Answers
Remember the two formulas:
P(A and B) = P(A) * P(B)
P(A or B) = P(A) + P(B) - P(A and B)
Related Questions
A certain quadratic function has x-intercepts at 2 and 3. What are the x-coordinates of its vertex?
a) 5/2 because by symmetry, both x-intercepts should be the same vertical distance from the vertex point which is at x = 5/2 or 2.5.
b) 7/2 because by symmetry, both x-intercepts should be the same vertical distance from the vertex point which is at x = 7/2 or 3.5.
c) 5/2 because by symmetry, both x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5.
d) 7/2 because by symmetry, both x-intercepts should be the same horizontal distance from the axis of symmetry at x = 7/2 or 3.5.
Answers
Because both of its x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5 according to symmetry, the vertex's x-coordinates are 5/2.
What is coordinates?A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
Here,
The parabola is symmetric around its vertex. This means that the roots are the same horizontal distance away from the vertex. Furthermore, we can apply the midpoint formula on the given roots to find the x coordinate of the vertex.
Find the midpoint of 2 and 3 to get
(2+3)/2 = 5/2
The x-coordinates of its vertex is 5/2 because by symmetry, both x-intercepts should be the same horizontal distance from the axis of symmetry at x = 5/2 or 2.5.
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Q2. On average, the surface area A of human beings is related to weight W and height H.
Measurements on several individuals give values of A in the following table:
H (cm) 182 180 179 187 189 194 195
193 200
W (kg)
74 88 94 78 84
98 76
86 96
A (m²) 1.92 2.11 2.15 2.02 2.09 2.31 2.02 2.16 2.31
Develop an equation to predict area as a function of height and weight using numerical method and MATLAB.
Use it to estimate the surface area for a 187-cm, 78-kg person
Answers
To develop an equation to predict the surface area of a person as a function of their height and weight using numerical methods and MATLAB, you can follow these steps:
The required details for MATLAB in given paragraph
Begin by organizing the given data into two separate arrays: one for height (H) and one for weight (W). For example, you might create the following arrays:
H = [182 180 179 187 189 194 195 193 200];
W = [74 88 94 78 84 98 76 86 96];
A = [1.92 2.11 2.15 2.02 2.09 2.31 2.02 2.16 2.31];
Use the MATLAB function "polyfit" to fit a polynomial function to the data. You can specify the degree of the polynomial function based on the number of variables you want to include in the model. For example, to fit a second-degree polynomial function, you can use the following command:
p = polyfit(H,A,2);
This will fit a polynomial function of the form A = p(1) * H^2 + p(2) * H + p(3) to the data, where p(1), p(2), and p(3) are the coefficients of the polynomial.
Use the MATLAB function "polyval" to evaluate the fitted polynomial function at a specific value of H. For example, to estimate the surface area for a person with a height of 187 cm, you can use the following command:
A_estimated = polyval(p,187);
This will return the estimated surface area for a person with a height of 187 cm. You can use similar commands to estimate the surface area for different values of H
what do you mean by MATLAB?
MATLAB (short for "Matrix Laboratory") is a programming language and software environment for numerical computation, visualization, and programming. It is commonly used in scientific, engineering, and mathematical fields to analyze and visualize data, develop algorithms, and build mathematical models.
A function in MATLAB is a self-contained block of code that performs a specific task or computation. Functions are useful because they allow you to reuse code and make your programs more modular and easier to understand. In MATLAB, you can define your own functions or use built-in functions that are provided with the software.
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Find the sector area for the following:
(Use pi=3.14 when necessary and round your final answer to the hundredths.)
Sector Area =
Answers
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =\frac{2\pi }{3} \end{cases}\implies A=\cfrac{~~ \frac{2\pi }{3 }\cdot 6^2 ~~}{2}\implies A=12\pi \implies A\approx 37.68[/tex]
At the halfway point of a telethon, a charity has only raised one quarter of its
target amount. If its total amount raised doubles each of the next two hours,
what percentage of its target amount will it have raised?
