Answer:
2. 5 miles
Step-by-step explanation:
Given that:
Rental cost = $30
Cost per mile driven = 18 cent
Daily budget = $75
Greatest distance you can drive each day while staying within budget :
Rental cost + (cost per mile driven * distance) ≤ daily budget
$30 + 18d ≤ $75
18d ≤ 75 - 30
18d ≤ 45
d ≤ 45 / 18
d ≤ 2.5
Greatest distance you can drive each day while staying within budget is 2.5 miles.
1 13/64 = 11/8x find the answer
Answer:
v in (-oo:+oo)
1.13/64 = (11/8)*v // - (11/8)*v
1.13/64-((11/8)*v) = 0
(-11/8)*v+1.13/64 = 0
0.01765625-11/8*v = 0 // - 0.01765625
-11/8*v = -0.01765625 // : -11/8
v = -0.01765625/(-11/8)
v = 0.01284091
v = 0.01284091
Step-by-step explanation:
1 13/64 = 11/8x
Rewrite the left side as an improper fraction:
77/64 = 11/8x
Divide both sides by 11/8
77/11 = 7
64/8 = 8
X = 7/8
Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house
Can you show the math as far as formulas go?
Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.
Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.
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Given the two functions, which statement is true?
f(x) = e^x, g(x) = e^x-2
g(x) is translated down 2 units compared to f(x)
g(x) is translated right 2 units compared to f(x)
g(x) is translated left 2 units compared to f(x)
g(x) is translated up 2 units compared to f(x)
NEED HELP!!!
Please HELP !!!!please help
Answer:
4y
Step-by-step explanation:
Hey There!
given the equation
y - (-3y)
the two negative signs cancel out and make it into
y + 3y which is equal to 4y
thus meaning the answer to your problem is 4y
What is the probability that the test will fail to decide
is true when in reality =72. 5?
Determined by various factors such as sample size, statistical significance, and the chosen level of confidence. the probability that the test will fail to decide that the true value is 72.5 when it is indeed 72.5.
In order to calculate the probability of a Type II error, one would need to know the specific details of the test being used, such as the sample size, the statistical power of the test, and the chosen level of significance.
In general, the probability of a Type II error increases as the sample size decreases and the level of significance decreases. This means that if the test being used is not sufficiently powered or if the level of confidence is too low, there is a higher probability of failing to detect a true effect.
If the test is not able to accurately determine if the statement is true or not when the actual value is 72.5, then there is a possibility that a Type II error has occurred. The probability of this error depends on the specific details of the test being used and cannot be determined without further information.
The probability of a test failing to decide a certain hypothesis is true, when it is actually true, can be determined using the concept of Type II error or false negative rate. In statistical hypothesis testing, Type II error (β) refers to the probability of failing to reject a false null hypothesis. These factors influence the power of the test, which is the probability of correctly rejecting the null hypothesis when it is false. The power of the test (1 - β) is complementary to the probability of making a Type II error.
In this case, the null hypothesis (H0) could be that the value is not equal to 72.5,
while the alternative hypothesis (H1) states that the value is equal to 72.5.
The probability you are looking for is the Type II error rate when the true value is 72.5.
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Find the value of x.
130°
(3x + 5)º
Answer:
15 = X . hope this helped
below. a) Which of the boxes has the smaller range of masses? b) What is the value of this range? Give your answer in grams (g). Box A 97653 4 Box A Box B 15 1469 5 6 2 478 39 835 8762 7 Box B Key 35 represents a mass of 53 g 51 represents a mass of 51 g
Box B has the smaller range of masses, with a range of 49 grams, compared to Box A's range of 97,649 grams.
The question asks which of the boxes has the smaller range of masses and what is the value of this range in grams (g).
To find the range, we need to subtract the smallest value from the largest value in each box.
In Box A, the smallest value is 4 and the largest value is 97653. So, the range in Box A is 97653 - 4 = 97649 g.
In Box B, the smallest value is 2 and the largest value is 8762. However, we are given that key 35 represents a mass of 53 g and key 51 represents a mass of 51 g. So, the actual largest value in Box B is 51. Therefore, the range in Box B is 51 - 2 = 49 g.
Comparing the ranges, we can see that the range in Box B (49 g) is smaller than the range in Box A (97649 g).
