This means that in order for the profits in 2022 to match those in 2020, the profits in 2021 would also need to match those in 2020.
[tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.
What does “mean profit” mean?Profits for mesne. According to Section 2(12) C.P.C., the term “mesne profit” refers to any earnings that the person who is in wrongful possession of a piece of property has actually received or may obtain in the future. High Court of Telangana.
The earnings in 2022 must match the profits in 2020, hence we must choose the value of r such that:
[tex]P \times(1-r/100)^² = P[/tex]
By simplifying and dividing both sides by P, we obtain:
[tex](1-r/100)^² = 1[/tex]
Taking the square root of both sides, we get:
1-r/100 = ±1
Each time we solve for r, we obtain:
[tex]1-r/100 = 1[/tex] , which implies [tex]r = 0[/tex]
and
[tex]1-r/100 = -1,[/tex] which implies [tex]r = 200[/tex]
We reject the [tex]r = 200[/tex] Option because a percentage drop cannot be larger than 100%.
Therefore, [tex]r = 0[/tex] % is the percentage drop in earnings from 2021 to 2022 that would indicate that profits were equal in both 2020 and 2022.
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Rumiya is a saleswoman who receives a base salary of 85000. On top of her base salary, she receives a 10% commission on x dollars of sales she makes for the year. If she aspires 100000 to make over this year, then what minimum amount of sales, , would she need to make?
mx+b>100000
m= b=
Rumiya's total earnings can be represented by the inequality: [tex]85000 + 0.1x > 100000[/tex] and she would need to make sales of at least $150,000 to earn over $100,000 for the year.
What do you mean by commission and inequality ?
A commission is a percentage of sales that a salesperson earns on top of their base salary. In this case, Rumiya earns a 10% commission on sales she makes for the year. An inequality is a statement that compares two values, indicating whether one is greater than, less than, or equal to the other. It is used to represent that Rumiya needs to make sales that exceed a certain amount in order to earn a desired amount.
Finding the minimum amount of sales :
Rumiya's total earnings for the year will be the sum of her base salary and commission on sales. We can represent this as an inequality:
[tex]85000 + 0.1x > 100000[/tex]
To solve for [tex]x[/tex], we first need to isolate the variable on one side of the inequality. We can do this by subtracting 85000 from both sides:
[tex]0.1x > 15000[/tex]
Next, we can solve for [tex]x[/tex] by dividing both sides by 0.1:
[tex]x > 150000[/tex]
Therefore, Rumiya would need to make sales of at least $150,000 to earn over $100,000 for the year. This means that her commission on these sales would be $15,000 (10% of $150,000).
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tapas and paella that originated in what country
Find the absolute maximum and minimum values of the function f(x,y) = x^2+y^2-2x
The function f(x,y) has only minimum value at (1,0) is -1 and maximum value does not exist.
The given function is f(x,y)=x²+y²-2x
First find the partial derivative with respect to x and y
f'(x)=2x-2
f'(y)=2y
f'(x)=0=f'(y)
2x-2=0
x=1
and y=0
Now we will cheak maxima and minima at (1,0)
f''(x,y)=2 and f"(x,y)=2 and f"(x,y)=0( derivative of first order of x with respect to y)
We know that
rt-s²≥0 and r positive then f is minimum and r negative maximum
r=2 , t=2 and s=0
rt-s²≥0 and r is positive so f(x,y) is minimum at (1,0)
f(1,0)=1-2=-1
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A doctor collects data on all the men in his practice. They have an average age of 45 years, with a standard deviation of 15 years. They have an average systolic blood pressure of 150 mmHg, with a standard deviation of 10 mmHg. The two variables have correlation r=0.7.
a) Using regression, calculate the predicted systolic blood pressure for a man in the practice who is i) 30 years old ii) 45 years old iii) 50 years old
b) The above predictions all are subject to error. The average size of such errors is about ___ mmHg, and 95% of the predictions we make using regression will be correct to within about ___ mmHg.
c) A man is selected at random from the practice. He is 60 years old, which means that he is ___ SD(s) above the average age of men in the practice. Another way of expressing his relative age is that he is at the ___ percentile of age among all men in the practice.
d) Using regression, we can predict the man from part (c) will have a blood pressure that is ___ SD(s) above average. Therefore, he is predicted to be at the ___ percentile of blood pressure.
