Answer:
12
Step-by-step explanation:
consider the function and then use calculus to answer the questions that follow 1 1/x 5/x^2 1/x^3 (a) Find the interval(s) where the function is concave up. (Enter your answer in interval notation,do not round). (b) Find the interval(s) where the function is concave down. (Enter your answer in intervalnotation, do not round).
Answer:
a)[tex]X=((-15-\sqrt{201},(-15+\sqrt{201}),(0,\infty)[/tex]
b)[tex]Y=(\infty,\frac{1}{2}(-15-\sqrt{201} ) ),(\frac{1}{2}()-15+\sqrt{201)},0 )[/tex]
Step-by-step explanation:
From the question we are told that
The Function
[tex]f(x)=1+\frac{1}{x} +\frac{5}{x^2} +\frac{1}{x^3}[/tex]
Generally the differentiation of function f(x) is mathematically solved as
[tex]f(x)=1+\frac{1}{x} +\frac{5}{x^2} +\frac{1}{x^3}[/tex]
[tex]f(x)=\frac{x^3+x^2+5x+1}{x^2}[/tex]
Therefore
[tex]f'(x)=\frac{x^2+10x+3}{x^4}[/tex]
Generally critical point is given as
[tex]f'(x)=0[/tex]
[tex]\frac{x^2+10x+3}{x^4}=0[/tex]
[tex]x=-5 \pm\sqrt{22}[/tex]
Generally the maximum and minimum x value for critical point is mathematically solved as
[tex]f'(-5 \pm\sqrt{22})[/tex]
Where
Maximum value of x
[tex]f'(-5 +\sqrt{22})<0[/tex]
Minimum value of x
[tex]f'(-5 +\sqrt{22})<0[/tex]
Therefore interval of increase is mathematically given by
[tex]f'(-5 -\sqrt{22}),f'(-5 +\sqrt{22})[/tex]
[tex]f(x)<0,-\infty<x<(f'(-5 -\sqrt{22})) ,(f'(-5 +\sqrt{22}))<x<0,0<x< \infty[/tex]
Therefore interval of decrease is mathematically given by
[tex](-\infty,-5 -\sqrt{22}),f'(-5 +\sqrt{22},0),(0,\infty)[/tex]
Generally the second differentiation of function f(x) is mathematically solved as
[tex]f''(x)=\frac{2(x^2+15x+6)}{x^5}[/tex]
Generally the point of inflection is mathematically solved as
[tex]f''(x)=0[/tex]
[tex]x^2+15x+6=0[/tex]
Therefore inflection points is given as
[tex]x=\frac{1}{2} (-15 \pm \sqrt{201}[/tex]
[tex]f''(x)>0,\frac{1}{2}(-15-\sqrt{201}) <x<\frac{1}{2}(-15-\sqrt{201}) <x<0[/tex]
a)Generally the concave upward interval X is mathematically given as
[tex]X=((-15-\sqrt{201},(-15+\sqrt{201}),(0,\infty)[/tex]
[tex]f''(x)<0,-\infty<x<\frac{1}{2}(-15-\sqrt{201}) , \frac{1}{2}(-15-\sqrt{201}) <x<0[/tex]
b)Generally the concave downward interval Y is mathematically given as
[tex]Y=(\infty,\frac{1}{2}(-15-\sqrt{201} ) ),(\frac{1}{2}()-15+\sqrt{201)},0 )[/tex]
Find the value of x.
The value of x is: A. 38°
Charlotte is a customer-satisfaction expert at a large pizza company. She took a random sample of 1,000
delivery orders and constructed a one-sample z interval to estimate the proportion of delivery orders that take
more than an hour to arrive. She decides to repeat this process, but this time she'll use a sample of 4,000 orders.
Assume that the point estimates from each sample are approximately equal.
What is true about the margins of error from these two samples?
The margin of error from the smaller sample will be about
select ratio v
the margin of error from the
larger sample.
Answer:
2 times
Step-by-step explanation:
Khan Academy
You can use the formula for margin of error and the fact that the point estimates of both the samples are same to calculate the ratio of margin of errors of both the samples.
The margin of error from the smaller sample will be about double of the margin of error from the larger sample.
[tex]MOE_1 = 2 \times MOE_2[/tex]
How to calculate the margin of error for a given sample from a population?Let the level of significance be [tex]\alpha[/tex] and the standard deviation of the population be [tex]\sigma[/tex] and the sample size be n, then we have:
[tex]\text{MOE(Margin of Error)} = Z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
Using the above formula to calculate the margin of errors for two specified samplesFor first sample :
[tex]\text{Sample size} = n_1 = 1000\\\\MOE_1 = Z_{\alpha/2}\dfrac{\sigma}{\sqrt{1000}}[/tex]
For second sample :
[tex]\text{Sample size} = n_1 = 1000\\\\MOE_2 = Z_{\alpha/2}\dfrac{\sigma}{\sqrt{4000}}[/tex]
(since it was given that they have same point estimates, so same standard deviation)
Their ratios are given by
[tex]\dfrac{MOE_2}{MOE_1} = \dfrac{Z_{\alpha/2}\dfrac{\sigma}{\sqrt{4000}}}{Z_{\alpha/2}\dfrac{\sigma}{\sqrt{1000}}} = \sqrt{\dfrac{1000}{4000}} = \dfrac{1}{2}\\\\\\MOE_1 = 2 \times MOE_2[/tex]
Thus,
The margin of error from the smaller sample will be about double of the margin of error from the larger sample.[tex]MOE_1 = 2 \times MOE_2[/tex]
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The Nike store sold 99 Kobe Bryant shirts for $24 each. All money will go to a charity in his name.How much money will be going to a charity?
Answer:
$2376
Step-by-step explanation:
We love you Kobe <3 We love you Gigi
if In x + ln(x – 4) = ln(7x), then x
Answer:
x=11
Step-by-step explanation:
ln rule: ln(ab)=ln(a)+ln(b)
ln(x)+ln(x-4)=ln(7x)
ln(x(x-4))=ln(7x)
x^2-4x=7x
x^2-11x=0
x(x-11)=0
x=0 or x=11
Since ln(x) is undefined when x is less or equal to 0
x=11
Suppose IQ scores were obtained from randomly selected couples. For 20 such pairs of people, the linear correlation coefficient is 0.939 and the equation of the regression line is y = -11 + 1.14x, where x represents the IQ score of the husband. Also, the 20 x values have a mean of 100.9 and the 20 y values have a mean of 100.9. What is the best predicted IQ of the wife, that the husband has an IQ of 100? Use a significance level of 0.05. The best predicted IQ of the wife is ______. (Round to two decimal places as needed.)
Answer:
The wife IQ is 103 when the husband IQ is 100.
Step-by-step explanation:
The given equation of the regression line is y = -11 + 1.14x, where x represents the IQ score of the husband.
If the husband IQ is 100 the the wife IQ is
y = -11 + 1.14x,
y = -11 + 1.14(100)
y = -11 + 114
y = 103
9) Maya has completed 35% of her math test. She answered 14 questions. 6 points
How many questions are on the test? *
9514 1404 393
Answer:
40
Step-by-step explanation:
If the number of questions on the test is Q, then we have ...
35% × Q = 14
Dividing by the coefficient of Q gives ...
Q = 14/0.35 = 40
There are 40 questions on the test.
Starmax is showing the same movie in three theaters. In theater A, 36 of 60 seats are taken. In theater B, 81 seats are taken and 9 are empty. In theater C, 12 of 80seats are empty which theater has the greatest percent of the seats taken?
Answer:
Theater B.
Step-by-step explanation:
Find out each theatre's percentage of seats taken.
Theater A =
100% = 60
1% = 60 ÷ 100 = 0.60
36 ÷ 0.60 = 60% of the seats taken.
Theater B =
81 + 9 = 90
100% = 90
1% = 90 ÷ 100 = 0.90
81 ÷ 0.90 = 90%
Theater C =
100% = 80
1% = 80 ÷ 100 = 0.80
80 - 12 = 68
68 ÷ 0.80 = 85%
Theater B have the greatest percentage of seats taken out of all 3.