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Abdul buys dress pants from a clothing company for p dollars. He then sells each pair of pants in his men’s clothing shop at a 40% markup. Select two of the expressions below that represent the new retail price of a pair of dress pants.
1.4p
1p-0.4p
0.6p
1p+0.4p
Answer:the last one
Step-by-step explanation:
helpppppppppppppppppppppppppppp
Answer:
96
Step-by-step explanation:
First we have to see how the pattern is increasing.
How did the sequence of numbers get from -3 to 6?
Try adding first.
To get from -3 to 6, add 9.
Move on to the next nunber.
Can we get from 6 to -12 through the same pattern (adding 9)?
No, so addition is not the pattern.
Next try multiplication.
To get from -3 to 6, multiply -2.
Move on to the next number.
Can we get from 6 to -12 through the same pattern (multiplying by -2)?
Yes!
Check the other numbers.
-12 × -2 = 24
24 × -2 = -48
Do they meet the pattern?
Yes!
To find the next number in the sequence, use the pattern: multiply the previous number by -2.
-48 × -2 = 96
Answer:
36 i think , datsss confusin Asfkkkkkkk
Step-by-step explanation:
Marjane wants to create a set of data with 6 values. She wants the mode to be as good as the median to represent the data set. Which set of data best represents what Marjane could create?
24, 24, 25, 29, 29, 29
24, 25, 26, 27, 30, 30
24, 25, 25, 25, 26, 26
24, 24, 25, 26, 26, 27
As per the median, the set of data that fulfilling Marjane's requirement is 24, 25, 25, 25, 26, 26 (option c).
In statistics, data is a collection of numbers or values that represent a particular phenomenon. One way to measure central tendency, or the typical or representative value of the data, is through the median and the mode.
The median is the middle value when the data is arranged in numerical order, and the mode is the value that appears most frequently.
The third set of data is 24, 25, 25, 25, 26, 26.
The median is the middle value, which is also (25+25)/2 = 25.
The mode is the value that appears most frequently, which is 25.
Therefore, the mode and median are the same, fulfilling Marjane's requirement.
Therefore, the correct option is (c).
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a) What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R= 4.44 mm (round your response to two decimal places). c) What are the UCL, and LCL;
Based on the given data, we can calculate the control limits using 3-sigma for the diameter of the auto pistons.
a) The value of x is 155.56 mm (rounded to two decimal places).
b) The value of R is 4.44 mm (rounded to two decimal places).
c) Using 3-sigma, the Upper Control Limit (UCL) for the diameter is calculated as:
UCL = x + 3R = 155.56 + 34.44 = 156.93 mm (rounded to two decimal places)
The Lower Control Limit (LCL) for the diameter is calculated as:
LCL = x - 3R = 155.56 - 34.44 = 154.19 mm (rounded to two decimal places)
d) Using 3-sigma, the Upper Control Limit for the Range (UCLR) is calculated as:
UCLR = D4 * R = 2.115 * 4.44 = 7.89 mm (rounded to two decimal places)
The Lower Control Limit for the Range (LCLR) is always 0 in this case since negative ranges are not possible.
e) If the true diameter mean should be 155 mm, the new centerline (nominal line) would be 155 mm. In this case, the UCL and LCL would be calculated using 3-sigma as follows:
UCL = Nominal + 3R = 155 + 34.44 = 156.37 mm (rounded to two decimal places)
LCL = Nominal - 3R = 155 - 34.44 = 153.63 mm (rounded to two decimal places)
Please note that the control limits calculated using 3-sigma assume a normal distribution and the data follows the same pattern in the future.
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The complete question is:
What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R= 4.44 mm (round your response to two decimal places). c) What are the UCL, and LCL; using 3-sigma? Upper Control Limit (UCL) = 156.93 mm (round your response to two decimal places). Lower Control Limit (LCL) = 154.19 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)= 7.89 mm (round your response to two decimal places). Lower Control Limit (LCLR)= 0.99 mm (round your response to two decimal places). e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL and LCL? Upper Control Limit (UCL)= 156.37 mm (round your response to two decimal places). Lower Control Limit (LCL;)= 153.63 mm (round your response to two decimal places). Refer to Table 56.1-Factors for Computing Control Chart Limits (3 sigma) for this problem Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day 1 2 3 4 5 Mean x (mm) 150.9 153.2 153.6 153.5 154.6 Range R (mm) 4.0 4.8 4.1 4.8 4.5
Estimate the unit rate.
178 students in 7 classes
Answer:
25.4 students in each class
Step-by-step explanation:
178/7 = 25.4285714286 rounded up to 25.4
Help with these 2 pls!
Answer:
2: option four
3: option four
Step-by-step explanation:
they are both option four
using the following data, state the errors in the box-and-whisker plot. 33, 27, 6, 34, 31, 59, 26, 1, 30
In order to find out the errors made in the data plot, we have to determine what the five-number summary of the data set that should be displayed by the box plot should be.
How to illustrate the informationFirstly, order the data set given:
1, 6, 26, 27, 30, 31, 33, 34, 59
The five-number summary are:
1. Min value = 1
2. Max value = 59
3. Median = 30
1, 6, 26, 27, (30),31, 33, 34, 59
4. Q1 = (26+6) ÷ 2 = 16
1, [6, 26], 27, (30), 31, 33, 34, 59
5. Q3 = (33+34) ÷ 2 = 33.5
1, 6, 26, 27, (30), 31, [33, 34], 59
The errors in the box and whisker plot are:
1. The min value was displayed as 0 instead of 1.
2. The first quartile (Q1) was displayed as 10 instead of 16
3. The third Quartile (Q3) was displayed as 35 instead of 33.5
4. The max value was displayed as 60 instead of 59.
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A baseball league finds that the speeds of pitches are normally distributed,with a mean of 89 mph and a standard deviation of 2.4 mph. One pitch isthrown at a speed of 85.2 mph. What is the Z-score of this pitch? Round youranswer to two decimal places.A. 1.58B. 1.28O C. -1.28OD. -1.58
Answer: D. -1.58
Explanation: The Z-score is calculated by taking the raw score, subtracting the mean, and then dividing by the standard deviation. This gives us (-85.2-89)/2.4 = -1.58
on her desk.
Susan has a box for paperclips
The box is 6 centimeters long, 3 centimeters
wide, and 2 centimeters high. What is the
volume of the box?
Answer:
36 cm³
Step-by-step explanation:
6x3x2 = (36 cm³)
Length x Width x Height
Pulling Apart Wood. Exer- cise 1.46 (page 44) gives the breaking strengths in pounds of 20 pieces of Douglas fir. Lib WOOD a. Give the five-number sum- mary of the distribution of breaking strengths. b. Here is a stemplot of the data rounded to the nearest hundred pounds. The stems are thousands of pounds, and the leaves are hundreds of pounds. 23 O 24 1 25 26 5 27 28 7 29 30 259 31 399 32 33 0237 The stemplot shows that the dis- tribution is skewed to the left. Does the five-number summary 007 of 4707 033677 Moore/Notz, The Basic Practice of Statistics, 9e, © 2021 W. H. Freeman and Company show the skew? Remember that only a graph gives a clear picture of the shape of a distribution.
a. The five-number summary of the distribution of breaking strengths is as follows:Minimum: 2300 pounds, First quartile (Q1): 2525 pounds, Median (Q2): 2750 pounds, Third quartile (Q3): 3125 pounds, Maximum: 3399 pounds
b. The stemplot provided shows that the distribution is skewed to the left.
The stemplot shows a concentration of values on the higher end of the scale (stems 3 and 2) and fewer values on the lower end (stems 0 and 1).
While the five-number summary provides important descriptive statistics about the distribution, such as the minimum, maximum, and quartiles, it does not directly indicate the skewness of the distribution. Skewness refers to the asymmetry in the distribution of the data.
To assess the skewness accurately, a graphical representation, such as a histogram or a box plot, is needed. These visual tools provide a clearer picture of the shape and skewness of the distribution. They allow us to see the frequency distribution of the data and identify any outliers or extreme values that might influence the skewness.
In summary, while the five-number summary provides valuable information about the distribution of breaking strengths, it does not explicitly show the skewness. To assess the skewness accurately, a graph is needed to visualize the distribution and determine the direction and degree of skewness.
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Note the complete question is
An investigator indicates that the power of his test (at a significance of 1%) of a sample mean resulting from his research is 0.87. If n increases, then the power of the test... doubles. increases. decreases. stays the same.
As the sample size (n) increases, the power of the statistical test also increases.
The power of a statistical test measures the ability of the test to detect a true effect or reject a false null hypothesis. In this case, the investigator states that the power of his test at a significance level of 1% is 0.87. If the sample size (n) increases, the power of the test increases.
Increasing the sample size generally leads to an increase in the power of a statistical test. This is because a larger sample size provides more information and reduces the variability in the data. With a larger sample size, the test has a greater chance of detecting a true effect and rejecting the null hypothesis when it is false. Consequently, the power of the test increases.
In summary, as the sample size (n) increases, the power of the statistical test also increases. This is because a larger sample size enhances the test's ability to detect true effects and reject false null hypotheses, resulting in higher statistical power. Therefore, in this scenario, increasing the sample size would lead to an increase in the power of the test.
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Find the missing side lengths.
Can someone help me?
9514 1404 393
Answer:
m = n = 5√2
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Sin = Opposite/Hypotenuse
sin(45°) = m/10
m = 10·sin(45°) = 10·(√2)/2 = 5√2
The triangle is isosceles, so m = n.
n = m = 5√2
_____
The side ratios of an isosceles right triangle are 1 : 1 : √2. That is, the legs are 10/√2 = 5√2 in this triangle. It can be useful to remember these ratios for this "special" triangle.
What is the positive solution to the equation 0 = –x2 2x 1? quadratic formula: x = startfraction negative b plus or minus startroot b squared minus 4 a c endroot over 2 a endfraction –2 startroot 2 endroot 2 – startroot 2 endroot 1 startroot 2 endroot –1 startroot 2 endroot
The positive solution of the quadratic equation \(\rm 0=-x^2+2x+1\) is x=2.41
It is given that the quadratic equation:
\(\rm 0=-x^2+2x+1\)
It is required to find the solution to the above quadratic equation.
What is a quadratic equation?A quadratic equation is a second-degree algebraic equation represented by the:
\(\rm ax^2+bx+c=0\)........(1)
Where a, b, and c are the constants and \(\rm a\neq 0\)
We know that:
\(\rm x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)
We have:
\(\rm 0=-x^2+2x+1\\\rm or \\\rm -x^2+2x+1=0\) ..........(2)
After comparing (1) and (2) we get:
\(\rm a=-1, b=2, and \ c=1\)
Put these values in the above formula we get:
\(\rm x=\frac{-2\pm \sqrt{2^2-(4)(-1)(1)}}{(2)(-1)}\\\rm x=\frac{-2\pm \sqrt{8}}{-2}\\\rm x=\frac{-2\pm 2\sqrt{2 }}{-2}\\\rm x={1\pm \sqrt{2}}\)
\(\rm x=1+\sqrt{2} \ or \ x=1-\sqrt{2} \\\\\sqrt{2} = 1.41\\\rm so \ x= 1+1.41 \ or \ x= 1-1.41\\\rm x=2.41 or \ x=-0.41\)
Thus, the positive solution of the quadratic equation is x=2.41
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Answer:
x= 2.41
Step-by-step explanation:
Lyla is rounding some numbers to the nearest tenth. Select the number that will have an 8 in the tenths place after rounding.
A. 5.74
B. 6.08
C. 7.79
D. 8.86
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
if u round 7.79 it will be 8 because 7 is greater than 5
Rewrite 48 + 60 using the distributive property
Answer:
12* ( 4+5)
Step-by-step explanation:
48 = 12 * 4
60 = 12 * 5
48 + 60 = 12*4 + 12*5
= 12*( 4 + 5)
= 12* 9
= 108
. Find the transfer function G(s)=Y(s)/R(s) for each of the following systems represented in state space: [Section: 3.6] a.
x
˙
=
⎣
⎡
0
0
−3
1
0
−2
0
1
−5
⎦
⎤
x+
⎣
⎡
0
0
10
⎦
⎤
r y=[
1
0
0
]x
x
˙
=
⎣
⎡
2
0
−3
−3
5
−5
−8
3
−4
⎦
⎤
x+
⎣
⎡
1
4
6
⎦
⎤
r y=[
1
3
6
]x c.
x
˙
=
⎣
⎡
3
1
−3
−5
−8
−6
2
7
2
⎦
⎤
x+
⎣
⎡
5
−3
2
⎦
⎤
r y=
The transfer functions for the given systems represented in state space are: a. G(s) = (s+5)/(s²+ s - 10), b. G(s) = (3s² - 13s + 2)/(s³ - 3s² + 4s + 10) and c. G(s) = (7s² - 10s + 24)/(s³ + 9s²+ 28s + 20)
To find the transfer function G(s) = Y(s)/R(s) for each of the given systems represented in state space, we can use the formula:
G(s) = C(sI - A)^-1B + D
where A, B, C, and D are matrices obtained from the given state space representation. Let's find the transfer function for each system:
a. Given state space representation:
x = [ 0 0 -3 ] x + [ 0 ] r
[ 1 0 -2 ] [ 0 ]
[ 0 1 -5 ] [ 0 ]
Output equation: y = [ 1 0 0 ] x
To find the transfer function, we need to calculate the matrices A, B, C, and D.
A = [ 0 0 -3 ]
[ 1 0 -2 ]
[ 0 1 -5 ]
B = [ 0 ]
[ 0 ]
[ 0 ]
C = [ 1 0 0 ]
D = [ 0 ]
Now, we can substitute these matrices into the transfer function formula:
G(s) = C(sI - A)^-1B + D
Calculating (sI - A):
sI - A = [ s 0 0 ] - [ 0 0 -3 ] = [ s 0 3 ]
[ 0 s 0 ] [ 1 0 -2 ] [ -1 s 2 ]
[ 0 0 s ] [ 0 1 -5 ] [ 0 -1 s+5 ]
Calculating (sI - A)^-1:
(sI - A)^-1 = [ (s+5)/(s² + s - 10) 3/(s² + s - 10) 3/(s+ s² - 10) ]
[ (-1)/(s² + s - 10) s/(s² + s - 10) 2/(s² + s - 10) ]
[ 0 -1/(s² + s - 10) (s+5)/(s² + s - 10) ]
Calculating C(sI - A)^-1B:
C(sI - A)^-1B = [ 1 0 0 ] [ (s+5)/(s²+ s - 10) 3/(s²+ s - 10) 3/(s²+ s - 10) ] [ 0 ] = (s+5)/(s²+ s - 10)
Finally, adding D:
G(s) = (s+5)/(s² + s - 10) + 0 = (s+5)/(s²+ s - 10)
b. Given state space representation:
x = [ 2 0 -3 ] x + [ 1 ] r
[ -3 5 -5 ] [ 4 ]
[ -8 3 -4 ] [ 6 ]
Output equation: y = [ 1 3 6 ] x
Following the same steps as above, we find:
A = [ 2 0 -3 ]
[ -3 5 -5 ]
[ -8 3 -4 ]
B = [ 1 ]
[ 4 ]
[ 6 ]
C = [ 1 3 6 ]
D = [ 0 ]
Calculating (sI - A):
sI - A = [ s-2 0 3 ]
[ 3 s-5 5 ]
[ 8 -3 s+4 ]
Calculating (sI - A)^-1:
(sI - A)^-1 = [ (s+5)/(s³ 3s² + 4s + 10) 3/(s³ - 3s² + 4s + 10) 3/(s³ - 3s²+ 4s + 10) ]
[ (-3)/(s³ - 3s² + 4s + 10) (s+2)/(s³ - 3s²+ 4s + 10) 5/(s³ - 3s²+ 4s + 10) ]
[ 8/(s³- 3s²+ 4s + 10) -3/(s^3 - 3s² + 4s + 10) (s-5)/(s³ - 3s² + 4s + 10) ]
Calculating C(sI - A)^-1B:
C(sI - A)^-1B = [ 1 3 6 ] [ (s+5)/(s³- 3s² + 4s + 10) 3/(s³ - 3s² + 4s + 10) 3/(s³ - 3s² + 4s + 10) ] [ 1 ] = (3s² - 13s + 2)/(s³ - 3s² + 4s + 10)
Finally, adding D:
G(s) = (3s² - 13s + 2)/(s³ - 3s² + 4s + 10) + 0 = (3s² - 13s + 2)/(s³- 3s²+ 4s + 10)
c. Given state space representation:
x = [ 3 1 -3 ] x + [ 5 ] r
[ -5 -8 -6 ] [ -3 ]
[ 2 7 2 ] [ 2 ]
Output equation: y = [ 0 5 2 ] x
Following the same steps as above, we find:
A = [ 3 1 -3 ]
[ -5 -8 -6 ]
[ 2 7 2 ]
B = [ 5 ]
[ -3 ]
[ 2 ]
C = [ 0 5 2 ]
D = [ 0 ]
Calculating (sI - A):
sI - A = [ s-3 -1 3 ]
[ 5 s+8 6 ]
[ -2 -7 s-2 ]
Calculating (sI - A)^-1:
(sI - A)^-1 = [ (s² - 6s + 9)/(s³ + 9s² + 28s + 20) (-s+2)/(s³ + 9s² + 28s + 20) (-3)/(s^3 + 9s² + 28s + 20) ]
[ (-5)/(s³+ 9s² + 28s + 20) (s²- 10s + 4)/(s³ + 9s² + 28s + 20) (-6)/(s³ + 9s² + 28s + 20) ]
[ (2)/(s³+ 9s² + 28s + 20) (7)/(s³+ 9s² + 28s + 20) (s² - 8s + 6)/(s³+ 9s² + 28s + 20) ]
Calculating C(sI - A)^-1B:
C(sI - A)^-1B = [ 0 5 2 ] [ (s- 6²s + 9)/(s³ + 9s² + 28s + 20) (-s+2)/(s³ + 9s² + 28s + 20) (-3)/(s³ + 9s² + 28s + 20) ] [ 5 ] = (7s² - 10s + 24)/(s³+ 9s² + 28s + 20)
Finally, adding D:
G(s) = (7s² - 10s + 24)/(s³ + 9s² + 28s + 20) + 0 = (7s²- 10s + 24)/(s³ + 9s²+ 28s + 20)
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compute the surface area of revolution of y=4x 3y=4x 3 about the x-axis over the interval [4,5][4,5].
The surface area of revolution of y = 4\(x^3\) about the x-axis over the interval [4, 5] is approximately 806.259 square units.
To find the surface area of revolution of the curve y = 4\(x^3\) about the x-axis over the interval [4, 5], we can use the formula:
S = 2π ∫ [a,b] y √(1 + \((dy/dx)^2\)) dx
where a = 4, b = 5, and dy/dx = 12\(x^2\).
Substituting these values, we get:
S = 2π ∫[4,5] 4x \(\sqrt{(1 + (12x^2)^2)}\) dx
Simplifying the expression inside the square root:
1 + \((12x^2)^2\) = 1 + 144\(x^4\)
= 144\(x^4\) + 1
The integral becomes:
S = 2π ∫[4,5] 4x √(144\(x^4\) + 1) dx
To evaluate this integral, we can make the substitution u = 144\(x^4\) + 1. Then, du/dx = 576\(x^3\), and dx = du/576\(x^3\).
Substituting these values, we get:
S = 2π ∫[577, 11521] 4x √u du / (576x^3)
Simplifying:
S = π/36 ∫[577, 11521] √u du
S = π/36 x (2/3) x \((11521^{(3/2)} - 577^{(3/2)})\)
S = π/54 x \((11521^{(3/2)} - 577^{(3/2)})\)
Using a calculator, we can approximate this value to be:
S ≈ 806.259
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(a) If log4x=5, then x= (b) If log6x=8, then x=
(a)If log₄x = 5, the base is 4 and the logarithm is 5 , then x = 1024. (b) If log₆x = 8 the base is 6 and the logarithm is 8 then x = 1679616.
(a) In the equation log₄x = 5, the base is 4 and the logarithm is 5. To solve for x, we need to rewrite the equation in exponential form. In exponential form, 4 raised to the power of 5 is equal to x. Therefore, x = 4^5 = 1024.
(b) In the equation log₆x = 8, the base is 6 and the logarithm is 8. Rewriting the equation in exponential form, 6 raised to the power of 8 is equal to x. Hence, x = 6^8 = 1679616.
In both cases, we used the property of logarithms that states: if logₐx = y, then a raised to the power of y equals x. By applying this property, we can convert the logarithmic equations into exponential form and find the values of x.
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f(x) = x^4-8x^2. enter thr critical points in increasing order. use
the derative to find all critical points.
x1=
x2=
x3=
use a graph to classify each critical point as a local maximum
or neither
In summary, the critical points in increasing order are:
x1 = -2
x2 = 0
x3 = 2
To find the critical points of the function f(x) = x^4 - 8x^2, we need to find the values of x where the derivative of f(x) is equal to zero or undefined.
First, let's find the derivative of f(x) with respect to x:
f'(x) = 4x^3 - 16x
To find the critical points, we set the derivative equal to zero and solve for x:
4x^3 - 16x = 0
Factoring out 4x, we have:
4x(x^2 - 4) = 0
Setting each factor equal to zero, we get:
4x = 0 --> x = 0
x^2 - 4 = 0 --> x^2 = 4 --> x = ±2
So, the critical points are:
x1 = -2
x2 = 0
x3 = 2
To determine the nature of these critical points, we can use the second derivative test or examine the behavior of the function around each critical point.
Taking the second derivative of f(x):
f''(x) = 12x^2 - 16
Now we can evaluate the second derivative at each critical point:
f''(-2) = 12(-2)^2 - 16 = 48 - 16 = 32
f''(0) = 12(0)^2 - 16 = -16
f''(2) = 12(2)^2 - 16 = 48 - 16 = 32
Since f''(-2) and f''(2) are both positive, the function has a local minimum at x = -2 and x = 2. Since f''(0) is negative, the function has a local maximum at x = 0.
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Which method do you prefer to use to find sums - count by tens and ones, use compaitble number, or use friendly number and adjust? explain why.
Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.
To find sums, I would prefer to use the method of using compatible numbers and adjusting. The reason behind this is that it can help me to perform mental calculations and solve mathematical problems faster.What are compatible numbers?Compatible numbers are numbers that are close to the actual numbers, but are easier to work with mathematically. They are rounded numbers that make it easier to perform mental math. Once we have the answer, we can adjust it to get the correct answer.To solve an addition problem using compatible numbers, we choose numbers close to the actual numbers in the problem. For example, if we are adding 45 and 32, we can round the numbers to 50 and 30. Then we add 50 and 30 to get 80, which is the compatible number sum. But this is not the actual answer because we rounded the numbers, so we need to adjust. We subtract 5 from 50 and add 3 to 30 to get 45 and 33, respectively. Then we add the adjusted numbers (45 and 33) to get the correct answer, which is 78.Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.
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hElP mE plS anD ty I hAd tO rEpoSt thiS :')
Answer:
1: below its initial height.
2: if Jimmy has 20 balls and Chris take 15,how many balls does Jimmy have?
3: I would want Mrbeast to be the President because he would help everyone.
solve the equation for x. give an exact solution if possible otherwise give an approximation to 3-decimal places.
log2 (3x + 5) = 2
x =
The equation log2(3x + 5) = 2x involves a logarithmic function and an exponential function.
Unfortunately, it does not have an exact algebraic solution that can be expressed in terms of elementary functions. Therefore, we need to use numerical methods to approximate the solution. By employing an iterative numerical technique such as the Newton-Raphson method or using a graphing calculator, we can find an approximate solution to the equation, typically rounded to three decimal places
To solve the equation log2(3x + 5) = 2x, we can start by rearranging the equation to isolate the logarithmic term:
log2(3x + 5) - 2x = 0.
Since there is no algebraic way to solve this equation, we need to resort to numerical methods. One commonly used method is the Newton-Raphson method, which involves making an initial guess and iteratively refining it until a satisfactory solution is obtained.
Alternatively, we can use a graphing calculator to plot the functions y = log2(3x + 5) and y = 2x and find their intersection point. This intersection point will correspond to an approximate solution to the equation.
By employing either of these methods, we can find an approximate solution to the equation log2(3x + 5) = 2x. The solution will be given as an approximation rounded to three decimal places.
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Brendan has $65 worth of balloons and flowers delivered to his mother. He pays the bill plus an 8.5% sales tax and an 18% tip on the total cost
including tax. He also pays a $10 delivery fee that is charged after the tax and tip. How much change does he receive it he pays with two $50
bills ? Round to the nearest cent
Answer:
6.77
Step-by-step explanation:
Answer:
Step-by-step explanation: