Due to the fact that the two candidates were chosen at random, we may assume that all options are equally likely, hence each sample point has a chance of 1/6.
What is probability?Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true.The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities.(a) The four candidates are marked as [tex]$A_1, A_2, A_3$[/tex], and M. The sample space is as follows because order doesn't matter (we just need two persons and it doesn't matter what order we choose):
[tex]$\mathcal{S}=\left\{A_1 A_2, A_1 A_3, A_1 M, A_2 A_3, A_2 M, A_3 M\right\}$[/tex]
(b) We may assume equally likely possibilities because the two candidates were selected at random, hence each sample point has a probability of 1 / 6
(c) Let C = {minority hired} Then P(C) =
[tex]P\left(A_1 M\right)+P\left(A_2 M\right)+P\left(A_3 M\right)=3 / 6=1 / 2$[/tex]
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There are 40 female performers in a dance recital. The ratio of men to women is 5 to 8 How many men are in the dance recital?
Answer: there would be 8 men
Step-by-step explanation:
can you give me brainliest
Answer: I believe there would be 25 men
Step-by-step explanation: We can see there are 40 women and the ration is 5 (men) to 8 (women)
If we take 40 and divide it by 8 we get 5
so for every 8 women there are 5 men and we do that 5 times
we get: 40 women and 25 men.
Write the solution set in interval notation and graph the inequality.
Set-Builder Notation: {x | 5/7
The set X can therefore be written as follows: The expression "A is the set of elements x such that x is a natural number less than 7" can be translated as "A is the set of elements x such that x is a natural number less than 7." A = x: x N, x 7 is another way to express the above set.
What is the Set Builder Form or Rule Method?If a set's components share a characteristic, the characteristic can be used to define the components. For instance, the natural numbers 1, 2, 3, 4, 5, and 6 in the set A have a trait in common that all of their members fall below the number 7. This trait is not shared by any other natural numbers. The set X can therefore be written as follows:The expression "A is the set of elements x such that x is a natural number less than 7" can be translated as "A is the set of elements x such that x is a natural number less than 7."A = x: x N, x 7 is another way to express the above set.The expression "the set of all natural numbers smaller than seven" can also be used to denote set A.The common property of the elements of a set is described in this instance inside braces. A set-builder form, often known as a rule technique, takes this simple structure.The Complete Question is Set Builder .
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Find the sum and product of Eigen value of matrix A = 3 1 4 0 2 6 0 0 5
The sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.
What is the eigenvalue?
Eigenvalues are the special set of scalar values that are associated with the set of linear equations most probably in the matrix equations. The eigenvectors are also termed characteristic roots.
To find the eigenvalues of matrix A, we can solve the characteristic equation |A - λI| = 0, where λ is a scalar and I is the identity matrix.
|A - λI| = 3- λ 1 4 0 2- λ 6 0 0 5- λ
= (3-λ)(5-λ) - 24 = λ^2 - 8λ - 15
Setting λ^2 - 8λ - 15 = 0, we can find the eigenvalues of the matrix by solving the quadratic equation.
λ^2 - 8λ - 15 = 0
λ = (8 ± √(8^2 + 4*15))/2
λ = (8 ± √(64 + 60))/2
λ = (8 ± √124)/2
So the eigenvalues of matrix A are λ_1 = (8 + √124)/2 and λ_2 = (8 - √124)/2
The sum of eigenvalues is λ_1 + λ_2 = (8 + √124)/2 + (8 - √124)/2 = 8
The product of eigenvalues is λ_1 * λ_2 = (8 + √124)/2 * (8 - √124)/2 = -15
Hence, the sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.
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Suppose that x is an int variable and y is a double variable and the input is: 10 20.7 Choose the values after the following statement executes: cin >> x >> y;.a. x=10,y=20 b. x=10,y=20.0c. x=10,y=20.7 d. x=10,y=21.0
x is an int variable and y is a double variable and the input is: 10 20.7.The output will be x = 10, y = 20.7
given that
x is an int variable
y is a double variable
The C++ double should have a floating-point precision of up to 15 digits as it contains a precision that is twice the precision of the float data type.
When you declare a variable as double, you should initialize it with a decimal value. For example, 3.0 is a decimal number. However, if you initialize it with 3, it will also work fine because although 3 and 3.0 seem to be identical i.e., an integer, there is a big difference in their internal representation.
the input is: 10, 20.7
after execution of the statement
cin >> x >> y
The output will be x = 10, y = 20.7
because x is declared as integer variable so it will print the same
y is declared as double integer variable so it will print same as given input , if it is declared as integer variable then it will be printed as 20
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Problem: Given an integer amount of money, you have to determinate which is the minimum amount of coins needed to arrive at the exact total. You have an infinite number of each, and may choose more than one. Coins available are $1, $5, $10, $25. Choose the highest-value coin available that does not exceed the total and repeat until you arrive at the desired amount.:
The solution is a simple process of subtracting the largest coin value from the total amount, adding any coins that fit, and repeating the process until the total amount is reached. This algorithm guarantees that the minimum number of coins needed to arrive at the total will be displayed.
1. Start by subtracting the largest coin value from the total amount.
2. If the difference is greater than 0, add the coin to the total and repeat the process.
3. If the difference is 0, move onto the next smallest coin value.
4. Repeat the process until the total amount is reached.
5. Once the total amount is reached, the minimum amount of coins needed to arrive at the total will be displayed.
The solution is a simple process of subtracting the largest coin value from the total amount, adding any coins that fit, and repeating the process until the total amount is reached. This algorithm guarantees that the minimum number of coins needed to arrive at the total will be displayed.
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answer? Drag the tiles to the correct boxes to complete the pairs.
Match each expression to its simplified form
The expression are matched to the simplest form as shown below
simplest form Equation
12 - 1/2r (13 - 3/2 r) - (1 - r)
r - 13/6 (7r - 3/2) - (2/3 + 6r)
13r + 20 (6r + 7) + (13 + 7r)
-12 + r (-8 - r) + (2r - 4)
How to find the simplest for m of each equation'The simplest form is solved by evaluating each of the equation in the problem
Evaluating the expressions
(6r + 7) + (13 + 7r)
collecting like terms
6r + 7r + 13 + 7
13r + 20
(13 - 3/2 r) - (1 - r)
opening the parenthesis (the negative sign before the second parenthesis changes the sign in the second parenthesis)
13 - 3/2 r - 1 + r
collecting like terms
13 - 1 - 3/2 r + r
12 - 1/2 r
(-8 - r) + (2r - 4)
collecting like terms
-8 - 4 - r + 2r
-12 + r
(7r - 3/2) - (2/3 + 6r)
opening the parenthesis (the negative sign before the second parenthesis changes the sign in the second parenthesis)
7r - 3/2 - 2/3 - 6r
collecting like terms
7r - 6r - 3/2 - 2/3
r - 13/6
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An isosceles triangle has two sides of length p and one length m. In terms of these lengths, write calculator-ready formulas for the sizes of the angles of this triangle. Please state your approach with a diagram and provide supporting theorems and properties used. Thank you!
The angle of your initial isosceles triangle was cut in half by drawing the vertical, therefore you multiply by two to determine theta top.
What are angles of triangle?The sum of the two interior angles that are not adjacent to it equals the exterior angles of a triangle, but the interior angles of a triangle always add up to 180°. Subtracting the angle of the desired vertex from 180° is another method for determining a triangle's exterior angle.The sum of a triangle's angles in a Euclidean space equals the straight angle. Three angles make up a triangle, one at each vertex and two on either side. If there are additional geometries for which this total is different, it has long been unknown.The top of the triangle can be connected to the base by a vertical line if you have two p side-lengths and one m side-length. With hypotenuse p and base 1/2*m, this will result in two equal right triangles.You may determine the base angles by using:
theta_base = arcos(m/2p)
The top angle can be calculated using:
theta_top = 2*arcsin(m/2p)
The angle of your initial isosceles triangle was cut in half by drawing the vertical, therefore you multiply by two to determine theta top. Therefore, arcosin(m/2p) would only return the first half of the angle value.To learn more about angles of triangle refer to:
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express the column matrix b as a linear combination of the columns of a. (use a1, a2, and a3 respectively for the columns of a.) a
We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.
First of all we put the vectors in terms of different variables, such as:
a1(1,-2,0)=(a,-2a,0);
a2(0,1,3)=(0,b,3b);
a3(6,-6,18)=(6c,-6c,18c);
To know that a vector is a linear combination we need to express it like a sum of other different vectors.
(2,-2,6)=(a,-2a,0)+(0,b,3b)+(6c,-6c,18c)
(2,-2,6)=(a+0+6c,-2a+b-6c,0+3b+18c)
We express this sum like a system of equations.
a+6c=2
-2a+b-6c=-2
3b+18c=6
We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.
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The number of miles y is proportional to the number of hours x as shown in the graph.
An equation to represent this proportional relationship is y = 65x.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
y represents the number of hoursx represents the number of miles.m represents the slope.Next, we would determine the linear equation representing the line which passes through the points (3, 195) and (6, 390) by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 195 = (390 - 195)/(6 - 3)(x - 3)
y - 195 = 195/3(x - 3)
y - 195 = 65(x - 3)
y = 65x - 195 + 195
y = 65x
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Please help me asap, it's missing :/
Step-by-step explanation:
g(f(x)) means that we first take x and calculate f(x).
then we take that result and use as input value for g(x).
x = -5
f(-5) = (-5)² + -5 - 12 = 25 - 5 - 12 = 8
and now
g(8) = -2×8 - 15 = -16 - 15 = -31
g(f(-5)) = -31
Describe how you can determine the domain and range of f(x) = −8x7 + 1.9x6 − 7x5 + 0.12x3 + 22x2 + 4.
The domain of a function is the set of possible values that can be plugged into it.
What is the Domain and Range of a Function?The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The collection of all possible inputs and outputs constitutes a function's domain and range, respectively. Important features of a function are the domain and range. The domain accepts all potential input values from the set of real numbers, and the range accepts all function output values.
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a 2.5 nm torque is applied to a flywheel for 10.0 seconds. if the flywheel is initially at rest and its moment of inertia is 2.0 kg m2, determine its angular momentum. group of answer choices
The angular momentum of the flywheel is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s.
1. Determine the angular momentum of the flywheel:
Angular momentum = Torque × Time × Moment of Inertia
= 2.5 Nm × 10.0 s × 2.0 kg m2
= 50 kg m2/s
The angular momentum of an object can be determined from the product of the applied torque, the time interval, and the moment of inertia. The moment of inertia is the rotational inertia of an object, which is the resistance to changes in its angular velocity. The angular momentum of the flywheel in this question is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s. This means that the flywheel will have an angular momentum of 50 kg m2/s after the 10-second interval when the torque is applied. The angular momentum of the flywheel will remain constant until another torque is applied to change it.
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John can mow his lawn in 3 hours and his sister, Julie, can mow it in 2 hours. How long will it take them to mow their lawn if they work together?
A. 1 hour 12 minutes
B. 1 hour 15 minutes
C. 1 hour 20 minutes
D. 1 hour 30 minutes
E. 1 hour 35 minutes
It would take 12 minute for them to mow their lawn if they work together
What is an equation?An equation is an expression showing the relationship between numbers and variables.
John can mow his lawn in 3 hours and his sister, Julie, can mow it in 2 hours.
Let t represent the time it would take them to mow their lawn if they work together, hence:
(1/3hours) * t + (1/2hours) * 2 = 1
t(1/3 + 1/2) = 1
(5/6)t = 1
t = 6/5 hours = 1 hour 12 minutes
It would take 12 minutes
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A survey was conducted that asked 1018 people how many books they had read in the past year. Results indicated that x=14.1 books and s=16.6 books. Construct a 99% confidence interval for the mean number of books people read. Interpret the interval. Construct a 99% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to two decimal places as needed.) A. There is a 99% probability that the true mean number of books read is between nothing and nothing. B. There is 99% confidence that the population mean number of books read is between nothing and nothing.
There is 99% confidence that the population mean number of books read is between 1.51 and 26.69. This confidence interval indicates that there is a 99% probability that the true mean number of books read by people in the past year falls between 1.51 and 26.69.
Confidence interval for the mean = (x - z(s/√n), x + z(s/√n))
Where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the critical value for the given confidence level (in this case, 99%).
Therefore, the confidence interval for the mean number of books read is:
(14.1 - 2.58(16.6/√1018), 14.1 + 2.58(16.6/√1018))
= (1.51, 26.69)
This confidence interval indicates that there is a 99% probability that the true mean number of books read by people in the past year falls between 1.51 and 26.69. In other words, it is likely that the average number of books read by people in the past year is between these values. This interval is an estimate of the population mean and the confidence level indicates how confident we can be that the true mean falls within this range.
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If y varies directly as x and the constant of variation is -2, which equation represents this relationship
The equation represents this relationship between the variables 'x' and 'y' will be y = -2x.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If y varies directly from x. Then the proportionality is given as,
y ∝ x
If the proportionality signature is removed then a constant is introduced. Then the equation is given as,
y ∝ x
y = kx
The constant of variation is -2. Then the equation is given as,
y = - 2x
The equation represents this relationship between the variables 'x' and 'y' will be y = -2x.
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WHATS THE ANSWER? WILL APPRECIATE SOO MUCH !!
(s+12)^3
I am wasting space here as you can tell but no fr the answer is (s+12)^3
QUICKKKK I NEED HELP Quadrilateral ABCD is given, the interior angle at vertex B is 97 degrees and the exterior angle at vertex A is 88 degrees. Lines AB and CD are parallel. What is the most precise name for this given special quadrilateral? What is the measure of angle 1? What is the measure of angle 2?
The measure of angle 1 is 92 and the measure of angle 2 is 83.
What are lines and angles?Lines are straight with little depth or width. Perpendicular lines, intersecting lines, transversal lines, and other types of lines will be covered. An angle is a shape formed by two rays emerging from a common point. In this field, you may also come across alternate and corresponding angles.
Given that ABCD is given, the interior angle at vertex B is 97 degrees and the exterior angle at vertex A is 88 degrees. Lines AB and CD are parallel.
The measure of angle 1 is,
∠1 = 180 - 92 = 88
The measure of angle 2 is,
∠2 = 180 - 97 = 83
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based on your answer(s) to part (a), complete the following statement to represent the length of candle remaining in terms of the burned length b .
The length of the remaining candle is equal to the total length of the candle minus the length of the candle that has been burned, or (total length - b).
The length of the remaining candle can be calculated by subtracting the length of the candle that has been burned (b) from the total length of the candle. This is because when a candle is burned, the length of the candle decreases. To calculate the remaining length of the candle, start by determining the total length of the candle. Then, subtract the length of the candle that has been burned (b). The result is the length of the remaining candle. The formula for this calculation is (total length - b). The length of the candle remaining is (b - 2). For example, if the total length of the candle is 6 inches and 2 inches of the candle have been burned, the remaining length of the candle would be 4 inches (6 - 2 = 4).
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A complete question: Based on your answer(s) to part (a), complete the following statement to represent the length of candle remaining in terms of the burned length bb.
assess reasonableness a monument will be at the circumcenter of a triangular plot of land at the state capital. on the coordinate grid, the vertices of the triangular plot of land are a(1, 5) , b(7, 5) , and c(8, 0) .
Yes, this is reasonable. The circumcenter of a triangle is found by taking the average of the x-coordinates of the three points and the average of the y-coordinates of the three points, so for this triangle, the circumcenter would be at (5.67, 2.67).
The circumcenter of the triangular plot of land with vertices at (1, 5), (7, 5), and (8, 0) is at (5.67, 2.67), which is reasonable.
1. Calculate the average of the x-coordinates of the three vertices: (1 + 7 + 8) / 3 = 16 / 3 = 5.67
2. Calculate the average of the y-coordinates of the three vertices: (5 + 5 + 0) / 3 = 10 / 3 = 2.67
3. Therefore, the circumcenter of the triangle is (5.67, 2.67).
The circumcenter of the triangular plot of land with vertices at (1, 5), (7, 5), and (8, 0) is at (5.67, 2.67), which is reasonable.
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I need help with the question below
Answer:
see below
Step-by-step explanation:
there are 3 points given
diff in y / diff in x = slope
so plug in any 2 points' Y and x and get the slope
because it's downward shaped, you know the slope MUST be negative.
so diff in Y = 23-29 = -6
diff in X = 3-7 =2
so slope is +3
intercept is given, when x=0 y = 32
it represents what F is when it's 0C°
Input (x) 1 2 4 5
Output (y) 6 12 18 24 30
1
6 12
2 3
18
4
24
5
30
The output is determined by the pattern of the input.
What is pattern?Pattern is a repeated design or motif used to create a visually pleasing effect. Patterns are often seen in nature, architecture, clothing, and artwork. Patterns can be used to create shapes, textures, and decorations. They can add interest and depth to a design. Patterns can be made up of geometric shapes, lines, curves, and combinations of those elements. They can be created with a variety of materials and techniques, including weaving, printing, embroidery, and painting. Patterns can be used to create continuity, emphasize a focal point, or provide a sense of balance. Patterns can be used to draw the eye to a particular area, or to create a sense of order and organization.
In this example, each output number is the sum of the two numbers before it. Therefore, the output is 6 (1 + 2), 12 (2 + 4), 18 (4 + 5), 24 (5 + 6), and 30 (6 + 8).
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Find the general solution of the first-order linear differential equation y' - (ln x)y = 3 x^x.
y(x)=
Note: Use C for the arbitrary constant.
The general solution of the first-order linear differential equation y' - (ln x)y = [tex]3 x^x[/tex] is [tex]y=3x^{x} + cx^{x} e^{-x}[/tex]
As per the give,n data the given differential equation is:
y' - (ln x) y = 3 [tex]x^x[/tex]
Here have to determine the general solution of the first-order linear differential equation.
The differential equation is linear if the dependent variable y and its derivative only occur in the first degree.
Then, [tex]$\frac{d y}{d x}-(\ln x) y=3 x^x$[/tex]
This is of the form [tex]$\frac{d y}{d x}[/tex] + P(x)y = Q(x) which is the linear equation.
In order to solve this kind of differential equation, we have to multiply it by an integrating factor.
Here, P = - ln (x), Q(x) = 3 [tex]x^x[/tex]
I F = [tex]e^{\int P d x}[/tex]
I F = [tex]e^{-\int \ln (x)}[/tex]
I F = [tex]e^{-(x \ln x-x)}[/tex]
I F = [tex]e^{x-x \ln x}[/tex]
I F = [tex]\frac{e^x}{e^{x \ln x}}[/tex]
I F = [tex]\frac{e^x}{x^x}[/tex]
Hence, the general solution is
[tex]& y(I F)=\int Q(x)(I F) d x+c \\[/tex]
[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=\int 3 x^x\left(\frac{e^x}{x^x}\right) d x+c \\[/tex]
[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=\int 3 e^x d x+c \\[/tex]
[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=3 e^x+c \\[/tex]
[tex]& \Rightarrow y=3 x^x+c x^x e^{-x}[/tex]
Hence, the general solution is [tex]y=3x^{x} + cx^{x} e^{-x}[/tex]
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12% of x =360 hhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
x = 3000
Step-by-step explanation:
Answer:
x=3000
Step-by-step explanation:
Given that, 12% of x=360
or, (x)× (12÷100)=360
or, (12x ÷100)=360
or, 12x=36000
or, x=36000÷12
or, x=3000
the sum of a number with the square of its following algebraic language
[tex]\bold{n + (n+1)^{2}}[/tex]
Step by step explanation:An unknown number can be interpreted with any letter of the alphabet, they will be our unknowns to be able to form an algebraic expression.
Well, in this case, I will use the variable n, to name the unknown number.
Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.
(grouping the data the following algebraic expression is obtained):
[tex]\bold{n + (n+1)^{2}}[/tex]
Answer:
(n + 1 )
Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.
..
In a class of 40 students, 8 are in the drama club, 12 are in the art club, and 5 are in the music club. If a student is selected at random, what is the probability that the selected student is in none of the clubs listed?
Considering the definition of probability, the probability that the selected student is in none of the clubs listed is 0.375 or 37.5%.
Definition of probabilityProbability is the greater or lesser chance that a given event will occur.
In other words, the probability establishes a relationship between the number of favorable events (number of cases in which event A may or may not occur) and the total number of possible events through the Laplace's Law as follow:
P(A)= number of favorable cases÷number of total cases
Probability that the selected student is in none of the clubs listedIn this case, you know:
Total number of students = 40 (number of possible cases)Total number of students in drama club= 8Total number of students in art club= 12Total number of students in music club= 5Total number of students in a club= 8 + 12 + 5= 25Total number of students in none of the clubs listed= 40 - 25= 15 (number of favorable cases)Replacing in the definition of probability:
P(A)= 15÷40
Solving:
P(A)= 0.375
Expressed as a percentage:
P(A)= 37.5%
Finally, the probability is 0.375 or 37.5%.
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You roll a 6-sided die.
What is P(greater than 5 or less than 3)?
2/6
2/3
1/2
1/6
1/6
The probability of an event is the number of ways the event can happen divided by the number of possible outcomes. In this case, the possible outcomes are the numbers on the die, which are 1, 2, 3, 4, 5, and 6.
The event of rolling a number greater than 5 or less than 3 can happen in two ways: rolling a 6 or rolling a 1 or 2. So the probability of this event is:
P(greater than 5 or less than 3) = (number of ways the event can happen) / (number of possible outcomes) = 2/6 = 1/3
So the answer is option D. 1/6
Julieta went shopping for a new phone. Sales tax where she lives is 7%. The price of the phone is $29. Find the total price including tax. Round to the nearest cent.
The total amount of money that the phone will cost including tax would be = $31.03
What is cost price?Cost price is the amount of money that a seller tags a particular product which is usually after the tax fees and other service fees has been added apart from the actual price of the product.
The price of the phone = $29
The percentage of tax = 7% of 29
= 7/100 × 29
= 203/100 = $2.03
Therefore, the total amount of money that the phone will cost including tax would be = 29 + 2.03 = $31.03
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PLS HELP TYY!!The diagram below shows the dimensions of a can of beans.
A can of beans is shown. A dashed line drawn across the top of the can is labeled seven centimeters. The height of the can is labeled eleven and six tenths centimeters.
How much tin was used to make the can rounded to the nearest square centimeter? Use 3.14 for π.
Enter the correct answer in the box.
Answer:
332 cm²
Step-by-step explanation:
You want to know the surface area of a tin can that is 7 cm in diameter and 11.6 cm high.
Surface areaThe area of a cylinder is given by the formula ...
SA = πd(d/2 +h) . . . . . where d is the diameter and h is the height
ApplicationUsing the given values, d=7 and h=11.6, we find the area to be ...
SA = (3.14)(7 cm)(3.5 +11.6 cm) ≈ 332 cm²
About 332 square centimeters of tin are required to make the can.
Polynomial 1: 4x2
+ 5x − 4
Polynomial 2: 4x2
+ 4x − 2 What is the product of the two polynomials?
Responses
A 32x4
+ 36x3
− x2
+ 26x + 432 x 4 + 36 x 3 − x 2 + 26x + 4
B 16x4
+ 36x3
− x2
+ 26x + 416 x 4 + 36 x 3 − x 2 + 26x + 4
C 8x4
+ 18x3
− 4x2
− 26x + 88 x 4 + 18 x 3 − 4 x 2 − 26x + 8
D 16x4
+ 36x3
− 4x2
− 26x + 8
The product of the two polynomials is 16x^4 + 36x^3 - 4x^2 - 26x + 8. The solution is obtained by the method of polynomial multiplication.
What is polynomial multiplication?
The process of multiplying two or more polynomials together is known as polynomial multiplication. To obtain the final polynomial, the terms of the first and second polynomials are multiplied. We can multiply polynomials in a variety of ways depending on the kinds we are using. Each form of polynomial has a different set of guidelines for multiplication. Polynomials are multiplied by multiplying the coefficient by another coefficient and the variable by another variable.
We are given two polynomials
Polynomial 1: 4x^2 + 5x − 4
Polynomial 2: 4x^2 + 4x − 2
Multiplying both, we get
⇒(4x^2 + 5x − 4)*(4x^2 + 4x − 2)
⇒16x^4 + 16x^3 - 8x^2 + 20x^3 + 20x^2 - 10x - 16x^2 - 16x + 8
⇒16x^4 + 36x^3 - 4x^2 - 26x + 8
Hence, the product of the two polynomials is
16x^4 + 36x^3 - 4x^2 - 26x + 8.
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Test market data shows that changing the price of a product changes the demand. Does this table indicate that purchase price is a function of demand? Why or why not?
The table indicates that purchase price is a function of demand, as each demand is mapped to a single purchase price.
When does a relationship represents a function?To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.
The input and output variables for this problem are given as follows:
Input: demand.Output: purchase price.In the table, there are no repeated demand values, meaning that the purchase price is a function of the demand, as there are no inputs mapped to multiple outputs.
Missing InformationThe table is given by the image presented at the end of the answer.
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