I’ll give points + brainalist for correct answer (:
Answer:
C) 2
Step-by-step explanation:
Emma: Range = 8
Arianna: Range = 6
The difference in the range is 2 (8-6)
Answer:
C) 2
Step-by-step explanation:
Emma:
Max = 20
Min = 12
Range = 20 - 12
Range = 8
Arianna:
Max = 18
Min = 12
Range = 18 - 12
Range = 6
Difference between the 2 ranges:
8 - 6 = 2
A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounces. If a sample of 9 cups is selected, find the probability that the mean of the sample will be less than 12.1 ounces.
Answer:
0.9332 = 93.32% probability that the mean of the sample will be less than 12.1 ounces.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 12 ounces and a standard deviation of 0.2 ounces.
This means that [tex]\mu = 12, \sigma = 0.2[/tex]
Sample of 9:
This means that [tex]n = 9, s = \frac{0.2}{\sqrt{9}}[/tex]
Find the probability that the mean of the sample will be less than 12.1 ounces.
This is the pvalue of Z when X = 12.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{12.1 - 12}{\frac{0.2}{\sqrt{9}}}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a pvalue of 0.9332
0.9332 = 93.32% probability that the mean of the sample will be less than 12.1 ounces.
solve for x please help besties!!
Answer:
if 2 means multiply by 2, the answer would be 12. If it just is there as a hint then the answer is 24.
Step-by-step explanation:
Hope this helps!
The American Community Survey (ACS), part of the United States Census Bureau, conducts a yearly census similar to the one taken every ten years, but with a smaller percentage of participants. The most recent survey estimates with 90% confidence that the mean household income in the U.S. falls between $69,720 and $69,922. Find the point estimate for mean U.S. household income and the error bound for mean U.S. household income.
Answer:
The point estimate used was of $69,821.
The error bound is of $101.
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The error bound is half the difference between these two values.
In this question:
90% confidence that the mean household income in the U.S. falls between $69,720 and $69,922.
Point estimate:
(69720+69922)/2 = 69821
The point estimate used was of $69,821.
Error bound:
(69922 - 69720)/2 = 101
The error bound is of $101.
What is the answer to: 20 - 6x = 4x -15 = ?
Answer:
20 - 6x = 4x - 15
35 - 6x = 4x
35 = 2x
x = 15.5
The solution to the equation 20 - 6x = 4x -15 is x = 3.5.
To solve the equation 20 - 6x = 4x - 15,
20 - 6x = 4x - 15
To isolate the variable terms on one side, add 6x to both sides:
20 - 6x + 6x = 4x - 15 + 6x
20 = 10x - 15
Next, add 15 to both sides to further isolate the variable term:
20 + 15 = 10x - 15 + 15
35 = 10x
Finally, divide both sides by 10 to solve for x:
35/10 = 10x/10
3.5 = x
Therefore, the solution to the equation is x = 3.5.
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What is m∠1 in this ixl
Answer:
m<1 = 137
Step-by-step explanation:
Exterior angles thm:
41 + 96 = m<1
m<1 = 137
Factor Зу2 - 4у.
y(4 - Зу)
y(Зу - 4)
y(4y-3)
Telephone Company Project
PLZ ANSWER FAST I HAVE TIME LIMIT Find exact values for all the solutions to the equation tan theta= - sqrt3/3 for, -2[tex]\pi[/tex] [tex]\leq[/tex] theta[tex]\leq[/tex] 2[tex]\pi[/tex]
Answer:90
Step-by-step explanation:
Find the properties of each Quadratic Function
Answer:
1.) up
2.) (-2,-5)
3.) x = -2
4.) (-2,-5)
5.) y = -5
6.) -∞ < x < ∞
7.) -5 < y < ∞
8.) (0,0)
9.) (0,0) and (-4,0)
10.) two solutions
Step-by-step explanation:
1.) because the parabola opens upward and the vertex is down
2.) the lowest point of the parabola is (-2,-5)
3.) If a line was drawn through the point x = -2, the two halves of the parabola would look symmetrical ( the same on both sides).
4.) The minimum point on the graph is ( -2,-5), because that is the lowest point on this upward parabola, and we can not determine the maximum.
5.) The minimum value of y is y = -5, because that is the lowest value of y on this graph, and we can not determine the maximum.
