The volume of the cake is 198 cubic inches.
How to determine the volume of the cakeWe are given that the volume of the cake is a function of its width:
V(w) = 1/2w^3 + 5/2w^2
To find the volume when the width is 6 inches, we simply substitute 6 for w in the equation:
V(6) = 1/2(6^3) + 5/2(6^2)
Expanding the exponents and simplifying:
V(6) = 1/2(216) + 5/2(36)
V(6) = 108 + 90
V(6) = 198 cubic inches
So the volume of the cake when the width is 6 inches is 198 cubic inches.
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what number should be removed from the list {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} so that the average of the remaining numbers is 6.1?
The number that should be removed from the list {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} so that the average of the remaining numbers is 6.1 is 5.
An average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.
The number in the list are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
The average of them total is 66 so there average is ,
using the formula,
Average = addition of total number/Total number
= (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11)/11
= 66/11
=6
To get average as 6.1 we need to remove 5 to make total addition of 61 so
66 - 5 = 61
Therefore, 61/10 = 6.1
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Answer:6.1
Step-by-step explanation:
What are the three types of solutions for a system of equation?
The required three types of solutions for a system of equation are Unique solution, no solution, infinite many solution.
What is system of equation?simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
According to question:Systems of linear equations can be classified as follows:
Dependent: There are countless possible solutions to the system. The same lines are shown on the equation graphs. ...
Independent: There is only one answer to the problem. The equations' graphs come together at a single point. ...
Inconsistent: There is no fix for the system.
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How many sides are there in 15?
A polygon has as many angles as it has sides. A pentadecagon has 15 sides and 15 angles.
What is polygon ?
A Polygon is a closed figure made up of line segments (not curves) in a two-dimensional plane. Polygon is the combination of two words, i.e. poly (means many) and gon (means sides). A minimum of three line segments is required to connect end to end, to make a closed figure.
A pentadecagon is a two-dimensional geometric shape that has 15 straight sides and 15 angles. It is a type of polygon, which is a closed shape that is made up of a finite number of straight line segments. The sum of the angles in a pentadecagon is equal to (15-2) x 180 = 2160 degrees. The interior angles of a regular pentadecagon are equal to (15-2) x 180/15 = 144 degrees. The formula to calculate the area of a regular pentadecagon is (15/4) x (apothem)^2 x (cot (180/15)) where apothem is the distance from the center of the shape to the midpoint of a side.
A polygon has as many angles as it has sides. A pentadecagon has 15 sides and 15 angles.
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Solve the system of equations using elimination: 4x + 3y = 49 and
-x-2y = 4.
Answer:
x = 22, y = -13
Step-by-step explanation:
4x + 3y = 49
- x - 2y = 4
x + 2y = -4
4x + 8y = -16
Subtract both equations,
5y = -65
y = -13
x - 26 = -4
x = 22
Cheers
if you took an iq test and your score was 2 standard deviations above average assuming normal distribution approximately what percent of all iq test takers would your score be higher than
In a normal distribution, approximately 68% of the scores fall within one standard deviation of the mean, and approximately 95% of the scores fall within two standard deviations of the mean.
IQ scores are often distributed in a bell-shaped curve, which is known as the normal distribution.
In a normal distribution, the mean is the center of the curve and the standard deviation is a measure of how spread out the scores are. In most IQ tests, the average score is 100 and the standard deviation is 15. If a score is 2 standard deviations above the average, it falls in the upper 2.5% of all scores.
This is because the normal distribution is symmetric, which means that the same percentage of scores falls above and below the average. In this case, if you took an IQ test and your score was 2 standard deviations above average, your score would be higher than approximately 97.5% of all IQ test takers, which is a relatively rare score.
However, it's important to note that IQ tests have many limitations and not all IQ tests have the same mean and standard deviation.
