a group with at least n k 1 people such that no two members of the group are friends,We will prove this statement by inductive hypothesis.
Base Case: If n=k+1, then we can easily find a group with nk1 people such that no two members of the group are friends. We simply select the k+1 people in the room, excluding Alex. Since Alex has k friends, and no other person in the room has more than k friends, it follows that none of these k+1 people are friends.
Inductive Step: Assume that the statement is true for n=k+1. Now we must show that it is true for n=k+2.
We can select a group of k+1 people from the room, again excluding Alex. By the inductive hypothesis, we know that no two members of this group are friends. Now, we select the remaining person in the room, and add them to the group. This person cannot be friends with any of the members of the group, since Alex has k friends and no other person in the room has more than k friends. Therefore, the group we have formed has at least nk1 people, and no two members of the group are friends.
Therefore, by induction, we have proved that we can find a group with at least nk1 people such that no two members of the group are friends.
Learn more about inductive hypothesis here
https://brainly.com/question/29525504
#SPJ4
A family's monthly income is $41360. The family spends 3 over 8 of this on food. How much is spent on food
Answer:
$15,510.00
Step-by-step explanation:
[tex]\frac{3}{8}[/tex] x [tex]\frac{41360}{1}[/tex] = [tex]\frac{124080}{8}[/tex]= 15510
Determine the area of the shaded region in the following figure.\
y=x
y=x^2-2
The area of the shaded region is 425 cm².
Determine the area of the shaded region ?Let us find the area of the entire figure first and subtract the unshaded region area to find the area of the shaded region.
The given figure is of a square of side 25 cm.
Total area = 25²
=> 625 cm²
The shaded figure inserted is a rhombus.
Apart from this , we can observe four unshaded triangles of equal area.
Area of each individual triangle :
=> ½ × 5 × 20
=> 50 cm²
Area of 4 triangles ;
=> 200 cm²
Remaining area of the shaded figure :
=> 625 - 200
=> 425 cm² .
To learn more about area refer
https://brainly.com/question/2607596
#SPJ1
Read the following prompt and type your response in the space provided.
Write a real-world problem that can be represented by the algebraic equation shown.
6x + 5 = 77
Answer:
One real-world problem that can be represented by the algebraic equation 6x + 5 = 77 is determining the number of items that must be sold at a certain price in order to reach a target profit. For example, suppose a business owner wants to make a profit of $77 by selling items for $6 each. The algebraic equation 6x + 5 = 77 can be used to determine the number of items that must be sold in order to reach this profit. In this case, x represents the number of items that must be sold, and the solution to the equation (x = 11) indicates that the business owner must sell 11 items in order to make a profit of $77.
A line passes through the point (-4,8) and has a slope of -6 .
Write an equation in slope-intercept form for this line.
Answer:
y = (-6)*x - 16
Step-by-step explanation:
The slope-intercept form of a line is given by the equation:
y = mx + b
where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
In this case, the line passes through the point (-4,8) and has a slope of -6, so we can plug these values into the equation to find the y-intercept:
y = (-6)*x + b
We know that the line passes through the point (-4,8), so we can substitute these values into the equation to solve for b:
8 = (-6)*(-4) + b
8 = 24 + b
b = -16
Therefore, the equation of the line in slope-intercept form is:
y = (-6)*x - 16
Practice Another Dimple gets paid $4,800 per month. She pays $960 a month for rent. What percent of her monthly pay goes to rent?
The percent of her monthly pay that goes to rent will be 20%.
How to calculate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this situation, Dimple gets paid $4,800 per month and then she pays $960 a month for rent.
The percent of her monthly pay that goes to rent will be:
= 960 / 4800 × 100
= 20%
The percentage is 20%.
Learn more about percentages on
brainly.com/question/24877689
#SPJ1
The local farmers' market usually sells potatoes for $0.90 per pound. on fridays, they sell potatoes at a 30% discount. the market also sells cantaloupes for $3.50 each. which of the following represents the total cost, c , if a customer buys 2 cantaloupes and p pounds of potatoes on a friday?
A. c = 0.63p + 7
B. c = 0.9p + 7
C. c = 0.3p +3.5
D. c = 0.9p + 3.5
If a customer buys 2 cantaloupes and p pounds of potatoes on friday from the local farmers' market, the total cost equation would be A. C = 0.63p + 7.
Equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation also often contain an algebra. Algebra is used in maths when you do not know the exact number in a calculation.
Based from the question above, we don't know the exact number of potato that the customer bought. We only know that the customer buys p pounds of potatoes.
Potato price = $0.90
on Friday, the potato price is (30% discount)
= 0.90 - (0.90 * 30%)
= $0.63
Since the customer buys for p pounds of potatoes, therefore the total cost of potatoes
= $0.63 * p
= 0.63p
From the question above, we know that the customer buys 2 cantaloupes.
cantaloupes price = $3.50 each
The total cost for cantaloupes
= 2 * $3.50
= $7
Now, let's put it into the total cost equation to find the answer from the multiple choice.
Total cost (c) = 0.63p + 7
Therefore, the answer is A.
Learn more about equation (in math) https://brainly.com/question/2228446
#SPJ4
9. (5.NBT.B.7} Adrian ran 8.547 km in 1.5 hours. How many kilometers did Adrian *
run in one hour?
O 5.689 km
O5.869 km
5.698 km
Adrian run in one hour is 5.698 km.
How to calculate speed, Distance and Time ?
To work out speed, divide the distance of the journey by the time it took to travel, so speed = distance divided by time. To calculate time, divide the distance by speed. To get the distance, multiply the speed by time. You may see these equations simplified as s=d/t, where s is speed, d is distance, and t is time.Given,
Adrian ran in 1.5 hours = 8.547 km
We know, in 1.5 hours there is 90 minutes
so, in 1 min adrian ran = 8.547 / 90
= 0.09496 km
We need to find the km in one hour means in 60 minutes
So, Adrian ran in 60 min = 60 * 0.09496
= 5.6979 km or 5.698 km per hour
Hence, Adrian run in one hour is 5.698 km.
To read more about Speed, Distance and Time
https://brainly.com/question/26582189
#SPJ1
Question 4 of 10
Which situation best illustrates the concept of absolute advantage?
A. A German factory can build more sports cars than foreign factories.
B. Most of the world's largest companies have operations in many different countries.
C. The total value of Japanese imports is greater than the total value of the country's exports.
D. A French restaurant buys food from nearby farms to support the local economy.
Situation which illustrates best the concept of absolute advantage is: Option A - A German factory can build more sports cars than foreign factories.
Absolute advantage is the potential of an individual, a company, or a country to produce a higher quantity of output than its competitors while using the same inputs. It means an institution with absolute advantage has more efficiency in producing a particular commodity than its rivals. It utilizes lower marginal cost (materials and labor), making its output much cheaper than others.
A factory in German has an absolute advantage because it can produce more sports car than foreign countries. Absolute advantage makes the factory more competitive in the market than its rivals.
Therefore, the correct answer is option A.
Learn more about absolute advantage here :-
https://brainly.com/question/27956614
#SPJ4
calculate the charge on the ping pong ball required for the dipole to levitate motionless in midair. please answer as a formula, you may use the terms 'q','s','r','m','l','m','g','k'.
Charge required to levitate a ball is [tex]1*10^{-2}C[/tex] given by the cross section of your pen 10 [tex]mm^{2}[/tex], which is of order 10 squared.
what is Coandă effect?The flow of air is drawn toward the ball by the low pressure area that surrounds it. As a result, the fluid (air) jet flows across the ping pong ball's curved surface. The "Coandă effect" refers to this phenomena.
The airflow's propensity to stick to the ball's surface is the Coandă effect in this situation. This indicates that the streamlines are curved at the ball's surface, with a radius of curvature roughly equal to the ball's radius. This curvature produces a pressure gradient, much like it does in the theory of lift, which I assume to be constant over the surface:
The equilibrium point, when the net forces acting on the ball cancel, is indicated by this, which points radially inward. Gravity causes the ball to hang below this spot during practice.
