The probability that it is in a winning position will be 0.8036.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
A coin that is 2 cm in diameter is tossed onto a grid of squares each having a side length of 4 cm. A coin is in a winning position if no part of it touches or crosses a grid line, otherwise it is in a losing position.
Then the probability of winning is calculated as,
P = [a² - πd² / 4] / (a²)
P = [4² - 3.14 x 2² / 4] / (4²)
P = (16 - 3.14) / 16
P = 0.8036
The probability that it is in a winning position will be 0.8036.
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Help please thank you
HELP :(, help on my other questions too :(
In ΔACE, BG = 7, GE = 14 is the centroid theorem and BE = 21 then BG = 7, GE = 14.
What is meant by centroid theorem?The method for determining a triangle's centroid is called the centroid formula. Any object's centroid is its geometric center. The point that divides the medians in half by two is referred to as a triangle's centroid. The geometric center of any geometric object, whether it be a one-dimensional curve, a two-dimensional region, or a three-dimensional volume, is called the centroid. Centroids can very handy for a variety of tasks in Statics and later courses, such as the study of distributed forces, beam bending, and shaft torsion.
The place where the triangle's three medians intersect is known as the centroid (each median connecting a vertex with the midpoint of the opposite side).
According to the centroid theorem, the centroid is located 2/3 of the way between each vertex and the middle of the opposing side.
Point G is 2/3 of the way from point E, and BE is the median:
GE = 2/3BE = 2/3(21) = 14
BG = BE - GE = 21 - 14 = 7
BG = 7, GE = 14
Therefore, the correct answer is option c) BG = 7, GE = 14.
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find a power series representation for the function g of x equals 2 over quantity x squared minus 1 end quantity given 1 over quantity 1 minus x end quantity equals the summation from n equals 0 to infinity of x to the n power period
The function g(x) = 2/(x^2 - 1) can be represented as a power series by finding its Taylor series expansion about the point x = 1.
We know that the power series representation of the function 1/(1-x) is given by the summation from n=0 to infinity of x^n.
So we can write:
g(x) = 2/(x^2 - 1) = 2*(1/(1-x))(1/(1+x)) = 2(1/(1-x^2))
We can use the formula for the Taylor series of a function:
f(x) = SUM(n=0 to infinity) (f^n(a)/n!) * (x-a)^n
where f(x) is the function, a is the point about which we are expanding, and n! is the factorial of n.
So we have:
g(x) = 2* SUM(n=0 to infinity) ( (1/(1-x^2))^n * (x-1)^n )
g(x) = 2* SUM(n=0 to infinity) ( (1/(1-x^2))^n * SUM(k=0 to n) (nCk * x^k * (-1)^(n-k) ) )
g(x) = 2* SUM(n=0 to infinity) ( SUM(k=0 to n) ( (1/(1-x^2))^n * (nCk) * x^k * (-1)^(n-k) ) )
where nCk is the binomial coefficient which is equal to n!/(k!(n-k)!).
So we have the power series representation of the function g(x) = 2/(x^2 - 1) as:
g(x) = 2 * SUM(n=0 to infinity) SUM(k=0 to n) ( (nCk) * ((-1)^(n-k) * (1/(1-x^2))^n) * x^k )
It's important to note that this power series is only valid for |x| < 1.
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PLS HURRYYYYYY identify the pair of angles as corresponding alternate interior both or nether
<4 <7
The pair of angles ∠4 and ∠7 are alternate interior angles.
What are parallel lines?In Mathematics, parallel lines can be defined as two (2) lines that are always the same distance apart and they never meet.
What is the Alternate Interior Angles Theorem?In Geometry, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent. Additionally, these angles are generally referred to as alternate interior angles in Mathematics, .
In this scenario, we can logically conclude that angle 4 (m∠4) and angle 7 (m∠4) forms a pair of alternate interior angles because line l is parallel to line m.
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Please answer the following question
Answer:
12
Step-by-step explanation:
Select the correct answer from each drop-down menu.
1. If , _____ then ∆ABC and ∆DEF are congruent by the ASA criterion.
A.) AB=DE
B.)CA=FD
C.)Angle B is congruent to angle E
D.)Angle A is congruent to angle D
2. If , ______ then ∆ABC and ∆DEF are congruent by the SAS criterion.
A.) AB=DE
B.)CA=FD
C.)Angle B is congruent to angle E
D.)Angle A is congruent to angle D
3. ∆ABC and ∆DEF are congruent if
A.) Angle A is congruent to angle D
B.) AB=DE
C.) AB=DF
ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.
What is congruent ?
In geometry, congruent refers to the condition where two or more figures have the same size and shape. Congruent figures have the same dimensions, angles, and proportions. Two figures are congruent if they can be superimposed exactly on each.
1) If, C.) Angle B is congruent to angle E then ∆ABC and ∆DEF are congruent by the ASA criterion.
2) If, D.) Angle A is congruent to angle D then ∆ABC and ∆DEF are congruent by the SAS criterion.
3) ∆ABC and ∆DEF are congruent if B.) AB=DE
ASA criterion: If in two triangles, two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent.
ASA: ∆ABC and ∆DEF are congruent if angle B is congruent to angle E. SAS: ∆ABC and ∆DEF are congruent if angle A is congruent to angle D and AB=DE.
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Find the midpoint of the segment with the following endpoints.
(−4,−9) and (4,−1)
Answer:(0,-5)
Step-by-step explanation: to start you add both x’s together then divide by two so you get 0 then you add both of the y’s together divide by 2 and you get -5 the answer you got from the x’s goes first then the answer from the y’s hence (0,-5)
i need help please.please show WORK
Answer:
Step-by-step explanation:
what are all the factor pairs for the sum of the 18 horses and 22 cows? Represent the factors with a diagram to show how you found all the factor pairs.
The requried factor pair of the sum of the horses and cows is given as 2 × 2 × 2 × 5.
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
here,
Some of the cows and horses = 18 + 22 = 40
The required factor pair of the sum can be formed as,
= 2 × 2 × 2 × 5
Thus, the requried factor pair of the sum of the horses and cows is given as 2 × 2 × 2 × 5.
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How many 0.5 inch cubes will fill the rectangular prism with side lengths of 3inches by 7.5 inches and 4 inches?
The number of cubes that can be filled in the rectangular prism is 720.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Volume of a rectangular prism = Length × Width × Height
Given a rectangular prism with side lengths 3inches by 7.5 inches and 4 inches.
Volume of rectangular prism = 3 × 7.5 × 4 = 90 inches³
Volume of a cube = (side length)³
Given cube has side length 0.5 inch.
Volume of cube = (0.5)³ = 0.125 inches³
Number of cubes that can be filled in the rectangular box = 90 / 0.125
= 720
Hence 720 cubes can be filled in the rectangular prism.
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Suppose there are 14 classes where quizzes are given and a student participates in 2 of them. In one of the classes, 5 quizzes are given. The student answers 3 of them, and 2 are correct. In the other class, 1 quiz is given. The student correctly answers this question. What is the average participation score after dropping the lowest 4 participation scores
The average participation score after dropping the lowest 4 participation scores is = 83.33%
In order to calculate the average participation score after dropping the lowest 4 participation scores, we need to first calculate the participation score for each class.
For the first class, the student answered 2 out of 3 quizzes correctly, so the participation score is (2/3) x 100 = 66.67%.
For the second class, the student answered 1 quiz correctly, so the participation score is 100%.
Now we need to find the average participation score after dropping the lowest 4 scores. Since the student only participated in 2 classes, we don't need to drop any scores, the average participation score is (66.67 + 100)/2 = 83.33%
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the scatter plot shows the price , in cents , of a postage stamp used to mail a letter in the united states for the years from 1958 to 2014. Also shown is a line of fit to model the data. the equation of the line of fit is y= -0.71 + 0.86x, where y represents the predicted price , in cents of a stamp and x represents the number of years since 1958
In the year 2046 the price of the stamp will reach 75 cents. The solution has been obtained using linear function.
What is a linear function?
A linear function is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear function with exponents greater than 1. Such a function on the graph, forms a straight line.
We are given y= -0.71 + 0.86x, where y represents the predicted price , in cents of a stamp and x represents the number of years since 1958
We need to find the year in which the price of the stamp will reach 75 cents. This means that
y = 75
Putting this in the equation, we get
⇒75= -0.71 + 0.86x
⇒x= 75.71/0.86
⇒x= 88.03
This means that after around 88 years from 1958 i.e. in 2046 the price of the stamp will reach 75 cents.
Hence, in the year 2046 the price of the stamp will reach 75 cents.
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Since, the question is incomplete, the complete question is attached below
Please help its finals
The number of people in attendance who would prefer chili on a hotdog is 3,380.
Option B is the correct answer.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of attendance = 8450
Number of people who prefer chili on a hotdog out of 150.
= 60
The percentage of people who prefer chili on a hotdog out of 150.
= 60/150 x 100
= 40%
Now,
The number of people who prefer chili on a hotdog from 8450 attendance.
= 40% of 8450
= 40/100 x 8450
= 3380
Thus,
3,380 in attendance would prefer chili on a hotdog.
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Rebecca carries a balance on her credit card each month. Today is the first day of the new. 28-day billing cycle. The current balance is x and the APR is 24%.
Rebecca is buying a friend an expensive gift that costs $1,400 that she plans to put on her credit card. This will be her only purchase this month. Sed she will be
making this purchase on the last day of the month. Part A if her finance charge will be $51 write and solve an equation to determine her current balance on her credit card show your work. Part B How much in finance charges can she save by making the purchase on the last day of the billing cycle
Part A: Rebecca's credit card balance can be calculated using the equation x = (51 - 1) 0.02 if her finance charge is $51.
Part B: By making the purchase on the final day of the billing cycle rather than the first day, Rebecca will be able to avoid paying $27 in finance charges.
How do equations work?
A mathematical statement proving the equality of values between two or more mathematical expressions is called an equation.
Equation symbols (=) are used to represent equations.
A finance charge is what?
The interest and other fees levied on credit cards are included in a finance charge.
Typically, the finance charge is based on a stated APR (annual percentage rate).
The month's billing cycle lasts for 28 days.
Balance at current starting = x.
APR = 24%, or annual percentage rate.
The monthly percentage rate (MPR) equals 2% (24% divided by 12).
The final day's purchase cost $1,400.
$51 is the total finance fee for the month.
($1,400 x 2% x 1/28) = $1 finance fee for the last-minute purchase.
$50 ($51 - $1) serves as the initial balance's finance charge.
The starting balance at this time is x = $2,500 ($50 x 2%).
Current Beginning Balance Equation: x = 51 - 1 0.02
($1,400 x 2%) Equals $28 in total loan charges for the last-minute purchase.
Finance charge savings from buying on the last day equals $27 ($28 - $1).
By buying the $1,400 gift for her friend on the last day of the billing cycle rather than the first, Rebecca can avoid paying $27 in finance charges.
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Kendra earns $70 per week mowing lawns. She saves 60% of the money she earns each week. How many weeks will it take Kendra to save enough money to buy a game system that costs $210 including tax?
Answer:
5 weeks
Step-by-step explanation:
Let's find how much money she saves a week by multiplying the decimal form of 60% and $70.
To get the decimal form of a percent you have to move the decimal to the left twice, like this: 60 ---> .60
Now that we have the decimal form of the percent we can multiply it by the 70 to find how much she saves a week:(70)(.6) = 42
Therefore, Kendra saves $42 each week. To find how many weeks it will take Kendra to buy the game system you divide $210 by the $42.
Like this:(210)/(42) = 5 All in all, it will take Kendra 5 weeks to save enough money to buy a game system that costs $210. I hope this helps!!
-Hadi
Answer:
Step-by-step explanation:
Answer:
5 weeks
Step-by-step explanation:
Let's find how much money she saves a week by multiplying the decimal form of 60% and $70.
To get the decimal form of a percent you have to move the decimal to the left twice, like this: 60 ---> .60
Now that we have the decimal form of the percent we can multiply it by 70 to find how much she saves a week:(70)(.6) = 42
Therefore, Kendra saves $42 each week. To find how many weeks it will take Kendra to buy the game system you divide $210 by the $42.
Like this:(210)/(42) = 5 All in all, it will take Kendra 5 weeks to save enough money to buy a game system that costs $210. I hope this helps!!
-Raf
Which question should you expect to be answered with variable data?
A. How tall are the students in my class?
B. How many phone calls did I make yesterday?
C. What was the highest grade on the last history test?
D. How many people attended the last middle school volleyball game?
B, C, and D are all questions that should be expected to be answered with variable data
Which questions are to be answered with variable data?Variable data refers to information that can change or vary, as opposed to fixed or constant data. In the context of statistics and data analysis, variable data refers to data that can take on different values for different individuals or observations.
B, C, and D are all questions that should be expected to be answered with variable data because the answer to each of these questions can change depending on the specific context or situation.
For example, the number of phone calls one makes on a given day can vary, the highest grade on a test can change from test to test, and the number of people who attend a volleyball game can also change.
A. How tall are the students in my class? is a question that should be expected to be answered with fixed data as the height of the students in the class will stay the same unless there is a significant change in their height.
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Jenny’s garden is 28 feet by 50 feet. What is the area of her garden? How could she use mental math to find the area?
Answer:
1400 square feet
Step-by-step explanation:
The area of a rectangle is found by multiplying its length by its width. So the area of Jenny's garden, which is 28 feet by 50 feet, is:
28 x 50 = 1400 square feet
To use mental math, Jenny could use the distributive property of multiplication.
First, she could break down the 28 into 20 and 8, and 50 into 40 and 10.
Then, she could think 20 x 50 = 1000 and 8 x 10 = 80
Finally, she could add 1000 + 80 = 1080.
So, the area of the garden can also be found by breaking down one of the dimensions into smaller parts, multiply them and add the results.
Another way to use mental math is to think of it as a square with side length of 50 ft, and then think of it as 28 rectangles of 1 ft by 50 ft. The area is then 50 x 28 = 1400 sq ft.
For what value of k does the pair of equations have an infinite number of solutions 8x 5y 9 KX 10y 18?
The required value of k will the system of linear equations has infinite number of solutions is -16.
What is Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
According to question:
We know that
8x + 5y - 9 = 0 . ..........(1)
KX+10y - 18=0 ..........(2)
Because there are infinity many solutions to linear equations.
[tex]\frac{a_{1}}{a_{2}} =\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}[/tex]
⇒ 8/k = 5/10 = -9/-18
8/k = 1/2
k = 16
Thus,required value of k is -16.
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In excrises 9-12 find the value of x and y that makes the quadrilateral a parellgram please help! Worth a lot of points image is below
Answer:
9. y=66 x=114
10.y=9 x=16
Step-by-step explanation:
How many solutions does the system of linear equations represented in the graph have? Coordinate plane with one line that passes through the points 0 comma 2 and 2 comma 1. No solution Infinitely many solutions One solution at (2, 0) One solution at (0, 2)
The graph represented is a single line and the solution is
Infinitely many solutionsHow to determine the solution of a single lineThe solution of a sets of linear equations is determined as follows
The location where the lines intersect will be the only solution if they intersect. If they run parallel, there won't be any solution. There will be numerous (infinite) solutions if they are on the same line.Since the coordinates are for a line hence it represents lines on the same line and this results to infinitely many solution
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Answer:
Infinite solutions
Step-by-step explanation:
Got it right on the test
Find the degree and determine whether the polynomial is a monomial, a binomial, or a trinomial. 5x ^ 2 * y ^ 2 * z + 10x ^ 2 * y ^ 2 * z
Please help fast with find the degree
The polynomial:
5x²*y²*z + 10*x²*y²*z
Is a monomial (it can be rewritten as 15*x²*y²*z)
And the degree is 5.
How to find the degree of the polynomial?Remember that the degree of a polynomial is equal to the maximum sum of exponents that we have on a single term.
The given polynomial here is:
5x²*y²*z + 10*x²*y²*z
First, notice that we can take "x²*y²*z" as a common factor, then we can rewrite:
5x²*y²*z + 10*x²*y²*z = 15*x²*y²*z
So we have only a term, thus, this is a monomial.
And the degree is the sum of the exponents, we will get:
2 + 2 + 1= 5
So the degree is 5.
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You have $5.00 and you need to make copies of a flyer at a store that charges $0.30
per copy. Find the inequality that represents the number of copies you can make. Use
x as the variable.
What is the maximum number of copies you can afford to make?
Answer:
The required number maximum number of copies can be afforded x < 24.28.
Given that,
We have $8.50 and you need to make copies of a flyer at a store that charges $0.35 per copy.
What is inequality?
Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the number of copies be x,
According to the question,
0.35x < 8.50
x < 8.50 / 0.35
x < 24.28
Thus, the required number maximum number of copies can be afforded x < 24.28.
Step-by-step explanation:
jim drinks 15 ounces of water each hour. which expression shows how much he drank
The amount of water drank in 12 hours will be 180 ounces.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jim drinks 15 ounces of water each hour. The amount of water drank by Jim in 12 hours will be,
Amount of water = 15 x 12
Amount of water = 180 ounces
Hence, the amount of water drank in 12 hours will be 180 ounces.
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Colin deposited $1,230 in an account that pays 3.19% simple interest for three years.
a. What will the interest be for the three years?
b. What will be the new balance after three years?
The interest after three years is $117.711 and new balance after three years is $1347.711
How to determine the interest for the three years?Simple interest is a type of interest calculated on the initial principal or starting amount of a loan or investment.
The formula for simple interest is:
I = PRT/100
Where:
I = Interest
P = Principal or starting amount
R = Interest rate
T = Time
a. Interest after three years:
I = PRT/100
P = $1,230, R = 3.19% and T = 3 years
I = (1,230 ×3.19 × 3)/100
I = $117.711
b. New balance after three years:
New balance = P + I
New balance = $1,230 + $117.711 = $1347.711
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I need help with this math assignment 1 and there will be more that I'll be asking you guys!
Answer:
Step-by-step explanation:
Then general form of a linear function is:
f(x) = mx + c
where m = the slope and c is the value of f(x) when x = 0 (the y-intersect on a graph)
f(0) = 4, so
f(0) = m(0) + c
4 = m(0) + c
Giving c = 4.
Slope = -6, so
f(x) = -6x + 4 (answer)
2. Finn has 3 hamsters and 8 fish at home. Shows the ratio of fish to total number of pets
in 3 different ways.
Finn has 3 hamsters and 8 fish at home, the ratio of fish to total number of pets is - 8 : 11
What is ratio?The ratio refers to the number that may be used to represent one quantity as a percentage of another, to put it simply. Only when the ratio's two numbers use the same unit can they be compared. To compare two objects, we utilize ratios. When the second integer in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. A percentage seems to be an equation in which two proportions are made equal to one another. Ratio, which is comfortably pronounced as the ratio, was directly derived from the Latin term. Everything from "reason," "calculation," and "proportion" were all included in the Latin word ratio.
Given that,
Hamsters: 3
Fish: 8
Thus, total = 3 + 8 = 11
Now, ratio of fish total number of pets:
= 8 : 11
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How many planes of symmetry does this sphere have? one two four infinitely many
Answer:
infintely many
Step-by-step explanation:
Simplify p2q6r8 / pq2r4
alex thinks $131^\circ$ are neat. what is the maximum number of interior angles of a convex $n$-gon that can have measure $131^\circ$?
The maximum number of interior angles of a convex n-gon that can have measure 131° is equals to the seven.
A polygon is said to be convex n-gon when no line segments between the points, goes inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°. Sum of interior angles of n sided polygon
= 180(n- 2) degrees
We have, Alex assume that one of interior angle of convex n-gon is 131° . Let total maximum number of interior angles of a convex n-gon or polygon that can have measure 131° be "x".
Total measures of all remaining interior angles, (n - x) of this polygon
= 180(n- 2) - 131x
But for a convex n-gon, interior angles of a convex polygon are less than 180°. So,
180(n- 2) - 131x < (n - x) 180
Now, solve this Inequality,
=> 180n - 360 - 131x < 180n - 180x
=> -360 + 180x - 131x < - 180x + 180x
=> - 360 + 49x < 0
=> 49x < 360
=> x < 360/49
=> x < 7.34 ~ 7
So, the required value of x is 7 .
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a furniture company manufactures dining room tables and chairs. each table requires 8 hours from the assembly department and 2 hours from the finishing department and contributes a profit of $90. each chair requires 2 hours from the assembly department and 1 hours from the finishing department and contributes a profit of $25. the maximum labor hours available each day in the assembly and finishing department is 400 and 120. how many chairs and tables should be manufactured to maximize and minimize the daily profit?
To maximize the profit only 52 Tables must be manufactured daily and to minimize the profit only 173 chairs must be manufactured working with the efficiency given.
What is efficiency?
The ratio of work accomplished by a machine or process to total energy expended or heat consumed is known as efficiency.
Efficiency refers to how close we can get to a specific outcome from a given input with the least amount of waste. Efficiency is the capacity to waste as little material, work, energy, and time as possible when executing a task or generating a desired outcome.
The ratio of usable output to total input can be used to calculate efficiency. The efficiency of a device is defined as the ratio of energy transferred to a usable form to the total energy provided originally.
Now
For table,
assembly hours=8
finishing hours = 2
profit/table=$90
For Chairs
assembly hours=2
finishing hours = 1
profit/chair=$25
Total assembly hours in a day=400
Total finishing hours in a day=120
As profit for table is more than profit for chair. Therefore, for maximum profit only Tables will be manufactured and will be
=total hours available/Time taken for one chair
=520/10
Tables manufactured=52
and for minimum profit only chairs will be manufactured
=520/3
chairs manufactured=173
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