On a graph, indicate the coordinate plane point (3,4). It's contains of two coordinate are x , y coordinate
Identify the first four positive units and draw the y-axis.
The x-axis is then drawn, and the first four positive units are labeled.
The x-coordinate is 3, thus.
The y-coordinate is 4, thus.
Plotting (3,4) requires us to start at the beginning.
The x-coordinate being positive 3, we shift 3 units to the right.
The y-coordinate being positive 4, we shift 4 units to the right .
The point's x-value indicates how it travels to the right or left along the x-axis. The rectangular axis, often known as the Cartesian plane, has this axis as its major horizontal line.
The point's y-value indicates how it goes up or down along the y-axis. The rectangular axis, often known as the Cartesian plane, is centered on this axis.
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What is domain and range of a function?.
Answer: Domain and Range. The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
Step-by-step explanation:
pls hell i’m stuck on this it’s hypotenuse leg theorem
By solving a system of equations we will see that:
t = 33 and u = 308
Which values of t and u make the triangles congruent?
The two triangles will be congruent if the correspondent sides have the same measure, then we can write two equations (or a system of equations) like the one below:
16t = 6u
20t -44 = 2u
So we have a little system of equations to solve.
We can isolate u on the second equation to get:
u = (20t - 44)/2
u = 10t - 22
Now we can replace that on the other equation to get:
16t = 6*( 10t - 22)
16t = 60t - 132
We can solve this for t to get:
132 = 60t - 16t
132 = 44*t
132/44 = t
33 = t
And the value of u is:
u = 10t - 22
u = 10*33 - 22 = 308
The values are t = 33 and u = 308
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Write A Exponential growth model
inital value 2,000 growth rate 6%
The exponential growth model is given by the equation y = 2000(1.06)ˣ
What is an equation?An equation is an expression showing the relationship between numbers and variables.
An exponential function is in the form:
y = abˣ
a is the initial value and b is the multiplication factor. if b > 1, it is an exponential growth whereas if b < 1, it is an exponential decay.
A Exponential growth model initial value 2,000 growth rate 6%, hence a = 2000, b = 100% + 6% = 1.06
The exponential model becomes y = 2000(1.06)ˣ
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What does an increase of 1 on the Richter scale mean?.
An increase of 1 on the Richter scale means that the scale has increased by approximately 31 units in terms of Richter scale.
A 1.0 increment in the Richter magnitude scale results in a 31-unit difference in the intensity of an earthquake. The Richter scale (ML), a numerical measure of an earthquake's size, was devised by American seismologists Charles F. Richter and Beno Gutenberg in 1935.
The magnitude of an earthquake is determined by taking the height of the largest seismic wave and dividing it by the logarithm of its amplitude. The original Richter scale has been replaced in modern science by newer, more accurate scales, yet it is still routinely misrepresented in news reports of earthquake intensity as the logarithmic scale on which earthquakes are measured.
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How do you find the domain and range given points on a graph?.
To find the domain and range from given points on a graph: the set of all x-coordinates is the input and the set of all y-coordinates is the output.
We know that the domain of function is the set of all possible input values for which the function is well defined.
And the range of function is the set of all possible output values for given input.
To find the domain and range of function we can graphical methhod.
We know that the input values of function are shown on the x-axis and the output values of the function are shown on the y-axis.
This means, the domain of a graph shown on the x-axis. Whereas the range is shown on the y-axis.
To find the domain and range when points on a graph are given:
the set of all x-coordinates would be the domain and the set of all y-coodinates is the range of function.
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The movie starts at 1:40 pm and ends at 6:03 pm. How long is the movie?
Answer:4 hours and 23 minutes
Step-by-step explanation:1:40-5:40 is 4 hours. Then add 20 minutes and you get to 6 o'clock. Then finally add 3 minutes and you get to 6:03. When you add 4 hr + 20 min + 3 min you get 4 hours and 23 minutes.
Write the relation as a set of ordered pairs. A relation. An arrow goes from 0 to 2, 2 to 6, and 4 to 10. a. ordered pairs: {(0, 2), (2, 6), (4, 10)} b. ordered pairs: {(2, 0), (6, 2), (10, 4)} c. ordered pairs: {(0, 2), (6, 2), (10, 4)} d. ordered pairs: {(2, 0), (2, 6), (4, 10)} Please select the best answer from the choices provided A B C D
The relation should be written as a set of ordered pairs as follows: A. . ordered pairs: {(0, 2), (2, 6), (4, 10)}.
What is a function?In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (x-value or domain) to an output variable (y-value or range).
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:
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Question What is the value of x? Enter your answer in the box. x = Two intersecting lines. The angle formed at the top is labeled 3 x plus 50 degrees. The angle formed at the bottom directly opposite it is labeled 6 x minus 10 degrees.
The value of x when solving for the alternate angles is; x = 20 degrees
How to solve alternate angles?Alternate angles are defined as angles that occur on the opposite sides of the transversal line and thus have the same size. There are two different types of alternate angles namely alternate interior angles and alternate exterior angles 3x + 50 degrees and 6x - 10 degrees are alternate angles and as such;
3x + 50 = 6x - 10
Rearrange to collect like terms to get;
6x - 3x = 50 + 10
3x = 60
x = 60/3
x = 20 degrees
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Determine which function(s) are exponential. Select all that apply.
A.
x 0 1 2 3 4
y 0 1 4 9 16
B.
x 0 1 2 3 4
y 13
1 3 9 27
C.
x 0 1 2 3 4
y 5 52
54
58
516
D.
x 0 1 2 3 4
y 4.5 4 3.5 3 2.5
Only table {1} represents a exponential function.
What is exponential function?The exponential function is a mathematical function denoted by the expression as - f(x) = eˣReal exponential function is commonly defined by the following power series as -[tex]$e^{x} =\sum _{k=0}^{\infty }{\frac {x^{k}}{k!}}=1+x+{\frac {x^{2}}{2}}+{\frac {x^{3}}{6}}+{\frac {x^{4}}{24}}+\cdots }[/tex]
Given are the function tables as shown in the question.
For the table {1}, we have -{x} → 0 1 2 3 4
{y} → 0 1 4 9 16
The value of {y} varies with respect to {x} as : y = x². This is an exponential function.Therefore, only table {1} represents a exponential function.
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Triangle def is formed by connecting the midpoints of the sides of triangle abc.
A triangle def is called a "midsegment triangle" and it is formed by connecting the midpoints of the sides of a triangle ABC.
The midsegment triangle is always parallel to the original triangle and has half the area. The three sides of the midsegment triangle are called the "midsegments" of the original triangle, and they are always parallel to the corresponding sides of the original triangle and have half the length.
A triangle defined by connecting the midpoints of the sides of triangle ABC is called a "midsegment triangle" or "medial triangle." The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle and is parallel to the third side. The three sides of the medial triangle are the midsegments of the original triangle, and the three angles of the medial triangle are equal to one-half of the angles of the original triangle.
TriangleA triangle is a geometric shape that has three sides and three angles. It is a fundamental shape in Euclidean geometry and is one of the basic shapes in geometry. Triangles are classified based on their angles and sides, such as acute, right, and obtuse triangles. The sum of the angles in a triangle is always 180 degrees. Triangles can also be classified as equilateral, isosceles, or scalene based on the lengths of their sides. They are used in a variety of fields such as construction, engineering, and physics.
The triangle's characteristics are:A triangle's (of all varieties) total sum of angles is 180°.The length of a triangle's two longest sides added together is longer than the third side.Similarly to this, the length of the third side of a triangle third side is shorter than the difference between its two sides.The longest of a triangle's three sides is the side that faces the larger angle.A triangle's exterior angle is always equal to the product of its inner and exterior opposing angles. The outer angle attribute of a triangle refers to this characteristic.When the corresponding angles of two triangles match up and the side lengths are proportionate, two triangles are said to be comparable.Triangles have an area equal to one-half of their base and height.A triangle's perimeter is equal to the sum of its three sides.To know more about triangles on brainly : brainly.com/question/2773823
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What Are sin cos and tan ratios?.
The three fundamental trigonometric ratios, namely sine, cosine, and tangent, each yield the ratio of the lengths of the two sides of a right-angled triangle.
We are aware that the sides of a right-angled triangle are called the "legs" and the "hypotenuse," respectively. Thus, the longest side of a right-angled triangle is still referred to as the "hypotenuse" in trigonometry, while the other two legs are referred to as the "opposite side" and "adjacent side."
The opposite, adjacent, and hypotenuse sides of a right-angled triangle are used to define the sin, cos, and tan functions in trigonometry. These are the sin, cos, and tan formulae.
sinФ = OppositeHypotenuse
cos Ф = AdjacentHypotenuse
tan Ф = OppositeAdjacent
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X and Y are 2 sets such that X has 15 elements, Y has 25 elements and X (union) Y has 40 elements.
Find the number of elements in X (intersection) Y
The number of elements in the set that represents the intersection of X and Y is given as follows:
Zero.
How to obtain the number of elements in the intersection of X and Y?The number of elements in the intersection of X and Y is obtained according to the rule presented as follows:
n(X or Y) = n(X) + n(Y) - n(X and Y).
The parameters for this problem have the values given as follows:
n(X) = 15.n(Y) = 25.n(X or Y) = 40.Hence the number of elements in the intersection set is given as follows:
n(X or Y) = n(X) + n(Y) - n(X and Y).
40 = 15 + 20 - n(X and Y)
n(X and Y) = 0.
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What are the 4 system of equations?.
There are four systems of equations in mathematics, namely linear equations, quadratic equations, polynomial equations, and exponential equations.
Each has its own unique properties that can be exploited for solving problems. Linear equations are the simplest system of equations and are the basic building blocks of more advanced systems of equations. Quadratic equations use the product of two terms to solve one equation. For example, 5x + 6y = 20 can be rewritten as 2x + 5y = 20. Polynomial equations use the power of a term squared to solve one equation. For example, x^2 + 7x + 12 = 55 can be written as x2 + 9x + 22 = 55. Exponential equations use the power to the base to solve one equation. For example, x^3 + 3x^2 - 10x - 16 = 0 can be written as x^3 + 3x^2 - 10x - 16 = 0e^-3 = e. These systems can be used to represent real world scenarios such as population growth,
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My brain is broke and I have no brain cells .
THIS IS DUE TODAY HURRYYYY! PLEASEE
Based on the table of values, the slope and y-intercept include the following:
Slope = 1/2.y-intercept = -1/2.What is y-intercept?In Mathematics, the y-intercept is also known as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0). Therefore, the y-intercept is equal to -1/2.
From the information provided in the table above, the slope and data points on this line include the following:
Points on x-axis (x) = (1, -1).Points on y-axis (y) = (0, 1).In Mathematics and Geometry, the slope of any straight line can be calculated by using this expression;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given points into the slope formula, we have;
Slope (m) = (1 - 0)/(1 + 1)
Slope (m) = 1/2
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In a student council election Kyle receives 120 votes for president. If Kyle receives 60% of the votes, how many students vote in the election?
Answer:
200 students vote in the election
Step-by-step explanation:
We know
120 votes = 60%
1% = 2 votes
To find how many students vote in the election, we take
2 x 100 = 200 votes
So, 200 students vote in the election
help me calculate the coordinates of points B, D and E
Answer:
B(-π/3, 1/2), D(7π/6, -√3/2), E(11π/12, -1/2)
Step-by-step explanation:
You want the coordinates of various points marked on the graph of the sine and cosine functions.
GraphThe horizontal divisions on the graph are multiples of π/6. That is, there are 6 divisions between 0 and π. This means the x coordinates of interest are ...
B = -π/3
D = 7π/6
E = 11π/6
Points B and D lie on the red curve, which the graph tells you is a plot of cos(x). Then the coordinates are ...
B = (-π/3, cos(-π/3)) = (-π/3, 1/2)
D = (7π/6, cos(7π/6) = (7π/6, -√3/2)
Point E lies on the blue curve, which is a plot of sin(x). Its coordinates are ...
E = (11π/6, sin(11π/6)) = (11π/6, -1/2)
__
Additional comment
The attachment shows the coordinates of points on the unit circle as (cos(θ), sin(θ)). On the given graph, θ is on the horizontal axis (x), and sine and cosine are on the vertical axis. To make use of the attachment, you find the angle, then look for the (cos, sin) coordinates at that angle.
Negative angles are clockwise from θ=0. To find the corresponding angle on the attachment, add 2π to any negative angle.
What degree is 3x1?.
The degree of 3x^1 is 1.
A degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 2x^3 + 4x^2 - 5x + 7, the degree is 3 (the highest power of x is x^3). A polynomial of degree 0 is a constant polynomial and a polynomial of degree 1 is a linear polynomial.
To find the degree of a polynomial, you can do the following:
→ Write the polynomial in standard form, with the terms arranged in descending order of exponents.
→ Take the exponent of the term with the highest exponent. This exponent is the degree of the polynomial.
3x^1 is a monomial with a coefficient of 3 and an exponent of 1. It is also called a linear term. The degree of a monomial is the exponent of the variable. So in this case, the degree of 3x^1 is 1.
Therefore, the degree of 3x^1 is 1.
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Mai has picked 1 cup of strawberries for a cake which is enough for 3/4 of the cake. How many cups does she need for the whole cake?
Answer:
Mai needs 4/3 cups of strawberries in order to make the whole cake.
Step-by-step explanation:
1 cup of strawberries being equal to 3/4 of the cake is also the same as 1 cup of strawberries equaling 75% of the cake. So, what times 0.75 is equal to 1? That is 4/3.
pls help i have to do this quickly :')
Answer:
Circumference = 56.55
Area=254.47
The speed of a ship is given 3/4 where d is the distance the ship travel in 3 hours.if the ship travels 48miles in 3 hours.what was the speed of the ship
By taking the quotient between the distance and the time, we will see that the speed is 16 miles per hour.
How to find the speed of the ship?Remember that the speed is defined as the quotient between the distance traveled and the time in which that distance is traveled.
Such that:
speed = (distance)/(time)
Here we know that the ship can travel 48 miles in 3 hours, so:
distance = 48 mi
time = 3 hours
Then the speed is:
S = 48mi/3h
S = 16 mi/h
So the speed of the ship is 16 miles per hour.
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Joseph wants to earn $850 this summer in order to pay for a down payment on a car. His summer break is 6 weeks. He has been offered 3 different jobs.
Which job should he take to earn the $850 quickest? Explain your response.
Working as a cashier in a bookstore that pays $7.50 an hour and he is expected to work 25 hours per week
Working at a summer camp as a camp counselor for a flat rate of $175 per week (the camp is only 4 weeks)
Working as a sales associate at a department store that pays $7.25 an hour with 5% commission on all sales (he is expected to work 20 hours per week and projected to sell $1,350 per week)
B. Which job will not help him get to his goal of $850?
Answer:
A - Sales associate
B - Summer Camp Counselor
Step-by-step explanation:
First, lets look at how much Joseph would averagely earn from each job.
Cashier in bookstore: in 6 weeks he will earn 900
Summer camp counselor: in 4 weeks 700
Sales associate: in 4 weeks he will earn 850
Overall, becoming a Sales associate will allow Joseph to earn his $850 quicker.
B - the Summer Camp Counselor job will not allow Joseph to make $850 because Summer Camp only lasts 4 weeks.
Can you please help, I'm offering 30 points!
if a1=5 and an=nan-1+2 then find the value of a4
Answer:
[tex]a_4 = 154[/tex]
Step-by-step explanation:
In this problem, we are asked to find the fourth term ([tex]\square_4[/tex]) of a sequence [tex]a[/tex] given that [tex]a_1 = 5[/tex] and [tex]a_n = na_{n-1} + 2[/tex].
To solve for this, we can first find the second term in the sequence by inputting [tex]a_2[/tex] into the sequence definition.
[tex]a_2 = 2a_{2-1} + 2[/tex]
Then, we can replace [tex]a_{2-1}[/tex] with the value that we were given: [tex]a_1 = 5[/tex].
[tex]a_2 = 2(5) + 2[/tex]
[tex]a_2 = 10 + 2[/tex]
[tex]a_2 = 12[/tex]
Next, we can solve for the third term in the sequence.
[tex]a_3 = 3a_{3-1} + 2[/tex]
And we can replace [tex]a_{3-1}[/tex] with the value that we just solved for: [tex]a_2 = 12[/tex].
[tex]a_3 = 3(12) + 2[/tex]
[tex]a_3 = 36 + 2[/tex]
[tex]a_3 = 38[/tex]
Finally, we can solve for fourth term in the sequence.
[tex]a_4 = 4a_{4-1} + 2[/tex]
We can again replace [tex]a_{4-1}[/tex] with the value that we just solved for: [tex]a_3 = 38[/tex].
[tex]a_4 = 4(38) + 2[/tex]
[tex]a_4 = 152 + 2[/tex]
[tex]a_4 = 154[/tex]
Answer:
a₄ = 154
Step-by-step explanation:
You want the value of a₄ given the recursive sequence definition ...
[tex]\begin{cases}a_1=5\\a_{n}=n\cdot a_{n-1}+2\end{cases}[/tex]
SolutionThe easiest way to find the first few terms of a recursively-defined sequence is to use the recursive definition directly:
[tex]a_2=2\cdot a_1 +2 = 2(5) +2 = 12\\\\a_3=3\cdot a_2+2=3(12)+2 =38\\\\a_4=4\cdot a_3+2=4(38)+2=154[/tex]
The value of a₄ is 154.
__
Additional comment
The terms of this sequence get rapidly larger. The 10th term is 23,357,002. The general term can be defined in terms of the Euler gamma function and the incomplete gamma function:
[tex]a_n=\Gamma(n+1)+2e\Gamma(n+1,1)[/tex]
What is the formula of sum of series?.
In the context of mathematics, a series has a stagnant difference between terms. Therefore , we can find out the sum of the terms in arithmetic series by multiplying the number of times the average of the very last and first terms.
Thus we can observe that series and knowing the sum of the terms of series is a very crucial task in mathematics. In this head, we will talk about some very known series and series formulas with instances.
Actually, a series in math is very easy the sum of the different numbers or elements of the series. For instance, to make a series from the channel of the first five positive integers 1, 2, 3, 4, 5 we will simply sum them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.
So, the series of a sequence is the sum of the sequence to some given number of terms, or occasionally til infinity. It is frequently written as S_n.
If the series is 2, 4, 6, 8, 10, … , then the sum of the first 3 terms:
S
3
=2+4+6
S3=12.
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Answer:
Step-by-step explanation:
In the context of mathematics, a series has a stagnant difference between terms. Therefore , we can find out the sum of the terms in arithmetic series by multiplying the number of times the average of the very last and first terms.
Thus we can observe that series and knowing the sum of the terms of series is a very crucial task in mathematics. In this head, we will talk about some very known series and series formulas with instances.
Actually, a series in math is very easy the sum of the different numbers or elements of the series. For instance, to make a series from the channel of the first five positive integers 1, 2, 3, 4, 5 we will simply sum them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.
So, the series of a sequence is the sum of the sequence to some given number of terms, or occasionally til infinity. It is frequently written as S_n.
If the series is 2, 4, 6, 8, 10, … , then the sum of the first 3 terms:
S
3
=2+4+6
S3=12.
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Graph a line that contains the point (-3,-4) and has a slope -5
Answer:
y = −5x − 19
Step-by-step explanation:
Find the equation using slope-intercept form.
y = −5x − 19
What is the slope and y − intercept of the equation y 2x 4 *?.
The curve has a y-intercept of -4 and a slope of 2. We will need two points on the line y = 2x - 4 to plot the graph.
Y = 2x + b, where b is the y-intercept, is how the equation y = 2x - 4 can be expressed in slope-intercept form. We must perform the b-solve in order to determine the slope and y-intercept of the equation.
The line's crossing of the y-axis is known as the y-intercept. Setting x equal to 0 in the equation yields y = 2(0) - 4 and the y-intercept, which can be found. As a result, the y-intercept is determined to be y = -4.
The pace at which a line increases is referred to as its slope. Using the coefficient of x, which is 2, we can get the slope. Consequently, the slope of the equation is 2. Y = 2x – 4.
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Full Question = What are the slope and y − intercept of the equation y 2x − 4?
A fair six-sided number cube has the following faces: 1, 1, 2, 2, 5, 6. This number cube is rolled 50 times. What is the
probability that fewer than 30% of the rolls result in a two?
Find the z-table here.
O 0. 309
O 0. 421
O 0. 450
O 0. 691
The probability that fewer than 30% of the rolls result in a two is 0.450.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
To find the probability that fewer than 30% of the rolls result in a two, we can use a normal distribution to model the number of twos rolled in 50 rolls.
Let's assume that the mean number of twos rolled in 50 rolls is μ = 50 * (2/6) = 16.67 (since the probability of rolling a two is 2/6). The standard deviation can be calculated as σ = sqrt(50 * (2/6) * (4/6)) = 2.94.
Now, we can use the normal distribution to find the probability that the number of twos rolled is less than 15 (30% of 50 rolls), which is P(X < 15) = P((X - μ) / σ < (15 - 16.67) / 2.94). We can use a standard normal table (z-table) to find this probability, which is approximately 0.450.
Therefore , the probability that fewer than 30% of the rolls result in a two is 0.450.
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There is a 0.450 percent probability that fewer than 30% of rolls will produce a two.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
We can predict the frequency of twos rolled in 50 rolls using a normal distribution to determine the likelihood that less than 30% of the rolls produce two.
Given that the probability of rolling a two is 2/6, let's assume that the mean number of twos rolled in 50 rolls is = 50 * (2/6) = 16.67.
Calculating the standard deviation is as follows:
sqrt(50 * (2/6) * (4/6) = 2.94.
The chance that the number of twos rolled is less than 15 (30% of 50 rolls) can now be calculated using the normal distribution, and it is given by P(X 15) = P((X - ) / (15 - 16.67) / 2.94). It is possible to determine this probability, which is around 0.450, using a common normal table (z-table).
As a result, 0.450 represents the likelihood that fewer than 30% of rolls will produce a two.
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Theo drove 228 miles in 4 hours. Lex drove 201 miles in 3 hours. At those rates, could either man drive 112 miles in 2 hours? Complete the explanation
Ankit visited in a mall with his father. He sees that three shops are situated at P, Q, R as shown in the figure from where they have to purchase things according to their need. Distance between shop P and Q is 8 m, that of between shop Q and R is 10 m and between shop P and R is 6 m.
The measure of angle PQR is given as follows:
How to obtain the measure of angle PQR?To obtain the measure of angle PQR, first we verify if the triangle PQR is a right triangle or not.
To verify if the triangle is a right triangle we apply the Pythagorean Theorem, which states that the length of the hypotenuse squared is equals to the sum of the lengths of each side squared, in the case of a right triangle.
Hence, for this problem, considering the side lengths, we have that:
10² = 6² + 8²
100 = 36 + 64
100 = 100.
Which is true, hence this is in fact a right triangle and the measure of angle PQR is of 90º.
Missing InformationThe problem asks for the measure of angle PQR.
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How do you write domain and range examples?.
The domain and range are described for a relation, and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively. For example, if the relation is R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then: Domain = {1, 2, 3, 4} and Range = {2, 3}.
The domain and range of a function are the elements of a function. The domain is the set of all the input elements of a function, and the range is the possible outcome given by the function.
Domain→ Function →Range. If there exists a function f: α → β such that every element of α are mapped to elements in β, then α is the domain, and β is the co-domain.
The image of an element 'p' under a relation R is given by 'q', where (p,q) ∈ R. The function's range is the set of images. The domain and range of a function are denoted in general as follows:
Domain(f) = {x ∈ R} and range(f) = {f(x): x ∈ domain(f)}.
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Yu Yan make a wall hanging from a piece of fabric. For the firt part, he cut off 1/3 of the length of the original piece of fabric. For the next two part, he cut off 10 inche and 5 inche from the length of the remaining fabric. In total, he cut 35 1/2 inche from the length of the original piece of fabric. How long wa the original piece of fabric? Write and olve an equation. Check your olution.
The length of the original piece of fabric is 61 1/2 inches.
Let x be the length of the original piece of fabric.
If the first cut is 1/3 of the length of the original fabric, then we can express that as an algebraic expression 1/3x.
The next two cuts made from the remaining fabric is 10 inches and 5 inches.
10 + 5 = 15 inches
Therefore, the total length that was cut off was 1/3x + 15 inches = 35 1/2 inches.
With the algebraic equation written, solve for x.
1/3x + 15 = 35 1/2
To solve for x, isolate the terms containing the variable x on one sie and the constant terms on the other side.
1/3x = 35 1/2 - 15
1/3x = 20 1/2
Multiply both sides by 3 to get x.
1/3x = 20 1/2
x = 61 1/2 inches
Therefore, the original length of the fabric was 61 1/2 inches.
We can check our solution by adding the length of the cuts off to the original length:
1/3(61 1/2 inches) + 10 inches + 5 inches = 20 1/2 + 10 + 5 = 35 1/2
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