Using the concept of conditional probability and the conditions provided, The answer is [tex]\frac {p^2}{2pq}[/tex] .
What do you mean by probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probabilities can be calculated using the ratio of the number of favorable outcomes to the total number of possible outcomes. It helps us to understand the uncertainty of events.
What do you mean by false positive results?A false positive result is when a test indicates that a particular condition or attribute is present, when in reality it is not. For example, in medical testing, a false positive result would occur when a test for a disease returns a positive result but the person being tested does not actually have the disease. False positives can have serious consequences, as they can lead to unnecessary treatments, further testing, and anxiety for the person being tested.
p=probability of occurrence
q=1-p
P(false positive for both subjects | false positive for one subject) = P(false positive for both subjects and false positive for one subject) / P(false positive for one subject)
P(false positive for both subjects | false positive for one subject) = p^2 / (2pq)
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OPEN ENDED NOT MULTIPLE CHOICE
Some recent studies suggest that a teenager sends an average of 60 texts per day. For each of
the following scenarios, find the linear function that describes the relationship between the input
value and the output value. Then, determine whether the graph of the function is increasing,
decreasing, or constant.
a. The total number of texts a teen sends is considered a function of time in days. The input is
the number of days, and output is the total number of texts sent.
b. A teen has a limit of 500 texts per month in his or her data plan. The input is the number of
days, and output is the total number of texts remaining for the month.
c. A teen has an unlimited number of texts in his or her data plan for a cost of $50 per month.
The input is the number of days, and output is the total cost of texting each month
Write the equation of the line, that passes through the points (- 6, 1) and (10, 0)
Equation:
Now, write an equation of a line that is parallel to the above line and passes through point (-7, 2) in all three forms below.
Point-Slope Form
Slope-Intercept Form
Standard Form
The equation of the line, that passes through the points (- 6, 1) and (10, 0) is y = - (1/16)x + (5/8) and the equation of a line that is parallel to the above line and passes through point (-7, 2) is y = - (1/16)x + (25/16).
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that the line passes through the points (- 6, 1) and (10, 0).
The slope of the line will be -
{m} = (0 - 1)/(10 + 6) = -1/16
{m} = -1/16
We can write the equation as -
y = - (1/16)x + c
For the point (10, 0), we can write -
0 = - (1/16) x 10 + c
0 = - (10/16) + c
c = 10/16
c = 5/8
So, we can write the equation as -
y = - (1/16)x + (5/8)
The equation of a line that is parallel to the above line and passes through point (-7, 2) is as follows -
y = - (1/16)x + c
2 = - (1/16) x - 7 + c
c = 2 - 7/16
c = 25/16
y = - (1/16)x + (25/16)
Therefore, the equation of the line, that passes through the points (- 6, 1) and (10, 0) is y = - (1/16)x + (5/8) and the equation of a line that is parallel to the above line and passes through point (-7, 2) is y = - (1/16)x + (25/16).
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2. Which of the following. are solutions to 5.7 + x = -3.5? Choose as many as
apply.
A. -3.5+5.7
B. 3.5-5.7
C. -3.5-(-5.7)
D.-3.5-5.7
Answer:
option D is correct
5.7+x=-3.5
x= -3.5-5.7
Answer:
D
Step-by-step explanation:
5.7 + x = - 3.5 ( subtract 5.7 from both sides )
x = - 3.5 - 5.7 ( x = - 9.2 )
In a math question, Magda correctly answered a question that asked for a typical measure of orange juice in a full family-size jug. Which was her answer
Magda said the typical measure of orange juice in a full family-size jug is 1 gal in value.
What is meant by mathematical expression?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression. Operations include addition, subtraction, multiplication, and division.
The collection of mathematical symbols that emerges from the right arrangement of numbers is known as a mathematical expression and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.
The three different types of algebraic expressions are monomial, binomial, and polynomial.
The complete question is : In a math question, Magda correctly answered a question that asked for a typical measure of orange juice in a full family-size jug. Which was her answer?
a. 2 cups
b. 1 gal
c. 10 gal
d. 10 fl oz
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How do you find the endpoint and midpoint?
To find the endpoint we have to calculate the distance between the known midpoint to the known endpoint. To calculate the midpoint we add two points and divide them by 2.
The formula for midpoint = (x1 + x2)/2, (y1 + y2)/2.
Substituting in the two x-coordinates and two y-coordinates from the endpoints.
Putting it together,
The endpoint formula is:
(x a ,ya)= ((2xm−xb),(2ym−yb))
( x a , y a ) = ( ( 2 x m − x b ) , ( 2 y m − y b ) ).
The end of a line at a point that is equally distant from both ends, a time interval between an event's beginning and end.
The point on a graph or figure where the figure stops might be referred to as the endpoint. It can be the point joining the sides of a polygon (the vertex), the common endpoint of two rays making an angle, the two extreme points of a line segment, the one end of a ray.
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A forest covers 78,000 acres. A survey finds that 0. 4% of the forest is old-growth trees. How many
acres of old-growth trees are there?
There are
acres of old-growth trees.
Answer:
There would be 312 acres of old tree growth for 0.4% of the forest. There would be 31.2 acres of old tree growth for 0.04%. I wasn't sure if you meant 0.4 or 0.04.
Match the following factored-form quadratics with their equivalent standard form
The factored quadratic functions with their equivalent standard form are given as follows:
1. e -> x² - 3x - 10 = (x - 5)(x + 2)
2. a -> x² + 7x - 10 = (x + 5)(x + 2).
3. c -> x² - 7x + 10 = (x - 5)(x - 2).
4. d -> x² - 2x - 63 = (x - 9)(x + 7)
5. f -> x² + 2x - 63 = (x + 9)(x - 7).
6. b -> x² + 16x + 63 = (x + 7)(x + 9).
How to factor a quadratic function?A quadratic function is defined as follows:
y = ax² + bx + c.
A quadratic function can be factored as a function of it's roots x* and x**, as follows:
y = a(x - x*)(x - x**).
For item a, the function is given as follows:
y = x² + 7x + 10.
The coefficients are given as follows:
a = 1, b = 7, c = +10.
The discriminant is of:
D = 7² - 4(1)(10)
D = 49 - 40
D = 9.
Hence the first root is of:
x = (-7 - square root of 9)/2
x = -5.
The second root is of:
x = (-7 + square root of 9)/2
x = -2.
Meaning that the factored expression is given as follows:
y = (x + 5)(x - 2).
Matched with the second expression of column A.
The same procedure is followed for the remaining quadratic functions.
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Flow chart to find the biggest of 3 numbers
The flowchart to find the biggest of 3 numbers is mentioned below:
Define Flowchart.A flowchart is a type of diagram that represents an algorithm, process, or workflow. It is a visual representation of the steps and decisions involved in a problem-solving or decision-making process. Flowcharts use a variety of symbols and shapes to represent different types of steps and decisions, such as inputs, outputs, process steps, and decision points. They are used to communicate the logic of a program or process to different stakeholders, such as developers, managers, and users.
Define Algorithm.An algorithm is a set of instructions or a step-by-step procedure for solving a problem or completing a task. It is a well-defined sequence of operations or actions that are taken in order to achieve a specific goal or outcome. Algorithms can be expressed using natural language, pseudocode, or programming languages. The steps in an algorithm must be unambiguous and have a clear stopping point.
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1. Cameron ran 3 miles in 24 minutes. Identify the equivalent ratio that represents Cameron's run. *
The equivalent ratio that represents Cameron's run is 1 : 8
Equivalent Ration:
In mathematics, the definition of equivalence ratio says: The equality of two ratios is also called a ratio. Front and follow have different values, but reducing them to their simplest form gives the same value.
For example, to find out if 2:3 and 16:24 are equivalent ratios, we need to reduce both ratios to their simplest form. The HCF of 2 and 3 is 1, so 2:3 is already in the simplest form. The HCF for 16 and 24 is 8. Divide these two numbers by 8 to get the reduced form. This means (16÷8):(24÷8) = 2:3. It's clear that 2:3 and 16:24 are the same value, equivalent ratios.
Based on the question :
Cameron ran 3 miles in 24 minutes.
Now,
Therefore we can say that :
Cameron ran 1 miles in 8 minutes;
Therefore, the equivalent ration is 1 : 8.
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Annie bought a brand new car for $32,000. The car is now worth $21,000.
(This is percent over change!!)
Using percentages we know that the value of a car decreases by 34% on average.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
So, we know that:
Annie brought a car at: $32000
Current price of the car: $21000
The decline in car percentage:
21000/32000 * 100
65.625%
⇒ 100 - 65.625 = 34.375%
Rounding off: 34%
Therefore, using percentages we know that the value of a car decreases by 34% on average.
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Complete question:
Annie bought a brand-new car for $32,000. The car is now worth $21,000.
By what percentage does the car's worth decrease?
3. Birr 6,500 was divided equally among a certain number of persons. Had there been 15 more persons, each would have got Birr 30 less. Find the original number of persons.
If the population grows by 15 people. The original number of people was 50, hence the new share of each person was Rs. (which is refused).
What is meant by Mathematical equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Let no. of persons = x
Each person get
= 6500/x
If there 15 persons were added more
= 6500/(x + 15)
(6500/x) - 6500/(x + 15) = 30
[tex]\Rightarrow 6500\left[\frac{(\mathrm{x}+15)-(\mathrm{x})}{\mathrm{x}(\mathrm{x}+15)}\right]=30[/tex]
[tex]\Rightarrow 6500\left[\frac{x+15-x}{x^2+15 x}\right]=30[/tex]
[tex]& \Rightarrow 1625\left[\frac{15}{x^2+15 x}\right]=3 \\[/tex]
Then,
[tex]& \Rightarrow \frac{24375}{x^2+15 x}=3 \\[/tex]
Simplifying the above equation,
[tex]& \Rightarrow 3 x^2+45 x=24375 \\[/tex]
[tex]& \Rightarrow 3 x^2+45 x-24375=0 \\[/tex]
[tex]& \Rightarrow x^2+15 n-3250=0 \\[/tex]
[tex]& \Rightarrow x^2+(65 n-50 n)-3250=0 \\[/tex]
Then we get,
[tex]& \Rightarrow x^2+65 n-50 n-3250=0 \\[/tex]
[tex]& \Rightarrow x+65)-50(x+65)=0[/tex]
[tex]\Rightarrow(\mathrm{x}-50)(\mathrm{x}+64)=0[/tex]
x = 50, x = -65
Since the number of people cannot be zero,
the number of people is 50.
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I GIVE THANKS AND MARK BRAINLIEST
What is the correct answer?
Please help.
Answer:if the siblings are less and the child are more u should remove the percent from the difference and put it to the another one the one from down there so the difference is 70% so try the same from down there is 18 so it got to be 20
Answer:20
Pressure =
force/area
A force of 70 newtons acts on an area of 20 cm?
berabils HBO
The force is increased by 10 newtons,
The area is increased by 10 cm?
Helen says,
"The pressure decreases by less than 20%"
Is Helen correct?
You must show how you get your answer.
Helen is not correct. The pressure decreases by 23.8% and not less than 20%.
Pressure = force/area
The initial pressure is 70 N / 0.2 m^2 = 350 Pa (Pascals). If the force is increased by 10 N and the area is increased by 10 cm^2, the new pressure is 80 N / 0.3 m^2 = 266.67 Pa
The difference in pressure between the initial and final states is 83.33 Pa (350 Pa - 266.67 Pa)To calculate the percentage change in pressure, we divide the change in pressure by the initial pressure and multiply by 100:
(83.33 Pa / 350 Pa) * 100% = 23.8%So Helen is not correct. The pressure decreases by 23.8% and not less than 20%.
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Complete the table with values for x or y that make this equation true : 3x+y=15.
Answer:
Step-by-step explanation:
So first, with the given table you need to "plug-in" the numbers that are there for x and y.
Ok, for example 2 is listed in the "x" row. So plug it 2 for "x":
3x+y=15
3(2)+y=15
6+y=15
-6 -6
y=9
So do this for all of them...the same goes with all of the values...just plug in one, complete the steps then you'll get the answer for the other variable.
Hope this helps!
F18) if y varies jointly as x and the inverse of z, and y = -5 and z = 6, find y when x = 5 and z = -8
Answer:
gfifhdrtjttt9668ztjt*
There are 8 employees on The Game Shop's sales team.
Last month, they sold a total of g games. One of the
sales team members, Chris, sold 17 fewer games than
what the team averaged per employee.
How many games did Chris sell?
Write your answer as
an expression.
games
According to the solving the team average is g/17 and Chris sold (g/8) - 17 games.
What do you mean by average?The term "Average" refers to a value that should be used to describe the sample as a whole. The average is determined by dividing the total number of values in a set by the total number of values. also known as the arithmetic mean.
How do you calculate the mean?Average A collection of integers are added, their count is divided, and the sum is used to determine the arithmetic mean.
According to the given information:average game sold = g/8
since Chris sold 17 games less than average
hence, Chris sold games
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The area of the rectangle is 15cm, the length is xt2cm, the width is xcm , find the value of x
You now have the total length for the remaining 2 sides. This number divided by 2 is the width.