(A) This means that the systolic blood pressure 100 is less than average blood pressure and 150is higher than the average blood pressure.
(B) The average size of such errors is about 125 mmHg, and 95% of the predictions we make using regression will be correct to within about 90 mmHg.
(C) He is 60 years old, which means that he is 1.7857 SD(s) above the average age of men in the practice.
(D) The percentile corresponding to -0.6 as27.43. this means that 27.43% of people with blood pressure reading above 125.
(A) We have to find the z statistics of systolic blood pressure 100 and 150.
We have:
z₁₀₀ = 100 -125/14
= -1.7857
And, Z₁₅₀ = 150-125/14
= 1.7857
So, the systolic blood pressure 100 is -1.7857 standard deviation to the left of the mean 125.
And, the systolic blood pressure 150 is 1.7857 standard deviation to the left of the mean 125.
This means that the systolic blood pressure 100 is less than average blood pressure and 150is higher than the average blood pressure.
(B) The above predictions all are subject to error. The average size of such errors is about 125 mmHg, and 95% of the predictions we make using regression will be correct to within about 90 mmHg.
-2.5 = x -125/14
⇒ x = -2.5 × 14 +125
⇒ x = 90.
(C) A man is selected at random from the practice. He is 60 years old, which means that he is 1.7857 SD(s) above the average age of men in the practice. Another way of expressing his relative age is that he is at the 96% percentile of age among all men in the practice.
(D) The z score is: z = 0.6
The percentile corresponding to -0.6 as27.43. this means that 27.43% of people with blood pressure reading above 125.
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francesca bought 27 keychains of two different kinds to make goodie bags for her birthday party. leather keychains were three dollars and beaded keychains for two dollars. she spent $73. how many keychains of each kind did she buy
Answer: Supergirl = 19 and Wonder Woman = 8
Step-by-step explanation:
Let g represent the quantity of Supergirl keychains and w represent the quantity of Wonder Woman keychains.
Qty Cost
Supergirl g $3g
Wonder Woman w $2w
Total 27 $73
Qty: g + w = 27 → -2(g + w = 27) → -2g - 2w = -54
Cost: 3g + 2w = 73 → 1(3g + 2w = 73) → 3g + 2w = 73
g = 19
Input g = 19 into one of the original equations to solve for w:
g + w = 27
(19) + w = 27
w = 8
3. Factor 72x³ +72x² +18x.
The expression's fully factored form is:[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]
Factored value is what?Factored Value, also known as "trended value," is the base annual value plus a yearly inflation factor based on a variation in the cost if live that is not to exceed 2% and is set by the State Agency of Equalization.
What is a factored expression example?Rewriting an expression as the sum of factors is referred to as factor expressions or factoring. For instance, 3x + 12y may be expressed as 3 (x + 4y), which is a straightforward equation. The computations get simpler in this method. Three or (x + 4y) were examples of factors.
We can factor out [tex]18x[/tex] from each term to simplify the expression:
[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{3} + 4x^{2} + 1)[/tex]
An expression enclosed in parentheses can now be calculated by grouping or factoring.
[tex]4x^{3} + 4x^{2} + 1 = (4x^{2} + 1)(x + 1)[/tex]
The expression's properly factored version has the following result,
[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]
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HELP ME ASAP PLEASE!!!!!!!!!
Answer:
See step by step.
Step-by-step explanation:
lets define the events:
A: cuban festival C: tropical Garden
B: street art show D: african festival
a) theoretically the probability is
[tex]P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\[/tex]
This is 25% (for each one, equally)
b) The experimental probability is given by:
[tex]P(A)= \frac{32}{150} =0.2133[/tex]
[tex]P(B)= \frac{38}{150} =0.2533[/tex]
[tex]P(C)= \frac{35}{150} =0.2333[/tex]
[tex]P(D)= \frac{45}{150} =0.3000[/tex]
c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.
(a) What is the expanded form of (a + b) 2? (b) The length of a rectangular mat is 3x-y meter and its breadth is 3-*meter. Find the area of the mat.
