Answer:
98.3
Step-by-step explanation:
I used trigonometry (cosine function) to plug in the information given and solve for what we were missing.
On a coordinate plane, a line goes through (negative 3, negative 4) and (2, negative 2). choose values for a and b to create infinitely many solutions to this system of equations. 10x – ay = 60 –10x 20y = b a = b =
The value for a = 10 and b = -[tex]\frac{16}{5}[/tex] to create infinitely many solutions to this system of equations.
STEPS FOR FIND a AND bThe given line can be represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept. To find m and b, we can use the coordinates of two points on the line:(x1, y1) = (negative 3, negative 4) and (x2, y2) = (2, negative 2).
The slope of the line is given by:m = (y2 - y1) ÷ (x2 - x1) = (-2 - (-4)) ÷ (2 - (-3)) = [tex]\frac{2}{5}[/tex]
The y-intercept of the line is given byb = y1 - mx1
= -4 - ( [tex]\frac{2}{5}[/tex])(-3)
= -4 - (- [tex]\frac{2}{5}[/tex])
= -4 + [tex]\frac{2}{5}[/tex]
So the equation of the line is:y = ( [tex]\frac{2}{5}[/tex])x - 4 + [tex]\frac{2}{5}[/tex] = [tex]\frac{2}{5}[/tex] x - [tex]\frac{16}{5}[/tex]
To create infinitely many solutions, we have to make sure that the line equation is equal to the equation of the other equation we have. and by using these values:10x - ([tex]\frac{16}{5}[/tex])y = 60
So we can say that, a = 10, b = - [tex]\frac{16}{5}[/tex]Learn more about equation y = mx + b here:
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With the hit and trial method of infinite number of solutions, the equation can be solved through:
A=20
B= -60
A system with infinite number of solutions is formed by equations which are a multiple of the other one. To create infinitely many solutions, we have to make sure that the line equation is equal to the equation of the other equation we have. Then, the following proportion must be observed:
A=10/-10 = -A/20 = 60/B
A= -1
-A/20 = -1
A=20
60/B= -1
B= -60
Hence the values for A and B are 20 and -60 respectively.
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add any number to the equation 12x +3=12x+____ to get ONE solution
Answer:
12x + 3 = 12x + x
Step-by-step explanation:
Because if we keep both x on each side equal to each other, we will always get a no-solution equation, so in this case, I add x.
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-7,-2)
(1,-4)
(5,0)
The coordinate of fourth vertex is (-3, 2) determined by using the properties of parallelogram.
What is parallelogram?
The quadrilateral whose opposite sides are equal and parallel to each other along with equal opposite angles is called parallelogram. The only difference of parallelogram from rectangle is that rectangle has four right angles, but parallelogram has not.
How to determine the coordinate of the fourth vertex given in the question?we are given, three vertices as (-7, -2), (1, -4) and (5, 0)
let, the fourth vertex is (x, y)
the above vertices can be named as A (-7, -2), B (1, -4) and C (5, 0)
and D (x, y)
We know the distance of two points (x₁, y₁) and (x₂, y₂) is given by the following formula.
√[(x₂-x₁) ²+(y₂-y₁) ²]
Now distance from A to B = √[(1+7)² + (-4+2) ²]
length of AB = √ (64 + 4) = √68
distance from B to C = √ [(5-1)² + (0+4) ²]
length of BC = √32 = 4√2
According to the properties of parallelogram, two opposite sides are equal and parallel to each other.
If ABCD is a parallelogram, then AB = CD and BC = AD
length of CD = √[(x-5) ² + (y- 0) ²] = AB
length of AD = √ [ (x+7) ² + (y+2) ²] = BC
√68 = √[(x-5)² + y²]
after squaring both sides, we get 68 = x² - 10x + 25 +y²
x²+ y² -10x -43 = 0 ... equation 1
4√2 = √[(x+7) ² + (y+2) ²]
32 = x² + 14x + 49 + y² + 4y + 4
x² + y² +14x + 4y +21 = 0 .......... equation 2
solving the equation 1 and 2 we determine the value x = -3 and y =2
hence, the fourth vertex D (x, y) = D(-3, 2)
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Identify the solution to the system of equations from the graph and check the solution algebraically in each equation y = x - 1
y = 3x -9
The solution to the system of equations from the graph and the algebraic method correlates with one another i.e. x = 4, y = 3
What is the process of solving systems of two equations?A system of linear equations is a grouping of one or more linear equations with the same variables. There are various ways for solving a system of two linear equations, these includes:
Graphical method,Substitutional method, Elimination method etc.In the Graphical method, to graph an equation system, we simply do so by plotting the equations on the same set of axes and searching for the point(s) where the two lines cross. This intersection point is the system's solution since it reflects the values of the variables that make both equations true at the same time.
The plot for the two systems of the equation can be seen in the image attached below.
y = x - 1
y = 3x - 9
From the graph, we could see that the two equations intersect at (4,3). It implies that in the order (x,y), x = 4, and y = 3.
Using the algebra elimination method.
y = x - 1 ..... (1)
y = 3x - 9 ..... (2)
From equation (1),
y - x = -1
y - 3x = -9
By Elimination method,
2x = 8
x = 8/2
x = 4
Replace the value of x into equation (1),
y = 4 - 1
y = 3
Therefore, we can conclude that the solution to the system of equations from the graph and the algebraic method correlates with one another i.e. x = 4, y = 3
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1) Equation: 70x-100 = 850
Word problem:
2) Inequality: 8x +15 < 40
Word problem:
The solution for the given equation is x=95/7 and for the given inequality is x<25/8.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=12x+6. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given an example: m=12 and b=6
For the other hand an expression mathematical that represents a non-equal relationship between a number or another algebraic expression is called an inequality. Therefore, it is common to the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).
The solutions for inequalities can be given by: a graph in a number line or numbers.
The exercise gives two topics:
Equation 1 : 70x-100 = 85070x=850+100
70x=950
x=950/70
x=95/7
Equation 2 : 8x +15 < 408x < 40 - 15
8x< 25
x< 25/8
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The solution of the equation 70x - 100 = 850 is x = 13.6.
The solution of the inequality is x < 3.125.
How to solve inequality and equation?Equations are mathematical expressions containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Let's solve the equation for the variable x.
70x - 100 = 850
70x = 850 + 100
70x = 950
divide both sides by 70
x = 950 / 70
x = 13.6
Let's solve the inequality as follows:
8x + 15 < 40
subtract 15 from both sides of the inequality
8x + 15 -15 < 40 - 15
8x < 25
divide both sides of the inequality by 8
x < 25 / 8
x < 3.125
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. the width of the pool is 25 m find the length of the acual pool?
Answer: How are you supposed to know the length if you only know the width. There isn't an answer to this question.
Samuel has 1 cup of rubbing alcohol and will use the entire amount. He plans to store the cleaning solution in containers that each hold a maximum of 6 cups. How many containers does he need.
Samuel needs a total of 6 containers for his plan
How to determine the number of container he needs?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
1 cup of rubbing alcohol = 1/(1/2) = 2 shares
Also, we have
1 cup of rubbing alcohol contains = 1 + 1/2 + 16 = 17.5
For the 2 shares calculated above, we have
2 shares = 17.5 * 2
Evaluate
2 shares = 35
Given that each can hold a maximum of 6 cups, the number of containers needed is
Container = 35/6
This gives
Container = 5.83
Round up
Container = 6
Hence, he needs 6 containers
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Suppose A is a 7x5 matrix. How many pivot columns must A have if its columns are linearly independent? Why? Select the correct answer below. A. The matrix must have 7 pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would be linearly dependent B. The matrix must have pivot columns. The statements "A has a pivot position in every row and the columns of A are linearly independent" are logically equivalent.C. The matrix must have 7 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. D. None of the columns of A are pivot columns. Any column of A that is a pivot column is linearly dependent with the other pivot columns.
The correct option is B. The matrix must have pivot columns. The statements "A has a pivot position in every row and the columns of A are linearly independent" are logically equivalent.
The data given in this question is,
Suppose A is a 7 × 5 matrix.
The objective of this question is to find how many pivot columns must have if its columns are linearly independent.
Explanation for step 1:
A key idea in linear algebra is linear independence. If no vector can be expressed as a linear combination of the others, then two or more vectors are said to be linearly independent.Consider the given data that A is a 7 × 5 matrix.
All fine columns of 7 × 5 matrix A must be Pivot Columns.
Otherwise the equation AX=0, would have a free variable, in which care the Columns of would be linearly dependent.
Explanation:
Each relationship of linear dependency between the columns of A relates to a complex solution to the equation Ax=0. If and only if the trivial solution exists for the equation Ax=0, then the column of matrix A are linearly independent.Therefore, the required answer for the given question is option (B) correct.
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Shaniece is working two summer jobs, making $11 per hour washing cars and $9 per hour walking dogs. Shaniece must earn no less than $130 this week. Write an
inequality that would represent the possible values for the number of hours washing
cars, w, and the number of hours walking dogs, d, that Shaniece can work in a given
week.
Answer:
11w + 9d ≥ 130
Step-by-step explanation:
The amount of money that she makes from her jobs in total has to be greater than or equal to 130.
The points (p, 6) and (4, 7) fall on a line with a slope of j. Then what would the value of p end up being?
Answer:
The slope of a line is given by the formula "rise over run," or (y2 - y1)/(x2 - x1). In this case, the rise is 7 - 6 = 1, and the run is 4 - p.
So the slope is equal to 1/(4 - p). We are told that this slope is equal to j, so we can set up the equation:
1/(4 - p) = j
To solve for p, we can multiply both sides of the equation by (4 - p) to get:
(4 - p) = j(4 - p)
Then we can simplify the left side and rearrange the terms on the right side to get:
4 - p = 4j - jp
Then we can add p to both sides to get:
4 = 4j - jp + p
Then we can combine like terms to get:
4 = (4 - p)j + p
Then we can rearrange the terms to solve for p:
p = 4 - (4 - p)j
p = 4 - 4j + pj
p = (1 - j)p + 4 - 4j
p(1 - j) = 4 - 4j
p = (4 - 4j)/(1 - j)
This is the value of p that will make the slope of the line with points (p, 6) and (4, 7) equal to j.
Answer:
p = -5
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Given values:
Let (x₁, y₁) = (p, 6)Let (x₂, y₂) = (4, 7)Slope (m) = 1/9Substitute the given points and slope into the slope formula:
[tex]\implies \dfrac{1}{9}=\dfrac{7-6}{4-p}[/tex]
[tex]\implies \dfrac{1}{9}=\dfrac{1}{4-p}[/tex]
Cross multiply:
[tex]\implies 4-p=9[/tex]
Subtract 4 from both sides:
[tex]\implies -p=5[/tex]
Divide both sides by -1:
[tex]\implies p=-5[/tex]
Therefore, the value of p is -5.
Find the values of the variables
Answer:
W = 59 degree
Y = 59 degree
Z = 53 degree
x = 121 degree
v = 121 degree
Step-by-step explanation:
W = 59 degrees because a triangle has a total of 180 degrees, and we know 2 of the angles, one is 31 degrees and the other is 90 degrees, so
90 + 31 = 121
180 - 121 = 59 degrees
So, W = 59 degrees
Y = 59 degrees because w and y are vertical angles.
z = 53 degrees because
68 + 59 = 127
180 - 127 = 53 degree
So, z = 53 degree
x = 121 degree, y = 121 degree because w, x, y, v add up to 360 degree
59 + 59 = 118
360 - 118 = 242
242 / 2 = 118 degree
So, x and y equal to 118 degrees.
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Sandy wears contact lenses. She starts the year with 5 pairs of lenses, and she uses 3 pairs of contacts every 2 months. Write an equation in standard form to represent Sand supply of contact lens pairs, y, after x months.
The equation to represent Sand supply of contact lens pairs, y, after x months is 5 + 1.5x.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Here, Sandy wears contact lenses. She starts the year with 5 pairs of lenses, and she uses 3 pairs of contacts every 2 months.
The equation to represent Sand supply of contact lens pairs, y, after x months so be:
5 + (3/2 × x)
5 + 1.5x
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Veda climbs up the mountain while Kaleb climbs down. The equation and the table represent the
elevations of the climbers in feet, y, as functions of time in minutes,.
LOOK AT PHOTO
Answer:
Veda: 10
Kaleb: 20
Step-by-step explanation:
Veda is seen in the equation:
y = 10x + 600
The 600 is telling us what elevation she started at and the 10 tells us her rate.
Kaleb:
We see that he went down 20 feet every second (570 - 550)
Answer: Hope This help:)
Step-by-step explanation:
A little boy accidentally let go of his balloon, and it floated away. It was 3 feet above the ground when he let go, and it steadily rose 3 feet per second.
The equation that shows the relationship between the number of seconds since the boy let the balloon go is y = 3x + 3.
What is a function?A function can be defined as the outputs for a given set of inputs. The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Here,
Given, A little boy accidentally let go of his balloon, and it floated away. It was 3 feet above the ground when he let go this height is our constant value in the function.
It steadily rose 3 feet per second.
Assuming time in seconds to be x and total height is y.
∴ An equation that shows the relationship between the number of seconds since the boy let the balloon go is,
y = 3x + 3
The link between the amount of seconds after the youngster let go of the balloon is shown by the equation y = 3x + 3.
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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD = 7
and DC 11, what is the length of BD in simplest radical form?
The length of BD in simplest radical form is √77 units
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
Hypotenuse AC = AD + DC = 7 + 11 = 18
Altitude = square root of the multiplication of AD and DC
√(7 x 11) = X
√77 = X
√77 can't be simplified further
Therefore, the length of BD is √77 units
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if a six sided die is tossed two times, the probability of obtaining two "4s" in a row is
Answer:
[tex]\frac{1}{36}[/tex]
Step-by-step explanation:
The probability of rolling a 4 is 1/6.
Using the multiplication rule, the required probability is [tex](1/6)^2=\frac{1}{36}[/tex].
The graph below shows the amount of money that Scott has to pay for extra labor for someone to help him work on his property. He hired his nephew to work after school and on weekends.
Which statement correctly describes the graph?
Responses
A Scott pays his nephew $15 per hour, and he initially had $900 for extra labor.Scott pays his nephew $15 per hour, and he initially had $900 for extra labor.
B Scott pays his nephew $10 per half-hour, and he initially had $900 for extra labor.Scott pays his nephew $10 per half-hour, and he initially had $900 for extra labor.
C Scott pays his nephew $10 per hour, and he initially had $900 for extra labor. Scott pays his nephew $10 per hour, and he initially had $900 for extra labor.
D Scott pays his nephew $20 per hour, and he initially had $900 for extra labor.
Scott pays his nephew $10 per hour, and he initially had $900 for extra labor. Then the correct option is C.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The graph below illustrates how much Scott must spend on additional labor to hire someone to assist him as he works on his property. He recruited his nephew to work on weekends and after school.
From the graph, the two points are (0, 900) and (800, 10). Then the slope of the line is given as,
m = (900 - 800) / (0 - 10)
m = - 100 / 10
m = - 10 dollars per hour
Then the equation is given as,
y = - 10x + 900
Scott pays his nephew $10 per hour, and he initially had $900 for extra labor. Then the correct option is C.
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At a community bake sale, Justin earned $1.50c selling cookies, $2.25m selling muffins, and $1.90b selling brownies. He paid $0.30b for the ingredients for the brownies, $0.19c for the cookie ingredients, and $0.59m for the muffin ingredients.
Which expression represents his total profit?
1.2c+2.06m+1.31b
1.8c+2.44m+2.49b
1.31c+1.66m+1.6b
1.69c+2.84m+2.2b
The expression that represents the profit Justin made is 1.31c + 1.66m + 1.6b ( option C)
What is linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.
Justin earned $1.50c selling cookies but he spent $0.19c. Therefore the profit on cookies = $(1.5-0.19)c. = $1.31c
He earned $2.25m by selling muffins and spent $0.59m on the ingredients. Therefore the profit He made on muffins = $(2.25-0.59) = $1.66m
He earned $1.90b selling brownies and he spent $0.30b on ingredients. The profit he made on brownies = $1.90-$0.30 = $1.60b
Therefore the expression for the total profit = $(1.31c+ 1.66m+1.6b)
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. A population of N = 100 scores has mean µ = 30 and standard deviation σ = 4. What
is the population variance?
A) 2
B) 4
C) 8
D) 16
Answer:
Step-by-step explanation:
a
lll
Option D is correct, the population variance is 16.
Given that a population of N = 100 scores has mean µ = 30 and standard deviation σ = 4.
We have to find the population variance.
The population variance (σ²) is calculated as the square of the standard deviation (σ).
In this case, since the standard deviation (σ) is given as 4, we can find the population variance as follows:
Population variance (σ²) = (Standard deviation)²
= 4²
= 16.
Therefore, the population variance is 16. Hence, the correct option is D) 16.
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Write a while loop that prints a. All squares less than n. For example, if n is 100, print 0 1 4 9 16 25 36 49 64 81.
Answer:
n = input()
a = 0
while pow(a, 2) < n:
print(pow(a, 2))
a += 1
Step-by-step explanation:
Which statements are correct interpretations of this graph?
Melanie pumps 4 in. of water every 4 hours
Melanie pumps 8 in. of water every 4 hours
Melanie pumps 0.5 in. of water every hour
Melanie pumps 14 in. of water every 7 hours
HELP ME PLEASE WITH THIS MATH PROBLEM
Answer:Sorry
Step-by-step explanation:
Two different containers with coins each have a volume of 500 mL. One container is full of quarters and the other container is full of pennies. What will happen to the volume if all of the coins are transferred into separate 1 L containers?
The total volume of coins will remain the same, but the two containers will now each have a volume of 1 L.
1. The two containers each have a volume of 500 mL.
2. Both containers are full of coins: one of quarters and the other of pennies.
3. All of the coins are transferred into separate 1 L containers.
4. The total volume of coins will remain the same (500 mL), but the two containers will now each have a volume of 1 L.
The original two containers each had a volume of 500 mL and were full of coins - one container with quarters, the other with pennies. All of the coins were then transferred into separate 1 L containers. After this, the total volume of coins remained the same (500 mL), but the two containers now had a volume of 1 L each. This means that the same amount of coins were contained in a larger space, which did not affect the amount of coins but did affect the volume of the containers. Therefore, when all of the coins were transferred into separate 1 L containers, the total volume of coins stayed the same, but the two containers each had a volume of 1 L.
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What is the surface area, in square meters, of the triangular prism?
Answer:
210m²
Step-by-step explanation:
We have 2 triangular faces with surface 5m*12m/2 = 30m² each
We have the top face with surface 5m*12m = 60m²
We have the bottom face with surgace 5m*13m = 65m²
And we have the "middle" with surface 5m*5m = 25m²
For a total of
30m² + 30m² + 60m² + 65m² + 25m² = 210m²
5 tomatoes for3.10. What was the cost per tomato
Answer:
0.62 cents
Step-by-step explanation:
divide 5 and 3.10
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Given the function: f(x)=2x^4 +x^2+5 A. Simplify f(-x)
The equation is f ( - x ) = 2x⁴ + x² + 5 and f ( x ) = f ( - x )
What is an 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.
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 data ,
Let the equation be represented as A
Now , the value of A is
f ( x ) = 2x⁴ + x² + 5 be equation (1)
On simplifying the equation , we get
When the value of x = -x
Substitute the value of x = -x in the equation , we get
f ( - x ) = 2 ( -x )⁴ + ( - x )² + 5
On further simplification , we get
f ( - x ) = 2 ( x )⁴ + ( x )² + 5
So ,
f ( - x ) = 2x⁴ + x² + 5 = f ( x )
Therefore , the value of f ( - x ) = 2x⁴ + x² + 5
Hence , the equation is f ( -x ) = 2x⁴ + x² + 5
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The length of a rectangular garden is 8 feet more than 2 times the width. If the perimeter of the garden is 50, find the width.
The width of the rectangular garden is 11 feet
How to determine the width of the rectangleThe formula for calculating the perimeter of a rectangle is expressed as;
Perimeter = 2(l+w)
Given that;
l is the length of the rectanglew is the width of the rectangleFrom the information given, we have that;
Length of the rectangle = 8 + 2wThe perimeter of the rectangle = 50Now, substitute the values
50 = 2(8 + 2w + w)
add the like terms
50 = 2(8 + 3w)
expand the bracket
25 = 8 + 3w
collect like terms
3w = 33
Divide by the coefficient of w
w = 11 feet
Hence, the value is 11 feet
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One event A is _________________ of another event B if the probability of event A has occurred given event B is the same as the probability that A will occur with no knowledge of B.
One event A is dependent on another event B if the probability of event A has occurred given event B is the same as the probability that A will occur with no knowledge of B.
When Two events are to be Dependent the outcome of the first event influences the outcome of the second event, and also defines if the outcome of one event affects the outcome of the other.
When two events, A and B are dependent, the probability of occurrence of A and B is:
P(A and B) = P(A) · P(B|A)
P(A) represents the probability of happening an event A.
P(B) represents the probability of happening an event B.
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The mass of a baby boy at birth was 3.6kg. When he was 6 months old and 12 months old, his masses were 7.2 kg and 10.0 kg respectively. What was the percentage increase in his mass at 12 months old when compared with (a) his mass at birth (b) his mass at 6 months old
Using the concept of fraction and percentage, the percentage increase of the baby at 12 months is 177.7 percent
What is Percentage IncreasePercentage increase is a mathematical concept that refers to the increase in a particular value over its initial amount. It is usually expressed as a percentage and is calculated by dividing the increase in the value by the original amount, then multiplying by 100.
In this problem, the data given are;
Initial mass = 3.6kgmass at 6 months = 7.2kgmass at 12 months = 10kgThe percentage increase at 12 months old can be calculated as
percentage increase = [(mass at 12 months - Initial mass) / Initial mass] * 100
percentage increase = [(10 - 3.6) / 3.6] * 100
percentage increase = 1.7 * 100
Percentage increase = 177.7%
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What is the slope of the line associated with the equation 5x- 6y=30
Answer:
so shortcut method for finding slope in equation is simply slope = - coefficent of x/ coefficient of y
Answer:
5/6
Step-by-step explanation:
put the equation into slope-intercept form: y = mx + b
5x - 6y = 30
-6y = -5x + 30
y = (-5/-6)x - (30/6)
y = 5/6x - 5
Therefore, slope = m = 5/6