How do you find the length and width of a rectangle when given the area?When given an area of A and a length of h, its width w is equal to A/h.
Its width is w = P/2h if you have the perimeter P and length h.
If you know the length h and the diagonal d, you can calculate the width using the formula w = (d2h2).
The height, area, diagonal, or perimeter of your rectangle are the two measurements that the width of a rectangle calculator uses to calculate the width of your rectangle. We'll also demonstrate various formulas for calculating the width of a rectangle based on the information at hand. The width of a rectangle can be determined in a variety of ways, depending on the information at hand.
A=w×h
P=(w+h)×2
d = w 2 +h 2
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The scores on the last math quiz are summarized in the following frequency table:
Score
10 9
8
7
6
4 3 2 1 0
7
5
3 2
1
0
0
10
0
Frequency 6
The information is then put into the following histogram:
Frequency
5
4
3
210
1 2 3 4 5 6 7 8 9 10
5
1
Score
Therefore , the answer to the above problem is 5.75 for the mean and 9 for the median.
What is mean?Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the amount of values present in the dataset by its total number of values in the data. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the integers in a data set and dividing the total by the total number of numbers. For example, in the data below
Here,
Spread it all out here first:
4, 5, 6, 7, 7, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10
The mean is calculated by dividing total total by the total number of scores. Add up each number.
There are 16 numbers total, and they add up to 92. 92 / 16 = 5.75
To get the median, identify the middle number among all the other numbers.
Sadly, there is no "center number" given that there are 16.
Add the ninth and eighth numbers together, then divide by to find the middle.
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Dominique decorates a round cake with fruits. The cake has a diameter of 16 inches. She frosts just the top if the cale. How many square inches of the cake are covered with icing?Use 3. 14 for π
The amount of square inches of the cake that are covered with icing is 201.06, calculated by using the formula (π * radius2), with π equal to 3.14 and the radius equal to 8 inches.
1. Use the formula (π * radius2), with π equal to 3.14
2. The radius is half of the diameter, divide the diameter (16 inches) by 2
3. Radius = 16 inches / 2 = 8 inches
4. Calculate π * radius2: 3.14 * (8 inches)2 = 201.06 square inches
π * (8 inches)2
= 3.14 * (64 inches2)
= 201.06 square inches
Dominique is decorating a round cake with fruits and has frosted just the top of the cake. To determine the area of the cake that is covered with icing, we can use the formula (π * radius2). Since the cake is round, we can determine the radius of the cake by dividing the diameter of the cake (16 inches) by 2, resulting in the radius being 8 inches. We can then calculate the area of the cake covered with icing by multiplying π by the radius squared. Using the number 3.14 for π, the calculation is 3.14 * (8 inches)2, which equals 201.06 square inches. Therefore, 201.06 square inches of the cake are covered with icing.
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expand this expression using the distributive property. 4(-2g+4-3t)
Answer:
-8g+16-12t is the answer
Step-by-step explanation:
multiply everything by 4
define why 2+2 is not 5
Answer:
Step-by-step explanation:
because 2 + 2 is 4
question is in the photo, please provide explanation as well
A rescue boat just picked up some sailors in a lifeboat. Now the rescue boat is heading north at 14 miles per hour. The lifeboat, which they abandoned, is drifting south at a speed of 3 miles per hour. How long will it be before the rescued sailors are 57 miles from their lifeboat?
The time it will take for the rescued sailors to be 57 miles from their life boat is given as follows:
3.35 hours.
What is relative velocity?Relative velocity is obtained considering the direction in which the objects are traveling, as follows:
Opposite direction: the relative velocity is given by the sum of the velocities of each object.Same direction: the relative velocity is given by the subtraction of the velocities of each object.For this problem, the sailors and the lifeboat are traveling in opposite directions, hence the relative velocity, considering each of their velocities is given as follows:
v = 14 + 3 = 17 miles.
(meaning that they get 17 miles farther each hour).
Velocity is distance divided by time, hence the time it will take for them to be 57 miles apart is given as follows:
17 = 57/t
17t = 57
t = 57/17
t = 3.35 hours.
