The number of points scored by each girl is 4 and each boy is 1 point.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
9 girls and 5 boys scored a total of 51 points.
The difference between the number of points scored by the 9 girls and the number of points scored by the 5 boys is 21 .
Each girl scored the same number of points and each boy scored the same number of points.
Let x be the number of points the 9 girls scored.
=> 51 - x is the number of points the 5 boys scored.
We have x + 21 = 51 - x
or x - 21 = 51 - x.
=> 2x = 30 or 2x = 72
=> x = 15 or x = 36
We reject x = 15
as 15 is not a multiple of 9
So x = 36,
each girl scored 36/9 = 4 points.
and,
=> 41 - (36) = 5,
each boy scored 5/5 = 1 points.
Hence, the number of points scored by each girl is 4
and each boy is 1 point.
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What number must you multiply the second equation by so that the sum of the x-coefficients is zero?
7x−y=55
x+3y=33
1. -7
2. 1/3
3. -1/3
4. 7
-7 must you multiply the second equation by so that the sum of the x-coefficients is zero.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The system of equations are
7x−y=55..(1)
x+3y=33..(2)
We have to multiply with -7 second equation by so that the sum of the x-coefficients is zero
-7x-21y=-231..(3)
Add equation 1 and equation 2
7x−y-7x-21y=33-231
-22y=-198
Hence, -7 must you multiply the second equation by so that the sum of the x-coefficients is zero.
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Write the augmented matrix for each of the following systems of linear equations. a. x – 3y=5 b. x+2y=0 x+y=1 c. x - y + z=2 x - z=1 d. y + 2x=0 y+z=0
The augmented matrix for the given systems of linear equations are obtained. a. x – 3y=5 b. x+2y=0 x+y=1 c. x - y + z=2 x - z=1 d. y + 2x=0 y+z=0
Explain the term augmented matrix?Two matrices are combined to form enhanced matrices.
A augmented matrix is often one in which the matrices have been merged so that they are next to one another. A divider which expresses the "border" of each matrix connects the last column of the initial matrix to the initial column of a second matrix. Augmented matrices can be used to visualize systems of equations.Thus, augmented matrix for the given systems of linear equations are obtained as:
a. x – 3y = 5 : [1 - 3 : 5]
b. x+2y=0 x+y=1 : [1 2 : 0]
[1 1 : 1]
c. x - y + z=2 and x - z=1 : [1 -1 1 : 2]
[1 0 -1 : 1]
d. y + 2x=0 y+z=0 : [2 1 0 : 0]
[0 1 1 : 0]
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A monument is made up of 50,123 sandstone blocks and 100,001 limestone ones. How many blocks make up the monument?
The monument is made up of 150,124 blocks.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Monument:
50,123 sandstone blocks
100,001 limestone blocks.
Now,
The total number of blocks.
= 50,123 + 100,001
= 150124
Thus,
150,124 blocks.
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consider the following data: −11,−5,−5,−11,13,−11,−5 step 2 of 3 : calculate the value of the sample standard deviation. round your answer to one decimal place.
The value of the sample variance rounded to one decimal place is 76.0.
What is the Mean?
The mean is a measure of the central tendency of a set of data, calculated as the sum of the values divided by the number of values in the set.
The sample variance of a set of data is a measure of the spread or dispersion of the data around the mean. To calculate the sample variance, you can follow these steps:
Calculate the mean of the data: First, find the sum of all the data points and divide by the number of data points (n).
For the given data, the mean is: (-11 + -5 + -5 + -11 + 13 + -11 + -5) / 7 = -7
Subtract the mean from each data point: Next, subtract the mean from each data point to get the deviations from the mean.
For the given data, the deviations are: (-11 - -7) = -4, (-5 - -7) = 2, (-5 - -7) = 2, (-11 - -7) = -4, (13 - -7) = 20, (-11 - -7) = -4, (-5 - -7) = 2
Square the deviations: Square each deviation to get rid of negative values.
For the given data, the squared deviations are: (-4)^2 = 16, (2)^2 = 4, (2)^2 = 4, (-4)^2 = 16, (20)^2 = 400, (-4)^2 = 16, (2)^2 = 4
Sum the squared deviations: Sum all the squared deviations.
For the given data, the sum of the squared deviations is: 16 + 4 + 4 + 16 + 400 + 16 + 4 = 456
Divide the sum by n - 1: Finally, divide the sum of the squared deviations by the number of data points minus 1 (n - 1). This gives us the sample variance.
For the given data, the sample variance is: 456 / (7 - 1) = 456 / 6 = 76
Hence, the value of the sample variance rounded to one decimal place is 76.0.
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Write these ratios in their simplest form
a 9:18
Answer:
1 : 2
Step-by-step explanation:
9 : 18
Both numbers are divisible by 9, thus:
9/9 : 18/2
[1 : 2]
Find the balance if you deposit 5000 that earns 4% annual interest compounded yearly for 6 years
Answer:
The balance after 6 years, assuming the deposit of 5000 earns 4% interest compounded yearly, would be 7400. This is calculated by using the formula A=P(1+r/n)^nt, where A is the balance, P is the principal (5000), r is the interest rate (0.04), n is the number of times the interest is compounded per year (1), and t is the number of years (6).
how to find the empirical formula from percentages
The empirical formula of a compound is the simplest and lowest whole number ratio of the atoms of each element that makes up a compound.
To find the empirical formula from percentages, you need to first calculate the mass of each element present in the compound, based on the percentage of each element. Once you have the mass of each element, divide each mass by the atomic mass of that element to get the number of moles of each element. Then divide each mole by the smallest number of moles to get the mole ratio. This ratio is the empirical formula for the compound.
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ind the values of the trigonometric functions of t from the given information. csc(t) = 7, cos(t) < 0
So, the values of the trigonometric functions of t are sin(t) = 1/7, cos(t) = -√(1 - (1/7)^2) and tan(t) = -(1/7)/(-√(1 - (1/7)^2)).
Given that csc(t) = 7 and cos(t) < 0, we can find the values of the other trigonometric functions of t using the relationships between the trigonometric functions.
csc(t) = 1/sin(t), so sin(t) = 1/7
Since cos(t) < 0, t is in the second or third quadrant, where sin(t) is positive. Hence, t is in the third quadrant.
Therefore, the values of the trigonometric functions of t are:
sin(t) = 1/7
cos(t) = -√(1 - sin^2(t)) = -√(1 - (1/7)^2)
tan(t) = sin(t)/cos(t) = -(1/7)/(-√(1 - (1/7)^2))
Note that the values of the other trigonometric functions, such as cot(t), sec(t), and csc(t), can be found using the definitions of these functions and the values of sin(t) and cos(t) that we have found.
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So, the values of the trigonometric functions of t are [tex]Sin(t)=\frac{1}{7}[/tex], [tex]Cos(t)=-\sqrt{[1-(\frac{1}{7})^2] }[/tex] and [tex]tan(t)=\frac{\frac{1}{7} }{-\sqrt{1-(\frac{1}{7})^2 } }[/tex].
Given that csc(t) = 7 and cos(t) < 0, we can find the values of the other trigonometric functions of t using the relationships between the trigonometric functions.
[tex]Cosec(t)=7[/tex]
We known
⇒ [tex]Sin(t)=\frac{1}{Cosec(t)} =\frac{1}{7}[/tex]
Since cos(t) < 0, t is in the second or third quadrant, where sin(t) is positive. Hence, t is in the second quadrant.
Therefore, the values of the trigonometric functions of t are:
⇒ [tex]Sin(t)=\frac{1}{7}[/tex]
⇒ [tex]Cos(t)=-\sqrt{[1-(Sin^2t)]}[/tex]
⇒ [tex]Cos(t)=-\sqrt{[1-(\frac{1}{7})^2] }[/tex]
⇒ [tex]tan(t)=\frac{Sin(t)}{Cos(t)}[/tex]
⇒ [tex]tan(t)=\frac{\frac{1}{7} }{-\sqrt{1-(\frac{1}{7})^2 } }[/tex]
∴ Note that The definitions of the other trigonometric functions, along with the values of Sin(t) and Cos(t), can be used to determine the values of cot(t), Sec(t), and Cosec(t).
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the lines containing the altitudes of a triangle are concurrent, and the point of concurrency is called the of the triangle.
The point of concurrency for the lines containing the altitudes of a triangle is called the orthocenter of the triangle.
The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.
The orthocenter for a triangle with an acute angle is located within the triangle.For the obtuse angle triangle, the orthocenter lies outside the triangle.The vertex of the right angle is where the orthocenter for a right triangle is located.The place where the altitudes connecting the triangle's vertices to its opposite sides intersect is known as the orthocenter.It is located inside the triangle in an acute triangle. For an obtuse triangle, it lies outside of the triangle. For a right-angled triangle, it lies on the vertex of the right angle.
The equivalent for all three perpendiculars is the product of the sections into which the orthocenter divides an altitude.Therefore, the point of concurrency for the lines containing the altitudes of a triangle is called the orthocenter of the triangle.
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Plans for a new park call for gardens directly across the sidewalk from each other to be congruent. This computer printout shows a rose garden.
If the vertices of a tulip garden are located at (x1,−y1), (x2,−y2), (x3,−y3), and (x4,−y4), will the tulip garden be congruent to the rose garden?
The lengths of all four sides of the tulip garden are equal to the lengths of the corresponding sides of the rose garden, then the two gardens will be congruent.
In order to determine if the tulip garden will be congruent to the rose garden, we must first calculate the lengths of the corresponding sides of each garden. The rose garden's vertices are labeled (x1, y1), (x2, y2), (x3, y3), and (x4, y4). The tulip garden's vertices are labeled (x1, −y1), (x2, −y2), (x3, −y3), and (x4, −y4). The length of the first side of the rose garden can be found using the distance formula, [tex]d = √((x2−x1)^2 + (y2−y1)^2)[/tex]. The corresponding length of the tulip garden can be found using the same distance formula, d = √((x2−x1)^2 + (y2−y1)^2) We can continue this process for the other three side of both gardens. If the lengths of all four sides of the tulip garden are equal to the lengths of the corresponding sides of the rose garden, then the two gardens will be congruent.
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87 is 120% of what number?
Answer: 72.5
Step-by-step explanation:
120% = 120/100 = 1.2
1.2*x = 87
x = 87/1.2 = 72.5
Determine the following limits, using [infinity] or −[infinity] whenappropriate, or state that they do not exist. a. limx→5+ 1/x−5 b. limx→5− 1/x−5 c. limx→5 1/x−5
The following limits a) the limit does not exist. b) the limit does not exist and c) the limit does not exist.
a) limx→5+ 1/x−5 = 1/0 which is undefined. Therefore, the limit does not exist.
b) limx→5− 1/x−5 = −1/0 which is undefined. Therefore, the limit does not exist.
c) The two-sided limit of 1/x−5 as x approaches 5 from both the left and the right side is undefined. Therefore, the limit does not exist.
A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis both rely heavily on limits, which are also needed to describe concepts like continuity, derivatives, and integrals.
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what is the value of (x - y) (x - y) if xy = 3 and x2 y2 = 25?
Answer:
19
Step-by-step explanation:
step by step
Kate and Jamal are racing their robots across the school gym. Kate's robot gets an 8-foot head start and travels 2 feet per second. Jamal's robot travels 3 feet per second. How long will it take for Jamal's robot to catch up to Kate's robot?
It will take Jamal's robot 8 seconds to catch up to Kate's robot.
How long will it take for Jamal's robot to catch up to Kate's robot?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
Let's t represent the time it takes for Jamal's robot to catch up to Kate's robot (in seconds).
During this time, Kate's robot will have traveled a distance of 2t + 8 feet.
Jamal's robot will have traveled a distance of 3t feet.
When Jamal's robot catches up to Kate's robot, these two distances will be equal:
2t + 8 = 3t
Solving for t:
3t -2t = 8
t = 8 seconds.
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15. The Atlanta Braves had a run differential of +134 in the 2021 season. What does this mean?
O A. They scored a total of 134 runs
O B. They scored 134 more rurks than they allowed their opponents to score.
O C. They allowed their opponents to score a total of 134 runs.
OD. They allowed their opponents to score 134 more runs than they scored.
They allowed their opponents to score 134 more runs than they scored.
What is the differential equation?
A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation.
A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.
A run differential of +134 for the Atlanta Braves in the 2021 season means that the team scored 134 more runs than their opponents over the course of the season.
A positive run differential indicates that a team has outscored their opponents, while a negative run differential means that a team has been outscored by their opponents.
Hence, They allowed their opponents to score 134 more runs than they scored.
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8. 6- 4x = 6x - 8x + 2
Answer: x=5.3
Solution:
6x−8x−2=8.6−4x
−2x−2=8.6−4x
2x−2=8.6
2x=10.6
x=5.3
What is the relationship between the ratios
Two ratios have proportional relationship.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
A ratio is a mathematical expression written in the form of a:b, where a and b are any integers.
Given question,
What is the relationship between the ratios?
Ratio defines the relationship between the quantities of two or more objects. It is used to compare the quantities of the same kind. If two or more ratios are equal, then it is said to be in proportion.
Hence, two ratio have the proportional relationship.
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Find the base area of a cone that
has a slant height of 4 inches and a
radius of 4 inches.
Answer:
AB≈50.27in²
Step-by-step explanation:
AB=πr2=π·42≈50.26548in²
Answer: 16π squared inches
Step-by-step explanation:
The base area of a cone is the area of a circle.
Formula for area of a circle = π[tex]r^{2}[/tex]
Since your r= 4 inches, you plug in 4 inches into the formula.
Area = π * [tex]4^{2}[/tex] = 16π
in a survey, the of respondents are identified as for for for and for anything else. the average (mean) is calculated for respondents and the resu
Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution.
Answer:0.69
Step-by-step explanation:
Let z = e^(2x). Then your equation is
z^2 +3z -28 = 0
(z +7)(x -4) = 0
z = -7 or 4
Taking the log of our definition of z, we have
ln(z) = 2x
x = ln(z)/2
So, the one real solution is
x = ln(4)/2 = ln(√4)
x = ln(2)
The decimal approximation is
x ≈ 0.69
For what values of h and k the system is consistent ?a)2h 2x1 – X2b)-6x1 + 3x2 k
For the system of equation " 2x₁ – x₂ = h ; -6x₁ + 3x₂ = k " , it will be consistent for all the values of h and k , which satisfy "k = -3h" .
The System Of Linear Equations is considered as consistent if it has at least one solution.
The system of equation is :
⇒ 2x₁ – x₂ = h .....equation(1) ;
⇒ -6x₁ + 3x₂ = k ....equation(2) ;
Now replacing the equation(2) by its sum with 3 times the first equation, the the system of equations become :
⇒ 2x₁ – x₂ = h .....equation(1) ;
⇒ 0 = k + 3h ;
Simplifying further ,
we have ;
⇒ k = -3h .
Therefore , the system will be consistent for values of "h" and "k" satisfying k = -3h .
The given question is incomplete , the complete question is
For what values of h and k the system Of Equations is consistent ?
2x₁ – x₂ = h ; -6x₁ + 3x₂ = k
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calculate the integral, assuming that ∫10()=−4, ∫20()=5, ∫41()=10.
The definite integral [tex]\int_{10}^{41}[/tex] f(x)dx = 14.
To calculate the definite integral of a function, we can use the Fundamental Theorem of Calculus, which states that the definite integral of a function is equal to the difference between the antiderivative of the function evaluated at the upper and lower limits of the integration interval. In this case, the definite integral is given as [tex]\int_{10}^{41}[/tex] f(x)dx.
Given that F(10) = -4, F(20) = 5, and F(41) = 10, where F(x) is the antiderivative of f(x), we can calculate the definite integral as follows:
[tex]\int_{10}^{41}[/tex] f(x)dx = F(41) - F(10) = 10 - (-4) = 14.
The Fundamental Theorem of Calculus (FTC) is a theorem in mathematics that establishes the connection between differentiation and integration.
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Solve the following system of equations for all three variables.
-3x - 5y + z = -8
2x + 8y - z = -4
x + 2y – z = 2
x,y,z
The solution to the system of equations is x = 0, y = 3, and z = 4.
What is algebraic equation ?
An algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some field, often the field of the rational numbers.
First, multiply the first equation by 2 and add it to the second equation to eliminate x:
-3x - 5y + z = -8
2 * (-3x - 5y + z) = 2 * -8
-6x - 10y + 2z = -16
2x + 8y - z = -4
-6x - 10y + 2z + 2x + 8y - z = -16 - 4
-4x - 2y + 3z = -20
Next, divide the third equation by 3 to obtain y:
x + 2y - z = 2
y = (2 - x + z) / 2
x + 2y - z = 2
x + 2 * (2 - x + z) / 2 - z = 2
x + 2 - x + z - z = 2
z = 4 - x,
y = (2 - x + 4 - x) / 2
y = (2 - 2x + 4) / 2
y = (6 - 2x) / 2
z = 4 - x
4 = 4 - x
x = 0
Plugging in the values of x and z into the equation for y:
y = (6 - 2x) / 2
y = (6 - 2 * 0) / 2
y = 6 / 2
y = 3
So, the solution to the system of equations is x = 0, y = 3, and z = 4.
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The solution to the system of equations for all three variables is x = -3, y = -5, and z = -15.
We can solve this system of equations using the elimination method or substitution method. Here, I will use the elimination method:
Starting with the first equation:
-3x - 5y + z = -8
Adding the second equation:
-3x - 5y + z + 2x + 8y - z = -8 + (-4)
-x + 3y = -12
Adding the third equation:
-x + 3y + x + 2y - z = -12 + 2
2y = -10
Solving for y:
y = -5
Substituting y back into the first equation:
-3x - 5(-5) + z = -8
-3x + 25 + z = -8
-3x + z = -33
Substituting y back into the second equation:
2x + 8(-5) - z = -4
2x - 40 - z = -4
2x - z = 36
Adding the two equations to eliminate x:
-3x + z + 2x - z = -33 + 36
-x = 3
Solving for x:
x = -3
Substituting x and y back into the third equation:
-3 + 2(-5) - z = 2
-3 - 10 - z = 2
-13 - z = 2
Solving for z:
z = -15
Therefore, the solution is x = -3, y = -5, and z = -15.
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Consider the problem of evaluating the function sin(x), in particular, the propagated data error, i. E. , the error in the function value due to a perturbation h in the argument x. (?) Estimate the absolute error in evaluating sin (x). (b) Estimate the relative error in evaluating sin(x). (c) Estimate the condition number for this problem. (d) For what values of the argument x is this problem highly sensitive?
The absolute error in evaluating sinx is [tex]cos x \triangle x[/tex].
(a)Consider the problem of evaluating the value of sin x.
The objective is to estimate the absolute error in sin x.
Assume r = sin x
The absolute error formula gives that:
[tex]\triangle r = \frac{\delta r}{\delta x} \triangle x[/tex]
[tex]= \frac{\delta sin x}{\delta x} \triangle x[/tex]
[tex]= cos x \triangle x[/tex]
(b) The objective is to estimate the relative error in sin x.
The relative error is given by:
[tex]\frac{\triangle r}{r} = \frac{cos x \triangle x}{sin x}[/tex]
[tex]= cot x \triangle x[/tex]
(c) The objective is to estimate the condition number for this problem.
The formula of a function r = f(x), its condition is given by:
[tex]\frac{x f'(x)}{f(x)}[/tex], here r = sin x
The condition number at point x is:
[tex]\frac{x\frac{d(sin x)}{dx} }{sin x}[/tex]
[tex]= \frac{x cos x}{sin x}[/tex]
= x cot x
(d) The objective is to find for what values of argument x is the problem highly sensitive.
Here, condition number is xcot x.
The cot function is highly sensitive at x=0.
Hence, the argument x is highly sensitive for x=0.
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Given p(x) = -37 +2/5(x²-14), what is the value of p(-9)?
The value of p(-9) is -10.2.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given is an equation,
p(x) = -37 + (2/5) (x² - 14)
To find the value of p(-9), substitute -9 in the place of x.
p(-9) = -37 + (2/5) ((-9)² - 14)
= -37 + (2/5) (81 - 14)
= -37 + (2/5) × 67
= -37 + 26.8
= -10.2
Hence the value of the function when x = -9 is -10.2.
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2. If you have cardboard pieces of 3ft, 3ft, 6ft ,9 ft and want to make a kite shape. What are the
possible dimensions that you can choose to make the kite shape. Draw the shape and explain.
To make a kite shape, we need two pairs of equal length sticks and a diagonal connecting the midpoints of each pair.
We can choose the following pairs of equal length sticks from the given pieces of cardboard: (3 ft, 3 ft), (6 ft, 6 ft), or (9 ft, 9 ft).
For the diagonal stick, we can choose the longest piece of cardboard, which is 9 ft.
Therefore, we can make a kite shape with dimensions (3 ft, 3 ft, 9 ft) or (6 ft, 6 ft, 9 ft) or (9 ft, 9 ft, 9 ft).
The resulting shape will have two sticks of equal length forming the top and bottom of the kite, and the longest stick forming the diagonal.
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From the cardboard pieces provided, we can select the following sets of equal-length sticks: (3 ft, 3 ft), (6 ft, 6 ft), or (9 ft, 9 ft).
We can use the longest 9-foot length of cardboard as the diagonal stick.
So, using the measurements (3 feet, 3 feet, 9 feet), (6 feet, 6 feet, 9 feet), or (9 ft, 9 ft, 9 ft).
Two sticks of equal length will form the top and bottom of the resulting shape, with the longest stick making the diagonal.
3/10 / p = 4/5 / 1/4
What is the value of people in this proportion?
The value of people in this proportion is equal to 165/10 or 10.67.
What is a proportion?In Mathematics, a proportion can be defined as an equation which is typically used to represent (indicate) the equality of two ratios. This ultimately implies that, proportions can be used to establish that two ratios are equivalent and solve for all unknown quantities.
By applying direct proportion to the given information, we have the following mathematical expression:
3/10/p = 4/5/1/4
3/10 × p = 4/5 × 4
3p/10 = 16/5
Cross-multiplying, we have the following:
15p = 160
People, p = 160/15
People, p = 10.67
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How do you convert 68 Kilogram (kg) to Pound (lb)?
There are 149.91 pounds in 68 kilogram, or 68 kilogram weighs 149.91 pounds.
How much in kilogrammes are converted to pounds?The Price Per Kilogram (Pk) shall replace the Price Per Pound (Pp) (Kg)
Just divide the kg price by 2.2046 to get the lb price to convert cost per kilogramme to cost per pound.
In principle, two pounds are equal to one kilogramme (there is a longer decimal position, but I abbreviate it to 2.2046).
The weight of a kilogramme is roughly 2.2046226218 pounds. The technique can be used to convert kilogrammes to pounds and is relatively simple. The value of a kilogramme merely needs to be multiplied by 2.2046226218.
68 kg weights 149.91 pounds, or 68 kg is 149.91 pounds. Conversion of wages 149.91434 pounds (lb), 68 kilogrammes (kg)
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when should you use the sum rule? what about the product rule? group of answer choices use the sum rule when determining the probability of independent events occurring together, the product rule when determining the probability of mutually exclusive events occurring use the product rule when determining the probability of independent events occurring together, the sum rule when determining the probability of mutually exclusive events occurring
The sum can be used when sum gives the situations in which the probability of a union of events can be calculated by summing probabilities together. and product rule If there are n(A) ways to do A and n(B) ways to do B, then the number of ways to do A and B is n(A) × n(B)
What is Probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Reason:
The probability rule of sum describes scenarios in which the probability of a union of events can be computed by adding probabilities. It is frequently used on mutually exclusive occurrences, which are events that cannot occur at the same moment.
If there are n(A) ways to perform A and n(B) ways to do B, then the total number of ways to accomplish A and B is n(A) n. (B). This is true if the number of possible ways to do A and B are independent; the number of options for doing B is the same regardless of the option you chose for A.
The probability product rule states that P(AnB) = P(A) * P (B)
This implies that the events must be distinct.
In contrast, for the probability sum rule.
P(A + B) = P(A) + P(B) (B)
This suggests that P(AnB) = 0, indicating that they are disjoint or mutually exclusive.
Box 2 states that the sum rule is used when events are independent, however this is not correct; it is employed when events are mutually exclusive.
Two events are said to be mutually exclusive in probability theory if they cannot occur at the same time or concurrently. In other words, discontinuous events are those that are mutually exclusive. If two occurrences are regarded discontinuous, the likelihood of both occurring at the same time is zero.
If A and B are the two events, then the probability of their disjoint is stated as:
P (A and B) = 0 for the probability of a disjoint (or mutually exclusive) event.
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The sum can be used when sum gives the situations in which the probability of a union of events can be calculated by summing probabilities together. and product rule If there are n(A) ways to do A and n(B) ways to do B, then the number of ways to do A and B is n(A) × n(B)
What is Probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Reason:
The probability rule of sum describes scenarios in which the probability of a union of events can be computed by adding probabilities. It is frequently used on mutually exclusive occurrences, which are events that cannot occur at the same moment.
If there are n(A) ways to perform A and n(B) ways to do B, then the total number of ways to accomplish A and B is n(A) n. (B). This is true if the number of possible ways to do A and B are independent; the number of options for doing B is the same regardless of the option you chose for A.
The probability product rule states that P(AnB) = P(A) * P (B)
This implies that the events must be distinct.
In contrast, for the probability sum rule.
P(A + B) = P(A) + P(B) (B)
This suggests that P(AnB) = 0, indicating that they are disjoint or mutually exclusive.
Box 2 states that the sum rule is used when events are independent, however this is not correct; it is employed when events are mutually exclusive.
Two events are said to be mutually exclusive in probability theory if they cannot occur at the same time or concurrently. In other words, discontinuous events are those that are mutually exclusive. If two occurrences are regarded as discontinuous, the likelihood of both occurring at the same time is zero.
If A and B are the two events, then the probability of their disjoint is stated as:
P (A and B) = 0 for the probability of a disjoint (or mutually exclusive) event.
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how to calculate standard deviation and variance with 7.2, 7.6, 8.5, 8.7, 9.0, 9.3, 9.4, 10.2, 10.9, 11.3
After determining the mean the variance is 1.5689 and standard deviation is 1.253.
The values are 7.2, 7.6, 8.5, 8.7, 9.0, 9.3, 9.4, 10.2, 10.9, 11.3.
Firstly we find the mean of the numbers.
Mean = Sum of the Numbers/Total numbers
Mean = (7.2 + 7.6 + 8.5 + 8.7 + 9.0 + 9.3 + 9.4 + 10.2 + 10.9 + 11.3)/10
Mean = 92.1/10
Mean = 9.21
Now we determine the variance.
The formula of variance is:
x x - Mean (x - Mean)^2
7.2 (7.2-9.21) = -2.01 4.0401
7.6 (7.6-9.21) = -1.61 2.5921
8.5 (8.5-9.21) = -0.71 0.5041
8.7 (8.7-9.21) = -0.51 0.2601
9.0 (9.0-9.21) = -0.21 0.0441
9.3 (9.3-9.21) = 0.09 0.0081
9.4 (9.4-9.21) = 0.19 0.0361
10.2 (10.2-9.21) = 0.99 0.9801
10.9 (10.9-9.21) = 1.69 2.8561
11.3 (11.3-9.21) = 2.09 4.3681
Total = 15.689
Variance = ∑(x - Mean)^2/10
Variance = 15.689/10
Variance = 1.5689
Standard Deviation = √Variance
Standard Deviation = √1.5689
Standard Deviation = 1.253
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