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I NEED 1-3 PLEASEEEEE HELP
1. The angle pair is straight angle pair or linear pair.
2. m∠4 = 80°
3. m∠5 = 100°
What is angle pairs and explain its types?Angle pairs are two angles whose sum add together to form a certain angle. Angle pairs are used to help identify angles in shapes and determine their measurements. There are three main types of angle pairs: complementary angles, supplementary angles, and vertical angles.Complementary angles add together to equal 90 degrees. These types of angles can be found in a variety of shapes. For example, the angles formed by two adjacent sides of a right triangle are complementary angles.Supplementary angles add together to equal 180 degrees. These types of angles can be found in a variety of shapes. For example, the angles formed by two opposite sides of a rectangle are supplementary angles.Vertical angles are opposite angles formed by two intersecting lines. These types of angles can be found in a variety of shapes. For example, the angles formed by two intersecting lines of a triangle are vertical angles.Overall, angle pairs are used to help identify angles in shapes and determine their measurements. The three main types of angle pairs are complementary, supplementary, and vertical angles. Knowing the types of angle pairs and how to identify them can help you understand geometry better.
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-16/25 - -12/15 rational numbers
The value of the expression is 4/25.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is,
-16/25 - (-12/15)
Two negatives become positive.
-16/25 - (-12/15) = (-16/25) + (12/15)
Doing the cross multiplication,
-16/25 - (-12/15) = [(-16 × 15) + (12 × 25)] / [25 × 15]
= 60 / 375
= 12/75
= 4/25
Hence we get the resulting value as 4/25.
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What number is ten more than 23?
The answer of 10 more than 23 is 33.
The answer of 10 more than 23 is 33 which can be derived using simple mathematical calculations.
To find 10 more than 23, you can add 10 to the original number 23.
10 + 23 = 33
It's a simple arithmetic operation where you add a specific number, in this case 10, to the original number.
An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.
Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.
Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.
Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.
Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.
Therefore, The answer of 10 more than 23 is 33.
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city snowfall (inches) january february boston, ma 32.8 56.4 buffalo, ny 70 94.2 cincinnati, oh 17.8 41.2 what was the average snowfall in boston over this period? round your answer to the first decimal. average snowfall:
The Average snowfall in Boston is 44.6 inches
Average is a single value that is taken as prototypically of a set or list of numbers. Depending on the context the average might have statistically different meanings like median or mode.
Average= sum of observation/number of observations
The temperature in january=32.8
the temperature in february= 56.4
∴Average= 32.8+56.4/2
=89.2/2
=44.6
Therefore, the Average snowfall in Boston over this period is 44.6 inches.
Some properties of average are:
If the number of observations is the same as the value of observation then the average is the same number. E.g- The average of 2,2 is 2+2/2=2monotonicityLinear Homogeneity- This states that if all numbers in the set are multiplied by the same positive integer then the average is also changed by the same factor.To know more about Average visit :
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In a polynomial equation, the sum of the multiplicities of the roots always add up to.
The sum of the multiplicities of the roots in a polynomial equation is equal to the degree of the polynomial (the highest power of the variable in the equation).
This is known as the Fundamental Theorem of Algebra. The multiplicity of a root is the number of times a root appears in a polynomial equation, and it can be a whole number, a fraction, or even an irrational number.
For example, if the polynomial equation is x³ + 2x² + 4x - 8 = 0, then the degree of the polynomial is 3 and the multiplicities of the roots are 1, 2, and 1, respectively.
Therefore, the sum of the multiplicities of the roots in this equation is 3. This is true for any polynomial equation: the sum of the multiplicities of the roots will always be equal to the degree of the polynomial.
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in how many ways can four men and four women be seated at a round table if no two men are to be in adjacent eats
If no two men are to sit next to each other, there are 144 ways to arrange four men and four women at a round table.
Combinations are mathematical operations that count how many possible combinations there are for a given set of components, regardless of the order in which they were chosen. One can choose the components of combos in any order.
First, arrange the four women so that there is a free seat between each pair of them at the round table. These four women can be seated at the round table in 3 different ways, for a total of 6 possible arrangements. This is written as 3! = 6.
Then, the four vacant seats will be occupied by the four men and this is written as ⁴P₄=4!=24. Then, the required number of ways to seat the two men who are not adjacent to each other is 6×24=144 ways.
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If the replacement set for x is the set of real numbers, which graph represents the inequality x + 6 > 13?
The inequality x > - 3 is represented by a line with an open circle at - 3 going toward infinity.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality x + 6 > 13 represented by a number line.
So, x + 16 > 13.
x > 13 - 16.
x > - 3.
A line with an open circle at - 3 and a direction toward infinity is used to illustrate the inequality x > - 3.
Q. If the replacement set for x is the set of real numbers, which graph represents the inequality x + 16 > 13?
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Simone wants to know whether a new chest of drawers will fit next to her bed. The chest she would like to buy is 85 centimeters wide. She knows that her room is 100 inches wide. The bed is 74 inches wide. Will the chest fit next to her bed?
On using subtraction it can be seen that Simone needs more 8 inches space in her room to fit the chest beside the bed. So, the chest cannot fit in Simone's room with the measurements of room = 100 inches and bed = 74 inches.
What is subtraction?
The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).
The measurement for Simone's room is, a = 100 inches.
The measurement for Simone's bed is, b = 74 inches.
The amount of space left in Simone's room = a - b.
Using the arithmetic operation of subtraction -
= 100 - 74
= 26
Hence, 26 inches of space is left in Simone's room.
The measurement for chest that Simone wants to fit in her room next to bed is 85 centimeters.
To convert 85 cm to inches divide the length by 2.5 -
Using the arithmetic operation of division -
85/2.5 = 34
Hence, the measurement of the chest in inches is 34 inches.
26 < 34
Using the arithmetic operation of subtraction -
34 - 26 = 8
So, Simone has 26 inches space left and the size of chest is 34 inches, which cannot be fitted in the room.
Therefore, Simone cannot fit the chest in her room.
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a data analyst notices that two variables in their data seem to rise and fall at the same time. they recognize that these variables are related somehow. what is this an example of?
This is an example of correlation. Correlation is a statistical measure that describes the relationship between two variables.
A correlation coefficient (r) ranges from -1 to 1, indicating the strength and direction of the relationship.
A coefficient of 1 indicates a perfect positive correlation, meaning that the variables move in the same direction together.
A coefficient of -1 indicates a perfect negative correlation, meaning that the variables move in opposite directions.
A coefficient of 0 indicates no correlation, meaning that the variables are not related.
The variables that the data analyst is observing, that seem to rise and fall at the same time, are positively correlated. This means they are moving in the same direction and as one variable increases, the other variable is also likely to increase.
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In 12 years I will be five times as old as it was 32 years ago. Write an equation and define your variable.
The expression for the word problem can be written as x + 12 = 5 ( x - 32).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that in 12 years I will be five times as old as I was 32 years ago. The expression in the mathematical form will be calculated as:-
x + 12 = 5 ( x - 32 )
Here, x will be the present age.
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Select all the equations that describe the situation and then find the solution. Part a. Tyler's playlist has 36 songs. Noah's playlist has one-quarter as many songs as Tyler's playlist. How many songs are on Noah's playlist? Group of answer choices 4w = 36 w = 4 · 36 w = 36 ÷ 4 w/4=36
Answer: 9
Step-by-step explanation:
Tyler's Playlist- 36 songsNoah's Playlist- 36 divided by 4 = 9
simplify the expression -3 -1
Answer:
-3+-1
(simplifies to -4)
Step-by-step explanation:
keep change change
show all work.
Emani subscribes to a Blind Box program that sends her random gifts from Japan every
month. The subscription has a one-time fee of $30 plus $9 per month and will continue
until she cancels.
a.
Emani plans to spend $210 or less from her summer job on this subscription. Write an
inequality to solve for the number of months she will be able to purchase this
subscription.
The inequality equation that represents this scenario is given as 9x + 30 ≤ 210
What is an equation?An equation shows the relationship between numbers and variables in an expression.
Let y represent the total amount of money paid for x months of subscription. If m is the constant rate and b is the initial amount of oil in the tank, hence:
y = mx + b
The subscription has a one-time fee of $30 plus $9 per month, hence:
b = 30, m = 9
y = 9x + 30
Emani plans to spend $210 or less from her summer job on this subscription. Therefore:
9x + 30 ≤ 210
The equation is given as 9x + 30 ≤ 210
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I need help please!!!
A) Evaluate f(0)
f(0) = 6*0 - 4 = -4
What does a math function mean?
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
B) Evaluate f(2)
f(2) = 6*2 - 4 = 8
C) Evaluate f(-2)
f(-2) = 6*(-2) - 4 = -12
D) Evaluate f(4)
f(4) = 6*4 - 4 = 20
E) Evaluate f(-3)
f(-3) = 6*(-3) - 4 = -16
Note: In the given function, x is replaced by z, so in order to evaluate the function for the given values of x, we need to replace x with z.
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If two lines intersect and one of the angles formed has a measure of
67°, which of the following statements is true? Explain!! your answers.*
*More than one answer may be correct; select all correct answers.
A:Vertical angles are congruent; therefore another angle must equal 67°.
B:The lines form linear pairs.
C:The lines form complementary angles.
D:One of the angles formed measures 23°
E:Two of the angles formed measure 113°
F:Two of the angles formed will have a sum of 180°
G:None of the above.
Following are some true statements, A other angle must be 67 degrees because vertical angles are equivalent. The total of two of the produced angles will be 180°.
When two lines cross, what happens?The sum of the two angles on a straight line at an intersection is 180°, and the vertical angles of two lines are always the same.Whenever two angles are vertically opposed, they are equal. Additionally, a vertical angle and the angle to it are supplementary angles because they add up to 180 degrees. For instance, if two lines cross and form an angle with a given value (X=45°), then the opposing angle also has a value of 45°.Whenever two angles are vertically opposed, they are equal. Additionally, a vertical angle and the angle to it are supplementary angles because they add up to 180 degrees.To learn more about intersecting lines refer to:
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What is the answer to this equation 3(4+s)=15?
Answer: S=1
Step-by-step explanation:
Degree 5. Double zero at x=2; zeros at x=3, x=1 and x= -5. Passes trough (0, -30)
So in problem number 7, we want a degree for polynomial. We wanted to have a 0 at x, equals 01 at x, equals negative 3 and double 0 at x. Equals 2 point so that polynomials going to look like x times, x, plus 3 times x, minus 2 quantity squared, but we wanted to pass through the .1 2 point.
What is polynomial?Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x2+x-12. In this example, there are three terms: x2, x and -12. The word polynomial is derived from the Greek words ‘poly’ means ‘many‘ and ‘nominal’ means ‘terms‘, so altogether it is said as “many terms”. A polynomial can have any number of terms but not infinite. In mathematics, a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x² − 4x + 7.To learn more about exponents refer to:
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when a fair six-sided die is tossed on a table top, the bottom face cannot be seen. what is the probability that the product of the numbers on the five faces that can be seen is divisible by $6$?
The probability will be 1.
What is probability?
Probability denotes the likelihood of something happening. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also utilised in probability distribution. To determine the likelihood of a particular event occurring, we must first determine the total number of possibilities.
Now,
It is absolute certain! That is, the probability is 1.
As,
Either 6 is on the bottom or it isn't.
1. If 6 is not on the bottom, then 6 can be seen, and so the product
will certainly be a multiple of 6, because 6 is included in the multiplying.
