The value of the given expression is 12167.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given expression is (14+√81)³.
= (14+9)³
= (23)³
= 12167
Therefore, the value of the given expression is 12167.
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Trey is 4 times older than his sister Kelli. If K stands for Kelli's age, write an expression to represent Trey's age . (help please lol)
Answer:
The expression is:
4K
But as an equation, it would be:
T = 4K
Step-by-step explanation:
K = Kelli's age
T = Trey's age
Trey is 4 times older than Kelli
T = (4)(K)
Find The General Solution Of The Given Differential Equation. Y' = 4y + X2 + 7
The required General Solution Of the Given Differential Equation is Y = e^(-4x) * (X^2/4 + 7x/4 + X^2/2 + 7x + C') + X^2/4 + 7x.
What is differential equation ?Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f (x) In this case, the variables "x" and "y" are independent and dependent, respectively. For illustration, dy/dx = 5x.
According to question:The general solution to the differential equation Y' = 4Y + X^2 + 7 can be found by using an integrating factor. The integrating factor is e^(4x), and the solution is:
Y = e^(-4x) * ∫(e^(4x) * (X^2 + 7)) dx - X^2/4 - 7x + C,
where C is an arbitrary constant of integration. The solution can be simplified by solving the definite integral
= ∫(e^(4x) * (X^2 + 7)) dx,
which results in:
Y = e^(-4x) * (X^2/4 + 7x/4 + X^2/2 + 7x + C') + X^2/4 + 7x,
where C' is another arbitrary constant of integration.
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-5q=8=r
what is the dependent variable and what is the independent variable.
Answer:
q is independent var, r is dependent
Step-by-step explanation:
−2x−x+8 simplified im doing cominding like terms
We are given with following vectors
a
=
[
−
2
0
]
,
b
=
[
−
5
3
]
We have to find parametric equation of the line passing through a
and parallel to b
The required equation has the form:
x
=
a
+
t
b
y = -t is parametric equation of the line passing through a and parallel to b
Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.
⇒ parametric equation of line passing through a point (a₁, b₁, c₁)
and parallel to a vector <a, b, c> is given by :
x =a₁ + at , y = b₁ + bt , z = c₁ + ct
now according to question:
given -
point, P(1, 0, -3)
line, x = −1 + 2t , y = 2−t, and z = 3+3t.
so from the line the vector is= <2, -1, 3>
now using above formula,
equation of line is = x = 1 + 2t , y = −t, and z = -3+3t.
we have to solve for 'y' only,
⇒ y = -t
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i asked my class what they had for breakfast. 10 students had cereal, 5 students had eggs, and 3 students had no breakfast. what kind of data do i have?
The kind of data we have is Categorical data. Data that can be broken down into groups or categories is known as categorical data.
There are three categories in this case: eggs, cereal, and no breakfast These groups include the 10 students who ate cereal, 5 students who ate eggs, and 3 students who did not eat breakfast at all.
A categorical variable is a variable in statistics that can have one of a limited, typically fixed number of possible values and assign each observational unit to a specific group or nominal category based on some qualitative property.
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For a school fundraiser, Mai will make school spirit bracelets. She will order bead wiring and alphabet beads to create the school name on the bracelets. Mai must spend $250 on wire and $5.30 per bracelet for beads.
Complete the table giving the total cost Mai will spend to make each specific number of bracelets.
The complete table is shown below.
The equation is: y= 53.x + 250.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Mai must spend $250 on wire and $5.30 per bracelet for beads.
a) 5.3 x 20 + 250 = 356 dollar
5.3 x 40 + 250 = 462 dollar
5.3 x 60 + 250 = 568 dollar
so, the complete table is
Number of bracelets cost in dollar
20 356
40 462
60 568
b) let the number of bracelets be x and the cost is y dollar
so, the equation is
y= 53.x + 250
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HELPP PLEASEE I NEED TO KNOW THE METHOD AND Determine if the triangles are similar if similar write a similarity statement that explain which method used
Triangle ABC is similar to triangle DEF because their corresponding angles, ∠A and ∠D, and ∠B and ∠E, are equal.
The AAA similarity is a theorem of a triangle which means "angle-angle-angle", that is, two triangles are similar to each other if they both have three corresponding angles that are congruent to each other.
The line BC divides the line AD and AE, we can state that the two triangles are similar by the Angle-Angle-Angle (AAA) Similarity Theorem.
The AAA Similarity Theorem states that if the three angles of one triangle are equal to the three angles of another triangle, then the two triangles are similar.
Here is an example similarity statement based on the Angle-Angle-Angle (AAA) Similarity Theorem: "Triangle ABC is similar to triangle DEF because they both have equal corresponding angles, ∠A and ∠D, ∠B and ∠E, and ∠C and ∠F, and because the line BC divides the line AD and AE."
Hence, Triangle ABC is similar to triangle DEF because their corresponding angles, ∠A and ∠D, and ∠B and ∠E, are equal.
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factor each expression
5a -25
On solving the provided question, we can say that the provided expression is = 5a -25 since it is linear expression, so it will have only one factor, a = 5
What is factor ?In mathematics, the integer m serves as the divisor (also known as factor n) of an integer n, which may be multiplied by the integers to get n. We may also state that n in this situation is a multiple of m. A number without a residue that divides another number is said to be a factor. In other words, if you multiply two integers to create a product, the numbers you multiply are factors of the product since the result is divisible by the numbers you multiply. Factors can be found using either division or multiplication.
the provided expression is = 5a -25
since it is linear expression, so it will have only one factor
5a -25
5a = 25
a = 5
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Mr. Copeland grows bacteria in a lab. The initial number of bacteria in a petri dish is
10. The number of bacteria doubles every hour.
Mr. Copeland makes a sketch of the graph of the situation. He labels the axes, the
point containing the y-intercept, and the point representing the number of bacteria
after 8 days.
What is the point at the y-intercept??
ind the solution to the initial-value problem then put the solution in the form of: y^3 dy/dx = (7y^4 + 14) sin(x); y(0)=c
The solution to the initial-value problem is y^4 = -2 + (c^4 + 2) e^28(1-cosx)
A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable. For example, dy/dx = 5x.
Given Differential Equation is y^3 dy/dx = (7y^4 + 14) sin(x)
we have to put y^4 = z and
then, reduce the differential equation to find out I.F value.
and next we have to find out general solution of z(I.F) = [tex]\int\limits\, (I.F)Q dx + c[/tex]
and then put y(0) to get c value
so, we get y^4 = -2 + (c^4 + 2) e^28(1-cosx)
Please refer below attached image for complete solving process.
Thus, the solution to the initial-value problem is y^4 = -2 + (c^4 + 2) e^28(1-cosx)
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let x be a random variable. show that: var(x) = e[x2 ] − (e[x])2
The variance of a random variable is a measure of its spread and is the variance of X is 25.
The variance of a random variable is a measure of its spread and is calculated as the average of the squares of the differences between each value and the mean. Mathematically, the variance of a random variable X is denoted as Var(X) and is computed as follows: Var(X) = E[X^2] - (E[X])^2, where E[X] is the expected value of X.
To illustrate, let X be a random variable with the following values: {2, 4, 6, 8}. The expected value of X is 5 (E[X] = (2+4+6+8)/4). Therefore, the variance of X can be computed as follows:
Var(X) = E[X^2] - (E[X])^2
= (2^2 + 4^2 + 6^2 + 8^2)/4 - (5)^2
= 50 - 25
= 25
Hence, the variance of X is 25.
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What is the numeric coefficient for 3x4y2
Answer: The numeric coefficient is 3.
Step-by-step explanation:
Identify which drawing of 1,2,3,4,5,6-hexamethylcyclohexane has all the methyl groups in axial positions, and which has all the methyl groups in equatorial positions
1,2,3,4,5,6-hexamethylcyclohexane is a six-membered ring molecule with six methyl groups attached to it. The arrangement of the methyl groups can be either axial or equatorial.
In an axial arrangement, the methyl groups are positioned along the axis of the ring and point up or down. An equatorial arrangement, on the other hand, has the methyl groups positioned on the equator of the ring, in a more coplanar arrangement. It is easier to distinguish between the two arrangements by visualizing the molecule in a chair conformation. In a chair conformation, the ring is twisted and two of the substituents are in axial positions and two are in equatorial positions. If all of the methyl groups in the molecule are in axial positions, they would point up or down in the chair conformation. If all of the methyl groups are in equatorial positions, they would be coplanar with the ring plane in the chair conformation.
In conclusion, the drawing of 1,2,3,4,5,6-hexamethylcyclohexane with all the methyl groups in axial positions shows the methyl groups pointing up or down in a chair conformation. The drawing with all the methyl groups in equatorial positions shows them to be coplanar with the ring plane in a chair conformation.
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two friends who take the subway to their jobs, from the same station, each arrive at the station at a random time between 7:00 and 7:20 in the morning. they are willing to wait for one another for 5 minutes, after which time they take a train, whether together or alone. what is the probability of their meeting at the station?
The probability that their meeting will be held at the station would be = 1/4
What is probability?Probability is defined as the representation of an expression which shows the possible outcome of an event.
The random time for the arrival of both friends at the station = ,7:20 - 7:00
= 20 minutes.
The extra minutes used to wait for each other which is outside the random time needed to arrive at the station = 5 min.
Therefore the probability for both of them meeting at the station = 5/20 = 1/4.
