600 were due from tenants at August 31.
7. The mortgage note is dated 1/1/2022. The mortgage interest rate is 8% per
year.
Instructions
a. Journalize the adjusting entries on August 31 for the 3-month period
June 1–August 31.
b. Prepare an adjusted trial balance on August 31.
Answer:
Step-by-step explanation:
Answer:
So the answer is
FMA Assignment 01
1. Jornal
2. Date (Mar) Accounts Title Debit ($) Credit ($)
1 Cash 60,000
Common Stock 60,000
3 Land 23,000
Buildings 9,000
Equipment 6,000
Cash 38,000
5 Advertising Expenses 1,600
Cash 1,600
6 Prepaid Insurance 1,480
Cash 1,480
10 Equipment 26,000
Accounts Payable 26,000
18 Cash 800
Golf Revenue 800
19 Cash (100 x 15) 1,500
Unearned Revenue 1,500
25 Dividends 1,000
Cash 1,000
30 Salaries Expenses 600
Cash 600
30 Accounts Payable 26,000
Cash 26,000
31 Cash 500
Golf Revenue 500
Brenda is placing tile on her
bathroom floor. The area of the
floor is 15x2-8x - 7 ft². The area
of one tile is x² - 2x + 1ft². To find
the number of tiles needed,
simplify the rational expression:
15x²-8x-7
x²–2x+1
(15x+7)/(x-1) is the simplified rational expression
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Polynomials are algebraic expressions made up of coefficients and variables. Occasionally, variables are referred to as indeterminates. We can execute arithmetic operations on polynomial expressions, such as addition, subtraction, multiplication, and positive integer exponents, but not division by variables.
Factors of 15x²-8x-7 are (15x+7)(x-1)
Factors of x²–2x+1 are (x-1)²
15x²-8x-7 / x²–2x+1 = (15x+7)(x-1) / (x-1)²
common factors cancel out
(15x+7)/(x-1) is the simplified rational expression
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A machinist must cut 12 strips of metal that are each 2 ft 6 7/8 in. long. What is the total length needed in inches?
The total length of the metal strips needed in inches is 370.5 inches
How to convert feet to inches?Number of strip metals = 12
Length of each strip metal = 2 ft 6 7/8 in.
Convert feet to inches:
1 feet = 12 inches
2 feet = 24 inches
2 ft 6 7/8 in = 30 7/8 inches
Total length of strip metals= Number of strip metals × Length of each strip metal
= 12 × 30 7/8 inches
= 12 × 247/8
= 2,964/8
= 370.5 inches
So therefore, the total length of the metal strips is 370.5 inches
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The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.Multiple Choice - Please provide how the answer is found.1)The decay rate is:a. 0.3333b. 0.5000c. 2d. 32)What is the median lifetime of these phones (in years)?a. 0.1941b. 1.3863c. 2.0794d. 5.5452
The decay rate of the cell phones is 0.3333, and the median lifetime of the phones is 2.0794 years.
The decay rate of the cell phones is 0.3333, and the median lifetime of the phones is 2.0794 years.
1)a. 0.3333
2)c. 2.0794
1)The decay rate is found by dividing 1 by the average lifetime (in this case, 3 years). Therefore, the decay rate is 1/3 = 0.3333.
2)The median lifetime of these phones is found by taking the natural logarithm of 0.5 (which is the probability of the phone failing within 2 years) and dividing it by the decay rate (0.3333). Therefore, the median lifetime is ln(0.5)/0.3333 = 2.0794.
The decay rate of the cell phones is 0.3333, and the median lifetime of the phones is 2.0794 years.
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decide if you are given enough information to prove that the quadrilateral is a parallelogram practice c
No, you are not given enough information to prove that the quadrilateral is a parallelogram.
In order to prove that the quadrilateral is a parallelogram, we must have four points to calculate the lengths of the sides and angles. We need to verify that the opposite sides of the quadrilateral are equal in length and that the opposite angles are equal. We can use the formula for the area of a parallelogram: A = b*h, where b is the length of the base and h is the height of the parallelogram. We can also use the formula for the sum of the angles of a quadrilateral: A1 + A2 + A3 + A4 = 360 degrees. Without having the four points, we cannot calculate the lengths of the sides or angles, so we cannot prove that the quadrilateral is a parallelogram.
