Answer:
19 small room and 25 big room
Step-by-step explanation:
Solve the problem by finding x. I don’t know how to? Do you.
Answer:
x = e^3 +7
Step-by-step explanation:
ln ( x-7) = 3
To solve for x, raise each side to base e
e ^ ( ln ( x-7) ^= e^3
x-7 = e^3
Add 7 to each side
x-7+7 = e^3 +7
x = e^3 +7
consider the initial value problem find the eigenvalue , an eigenvector , and a generalized eigenvector for the coefficient matrix of this linear system. -4 , 1 0 , c 0 find the most general real-valued solution to the linear system of differential equations. use as the independent variable in your answers.
The eigenvalue for this coefficient matrix is c, the eigenvector is (1, 0) and the generalized eigenvector is (1, -4).The most general real-valued solution to the linear system of differential equations is given by:y(x) = c1e^(-4x) + c2xe^(-4x),
To find the eigenvalue, we need to solve the characteristic equation of the coefficient matrix, which is given by det(A - cI) = 0. In this case, the characteristic equation is -c^2 + 4c = 0, which has a single solution of c = 4. Thus, the eigenvalue is c = 4.
To find the eigenvector, we need to solve the linear system (A - cI)v = 0. For this coefficient matrix, the linear system is (A - 4I)v = 0, which has the solution v = (1, 0). Thus, the eigenvector is (1, 0).
To find the generalized eigenvector, we need to solve the linear system (A - cI)w = v, where v is the eigenvector. In this case, the linear system is (A - 4I)w = (1, 0), which has the solution w = (1, -4). Thus, the generalized eigenvector is (1, -4).
Finally, the most general real-valued solution to the linear system of differential equations is given by y(x) = c1e^(-4x) + c2xe^(-4x), where c1 and c2 are arbitrary constants.
Characteristic equation: det(A - cI) = 0
-c2 + 4c = 0
c = 4
Eigenvector: (A - 4I)v = 0
v = (1, 0)
Generalized eigenvector: (A - 4I)w = v
w = (1, -4)
Most general solution: y(x) = c1e^(-4x) + c2xe^(-4x), where c1 and c2 are arbitrary constants.
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43. Ford Davis borrowed $14,000 of a non-interest-bearing, simple discount, 8% , 90-day note. Assume ordinary interest. What are Ford's proceeds?
A. $14,000
B. $13,720
C. $13,000
D. $17,320
Answer: B. $13,720
Step-by-step explanation: To calculate Ford's proceeds, we need to first find the discount, which is equal to the interest on the loan multiplied by the principal amount of the loan. The interest is 8% of $14,000, or $1,120. The discount is then $1,120 * 90/360, or $310. The proceeds are equal to the principal amount minus the discount, or $14,000 - $310 = $13,720.
Use the given conditions to find the values of all six trigonometric functions. (If an answer is undefined, enter UNDEFINED.) sec(x) = − 9/5, tan(x) < 0
sin(x)=
cos(x)=
tan(x)=
csc(x)=
sec(x)=
cot(x)=
Answer:
Step-by-step explanation
sec x = -9/5.
cos x = 1/ secx
So, here
cos x = 1 / -9/5
= -5/9
sin x = √(1 - cos^2 x)
= √(1 - 25/81)
= √(56/81)
= √56/9
tan x = sinx / cos x
= √56/9 / -5/9
= -√56/5
cosec x = 1 / sin x
= 1 / √56/9
= 9/√56.
cot x = 1/tanx
= 1/-√56/5
= -5/√56
Consider n independent flips of a coin having probability p of landing on heads. Say that a changeover occurs whenever an outcome differs from the one preceding it. For instance, if n=5 and the outcome is HHTHT, then there are 3 changeovers. Find the expected number of changeovers. Hint: Express the number of changeovers as the sum of n-1 Bernoulli random variables.
The expected number of transitions is 22p(1-p) when take into account n separate coin flips with a p percent chance of landing on heads.
Given that,
Take into account n separate coin flips with a p percent chance of landing on heads. Say a changeover happens any time an outcome diverges from the one that came before it. For instance, there are 3 changeovers if n=5 and the result is HHTHT.
We have to determine the anticipated number of transitions.
We know that,
Independent flips,
n =12
Probability of heads =p
Probability of tails =(1-p)
Let m=1,2,...n
If mth term may be head then (m+1)th outcome could be head or vice-versa.
Probability of change overs from mth to (m+1)th outcome =2p(1-p)
So, the expected changeovers is given by
E[change overs] = (n-1) *2p(1-p)
= (12-1) × 2p(1-p)
=11 × 2p(1-p)
=22p(1-p)
Therefore, the expected number of transitions is 22p(1-p) when take into account n separate coin flips with a p percent chance of landing on heads.
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A market receives the following sell orders. How are they ranked? That is, in whatorder will they be executed (1=first, 2=second, …, 5=last)
The sell order with the fifth lowest price (lowest bid) will be ranked fifth and will be executed last. In this case, the sell order with a price of $14 and a quantity of 10 will be executed last.
1. $10 - 20
2. $11 - 30
3. $12 - 50
4. $13 - 40
5. $14 - 10
1. The sell order with the lowest price (highest bid) is ranked first and will be executed first. In this case, the sell order with a price of $10 and a quantity of 20 will be executed first.
2. The sell order with the second lowest price (second highest bid) will be ranked second and will be executed second. In this case, the sell order with a price of $11 and a quantity of 30 will be executed second.
3. The sell order with the third lowest price (third highest bid) will be ranked third and will be executed third. In this case, the sell order with a price of $12 and a quantity of 50 will be executed third.
4. The sell order with the fourth lowest price (fourth highest bid) will be ranked fourth and will be executed fourth. In this case, the sell order with a price of $13 and a quantity of 40 will be executed fourth.
5. The sell order with the fifth lowest price (lowest bid) will be ranked fifth and will be executed last. In this case, the sell order with a price of $14 and a quantity of 10 will be executed last.
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a bag of mixed peanuts and cashews contains pounds of peanuts that cost per pound and pound of cashews that cost per pound
The number of pounds of peanuts needed is 29.167.
Multiply the number of pounds of each type and multiply by the cost per pound to get the total cost of that part contribution to the total. Add them together and set it equal to the final total pounds (50) multiplied by its cost per pound ($2.90)
There are 5 pounds of mixed nuts.
let x = pounds of peanuts
cost of each pound of peanuts is $1.50
45 - x = pounds of cashews
Cost of each pound of cashew is $4.50
This way total pounds = 50
5 pounds($6) + x pounds ($1.50) + (45-x)pounds($4.50) = 50 pounds($2.90)
30 + 1.50x + 202.5 - 4.50x = 145
-3x = -87.5
x = 29.167
Therefore, the number of pounds of peanuts needed is 29.167.
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Disclaimer
The question given by you is incomplete, the abouve asnwer is done as per a similar question, the question is
A merchant has 5 pounds of mixed nuts that cost $30. he wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. how many pounds of peanuts are needed?
The function f(x) = Negative Startroot x EndRoot is shown on the graph
Which statement is correct?
The domain of the function is all real numbers less than or equal to −1.
The range of the function is all real numbers greater than or equal to 0.
The range of the function is all real numbers less than or equal to 0.
The domain of the function is all real numbers less than or equal to 0.
Answer:
C) The range of the function is all real numbers less than or equal to 0.
Step-by-step explanation:
Given function:
[tex]f(x)=-\sqrt{x}[/tex]
Domain
The domain of a function is the set of all possible input values (x-values).
As the square root of a negative number cannot be taken, x ≥ 0.
Therefore, the domain of the function is all real numbers greater than or equal to 0.
Range
The range of a function is the set of all possible output values (y-values).
As the domain is x ≥ 0, the range of the function is all real numbers less than or equal to 0.
Answer:
C) The range of the function is all real numbers less than or equal to 0.
Which equation will produce the graph shown?
Answer:
D
Step-by-step explanation:
Since this we have rose petal, the equation will be either
[tex]r = a \sin(n \alpha ) [/tex]
or
[tex]r = a \cos( n\alpha ) [/tex]
Since we have 3 petals, which is a odd number, n=3
so the answer must be either
[tex]r = a \cos(3a) [/tex]
[tex]r = a \sin(3 \alpha ) [/tex]
Where a is some constant real number.
So D is the answer
A bag contains 3 gold marbles, 6 silver marbles, and 29 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
The expected value of the game that you play will be negative 0.21.
What is the expected value?In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
A pack contains 3 gold marbles, 6 silver marbles, and 29 dark marbles. Somebody offers to play this game: You haphazardly select one marble from the pack. Assuming it is gold, you win $3. Assuming it is silver, you win $2. Assuming it is dark, you lose $1.
The expected value is given as,
E(x) = 3(3/38) + 2(6/38) - 1(29/38)
E(x) = 0.2368 + 0.3158 - 0.7632
E(x) = -0.21
The expected value of the game that you play will be negative 0.21.
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Please help…
Geometry
The proof that shows that ∠B ≅ ∠D by the CPCTC is explained in the table below.
What is CPCTC?CPCTC is a postulate that stands for "corresponding parts of congruent triangles are congruent". It says that if you prove that two triangles are congruent to each other, then every of their corresponding parts are congruent.
Therefore, the proof below shows how to use CPCTC to prove that ∠B ≅ ∠D.
Statement Reason
1. BC ≅ CD 1. Given
2. AC ≅ EC 2. Given
3. ∠ACB ≅ ∠ECD 3. Vertical angles theorem
4. ΔACB ≅ ΔECD 4. SAS theorem
5. ∠B ≅ ∠D 5. CPCTC
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If f(x)=3x-1/2,find f^-1(x)
Answer: x=3y-1/2 or y=(x+1/2)/3
Step-by-step explanation:
f^-1(x) is just the inverse so all you need to do is switch x and y.
right now you have y=3x-1/2
so switch the x and y to get your answer of x=3y-1/2
if you're asked to solve for y, follow these steps:
1. x +1/2 = 3y-1/2 +1/2 -> x+1/2=3y
2. divide both sides by 3 -> (x+1/2)/3=y
For linear function f, f(2)=0 and f(4)=-6.
Write function f in slope-intercept form.
Hint
Examples:
f(5)=0 means (5,0) is a point on the line.
f(3)=-2 means (3,-2) is a point on the line.
How do you find the slope of the line when you have 2 points?
The function f in slope - intercept form is y = -3x + 6 .
Given :
For linear function f, f(2)=0 and f(4)=-6.
Examples :
f(5)=0 means (5,0) is a point on the line.
f(3)=-2 means (3,-2) is a point on the line.
so f ( 2 ) = 0 means ( 2 , 0 )
f ( 4 ) = -6 means ( 4 , -6 )
slope m = -6 - 0 / 4 - 2
= -6 / 2
= -3
substitute m and ( 2 , 0 ) in y = mx + b
0 = -3 * 2 + b
b = 6
substitute m and b value
y = -3x + 6
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Mia's plant grows at an average rate of 5cm each month.
When she bought it, it was 18 cm tall.
Select the function that models the relationship between y, the height of the plant in cm, and x, the time in months that it grows.
A. y = 18x + 5
B. y = 18 + 5x
C. y = x + 18
D. y = 23x
Answer:
B
Step-by-step explanation:
The 18 is the intitial value. It does not change. What does change is the height every month. You would substitute in the number of months for x to find the height of the plant.
A $810 washing machine in a laundromat is depreciated for tax purposes at a rate of $90 per year. Find a function
for the depreciated value of the washing machine as it varies with time. When does the depreciated value reach $0?
help solve this there is reward
you have ten mangoes and twelve carrots that cost 23$ in total, five mangoes and four carrots cost ten dollars what does one mango and one carrot cost
Answer:1 carrot cost .75 cents and a mango cost 1.40
Step-by-step explanation:
12 carrots + 10 mangoes = 23$
4 carrots + 5 mangoes = 10$
I know to get from 5 mangoes to 10 mangoes you have to multiply twice. so it wil come up to 20 dollars
8 carrots + 10 mangoes = 20$
divide by 2
that will leave 4 carrots and 3 dollars.
4/3 = .75
17 dollars is left
so 10 carrots is equal to 14 dollars
14/10 = 1.4 dollars
Two independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n1 - 25 and n2-35. The correct distribution to use is the 1) t distribution with 59 degrees of freedom 2) t distribution with 58 degrees of freedom. 3) t distribution with 61 degrees of freedom. 4) t distribution with 60 degrees of freedom e in tne abintres of students enroled n staustucs today if there is any diffe statistics teacher wants to see and those enrolled five years ago.
2- T-distribution with 58 degrees of freedom
When the estimated standard deviation rather than the actual standard deviation is used as the denominator, the t-distribution is a continuous probability distribution of the z-score.
The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. If there is a remaining requirement for the data sample, particular data sample items must be picked after the degree of freedom quantity has been decided.
[tex]t[/tex] = Student's t-distribution
[tex]X{i}[/tex] = sample mean
μ = population mean
[tex]s[/tex] = sample standard deviation
[tex]n[/tex] = sample size
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The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. If there is a remaining requirement for the data sample, particular data sample items must be picked after the degree of freedom quantity has been decided.
When the estimated standard deviation rather than the actual standard deviation is used as the denominator, the t-distribution is a continuous probability distribution of the z-score.
a teacher figures that final grades in the statistics department are distributed as: a, 25%; b, 25%; c, 40%; d, 5%; f, 5%. at the end of a randomly selected semester, the following number of grades were recorded. find only the test statistics to test the claim that the grade distribution for the department is different than expected. be sure to set up the equation. do not conduct the hypothesis testing. grade a b c d f number 42 36 60 8 14
The critical value is 13.28 when the distribution of final marks in the statistics department.
Given that,
According to a teacher, the distribution of final marks in the statistics department is: A, 25%; B, 25%; C, 40%; D, 5%; and F, 5%. The following number of grades were recorded at the conclusion of a randomly chosen semester.
We have to recognize the important value.
We know that,
Given a=0.01,
The critical value of chi-square with 0.99,
df=n-1=4 is
13.28 (From chi-square table)
Therefore, The critical value is 13.28 when the distribution of final marks in the statistics department.
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A student is assessing the correlation between the number of workers in a factory and the number of units produced daily. The table shows the data:
Number of workers
0 10 20 30 40 50 60 70 80 90
Number of units 2 52 102 152 202 252 302 352 402 452
(
Part A: Is there any correlation between the number of workers in a factory and the number of units produced daily? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What do the slope and y-intercept of the plot indicate? (3 points)
Answer: Part A: Yes there is. As the number of workers increases, so does the production.
Part B: y = 5x + 2
Part C: The slope indicates that for every person there is 5 units being produced, and the y-intercept indicates that 2 units are being made every day, regardless of if there are no workers ( this, however is unrealistic but it is how the data is )
Step-by-step explanation:
Fifty part time college students were asked how many hours they work per week. The graphs below summarize their responses. Frequency 12+ 10 81 6 0 10 30 40 0 10 30 40 20 Hours 20 Hours What is the best measure of center for this data? Estimate the value of that measure of center.
The best measure of center for the frequency of the data is Mean. The value of the measure of the center is 30.
The Mean value refers to an intermediate value between a discrete set of numbers. It is a measure of central tendency in a data set. In statistics, the term average refers to any of the measures of central tendency. The arithmetic mean of a set of observed data is defined as being equal to the sum of the numerical values of each and every observation, divided by the total number of observations. Fifty part time college students were asked how many hours they work per week.
Frequency 12 10 81 6 0 10 30 40 0 10 30 40 20 Hours 20 Hours.
we can calculate mean by adding all the frequencies and then divide it by the number of observations.
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20. college majors there are three sections of english 101. in section i, there are 25 students, of whom 5 are mathmatics majors. in section ii, there are 20 students
The probability that the student is from Section I, given that he or she is a mathematics major, is 0.214 and the probability that the student is from Section 1, is 0.294.
In the give question;
There are three sections of English 101.
In Section 1, there are 25 students, of whom 3 are mathematics majors.
In Section II, there are 20 students, of whom 7 are mathematics majors.
In Section lIl, there are 40 students, of whom 4 are mathematics majors.
We have to find the probability that the student is from Section I, given that he or she is a mathematics major and the probability that the student is from Section 1.
Total number of students in all sections = 25+20+40 = 85
Total number of students major in mathematics = 3+7+4 = 14
The probability that the student is from Section I, given that he or she is a mathematics major is represented as
P(I | M) = P(I∩M)/P(M)
P(I∩M) = (Student in section II - Student in section III)/Total student in all sections
P(I∩M) = (7 - 4)/85 = 3/85
P(M) = Total student of mathematics/Total student in all sections
P(M) = 14/85
Now putting the values
P(I | M) = (3/85)/(14/85)
P(I | M) = 3/14
P(I | M) = 0.214
Now finding the probability that the student is from Section 1.
Probability that student is from section I = Total students in section I/ total students
Probability that student is from section I = 25/85
Probability that student is from section I = 0.294
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The right question is:
There are three sections of English 101. In Section 1, there are 25 students, of whom 3 are mathematics majors, In Section II, there are 20 students, of whom 7 are mathematics majors. In Section lil, there are 40 students, of whom 4 are mathematics majors. A student in English 101 is chosen at random. Find the probability that the student is from Section I, given that he or she is a mathematics major. The probability that the student is from Section 1 is (Simplify your answer. Round to three decimal places as needed.)
use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine, as in example 4. cos4(x) sin2(x)
The expression in terms of first power of cosine cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.
How to lower the power of expression in trigonometry?
The cosecant and cotangent functions, which exist in the numerator and denominator, can be used to simplify a trigonometric statement by writing it in terms of the sine and cosine functions.sin2x+cos2x = 1 and cos2x = (1+cos(2x))/2
Using the first identity, we have sin2x = 1-cos2x.
So we have that cos4x*sin2x = cos4x(1-cos2x)
Expanding, we have cos4x-cos6x.
Since cos2x= (1+cos(2x))/2, this implies cos4x = ((1+cos(2x))/2)² and cos6x=((1+cos(2x))/2)³.
Expanding each one, we have
cos4x - cos6x = 1/4(1+2cos(2x) + cos2(2x)) - 1/8(1+3cos(2x) + 3cos2(2x) + cos3(2x)).
Simplifying we get
cos4x - cos6x = 1/8 + 1/8(cos(2x) - cos2(2x) - cos3(2x)).
cos2(2x) = 1/2(1+cos(4x)) and cos3(2x)
= cos2(2x)*cos(2x)
= 1/2(1+cos(4x)) * cos(2x)
= 1/2(cos(2x) + cos(4x)*cos(2x))
Substituting, we get
cos4x - cos6x = 1/8 + 1/8(cos(2x) - 1/2(1+cos(4x)) - 1/2(cos(2x) + cos(4x)*cos(2x)))
Cleaning it up, we get
cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.
Hence, The expression in terms of first power of cosine cos4x*sin2x = 1/16 + cos(2x)/16 - cos(4x)/16 - cos(4x)cos(2x)/16.
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Which of the following are rational numbers? Select three that apply.
[tex] \sqrt{?} [/tex]
[tex] \sqrt{9} [/tex]
[tex] \sqrt{5} [/tex]
[tex] \sqrt{3} [/tex]
[tex] \sqrt{8} [/tex]
[tex] \sqrt{4} [/tex]
The rational numbers are √9, √4, √1. Options A, B and F
What are rational numbers?
A rational number is defined as a number expressed as the ratio of two integers, such that the denominator should not be equal to zero.
These numbers can be expressed as quotients of two integers.
It is a number whose decimal form is finite or recurring in nature.
It is determined by dividing an integer with another integer, an exception is made with zero.
It is important to note the following;
The square roots of perfect squares are rational numbers The square roots of non-perfect squares are not rational numbersFrom the numbers given, the rational numbers are;
√9, √4, √1
Hence, the values are √9, √4, √1
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↓
edpuzzle
YOUR TURN: FIND THE VALUE OF X AND Y:
12
!!!
MULTIPLE CHOICE QUESTION
Find the value of x:
3√4
8
4√3
4√8
8√4
please help me within today loll it’s due tonight 11:59pm!!
Answer:
Step-by-step explanation:
in similar triangles
sides are proportional.
An LG Dishwasher, which costs $800, has a 14% chance of needing to be replaced in the first 2 years of purchase. A two-year extended warrantee costs $112.10 on a dishwasher. What is the expected value of the extended warranty assuming it is replaced in the first 2 years?
The expected value of the extended warranty is $687.90 assuming it is replaced in the first 2 years.
Here, we are assuming that the dishwasher is replaced in the first 2 years in order to calculate the expected value of the extended warranty.
Because there is 14% chance of replacement:
Value of warranty = 14%*$800 - $112.10
Value of warranty = $112.00 - $112.10
Value of warranty = -$0.10
Now, because it is assumed that replacement will be done in first 2 years, then,
Value of warranty will increase to $687.90 ($800 - $112.10).
Therefore, the expected value of the extended warranty is $687.90 assuming it is replaced in the first 2 years.
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Suppose you want to purchase a $ 195000 house. If you put 20% down and finance the rest in a 15 year mortgage at an interest rate of 4%, what will your monthly payments be?
Monthly payment
The monthly payment on a principal of $156000 with interest rate of 4% over a time period of 15 years is $1153.91
Monthly PaymentThe monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.
The formula of monthly payment is given as;
A = P [r(1 + r)ⁿ] / [(1 + r)ⁿ - 1]
A = Monthly paymentr = ratep = principaln = number of paymentThe principal of the loan can be calculated as 20 % of 195000
20 / 100 = x / 195000
0.2 = x / 195000
x = 39000
The principal is 195000 - 39000 = 156000
The principal is 156000, rate is 4% and time is 15 year
Substituting the values into the formula
A = 156000[0.04(1 + 0.04)¹⁸⁰] / [(1 + 0.06)¹⁸⁰ - 1]
A = 1153.91
The monthly payment is $ 1,153.91
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Real numbers a and b satisfy the equations 3ª = 815+2 and 125=5ª-3. What is ab?
(A) -60
(B)-17
(C) 9
(D) 12
(E) 60
By solving a simultaneous linear equation, it can be calculated that-
Value of ab = 60
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a simultaneous linear equation needs to be solved
[tex]3^a = 81^{b+2}[/tex] and [tex]125^b = 5^{a-3}[/tex]
[tex]3^a = 3^{4(b+2)}[/tex]
a = 4(b + 2)
a = 4b + 8
a - 4b = 8 ... (1)
[tex]125^b = 5^{a-3}\\5^{3b} = 5^{a-3}\\[/tex]
3b = a - 3
a - 3b = 3 .... (2)
Subtracting (1) from (2)
b = -5
Putting the value of b in (2)
a - 3(-5) = 3
a + 15 = 3
a = 3 - 15
a = -12
Value of ab = (-12) [tex]\times[/tex](-5) = 60
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Write a polynomial function of least degree with zeroes
–
1, 5,9
Write your answer using the variable x and in standard form with a leading coefficient of 1
Jill Paa obtained a $1,450 installment loan to pay for a new laptop computer for her classwork. She agreed to
repay the loan in 18 monthly payments at an APR of 8%.
The monthly payment is $966.76.
What is monthly payment?
The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original lent amount, but also the interest that accrues, must be repaid.
Given the amount of the loan is $1,450.
The number of installment is 18.
The APR of the loan is 8%.
The monthly rate of interest is 8%/12 = 2/3%
The formula of monthly installment is
[tex]M=P[\frac{r}{1-(1+r)^{-n}} ][/tex]
P = principal = 1,450
r = rate of interest = 2/3%
n = number of instalment = 18
[tex]M=1450[\frac{0.67}{1-(1+0.67)^{-n}} ][/tex]
M = 966.76
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The weight of a medium-sized orange selected at random from a large bin of oranges at a local supermarket is a random variable with mean μ = 12 ounces and standard deviation σ = 1.2 ounces. Suppose we independently select two oranges at random from the bin. The difference in the weights of the two oranges (the weight of the first orange minus the weight of the second orange) is a random variable with a standard deviation equal to
The standard deviation of the difference in the weights of the two oranges is equal to sqrt(1.2^2 + 1.2^2) = 1.7 ounces.
What do you mean by 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.
The standard deviation of the difference in the weights of the two oranges is equal to the square root of the sum of the squares of the standard deviations of the two oranges. This is because the weights of the two oranges are independent random variables.
Therefore, the standard deviation of the difference in the weights of the two oranges is equal to sqrt(1.2^2 + 1.2^2) = 1.7 ounces.
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