6.) Because the arms of the parabola continue traveling through negative infinity and positive infinity on the x-axis, the domain is -∞ < x < ∞.
7.) The arms of the parabola go from y = -5 to infinity, so the range of the parabola is -5 < y < ∞.
8.) The parabola first crosses the y-axis at the point (0,0)
9.) The parabola first crosses the x-axis at the points (0,0) and (-4,0)
10,) The solution to the parabola is the variable x. The solutions (x intercepts) of the parabola are x = 0 and x = -4.
Does this help you?
a 300 gallon tank is initially full and water is being drained at a rate of 4 gallons per minute.
does the intercept involving time have any physical meaning in this problem? explain
Answer:
Yes, it's when the tank is out of water.
Step-by-step explanation:
Help me with this question
In the diagram, the measures of 1 and 4 are 100. The measure of 5 and 8 are 110. Are lines C and D parallel
B on Ap3x.............
Answer:
B
Step-by-step explanation:
PLEASE HELP!!!
A)
B)
C)
D)
Answer:
b i think
Step-by-step explanation:
Solve for x to the nearest degree.
Answer:
Using Pythagoras Theorem, squareroot 15^2 - 5^2.
After you found the opposite length, use the cosine rule to find angle x.
Translate to a quadratic equation, then solve using the quadratic formula.
A positive integer squared plus 5 times its consecutive integer is equal to 11. Find the integers.
Answer:
The integer is 1
Step-by-step explanation:
Required
Translate and solve
Let the positive integer be x.
So, we have;
The square of the integer is: x^2
Plus 5 times its consecutive integer is: x^2 + 5(x + 1)
Equals 11 is: x^2 + 5(x + 1) = 11
So, we have:
[tex]x^2 + 5(x + 1) = 11[/tex]
Open bracket
[tex]x^2 + 5x + 5= 11[/tex]
Subtract 11 from both sides
[tex]x^2 + 5x -6= 0[/tex]
Expand
[tex]x^2 + 6x - x-6= 0[/tex]
Factorize:
[tex]x(x + 6) - 1(x+6)= 0[/tex]
Factor out x + 6
[tex](x - 1) (x+6)= 0[/tex]
Split
[tex]x - 1 = 0\ or\ x + 6 = 0[/tex]
Solve for x in both cases
[tex]x = 1\ or\ x = -6[/tex]
Since the number is positive, then [tex]x = 1[/tex]
What is a 7 - 0.9 = *
Answer: 6.1
Step-by-step explanation:
Answer:
6.1
Step-by-step explanation:
have a good day/night may i please have a branlliest
So I tried everything I could but I still don’t know
Step-by-step explanation:
app it's a standard 30 60 90 triangle. there are rules for this.
x = 3
y = 6
ZABC and ZQRS are supplementary angles.
If the measure of ZABC = 100°. what is the
measure of ZQRS?
mZQRS = [?]°
The measure of other supplementary angle where one angle is 100° is 80°
In the above question, it is given that two angles are supplementary angles and,
Two angles are said to be supplementary angles if their sum is 180 degrees.
We have,
The measure of one angle is = 100°
Let the angle which needs to be find as ∠x
That means, we need to find the measure of ∠x
So, according to the supplementary angles property,
100° + ∠x = 180°
∠x = 180 - 100
∠x = 80°
Hence, the measure of other supplementary angle where one angle is 100° is 80°
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Determine if the following relations are functions. If they are functions, also state the domain and range.
Answer:
desculpa mas eu não sei a resposta mais eu vou ver se posso te ajudar taaa
The Cramer's Rule states that, in a system of equation in two unknowns, in which determinants D is not 0, X=_____and Y=_____.
Answer:
Step-by-step explanation:
[tex]x=\frac{D_{1}}{D} \\y=\frac{D_{2}}{D}[/tex]
Michael is debating the two job offers below. Determine which will result in a higher income.
OFFER A
$34,500 ANNUALLY
OFFER B
$2,885 MONTHLY
B
Step-by-step explanation:
In a year, offer B would be more. Since annually is once a year and there are 12 months in a year, multiplying B by 12 would get each to a year.