The Charge required to levitate a ball is [tex]1*10^{-2}C[/tex] given by the cross section of your pen 10 [tex]mm^{2}[/tex], which is of order 10 squared.
To know more about Coandă effect visit:-
https://brainly.com/question/20726735
#SPJ4
se the alternating series estimation theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error. check your answer graphically. (round your answers to three decimal places.) |error| < 0.05
The percent of error for the given measured value and the absolute error is equal to 0.392%
As given in the question,
Measurement value is equal to 12.8 inches
Absolute error in the measurement is equal to 0.05
True value is equal to ( Measurement value - absolute error )
= ( 12.8 + 0.05 )
= 12.75
Percent of error is given by
= |True value - Measured value |/ (true value) × 100
= [ | 12.75 - 12.8 |/ 12.75 ] × 100
= 0.392%
Therefore, the percent of error for the given measured value and the absolute error is equal to 0.392%
The given question is incomplete, I answer the question in general according to my knowledge:
A measurement is taken to be 12.8 in. and the absolute error is 0.05 in. What is the percent of error? Round off your answer to 3 decimal places.
Learn more about percent of error here
brainly.com/question/10501147
#SPJ4
The segment addition rule states if B is between A and C, then AC = AB + BC.
False
True
Answer: The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC
the cost in millions of dollars for a company to manufacture x thousand automobiles is given by the function C(x)=5x^2-20x+36. find the number of automobiles that must be produced to minimize the cost.
Answer:
7
Step-by-step explanation:
please help me with this
Two buses are driving along parallel freeways that are 12 mi apart, one heading east and the other heading west. Assuming that each bus drives a constant 58 mph, find the rate at which the distance between the buses is changing when they are 13 mi apart and heading toward each other. (Round to 2 decimal places) a. -44.62 mph b. 44.62 mph c. 22.31 mph d. -22.31 mph
The rate at which the distance between the buses is changing when they are 13 miles apart is -85.25 mph.
Given, two buses are driving along parallel freeways that are 12 miles apart, one heading east and the other heading west.
Assuming that each bus drives a constant 58 mph.
Now, we have to find the rate at which the distance between the buses is changing when they are 13 miles apart and heading towards each other.
Considering distance as a function of time,
D = f(t) = √((12)² + (13 - 116t)²)
f'(t) = (13 - 116t)(-116)/√((12)² + (13 - 116t)²)
f'(0) = (13 - 116(0))(-116)/√((12)² + (13 - 116(0))²)
f'(0) = -1508/√(144 + 169)
f'(0) = -1508/√313
f'(0) = -85.25
So, the rate of distance is decreasing at the rate of 85.25
Hence, the rate of distance is decreasing at the rate of 85.25
Learn more about Application of Derivatives here https://brainly.com/question/25081524
#SPJ4
2.
At Benny's Café, a mixed-greens salad costs $5.75.
Additional toppings can be added for $0.75 each.
Which function could be used to determine the
cost, c(s), in dollars, of a salad with s additional
toppings?
A.
C.
c(s) = 0.75s +5.75
D.
D. c(s) = 0.75s +5.00
c(s) = 5.75s +0.75 B.
B.
c(s) = 5.00s +0.75
briefly explain why a maclaurin polynomial cannot be created for the function . your answer should only be one or two sentences.
A Maclaurin polynomial can only be created for functions that are infinitely differentiable, and the given function is not infinitely differentiable.
What is Maclaurin polynomial?Maclaurin polynomial is an important type of Taylor series, developed by the Scottish mathematician Colin Maclaurin in the 18th century. It is a special case of the Taylor series, which is used to approximate a function near a given point. Maclaurin polynomials are polynomials that are used to approximate a function near the origin. They are derived from the Taylor series expansion of a function around the zeroth order derivative. The general form of a Maclaurin polynomial is given by ⌊f(x)=∑n=0∞a_nx^n⌋, where a_n is the nth derivative at x=0. Maclaurin polynomials are used to approximate a variety of functions, from simple polynomials to more complicated ones such as trigonometric, exponential, and logarithmic functions. They can also be used to approximate certain integrals and derivatives. Maclaurin polynomials are widely used in mathematics, physics, engineering, and other sciences.
To learn more about Maclaurin polynomial
https://brainly.com/question/29652576
#SPJ4
use generating functions to find the number of ways to distribute r jelly beans among eight children if
(a) each child gets at least one jelly bean
(B) each child gets an even number of beans
please show all work
With the Application of probability The expression is [ x^r] = C ( r - 1, r - 8 ).
What is probability?
There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event. It is possible to claim that probability is the likelihood that a specific event will occur as the two words are equivalent.
solution:
G(x) = ( x^1 + x^2 + x^3 .....)^8
G(x) = (x( x^1 + x^2 + x^3 .....) )^8
Then using infinite geometric series,
= x^8 ( 1 / ( 1 - x )) ^8
Then using negative binomial series:
So [ x^r] = 0 if r = 0, 1, 2, 3...7 and [ x^r] = C ( r - 1, r - 8 ) if r > 7
Therefore, The expression is [ x^r] = C ( r - 1, r - 8 )
To learn more about probability from the given link
https://brainly.com/question/13604758
#SPJ1
answer.
3) Samantha baked 16 chocolate cupcakes for her children. If the cupcakes are shared
equally among four of her children, how many cupcakes will each child get?
cupcakes are shared
equally among four of her children, 4 Cupcakes will each child get
what do you mean by share?
An equity ownership stake in a corporation is represented by a share. Dividends from any earnings the company makes are owed to the shareholders. They also bear the brunt of any losses the business may sustain.
Ordinary shares.
Non-voting shares.
Preference shares.
Redeemable shares.
There are a number of different types of shares including equity shares, preference shares, right shares, bonus shares, sweat equity shares (where companies issue shares at a discount or for consideration) and employees stock options plans.
To learn more about share visit:
https://brainly.com/question/28392295
#SPJ1
Assume the random variable X is normally distributed with mean μ = 50 and standard deviation σ= 7, Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. P(X> 37) Click the icon to view a table of areas under the normal curve. Which of the following normal curves corresponds to P(X> 37)? OA. OC. 37 50 37 50 37 50 PX-37)-□ (Round to four decimal places as needed.)
The normal curve that corresponds to P (X > 37) is C, as the shaded area corresponds to the probability of 0.4207.
The normal curve is a bell-shaped curve which is used to represent a continuous probability distribution. It is used to represent the probability of a random variable X, which is normally distributed with mean μ and standard deviation σ. In this case, we have X with mean μ = 50 and standard deviation σ = 7. To compute the probability P(X > 37), we first draw a normal curve with the area corresponding to the probability shaded. Then, we can look up the area from the table of areas under the normal curve. The area corresponds to 0.4207, and the normal curve that corresponds to this probability is C, as the shaded area corresponds to the probability of 0.4207. This normal curve has the mean of 50 and the standard deviation of 7, with the area beyond 37 shaded.
P(X > 37)
= 1 - P(X ≤ 37)
= 1 - 0.4207
= 0.5793
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
which of the following refers to a set of procedures in which the sample size and sample statistics are used to make estimates of population values or facts?
Generalization refers to a set of procedures in which the sample size and sample statistics are used to make estimates of population values or facts.
Statistics is a branch of applied mathematics that involves the collection, description, analysis, and conclusion of conclusions from quantitative data. Sample size determination is the act of choosing the number of compliances or replicates to include in a statistical sample.
Statistical conception involves statistically calculating the likely parameters of a population using data from an arbitrary sample of that population.
One of the primary operations for data conception is when you need to analyze data that you've collected, but also need to ensure the sequestration of the individualities who are included in that data.
To know more about Generalization,
brainly.com/question/29731872
#SPJ4
Let R = [0,6] [0, 6]. Subdivide each side of R into m =n = 3 subintervals and use the Midpoint Rule to estimate the value f JI.(v 22) dA.
2f(3,1)
To use the midpoint rule to estimate the value of the double integral of a function f(x,y) over the region R=[0,6]x[0,6], we need to divide the region R into a grid of subintervals, with m subintervals in the x-direction and n subintervals in the y-direction. In this case, m=n=3, so we divide each side of the region R into 3 subintervals of equal length.
The midpoint rule states that the approximation of the integral is given by the sum of the areas of the rectangles formed by the subintervals, where the height of each rectangle is given by the value of the function at the midpoint of the subinterval.
To implement the midpoint rule, we first need to determine the width and height of each subinterval. The width of the subintervals in the x-direction is given by (6-0)÷3 = 2, and the width of the subintervals in the y-direction is also given by 2. The height of each rectangle is given by the value of the function f at the midpoint of the subinterval.
We can then evaluate the double integral by summing the areas of the rectangles formed by the subintervals. For example, the first rectangle would have a height equal to the value of the function at (0+2)÷2=1 and a width of 2, so its area would be 2f(1,1). The second rectangle would have a height equal to the value of the function at (2+4)÷2=3 and a width of 2, so its area would be 2f(3,1)
learn more about the midpoint rule on https://brainly.com/question/3508299
#SPJ4
sweet-fit jeans has a factory that makes two styles of jeans; super-fit and super-hug. each pair of super-fit takes 20 minutes to cut and 30 minutes to sew and finish. each pair of super-hug takes 20 minutes to cut and 55 minutes to sew and finish. the plant has enough workers to provide at most 18,999 minutes per day for cutting and at most 40,999 minutes per day for sewing and finishing. the profit on each pair of super-fit is $6.50 and
The maximum number of pairs of super-fit jeans the factory can produce in a day is 949.the profit on each pair of super-hug is $9.50.
Given the information provided, the maximum daily profit the factory can make is $201,248.50. The maximum number of pairs of super-fit jeans the factory can produce in a day is 949, since it takes 20 minutes to cut each pair and there are only 18,999 minutes available for cutting each day. The maximum number of pairs of super-hug jeans the factory can produce in a day is 824, since it takes 55 minutes to sew and finish each pair and there are only 40,999 minutes available for sewing and finishing each day.
Maximum daily profit = (949 x $6.50) + (824 x $9.50)
= $201,248.50
Learn more about profit here
https://brainly.com/question/28856941
#SPJ4
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis
y=x3,y=8,x=0; about x=9
The volume of the cylinder generated by rotating the region bounded by y = x³ , y = 8 , x = 0 and x = 9 be, 1608.25 cubic units.
Given, a cylinder generated by rotating the region bounded by the given curves about the specified axis
y = x³ , y = 8 , x = 0 and x = 9
we have to find the volume of the cylinder generated by the given region,
So, using the concept of integration, we get
Volume of the cylinder = Integrating y from x³ to 8 then integrating x from 0 to 9.
Volume of the cylinder = ∫∫dy dx
Volume of the cylinder = ∫(x³ - 8) dx
Volume of the cylinder = x^4/4 - 8x
Volume of the cylinder = (9)^4/4 - 8(4)
Volume of the cylinder = 1640.25 - 32
Volume of the cylinder = 1608.25
So, the volume of the cylinder be 1608.25 cubic units.
Hence, volume of the cylinder be 1608.25 cubic units.
Learn more about Integration here https://brainly.com/question/28192435
#SPJ4
Consider the model y-80 + β1x1 + β2x2 + β3x3 +e, where x1 is a quantitative variable and x2 and x3 are dummy variables describing a qualitative variable at three levels using the coding schemex2 - y 45.5+ 1.7x1 + 11.5x2 + 16.7x3. Complete parts a and b a. What is the response line (equation) for E(y) when x2 x3 0? When x2 1 and x3 0? When x2 0 and x3-1? Choose the correct equation for x2 x3 0 1 if level2 1 if level3 and x3- . The resulting least squares prediction equation is 0 otherwise 0 otherwise Choose the correct equation for x2 1 andx3-0 Choose the correct equation for x2 0 andx3-1 b. What are the least squares prediction equations associated with level 1, level 2, and level 3? The equation for level 1 is Ey)x The equation for level 2 is E(y) = The equation for level 3 is E(y)-D+D-1 Choose the correct graph of these three lines below. OA Ов. O C. Y L2 L3 し2 L1 L1 5 L3 5 L3 -5
The equation is y = 45.5+ 1.7x₁ + 11.5x₂+ 16.7x₃ when x₂ = x₃ = 0.
What is meant by equation?
In math, equation refers a mathematical statement that is made up of two expressions connected by an equal sign.
Here we have given that, x1 is a quantitative variable and x2 and x3 are dummy variables describing a qualitative variable at three levels using the coding scheme.
and we need to find the correct equation when the value of x₂ = x₃ = 0.
Here while we looking into the given question we have identified that the value of x₂ =0 and x₃ = 0.
Then the given equation will be remain same withouth any changes.
Therefore, the resulting equation of the given condition is written as,
=> y = 45.5+ 1.7x₁ + 11.5x₂+ 16.7x₃
To know more about Equation here.
https://brainly.com/question/10413253
#SPJ4
diane will donate up to to charity. the money will be divided between two charities: the city youth fund and the educational growth foundation. diane would like the amount donated to the educational growth foundation to be at least three times the amount donated to the city youth fund. let denote the amount of money (in dollars) donated to the city youth fund. let denote the amount of money (in dollars) donated to the educational growth foundation. shade the region corresponding to all values of and that satisfy these requirements.
The value of x is $53.34 but cannot exceed $115, while the value of y can be as low as $160 but cannot exceed $345.
What is an inequality?Relationships that compare two numbers or other mathematical expressions in an unequal manner are known in mathematics as inequalities. The most common use is to compare the magnitude of two numbers on a number line.
The answer to the query is
Diane will make a charitable donation "up to $460," which indicates it can be less than or equal to 460 but not more. Then,
$460 donated to charity (max)
plus $160 for educational (160 being the minimum)
Education is also stated to be three times (or greater) than City.
If x represents the city and y represents education, then
x + y = 460 . And we are aware that y 3x.
x + 3x = 4x = 460
x = 115.
This implies that she will contribute $345 to Educational when she donates 3 times (or $115) to City. The maximum value is these.
She won't provide more than $460.
Earlier, Educational had a minimal need.
When y = 160,
x equals y/3,
=> x = 160/3 = $53.34. She so gave 213.34 dollars, which is still less than $460.
As a result, x (which is City) might be anywhere between $53.34 and $115.
x, which stands for educational, might be as little as $160 or as high as $345.
To know more about inequality visit:
https://brainly.com/question/28823603
#SPJ4
Hamadi and Aisha solve this problem in two different ways.
Carlos paid a total of $64 to rent a car.
The rental company charges a one-time fee of $20, with an additional charge of $0.50
per mile driven.
How many miles did Carlos drive the rental car?
Use the drop-down menus to complete the sentences below.
The number of miles Carlos drove the rental car is 88 miles.
How to find the number of miles Carlos drove?Carlos paid a total of $64 to rent a car. The rental company charges a one-time fee of $20, with an additional charge of $0.50 per mile driven.
Therefore, the number of miles Carlos drive the rental car can be calculated as follows:
Using equation,
let
x = number of miles driven
64 = 20 + 0.50x
subtract 20 from both sides of the equation'
64 - 20 = 20 - 20 + 0.50x
44 = 0.50x
divide both sides by 0.50
Therefore,
44 / 0.50 = 0.50x / 0.50
x = 88
Therefore, the number of miles is 88 miles.
learn more on equation here: https://brainly.com/question/12858855
#SPJ1
please solve variable expression m+8+6n−3
Answer:
You can't solve this unless its is the form of an equation!
Accounts receivable have been grouped into the following states:
State 1: Paid
State 2: Bad debt
State 3: 0–30 days old
State 4: 31–60 days old
Sixty percent of all new bills are paid before they are 30 days old. The remainder go to state 4. Seventy percent of all 30-day-old bills are paid before they become 60 days old. If not paid, they are permanently classified as bad debts. What is the probability that an account in state 4 will be in bad debt?
0.3
0.12
0.7
0.8
The probability that an account in state 4 will be in bad debt be 0.3
Given, accounts receivable have been grouped into the following states:
State 1: Paid
State 2: Bad debt
State 3: 0–30 days old
State 4: 31–60 days old
Sixty percent of all new bills are paid before they are 30 days old.
The remainder go to state 4.
Seventy percent of all 30-day-old bills are paid before they become 60 days old.
If not paid, they are permanently classified as bad debts.
P(State 1 and State 3) = 0.6
P(State 4) = 0.40
We have to find the P(State 4 and State 2)
P(State 4 and State 2) = P(State 4) + P(State 2) - P(State 4 or State 2)
P(State 4 and State 2) = 0.4 + 0.6 - 0.7
P(State 4 and State 2) = 0.3
So, the required probability be, 0.3
Hence, the required probability be, 0.3
Learn more about Probability here https://brainly.com/question/27745646
#SPJ4
Lines CD and DE are tangent to circle A shown below:
Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 126 degrees. Point B lies on circle A.
If Arc CE is 126°, what is the measure of ∠CDE? (4 points)
126°
63°
117°
54°
The measure of ∠CDE is 54°
What is measure ?
When attributes of an item or event are quantified, they can be compared to other objects or events and utilized as a basis for comparison. Determining how big or little a physical quantity is in relation to a fundamental reference quantity of the same kind is the process of measurement, in other words.
A measure is a piece of mathematics that expresses the size of sets in numerical terms. A different method of determining how large a set is is embodied by each unique measure. Initially, it could seem as though a set's cardinality is the only natural way to determine its size.
<CDE = far arc - near arc / 2
i.e
<CDE = arcCBE - arcCE / 2
arcCE = 126°
arcCBE = 360° - 126° = 234°
<CDE = (234° - 126°)/ 2
<CDE = 108 / 2
<CDE = 54°
Therefore the measure of < CDE is 54°
To learn more about measure from the given link
https://brainly.com/question/25716982
#SPJ1
Use the One-to-One Property to solve the equation for x. 3x − 1 = 1 /9 x =
Answer: Part 1) Option A
Part 2) Option B
Part 3) Option C
Part 4) Option C
Part 5) Option D
Part 6) Option B
Part 10) Option B
Part 11) Option A
Part 13) Option A
Part 14) Option D
Part 15) Option D
Part 16) Option C
Part 17) Option D
Part 18) Option D
Part 19) Option D distribute the to the and ; distribute the to the and
Part 20) Option B
Step-by-step explanation:
Part 1) we have
solve for x
Part 2) we have
solve for x
Part 3) we have
solve for x
Part 4) we have
solve for x
Part 5) we have
solve for x
Part 6) we have
solve for x
remember that
convert to mixed number
Part 7) The model is not included
Part 8) The model is not included
Part 9) The model is not included
Part 10) we have
solve for x
Part 11) we have
solve for x
Part 12) The model is not included
Part 13) we have
solve for r
Part 14) and Part 15)
the answer is the option D
Look for parenthesis and apply the distributive property; combine like terms; move your variable terms to one side and constants to the other side of the equal sign; go in reverse PEMorDAorS to isolate the variable using inverse operations
Part 16)
Let
n------> the number
we know that
-----> algebraic expression that represent the situation
solve for n
Part 17) we have
solve for y
Part 18) we have
solve for x
Part 19) we have
------> distribute the to the and ; distribute the to the and
Part 20) we have
step 1
distribute the to the and ; distribute the to the and
step 2
Group terms that contain the same variable and move the constant to the other side
step 3
Combine like terms
step 4
Divide by both sides