2. If 6 is on the bottom, then both 2 and 3 can be seen, and since
their product is 6, the product of all faces that can be seen will certainly
be a multiple of 6, since 2 and 3 will both be included in the multiplying.
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1 less than twice a number
solve the system of equations using substitution
x+y=12
y=3x
Answer:
(3, 9 )
Step-by-step explanation:
x + y = 12 → (1)
y = 3x → (2)
substitute y = 3x into (1)
x + 3x = 12
4x = 12 ( divide both sides by 4 )
x = 3
substitute x = 3 into (2) and solve for y
y = 3x = 3 × 3 = 9
solution is (3, 9 )
What are independent and dependent systems?
An independent system is a system that does not interact with its environment or any other system. A dependent system, on the other hand, is a system that interacts with its environment or other systems. In other words, the behavior of a dependent system is affected by external factors, whereas the behavior of an independent system is not.
Independent and Dependent SystemIndependent systems are self-sufficient and don't rely on external factors to function or operate. They can function and make decisions on their own without being affected by anything else. For example, a calculator is an independent system, it performs mathematical operations on its own and does not depend on anything else to work.
On the other hand, dependent systems are not self-sufficient and rely on external factors to function or operate. They are affected by and interact with their environment, and their behavior is influenced by external factors. For example, a car is a dependent system, it needs gasoline to run and is affected by the road conditions, traffic, and weather.
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bill can finish a report in 2 hours. maria can finish the same report in 4 hours. how long will it take them to finish the report if they work together?
Working together, Bill and Maria can finish the same report in 4/3 or 1 1/3 hours.
Work rate:
The job: 1
Bill: 1/2
Maria: 1/4
Working together: 1/x
Equation:
1/2 + 1/4 = 1/x
2/4 + 1/4 = 1/x
3/4 = 1/x
3x = (4)(1)
3x/3 = 4/3
x = 4/3 hours
Working together, Bill and Maria can finish the same report in 4/3 or 1 1/3 hours.
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Write the equation of the line represented by y=-2/3x+4 in standard form.
the line's equation, written in standard form as 2x + 3y = 4, is y=-2/3x+4.
What is a Linear equation?A linear equation is an algebraic equation of the form ax + by = c, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given a linear equation y= -2/3x + 4
from the general formula of standard form
The standard form for linear equations in two variables is Ax+By=C.
From equation 1
y = -2/3x + 4
multiply by 3 on both sides
3y = -2x +4
Taking variable terms on one side
2x + 3y = 4
therefore, the equation of the line represented by y=-2/3x+4 in standard form as 2x + 3y = 4.
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What is 9/4= what is the answer
Answer: 9/4 would be 2.25
Answer: 2.25 heeehee
Step-by-step explanation:
is cereal a soup? Cheers that’s all for now darling
the length of another kind of fish is normally distributed with mean 66.7 and standard deviation 8.5. a random sample of 190 fish is collected from the ocean. what is the lower bound for a 95% confidence interval for the average length of the entire population of fish?
The lower bound for a 95% confidence interval for the average length of the entire population of fish is 65.492.
Let the sample mean be ( x ) = 66.7
Standard deviation for the given sample be = s = 8.5
random sample of 190 fish is collected from the ocean so ( n )= 190
Confidence level be 95% so the Z-score be 1.959 ≈ 1.96.
By using the formula ,
x ± [tex]Z\frac{s}{\sqrt{n} }[/tex]
= 66.7 ± 1.96 (8.5/√190)
= 66.7 ± 1.208
where 1.208 indicates margin error (E).
So upper bound be 66.7 + 1.208 = 67.908
and lower bound be 66.7 - 1.208 = 65.492.
95% of samples contain the population mean (μ) within the confidence interval x ± E.
"A confidence interval is the range of values, obtained from sample statistics, that is likely to include the value of an unknown population parameter," according to the definition.
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