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Please answer it asap, it's missing
To find the value of f(g(-4)), we need to first substitute -4 into the definition of g(x) and then substitute the result into the definition of f(x).
First we substitute -4 into g(x):
g(-4) = 2(-4)^2 + 4(-4) - 8
g(-4) = 2(16) + (-16) - 8
g(-4) = 32 - 16 - 8
g(-4) = 8
Now we substitute 8 into f(x):
f(g(-4)) = f(8) = 2(8) - 4 = 16 - 4 = 12
So the value of f(g(-4)) is 12.
Answer:
28
Step-by-step explanation:
The expression: f(g(-4)) just means calculate the value of g at x = -4 and then calculate what f is equal to at that value g is equal to, so we have to first calculate g(-4) which we can do by substituting in -4 as x.
g(-4) = 2(-4)^2 + 4(-4) - 8
g(-4) = 2(16) - 8 - 8
g(-4) = 32 - 16
g(-4) = 16
Now from here we can substitute 16 as g(-4) in the expression f(g(-4)) which means we want to evaluate g(16) which we can do by substituting in 16 as x.
f(16) = 2(16) - 4
f(16) = 32 - 4
f(16) = 28
So that means f(g(-4)) = 28
convert 47 in^2 into square centimeters?
47 square centimeters is equal to 303.225 square inches.
How is cm2 converted from cm?
Measure the length and width of an object, such as a rectangle, and multiply the results to get the number in square centimeters. In the event that the length and width are 15 cm and 10 cm, respectively, the formula is 15 cm*10 cm, which equals 150 cm2.
Any number that is multiplied by itself is transformed into a square. A different word for this is a number squared. The symbol for "squared" is 22 since 2 x 2 equals 4.
In mathematics, the squared sign (2), an arithmetic operator, stands in for multiplying an integer by itself. The "square" of an integer is the sum of that number and itself. Therefore, 10,000 square meters are represented by one square centimeter.
1 square inch = 6.4516 square centimeters.
47 in^2 = 47 × 6.4516
= 303.225 sq. cm
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...........,.........,
Answer:
Step-by-step explanation:bmmmv m
suppose you are solving a regression problem. you have 1000 labeled examples and decide to use ridge regression
Ridge regression is a type of linear regression used to reduce the effects of multi-collinearity. It is used with 1000 labeled examples to minimize the sum of the squared errors of the model.
Ridge regression is a type of linear regression used to reduce the effects of multi-collinearity. It adds a penalty term to the cost function that penalizes large coefficients, thus reducing their magnitude. The penalty term is a regularization term that is added to the cost function to minimize overfitting. To use ridge regression, one must select a value for the regularization parameter. This parameter determines how much the model weights the penalty term, and is usually determined through cross-validation. With 1000 labeled examples, ridge regression can be used to minimize the sum of the squared errors of the model. The model is then trained on the data, and predictions can be made. Ridge regression is a powerful tool for reducing the effects of multi-collinearity, and can be used to accurately model relationships between variables.
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2.87 x 7.8
eeeeeeeeeeeeeee
Answer:
22.386
Step-by-step explanation:
determine whether the relation represents y as a function of x
x = y^2
determine whether the relation represents y as a function of x
x^2 + y^2 =25
show work
It is false that x is a function of y
How to determine the truth or falsity?The given equation to be used to determine the truth and falsity of the statement is given as:
The given parameters are function of x
x = y²
determine whether the relation represents y as a function of x
x^2 + y^2 =25
x = y²
Set y = 2
x = (2)²
Taking the square root of the value
x = 4
Set y = -2
x = (-2)²
x = 4
From the experiment, the different values of y give the same x value.
therefore, this means that x is not a function of y
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Chose two situations that describe volume
A measuring
The two situations that describe the volume:
A. the amount of shampoo in a bottle.
B. the amount of soap in a bar of soap.
What is volume?The space occupied by an object in three-dimensional space is called the volume of an object. In simple words, space is taken by an object.
Four phrases are given.
A. the amount of shampoo in a bottle.
This describes the volume.
B. the amount of soap in a bar of soap.
This also describes the volume.
c. the amount of border around a chalkboard.
This describes the perimeter.
D. the amount of wrapping paper covering a gift
This describes the surface area.
Therefore, A and B describe the volume.
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The complete Question:
Choose all the examples that describe volume.
A. the amount of shampoo in a bottle
B. the amount of soap in a bar of soap
c. the amount of border around a chalkboard
D. the amount of wrapping paper covering a gift
John is 6 feet tall and standing 4 feet from a tree. If Johns shadow is 12 feet long, how tall is the tree
The height of the tree is 8 feet.
What are Similar triangles:Triangles which has the same shape but are different in size are said to be similar triangles for example all equilateral triangles are similar triangle.
It is also defined as if the corresponding sides of two triangles are in proportion then the two triangles are said to be a similar triangles. The symbol ‘~’ is used to denote the similarity between two triangles.
If two triangles ΔABC and ΔXYZ are two similar triangles then the condition between corresponding sides is given by
AB: XY = BC: YZ = AC: XZHere we have
John's height is 6 feet
He standing 4 feet from a tree
Johns's shadow is 12 feet long
We can represent the whole scenario as two similar triangles
[ Picture is given below ]
As we know in Similar triangles the ratio of corresponding sides is equal
Let 'x' be the height of the tree
From given figure
=> AC: DE = BC: EB
=> x : 6 = 16 : 12
=> x/6 = 16/12
=> 12x = 16 × 6
Divided by 6
=> 2x = 16
Divided by 2
=> x = 8
Therefore,
The height of the tree is 8 feet.
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In the figure below lines A and B are parallel.Find the m<5 if m<1=75 and m <3=40
The unknown angle in the parallel lines is a follows;
m∠5 = 75 degrees
How to find angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.
Therefore, let's use the angle relationships to find the m∠5 in the parallel lines.
The angle m∠1 and m∠5 are corresponding angles.
Corresponding angles are congruent.
Therefore,
m∠1 = m∠5 = 75 degrees.
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A linear relationship is given in the table.
x y
−1 6
0 3
1 0
2 −3
What is the slope of the relationship?
−3
−2
2
3
From the given points, it was found that the slope is m= -3.
Linear FunctionYou can correlate two data from a function. An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=9x+5. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=9 and b=5.
The question gives some points of the linear function, see below.
x y
−1 6
0 3
1 0
2 −3
From the given data you can find the slope by solving the system linear equation.
You can write a system linear equation using the points: (-1,6) and (2,-3), for example.
6=m*(-1)+b (1)
-3=2m+b (2)
Multiplying equation 2 by -1, you have
6=-m+b (1)
3= -2m-b (2)
Summing the previous equation, you have:
9=-3m
m= -9/3
m= -3
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Answer: the answer is A
Step-by-step explanation: I took the text and got it right
two students just finished ba 215. sam slacker did not complete any of the career smart goals assignments and reports. denise diligence, on the other hand, took the assignment to heart (didn't just jump through hoops) and scored 95% on all of them. assuming that each point earned will result in a $1500 increase in salary 20 years from now, how much higher will denise's salary be than slacker's? enter your answer to the nearest whole dollar. do not include the $ symbol. hint: you will need to first know how many total points all of the smart goals assignments and reports (career preparation and development section of the syllabus) are worth in order to make the calculations.
The difference in salary will be $71,250.
What is multiplication in mathematics?
Multiplication is a mathematical operation that is used to find the product of two or more numbers. It is usually represented by the symbol "x" or "*", and is often referred to as repeated addition.
Career Preparation and Development (Career SMART Goals) worth 50 points.
Denise Diligence scored 95/100 on all of the assignments and reports, so she earned a total of 47.5 points.
Since each point earned will result in a $1500 increase in salary 20 years from now, Denise's salary will be $1500 x 47.5 = $71,250 higher than Slacker's.
Sam Slacker did not complete any of the career smart goals assignments and reports, so he earned a total of 0 points.
Hence, the difference in salary will be $71,250.
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Solve using the following equation and the listed values for the variables. Round your final answer to 2 decimal places A+B)/2) (a+b)/2) Where A = 21, B = 20,X = 19, Y = 20.
The average of two numbers, A and B, is calculated by adding them together and then dividing by two. In this case, A = 21, B = 20, X = 19, and Y = 20. When we calculate (A + B) / 2, we get 20.00.
1. Add A and B together: 21 + 20 = 41
2. Divide the sum by 2: 41 ÷ 2 = 20.50
3. Round the answer to two decimal places: 20.50 → 20.00
The average of two numbers, A and B, is calculated by adding them together and then dividing by two. This formula is expressed as (A + B) / 2. In this problem, we were given the values A = 21, B = 20, X = 19, and Y = 20. To solve for the average, we first need to add A and B together and get 41. Then we divide this sum by two and get 20.50. To get the final answer, we need to round this value to two decimal places, which results in the answer 20.00. This answer indicates that the average of 21 and 20 is 20.00.
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What is the vertex for the graph below ? 10 A . (- 2, 0) B . (0, - 2) . (2, 0) D . (0, 2)
The vertex for the graph is at (2, 0).
What is a parabola?A parabola is formed by cutting a right circular cone in half along a plane perpendicular to the cone's generator. It is a locus of a moving point whose separation from the focus is equal to its separation from a stationary line (directrix)
Focus is a fixed point.
Directrix is the name for fixed lines.
Given the graph is a parabola,
A parabola's vertex is the location where its symmetry line and parabola intersect. The vertices of a parabola whose equation is provided in standard form will be the lowest (lowest point) and highest (highest point) points on the graph, respectively.
The minimum point in graph is (2, 0)
Hence vertex is (2, 0).
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The complete question is in image,
data was collected at two local bookstores to determine if the average price of new textbooks was significantly lower at an independent bookstore than at the uf bookstore. the p-value was 0.00, and the 95% confidence interval was ( -11.98, -4.52).
An Interval is all the numbers between two given numbers. 95% confidence level would result in a wider confidence interval.
What is interval in math?
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.Introducing intervals, bounded collections of numerical values that are highly helpful in explaining domain and range. To demonstrate where a value lies in relation to two endpoints, we can use interval notation. For instance, the expressions -3x2, [-3,2], and xR|-3x2 all denote that x is between -3 and 2, and either endpoint could be it.An inequality can be used to find an interval. The interval employs the inequality symbols to show whether the endpoints are included in the interval and uses the boundaries of the inequality as endpoints. The interval is defined as the values lying between the endpoints.Given data :
confidence interval = ( -11.98, -4.52)
-11.98≤x≤-4.52, [-11.98,-4.52], and {x∈ℝ|-11.98≤x≤-4.52} all mean that x is between -11.98 and -4.52 and could be either endpoint.
95% confidence level would result in a wider confidence interval. Increasing the confidence level increases the length of the confidence interval.
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Simplify the expression 5y + 3x + 9
What is the coefficient of y?
What is the constant?
Answer:
Expression: 5y+3x+9
Coefficients: (of y) 5, (of x) 3
Constant: 9
Hope this helps :)
Step-by-step explanation:
The coefficient(s) of an equation will always be the number that sits next to/attached to a variable. The constant of an equation will always be the number(s) that stands alone.
the probability of rolling an even number when an unfair die is rolled is about 0.65. which of the following is closest to the probability that an even number is rolled 15 or fewer times when the die is rolled 25 times total
The probability that an even number is rolled 15 or fewer times when the die is rolled 25 times total can be calculated using the binomial probability formula. In this case, the probability of success is rolling an even number (0.65) and the number of trials is 25.
Using the binomial probability formula, we can calculate the probability of getting 15 or fewer even numbers when the die is rolled 25 times as follows:
P (X <= 15) = P (X = 0) + P (X = 1) + P (X = 2) + ... + P (X = 15)
Where X is the number of even numbers rolled and P(X) is the probability of getting X even numbers.
Using the binomial probability formula:
P(X) = (25 choose X) * (0.65)^X * (0.35)^(25-X)
Plugging in the values, we get:
P(X <= 15) = (25 choose 0) * (0.65)^0 * (0.35)^25 + (25 choose 1) * (0.65)^1 * (0.35)^24 + (25 choose 2) * (0.65)^2 * (0.35)^23 + ... + (25 choose 15) * (0.65)^15 * (0.35)^10
After calculating all the values, we get that the probability of rolling an even number 15 or fewer times when the die is rolled 25 times is about 0.28.
Therefore, the closest answer choice to the probability that an even number is rolled 15 or fewer times when the die is rolled 25 times is 0.25.
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given constants $a,$ $b,$ and $c,$ let $\alpha$ and $\beta$ be solutions to the equations \[a \cos \theta b \sin \theta
A constant is fixed, which is arbitrary since you don't know what that fixed number is the arbitrary denotes that no particular value has been ascribed.
The order of a differential equation is equal to the number of arbitrary constants in its general solution.
The highest-order derivative that a differential equation has is used to define the equation's order. The highest-order derivative of a differential equation is defined as its degree, which is expressed as a power. The formula:
c1=a1+ib1
and c2=a2+ib2
the solution will be
y(x)=(a1+ib1+a2+ib2)cos(ax)+i(a1+ib1−a2−ib2)sin(ax)
If and only if
a2=a1
and b2=−b1
will be the solution real because of complex conjugates using this property.
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Full question
Can arbitrary constants in solutions to 2nd-order linear differential equations be complex?
The data represent the time, in minutes, spent reading a political blog in a day. Construct a frequency distribution using classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest frequency and which has the least frequency?
10. 9. 5. 19. 17
13. 2. 0. 4. 10
1. 16. 9. 7. 3
15. 17. 18. 16. 6
The class interval [15-19] has the greatest frequency, and the class interval [10-14] has the least frequency
How to determine the frequency distributionFrom the question, we have the following parameters that can be used in our computation:
10. 9. 5. 19. 17
13. 2. 0. 4. 10
1. 16. 9. 7. 3
15. 17. 18. 16. 6
Using a class of 5, we have the following class intervals
0 - 4, 5 - 9, 10 - 14 and 15 - 19
When the frequencies of each class are counted, we have the following table
Interval Midpoint Frequency R/F C/F
0 - 4 2 5 5/20 5
5 - 9 7 5 5/20 10
10 - 14 12 3 3/20 13
15 - 19 17 7 7/20 20
using the above as a guide, we have the following:
The class interval [15-19] has the greatest frequency 7
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Solve:
(-4)^7*(-8^)^3+12/2=?
Show your work
Answer:
−16890
Step-by-step explanation:
Simplify the expression.
A bakery is selling breakfast platters. A platter of 12 bagels costs $9.60. Additionally, it costs $8.80 for a gallon of coffee.
What is the slope of this situation?
0.80
0.73
9.60
8.80
The slope of this situation is equal to: A. 0.80.
How to calculate the slope of this situation?In Geometry, the rate of change of any straight line simply refers to its gradient or slope and it can be calculated by using this mathematical expression;
Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Based on the information provided, we can logically deduce the following slope and data points on the line:
Points on x-axis = 12
Points on y-axis = 9.6.
Substituting the given data points into the slope formula, we have the following;
Rate of change (slope), m = 9.6/12
Rate of change (slope), m = 0.80.
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(3,7) & (-2,-1)
find the slope!!
The slope of the line passing through (3, 7) and (-2, -1) is 1.6
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
A linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the initial value
The slope of the line passing through (3, 7) and (-2, -1) is:
Slope = (-1 - 7) / (-2 - 3)
Slope = -8/-5 = 8 / 5
Slope = 1.6
The slope is 1.6
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The shipping container is a rectangular prism. Write a polynomial that represents the volume of the container. Express the answer in standard form.
The volume of the container is (x+6)(x-2)(x-1) cubic feet and it can be express as the form of polynomial.
Six faces make up the three-dimensional shape of a rectangular prism. The prism's faces are all rectangles. The shape of a rectangular prism is cuboidal.
There are two sets of parallel and congruent bases in this polyhedron. It has eight vertices, 12 sides, and six faces. Rectangular prisms are also known as a right rectangular prism, rectangular parallelepiped, and rectangular hexahedron.
Right rectangular prisms and oblique prisms are the two primary varieties of rectangular prisms. The bases of a right rectangular prism are parallel to the other faces.
