Ratio analysis is the best way to ensure reliable financial information, as it allows investors to evaluate the financial strength of a company and the reliability of its financial information by calculating ratios such as the current ratio, quick ratio, and debt-to-equity ratio.
Reliable financial information is information that is accurate and up-to-date. It is the foundation of any investor’s decision-making process, as it allows them to make informed decisions. One of the best ways to ensure reliable financial information is to perform a ratio analysis. Ratio analysis is the process of evaluating financial information by calculating ratios such as the current ratio, quick ratio, and debt-to-equity ratio.
The current ratio is calculated by dividing a company’s current assets by its current liabilities. This ratio measures a company’s ability to pay its short-term obligations. The quick ratio is calculated by dividing a company’s current assets minus inventory by its current liabilities. This ratio measures a company’s ability to pay its short-term obligations without having to sell its inventory. The debt-to-equity ratio is calculated by dividing a company’s total liabilities by its total number. This ratio measures how much debt a company has relative to its equity.
By looking at these ratios, investors can get an idea of the financial strength of a company and the reliability of its financial information. The higher the ratios, the more reliable the financial information is likely to be
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Complete question:
How can investors ensure reliable financial information?
A(1)=20 a(n)=a(n−1)⋅ 2 3 What is the 3 rd 3 rd 3, start superscript, start text, r, d, end text, end superscript term in the sequence?
The third term of the given sequence is =60.
The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers
a(1)=20
and
[tex]a_n=a(n-1)*\frac{3}{2}\\\\n=3\\\\a_3=20(2)*\frac{3}{2}\\\\a_3=60[/tex]
The complete question is-
a(1)=20 a(n)=a(n-1)*3/2 What is the 3rd term in the sequence?
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First, how long will it take for the music player to fall to the bottom of the ravine? Solve the equation and find the values of t. (2 points: 1 point for each value)
The equation of the ravine time function is a quadratic equation, the time, t that will take for the music player to fall to the bottom of the ravine is equals to the 1.5 seconds.
We have the construction workers likes to listen to music on the job. The time it takes for the music player to fall from the bridge to the bottom of the ravine can be modeled by the following
equation, t = √(8t+24)/16 --(1)
where t--> the amount of time since the construction worker dropped his music player. Now, we have to solve equation (1). Squaring both sides in equation (1)
=> t² = (√(8t + 24)/16)
=> t² = [((8t + 24)/16)½]²
=> t² = ( 8t + 24)/16
Cross multiplication
=> 16t² = 8t + 24
=> 16t² - 8t - 24 = 0 --(2)
which is a quadratic equation with variable 't'. To solve the quadratic equation or value of t, we use "quadratic formula". The quadratic equation formula to solve the equation ax² + bx + c = 0 is x = [-b ± √(b² - 4ac)]/2a. Here we obtain the two values of x. Now, comparing the equation (2) with
second order equation, ax² + bx + c = 0, we get a = 16 , b = -8 , c = -24
So, t = [-b ± √(b² - 4ac)]/2a
=> t = [ -(-8) ± √((-8)² - 4×16×(-24))]/2×16
=> t = [8 ± √64 + 1536 ]/32
=> t = ( 8 ± √1600)/32
=> t = (8 ± 40)/32
either t = (8 + 40)/32 or t = (8 - 40)/32
either t = 48/32 or t = -32/32 = -1
either t = 3/2 = 1.5 or t = -1
but time, t cannot be equal to negative value. So, the required time value, t is 1.5 seconds.
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Complete question:
One of the construction workers likes to listen to music on the job. Unfortunately, he also has a bad habit of accidentally dropping his music player into the ravine! Luckily, his daughter is good with physics and has built a safety balloon for his latest music player that will release after the music player has been falling for 1 second.
The time it takes for the music player to fall from the bridge to the bottom of the ravine can be modeled by the following equation,t = √(8t+24)/16
where tis the amount of time since the construction worker dropped his music player. First, how long will it take for the music player to fall to the bottom of the ravine?
Solve the equation and find the values of t. (2 points: 1 point for each value)
According to an article, 44% of adults have experienced a breakup at least once during the last 10 years. Of 9 randomly selected adults, find the probability that the number, X, who have experienced a breakup at least once during the last 10 years is:
a. exactly five; at most five; at least five.
b. at least one; at most one.
c. between five and seven, inclusive.
d. Determine the probability distribution of the random variable X.
The prοbabilities are,
a) P(X = 5)=0.204 , P(X ≤ 5) =0.849 and P(X ≥ 5)= 0.355
b) P(X ≥ 1) = 0.995 , P(X ≤ 1)=0.044
c) P(5 ≤ X ≤ 7)= 0.571
What is prοbability?Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.
a) Prοbability οf exactly 5, P(X = 5) then
Using excel binοmial functiοn:
=> BINOM.DIST(5, 9, 0.44, 0)
=> 0.204
Prοbability οf at mοst 5, P(X ≤ 5) then
Using excel binοmial functiοn:
=> BINOM.DIST(5, 9, 0.44, 1
=> 0.849
Prοbability οf at least 5, P(X ≥ 5) = 1 - P(X ≤ 4)
Using excel binοmial functiοn:
=> 1 - BINOM.DIST(4, 9, 0.44, 1)
=> 0.355
b)Prοbability οf at least 1, P(X ≥ 1) = 1 - P(X ≤ 0)
Using excel binοmial functiοn:
=> 1 - BINOM.DIST(0, 9, 0.44, 1)
=> 0.995
Prοbability οf at mοst 1, P(X ≤ 1) =
Using excel binοmial functiοn:
=> BINOM.DIST(1, 9, 0.44, 1)
=> 0.044
c) Prοbability between 5 and 7, P(4 ≤ X ≤ 6) = P(X ≤ 7) - P(X < 5)
=> P(X ≤ 6) - P(X ≤ 3)
=> BINOM.DIST(6, 9, 0.44, 1) - BINOM.DIST(3, 9, 0.44, 1)
=> 0.571
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please help me I need to turn this in now
The volume of a right circular cone that has a height of 3.5 ft and a radius of 18.9 ft is given as follows:
1308.6 ft³.
How to obtain the volume a cone?The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.
V = πr²h/3.
The parameters for the cone in this problem are given as follows:
Radius of r = 18.9 ft.Height of h = 3.5 ft.Hence the volume of the cone is given as follows:
V = 3.14 x 18.9² x 3.5/3
V = 1308.6 ft³.
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what is the acceleration of a bus whose speed changes from 126 m/s to 306 m/s over a period of 3seconds
Answer: The acceleration of the bus can be calculated using the formula:
a = (v2 - v1) / t
where:
a = acceleration
v2 = final velocity = 306 m/s
v1 = initial velocity = 126 m/s
t = time = 3 seconds
Substituting the given values into the formula, we get:
a = (306 m/s - 126 m/s) / 3 s
a = 180 m/s / 3 s
a = 60 m/s^2
Therefore, the acceleration of the bus is 60 m/s^2.
Step-by-step explanation:
What is x-^2y(x^3y^5)^3 in simplest form for all values of x and y where the expression is defined?
The simplified form of the expression x⁻²y(x³y⁵)³ is x⁷y¹⁶ for all values of x and y where the expression is defined.
How to determine the expression in the simplest formTo simplify this expression, we need to use the rules of exponents, specifically the rule for raising a power to a power, which states that (aᵇ)ˣ = aᵇˣ.
Using this rule, we can simplify the expression as follows:
x⁻²y(x³y⁵)³
Open bracket
= x⁻²y(x³ˣ³y⁵ˣ³) (apply the rule for raising a power to a power)
Evaluate
= x⁻²y(x⁹y¹⁵)
Apply the law of indices in multiplying again
x⁷y¹⁶
Hence, the solution is x⁷y¹⁶
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Write the equation of the line parallel to line p that passes through (2, 5).
Thus, the equation of the line parallel to line p that passes through (2, 5) is y = mx - 2m + 5, where m is the slope of line p.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It contains one or more variables, and the goal is to solve for the value(s) of the variable(s) that make the equation true.
For example, the equation 2x + 5 = 11.
Given by the question.
To find the equation of a line parallel to line p that passes through the point (2, 5), we need to know the equation of line p.
Assuming that we have the equation of line p in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we can use the fact that parallel lines have the same slope to find the equation of the desired line.
Therefore, the equation of the line parallel to line p that passes through (2, 5) is:
y = mx + b (equation of line p)
y - 5 = m (x - 2) (point-slope form with (2, 5))
y = m (x - 2) + 5 (slope-intercept form)
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if p 62-5x and r =133 find qrs
The answer to this question is that we cannot find qrs without additional information about what q and s represent. We can only make educated guesses based on the context of the problem.
Sure, I'd be happy to help! To find qrs, we need to know what these variables represent. Based on the given information, we know that p=62-5x and r=133, but we don't know what q represents. Therefore, we cannot directly solve for qrs.
However, we can make an educated guess based on the context of the problem. It's possible that q is related to p and r in some way. For example, q could be the sum of p and r, or it could be the product of p and r. Without more information, we can't be sure.
Another possibility is that qrs is actually three separate variables, q, r, and s. In this case, we would need to know what s represents in order to solve for qrs.
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2. Kadesh bought 20 shirts at a total cost of R 980. If the large shirts cost
R 50 and the small shirts cost R 40. How many of each size did he buy?
Answer:
18 large shirts
2 small shirts
Step-by-step explanation:
trial and error my boi
Luke’s parents started a savings account to help him pay for college or a technology school when he turned 11 years old. Each month they put $125 into the savings account, and they continued this until he was 18 years old. The savings account did not accumulate any interest. Luke figured out that the first year of a technology school that he wanted to attend would cost him $12,480. If he had one year to save the rest of the money, how much would he need to save each month?
A. 165
B.40
C.1980
D.1040
B has a savings account, into which he must deposit $40 each month.
What's the point of the example?Interest is frequently calculated as an annual percentage of the amount borrowed. This percentage represents the loan's interest rate. For instance, a bank will pay interest if you deposit money in a high-yield savings account.
From the time he was 11 to the time he was 18, Luke's parents saved for him for 8 years, or 8 years x 12 months every year, or 96 months.
Since they were saving $125 per month throughout this time, Luke had amassed the following sum:
$125/month x 96 months = $12,000
Luke must still pay the following expenses because he needs $12,480 for his first year of technological school:
$12,480 - $12,000 = $480
If he has one year left to save this amount, he will need to save:
$480÷12months = $40per month
Therefore, the answer is B. $40.
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A student used factor by grouping to factor the expression below. How can you tell that the student made an error when factoring? explain the error.
students work:
6x^2 - x - 12
6x^2 - 9x + 8x - 12
3x(2x - 3)-4(-2 + 3)
The student made an error when factoring because they did not factor the expression correctly. The correct factoring of the expression is 6x^2 - x - 12 = 6x(x - 2) - 3(4).
What is common factor?A common factor in math is a number that can be divided into two or more numbers without a remainder. For example, the common factors of 10 and 15 are 1, 5, and 10. The greatest common factor (GCF) is the largest number that divides both numbers evenly. In this example, the GCF of 10 and 15 is 5. Common factors are useful for simplifying fractions, solving equations, and finding the lowest common multiple.
When factoring by grouping, it is important to remember that the factors of the first and last terms of the expression must multiply to equal the middle terms. In this example, the first and last terms are 6x^2 and -12 respectively. These numbers do not multiply to equal -x, which is the middle term.
The student should have factored the expression by dividing the first and last terms by the greatest common factor (GCF). The GCF of 6x^2 and -12 is 6x, so the expression can be factored as 6x(x - 2) - 3(4).
When factoring by grouping, it is also important to remember to factor out the common factor first. In this example, the common factor is 3x, so the expression should be factored as 3x(2x - 3) - 4(2 - 3).
In conclusion, the student made an error when factoring the expression because they did not factor the expression correctly. The proper way to factor the expression is to divide the first and last terms by the greatest common factor and factor out the common factor first.
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Sylvie bakes 4 trays of muffins. Each tray contains 8 muffins. She gives away 12 muffins to friends. Let m represent the number of muffins Sylvie has left. Which equation could be used to find the value of m?
The equation that could be used to find the value of "m" is: m = 20
To find the equation to determine the number of muffins Sylvie has left after baking and giving away some, we need to follow these steps:
Calculate the total number of muffins baked by Sylvie: 4 trays x 8 muffins/tray = 32 muffins
Subtract the number of muffins given away from the total baked: 32 muffins - 12 muffins = 20 muffins
Assign the number of muffins left to the variable "m"
Therefore, the equation that could be used to find the value of "m" is:
m = 20
This means that Sylvie has 20 muffins left after giving away 12 to her friends. It's important to note that we used basic arithmetic operations to solve this problem, including multiplication and subtraction, and then assigned the remaining value to a variable to create the equation.
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Ben went on holiday to Australia. He changed £350 into Australian dollars ($).
The exchange rate was £1 = $2.1
(a) Work out how many Australian dollars Ben should have received.
$.......
Ben should have received $735 in Australian dollars at the given exchange rate.
What is an exchange rate?The value of one currency represented in terms of another is called an exchange rate. It is the cost associated with exchanging one currency for another. The dynamics of supply and demand in the market dictate exchange rates, which are continually changing in response to a variety of political and economic variables including inflation, interest rates, trade balances, and geopolitical events. Currency rates have an impact on the price and profitability of transactions between nations, making them crucial for international commerce and investment. As they govern how much foreign currency can be received for a certain quantity of local currency, they are especially crucial for those who travel or transfer money overseas.
Given that, the exchange rate was £1 = $2.1.
Thus,
£350 * $2.1/£1 = $735
Therefore, Ben should have received $735 in Australian dollars.
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g(x)
121x
10
8
6
fo
-6-5-4-3-2-1₂
Of(0) = g(0)
Of(-2) = g(-2)
Of(0) = g(-2)
Of(-2) = g(0)
2
799
-6
-10-
-12+
23
3 4 5 6 x
10)
The statement that is true regarding the graphed functions is that: B. f(-2) = g(-2).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (2, 0), an equation of the line f(x) can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 0 = (-4 - 0)/(-2 - 2)(x - 2)
y = -x + 2
For line g(x), we have:
y - 4 = (-2 - 4)/(0 + 2)(x + 2)
y = -3(x + 2) + 4
y = -3x - 2
When x = 0, we have:
g(0) = 0 + 2 = 2
f(0) = 0 - 2 = -2.
When x = -2, we have:
g(-2) = -(-2) + 2 = 4
f(-2) = -3(-2) - 2 = 4.
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what is the multiplier for 0.85% and 300% growth?
"The multiplier for 0.85% growth is calculated by adding 1 to the percentage as a decimal:
Multiplier for 0.85% growth = 1 + 0.0085 = 1.0085
The multiplier for 300% growth is calculated in the same way:
Multiplier for 300% growth = 1 + 3.00 = 4.00
Therefore, the multipliers for 0.85% and 300% growth are 1.0085 and 4.00, respectively." (ChatGPT, 2023)
You have 125% of the tickets required for a prize. What fraction of the required tickets do you have? Do you need more tickets for the prize? Explain.
Yοu dο nοt need mοre tickets fοr the prize, as yοu already have mοre than enοugh.
If yοu have 125% οf the tickets required fοr a prize, it means yοu have mοre than the number οf tickets required.
Tο find the fractiοn οf the required tickets that yοu have, yοu can cοnvert 125% tο a fractiοn and simplify 125% = 125/100 = 5/4
Sο, yοu have 5/4 οf the required tickets. Tο find the fractiοn οf the required tickets that yοu have, yοu need tο divide the number οf tickets yοu have by the number οf tickets required:
fractiοn οf required tickets = (number οf tickets yοu have) / (number οf tickets required)
Let's say the number οf tickets required is x. Then, the number οf tickets yοu have is 1.25 times x, οr 5/4 times x:
(number οf tickets yοu have) = 5/4 * x
Sο, the fractiοn οf required tickets that yοu have is:
fractiοn οf required tickets = (5/4 * x) / x = 5/4
This means yοu have 5/4, οr 1.25 times, the required number οf tickets. Therefοre, yοu dο nοt need mοre tickets fοr the prize, as yοu already have mοre than enοugh.
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it is believed that 4% of children have a gene that may be linked to juvenile diabetes. researchers at a firm would like to test new monitoring equipment for diabetes. hoping to have 19 children with the gene for their study, the researchers test 729 newborns for the presence of the gene linked to diabetes. what is the probability that they find enough subjects for their study?
The probability of obtaining sufficient participants for their study is 0.0029.
The probability of researchers at a firm finding enough subjects for their study can be calculated using binomial probability.
What is binomial probability?Binomial probability is a probability distribution that calculates the probability of one event's occurrence in a specified number of experiments or trials that produce either positive or negative outcomes.
The probability that an event will occur in n number of trials or experiments is determined using the following formula:
P(X=a) = ⁿCₐ * p^a * (1-p)^(n-a)
Where ⁿCₐ is the number of combinations of "n" items taken "a" at a time.
"p" is the probability of an event occurring.
"(1-p)" is the probability of an event not occurring.
"n" is the number of experiments, and "a" is the number of successful events.
Let us solve the problem now. We have n = 729 and p = 0.04
We need to find out the probability of finding 19 children with the gene for their study. This means that we need to find out P(X=19)Now, we can calculate it as:
P(X=19) = ⁿCₐ * p^a * (1-p)^(n-a)
Putting the given values, we get:
P(X=19) = ⁷²⁹C₁₉ * (0.04)^19 * (1 - 0.04)^(729 - 19)
≈ 0.0029
Hence, the probability of finding enough subjects for their study is 0.0029.
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Your organization is selling tickets to the school dance.
On the first day, the school sold 10 student tickets and
5 guests tickets for a total of $200. On the second day,
you sold 6 student tickets and 2 guest tickets for a total
of $105. What is the price of each ticket?
The price of each student ticket is $12.50 and the price of each guest ticket is $15.
What is substitution method?The substitution method is a technique in algebra for solving systems of equations, which involves solving one equation for one variable, and then substituting that expression into the other equation.
According to question:Let's start by assigning variables to represent the unknown prices of the student and guest tickets.
Let:
x be the price of a student ticket
y be the price of a guest ticket
Using this information, we can set up two equations based on the given information:
Equation 1: 10x + 5y = 200 (from the first day's sales)
Equation 2: 6x + 2y = 105 (from the second day's sales)
Now we have two equations with two unknowns, which we can solve using algebra. To do this, we can use a method called substitution, which involves solving one equation for one variable, and then substituting that expression into the other equation. Here's how to do it:
Solve Equation 1 for y:
10x + 5y = 200
5y = 200 - 10x
y = (200 - 10x)/5
y = 40 - 2x
Substitute y into Equation 2:
6x + 2y = 105
6x + 2(40 - 2x) = 105
6x + 80 - 4x = 105
2x = 25
x = 12.50
So the price of a student ticket is $12.50.
To find the price of a guest ticket, we can substitute x = 12.50 into Equation 1:
10x + 5y = 200
10(12.50) + 5y = 200
125 + 5y = 200
5y = 75
y = 15
So the price of a guest ticket is $15.
Therefore, the price of each student ticket is $12.50 and the price of each guest ticket is $15.
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The polygons are similar: Find the value of x.
The missing lengths of x of the given similar figures are:
9) x = 18
10) x = 5
How to find the length of similar figures?Similar polygons are polygons that have the same shape, but their sizes may vary. Thus, if two polygons are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
9) From the concept of similar triangles, their ratios of similar sides are equal and as such we have:
x/6 = 6/2
x = 6 * 3
x = 18
10) From the concept of similar triangles, their ratios of similar sides are equal and as such we have:
21/7 = 15/x
3x = 15
x = 5
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Factor equation
4x^6-20x^5+25x^4
Answer:
(14x + y)(14x - y)
Step-by-step explanation:
What is the area of a sector with a central angle of 30° and a radius of 12.5 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
The area of the sector with a central angle of 30 degrees and a radius of 12.5 cm is 40.89 cm².
What is the area of a sector?The area of a sector is expressed as;
A = ( θ/360 ) × π × r²
where θ is the central angle in degrees, r is the radius, and π is approximately 3.14.
Given the data in the question;
Central angle θ = 30 degreesRadius r = 12.5cmConstant pi π = 3.14Area A = ?Substituting the given values, we get:
Area = ( θ/360 ) × π × r²
Area = (30/360) × 3.14 × 12.5²
Area = 40.885 cm²
Area = 40.89 cm²
Therefore, the measure of the area is 40.89 cm².
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Find the median of first 15 odd numbers 
Answer:
15
Step-by-step explanation:
The first 15 odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29
The formula to find the median of a set of numbers is:
Median = [(n + 1) / 2]th term
where n is the total number of terms in the set.
In this case, we have 15 terms in the set of the first 15 odd numbers. So, substituting n = 15 in the formula, we get:
Median = [(15 + 1) / 2]th term
Median = 8th term
To find the 8th term, we can simply list the first 15 odd numbers in ascending order and count 8 numbers from the beginning of the list. The 8th term is 15.
Therefore, using the formula, we get:
Median = 8th term = 15.
So, the median of the first 15 odd numbers is 15.
Based on past experience, a bank believes that 8% of the people who receive loans will not make payments on time. The bank has recently approved 200 loans.(1) (7 points) What's the probability that over 10% of these clients will not make timely payments?(2) (11 pouts) 45% of the timely payments will not be made by under how many percentages of clients?
Thus, 45% of timely payments will not be made by under 100 - (165/200)*100% = 17.5% of clients.
what is binomial distribution?
The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial can result in either a success or a failure.
The distribution is characterized by two parameters: the number of trials n and the probability of success in each trial p. The probability of exactly k successes in n trials can be calculated using the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
(1) To find the probability that over 10% of the clients will not make timely payments, we need to use the binomial distribution. Let X be the number of clients out of 200 who do not make timely payments. Then X has a binomial distribution with parameters n = 200 and p = 0.08. We want to find P(X > 0.1*200) = P(X > 20).
Using the normal approximation to the binomial distribution, we can approximate X with a normal distribution with mean μ = np = 2000.08 = 16 and standard deviation σ = sqrt(np(1-p)) = sqrt(2000.08*0.92) = 3.36.
P(X > 20) can be approximated as P(Z > (20 - 16)/3.36) = P(Z > 1.19), where Z is a standard normal variable. Using a standard normal table or a calculator, we can find that P(Z > 1.19) = 0.1179.
Therefore, the probability that over 10% of the clients will not make timely payments is approximately 0.1179.
(2) Let Y be the number of clients out of 200 who make timely payments. Then Y has a binomial distribution with parameters n = 200 and p = 0.92 (since 8% of clients do not make timely payments, 92% do). We want to find the smallest k such that P(Y < k) > 0.45.
We can use a table of the cumulative binomial distribution or a calculator to find that P(Y < 164) = 0.4443 and P(Y < 165) = 0.4658. Therefore, the smallest k such that P(Y < k) > 0.45 is 165.
Thus, 45% of timely payments will not be made by under 100 - (165/200)*100% = 17.5% of clients.
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The probability that over 10% of these clients will not make timely payments is approximately 0.03.
What exactly is probability?
Probability is a branch of mathematics that deals with the measurement and analysis of uncertainty. It is used to quantify the likelihood or chance of an event occurring, and is expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.
Now,
(1) Let X be the number of clients who will not make timely payments out of 200 loans approved. We are given that the probability of not making timely payments is 8%, or 0.08. Since X follows a binomial distribution with n = 200 and p = 0.08, we can use the normal approximation to the binomial distribution to find the probability that over 10% of these clients will not make timely payments:
First, we need to calculate the mean and standard deviation of X:
mean = n * p = 200 * 0.08 = 16
standard deviation = sqrt(n * p * (1 - p)) = sqrt(200 * 0.08 * 0.92) = 3.19
Now we can use the normal distribution with a continuity correction to find the probability:
P(X > 0.1 * 200) = P(X > 20) = P((X - mean) / standard deviation > (20 - mean) / standard deviation)
= P(Z > 1.88) ≈ 0.03
Therefore, the probability that over 10% of these clients will not make timely payments is approximately 0.03.
(2) Let Y be the number of clients who make timely payments out of 200 loans approved. We are given that 45% of the timely payments will not be made, so the probability of making a timely payment is 1 - 0.45 = 0.55. Since Y also follows a binomial distribution with n = 200 and p = 0.55, we need to find the largest value of k such that the probability of at least k clients making timely payments is at least 0.45.
We can use a cumulative binomial distribution to find the probability:
P(Y ≥ k) = 1 - P(Y < k) = 1 - binom.dist(k - 1, n, p, TRUE)
We can then use trial and error to find the largest value of k such that P(Y ≥ k) ≥ 0.45:
P(Y ≥ 127) ≈ 0.455 > 0.45
P(Y ≥ 128) ≈ 0.426 < 0.45
Therefore, the largest value of k such that the probability of at least k clients making timely payments is at least 0.45 is 127. This means that under 63.5% of clients (127/200) will make timely payments.
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Draw bar (AB) of length 7.3cm and find its axis of symmetry. Draw a line segment of length 9.5cm and construct its perpendicular bise
According to the information, the symmetry axis of the 7.3cm bar would be located at 3.65cm. Additionally, the perpendicular bise of the 9.5cm line would be located in 4.75cm
What is the axis of symmetry?An axis of symmetry is a term that refers to an imaginary reference line that allows any figure to divide in two parts, its opposite points are equidistant to each other, that is, they are symmetrical.
What is the perpendicular Bise?The perpendicular Bise is a term to refer to a straight line perpendicular to a given segment. A characteristic of the perpendicular Bise is that it is located at the midpoint of the segment.
According to the above to find the axis of symmetry and the perpendicular bise we must divide the values into 2 to find its half.
7.3cm / 2 = 3.65cm9.5cm / 2 = 4.75 cmNote: This question is incomplete. Here is the complete information:
Attached image
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three linear funtions are represented below
help me please
Answer: B
Rate of change is the slope which is the [tex]\frac{rise}{run}[/tex]= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
In the first equation, we will substitute x with any two random numbers to get the y value, which gives us two points. The number you take doesn't matter.
y=2, taking x as 2 so the point is (2,2)
y=1, taking x as 1 so the point is (1,1)
m=[tex]\frac{2-1}{2-1}=1[/tex] SO THE SLOPE FOR A IS 1
In the second equation, we can just pick 2 points on the graph that the line runs through. I picked (2,-1) and (0,-4) to make calculations easy
[tex]m=\frac{-4-(-1)}{0-2}\\ =\frac{-3}{2}\\[/tex]OR THE SLOPE IS -1.5
In the thrid equation, we can again just pick points to find the ROC.
[tex]m=\frac{9-6}{5-4} \\ =3[/tex]THE SLOPE IS 3
Now that we have found this out, we can now find out which one has a bigger ROC.
-1.5<1<3=B<A<C
MARK BRAINLIST IF THIS HELPED PLEASE! LOVE YA <3
Henry's banks said they will put 20% interest annually if he keeps at least $5,000 in his savings account. How much money in interest will the bank put Henry's account?
The amount of money that in the interest will the bank put Henry's account is $1000
If Henry keeps at least $5,000 in his savings account, the bank will put a 20% interest on it annually.
To find out how much interest Henry will earn, we can use the formula:
Interest = Principal x Rate
Where the,
Principal is the amount of money , Henry keeps in his savings account, which is $5,000 or more.
Rate is the interest rate, which is 20% or 0.20 in decimal form.
So, the interest Henry will earn is:
Interest = $5,000 x 0.20
Interest = $1,000
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help me please I need help
Answer:
6cm
Step-by-step explanation:
The volume of the cylinder = π · r² · h
r = 4
h = ?
Let's solve
96π = π · 16 · h
96 = 16 · h
h = 6cm
So, the height is 6cm
What is in the third quadrant of the unit circle
The third quadrant of the unit circle is the region of the circle that lies between 180 degrees and 270 degrees
The unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane.
In the coordinate plane, the third quadrant is the quadrant that lies below the x-axis and to the left of the y-axis.
To find what is in the third quadrant of the unit circle, we need to look for the points on the circle that have negative x-coordinates and negative y-coordinates.
Since the radius of the unit circle is 1, we know that any point on the circle can be represented in terms of sine and cosine. Specifically, for any point (x, y) on the circle, we have:
x = cos(θ)
y = sin(θ)
where θ is the angle between the positive x-axis and the line connecting the origin and the point (x, y).
In the third quadrant, both the x-coordinate and the y-coordinate are negative. Therefore, we need to find the angle θ such that cos(θ) is negative and sin(θ) is negative.
We know that cos(θ) is negative in the second and third quadrants, and sin(θ) is negative in the third and fourth quadrants. Therefore, the third quadrant of the unit circle contains the points where:
cos(θ) is negative (i.e., θ is between 90 and 270 degrees or π/2 and 3π/2 radians), and
sin(θ) is negative (i.e., θ is between 180 and 360 degrees or π and 2π radians).
So the third quadrant of the unit circle contains all the points where:
-1 ≤ x ≤ 0 (cosine is negative in this quadrant), and
-1 ≤ y ≤ 0 (sine is also negative in this quadrant).
In other words, the third quadrant of the unit circle is the region of the circle that lies between 180 degrees and 270 degrees (or π and 3π/2 radians) and has both x and y values that are negative.
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If I simplify the expression completely for 15 + 8(2y - 9) what do I get?
Answer:
Step-by-step explanation:
16y-57
giving brainly Which equation would you use to find the distance between the two points? A. |2 - 4| B. |2 - (-4)| C. |-5 - 5| D. |2 + (-4)|
The equation we would use to find the distance between the two points is d = √((x2 - x1)² + (y2 - y1)²) = √((2 - (-4))² + (y2 - y1)²) = √(6² + (y2 - y1)²) = √36 + (y2 - y1)²)
To find the distance between two points on a number line or in a coordinate plane, we use the distance formula. The distance formula is given by:
d = √((x2 - x1)² + (y2 - y1)²)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
None of the options provided represents the distance formula in its entirety. However, we can use option B as the first part of the distance formula, since it represents the absolute value of the difference between the x-coordinates of the two points:
|2 - (-4)|
Simplifying this expression gives:
|2 + 4|
|6|
Therefore, the equation we would use to find the distance between the two points is:
d = √((x2 - x1)² + (y2 - y1)²) = √((2 - (-4))² + (y2 - y1)²) = √(6² + (y2 - y1)²) = √36 + (y2 - y1)²)
We still need to determine the y-coordinates of the two points in order to complete the distance formula.
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