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Use the given inverse of the coefficient matrix to solve the following system. 5x1 + 3x2 = 11 6 -6x1 - 3x2 = -6 -2 A^-1 = [-1 -1 2 5/3] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice A. x1 = ______ and x2 = ________ (Simplify your answers.) B. There is no solution.
The value of x1 = -4 and the value of x2 = 26/3 for the given inverse of the coefficient matrix.
What is matrix?The placement of numbers in rows and columns to create an array is known as a matrix.
A row is a horizontal arrangement, whereas a column is a vertical arrangement. Every integer in the matrix is referred to as an element, and its location is symbolized by A_mn.
Using the matrix, we can write the equation as:
AX = B
X = A^-1 B
[tex]\left[\begin{array}{c}X_1&X_2\end{array}\right] = \left[\begin{array}{cc}-1&-1\\2&\frac{5}{3} \end{array}\right] \left[\begin{array}{cc}6\\ -2\end{array}\right][/tex]
Using the matrix multiplication, we have:
[tex]\left[\begin{array}{c}X_1&X_2\end{array}\right] = \left[\begin{array}{cc}-4\\ \frac{26}{3} \end{array}\right][/tex]
Hence, the value of x1 = -4 and the value of x2 = 26/3 for the given inverse of the coefficient matrix.
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f(x)=2x+3, g(x)=-x^2+5, (f \circ g)(x)
(f ◦ g)(x) = -2x^2 + 11.
What is Composition of two functions ?
The new function obtained by performing f first and then g is the combination of two functions g and f.
The composition of two functions f and g, denoted by (f ◦ g)(x), is defined as the function that maps x to f(g(x)).
Given the functions f(x) = 2x + 3 and g(x) = -x^2 + 5, the composition of these two functions is:
(f ◦ g)(x) = f(g(x)) = f(-x^2 + 5) = 2(-x^2 + 5) + 3 = -2x^2 + 11
So, (f ◦ g)(x) = -2x^2 + 11.
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What is the equation in standard form of the line that passes through the point (6, 1) and is parallel to the line represented by 8x + 3y= 15?.
The equation in standard form of the line that passes through the point (6, 1) and is parallel to the line represented by 8x + 3y= 15 is equal to y = -8x + 43.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided above, we have the following slope and data points on the line:
Points = (6, 1).Slope, m = -8.In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ ⇒ -8 = -8
At data point (6, 1), a linear equation of this line can be calculated in point-slope form as follows:
y - 1 = -8(x - 6)
y - 1 = -8x + 42
y = -8x + 42 + 1
y = -8x + 43
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Select the correct answer. Which inequality is equivalent to the given inequality? -4(x+7)< 3(x-2)
The inequality is equivalent to the given inequality? -4(x+7)< 3(x-2) is x>-22/7
How to find the inequality?Inequality is a mathematical statement which shsow that two quantities are not the same or that they are not equal.
The given inequality is -4(x+7) < 3(x-2)
Opening the brackets to have
-4x-28<3x-6
Collecting like terms to have
-4x-3x<-6+28
This shows that -7x<22
Making x the subject of the relation we have
x>-22/7
The inequality that satisfies the given inequality is x>-22/7
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please help me solve the slope and the equation
Answer:the answer of this slope is 7 an 24
Step-by-step explanation:
Write the decimal expansion for 5 9. ( 7Th GRADE)! HURRY HELPPPP…
Answer: 0.56
Step-by-step explanation: convert from fraction to decimal
How do you convert 50 Kilogram (kg) to Pound (lb)?
Multiply the mass in kilogrammes by 2.2046226218 to convert 50 kg to pounds.
What makes anything a lb?Libra pondo, which meaning "a pound by weight," was the unit of measurement in ancient Rome when the word "pound" first appeared. According to the BBC, the pondo portion of the sentence is where the English term "pound" originates. However, the word's libra portion is where the abbreviation "lb" comes from.Follow these easy procedures to convert a weight or mass measurement from kilogrammes (kg) to pounds (lbs): Add the conversion factor 2.2046 to the weight. Therefore, 50 kg would be equal to 110.23 kg when multiplied by 2.2046.Multiply the mass in kilogrammes by 2.2046226218 to convert 50 kg to pounds. [lb] = 50 * 2.2046226218 is the formula to convert 50 kilogrammes to lbs.To learn more about Kilogram refer to:
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Factoriser l'expression suivante :
−35y−5
Answer:
-5(7y+1)
Step-by-step explanation:
-35y-5
Trouver le plus grand facteur commun et le diviser
Le plus grand facteur commun est -5
-35y/-5=7y
-5/-5=1
Simplifiez l'équation
-5(7y+1)
Je ne parle pas français mais j'espère que cela vous aidera.
The expression quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity.
The simplifies expression is -5x/6 - 8
The expression "quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity" represents:
-(2/3)x - 6 - ( -14 + (1/6)x)
The process of simplifying an expression involves reducing the expression to its simplest form, making it easier to understand and manipulate. To simplify an expression, we combine like terms by adding or subtracting the coefficients.
We need to simplify this expression into its simplest form.
Thus,
-(2/3)x - 6 - ( -14 + (1/6)x) equals,
= -2x/3 - 6 +14 - x/6
= -(4+1)x/6 - 8
= -5x/6 - 8
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find the limit l (if it exists). if it does not exist, explain why. (if an answer does not exist, enter dne.) lim x→49 x − 7x − 49
The limit does exist for lim x→49 (x^2 - 7x - 49) and it approaches value of 2009.
The limit can be found using algebraic manipulation. First we will try plug in the value and see if we can determine the limit. We have:
lim x→49 (x^2 - 7x - 49) = 49^2 - 7×49 - 49 = 2009
So limit exist at x^2 - 7x - 49 and it can be found out by simple substitution.
So, as x approaches 49, the expression x^2 - 7x - 49 approaches 2009.
Therefore, lim x→49 x^2 - 7x - 49 = 343.
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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.y = ex, y = 0, x = −2, x = 2;about the x-axisV =Sketch the region.
The required volume of the solid which was obtained by rotating the region bounded by the curve about a line is equal to ( π/2 ) ( e⁻⁴ + e⁴).
Graph is attached.
Volume of the solid rotating the region bounded by the curves about a line with y = eˣ with x = −2, x = 2 about x-axis.
=π [tex]\int_{-2}^{2}[/tex] [( eˣ - 0)² ] dx
= π [tex]\int_{-2}^{2}[/tex] e⁽²ˣ⁾ dx
= π (e²ˣ) / ( 2 [tex]|_{-2}^{2}[/tex]
= ( π/2 )[ e⁻⁴ - e⁴ ]
= ( π/2 ) ( e⁻⁴ + e⁴ )
Graph is attached.
Therefore, the volume of the solid of the rotating region bounded by curves about line is equal to ( π/2 ) ( e⁻⁴ + e⁴ ).
Graph is attached.
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how to find aro for once per one week?
To find your “Aro for once per one week”, you need to first create an account on the Aro app.
Once you have created an account, you can add your weekly commitments, such as meetings, classes, or other activities, to your calendar. You can then set up a recurring event that will occur once per week.
You can also customize the recurring event by setting the date and time, adding a description and location, and inviting other people to join. Once you have created the recurring event, you can view it on your calendar and easily adjust it if something changes.
Aro makes it easy to plan and manage your weekly commitments by allowing you to create recurring events. With Aro, you can easily keep track of your weekly commitments and ensure that you don’t miss any important appointments.
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in a party, 5 male-female couples attend. the males and females are randomly paired for a dance. what is the probability that exactly two couples are dancing together?
The probability of exactly 2 couples dancing together is 100/45 = 20/9.
To find the probability of the total number of ways to form pairs of 5 couples is C(10, 2) = 45, because there are 10 people and we need to choose 2 at a time.
The number of ways to form exactly 2 couples dancing together is C(5, 2) * C(5, 2) = 10 * 10 = 100. This is because we first choose 2 couples out of the 5 couples and then pair the males and females within each chosen couple.
So the probability of exactly 2 couples dancing together is 100/45 = 20/9.
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The probability of exactly 2 couples dancing together is 100/45 = 20/9.
To find the probability of the total number of ways to form pairs of 5 couples is C(10, 2) = 45, because there are 10 people and we need to choose 2 at a time.
The number of ways to form exactly 2 couples dancing together is C(5, 2) * C(5, 2) = 10 * 10 = 100. This is because we first choose 2 couples out of the 5 couples and then pair the males and females within each chosen couple.
So the probability of exactly 2 couples dancing together is 100/45 = 20/9.
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Jason walks a 5-mile scenic walkway that stretches from the west to the east end of the park. There is a distance marker at each
mile and one at the east end of the walkway.
What is the total number of markers along the walkway?
Answer:
The total number of markers along the 5-mile walkway is 6.
This includes markers at each mile (5 markers) and one marker at the east end of the walkway.
Who will have traveled for a greater amount of time when their distance from New York stops decreasing and starts increasing?
A.
Charlie
B. They will have traveled the same amount of time.
C.
Annabeth
D. This cannot be determined from the given information.
The answer is B. Both Charlie and Annabeth will have travelled for the same amount of time.
They will have travelled the same amount of time. This is because the time spent traveling is determined by the total distance travelled, not the direction of travel. In this case, the distance between New York and the travellers' current location is decreasing at first and then increasing, suggesting that they have reached their destination and are now returning. Since the total distance travelled is the same regardless of the direction, the time spent traveling will also be the same for both travellers. Therefore, both Charlie and Annabeth will have travelled for the same amount of time.
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