The probability of advancing five spaces is 0.2307.
Given that, the odds in favor of advancing five spaces are 3/10.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
The probability of advancing five spaces can be obtained as:
P =Odds/1+Odds
= [tex]\frac{\frac{3}{10} }{1+\frac{3}{10} }[/tex]
= [tex]\frac{\frac{3}{10} }{\frac{13}{10} }[/tex]
= 3/13
= 0.2307
Therefore, the probability of advancing five spaces is 0.2307.
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When a transversal cuts parallel lines, how can one angle measurement be used to determine all of the other measurements?
Answer: If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Step-by-step explanation:
For each function, select whether it’s inverse is a function or not a function. refer to the attached picture.
Function
y=x⁴
y=x⁹
y=x⁸
y=x¹¹
The inverses of the functions y= x⁹ and y= x¹¹ are functions.
The inverses of the functions y = x⁴ and y= x⁸ are not functions.
How is the functionality of the given functions determined?(a )Consider ,the inverse of the function is a function
(2 ) y= x⁹
The inverse of the function is given by,
x = [tex]\sqrt[9]{y}[/tex]
Here y is an element of the real numbers.
i.e. y ∈R
So, this is a function.
(4) y= x¹¹
The inverse of the function is given by,
x = [tex]\sqrt[11]{y}[/tex]
Here y is an element of the real numbers.
i.e. y ∈R
Similarly , this is a function.
(b ) Consider ,the inverse of the function is a not a function
(1 )y = x⁴
The inverse of the function is given by,
x = [tex]\sqrt[4]{y}[/tex] (y ≥0)
It is of one- one correspondence,
when y = 4 ,
x = ±√2
Thus, it is not a function.
(3) y= x⁸
The inverse of the function is given by,
x = [tex]\sqrt[8]{y}[/tex]
Likewise , this is not a function.
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The equation of line T, shown below, can be written in the form y=mx+c.
What are the values of m and c?
Give each of your answers as an integer or as a fraction in its simplest form.
The straight line has the equation, y = 5x - 4.
What is the equation of a straight line?A straight line is made up of an infinite number of points that are joined on both sides of the point.
Any straight line's slope 'm' is given by:
m = y2 - y1 / x2 - x1
In slope-intercept form, a linear equation has the formula y = mx + b. The variables in the equation are X and Y. The values m and b represent the slope (m) of the line and the value of y when x = 0.
The obtained points from the graph are (0,-4) and (1,1)
The slope is ,
m = 1-(-4) / 1-0
= 5/1
= 5
Because it intersects the y-axis at the point where the intercept C = -4,
The line's equation will be:
⇒ y = mx + c
⇒ y = 5x + (-4)
⇒ y = 5x - 4
As a result, the equation for the straight line shown below is y = 5x - 4.
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Determine the length of the line segment shown 4 units
18 units
19 units
21 units
The length of the line segment will be 4 units. Then the correct option is A.
What is the distance between two points?The line joining the two points is known as a line segment. Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x - h)² + (y - k)²
From the graph, the two points are (2, -2) and (2, 2). Then the distance between the points is calculated as,
D² = (2 - 2)² + (2 + 2)²
Simplify the equation, then we have
D² = (2 - 2)² + (2 + 2)²
D² = (4)²
D = 4 units
The length of the line segment will be 4 units. Then the correct option is A.
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The missing diagram is attached below.
where is the incenter of any given triangle
The incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle
we know that
The incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle's incircle.
therefore
Is the point of concurrency of the angle bisectors of the triangle
Part 2)
we know that
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side
therefore
Is a segment drawn from a vertex to the midpoint of the opposite side
Therefore, the incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle
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The graph shows g(x), which is a translation of f(x)=|x|. Write the function rule for g(x).
Write your answer in the form a|x-h| + k, where a, h, and k are integers or simplified fractions.
g(x)=____
From the graph it can be calculated that Function rule for g(x) g(x) = |x - 7|
What is graph of a function?
The collection of ordered pairs with the (x,y)(x,y) sign is known as the graph of the a function in mathematics, where f(x)=y. x and f seem to be Cartesian coordinates of pts in two-dimensional space, and in the typical case where they are real numbers, they form a subset of the this plane.
Instead of the pairs "((x,y),z)" and "((x,y),z)" as in the definition above, the graph for functions of two variables, i.e. functions for whom the domain consists of pairs "(x,y)," "(x,y)," is typically the set of ordered triples "(x,y,z)" and "(x,y,z)" where "A surface for a constant real-valued function of the two real variables, this set is indeed a sub - set of three-dimensional space.
Graph of a function f(x) is the collection of points of the form (x, f(x))The given graph is a translation of |x| only,
So value of a is 1
Now since the tip of the graph lies on x- axis, k = 0So the value of g(x) is
g(x) = |x - h|g(7) = 0|7 - h| = 07 - h = 0h = 7
Function rule for g(x) g(x) = = |x - 7|
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How do you make an exponential decay model?
The exponential decay formula can take one of three forms:
f (x) = abˣ , f (x) = a (1 – r)ˣ , P = P₀[tex]e^{-kt}[/tex]
Where,
a (or) P₀ = Initial amount ,b = decay factor, e = Euler’s constant, r = Rate of decay (for exponential decay), k = constant of proportionality
What is Exponential Decay ?
Exponential decay occurs in mathematical functions when the pace by which changes are occurring are decreasing and must thus reach a limitation, which is the horizontal asymptote of an exponential function.
The amount drops gradually, followed by a quick reduction in the speed of change and increases over time. The exponential decay formula is used to determine the decrease in growth. The exponential decay formula can take one of three forms:
f (x) = abx
f (x) = a (1 – r)x
P = P0 e-k t
Where,
a (or) P0 = Initial amount
b = decay factor
e = Euler’s constant
r = Rate of decay (for exponential decay)
k = constant of proportionality
x (or) t = time intervals (time can be in years, days, (or) months, whatever you are using should be consistent throughout the problem).
In exponential decay, the quantity decreases very rapidly at first, and then more slowly. The rate of change decreases over time. The rate of decay becomes slower as time passes. Hence, the exponential decay graph is denoted as
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Whats the width of her head
Answer: 12 inches
Step-by-step explanation:
Answer: 15 cm
Step-by-step explanation:
Ameekah is working with consecutive integers. If she uses x to represent her first number, what should she use to represent her second number?
A x
B x + 1
C x + 2
D 2x
Answer:
B) x + 1
Step-by-step explanation:
Consecutive integers mean continuous integers ( 1, 2 , 3 ,....). We will get the next number by adding 1 to the previous number.
Eg: 5 , 6 , 7 ,.....
6 = 5 + 1
7 = 6 + 1
So, if first number is x, then the next number will be x + 1
find the domain and range of 1 - x^2
The range and the domain of the function f(x) = 1 - x^2 is less than or equal to 1 and all values of x are a real number (R).
Domain: x ∈ R
Range: f ( x ) ≤ 1, ∈ R
f ( x ) = 1 − x^2 is defined for all Real values of x, and therefore the domain is all real values ( R ).
x^2 has a minimum value of 0 (for x ∈ R ) and therefore − x^2 has a maximum value of 0 and − x^2 + 1 = 1 − x^2 has a maximum value of 1.
Therefore f (x) has a maximum value of 1 and the range of f ( x ) is ≤ 1.
So, the range of f(x)≤ 1, and the domain is all real values ( R ).
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write 3/5 as a fraction or as a whole or mixed number
Answer:
Step-by-step explanation:
1) 4 1/4 + 5 1/2
= 9 3/4
2) 10 4/5 - 6 1/5
= 4 3/5
3) 3 1/4 - 1 3/4
= 1 1/2
4) 3 2/5 + 7 7/10
= 11 1/10
5 ) 10 3/13 + 2 10/13
= 13
Answer:
1
Step-by-step explanation:
Its for sure 1
In a clothing store, a shirt that sells for $15 is marked “10% off.” What is the discount? What is the sale price of the shirt?
Answer:
$13.50
Step-by-step explanation:
If the shirt is 10% off, that means the shirt is 90% of the original cost, which is $15.
If the shirt is 90% of the original cost which is 15, that means that we must turn the percentage into a decimal (0.9) and multiply it by 15.
0.9*15 = 13.5
The sale price of the shirt is $13.50
When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle it means that we are going to use what postulate?
The used postulate is explained below.
What is congruent triangles?
Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.
When angles and facet blanketed in among those angles of 1 triangle are identical as any other one, each those triangle are Congruent.
This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.
Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.
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what is the center of a circle whose equation is x2 y2 12x 2y 12 0
The center is (6, 1) of the given circle with the equation x²+y²-12x-2y+12=0.
What are circles?Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.
A circle is a closed shape that can be created by following a moving point in a plane while maintaining a constant distance from another point.
The Greek word kirks, which means hoop or ring, is whence the word circle gets its form.
So, we have the equation: x²+y²-12x-2y+12=0
Compared to the circle's basic equation:
2 + y² + 2gx + 2fy + c = 0
2g = -12, 2f = -2, c = 12
g = -6, f = -1
Centre = (-g, -f)= (6, 1)
Now, fill in the square:
x² - 12x + 36 + y² - 2y + 1 = -12 + 36 + 1
(x - 6)² + (y - 1)² = 25
(x - 6)² + (y -1)² = 52
When compared to the equation for a circle with the centers at (h, k) and radius "r," Centre = (h, k) = (6,1).
Therefore, the center is (6, 1) of the given circle with the equation x²+y²-12x-2y+12=0.
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Correct question:
What is the center of a circle whose equation is x²+y²-12x-2y+12=0?
Answer:
6,1
Step-by-step explanation:
trust me
Please help will mark Brainly
The rate of change in the given interval would be 1.25 ft/s.
What is the rate of change?
The slope of a graphed function is determined using the average rate of change formula. Divide the change in y-values by the change in x-values to find the average rate of change.
By observation, we can take the points from the graph in between the given interval.
The points would be (3, 2.5) and (5, 4)
Then the rate of change = y2 - y1/ x2 - x1
= 4 - 2.5/5 - 3
= 2.5/2
= 1.25 ft/s.
Hence, the rate of change in the given interval would be 1.25 ft/s.
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if the diagonals of a parallelogram bisect each other then it must be a rhombus
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
What is rhombus?Due to the fact that it is a quadrilateral with two pairs of parallel sides, a rhombus can be considered a particular parallelogram.A rhombus also has equal sides on all four sides, exactly like a square. Because of this, it is often referred to as a tilted square.To comprehend the relationship between the rhombus shape, parallelogram, and square, look at the graphic below.
All parallelograms are parallelograms, however not all parallelograms are rhombuses or rhombi.All squares are rhombuses, but not all rhombuses are squares.There are three additional names for a rhombus:
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Directions: Find the value of each variable.
11) x=?
y=?
12) x=?
y=?
13) x=?
y=?
14) x=?
y=?
15) x=?
y=?
z=?
The value of the variables x and y are,
11) x = 13, y = 18.4
12) x = 6.9, y = 8.
What is right angle triangle?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
11)Let the given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(45) = \frac{x}{13} \\x = 13(tan(45))\\x = 13[/tex]
Using this to find the value of y.
[tex]sin(45) = \frac{x}{y} \\sin(45) = \frac{13}{y} \\y = \frac{13}{sin(45)} \\y = 18.4[/tex]
So, the values of x and y are x = 13 and y = 18.4.
12) The given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(30) = \frac{4}{y}\\ y = \frac{4}{tan(30)} \\y = 6.9[/tex]
Now to find the value of x.
[tex]sin(30) = \frac{4}{x} \\x = \frac{4}{sin(30)} \\x = 8[/tex]
Hence, the values of x and y are, x = 6.9 and y = 8.
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Toby created a sculpture for art class using different-sized cubes. The smallest cube is 1.5 inches along each edge. The largest cube is 7.5 inches along each edge.
How many of the smallest cubes would it take to fill the largest cube?
Write your answer as a whole number or decimal. Do not round.
There are 125 of the smallest cubes that will fill the largest cube using the size of their respective volume
Volume of cubeThe volume of cube is calculated by using a × a × a = a³ where "a" is the edge.
The volume of the smallest cube = 1.5inches × 1.5inches × 1.5inches
The volume of the smallest cube = 3.375inches³
The volume of the largest cube = 7.5inches × 7.5inches × 7.5inches
The volume of the largest cube = 421.875inches³
Thus, the number of the smallest cubes it would take to fill the largest cube is derived by
421.875inches³/3.375inches³ = 125.
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Select the correct answer.
What is the approximate solution to this equation?
19 + 2 ln x= 25
Answer:
3
Step-by-step explanation:
Hope this helps..
Functions are in the world all around us. You have used functions to model phenomena and to make predictions. Mathematically, you can add, subtract, multiply, and divide functions, and you can also create a composition of functions.
A composition of functions occurs when you evaluate one function using another function, or even with the same function. A composition of functions is useful when a change in one function will create a change in another function, which, in turn, affects a third function. For example, suppose that humans build a housing development on land that was previously used as a corn field. This change in land usage causes the number of birds in the area to decrease, which causes the number of mosquitos to increase. You could model the increase in the number of mosquitoes as a function of the number of birds in the area, which is a function of the number of humans that live on that land.
You can also use the composition of functions to show that one function is the inverse of another function. Recall that the graphs of inverse functions are reflections of each other over the line. Think about these ideas as you read through the scenario below.
Last night it started raining as Hiba was closing up the store where she works. By 3 am, the roof of the store developed a small hole and water began to leak onto the sales floor. The water created a circular puddle on the floor. At any time, t, in minutes, the radius of the puddle increases by 0.1 cm. The rain continued through the night, but stopped by the time the morning shift arrived at the store at 7 am.
When the employees arrived at work, the leak and water puddle were discovered. The employees cleaned up the water puddle and placed a tall circular bucket underneath the leak, which was still slowly dripping. The capacity of the bucket can be expressed as. By 10 am, the amount of water in the bucket is.
Function composition is only one way to combine existing functions. Another way is to carry out the usual algebraic operations on functions, such as addition, subtraction, multiplication and division.
What is composition function ?The procedure known as "function composition" in mathematics takes two functions, f and g, and creates a function, h = g f, such that h(x) = g(f(x)). The combination of two functions to create a third function is known as function composition. Simply using the first function's output as the input for the second function is how it works.The function g is applied in this operation on the outcome of applying the function f to x. In other words, a function that maps x in domain X to g(f(x)) in codomain Z is produced by composing the functions f: X Y and g: Y Z. It makes sense that z would be a function of x if z were a function of y and y was a function of x. The resulting composite function is designated as (g f )(x) = g(f(x)) for all x in X, and is written as g f: X Z. [nb 1]Find the attachment of answer
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What is the volume of the following rectangular prism? 4/3units 23/4units2 Volume ==equals units^3 3 cubed
The volume of the rectangular prism with length of 5 units, width of 4 units and height of 3 units is 60 unit³
What is an equation?An equation is an expression that is used to show the relationship between two or more numbers and variables.
Volume is the amount of space occupied by a three dimensional side or object.
Let us assume that the rectangle prism have length of 5 units, width of 4 units and height of 3 units. Hence:
Volume of prism = length * width * height
Volume = 5 units * 4 units * 3 units = 60 unit³
The volume is 60 unit³
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Does 15 36 39 form a right triangle?
1521=1521 therefore a triangle has sides with lengths of 15 inches, 36 inches, and 39 inches form a right triangle.
What is Right traingle?
A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.
When we enter the values of the triangle's legs (15 and 36) and hypotenuse (39),
assuming it is a right triangle, into the Pythagoras theorem, the values of each side of the equation will be equal;
The Pythagoras Theorem is:
[tex]a^2+b^2=c^2[/tex]
Making substitutions and applying the math results in:
[tex]15^2 + 36^2= 39^2[/tex]
225 + 1296 = 1521
1521 = 1521
Therefore, it is a right traingle.
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percent proportions and equations what do you call a destroyed angle
The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.
Given, a destroyed angle
A destroyed angle is called a figure in Geometry also known as Rectangle.
A rectangle is a quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.
So, A destroyed angle is the quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.
Therefore, the destroyed angle is a rectangle.
Hence, The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.
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What type of triangle is def?
An isosceles triangle therefore has both two equal sides and two equal angles.
What is traiangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
What is isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Any triangle with (at least) two equal sides is said to be isosceles. The remaining side in the previous illustration has length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal. Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg).
An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal. Therefore, an equilateral triangle is a specific example of an isosceles triangle that has equal sides and angles on all three of its faces. The isosceles right triangle is yet another unique instance of an isosceles triangle.
The Pythagorean theorem can be used to determine the height of the isosceles triangle shown in figure:
[tex]h = \sqrt{b^2-\frac{1}{4}a^2 }[/tex]
Consequently, the region is given by:
A=1/2ah
A = [tex]\frac{1}{2}a\sqrt{b^2-\frac{1}{4}a^2 }[/tex]
[tex]A = \frac{1}{2}a^2\sqrt{\frac{b^2}{a^2}-\frac{1}{4} }[/tex]
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at a field trip for every 8 students there is 1 chaperone. if the teacher purchased 108 total tickets, how many tickets were for students?
First, 108/9=12
This means that are 12 groups of people.
If there are 8 students in each group, 12 x 8 = 96.
96 should be your answer.
Twenty members of a health club who jog were asked how many miles they jog per week. The responses are to the right. Construct a stem-and-leaf display. For single digit data, use a stem of 0. 14 26 8 14 14 22 26 25 4 34 44 34 6 18 24 17 11 6 19 17
The steam-leaf display is shown as follows
How do stem and leaf displays work?A stem and leaf plot resembles a bar graph in appearance. The term stems from the fact that each number in the data is divided into a stem and a leaf. The number's final digit is not part of the stem. The number's leaf will always be one digit.
What are the advantages of stem and leaf display?Pencil and paper can be used to quickly create the plot. The plot can be used to determine the values of each individual data point. Since the stem is not repeated across multiple data points, the data is organized compactly.
The stem-and-leaf display for the given data is shown below followed by a detailed explanation.
0|358
1|25179476
2|73823
3|44
4|0
Note that it is often customary to organize the "leaf" values from lowest to highest as follows:
0|3578
1|12456779
2|23378
3|44
4|0
Each row's initial number is referred to as the stem, and the group of numbers that come after it as the leaves. The tenth position of the numerals is indicated by the stem. Therefore, a stem of 0 indicates a single-digit number, a stem of 1 indicates a number between 10 and 19, and so on. The leaves identify the numerals' unit position. If the number is 28, for instance, the stem and leaf are each two.
The data for stem 0 contains four one-digit numbers, which are 3, 5, 8 and 7 in appearance order. Therefore, the stem 0's leaves are 3, 5, 8, and 7.
Eight values between 10 and 19 may be found in the data for stem 1, and they are 12, 15, 11, 17, 19, 14, and 16 in that sequence. Therefore, 2, 5, 1, 7, 9, 4, and 6 make up the stem 1's leaves.
Five values between 20 and 29 may be found in the data for stem 2, and they are 27, 23, 28, 22, and 23 in that sequence. As a result, the stem 2's leaves are 7, 3, 8, and 3.
For stem 3, the data contain two integers between 30 and 39 that, in the order of appearance, are 34 and 34. The leaves for the stem 3 are therefore formed by 4 and 4.
For stem 4, the data only contains the number 40, which falls within the range of 40 to 49. Consequently, 4 creates the leaf for stem 2.
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What is the upfront cost to secure this apartment?
A) $1,876
B) $1,225
C) $2,105
D) $1,025
B: 1000 + 25 + Water deposit (50) + Phone connection (40) + Elect. connection (60)
1000 + 25 + 200 = 1225
Write the function for the graph of
g(x)
g(x)=[2x]
g(x)= [x]+2
g(x)= [x-2]
g(x)=[x]-2
The function of the graph is g(x) = [x]+2
What is linear function?A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of terms
y = output variable
x = input variable
m = slope
c = y intercept
The c from the graph is +2
m for points (1, 3) and (-3, -1)
= (-1 - 3) / (-3 - 1)
= -4/-4
= 1
substituting to the equation y = mx + c
y = x + 2
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A box is 36 inches long,18 inches wide, and 6 inches deep. How many
cubic feet are in the box?
A 2.25 cubic feet
B) 4.5 cubic feet
C) 5 cubic feet
D) 3 cubic feet
Answer:
A
Step-by-step explanation:
The volume in cubic inches is [tex](36)(18)(6)=3888[/tex].
This is equal to [tex]3888/12^3=2.25[/tex] cubic feet.
How do you solve an isosceles triangle problem?
Isosceles triangle problem can be solved by given steps
what is isosceles triangle ?
An isosceles triangle in geometry is a triangle with two sides that are the same length. Sometimes it is stated as having exactly two sides that are the same length, and other times it is specified as having at least two sides that are the same length, the latter form containing the equilateral triangle as a particular case.
explanation:
In isosceles triangle
1. Two sides of the triangle are congruent
2. The angle opposite those sides are congruent
x + 72 +72 = 180
x = 180 -144
x = 36
Hence the isosceles triangle problem can be solved by above steps and explanation
To learn more about isosceles triangle from the given link
https://brainly.com/question/1475130
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