Answer:
9
i got it right on my test
The equivalent expressions to 243 Superscript two-fifths will be 9.
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple, we simplify it.
Simplification usually involves making the expression simple and easy to use later,
The given expression is;
[tex]243^{2/5}[/tex]
We know that 2/3 = 0.4
So, the equivalent expressions to the given function;
[tex]243^{0.4}\\\\= 9[/tex]
Thus, The equivalent expressions to 243 Superscript two-fifths will be 9.
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Pls help with this area question
Answer:
1
Step-by-step explanation:
The lateral area of a cylinder is ...
LA = 2πrh
The total area is that added to the areas of the two circular bases:
A = 2πr² +2πrh
We want the ratio of these to be 1/2:
LA/A = (2πrh)/(2πr² +2πrh) = h/(r+h) = 1/2 . . . . cancel factors of 2πr
Multiplying by 2(r+h) gives ...
2h = r+h
h = r . . . . . subtract h
So, the desired ratio is ...
h/r = h/h = 1
The ratio between height and radius is 1.
It was reported that 23% of U.S. adult cellphone owners called a friend for advice about a purchase while in a store. If a sample of 15 U.S adult cellphone owners is selected, what is the probability that 7 called a friend for advice about a purchase while in a store
Answer:
[tex] P(X=7)[/tex]
And using the probability mass function we got:
[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=15, p=0.23)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find the following probability:
[tex] P(X=7)[/tex]
And using the probability mass function we got:
[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]
Is the area of this shape approximately 24 cm* ? If not give the correct area.
311
101
True
False
Answer:
19.2 feet square
Step-by-step explanation:
We khow that the area of an octagon is :
A= 1/2 * h * P where h is the apothem and p the perimeter
A= (1/2)*1.6*(3*8) = 19.2 feet squarePlease help! V^2 = 25/81
Answer:
C and D
Step-by-step explanation:
khan acedemy
An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the given equation v²=25/81 can be found as shown below.
v²=25/81
Taking the square root of both sides of the equation,
√(v²) = √(25/81)
v = √(25/81)
v = √(5² / 9²)
v = ± 5/9
Hence, the solutions of the given equation are A, B, and C.
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Would this be correct even though I didn’t use the chain rule to solve?
Answer:
Dy/Dx=1/√ (2x+3)
Yeah it's correct
Step-by-step explanation:
Applying differential by chain differentiation method.
The differential of y = √(2x+3) with respect to x
y = √(2x+3)
Let y = √u
Y = u^½
U = 2x +3
The formula for chain differentiation is
Dy/Dx = Dy/Du *Du/Dx
So
Dy/Dx = Dy/Du *Du/Dx
Dy/Du= 1/2u^-½
Du/Dx = 2
Dy/Dx =( 1/2u^-½)2
Dy/Dx= u^-½
Dy/Dx=1/√ u
But u = 2x+3
Dy/Dx=1/√ (2x+3)
An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.
Answer:
3, 12
Step-by-step explanation:
Et x and y be the required integers.
Case 1: x = 5y - 3...(1)
Case 2: xy = 36
Hence, (5y - 3)*y = 36
[tex]5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}[/tex]
Hence, the required integers are 3 and 12.
let
x = one integer
y = another integer
x = 5y - 3
If the product of the two integers is 36, then find the integers.
x * y = 36
(5y - 3) * y = 36
5y² - 3y = 36
5y² - 3y - 36 = 0
Solve the quadratic equation using factorization method
That is, find two numbers whose product will give -180 and sum will give -3
Note: coefficient of y² multiplied by -36 = -180
5y² - 3y - 36 = 0
The numbers are -15 and +12
5y² - 15y + 12y - 36 = 0
5y(y - 3) + 12 (y - 3) = 0
(5y + 12) (y - 3) = 0
5y + 12 = 0 y - 3 = 0
5y = - 12 y = 3
y = -12/5
The value of y can not be negative
Therefore,
y = 3
Substitute y = 3 into x = 5y - 3
x = 5y - 3
x = 5(3) - 3
= 15 - 3
= 12
x = 12
Therefore,
(x, y) = (12, 3)
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Estimate the area under the graph of f(x)=2x^2-12x+22 over the interval [0,2] using four approximating rectangles and right endpoints.
Answer:
The right Riemann sum is 21.5.
The left Riemann sum is 29.5.
Step-by-step explanation:
The right Riemann sum (also known as the right endpoint approximation) uses the right endpoints of a sub-interval:
[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_1)+f(x_2)+f(x_3)+...+f(x_{n-1})+f(x_{n})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].
To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using right endpoints you must:
We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].
Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]
Now, we just evaluate the function at the right endpoints:
[tex]f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5\\\\f\left(x_{4}\right)=f(b)=f\left(2\right)=6[/tex]
Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\frac{1}{2}(16.5+12+8.5+6)=21.5[/tex]
The left Riemann sum (also known as the left endpoint approximation) uses the left endpoints of a sub-interval:
[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].
To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using left endpoints you must:
We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].
Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]
Now, we just evaluate the function at the left endpoints:
[tex]f\left(x_{0}\right)=f(a)=f\left(0\right)=22\\\\f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\\\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5[/tex]
Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\frac{1}{2}(22+16.5+12+8.5)=29.5[/tex]
The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it.
The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten. Use 3.14 for pie.
A. 1,980
B. 1,788
C. 1,034
D. 1,884
Answer:
B. 1788
Step-by-step explanation:
The volume of solid shaped is expressed in cubic yards. The sides of the shape are multiplied or powered as 3 for the volume determination. Volume is the total space covered by the object. It includes height, length, width. The three dimensional objects volume is found by
length * height * width
The volume for current object is :
12 * 28 * 5
= 1788 cubic yards.
Answer: 1778
Step-by-step explanation:
because Ik I had the question
Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1
The area bounded by region between the curve [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] is
[tex]0[/tex] square units.
To find the Area,
Integrate the difference between the two curves over the interval of intersection.
Find the points of intersection between the curves [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] .
The point of Intersection is the common point between the two curve.
Value of [tex]x[/tex] and [tex]y[/tex] coordinate will be equal for both curve at point of intersection
In the equation [tex]y = x^2- 24[/tex], Put the value of [tex]y = 1[/tex].
[tex]1 = x^2-24[/tex]
Rearrange, like and unlike terms:
[tex]25 = x^2[/tex]
[tex]x =[/tex] ±5
The point of intersection for two curves are:
[tex]x = +5[/tex] and [tex]x = -5[/tex]
Integrate the difference between the two curve over the interval [-5,5] to calculate the area.
Area = [tex]\int\limits^5_{-5} {x^2-24-1} \, dx[/tex]
Simplify,
[tex]= \int\limits^5_{-5} {x^2-25} \, dx[/tex]
Integrate,
[tex]= [\dfrac{1}{3}x^3 - 25x]^{5} _{-5}[/tex]
Put value of limits in [tex]x[/tex] and subtract upper limit from lower limit.
[tex]= [\dfrac{1}{3}(5)^3 - 25(5)] - [\dfrac{1}{3}(-5)^3 - 25(-5)][/tex]
= [tex]= [\dfrac{125}{3} - 125] - [\dfrac{-125}{3} + 125][/tex]
[tex]= [\dfrac{-250}{3}] - [\dfrac{-250}{3}]\\\\\\= \dfrac{-250}{3} + \dfrac{250}{3}\\\\\\[/tex]
[tex]= 0[/tex]
The Area between the two curves is [tex]0[/tex] square units.
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The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is a. k – 1. b. A chi-square distribution is not used. c. number of rows minus 1 times number of columns minus 1. d. n – 1.
Answer:
Option C
Step-by-step explanation:
The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.
It tests the claim that the row and column variables are independent of each other.
The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.
Convert into the following unit into 30 cm into miter
Answer:
it we'll be 0.3
Step-by-step explanation:
trust me man I like to explain but it's long
Answer:
0.3 meter or 3/10 meter
Step-by-step explanation:
As there are 100cm in 1 meter and you want to find 30cm in terms of meters.
It will be as
100cm = 1 meter (rule/lax)
100/100 cm = 1/100 meter (divide both sides of equation with 100)
1 cm = 1/100 meter
1 *30 cm = (1/100)*30 meter (multiply both sides with 30)
30 cm = 30/100 meter
30/100 more shortly can be written as 3/10 meter or in decimals 0.3 meter.
Profit Function for Producing Thermometers The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. (Enter your answer using interval notation.) P(x) = −0.004x2 + 6x − 5,000 Increasing: Decreasing:
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
Step-by-step explanation:
Critical points:
The critical points of a function f(x) are the values of x for which:
[tex]f'(x) = 0[/tex]
For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.
The critical points help us find these intervals.
In this question:
[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]
So
[tex]P'(x) = -0.008x + 6[/tex]
Critical point:
[tex]P'(x) = 0[/tex]
[tex]-0.008x + 6 = 0[/tex]
[tex]0.008x = 6[/tex]
[tex]x = \frac{6}{0.008}[/tex]
[tex]x = 750[/tex]
We have two intervals:
(0, 750) and [tex](750, \infty)[/tex]
(0, 750)
Will find P'(x) when x = 1
[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]
Positive, so increasing.
Interval [tex](750, \infty)[/tex]
Will find P'(x) when x = 800
[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]
Negative, then decreasing.
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
The graphed line shown below is y = 3 x minus 1. On a coordinate plane, a line goes through (0, negative 1) and (1, 2). Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions? y + 1 = 3 x y = negative 3 x + 1 y = 3 x + 1 y minus 3 x = negative 3
Answer:
y + 1 = 3x
Step-by-step explanation:
In order for there to be an infinite number of solutions, the two lines need to be the same.
y+1 = 3x
y=3x-1 are both the same
Answer:
a)y + 1 = 3x
Step-by-step explanation:
Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.)
Answer:
85.932 cm³
Step-by-step explanation:
The volume of rectangular prism is obtained as the product of its length (l) by its width (w) and by its height (h):
[tex]V=l*w*h[/tex]
The volume of a prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm is:
[tex]V=4.4*3.1*6.3\\V=85.932\ cm^3[/tex]
The volume of this prism is 85.932 cm³.
Help me please! I need an answer!
Answer: [tex]\bold{\dfrac{b_1}{b_2}=\dfrac{3}{2}}[/tex]
Step-by-step explanation:
Inversely proportional means a x b = k --> b = k/a
Given that a₁ = 2 --> b₁ = k/2
Given that a₂ = 3 --> b₂ = k/3
[tex]\dfrac{b_1}{b_2}=\dfrac{\frac{k}{2}}{\frac{k}{3}}=\large\boxed{\dfrac{3}{2}}[/tex]
The ratio of the areas of two circles is 121/100. What is the ratio of the radii of the two circles
Answer:
11/10
Step-by-step explanation:
The area ratio is the square of the radius ratio (k):
(121/100) = k²
k = √(121/100) = 11/10
The ratio of radii is 11/10.
whats the answer ?? ill mark brainliest
Answer:
[tex]\boxed{Option A ,D}[/tex]
Step-by-step explanation:
The remote (non-adjacent) interior angles of the exterior angle 1 are <4 and <6
For the triangle show, what are the values of x and y (urgent help needed)
we just have to use the Pythagoras theorem and then calculate the value of x and y.
please please please please help i need to pass please
Answer:
D
Step-by-step explanation:
Solution:-
The standard sinusoidal waveform defined over the domain [ 0 , 2π ] is given as:
f ( x ) = sin ( w*x ± k ) ± b
Where,
w: The frequency of the cycle
k: The phase difference
b: The vertical shift of center line from origin
We are given that the function completes 2 cycles over the domain of [ 0 , 2π ]. The number of cycles of a sinusoidal wave is given by the frequency parameter ( w ).
We will plug in w = 2. No information is given regarding the phase difference ( k ) and the position of waveform from the origin. So we can set these parameters to zero. k = b = 0.
The resulting sinusoidal waveform can be expressed as:
f ( x ) = sin ( 2x ) ... Answer
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145 a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Answer:
a. Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. P(at least B) = 0.330
c. P(pass) = 0.855
Step-by-step explanation:
Professor Sanchez has been teaching Principles of Economics for over 25 years.
He uses the following scale for grading.
Grade Numerical Score Probability
A 4 0.090
B 3 0.240
C 2 0.360
D 1 0.165
F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The cumulative probability distribution is given by
Grade = F
P(X ≤ x) = 0.145
Grade = D
P(X ≤ x) = 0.145 + 0.165 = 0.310
Grade = C
P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670
Grade = B
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910
Grade = A
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1
Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
At least B means equal to B or greater than B grade.
P(at least B) = P(B) + P(A)
P(at least B) = 0.240 + 0.090
P(at least B) = 0.330
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Passing the course means getting a grade of A, B, C or D
P(pass) = P(A) + P(B) + P(C) + P(D)
P(pass) = 0.090 + 0.240 + 0.360 + 0.165
P(pass) = 0.855
Alternatively,
P(pass) = 1 - P(F)
P(pass) = 1 - 0.145
P(pass) = 0.855
my dad is designing a new garden. he has 21 feet of fencing to go around the garden. he wants the length of the garden to be 1 1/2 feet longer than the width. how wide should he make the garden?
Answer:
21=2w+2w+3 18=4w w=4.5
Which equation represents the statement below?
Thirteen less than a number is forty-two.
Select one:
a. n – 13 = 42
b. 42 – 13 = n
c. 13 – n = 42
d. 13 – 42 = n
The answer is option A
Step-by-step explanation:
Thirteen less than a number is written as
n - 13
Equate it to 42
We have
n - 13 = 42
Hope this helps you
Determine what type of study is described. Explain. Researchers wanted to determine whether there was an association between high blood pressure and the suppression of emotions. The researchers looked at 1800 adults enrolled in a Health Initiative Observational Study. Each person was interviewed and asked about their response to emotions. In particular they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10. Each person's blood pressure was also measured. The researchers analyzed the results to determine whether there was an association between high blood pressure and the suppression of emotions.
Answer:
Experimental Study
Step-by-step explanation:
In an experimental study, the researchers involve always produce and intervention (in this case they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10) and study the effects taking measurements.
These studies are usually randomized ie subjects are group by chance.
As opposed to observation studies, where the researchers only measures what was observed, seen or hear without any intervention on their parts.
A fair die is rolled repeatedly. Calculate to at least two decimal places:__________
a) the chance that the first 6 appears before the tenth roll
b) the chance that the third 6 appears on the tenth roll
c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.
d) the expected number of rolls until six 6's appear
e) the expected number of rolls until all six faces appear
Answer:
a. 0.34885
b. 0.04651
c. 0.02404
d. 36
e. 14.7, say 15 trials
Step-by-step explanation:
Q17070205
Note:
1. In order to be applicable to established probability distributions, each roll is considered a Bernouilli trial, i.e. has only two outcomes, success or failure, and are all independent of each other.
2. use R to find the probability values from the respective distributions.
a) the chance that the first 6 appears before the tenth roll
This means that a six appears exactly once between the first and the nineth roll.
Using binomial distribution, p=1/6, n=9, x=1
dbinom(1,9,1/6) = 0.34885
b) the chance that the third 6 appears on the tenth roll
This means exactly two six's appear between the first and 9th rolls, and the tenth roll is a six.
Again, we have a binomial distribution of p=1/6, n=9, x=2
p1 = dbinom(2,9,1/6) = 0.27908
The probability of the tenth roll being a 6 is, evidently, p2 = 1/6.
Thus the probability of both happening, by the multiplication rule, assuming independence
P(third on the tenth roll) = p1*p2 = 0.04651
c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.
Again, using binomial distribution, probability of 3-6's in the first 10 rolls,
p1 = dbinom(3,10,1/6) = 0.15504
Probability of 3-6's in the NEXT 10 rolls
p1 = dbinom(3,10,1/6) = 0.15504
Probability of both happening (multiplication rule, assuming both events are independent)
= p1 * p1 = 0.02404
d) the expected number of rolls until six 6's appear
Using the negative binomial distribution, the expected number of failures before n=6 successes, with probability p = 1/6
= n(1-p)/p
Total number of rolls by adding n
= n(1-p)/p + n = n(1-p+p)/p = n/p = 6/(1/6) = 36
e) the expected number of rolls until all six faces appear
P1 = 6/6 because the firs trial (roll) can be any face with probability 1
P2 = 6/5 because the second trial for a different face has probability 5/6, so requires 6/5 trials
P3 = 6/4 ...
P4 = 6/3
P5 = 6/2
P6 = 6/1
So the total mean (expected) number of trials is 6/6+6/5+6/4+6/3+6/2+6/1 = 14.7, say 15 trials
Irvin buys a car for $21 comma 804. It depreciates 25% each year that he owns it. What is the depreciated value of the car after 1 yr? after 2 yr? The depreciated value of the car after 1 yr is $? The depreciated value of the car after 2 yr is $?
Answer:
The depreciated value of the car after 1 yr is $16,353
The depreciated value of the car after 2 yr is $12,264.75
Step-by-step explanation:
Given
purchase amount P= $21,804
rate of depreciation R= 25%
applying the formula for the car deprecation we have
[tex]A= P*(1-\frac{R}{100} )^n[/tex]
Where,
A is the value of the car after n years,
P is the purchase amount,
R is the percentage rate of depreciation per annum,
n is the number of years after the purchase.
1. The depreciated value of the car after 1 yr is
n=1
[tex]A= 21,804*(1-\frac{25}{100} )^1\\\\A= 21,804*(1-0.25 )^1\\\\A= 21,804*0.75\\\\A= 16353[/tex]
The depreciated value of the car after 1 yr is $16,353
2. The depreciated value of the car after 2 yr is
n=2
[tex]A= 21,804*(1-\frac{25}{100} )^2\\\\A= 21,804*(1-0.25 )^2\\\\A= 21,804*0.75^2\\\\A= 21,804*0.5625\\\\A= 12264.75[/tex]
The depreciated value of the car after 2 yr is $12,264.75
Betty tabulated the miles-per-gallon values for her car as 26.5, 28, 30.2, 29.6, 32.3, and 24.7. She wants to construct the 95% two-sided confidence interval. Which value should Betty use for the value of t* to construct the confidence interval?
Answer:
Betty should use T = 2.571 to construct the confidence interval
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.571
Betty should use T = 2.571 to construct the confidence interval
Solve the algebraic expressio (0.4)(8)−2
Answer: -6.4
Step-by-step explanation:
(0.4)(8)(-2)
3.2*-2
-6.4
By what percent will the fraction increase if its numerator is increased by 60% and denominator is decreased by 20% ?
Answer:
100%
Step-by-step explanation:
Start with x.
x = x/1
Increase the numerator by 60% to 1.6x.
Decrease the numerator by 20% to 0.8.
The new fraction is
1.6x/0.8
Do the division.
1.6x/0.8 = 2x
The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.
The increase is 100%.
Answer:
33%
Step-by-step explanation:
let fraction be x/y
numerator increased by 60%
=x+60%ofx
=8x
denominator increased by 20%
=y+20%of y
so the increased fraction is 4x/3y
let the fraction is increased by a%
then
x/y +a%of (x/y)=4x/3y
or, a%of(x/y)=x/3y
[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]
therefore a=33
anda%=33%
heres a list of numbers 3 6 9 7 4 6 7 0 7 Find median,mean,range and mode
median=order them and find the middle=6
mean=add them all up and divide by the amount of numbers=(3+6+9+7+4+6+7+0 +7)/9=5.4
range= the difference between the smallest and largest number=9-3=6
mode= the one that appears the most= 7
The median, mean, range and mode will be 6, 5.4, 9 and 7.
The median is the number in the middle when arranged in an ascending order. The numbers will be:
0, 3, 4, 6, 6, 7, 7, 7, 9.
The median is 6.
The range is the difference between the highest and lowest number which is: = 9 - 0 = 9
The mode is the number that appears most which is 7.
The mean will be the average which will be:
= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.
= 49/9
= 5.4
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graph y=8 sec1/5 Ø the answers are graphs I am just unsure of how to answer
Answer:
Use a graphing calc.
Step-by-step explanation: