Answer:
15/28
Step-by-step explanation:
((5x+2)/2)-((5x-2)/4)=3
Answer:
Explanation:
Given:
\(\frac{5x+2}{2}-\frac{5x-2}{4}=3\)To solve for the value of x, we simplify it first. So,
We multiply both sides by 4.
\(\begin{gathered} \frac{5x+2}{2}-\frac{5x-2}{4}=3 \\ 4(\frac{5x+2}{2}-\frac{5x-2}{4})=3(4) \\ \text{Simplify and rearrange} \\ 2(5x+2)-(5x-2)=12 \\ 10x+4-5x+2=12 \\ 5x+6=12 \\ 5x=12-6 \\ 5x=6 \\ x=\frac{6}{5} \end{gathered}\)Therefore, the answer is x=6/5.
what is the explicit formula for this sequence? -7,-3,1,5,…
Answer:
\(a_n=4n-11\)
Step-by-step explanation:
The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:
\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)
Derive u(c,n)=ln(c)+0.4×ln(1−n) w.r.t. n which stands for labor. 1/c 1/n 0.4/(1−n) 0.4 ∗
1/(1−n) ∗
(−1) QUESTION 18 Derive the following function u(c,n,h)=(5×ln(c)×2×ln(1−n))+ 1−γ
h 1−γ
where γ=2.5 w.r.t. h. The evaluate the numeric value of this derivative at the point c=1, n=0.5, and h=2
To derive the function u(c, n, h) = \((5 * ln(c) * 2 * ln(1 - n)) + (1 - γ) / h\)with respect to h, we can follow the standard rules of differentiation. the numeric value of the derivative at the given point is -0.375.
Step 1: Take the derivative of each term separately.
The derivative of 5 * ln(c) * 2 * ln(1 - n) with respect to h is 0 since h does not appear in this term.
The derivative of (1 - γ) / h with respect to h can be found using the quotient rule:
\(d/dh [(1 - γ) / h] = [(h * 0 - (1 - γ) * 1) / h^2] = -(1 - γ) / h^2\)
Step 2: Simplify the derivative.
The derivative of u(c, n, h) with respect to h is -(1 - γ) / h^2.
Now, we can evaluate the numeric value of this derivative at the point c = 1, n = 0.5, and h = 2.
γ = 2.5
c = 1
n = 0.5
h = 2
Substituting these values into the derivative expression:
\(d/dh [(5 * ln(c) * 2 * ln(1 - n)) + (1 - γ) / h]\)
= -(1 - γ) / h^2
= -(1 - 2.5) / 2^2
= -1.5 / 4
= -0.375
Therefore, the numeric value of the derivative at the given point is -0.375.
Learn more about rules of differentiation.
https://brainly.com/question/29252522
#SPJ11
what is a binomial with leading coefficient 3 and degree 5
Find the factors from the roots, then multiply the factors together .y=x2−8x+15
suppose we want to choose 2 letters without replacement from four letters ABCD. (A)how many ways can the speed on if the order of choices is taken into consideration?(B) how many ways can this be done if the order of choices is not taken into consideration ?
A)
If the order of choice is taken into consideration, we consider four possibilities for the first choice and three for the second. Then the total number of ways is given by:
\(4\cdot3=12\)B)
If the order of choices is not taken into consideration, we must divide the the previous result by 2, which is the total number of ways by which we can organize two letters (ex: AB and BA):
\(\frac{12}{2}=6\)a fair coin is tossed 5 times. how many possible distinct sequences are there where 2 heads in a row are tossed.
If a fair coin is tossed 5 times. When 2 heads in a row are tossed, the total number of possible sequences is 16.
To determine the number of possible distinct sequences where 2 heads in a row are tossed if a fair coin is tossed 5 times, we need to use the permutation and combination concept. Permutation is defined as the number of ways an object can be arranged in a particular order while combination refers to the number of ways an object can be combined.
Therefore, the possible distinct sequence where 2 heads in a row are tossed can be found using permutation by taking the product of the number of ways 2 heads can be arranged in a row, and the remaining tails and heads can be arranged in the remaining three tosses.
We can illustrate this as follows: The possible ways of tossing 2 heads in a row: H H and the other three tosses can be arranged in 2³ or 8 ways such that the number of tails is the same as the number of heads (equal probability). Therefore, the total number of possible sequences is 2 x 8 = 16 possible sequences where two heads in a row are tossed if a fair coin is tossed 5 times.
You can learn more about sequences at: brainly.com/question/30262438
#SPJ11
the center for medicare and medical services reported that there were appeals for hospitalization and other part a medicare service. for this group, of first round appeals were successful (the wall street journal). suppose first-round appeals have just been received by a medicare appeals office. refer to binomial probability table. round your answers to four decimal places. a. compute the probability that none of the appeals will be successful. b. compute the probability that exactly one of the appeals will be successful. c. what is the probability that at least two of the appeals will be successful? d. what is the probability that more than half of the appeals will be successful?
The probability that more than half of the appeals will be successful is 0.4543 (rounded to four decimal places).
When answering questions on Brainly, it is important to always be factually accurate, professional, and friendly. It is also important to be concise and not provide extraneous amounts of detail. Ignoring typos or irrelevant parts of the question and repeating the question in the answer is unnecessary, but providing a step-by-step explanation and using relevant terms is necessary for a good answer.
Given that the center for Medicare and Medical Services reported that there were appeals for hospitalization and other part A Medicare service. For this group, of the first-round appeals, were successful (The Wall Street Journal). Suppose first-round appeals have just been received by a Medicare appeals office. We need to compute the probability using a binomial probability table.
The probability that none of the appeals will be successful:
First, we calculate the probability of a successful appeal:
p = 0.51 (51% of appeals were successful in the first round).
Next, we use the binomial probability formula to find the probability that none of the appeals will be successful:
P(X = 0) = nCx * p^x * (1-p)^(n-x)
Where:
n = total number of appeals = 10
x = number of successful appeals = 0
P(X = 0) = 10C0 * 0.51^0 * (1-0.51)^(10-0)
P(X = 0) = 0.0059
Therefore, the probability that none of the appeals will be successful is 0.0059 (rounded to four decimal places).
The probability that exactly one of the appeals will be successful:
We can use the same formula to find the probability that exactly one of the appeals will be successful:
P(X = 1) = nCx * p^x * (1-p)^(n-x)
Where:
n = total number of appeals = 10 x = number of successful appeals = 1
P(X = 1) = 10C1 * 0.51^1 * (1-0.51)^(10-1)
P(X = 1) = 0.0541
Therefore, the probability that exactly one of the appeals will be successful is 0.0541 (rounded to four decimal places).
The probability that at least two of the appeals will be successful:
To calculate this probability, we need to find the probability that no appeals are successful or that only one appeal is successful and subtract that probability from 1:
P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)
P(X ≥ 2) = 1 - 0.0059 - 0.0541
P(X ≥ 2) = 0.94
Therefore, the probability that at least two of the appeals will be successful is 0.94 (rounded to four decimal places).
The probability that more than half of the appeals will be successful:
To find the probability that more than half of the appeals will be successful, we need to find the probability that at least six appeals will be successful:
P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
We can use the binomial probability formula to calculate each of these probabilities:
P(X = 6) = 10C6 * 0.51^6 * (1-0.51)^(10-6) = 0.2501
P(X = 7) = 10C7 * 0.51^7 * (1-0.51)^(10-7) = 0.1449
P(X = 8) = 10C8 * 0.51^8 * (1-0.51)^(10-8) = 0.0492
P(X = 9) = 10C9 * 0.51^9 * (1-0.51)^(10-9) = 0.0092
P(X = 10) = 10C10 * 0.51^10 * (1-0.51)^(10-10) = 0.0008
Therefore,
P(X ≥ 6) = 0.2501 + 0.1449 + 0.0492 + 0.0092 + 0.0008 = 0.4543
Therefore, the probability that more than half of the appeals will be successful is 0.4543 (rounded to four decimal places).
Learn more about Probability
brainly.com/question/30034780
#SPJ11
Let three types of consulting services that audit firms are now prohibited from providing to clients that are public companies
The three types of consulting services that audit firms are now prohibited from providing to clients that are public companies are:
1. Bookkeeping services: Audit firms are prohibited from providing bookkeeping services to their audit clients. Bookkeeping involves the recording, organizing, and maintaining of financial transactions.
By prohibiting audit firms from providing bookkeeping services, it helps to ensure independence and objectivity in the audit process. This separation reduces the risk of potential conflicts of interest that could compromise the integrity of the audit.
2. Legal services: Audit firms are also prohibited from providing legal services to their audit clients. Legal services include activities such as drafting legal documents, providing legal advice, and representing clients in legal proceedings.
The prohibition on providing legal services aims to maintain independence and prevent any potential conflicts of interest that could arise if the audit firm were to also provide legal advice or services to the audited company.
3. Financial information systems design and implementation: Audit firms are further prohibited from designing and implementing financial information systems for their audit clients.
This involves the development and implementation of computerized systems that record and process financial data. The prohibition on providing financial information systems design and implementation services helps to avoid any potential bias or lack of objectivity in the audit process,
as the audit firm should remain independent and not be involved in the design and implementation of the systems they are auditing.
By prohibiting audit firms from providing these consulting services, it helps to ensure that the audit process is conducted objectively and independently, without any conflicts of interest.
This enhances the credibility and reliability of financial statements and promotes transparency and trust in the financial markets.
To know more about public companies refer here:
https://brainly.com/question/30957339
#SPJ11
help fast, thanks
(6-62)
Answer: A+P=11, 0.60A+0.35P=5.60
Please help 50 points!
Simplify the expressed
Answer:
Step-by-step explanation:
\(\frac{x^{2} -x-12}{x+4} * \frac{2x^{2}-32 }{x^{2} -8x+16}\) rewrite as multiplication
\(\frac{x^{2} +3x-4x-12}{x+4} * \frac{2(x^{2}-16) }{x^{2} -8x+16}\) look to factor
\(\frac{x(x+3)-4(x+3)}{x+4} * \frac{2(x-4)(x+4) }{(x-4)^{2}}\) , difference of 2 squares and perfect square
\(\frac{(x+3)(x-4)}{x+4} * \frac{2(x-4)(x+4) }{(x-4)^{2}}\), finish factoring and simplify
2(x+3)
The box part of the box plot contains all the values between which numbers?A box-and-whisker plot. The number line goes from 25 to 50. The whiskers range from 27 to 40, and the box ranges from 32 to 37. A line divides the box at 36.A. between 27 and 36 and between 37 and 40B. between 32 and 36C. between 32 and 37D. between 27 and 32 and between 37 and 40 ill mark brainiest if you help me out
The correct option is c) between 32 and 37. The box part of the box plot contains all the values between 32 and 37.
A box-and-whisker plot, also known as a box plot, is a visual representation of a set of data that shows the distribution and variability of the data. The box part of the box plot contains the middle 50% of the data, which is also known as the interquartile range (IQR).
In the given example, the box ranges from 32 to 37, which means that 50% of the data falls within this range. The line that divides the box at 36 represents the median, which is the middle value of the data set.
The whiskers, on the other hand, extend from the box to the minimum and maximum values in the data set that are not considered outliers. In this example, the whiskers range from 27 to 40, which means that the minimum and maximum values in the data set are 27 and 40 respectively.
Therefore, the answer to the question is option C, between 32 and 37, as this is the range that the box covers. The other options do not correctly represent the range of values that fall within the box.
Overall, box-and-whisker plots are useful tools for summarizing and comparing data sets, as they provide a clear and concise visual representation of the distribution and variability of the data.
To learn more about box plot, refer here:
https://brainly.com/question/1523909#
#SPJ11
Three friends were playing a game of marbles.
At the end of the game, Marcy had 25% of the
marbles, Roger had
2
1
of the marbles, and Ann
had the rest of the marbles. If there were 100
marbles altogether, how many marbles did Ann
have at the end of the game?
The number of marbles Ann had at the end is 54.
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,
Total marbles = 100
The number of marbles:
Marcy:
= 25% of 100
= 1/4 x 100
= 25
Roger:
= 21
Now,
The number of marbles:
Ann = 100 - (25 + 21) = 100 - 46 = 54
Thus,
Ann has 54 marbles at the end.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ1
Please help me solve these, I tried solving them but I got confused with the signs,
a) -6x = 30 b) -3x = -9
c)-5x = 25
Answer:
a) x= -5
b) x= 3
c) x= -5
classify the polynomial x9
Answer:
A polynomial is a combination of terms separated by
+
or
−
signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms.
Polynomial
Step-by-step explanation:
The generalized 9th degree polynomial is given below \(a_1x^9+a_2x^8+a_3x^7+a_4x^6+a_5x^5+a_6x^4+a_7x^3+a_8x^2+a_9x+a_{10}=0\) where \(a_1,a_2,....a_9\) are the coefficients and \(a_{10}\) is constant. The polynomial \(x^9\) is known as the nonic equation.
Given :
Polynomial -- \(x^9\)
The following steps can be used in order to classify the given polynomial:
Step 1 - The generalized polynomial equation is given below:
\(a_1x+a_2x^2 + a_3x^3+a_4x^4+a_5x^5+.............+a_nx^n=0\)
where \(a_1,a_2,....,a_n\) are the coefficients.
Step 2 - The generalized quadratic equation is given below:
\(ax^2+bx+c=0\)
where a, b are the coefficients and c is the constant.
Step 3 - So the generalized 9th degree polynomial is given by:
\(a_1x^9+a_2x^8+a_3x^7+a_4x^6+a_5x^5+a_6x^4+a_7x^3+a_8x^2+a_9x+a_{10}=0\)
where \(a_1,a_2,....a_9\) are the coefficients and \(a_{10}\) is constant.
The polynomial \(x^9\) is known as the nonic equation.
For more information, refer to the link given below:
https://brainly.com/question/2263981
Adrian bought a car worth $12000 on 36 easy installments of $375. Answer the following questions. (1) How much total amount did Adrian pay in 36 months? Answer: Total payment A = $ (2) Identify the letters used in the simple interest formula I = Prt. I= $ P= $ and t years. (3) Find the rate of interest in percentage. Answer: r %. ASK YOUR TEACHER
3) since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.
(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:
Total payment A = Monthly installment * Number of installments
= $375 * 36
= $13,500
Therefore, Adrian paid a total of $13,500 over the course of 36 months.
(2) In the simple interest formula I = Prt, the letters used represent the following variables:
I: Interest (the amount of interest paid)
P: Principal (the initial amount, or in this case, the car worth)
r: Rate of interest (expressed as a decimal)
t: Time (in years)
(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:
r = (I / Pt) * 100
To know more about Number visit:
brainly.com/question/3589540
#SPJ11
George walks around one quarter of a quarter of a circular garden. He walks a total of 30 meters. To the nearest tenth of a meter, what is the radius of the circular garden?
The radius of the circular garden is 14.3 meters
The radius of a circle:Any line connecting a circle's center and circumference is said to be the circle's radius. Within a circle, a diameter is equal to the sum of two radii. The area and circumference of a circle are determined using the radius of the circle.
The perimeter of a circle with a radius of r is given by
Perimeter = 2πrHere we have
George walks around one-quarter of a quarter of a circular garden.
He walks a total of 30 meters.
Let x be the Perimeter or circumference of the circular garden
Given that George walks around one-quarter of a quarter of a circular garden.
=> The length of the path that George walked = x/3
Given that He walks a total of 30 meters
=> x/3 = 30 meters
=> x = 90 meters
So we can conclude that circumference of the circular garden = 90 m
As we know Perimeter of the circle = 2πr
=> 2πr = 90
=> πr = 45
=> 22/7(r) = 45
=> 22(r) = 315
=> r = 14.318181818181 ≅ 14.3
Therefore,
The radius of the circular garden is 14.3 meters
Learn more about Circles at
https://brainly.com/question/28946570
#SPJ1
For each function, find f(1), f(2), f(3) , and f(4) .
f(x)=-3 x-9
The values of f(1), f(2), f(3), and f(4) for the given function are -12, -15, -18, and -21, respectively.
Given function is f(x) = -3x - 9.We are supposed to find f(1), f(2), f(3), and f(4).
To find f(1), we need to substitute 1 in the place of x. So, f(1) = -3(1) - 9= -3 - 9= -12.
To find f(2), we need to substitute 2 in the place of x.
So, f(2) = -3(2) - 9= -6 - 9= -15.
To find f(3), we need to substitute 3 in the place of x.
So, f(3) = -3(3) - 9= -9 - 9= -18.
To find f(4), we need to substitute 4 in the place of x. So, f(4) = -3(4) - 9= -12 - 9= -21.
To know more about function visit :
https://brainly.com/question/30721594
#SPJ11
Which expression is undefined?
Answer:
Option D is the correct answer
Step-by-step explanation:
\( \frac{8}{( - 2 + 2)} = \frac{8}{0} = undefined \\ \)
show that the equation x^3-15x+c=0 has at most one root in the interval parentheses -2, 2.
Therefore, the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2).
To show that the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2), we can use the concept of the Intermediate Value Theorem and Rolle's Theorem.
Let's assume that the equation has two distinct roots, denoted as a and b, in the interval (-2, 2). Without loss of generality, we assume a < b.
Since the function is continuous on the closed interval [-2, 2] and differentiable on the open interval (-2, 2), we can apply Rolle's Theorem. According to Rolle's Theorem, there exists a point c in the open interval (a, b) such that the derivative of the function at c is zero.
Consider the derivative of the function f(x) = x^3 - 15x + c:
f'(x) = 3x^2 - 15
Setting f'(c) = 0, we have:
3c^2 - 15 = 0
c^2 - 5 = 0
c^2 = 5
Taking the square root of both sides, we get:
c = ±√5
Now, let's consider the function values at the endpoints of the interval (-2, 2):
f(-2) = (-2)^3 - 15(-2) + c = -8 + 30 + c = 22 + c
f(2) = (2)^3 - 15(2) + c = 8 - 30 + c = -22 + c
If c = √5, then f(-2) = 22 + √5 and f(2) = -22 + √5.
If c = -√5, then f(-2) = 22 - √5 and f(2) = -22 - √5.
In either case, the function values at the endpoints have different signs. This implies that there exists at least one value, say k, in the interval (-2, 2) such that f(k) = 0, according to the Intermediate Value Theorem.
However, we assumed at the beginning that there are two distinct roots in the interval (-2, 2), denoted as a and b. This contradicts our finding that there is at most one root in the interval. Hence, our assumption of having two distinct roots is false.
To know more about equation,
https://brainly.com/question/27695523
#SPJ11
Translate the following phrase into an algebraic expression using the variable m. Do not simplify. the cost of renting a car for one day and driving m miles if the rate is $53 per day plus 25 cents per mile
Answer:
($53/day)(1 day) + ($0.25/mile)*m
Step-by-step explanation:
Let m be the number of miles driven on the rental car.
Total Cost for 1 day rental and m miles is:
($53/day)(1 day) + ($0.25/mile)*m
1 day and 100 miles would be: ($53/day)(1 day) + ($0.25/mile)*(100 miles) =
$53 + ($25) = $78
The algebraic expression for one day is \(\$ 53+ \$ 0.25 \times m\) .
What is algebraic expression?An algebraic expression in mathematics is an expression created using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c. The following is also an algebraic expression because raising to the power is equivalent to taking the square root. Any expression that can be converted into a rational fraction using the properties of the arithmetic operations is said to be rational (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions). In other terms, a rational expression is one that can be created using only the four operations of arithmetic and the variables and constants.
Given variable is m.
Driving rate is $53 per day.
Extra $0.25 per mile.
Therefore, the algebraic expression for one day is \(\$ 53+ \$ 0.25 \times m\) .
To learn more about algebraic expression from the given link:
https://brainly.com/question/4344214
#SPJ4
If the sphere shown above has a radius of 17 units, then what is the approximate volume of the sphere?
A.
385.33 cubic units
B.
4,913 cubic units
C.
6,550.67 cubic units
D.
3,275.34 cubic units
Answer:
20582.195 unitsStep-by-step explanation:
This problem is on the mensuration of solids.
A sphere is a solid shape.
Given data
radius of sphere = 17 units
The volume of a sphere can be expressed as below
\(volume = \frac{4}{3}\pi r^3\)
Substituting our data into the expression we have
\(volume = \frac{4}{3}*3.142*17^3\)
\(volume = \frac{4}{3}*3.142*4913\\\\volume = \frac{61746.584}{3}= 20582.195\)
The volume of the sphere is given as
20582.195 units
what is the probability of 45 heads in 100 tosses of a coin given the probability of heads is 50%? binomial distribution
The probability of 45 heads in 100 tosses of a coin given the probability of heads is 50% is 7.1%.
Coin Toss Probability CalculationThe binomial probability formula is used to calculate the probability of getting a certain number of heads (or success) in a certain number of coin tosses (or trials) when the probability of getting a head (or success) in each individual coin toss is known. The formula is:
P(x) = (n choose x) * (pˣ) * (1-p)^(n-x)
Where,
P(x) is the probability of getting x heads (or success) in n coin tosses (or trials)
n is the number of coin tosses
x is the number of heads (or success)
p is the probability of getting a head (or success) in a single coin toss
1-p is the probability of getting a tail (or failure) in a single coin toss
(n choose x) is the binomial coefficient, which is the number of ways to choose x heads (or success) from n coin tosses (or trials)
In this case, the probability of getting 45 heads in 100 tosses of a coin with a probability of heads of 50% can be calculated using the formula: (100 choose 45) * (0.5⁴⁵) * (0.5⁵⁵) which is approximately 0.071, or 7.1%.
Learn more Coin Toss Probability Calculation here:
https://brainly.com/question/9829298
#SPJ4
factor the binomials using gcf 16p + 4
how many ways can a parent distribute five one-dollar bills to her three children? (b) how many ways can she accomplish this if each child gets at least one dollar?
By the concept of Permutations and Combinations, we get:
Number of ways to distribute 5 dollar bills among three children = 21
and
Number of ways to distribute 5 dollar bills such that each child gets at least one dollar = 6
What is permutations and combinations?A permutation is an orderly arrangement of the items or numbers. Combinations are a means to choose items or numbers from a collection or set of items without regard for the items' chronological sequence.Given:
Number of 1 dollar bills = 5Number of children = 3To find: (A) number of ways to distribute the dollar bills among the children
(B) number of ways to do the same if each child gets at least a dollar.
Finding:
By using the formula: \(\binom{n+r-1}{r-1}\),
Number of ways to distribute 5 dollar bills among three children = \(\binom{5+3-1}{3-1} = \binom{7}{2}= \frac{7\times6}{2}\) = 21 ways.
Similarly, upon modifying the above formula as: \(\binom{n-1}{r-1}\),
Number of ways to distribute 5 dollar bills such that each child gets at least one dollar is =
\(\binom{5-1}{3-1}= \binom{4}{2}=\frac{4\times3}{2}\) = 6 ways.
To learn more about permutations and combinations, refer to the link: https://brainly.com/question/11732255
#SPJ4
O is the centre of a circle.
M is a point on chord AB.
The length of chord AB is 12 cm.
OM is perpendicular to AB. OM is 8 cm.
a Work out the length of AM. State any circle theorems that you use.
b What is the length of the radius of the circle?
If "O" is the center of a circle, "M" a point on chord AB of the same circle whose length is 12 cm, and if OM whose length is 8 cm is perpendicular to AB, then the length of AM is 6 cm, and the radius of the circle is 10 cm.
As per the question statement, "O" is the center of a circle, "M" a point on chord AB of the same circle whose length is 12 cm, and OM whose length is 8 cm, is perpendicular to AB,
And we are required to determine the length of the segment AM, and the radius of the circle.
To solve this question, we need to the know an important theorem regarding the perpendiculars from the center to the chords of a circle, which is, "The perpendicular to any chord of a circle from it's center bisects the chord".
Here since AB is a chord of our concerned circle, and OM is the perpendicular to AB from the center, therefore, as per the above mentioned theorem, OM must also bisect AB at M, that is,
[AM = BM = (AB/2)]
Or, [AM = (12/2) cm]
Or, (AM = 6 cm]
Now, since (OM ⊥ AB) at M, therefore, (∠AMO = ∠BMO = 90°), and both A and B are two points on the circumference of the circle. If we join AO and BO with straight lines, we will have two congruent right-angled triangles, ΔAMO and ΔBMO. Advancing with ΔAMO, we will get, "OM" to be the perpendicular or altitude of the triangle, "AM" to be the base, and "AO" to be the hypotenuse of it. And as per the Pythagorus theorem, we know that, [(hypotenuse)² = {(perpendicular)² + (base)²}]
Or, [AO² = (OM² + AM²)]
Or, [AO² = (8² + 6²)]
Or, [AO² = (64 + 36)]
Or,(AO² = 100)
Or, [√(AO)² = √100]
Or, (AO = 10)
And since any straight line from the center of a circle to any point on it's circumference is the radius of it, therefore, "AO" is a radius of our concerned circle. Hence, the radius of this circle is 10 cm.
Circle: A circle is a standard, two-dimensional, round, bounded, geometric shape such that every point on the boundary us equidistant from the center.To learn more about Circles and their chords and radii, click on the link below.
https://brainly.com/question/20691207
#SPJ9
What are 2 multiplication expressions that have the product of 28.34 ?!?!?!? NEED HELP ASAP!!!!
Answer:
28.34 x 1 = 28.34
14.17 x 2 = 28.34
There are required two multiplication expressions that might generate the result 28.34. Here are a number of such examples:
28.34 × 1
14.17 × 2
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
We have to determine two multiplication expressions that have the product of 28.34
As per the given question, the required solution would be as:
There are many possible multiplication expressions that could result in the product of 28.34. Here are two examples:
28.34 × 1
14.17 × 2
In the first example, the product is 28.34 because any number multiplied by 1 is equal to itself.
In the second example, the product is 28.34 because 14.17 multiplied by 2 is equal to 28.34.
Hence, the required answers are 28.34 × 1 and 14.17 × 2
Learn more about Multiplication operations here:
brainly.com/question/25834626
#SPJ2
Math is the only place where is not questionable as to why someone has 83.
Answer:
true
Step-by-step explanation:
I’ll give brainliest help ASAP
Answer:
6 weeks of culinary school
3^-2 × 3^-5
3^-7
3^-3
3^10
3^7
\( {3}^{ - 2} \times {3}^{ - 5} = {3}^{ - 7} \)
Answer:
A) 3^-7
Step-by-step explanation:
fill in the blank. _____sample
The population is first split into groups. The overall sample consists of every member from some of the groups. The groups are selected at random.
Example—An airline company wants to survey its customers one day, so they randomly select 555 flights that day and survey every passenger on those flights.
Why it's good: A cluster sample gets every member from some of the groups, so it's good when each group reflects the population as a whole.
it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.
What is intra-cluster sample?A cluster sample is a sampling technique where the population is divided into clusters or groups, and a subset of clusters is selected at random to form the overall sample. In this type of sampling, all members of the selected clusters are included in the sample.
In the given example, the airline company selects 555 flights as clusters and surveys every passenger on those flights. Each flight represents a cluster, and by selecting random flights, the company includes every passenger on those selected flights in the survey.
This cluster sampling approach is suitable when each group or cluster is representative of the overall population. It is useful when it is impractical or costly to sample every individual unit within the population, but the selected clusters are expected to reflect the characteristics of the entire population.
Cluster sampling allows for more practical data collection, particularly when dealing with large populations or geographically dispersed units. However, it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.
Learn more about cluster sampling on:
https://brainly.com/question/15357818
#SPJ4