75%
80%
87.5%
93%
100%
Answers
Answer:75%
Step-by-step explanation:
Let R be the relation defined on P({1,……,100}) by A R B , if and only if |A n B| is even.
Is R reflexive? Is R symmetric? Is R anti-symmetric? Is R transitive?
Answers
Only the transitive relation is true for the provided relation for (x, y) R if x y defined on the set of positive integers.
Step-by-step explanation:Assuming (x, y), R
To determine whether or not a relation is transitive, symmetric, antisymmetric, reflexive, or a partial order:
If (x, x)R for all x R x x for all x R, which is false.
b. Symmetric: For all (x, y) R, if "x" and "y" are related, then "y" is also related to "x."
In this case, x y y x for all (x, y) R, which is false.
c. Antisymmetric: If "x" and "y" are related, then "x" equals "y" for all (x, y) R.
In this case, x y and y x x = y are false.
not in opposition.
c. Transitive: If "x" and "y" are related, then
For all values of x, y, and z R, 'x' is connected to 'z'.
For any x, y, and z R, x y, y z x z.
True.
Therefore, only the transitive relation for the given relation for (x, y) R if x y defined on the set of positive integers is true.
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Shureka Washburn has scores of 67, 65, 64, and 88 on her algebra tests.
a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 73 or higher, given that the final exam counts as two tests.
b. Explain the meaning of the answer to part (a).
Answers
BY using the inequality,
(67 + 65 + 64 + 88 + 2x)/5 ≥ 73,
we find the score she must make on final exam to pass the courses with an average of 73 or higher is x>=80.
What is inequality?An inequality is a mathematical statement that shows that one quantity is greater than or less than another quantity.
What is average?The average, or mean, of a set of numbers is a measure of the central tendency of the set.
This inequality states that the average of Shureka's scores on the four tests and the final exam must be greater than or equal to 73 in order for her to pass the course. Solving for x, we find that x ≥ 80.
The meaning of the answer to part (a) is that Shureka must make a score of 80 or higher on the final exam in order to pass the course with an average of 73 or higher. In other words, if Shureka makes a score of 80 or higher on the final exam, her average score on the five tests will be 73 or higher, which is the minimum required to pass the course. If she makes a score lower than 80 on the final exam, her average score will be less than 73, and she will not pass the course.
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Which of the following statements is true regarding that equation |x+3|-2=k?
There are no solutions when k=-1 or when k=-3.
If k=-1 there are solutions, but if k=-3 there are no solutions.
If k=-3 there are solutions, but if k=-1 there are no solutions.
There are solutions when k=-1 and when k=-3.
Answers
There are solutions when k = -1 and when k = -3
What is Linear Equation in One Variable?
A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.
Solution:
|x + 3| - 2 = k
Removing the modulus sign
x + 3 - 2 = k -----(i) = x + 1 = k
-x - 3 - 2 = k -----(ii) -x - 5 = k
Putting k = -1
(i) x = -2 and (ii) x = -4
Putting k = -3
(i) x = -4 and (ii) x = -2
Since, x has solution on both the values of k
We can say that,
There are solutions when k = -1 and when k = -3
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If 250 ml of milk has 154 calories, how many calories does 60 ml of milk have?? (pls respond fast!))
Answers
Answer:
36.96 calories
I don’t remember how to do this. Help
Answers
For question one is Another name of bj would be boj
Find (fog)(x).
f(x) = 5x
g(x) = 6x
Write your answer as a polynomial in simplest form.
(fog)(x) =
Answers
Answer: (fog)(x) = f(g(x)) = f(6x) = 5(6x) = 30x
So (fog)(x) = 30x, which is a polynomial in simplest form
An artist is building a pedestal out of wood that will be used to display a piece of sculpture. She plans to cover the pedestal with tile. How much tile will it take to cover the pedestal, including the bottom?
224 square feet
192 square feet
144 square feet
288 square feet
Answers
tile will it take to cover the pedestal, including the bottom is 288 square feet
How much tile will it take to cover the pedestal, including the bottom?It depends on how big the pedestal is and how big the tiles are that are being used. It would require 192 square feet of tile to cover the pedestal, including the bottom, if the tiles were one foot square and the pedestal was four feet tall.To cover the pedestal, however, would require 224 square feet of tile if it were five feet tall and the chosen tiles were two feet square.Similar to this, 144 square feet of tile would be required to cover a pedestal that is three feet tall and two feet square. The pedestal would require 288 square feet of tile to cover it, including the bottom, assuming the tiles were one foot square and the pedestal was five feet tall.As you can see, the size of the pedestal and the tiles being used both affect how many tiles are needed to completely cover the pedestal.To learn more about a tiling project refer to:
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Help
Is it correct?
Answers
Answer:
minimum value = 10
Step-by-step explanation:
the minimum value is at the left side of the whisker in the box plot, then
minimum value = 10
URGENT 20 points please
The ancient Greek mathematician Euclid is credited with the development of the theorem that the sum of the angles of
a triangle is 180 degrees.
Use the previous information to solve for the measure of the two unknown angles of an isosceles triangle where the
third angle measures 32 degrees.
If the third angle measures 32 degrees, the other two angles measure ____ and ____
Answers
do 180-32=148 and then do 148÷2=74
How many solutions does this system of equations have? 2x+y=1 4x+2y=2 O Exactly two None O Exactly one Infinitely many
Answers
Answer:
Infinitely many
Step-by-step explanation:
2x+y=1
4x+2y=2
Divide both sides of the second equation by 2.
2x + y = 1
This is the same as the first equations. Both equations are the same equation. Since you have only one equation and two variables, there is an infinite number of solutions.
Answer: Infinitely many
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
The area of the shaded region is (Round to four decimal places as needed.)
Answers
The area of the shaded region is given as follows:
0.879.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.Considering the percentile, the area in this problem is given by one subtracted by the p-value of z = -1.17, which is of 0.121.
Hence:
1 - 0.121 = 0.879.
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solve the following expression when t=6 and d=8. t+d divided by 8-6. help
Answers
6 + 8 = 14
You have to divide this by 8-6 which is 2
14 / 2 = 7
Your answer should be 7
for a roll of a fair die, each of the outcomes 1, 2, 3, 4, 5, or 6 is equally likely. a red die and a green die are rolled simultaneously, and the difference of the outcomes (red - green) is computed. this is repeated for a total of 500 rolls of the pair of dice. which of the following graphs best represents the most reasonable distribution of the differences?
Answers
Option B is the graph best represents the most reasonable distribution of the differences.
What is random variables?Any variable whose value is uncertain or any function that values each result of an experiment is referred to be a random variable. Discrete (having definite values) or continuous random variables are also possible (any value in a continuous range).
As a result, the random variables are so-called because it is impossible to determine their value with certainty; instead, we can only guess, and this estimate is known as the probability that a random variable will have a given value.
Here we assume the random variable X denotes the difference between the outcomes of rolling the two dice.
here the number of rolls is 500. As we know by central limit theorem every distribution approaches to normal distribution irrespective of the parent distribution. Since Normal is symmetric about the mean the most reasonable distribution is the second figure.
Option B is the correct answer.
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The complete question is as follows:
12 M Attend to Precision Ricardo has 325 tiles to make 4
mosaics. He uses the same number of tiles for each mosaic.
How many tiles does Ricardo use for each mosaic? How
many tiles does he have left over?
Divide
3
Answers
The number of tiles Ricardo use for each mosaic is 81 and 1 tile left over.
What is the division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Given that, M Attend to Precision Ricardo has 325 tiles to make 4 mosaics.
Here, the number of tiles need for each mosaic is 325/4
4|325|81
324
______
1
Therefore, the number of tiles Ricardo use for each mosaic is 81 and 1 tile left over.
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The graph represents the journey of a bus from the bus stop to different locations:
The title for the graph is Bus Journey. The label on the y-axis is Distance in miles, and the label on the x-axis is Time in hours. The graph shows 5 parts. The part labeled 1 is a smooth curve going up from the origin. The part labeled 2 is a straight horizontal line. The part labeled 3 is a smooth curve going up. The part labeled 4 is a straight horizontal line. The part labeled 5 is a smooth curve going down that touches the x-axis.
Part A: Use complete sentences to describe the motion of the bus in parts 1, 2, 3, 4, and 5 of the journey. (4 points)
Part B: In which parts of the graph is the function increasing, decreasing, and constant? (4 points)
Part C: Is the graph linear or non-linear? Explain your answer. (2 points)
Answers
Answer:
Part A is 100
Part B is 50
Part C is 25
all of it goes down by 15 so just keep subtracting
Step-by-step explanation:
I used common since and a sheet of paper
A football club sells, on average, 23000 tickets per match. In one season they play, on average, 46 matches.How many tickets do they sell, on average, each season?
Answers
Answer:
the football team sells 805,000 tickets each season
Step-by-step explanation:
average number of tickets sold per match=23,000
the average number of games played each session=35
the number of tickets sold on average each session = 23,000 x 35 which equals 805,000
so the average football club sells 805,000 tickets each season
What is the end behavior of f(x)=−x^4−2x^3+2x^2−5?
Answers
Using the Leading Coefficient Test the end behavior of the given function f(x) = −x⁴ − 2x³ + 2x² − 5 is
x tends to -∞, f(x) tends to -∞What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of functionThe given function is:
f(x) = −x⁴ − 2x³ + 2x² − 5
The end behavior is determined by the leading Coefficient = −x⁴ and it is described as
x ⇒ ∞ f(x) ⇒ ∞
x ⇒ -∞ f(x) ⇒ -∞
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find f^-1(x) for the function f(x)=x/2-4.
Answers
Answer:
f(x)=x/2-4
-f(x)=a
a=x/2-4
x=a/2-4
a/2-4=x /×2
a-8=2x
a=8+2x -> f^-1(x)=8+2x
One side of a rectangle is 8 cm and the perimeter is 48 cm. Find the area.
Answers
Answer: 128 square centimeters
Step-by-step explanation:
If the perimeter is 48 cm, then the sum of the lengths of any two adjacent sides must be 24 cm.
Since the length of one of these sides is given to be 8 cm, it follows the length of the corresponding adjacent side is 16 cm.
Thus, using the formula for the area of a rectangle, the area is 128 square centimeters.
In triangle ABC, m∠B = (13x − 16)° and the measure of the exterior angle to ∠B is (8x − 14)°. Find m∠B.
10°
66°
49°
114°
Answers
The measure of angle B is (d) 114 degrees
How to determine the measure of angle B?From the question, we have the following parameters that can be used in our computation:
B = 13x - 16
Exterior of B = 8x - 14
As a general rule, the sum of an angle and its exterior is 180 degrees
This means that
13x - 16 + 8x - 14 = 180
Evaluate the like terms
So, we have
21x = 210
Divide both sides
x = 10
Recall that
B = 13x - 16
So, we have
B = 13 x 10 - 16
Evaluate
B = 114
Hence, the measure is 114 degrees
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Answer:
The measure of angle B is (d) 114 degrees
Step-by-step explanation:
At noon, ship A is 130 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?
Answers
√5 km/h fast is the distance between the ships changing at 4:00 PM .
What is the Pythagorean theorem ?
The Pythagorean theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.
This is represented by the equation a2 + b2 = c2 in common algebraic notation.
Ship A is sailing 25 km/h east and Ship B is sailing 15 km north. They are giving us the time frame, which is 4 hours ( t = 4). Recall that Distance = Rate * time. Let us find the distance for each ship after 4 hours
Ship A Ship B
d=25*4 = 100 km d=15*4= 60 km
the Pythagorean theorem.
a2+b2=c2
(30)2+(60)2=c2
c=30√(5)
From the question, "How fast" is asking us for a rate. The rate on the hypotenuse side. We have to take the derivative of the pythagorean theorem with respect to time.
2a(da/dt) + 2b(db/dt) = 2c(dc/dt)
Solve for dc/dt
dc/dt = [a(da/dt) + b(db/dt)] / c
dc/dt = [30(-25) + 60(15)] / 30√5 ****Note: we have -25 as time increases, the distance is smaller
dc/dt = √5 km/h
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standard form. (x+8)(x−6)
Answers
Answer:
x^2-2x-48
Step-by-step explanation:
FOIL
Firsts = x*x = x^2
outside = x*-6 = -6x
inside = 8*x = 8x
lasts = 8*-6 = -48
add all together x^2-6x+8x-48 = x^2-2x-48
Answer:
x² + 2x - 48
Step-by-step explanation:
( x + 8 ) ( x - 6 )
= x ( x - 6 ) + 8 ( x - 6 )
= x*x - 6*x + 8*x + 8*( - 6 )
= x² - 6x + 8x - 48
= x² + 2x - 48
find the area under the standard normal curve between the z-scores 0.97 and 1.26. do not round your answer.
Answers
Area under the given standard normal curve for the z-score between 0.97 to 1.26 is equal to 0.06219.
As given in the question,
Given values to find area under the standard normal curve = 0.97 to 1.26
From the table of area under the given standard normal curve
z - score of 0.97 is equal to 0.33398
z-score of 1.26 is equal to 0.39617
Area under given standard normal curve between z-scores 0.97 and 1.26
= P ( 0.97 < z < 1.26 )
= 0.39617 - 0.33398
= 0.06219
Therefore, the area under the given standard normal curve for the z-score between 0.97 to 1.26 is equal to 0.06219.
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Which statements about the cylinder are true? Select two options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is 1÷4π.x²
The area of the cylinder's base is 1÷2π.x²
The height of the cylinder is 2x units
The height of the cylinder is 4x units
Answers
The area of the cylinder's base is 1÷4π.x² is the correct option
What is a cylinder?
A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centres of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.
The three-dimensional form of a cylinder is made up of two parallel circular bases connected by a curving surface. The right cylinder is created when the centres of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centres.
The cylinder seems to be a rectangle from the side perspective and a circle from the top view.
Since a cylinder has a curved form and no straight lines, it lacks vertices in contrast to cones, cubes, and cuboid shapes. Two of its faces are round.
According to the question volume of the cylinder is
1. πr^2h = πr^3
h=r=x/2
2.
The radius of cylinder is
= x/2
3.
The area of the cylinder's base is
= πr^2
= (π x^2)/4
4.
The height of the cylinder is =
radius= height =x/2
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please help me with this question
Answers
a) The probability that both are girls is of: 21/150.
b) The probability that both are from the same school is of: 0.7333 = 73.33%.
How to obtain the probabilities?
The probabilities are obtained as the division of the number of desired outcomes by the number of total outcomes.
For item a, the outcomes are given as follows:
One girl from school A -> 7/15 probability.
One girl from school B -> 3/10 probability.
Hence the probability that both are girls is of:
p = 7/15 x 3/10 = 21/150.
The probability that the two boys are from the same school can be given by these two cases:
School A: 8/15 x 7/14.
School B: 7/10 x 6/9.
Then the probability is of:
p = 8/15 x 7/14 + 7/10 x 6/9 = 0.7333 = 73.33%.
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Solve for x: -(2x-6)+10x=-5x-2(-7x-7)