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m(x)=−2(x−3)(x−9) solve for y-intercept
Answer:
(0, -54)
Step-by-step explanation:
We find the y-intercept by plugging in 0 for x:
[tex]y=-2(x-3)(x-9)\\y=-2(0-3)(0-9)\\y=-2*-3*-9\\y=6*-9\\y=-54[/tex]
I need help with this, please
Use the graph of the function to find the domain and range of f (Enter your answers using interval notation)
In the given graph the domain and range of function y=f(x) is
Domain: (-2,2]
Range : [-4, 5)
What is domain and range?A function's domain is the set of all possible inputs to the function. This means it can be any number that can be entered into a function. For the majority of functions, this will be any number that can be substituted for the letter x. Except for a few exceptions such as square root functions and rational numbers, your domain will almost always be all real numbers.
The set of all possible outputs of a function is referred to as its range. This is usually represented by the letters y or f(x). The range is any number obtained by substituting any number for x.
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A sphere is inscribed in a cone with height 4 and base radius 3. What is the ratio of the volume of the sphere to the volume of the cone
The radius of the sphere 1.5 units
The volume of the cone is pi (3)^2 *4 / 3 units^3 = 12pi units^3
The volume of the sphere is (4/3)pi (1.5)^3 units^3 = 4.5 units^3
So ratio of the volume of the sphere to the cone is :
4.5 pi / 12 pi = 4.5 / 12 = (9/2) / (24/2) = 9 / 24 = 3 / 8
What is radius?In geometry, the radius is defined as a line segment joining the center of the circle or a sphere to its circumference or boundary. It is an important part of circles and spheres which is generally abbreviated as 'r'. The plural of radius is "radii" which is used when we talk about more than one radius at a time. The largest line segment in a circle or sphere joining any points lying on the opposite side of the center is the diameter, and the length of the radius is half of the length of the diameter. It can be expressed as d/2, where 'd' is the diameter of the circle or sphere. Look at the image of a circle given below showing the relationship between radius and diameter.To learn more about diameter refer to:
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What is a power of 3 equation called?
A power of 3 equation is called as cubic equation.
The term equation in math is known as a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Here we need to find the term that has been used for power of 3 equation.
Here we have to know that the power of 3 equation is known as cubic equation.
in other terms the polynomial equation which has a degree of three is called a cubic polynomial equation or trinomial polynomial equation.
As we all know that the power of the variable is the maximum up to 3, therefore, we get three values for a variable, say x.
The general form of the power of 3 equation is written as
=> ax³ + bx² + cx + d = 0
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A cylindrical cooler ha a diameter of 30 inche and a height of 24 inche. Runner in
a marathon can ue cone haped cup to get a drink from the cooler. If the cup have a
diameter of 3 inche and a height of 4 inche, how many full cup would be able to
be filled from the cooler?
So, 600 full cup would be able to be filled from the cooler. This can be solved using the concept of volume of cylinder.
What is volume of cylinder?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 centers of the circular bases cross each other. The measure of space within a cylinder is measured by its volume. Find it by dividing the base area by the height. V = πr²h is the formula for the volume of a cylinder with base radius "r" and height "h."
Given that,
diameter of cylinder = 30 inch
diameter of cup = 3 inch
height of cylinder = 24 inch
height of cup = 4 inch
Calculate the volume of the cylinder:
Volume = πr²h
putting the values we get:
Volume = (3.14)(30/2)²(24)
Volume = (3.14)(15)²(24)
Volume = (3.14)(225)(24)
Volume = 16959 in³
Calculate the volume of the cup:
Volume = (3.14)(3/2)²(4)
Volume = (3.14)(1.5)²(4)
Volume = (3.14)(2.25)(4)
Result
Volume = 28.26 in³
Divide the volume of the cylinder by the volume of the cup, we get:
Number of full cups = 16959 in³ / 28.26 in³
Number of full cups = 600
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Is Infinity a interval?
To represent "infinity" or the notion that an interval lacks an ending, we use the symbol.
Is infinity an open interval?The endpoints of infinity and negative infinity can be seen in two different ways. One the one hand, we can never get to infinity because it is a concept and not a real quantity.
In this sense, the interval is said to be open because it excludes the endpoints infinity and negative infinity. The infinity symbol is placed on the right side since there is no higher endpoint (all values must be larger than or equal to -3). An interval is closed if its boxed end is on -3. Because there is no endpoint on that side, infinity always has a curved end.
To represent "infinity" or the notion that an interval lacks an ending, we use the symbol. The symbol shouldn't be used with a square bracket because it's not a number. Visit this tutorial on set-builder and interval notation for a more thorough discussion of set notation and interval notation.
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