The volume of a rectangular prism is simply the product of its three dimensions: in your case, the volume of the prism is, given x
[tex](x+6)(x-2)(x-1)[/tex]
A polynomial is a sum (with some coefficients) of powers of x, so, if we expand the product just written, we have.
[tex]=(x+6)(x-2)(x-1)\\\\=(x^2-2x+6x-12)(x-1)\\\\=(x^3+4x^2-12x-x^2-4x+12)\\\\=(x^3+3x^2-16x+12)[/tex]
Which is a polynomial and expresses the volume of the prism.
the complete question is,
How do you write a polynomial that represents the volume of a box that is a rectangular prism has the dimensions length x+6, width x-2, and height x-1?
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A car owner pays for new brakes that cost $756.25, with a credit card that has an annual rate of 24.5%. Determine the total amount paid, if the car owner pays $100 a month, until the balance is paid off.
The total amount paid with a monthly payment of $100 for a credit of $756.25 at an annual rate of 24.5% is $871.69.
What is a periodic payment?The periodic payment is the amount the car owner pays monthly to offset the balance on the credit card for purchasing new brakes.
The periodic payment is determined using an online finance calculator as follows:
N (# of periods) = 1 year
I/Y (Interest per year) = 24.5%
PV (Present Value) = $756.25
PMT (Monthly Payment) = $100
Results:
Sum of all periodic payments = $871.69
Total Interest = $115.44
Thus the total payment made by the car owner is $871.69 with an interest of $115.44.
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Answer:
$830.52
Step-by-step explanation:
I got it right on the test :)
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Find the height of the trapeziod.
Answer:
h = 6 m
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the perpendicular height between the bases b₁ and b₂
given A = 51 , b₁ = 10 and b₂ = 7 , then
[tex]\frac{1}{2}[/tex] h (10 + 7) = 51 ( multiply both sides by 2 to clear the fraction )
17h = 102 ( divide both sides by 17 )
h = 6 m
Find the height of the trapezoid.
if the area of the trapezoid is [tex]51m^{2}[/tex] and parallel sides are [tex]7m[/tex] and [tex]10m[/tex].
To find the height of the trapezoid, substitute the area and parallel sides into the formula for the area of the trapezoid.
Trapezoid area formula is
[tex]L=\frac{1}{2}(number of parallel sides)(height)\\ L=\frac{1}{2} (a+b)(t)[/tex]
The next step is substitute the area and parallel sides into the formula for the area of the trapezoid.
[tex]51=\frac{1}{2}(7+10)(t)[/tex]
Complete the arithmetic operation
[tex]51=\frac{1}{2}(17)(t)\\ 51=\frac{17}{2}(t)[/tex]
Multiply each side by [tex]\frac{2}{17}[/tex]
[tex]51(\frac{2}{17}) =\frac{17}{2}(\frac{2}{17})(t)\\ 6=t[/tex]
So the height of the trapezoid is [tex]6m[/tex]
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Answer these two I got them wrong
a) This equation holds true for all x values except x=0, because it would result in division by zero.
b) This equation holds true for all x values except x=0, because it would result in division by zero.
What is inequality?
An inequality is a statement that compares two expressions and is represented by one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), ≠ (not equal to).
a) 6x² - x³ = -x² + 2x + 3
b) 6x² - x³ ≤ -x² + 2x + 3
To solve for x in the given inequalities:
a) 6x² - x³ = -x² + 2x + 3
Start by isolating x³ on one side of the equation:
x³ = 6x² + (-x² + 2x + 3)
x³ = 6x² + 2x + 3
Now we can factor out x² from the right side of the equation:
x³ = (x²)(6 + 2/x) + 3
This equation holds true for all x values except x=0, because it would result in division by zero.
b) 6x² - x³ ≤ -x² + 2x + 3
Start by isolating x³ on one side of the inequality:
x³ ≤ 6x² + (-x² + 2x + 3)
x³ ≤ 6x² + 2x + 3
Now we can factor out x² from the right side of the inequality:
x³ ≤ (x²)(6 + 2/x) + 3
This inequality holds true for all x values except x=0, because it would result in division by zero.
Hence,
a) This equation holds true for all x values except x=0, because it would result in division by zero.
b) This equation holds true for all x values except x=0, because it would result in division by zero.
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