Answer: 9x - 3x* - 3y + y* square meters
Step-by-step explanation:
(a) The expanded form of (a + b) 2 is:
(a + b) 2 = a2 + 2ab + b2
(b) The area of the rectangular mat is:
Area = Length × Breadth
Given that the length is 3x - y meters and the breadth is 3 - * meters.
So, the area of the rectangular mat can be calculated as:
Area = (3x - y) × (3 - *)
= 9x - 3x* - 3y + y*
Therefore, the area of the rectangular mat is 9x - 3x* - 3y + y* square meters.
Answer:
Step-by-step explanation:
A brand new stock is called an initial public offering or IPO. Remember that in this model the period immediately after the stock is issued offers excess returns on the stock(ie it is selling for more than its actually worth). One such model for a class of internet IPOS predicts the percentage overvaluation of a stock as a function of time, as R(t)=2501^2/e^3t where R(t) is the overvaluation in percent and t is the time in months after issue. Use the information provided by the first derivative and second derivate, and asymptotes to prepare advice for clients as to when they should expect a signal to buy or sell (Inflection point), the exact time when they should buy or sell(max/min) and any false signals prior to an as- ymptote. Explain your reasoning. Make a rough sketch of the function.
The Function of maximum or minimum for t is infinity.
What is first and second subsidiary test?While the principal subordinate can let us know if the capability is expanding or diminishing, the subsequent subsidiary. tells us in the event that the primary subsidiary is expanding or diminishing. On the off chance that the subsequent subsidiary is positive, the first.
To analyze the function R(t) = 2501² / e(3t), we can take the first and second derivatives:
R'(t) = -7503 * 2501² / e(3t)
R''(t) = 22509 * 2501² / e(3t)
To find the inflection point, we can set R''(t) = 0 and solve for t:
22509 * 2501² / e(3t) = 0
t = ln(0) / -3 = undefined
Since there is no real solution to this equation, there is no inflection point for this function.
To find the maximum or minimum, we can set R'(t) = 0 and solve for t:
-7503 * 2501² / e(3t) = 0
t = infinity
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Please help! Need answers as soon as possible!
1. Time taken to fill one community pool is 2hours 24 minutes.
2. Time taken to audit 30 files is 4 hours 41 minutes.
3. The time taken to erect is 54/7 hours or 7 hours 43 minutes
Define the time and work?Time and work is a branch of mathematics that deals with the calculation of the amount of time required to complete a job or task by a worker or a group of workers working at a certain rate.
1. Job: Fill one community pool Rate Time Work Completed
Reserve water tower 1/6 x x/6
City water pipes 1/4 x x/4
Solution: Fill one community pool; [tex]\frac{x}{6} + \frac{x}{4} = 1[/tex]
Simplify, x = 12/5 hours or 2hours 24 minutes
Time taken to fill one community pool is 2hours 24 minutes.
2. Job: Work together Rate Time Work Completed
Mr. Dupree 12/5 x 12x/5
Ms. Carmichael 16/4 x 16x/4
Solution: If they work together, time taken to audit one file is
[tex]\frac{12x}{5} + \frac{16x}{4} = 1[/tex]
Simplify, x = 5/32 hours
So, time taken to audit 30 file, (5/32)×30 = 75/16 hours or 4 hours 41 minutes
Time taken to audit 30 files is 4 hours 41 minutes.
3. Job: Work together Rate Time Work Completed
Macon Construction 100/8 x 100x/8
Thomson Masonry 200/12 x 200x/12
Solution: If they work together, time taken to complete a work
[tex]\frac{100x}{8} + \frac{200x}{12} = 1[/tex]
Simplify, x = 6/175
Macon Construction 2 hours before so,
remaining work = 250 - (100×2hour/8) = 225 feet
then, the time taken to erect 225 feet rock facing by together is
6/175 × 225 = 54/7 hours or 7 hours 43 minutes
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1. Time taken to fill one community pool is 2hours 24 minutes. 2. Time taken to audit 30 files is 4 hours 41 minutes. and 3. The time taken to erect is 54/7 hours or 7 hours 43 minutes.
Define the audit?An audit is an independent review of financial statements and related documents in order to confirm their accuracy and compliance with relevant regulations.
1. Job: Fill one community pool Rate Time Work Completed
Reserve water tower 1/6 x x/6
City water pipes 1/4 x x/4
Solution: Fill one community pool;
Simplify, x = 12/5 hours or 2hours 24 minutes
Time taken to fill one community pool is 2hours 24 minutes.
2. Job: Work together Rate Time Work Completed
Mr. Dupree 12/5 x 12x/5
Ms. Carmichael 16/4 x 16x/4
Solution: If they work together, time taken to audit one file is
Simplify, x = 5/32 hours
So, time taken to audit 30 file, (5/32)×30 = 75/16 hours or 4 hours 41 minutes
Time taken to audit 30 files is 4 hours 41 minutes.
3. Job: Work together Rate Time Work Completed
Macon Construction 100/8 x 100x/8
Thomson Masonry 200/12 x 200x/12
Solution: If they work together, time taken to complete a work
Simplify, x = 6/175
Macon Construction 2 hours before so,
remaining work = 250 - (100×2hour/8) = 225 feet
then, the time taken to erect 225 feet rock facing by together is
6/175 × 225 = 54/7 hours or 7 hours 43 minutes
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PLease soemone help me you would make my life and day just answer true or false. I will give you 20 points just please answer the question with a true or false.
Answer: first 4 are false last one is true
Step-by-step explanation:
HEEELLLLPPPPP MEEEEEEEEE
1. Solve.
a. 2/5t = 6
b. -4.5 = a-8
c. 1/2+p=-3
d. 1/2 = x3
e. -12 = -3y
The equation is saying that -12 is equal to -3 multiplied by y. To solve for y, divide both sides by -3. This would give an answer of 4.
What is equation?An equation is a mathematical statement that expresses the equality or inequality of two values or expressions. It consists of two expressions connected by an equals sign, inequality sign or other relational operator. Equations can involve numbers, variables, and operations such as addition, subtraction, multiplication, division and exponentiation. An equation can be used to solve problems related to mathematics, science, engineering, finance, and many other disciplines. Equations can also be used to model and describe real-world phenomena.
t = 30
a = 12.5
p = -5.5
x = 2/3
y = 4.
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a. t = 30/2; To solve this equation, divide both sides by 2/5. The resulting equation is t = 30/2.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions by using an equals sign (=). It states that the two expressions on either side of the equals sign are equal in value. An equation is an example of a mathematical problem, which can be used to solve real-world problems.
b. a = 4.5; To solve this equation, add 8 to both sides. The resulting equation is a = 4.5.
c. p = -7/2; To solve this equation, add 3 to both sides. The resulting equation is p = -7/2.
d. x = 2; To solve this equation, divide both sides by 3. The resulting equation is x = 2.
e. y = 4; To solve this equation, divide both sides by -3. The resulting equation is y = 4.
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The absolute value function, shifted to the left 2 units.
This is the absolute value function shifted to the left 2 units:
| x+2 | = {
x+2 if x >= -2,
-(x+2) if x < -2
}
What is function?In mathematics, a function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is a rule or a set of rules that assigns each input value exactly one output value. Functions can be represented using equations, graphs, or tables. They are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and finance.
Here,
The absolute value function is defined as:
| x | = {
x if x >= 0,
-x if x < 0
}
To shift the function to the left 2 units, we can replace x with (x+2):
| x+2 | = {
x+2 if x+2 >= 0,
-(x+2) if x+2 < 0
}
Simplifying further, we get:
| x+2 | = {
x+2 if x >= -2,
-(x+2) if x < -2
}
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Complete question:
The absolute value function is defined as:
| x | = {
x if x >= 0,
-x if x < 0
}
Find the function when shifted to the left 2 units.
Find the missing side lengths. Leave your answers as radicals in simplest form.
Answer:
Step-by-step explanation:
Team A scored twice as many points as Team B. If the total number of points scored by both teams was 12, find the number of points scored by each team.
Answer:
Step-by-step explanation:
Let x be the number of points scored by Team B.
Then, Team A scored twice as many points, or 2x.
The total number of points scored by both teams is 12, so we can set up the equation:
x + 2x = 12
Combining like terms, we get:
3x = 12
Dividing both sides by 3, we get:
x = 4
So Team B scored 4 points, and Team A scored twice as many, or 8 points.
After y - 4x = 12 is put in slope-intercept form, what is the slope?
-4
-1/4
-3
4
Ms. Do Bee, the 8th grade mathematics teacher gives exams that are 20 multiple choice questions. Each question has for possible answers. Ms. Do Bee has a standing offer. if you get every question wrong, your grade on the exam is A.
a) supposed (especially having done no studying) you simply guess I each question. Find the probability you get none correct. Explain where this probability comes from.
b) does Ms. Do Bee’s offer make sense? Why or why not? explain.
In response to the stated question, we may state that As a result, the probability of correctly answering none of the 20 questions is roughly 0.0000262, or 0.00262%.
What is probability?Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.
The likelihood of getting any one question accurate is 1/4 if you merely guess on each question. The binomial distribution formula may be used to calculate the chance of correctly answering none of the 20 questions:
P(X=0) = (n choose X) * pX * (1-p) (n-X)
[tex]If n=20, X=0, and p= 1/4\\P(X=0) = (20 pick 0) (20 choose 0) * (1/4)^0 * (3/4)^20\\P(X=0) = 1 * 1 * 0.0000262\\P(X=0) = 0.0000262[/tex]
As a result, the probability of correctly answering none of the 20 questions is roughly 0.0000262, or 0.00262%.
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What is the equation of the line graphed?
Answer:
The simplest possible equation for the line on the graph would be x = - 2
Decide if the function is an exponential growth function or exponential decay function, and describe its end behavior using
limits.
Y=(1/6) ^-x
Answer:
The given function is an exponential growth function, not an exponential decay function because as the exponent x increases, the value of y also increases instead of decreasing.
To describe its end behavior using limits, we need to find the limit of the function as x approaches infinity and as x approaches negative infinity.
As x approaches infinity, the exponent -x approaches negative infinity, and the base (1/6) is raised to increasingly larger negative powers, causing the function to approach zero. So, the limit as x approaches infinity is 0.
As x approaches negative infinity, the exponent -x approaches infinity, and the base (1/6) is raised to increasingly larger positive powers, causing the function to approach infinity. So, the limit as x approaches negative infinity is infinity.
Therefore, the end behavior of the function is that it approaches zero as x approaches infinity and approaches infinity as x approaches negative infinity.
Determine the values of A, B, and C when y - 7 = 3(x - 4) is written in standard form, Ax + By = C.
Answer:
To convert the equation y - 7 = 3(x - 4) to standard form Ax + By = C, we need to rearrange it so that it has the form Ax + By = C, where A, B, and C are constants.
y - 7 = 3(x - 4)
y - 7 = 3x - 12 (distribute the 3)
3x - y = 7 - 12 (move y to the left-hand side)
3x - y = -5
Now we have the equation in standard form, where:
A = 3
B = -1
C = -5
Therefore, the values of A, B, and C are 3, -1, and -5, respectively.
FILL IN THE BLANK Suppose you look by eye at a star near the edge of a dusty interstellar cloud. The star will look ______ than it would if it were outside the cloud.
Suppose you look by eye at a star near the edge of a dusty interstellar cloud. The star will look dimmer than it would if it were outside the cloud.
Interstellar clouds are vast, dense regions of dust and gas that exist between stars. These clouds contain tiny solid particles of dust, which scatter and absorb light as it passes through them.
When we observe a star that is located near the edge of an interstellar cloud, the light from that star has to pass through a greater amount of dust before it reaches our eyes or telescopes. The dust scatters and absorbs some of the light, causing the star to appear dimmer than it would if it were outside the cloud.
This effect is similar to how the sun appears dimmer when it is viewed through a thick layer of clouds or fog. In both cases, the amount of light that reaches us is reduced due to the presence of a barrier that scatters and absorbs some of the light.
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Synthetic Division to Find Zeros
if f(x)=x^3−3x^2+16x+20 and x+1 is a factor of f(x), then find all of the zeros of f(x) algebraically.
Answer:
Step-by-step explanation:
Since we know that x + 1 is a factor of f(x), we can use synthetic division to find the other factor and then solve for the remaining zeros.
We set up synthetic division as follows:
-1 | 1 -3 16 20
| -1 4 -20
|_____________
1 -4 20 0
The last row of the synthetic division gives us the coefficients of the quadratic factor, which is x^2 - 4x + 20. We can use the quadratic formula to find its roots:
x = (-(-4) ± sqrt((-4)^2 - 4(1)(20))) / (2(1))
= (4 ± sqrt(-64)) / 2
= 2 ± 2i√2
Therefore, the three zeros of f(x) are -1, 2 + 2i√2, and 2 - 2i√2.
Rewrite without absolute value for the given condition: y=|x−3|+|x+2|−|x−5|, if 3 < x < 5
When 3 < x < 5, y can be expressed as y = 3x - 6 without absolute value notation.
What is absolute value notation ?
Absolute value notation is a mathematical notation used to represent the magnitude or distance of a real number from zero. It is denoted by vertical bars or pipes around the number. For example, the absolute value of x is written as |x|.
When 3 < x < 5, the expression |x-3| evaluates to x-3, the expression |x+2| evaluates to x+2, and the expression |x-5| evaluates to 5-x. Therefore, we can rewrite the expression y = |x-3| + |x+2| - |x-5| as:
y = (x-3) + (x+2) - (5-x)
Simplifying this expression, we get:
y = 3x - 6
Therefore, when 3 < x < 5, y can be expressed as y = 3x - 6 without absolute value notation.
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Consider the function f (x) = -2/3x + 5.
What is f(-1/2)?
Enter your answer, as a simplified fraction, in the box.
f(-1/2) =
Answer: f(-1/2) = 16/3
Step-by-step explanation:
Substituting -1/2 for x in the given function:
f(-1/2) = (-2/3)(-1/2) + 5
f(-1/2) = 1/3 + 5
f(-1/2) = 16/3
Therefore, f(-1/2) = 16/3.
find average speed that was traveled from city a to city p if trip took a half an hour to travel 23 miles
Step-by-step explanation:
Speed = distance / time
you are given distance = 23 miles and time = .5 hr
distance / time = 23 miles / .5 hr = 46 mph
Linda deposits $50,000 into an account that pays 6% interest per year, compounded annually. Bob deposits $50,000 into an account that also pays 6% per year. But it is simple interest. Find the interest Linda and Bob earn during each of the first three years. Then decide who earns more interest for each year. Assume there are no withdrawals and no additional deposits. Year First Second Third Interest Linda earns (Interest compounded annually) Interest Bob earns (Simple interest) Who earns more interest? Linda earns more. Bob earns more. They earn the same amount. Linda earns more. Bob earns more. They earn the same amount. Linda earns more. Bob earns more. They earn the same amount.
Answer:
Step-by-step explanation:
To calculate the interest earned by Linda for the first year, we can use the formula:
A = P(1 + r/n)^(nt)
Where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
For the first year, we have:
A = $50,000(1 + 0.06/1)^(1*1) = $53,000
So, the interest earned by Linda for the first year is:
Interest = $53,000 - $50,000 = $3,000
For the second year, we can use the same formula with t = 2:
A = $50,000(1 + 0.06/1)^(1*2) = $56,180
Interest = $56,180 - $53,000 = $3,180
For the third year, we can use the same formula with t = 3:
A = $50,000(1 + 0.06/1)^(1*3) = $59,468.80
Interest = $59,468.80 - $56,180 = $3,288.80
Now, to calculate the interest earned by Bob for each of the first three years, we can use the formula:
Interest = Prt
Where P is the principal amount, r is the annual interest rate, and t is the time in years.
For the first year, we have:
Interest = $50,0000.061 = $3,000
For the second year, we have:
Interest = $50,0000.061 = $3,000
For the third year, we have:
Interest = $50,0000.061 = $3,000
As we can see, Linda earns more interest than Bob for each year, as her interest is compounded annually, while Bob's interest is simple interest. Therefore, the answer is:
Linda earns more.
Answer:
Linda earns $9550.8 interest and bob earns $9000 interest
Step-by-step explanation:
Linda takes compound interest: C.I. = Principal (1 + Rate)Time − Principal
interest= 50,000(1+6/100)³
=59550.8 - 50000
Linda earns $9550.8 interest in 3 years.
bob takes simple interest: S.I = prt/100
interest = 50,000*6*3/100
Bob earns $9000 in 3 years.
thus, Linda earns more interest than bob.
Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Round your final answer to three decimal places. Intermediate calculations should be rounded to a minimum of four places. n = 15, p = 0.4 a. Find P(2). Round to three decimal places. b. Find P(2 or fewer). Round to the three places.
a. The value of P(2) is 0.022
b. The value of P(2 or fewer) is 0.027
From the question; n = 15, p = 0.4
a. We have to determine P(2).
P(X = x) = ⁿCₓ·Pˣ·(1 - P)ⁿ⁻ˣ
P(X = 2) = ¹⁵C₂·(0.4)²·(1 - 0.4)¹⁵⁻²
We can write ⁿCₓ = [tex]\frac{n!}{x!(n - x)!}[/tex]
P(X = 2) = [tex]\frac{15!}{2!(15 - 2)!}[/tex] · (0.16) · (0.6)¹³
P(X = 2) = [tex]\frac{15\times14\times13!}{2\times1\times13!}[/tex] · (0.16) · (0.6)¹³
P(X = 2) = (15 × 7) · (0.16) · (0.6)¹³
After simplification
P(X = 2) = 0.022(approx)
b. We have to determine P(2 or fewer).
P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)
P(x ≤ 2) = ¹⁵C₀·(0.4)⁰·(1 - 0.4)¹⁵⁻⁰ + ¹⁵C₁·(0.4)¹·(1 - 0.4)¹⁵⁻¹ + ¹⁵C₂·(0.4)²·(1 - 0.4)¹⁵⁻²
After simplification like above
P(x ≤ 2) = 0 + 0.005 + 0.022
P(x ≤ 2) = 0.027
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she works a 35
-hour week earning $17.10
an hour.
How much does she earn in one year? (Use 52
weeks in one year.)
$
Answer:
$31122.00
Step-by-step explanation:
We know
She works 35 hours a week, earning $17.10 an hour.
17.10 x 35 = $598.50 a week
How much does she earn in one year?
We Take
598.50 x 52 = $31122.00
So, she earns $31122.00 one year.
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An 800 seat multiplex cinema is divided into 3 theatres. There are 270 seats in
Theatre 1, and there are 150 more seats in Theatre 2 than in Theatre 3. How many
seats are in Theatre 2?
Answer:
340 seats in Theatre 2
Step-by-step explanation:
let n be the number of seats in Theatre 3 then the number of seats in theatre 2 is n + 150
summing and equating gives
27 0 + n + 150 + n = 800
420 + 2n = 800 ( subtract 420 from both sides )
2n = 380 ( divide both sides by 2 )
n = 190
then
number of seats in Theatre 2 = n + 150 = 190 + 150 = 340
Answer:
Theatre 3 has 190 seats, and Theatre 2 has 190 + 150 = 340 seats.
Step-by-step explanation:
Let x be the number of seats in Theatre 3.
Then the number of seats in Theatre 2 is x + 150.
And the total number of seats in the multiplex is 270 + x + (x + 150) = 800.
Simplifying the equation, we get
2x + 420 = 800
2x = 380
x = 190
Therefore, Theatre 3 has 190 seats, and Theatre 2 has 190 + 150 = 340 seats.
A random sample of 14
deer mice in a rich forest habitat gives an average body length of ¯=91.1
mm.
The standard deviation for the given mean length x is found to be: 2.138.
Explain about the standard deviation ?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Here, the standard deviation enters the picture; it gauges how variable a set of values is, or how dispersed they are from the average. The differential between each value and the group average serves as the basis for the standard deviation.
Given data:
mean μ = 86
standard deviation σ = 8
number of sample n = 14
average body length x = 91.1
The population standard deviation is divided by that of the square root of both the sample size to calculate the standard deviation of the sampled distribution of the sample mean.
So,
σₓ = σ / √n
σₓ = 8 / √14
σₓ = 2.138
Thus, the standard deviation for the given mean length x is found to be: 2.138.
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The complete question is-
Deer mice (Peromyscus manicul.atus) are small rodents native of North America. Their adult body lengths (excluding tail) are known to vary approximately Normally, with mean 86 mm and standard deviation 8 mm. Deer mice are found in diverse habitats and exhibit different adaptations to their environment. A random sample of 14 deer mice in a rich forest habitat gives an average body length of x = 91.1 mm. Assume that the standard deviation σ of all deer mice in this area is also 8 mm.
What is the standard deviation of the mean length x?