Answer:
A. 17 years
Step-by-step explanation:
Use the simple interest equation, I = prt, where I is the interest money gained, p is the starting amount of money, r is the interest rate in decimal form, and t is the time in years.
Plug in the values to solve for t:
417.69 = (630)(0.039)(t)
417.69 = 24.57t
17 = t
= 17 years
So, the correct answer is A, 17 years
Evaluate the expression 8p6
Answer:
Evaluate 8P6 P 6 8 using the formula nPr=n!(n−r)! P r n = n ! ( n - r ) ! . 8!(8−6)! 8 ! ( 8 - 6 ) ! Subtract 6 6 from 8 8 . 8!(2)! 8 ! ( 2 ) ! Simplify 8!(2)! 8 !
Step-by-step explanation:
evaluate" usually means to put a value in for the variable, but you don't give us a value for p. also, it is unclear if you ...
The value of the expression [tex]^8P_6[/tex] is 20160.
What is permutation?A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order.
The value of the expression is calculated as:-
[tex]^8P_6=\dfrac{8!}{8!-6!}=\dfrac{8!}{2!}[/tex]
[tex]^8P_6 =\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2}{2}[/tex]
[tex]^8P_6[/tex] = 20160
Hence, the value is 20160.
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Starting with x1 = 2, find the third approximation x3 to the root of the equation x3 − 2x − 2 = 0.
Answer:
0.8989
Step-by-step explanation:
Using the Newton's Raphson approximation formula.
Xn+1 = Xn - f(Xn)/f'(Xn)
Given f(x) = x³-2x+2
f'(x) = 3x²-2
If the initial value X1 = 2
X2 = X1 - f(X1)/f'(X1)
X2 = 2 - f(2)/f'(2)
f(2) = 2³-2(2)+2
f(2) = 8-4+2
f(2) = 6
f'(2) = 3(2)²-2
f'(2) = 10
X2 = 2- 6/10
X2 = 14/10
X2 = 1.4
X3 = X2 - f(X2)/f'(X2)
X3 = 1.4 - f(1.4)/f'(1.4)
f(1.4) = 1.4³-2(1.4)+2
f(1.4) = 2.744-2.8+2
f(1.4) = 1.944
f'(1.4) = 3(1.4)²-2
f'(1.4) = 3.880
X3 = 1.4- 1.944/3.880
X3 = 1.4 - 0.5010
X3 = 0.8989
Hence the value of X3 is 0.8989
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65. Can the company conclude that the correlation is positive
Complete Question
Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 14 stations last Tuesday, the correlation was 0.65.At the 0.01 significance level Can the company conclude that the correlation is positive
Answer:
Yes the company conclude that the correlation is positive
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The correlation is r = 0.65
The null hypothesis is [tex]H_o : r < 0[/tex]
The alternative hypothesis is [tex]H_1 : r > 0[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]Sr = \sqrt{1- r}[/tex]
[tex]Sr = \sqrt{1- 0.65}[/tex]
[tex]Sr = 0.616[/tex]
The degree of freedom for the one-tail test is
[tex]df = n- 2[/tex]
[tex]df = 14- 2[/tex]
[tex]df = 12[/tex]
The standard error is evaluated as
[tex]SE = \frac{0.616}{ \sqrt{12} }[/tex]
[tex]SE =0.1779[/tex]
The test statistics is evaluated as
[tex]t = \frac{r }{SE}[/tex]
[tex]t = \frac{0.65 }{0.1779}[/tex]
[tex]t = 3.654[/tex]
The p-value of of t is obtained from the z table, the value is
[tex]p-value = P(t < 3.654) = 0.00012909[/tex]
Given that [tex]p-value < \alpha[/tex] then we reject the null hypothesis
Hence the company can conclude that the correlation is positive
what would it be help!
Answer:
35°
Step-by-step explanation:
If BCD is 75, then BCA is 105.
105+40=145
180-145=35
So ABC is 35°
Please answer quick!!!
Find the interquartile range of the data set represented by this box plot.
30
56
20
10
Answer:
A. 30
Step-by-step explanation:
The interquartile range for a box and whiskers plot, is the value from the right side of the box minus the value of the left side of the box.
In this case at the far right side of the box it is at 130, at the far left side of the box it is at 100.
130-100=30
Answer:
[tex]\huge\boxed{IQR = 30}[/tex]
Step-by-step explanation:
Q1 = 130 (Left hand edge of the box)
Q3 = 100 (Right Hand edge of the box)
Interquartile Range = Q3-Q1
IQR = 130-100
IQR = 30
You have two lines. Line A measures 12/16, and line B measures 3/4.
a) Line A is longer
b) The lines are equal.
c) Line B is longer.
Answer:
B
Step-by-step explanation:
Let's compare the two values of 12/16 and 3/4.
Notice that 12/16 isn't a simplified fraction; both the numerator and denominator are divisible by 4. So divide the top and bottom by 4:
12 / 4 = 3
16 / 4 = 4
We are left with:
12/16 = 3/4
Now, we see that Line A and Line B are equal in length, so the answer is B.
~ an aesthetics lover
Find the first term in the sequence when u(subscript)31=197 and d= 10.
Answer:
197 = 10(31-1) + a
197 = 300 + a
-103 = a
What integer is closest to 13/3 divided 2/11 I have been looking at this for while and my brain is going (⊙_◎)
Answer:
24
Step-by-step explanation:
13/3 / 2/11 = 13/3 * 11/2 = 143/6 = 23 and 5/6
23 and 5/6 is closest to 24.
Answer:
23 5/6
Step-by-step explanation:
-10 + 7x + 24 - 2x
Your answer
If the sample size is increased and the standard deviation and confidence level stay the same, then the margin of error will also be increased.
a. True
b. False
False!
The answer is: False.
Whomever stated the answer is "true" is wrong.
is -54 rational number whole number or integersis
Answer:
-54 is a integer and rational number
Step-by-step explanation:
Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. His dad tells him that he can check by using the inequality 2f < 223, where f is the time skied in seconds for each person. Plug the values for the time skied by each person into the inequality to find the answer.
Lori 55
Vanessa 265
Devon 172
Celia 112
Arnold 356
Answer:
Kelvin did not skied without falling more than twice as long as anyone else in his family.
Step-by-step explanation:
The inequality representing the event where Kelvin skied without falling more than twice as long as anyone else in his family is:
[tex]2f<223[/tex]
Here 223 is the time for Kelvin.
Check for Lori as follows:[tex]2f<223[/tex]
[tex]2\times 55=110<223[/tex]
Kelvin skied without falling more than twice as long as Lori.
Check for Vanessa as follows:[tex]2f<223[/tex]
[tex]2\times 265=530>223[/tex]
Kelvin skied without falling less than twice as long as Vanessa.
Check for Devon as follows:[tex]2f<223[/tex]
[tex]2\times 172=344>223[/tex]
Kelvin skied without falling less than twice as long as Devon.
Check for Celia as follows:[tex]2f<223[/tex]
[tex]2\times 112=224>223[/tex]
Kelvin skied without falling less than twice as long as Celia.
Check for Arnold as follows:[tex]2f<223[/tex]
[tex]2\times 356=712>223[/tex]
Kelvin skied without falling less than twice as long as Arnold.
Thus, Kelvin did not skied without falling more than twice as long as anyone else in his family.
Answer:
Yes, Kevin skied 2x as long as Lori.
Step-by-step explanation:
Kevin's time was 223 seconds; Lori's time was 110 seconds.
110^2 = 220 or 110 multiplied by 2 equals 220 or 110 x 2 = 220 or
110 * 2 = 220
Thus, Kevin indeed, skied twice as long as Lori.
2.1x10^8 is how many times the value of 4.2x 10^2
Answer:
500,000
Step-by-step explanation:
(2.1 * 10^8)/(4.2 * 10^2) =
= 2.1/4.2 * 10^8/10^2
= 0.5 * 10^6
= 500,000
The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10².
What is a number system?The number system is a way to represent or express numbers.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
As per the given exponents 2.1 × 10⁸
Let's assume 2.1 × 10⁸ is x times 4.2 × 10².
2.1 × 10⁸ = x (4.2 × 10²)
x = 2.1 × 10⁸/4.2 × 10²
x = 500000
Hence "The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10²".
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A project has an initial cost of $40,000, expected net cash inflows of $10,000 per year for 8 years, and a cost of capital of 14%. What is the project's NPV? (Hint: Begin by constructing a time line.) Do not round intermediate calculations. Round your answer to the nearest cent.
Answer:
50k
Step-by-step explanation:
which rigid transformation would map triangle AQR to triangle AKP
Step-by-step explanation:
A rotation about point A a reflection across the line containing AR a reflection across the line containing AQ a rotation about point R
Answer:
A rotation about point A
Step-by-step explanation:
I am taking the test if it is wrong I will add a comment
IQ tests are scaled so that the mean score in a largepopulation should be μ =100. We suspect that the very-low-birth-weight population has mean score less than100. Infants weiging less than 1500 grams at birth are classed as "very low birth weight". Low birth weight carriesmany risks. One study followed 113 male infants with very low birth weight to adulthood. At age 20, the mean IQ score for these men was (x bar=87.6.) Iq scores vary Normally with standard deviation σ=15. Give a 95% confidence interval for the mean IQ score at age 20 for allvery-low-birth-weight males. Use the four-step process for confidence interval.
Answer:
The 95% confidence interval is [tex]84.83< \mu < 90.37[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 113[/tex]
The sample mean is [tex]\= x = 87.6[/tex]
The standard deviation is [tex]\sigma = 15[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma}{ \sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 15}{ \sqrt{113} }[/tex]
=> [tex]E = 2.77[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]87.6 - 2.77< \mu < 87.6 + 2.77[/tex]
[tex]84.83< \mu < 90.37[/tex]
The mean income per person in the United States is $41,500, and the distribution of incomes follows a normal distribution. A random sample of 10 residents of Wilmington, Delaware, had a mean of $47,500 with a standard deviation of $10,600. At the .01 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?
(a) State the null hypothesis and the alternate hypothesis.
H0: ? ?
H1: ? >
(b) State the decision rule for .01 significance level. (Round your answer to 3 decimal places.)
Reject H0 if t >
(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic
(d) Is there enough evidence to substantiate that residents of Wilmington, Delaware have more income than the national average at the .01 significance level?
Answer:
A) Null Hypothesis; H0: μ = $41,500
Alternative hypothesis; H1: μ > $41,500
B) Reject H0 is t > 2.821433
C) t = 1.79
D) there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average
Step-by-step explanation:
A) The hypotheses is given as;
Null Hypothesis; H0: μ = $41,500
Alternative hypothesis; H1: μ > $41,500
B) From online t-score calculator attached using significance level of 0.01 and DF = n - 1 = 10 - 1 = 9, we have;
t = 2.821433
Normally, when the absolute value of the t-value is greater than the critical value, we reject the null hypothesis. However, when the absolute value of the t-value is less than the critical value, we fail to reject the null hypothesis.
Thus, if t > 2.821433, we will reject the null hypothesis H0.
C) Formula for the test statistic is;
t = (x' - μ)/(s/√n)
We have, μ = 41500, x' = 47500, s = 10600, n = 10
t = (47500 - 41500)/(10600/√10)
t = 1.79
D) So, 1.79 is less than the t-critical value of 2.821433. Thus, we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average
Say we decided to expand our study and asked ten more urban homeowners what they pay each month for rent. Assume the sample deviation remains the same. What will happen to our samples standard error
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is C
Step-by-step explanation:
Generally the sample standard error is mathematically represented as
[tex]\sigma_{\= x } = \frac{\sigma }{ \sqrt{n} }[/tex]
Where [tex]\sigma[/tex] is the standard deviation and n is the sample size
Now looking at the formula we see that
[tex]\sigma_{\= x } \ \ \ \alpha \ \ \ \frac{1}{ \sqrt{n} }[/tex]
So at constant [tex]\sigma[/tex] if n increases [tex]\sigma_{\= x }[/tex] decreases
So from the question if ten more urban homeowners are asked the question the samples standard error decreases
Suppose that the director of manufacturing at a clothing factory needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer’s specifications, which indicate that the cloth should have a mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. A sample of 49 pieces reveals a sample mean of 69.1 pounds.
(a) State the null and alternative hypotheses.
(b) Is there evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength? (Use a 0.05 level of significance.)
(c) Compute the p-value and interpret its meaning.
(d) What will your answer be in (b) if the standard deviation is 1.75 pounds?
(e) What will your answer be in (b) if the sample mean is 69 pounds?
Answer:
a.H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test
b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
Step-by-step explanation:
Formulate the null and alternative hypotheses as
a) H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test
Here ∝= 0.005
For alpha by 2 for a two tailed test Z∝/2 = ± 1.96
Standard deviation = s= 3.5 pounds
n= 49
The test statistic used here is
Z = x- x`/ s/√n
Z= 69.1- 70 / 3.5 / √49
Z= -1.80
Since the calculated value of Z= -1.80 falls in the critical region we reject the null hypothesis.
b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
d) If standard deviation is 1.75 pounds
The test statistic used here is
Z = x- x`/ s/√n
Z= 69.1- 70 / 1.75 / √49
Z= -3.6
This value does not fall in the critical region.
d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
e) If the sample mean is 69 pounds
Z = x- x`/ s/√n
Z= 69.1- 69 / 3.5 / √49
Z= 0.2
This value falls in the critical region
e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
The mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days. Suppose that the rain pattern is Normally distributed. what is the probability of raining if the number of days are more than 23?
Answer:
The probability of raining if the number of days is more than 23 is 0.0668.
Step-by-step explanation:
We are given that the mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days.
Let X = Number of days of observing rain in a particular city.
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean number of days = 20 days
[tex]\sigma[/tex] = standard deviation = 2 days
So, X ~ Normal([tex]\mu=20, \sigma^{2} = 2^{2}[/tex])
Now, the probability of raining if the number of days is more than 23 is given by = P(X > 23 days)
P(X > 23 days) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{23-20}{2}[/tex] ) = P(Z > 1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)
= 1 - 0.9332 = 0.0668
The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.
Can someone help??????????
Answer:
(C) 1 and 3
Step-by-step explanation:
Corresponding angles are angles that are at the same corner at the different intersections.
We can see that 1 is on the bottom right corner of the bottom line, now we need to see what angle is at the bottom right corner of the top line?
That's 3.
So 1 and 3 are congruent because they are corresponding.
Hope this helped!
Simplify -(7/x-2)+(2x/x) Simplify your answer as much possible
Answer:
[tex]\dfrac{2x-11}{x-2}[/tex]
Step-by-step explanation:
Simplify the fractions, then add.
[tex]-\dfrac{7}{x-2}+\dfrac{2x}{x}=\dfrac{-7}{x-2}+2=\dfrac{-7}{x-2}+\dfrac{2(x-2)}{x-2}\\\\=\dfrac{2x-4-7}{x-2}=\boxed{\dfrac{2x-11}{x-2}}[/tex]
_____
Note that this comes with the restriction that x ≠ 0.
Ellen baked 115 cookies and shared them equally with her 23 classmates. How many whole cookies each can Ellen and her classmates have?
Step-by-step explanation:
Ellen - 115/23
Classmates and Ellen got = 5 each
3(2+7) - 9 x 7 = 3+8 x 2 x 2 - 4 = 16 ÷ 2 x 5 x 3 ÷ 6 = Please answer! ✨✨
Answer:
At first, we have 3 expressions that are equal.
[tex]3(2+7) - 9 \cdot 7= 3+8 \cdot 2 \cdot 2 - 4[/tex]
[tex]6+21 - 63= 3+32 - 4[/tex]
[tex]-36=31[/tex]
[tex]-36\neq 31[/tex]
This is not true.
In cooking class, Shivani measures a stick
of butter. It is 13 centimeters long, 3
centimeters wide, and 3 centimeters tall. What
is the volume of the stick of butter?
Answer:
117 cm³
Step-by-step explanation:
To find the volume of a rectangular prism, we can simply multiply the length, width and height so the answer is 13 * 3 * 3 = 117 cm³.
Answer:
117 cubic centimeters
Step-by-step explanation:
Assuming that the stick of butter is a perfect rectangular prism, we can calculate the volume by simply multiplying the length, width, and the height as modeled by the volume equation:
V = LWH
For this, the L = 13cm, W = 3cm, and H = 3cm
So our volume in cubic centimeters will be:
V = LWH
V = (13cm) * (3cm) * (3cm)
V = (13cm) * (9cm^2)
V = 117 cm^3
So the volume of the stick of butter is 117 cubic centimeters.
Cheers.
A survey of 500 randomly selected adults found that 57% say that they would take a ride in a fully self-driving car. The 95% confidence interval for the true proportion of all adults who would take a ride in a full self-driving car is found to be (0.5266, 0.6134). Can we conclude that the majority of all adults would take a ride in a fully self-driving car?
Yes; Since the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
No; The data does not include all adults, so we cannot make a conclusion about the population.
No; The confidence interval limits are not large enough to determine that a majority rely only on cellular phones. The proportion would need to be much greater than 50%, and the one above is only slightly larger.
Yes; Since the proportion of adults who said yes is 57%, and this is higher than 50%, we can conclude that a majority would take a ride in a fully self-driving car.
Answer:
Yes; Since the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
Step-by-step explanation:
From the question we are told that
The sample size is n = 500
The sample proportion is [tex]\r p = 0.57[/tex]
The 95% confidence interval is (0.5266, 0.6134)
Looking at the 95% confidence level interval we see that the sample proportion is within the interval and given that the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
THE PRICE OF AN ITEM FROM $10 TO $17. WHAT WAS THE PERCENT INCREASE IN THE PRICE OF THE ITEM?
Answer:
70%
Step-by-step explanation:
The method to find out percentage increase is by subtracting the original price from the increased price and making it into a fractional form with the denominator as 10 (out of 100%). So it results to this.
(original price - increased price) / 10
(17 - 10) / 10 = 7/10
7/10 can be converted from its fractional form to 70% i.e.its percentage.
Hope this helps and please mark as the brainliest.
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
Assume that f(x)=ln(1+x) is the given function and that Pn represents the nth Taylor Polynomial centered at x=0. Find the least integer n for which Pn(0.2) approximates ln(1.2) to within 0.01.
Answer:
the least integer for n is 2
Step-by-step explanation:
We are given;
f(x) = ln(1+x)
centered at x=0
Pn(0.2)
Error < 0.01
We will use the format;
[[Max(f^(n+1) (c))]/(n + 1)!] × 0.2^(n+1) < 0.01
So;
f(x) = ln(1+x)
First derivative: f'(x) = 1/(x + 1) < 0! = 1
2nd derivative: f"(x) = -1/(x + 1)² < 1! = 1
3rd derivative: f"'(x) = 2/(x + 1)³ < 2! = 2
4th derivative: f""(x) = -6/(x + 1)⁴ < 3! = 6
This follows that;
Max|f^(n+1) (c)| < n!
Thus, error is;
(n!/(n + 1)!) × 0.2^(n + 1) < 0.01
This gives;
(1/(n + 1)) × 0.2^(n + 1) < 0.01
Let's try n = 1
(1/(1 + 1)) × 0.2^(1 + 1) = 0.02
This is greater than 0.01 and so it will not work.
Let's try n = 2
(1/(2 + 1)) × 0.2^(2 + 1) = 0.00267
This is less than 0.01.
So,the least integer for n is 2
In this exercise we have to use the knowledge of Taylor Polynomial to calculate the requested function, this way we will have;
the least integer for n is 2
The function given in this exercise corresponds to:
[tex]f(x) = ln(1+x)[/tex]
knowing that the x point will be centered on:
[tex]x=0\\Pn(0,2)\\Error < 0.01[/tex]
By rewriting the equation we have to:
[tex][[Max(f^{(n+1)} (c))]/(n + 1)!] *0.2^{(n+1)} < 0.01[/tex]
So doing the derivatives related to the first function given in the exercise we have to:
[tex]f(x) = ln(1+x)[/tex]
First derivative: [tex]f'(x) = 1/(x + 1) < 0! = 1[/tex] 2nd derivative: [tex]f"(x) = -1/(x + 1)^2 < 1! = 1[/tex] 3rd derivative: [tex]f"'(x) = 2/(x + 1)^3 < 2! = 2[/tex] 4th derivative: [tex]f""(x) = -6/(x + 1)^4 < 3! = 6[/tex]Following this we have to:
[tex]Max|f^{(n+1)} (c)| < n![/tex]
Thus, error is;
[tex](n!/(n + 1)!) * 0.2^{(n + 1)} < 0.01[/tex]
[tex](1/(n + 1))* 0.2^{(n + 1)} < 0.01[/tex]
Let's try n = 1
[tex](1/(1 + 1)) *0.2^{(1 + 1)} = 0.02[/tex]
This is greater than 0.01 and so it will not work. Let's try n = 2
[tex](1/(2 + 1)) * 0.2^{(2 + 1)} = 0.00267[/tex]
This is less than 0.01. So,the least integer for n is 2.
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A plan for a dog park has a grassy section and a sitting section as shown in the figure. Which equation can be used to find the area of the grassy section?
Answer:
[tex]Area=\frac{1}{2} (B\,+\,b)\,h[/tex]
Step-by-step explanation:
The grassy area is that of a trapezoid, so recall the formula for the area of a trapezoid:
[tex]Area=\frac{1}{2} (Base\,+\,base)\,height[/tex]
where:
Base stands for the larger base (in our case the dimension "B" in the attached image)
base stands for the shorter base parallel to the largest Base (in our case the dimension "b" in the attached image)
and
height stands for the distance between bases (in our case the dimension "h" in the attached image.
Therefore the formula for the area of the grassy section becomes:
[tex]Area=\frac{1}{2} (Base\,+\,base)\,height\\Area=\frac{1}{2} (B\,+\,b)\,h[/tex]
Answer:
1/2 (b+b) h
here is the actual picture
