Answer:
[tex]f(126) \approx 5.01333[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[3]{126}[/tex]
Required
Solve using differentials
In differentiation:
[tex]f(x+\triangle x) \approx f(x) + \triangle x \cdot f'(x)[/tex]
Express 126 as 125 + 1;
i.e.
[tex]x = 125; \triangle x = 1[/tex]
So, we have:
[tex]f(125+1) \approx f(125) + 1 \cdot f'(125)[/tex]
[tex]f(126) \approx f(125) + 1 \cdot f'(125)[/tex]
To calculate f(125), we have:
[tex]f(x) = \sqrt[3]{x}[/tex]
[tex]f(125) = \sqrt[3]{125}[/tex]
[tex]f(125) = 5[/tex]
So:
[tex]f(126) \approx f(125) + 1 \cdot f'(125)[/tex]
[tex]f(126) \approx 5 + 1 \cdot f'(125)[/tex]
[tex]f(126) \approx 5 + f'(125)[/tex]
Also:
[tex]f(x) = \sqrt[3]{x}[/tex]
Rewrite as:
[tex]f(x) = x^\frac{1}{3}[/tex]
Differentiate
[tex]f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}\\[/tex]
Using law of indices, we have:
[tex]f'(x) = \frac{x^\frac{1}{3}}{3x}[/tex]
So:
[tex]f'(125) = \frac{125^\frac{1}{3}}{3*125}[/tex]
[tex]f'(125) = \frac{5}{375}[/tex]
[tex]f'(125) = \frac{1}{75}[/tex]
So, we have:
[tex]f(126) \approx 5 + f'(125)[/tex]
[tex]f(126) \approx 5 + \frac{1}{75}[/tex]
[tex]f(126) \approx 5 + 0.01333[/tex]
[tex]f(126) \approx 5.01333[/tex]
suppose you borrow $1000 for 3 years and you owe $200 interest. what is the interest rate?
Answer:
6.67%
Step-by-step explanation:
By question I borrow $1000 for 3 years and I owe $200 interest . We can use the formula of Simple Interest as ,
[tex]\implies SI =\dfrac{ P*R*T}{100}[/tex]
Plug in the values .[tex]\implies \$200 =\dfrac{3*\$1000*R }{100}\\\\\implies R = \dfrac{ \$ 200 * 100}{3*\$ 1000} \\\\\implies\underline{\underline{ R = 6.67 \%}} [/tex]
A line has a slope of -2/3 and passes through the point (-3, 8). What is the equation of the line?
y= -2/3x + 6
y= -2/3x + 8
y= 6x- 2/3
y= 8x- 2/3
Answer:
y= -2/3x+6
Step-by-step explanation:
Using slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -2/3x +b
Substitute the point into the equation
8 = -2/3(-3) +b
8 = 2+b
8-2 =b
6=b
y= -2/3x+6
Camille bought a set of kitchen chairs discounted 25% off of the original price of $170. What was the dollar amount of discount of the set of chairs?
Answer:
$42.50
Step-by-step explanation:
All you have to do is simply multiply
170 x 0.25=$42.50
The graph below represents the distance of a dog from a trainer after a command is given.
Which statement could describe the dog’s movement 5 seconds after the command was given?
The dog stopped to lie down and obey the trainer’s command.
The dog was running towards the trainer to receive a treat.
The dog was running away from the trainer to chase a squirrel.
The dog was stopped but began running towards the trainer.
Answer:
.
Step-by-step explanation:
If you apply for a job with Globo Corp, there is a 75% chance that you will get an interview.
If you get an interview, there is a 48% chance that you will get the job.
If you apply for a job with Globo Corp, what is the probability that you will get the job?
Express your answer as a decimal, rounded to the nearest hundredth.
Answer:
The probability that you will get the job If you apply for a job with Globo Corp=0.36
Step-by-step explanation:
We are given that
If you apply for a job with Globo Corp, then the probability of getting interview P(A)=75%=0.75
If you get an interview, then the probability of getting job=P(B)=48%=0.48
We have to find the probability that you will get the job If you apply for a job with Globo Corp.
If you apply for a job with Globo Corp, the probability of getting job=[tex]P(A)\times P(B)[/tex]
If you apply for a job with Globo Corp, the probability of getting job=[tex]0.75\times 0.48[/tex]
If you apply for a job with Globo Corp, the probability of getting job=0.36
Hence, the probability that you will get the job If you apply for a job with Globo Corp=0.36
Use cylindrical shells to find the volume of the solid generated when the region
R under y = x2 over the interval (0,2) revolved about the line y = -1
Answer:
[tex]\displaystyle V = \frac{176 \pi}{15}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsExpandingFunctionsFunction NotationGraphingExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Integrals
Definite IntegralsArea under the curveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method:
[tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] x is the radius[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is the volumeStep-by-step explanation:
Step 1: Define
Identify
Graph of region
y = x²
x = 2
y = 4
Axis of Revolution: y = -1
Step 2: Sort
We are revolving around a horizontal line.
[Function] Rewrite in terms of y: x = √y[Graph] Identify bounds of integration: [0, 4]Step 3: Find Volume Pt. 1
[Shell Method] Find distance of radius x: [tex]x = y + 1[/tex][Shell Method] Find circumference variable f(x) [Area]: [tex]\displaystyle f(x) = 2 - \sqrt{y}[/tex][Shell Method] Substitute in variables: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - \sqrt{y})} \, dy[/tex][Integral] Rewrite integrand [Exponential Rule - Root Rewrite]: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(y + 1)(2 - y^\bigg{\frac{1}{2}})} \, dy[/tex][Integral] Expand integrand: [tex]\displaystyle V = 2\pi \int\limits^4_0 {(-y^\bigg{\frac{3}{2}} + 2y - y^\bigg{\frac{1}{2}} + 2)} \, dy[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{-2y^\bigg{\frac{5}{2}}}{5} + y^2 - \frac{2y^\bigg{\frac{3}{2}}}{3} + 2y \bigg) \bigg| \limits^4_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle V = 2\pi (\frac{88}{15})[/tex]Multiply: [tex]\displaystyle V = \frac{176 \pi}{15}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
expand and simplify (x-2)(x+5)(2x-1)
Answer:
simplified: 2x^3+5x^2-23x+10
Step-by-step explanation:
How do you solve this problem and what did you do to gain the answer 1/64+5/8-3/32=?
Answer:
the answer is 35/64(in fraction) but in decimals it's 0.55
HELPPP
3p-4-8p<-19
i need the steps as well
9514 1404 393
Answer:
p > 3
Step-by-step explanation:
3p -4 -8p < -19 . . . . . . given
-5p -4 < - 19 . . . . . . . . collect terms
-5p < -15 . . . . . . . . . . . add 4
p > 3 . . . . . . . . . . . . . . divide by -5 (reverses the inequality symbol)
What is the midpoint of the segment shown below?
10
A. (5,-4)
(16,5)
B. (10,-4)
C. (10,-2)
10
15
(-6.-9)
D. (5,-2)
Answer:
D
Step-by-step explanation:
Use the midpoint formula to find the midpoint of the line segment.
Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed. A 90% confidence interval for a mean μ if the sample has n-80 with X-22.1 and s = 5.6, and the standard error is SE = 0.63.
The 90% confidence interval is to :_________
Answer:
(21.064 ; 23.136)
Step-by-step explanation:
Given :
Sample, n = 80
Mean, xbar = 22.1
Standard deviation, s = 5.6
Standard Error, S. E = 0.63
Confidence interval :
Xbar ± Zcritical * S.E
22.1 ± (1.645 * 0.63)
22.1 ± 1.036
Lower boundary = 22.1 - 1.036 = 21.064
Upper boundary = 22.1 + 1.048 = 23.136
(21.064 ; 23.136)
According to Okun's law, if the unemployment rate goes from 5% to 3%, what will be the effect on the GDP?
A. It will increase by 7%.
B. It will decrease by 7%.
C. It will decrease by 1%.
D. It will increase by 1%.
Answer:
D. It will increase by 1%.
Step-by-step explanation:
Given
[tex]u_1 = 5\%[/tex] --- initial rate
[tex]u_2 = 3\%[/tex] --- final rate
Required
The effect on the GDP
To calculate this, we make use of:
[tex]\frac{\triangle Y}{Y} = u_1 - 2\triangle u[/tex]
This gives:
[tex]\frac{\triangle Y}{Y} = 5\% - 2(5\% - 3\%)[/tex]
[tex]\frac{\triangle Y}{Y} = 5\% - 2(2\%)[/tex]
[tex]\frac{\triangle Y}{Y} = 5\% - 4\%[/tex]
[tex]\frac{\triangle Y}{Y} = 1\%[/tex]
This implies that the GDP will increase by 1%
Answer: A. It will increase by 7%.
Step-by-step explanation: I took this course!
The pre-image, ΔSTU, has undergone a type of transformation called a rigid transformation to produce the image, ΔVWX. Compare the measures of the triangles by dragging the image to the pre-image.
Which measures are equal? Check all that apply.
ST = VW
SU = VX
TU = WX
m∠SUT = m∠VXW
m∠TSU = m∠WVX
m∠UTS = m∠XWV
Answer:
its all of them
Step-by-step explanation:
since its the same shape as the old one all the measurements are the same.
Answer:
its all of them
Step-by-step explanation:
Please hlep x^2+6x+1=0
Answer:
Substitute into the quadratic formula
-6 ± √32 / 2
= -3 ± √16
= 1 and -1 are the answer
Answer:
x = - 3 ± 2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
x² + 6x + 1 = 0 ( subtract 1 from both sides )
x² + 6x = - 1
Using the method of completing the square
add/ subtract ( half the coefficient of the x- term)² to both sides
x² + 2(3)x + 9 = - 1 + 9
(x + 3)² = 8 ( take the square root of both sides )
x + 3 = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ( subtract 3 from both sides )
x = - 3 ± 2[tex]\sqrt{2}[/tex]
Then
x = - 3 - 2[tex]\sqrt{2}[/tex] , x = - 3 + 2[tex]\sqrt{2}[/tex]
Does it pay to ask for a raise? A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one. According to the survey, of the men interviewed, 21% had asked for a raise and 60% of the men who had asked for a raise received the raise. If a man is selected at random from the survey population of men, find the following probabilities. (Enter your answers to three decimal places.)
Answer:
a) P(man asked for a raise) = 0.21.
b) P(man received raise, given he asked for one) = 0.6.
c) P(man asked for raise and received raise) = 0.126.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
21% asked for a raise, so:
P(man asked for a raise) = 0.21.
Question b:
Event A: Asked for a raise.
Event B: Received a raise:
21% had asked for a raise and 60% of the men who had asked for a raise received the raise:
This means that [tex]P(A) = 0.21, P(A \cap B) = 0.21*0.6[/tex], thus:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.21*0.6}{0.6} = 0.6[/tex]
P(man received raise, given he asked for one) = 0.6.
Question c:
[tex]P(A \cap B) = 0.21*0.6 = 0.126[/tex]
P(man asked for raise and received raise) = 0.126.
At an intersection, the red light times are normally distributed with a mean time of 3 minutes and a standard deviation of 0.25 minutes. Approximately what percent of red lights last between 2.5 and 3.5 minutes? (2 points)
Answer:
95.4%
Step-by-step explanation:
Z(low)=-2 0.022750132
Z(upper)=2 0.977249868
ora started watching a movie at 2:45 p.m. She watched the movie for hours before stopping the movie for hours to eat dinner. After dinner, Nora finished watching the remaining hours of the movie. At what time did the movie end?
Answer: Movies Average around 1 hour to 2 hours long. 1:30 to 2:30 so id say somewhere around 4-5 pm. Which leaves time for dinner after
Step-by-step explanation:
To add radical expressions, the expressions must have the same index and radicand,
True
False
Assume that there is a 8% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
Answer:
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
Step-by-step explanation:
For each disk, there are only two possible outcomes. Either it works, or it does not. The probability of a disk working is independent of any other disk, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Assume that there is a 8% rate of disk drive failure in a year.
So 100 - 8 = 92% probability of working, which means that [tex]p = 0.92[/tex]
Two disks are used:
This means that [tex]n = 2[/tex]
What is the probability that during a year, you can avoid catastrophe with at least one working drive?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.92)^{0}.(0.08)^{2} = 0.0064[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0064 = 0.9936[/tex]
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
Circle O has radius 5 m with an arc AB intercepted by a central angle of π5π5 radians. What is the length of arc AB expressed in terms of ππ?
Answer:
I am assuming that you meant to write π/5.
Step-by-step explanation:
Radius r = 5 meters
Circumference = 2πr = 10π
Central angle θ = π/5 radian
Arc length = 10π × θ/(2π radians)
= 5θ
= π meters
what is the factors of p(x)=x^2+7√2x+4
PLEAE HELP!
Answer:
aasha here it is.
Step-by-step explanation:
3x−1)(2x+3)
6x2+7x−3
=6x2+9x−2x−3
=3x(2x+3)−1(2x+3)
=(2x+3)(3x−1)
and hiii
Hw help ASAP PLZZZZZZ
Answer:
Your answer is C. X = 29/8c
Step-by-step explanation:
2/3(cx + 1/2) - 1/4 = 5/2
2cx/3+1/3-1/4=5/2
2cx3+1/12=5/2
2cx/3=5/2-1/12
2cx/3=29/12
(3)2cx/3=29/12(3)
2cx= 31/4
(2c)2cx=29/4(2c)
X=29/8c
Your answer is C. X = 29/8c
What is the measure of angle b
Answer:
51 ?
Step-by-step explanation:
90-39= 51. I hope its correct
Answer:
51 degrees
Step-by-step explanation:
Well if you look at the picture angle b and the 39 degrees angle together must make a 90 degree angle
90-39 is 51 so therefor angle b must be 51 degrees
The perimeter of an equilateral triangle is 126mm.
State the length of one of its sides.
Explanation:
Divide 126 over 3. This is because any equilateral triangle has all three sides the same length
126/3 = 42
Each side is 42 mm long
So its perimeter is 3*42 = 126 mm
Side note: if your teacher says a triangle is equiangular, then it's automatically equilateral as well (and vice versa).
The length of one of its sides of an equilateral triangle is 42 mm.
What is equilateral triangle?In geometry, an equilateral triangle exists as a triangle that contains all its sides equivalent in length. Since the three sides stand equivalent therefore the three angles, opposite to the equivalent sides, stand equivalent in measure. Thus, it stands also named an equiangular triangle, where each angle measure 60 degrees.
The perimeter of an equilateral triangle exists 126 mm.
The equilateral triangle contains all three sides of the same length
126/3 = 42
Each side stands 42 mm long
So its perimeter stands 3 [tex]*[/tex] 42 = 126 mm
Therefore, the length of one of its sides = 42 mm.
To learn more about equilateral triangle
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what is the approximate value of x in the diagram below?
Answer:
Where is the diagram though..
Step-by-step explanation:
If a business borrows $12,600 and repays $23,940 in 5 years, what is the simple interest rate?
Answer:
18%
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Simple Interest Rate Formula: A = P(1 + rt)
P is principle amountr is ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 12600
A = 23940
t = 5
Step 2: Solve for r
Substitute in variables [Simple Interest Rate Formula]: 23940 = 12600(1 + 5r)[Division Property of Equality] Divide 12600 on both sides: 19/10 = 1 + 5r[Subtraction Property of Equality] Subtract 1 on both sides: 9/10 = 5r[Division Property of Equality] Divide 5 on both sides: 9/50 = rRewrite: r = 9/50Evaluate: r = 0.18Convert: r = 18%some pleaseeeeee help!!
f(x) = 3x + 4 + 2
g(x) = 4
Find (f +g)(x).
Answer:
3x^2 + 10x
Step-by-step explanation:
If u wrote it correctly it would be ((x+4+2)+4)(x)
Which of the following is not true regarding the flow of information from the adjusted trial balance on the end-of-period spreadsheet?
The correct statement about the flow of information from the adjusted trial balance on the end-of-period spreadsheet is A. The revenue and expense account balances flow into the income statement.
What is an Adjusted Trial Balance?This refers to the general ledger balance after some changes have been done an account balance such as accrued expenses, depreciation, etc.
Therefore, we can see that from the complete information, the statement that is false about the adjusted trial balance on the end-of-period spreadsheet is option A because the revenue and expense account balances does not flow into the income statement.
The other options from the complete text are:
a. The revenue and expense account balances flow into the income statement.b. The asset and liability account balances flow into the retained earnings statement.c. The revenue and expense account balances flow into the retained earnings statement.d. The retained earnings and dividends account balances flow into the balance sheet.
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The sample mean, x , is a statistic.
True or False
Answer:
True
Step-by-step explanation:
The statistic is a numerical value which describes the characteristic of a particular sample data. The sample is a set of data which represents a smaller subset randomly selected from the population or a larger dataset.
The sample mean, refers to the mean or average value of a sample data, therefore, a sample mean is a numerical characteristic of the sample dataset and it is therefore a statistic. On the other hand, numerical characteristics of a population data is called the parameter.
Leroy borrowed $1500 at an annual simple interest rate of 12%. He paid $270 in interest. For what time period did Leroy borrow the money?
Answer:
i hope you understand easily
mark me brainlist
Step-by-step explanation:
