I think the given series is
[tex]\displaystyle\sum_{n=2}^\infty \frac{n^2}{n^3+1}[/tex]
You can use the integral test because the summand is clearly positive and decreasing. Then
[tex]\displaystyle\sum_{n=2}^\infty\frac{n^2}{n^3+1} > \int_2^\infty\frac{x^2}{x^3+1}\,\mathrm dx[/tex]
Substitute u = x ³ + 1 and du = 3x ² dx, so the integral becomes
[tex]\displaystyle \int_2^\infty\frac{x^2}{x^3+1}\,\mathrm dx = \frac13\int_9^\infty\frac{\mathrm du}u = \frac13\ln(u)\bigg|_{u=9}^{u\to\infty}[/tex]
As u approaches infinity, we have ln(u) also approaching infinity (whereas 1/3 ln(9) is finite), so the integral and hence the sum diverges.
Evaluate the expression when x = 12/7
The value of the expression when x equals is ???
PLEASE HELP!!
Answer:
82
Step-by-step explanation:
1/3( x+9/7) + 3^4
Let x = 12/7
1/3( 12/7+9/7) + 3^4
PEMDAS says parentheses first
1/3( 21/7) + 3^4
1/3(3) +3^4
Then exponents
1/3(3)+81
Then multiply
1+81
82
At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 1997, a simple random sample of 100 entering freshmen found that only 10 finished in the bottom third of their high school class. Let p 1 and p 2 be the proportions of all entering freshmen in 1993 and 1997, respectively, who graduated in the bottom third of their high school class. What is a 90% plus four confidence interval for p 1 – p 2?
Answer:
The 90% confidence interval for the difference of proportions is (0.01775,0.18225).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
p1 -> 1993
20 out of 100, so:
[tex]p_1 = \frac{20}{100} = 0.2[/tex]
[tex]s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
p2 -> 1997
10 out of 100, so:
[tex]p_2 = \frac{10}{100} = 0.1[/tex]
[tex]s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
Distribution of p1 – p2:
[tex]p = p_1 - p_2 = 0.2 - 0.1 = 0.1[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05[/tex]
Confidence interval:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.1 - 1.645*0.05 = 0.01775 [/tex]
The upper bound of the interval is:
[tex]p + zs = 0.1 + 1.645*0.05 = 0.18225 [/tex]
The 90% confidence interval for the difference of proportions is (0.01775,0.18225).
The volume of the triangular prism is 54 cubic units.
What is the value of x?
5
9
4
3
Answer: the answer is 3
Step-by-step explanation:
I just took the test
(x2 + 3x + 1) + (2x2 + 2x)
HINT
Answer:
3x^2+5x+1
Step-by-step explanation:
(x^2 + 3x + 1) + (2x^2 + 2x)
Combine like terms
x^2 + 2x^2 + 3x +2x +1
3x^2+5x+1
Answer:
[tex]3x^{2} + 5x + 1[/tex]
Step-by-step explanation:
Step 1: Combine like terms
[tex](x^{2} + 3x + 1) + (2x^{2} + 2x)[/tex]
[tex](x^{2} + 2x^{2} + (3x + 2x) + (1)[/tex]
[tex]3x^{2} + 5x + 1[/tex]
Answer: [tex]3x^{2} + 5x + 1[/tex]
Find the minimum sample size needed to be 99% confident that the sample's variance is within 30% of the population's variance.
The Minimum sample size table is attached below
Answer:
[tex]X=173[/tex]
Step-by-step explanation:
From the question we are told that:
Confidence Interval [tex]CI=99\%[/tex]
Variance [tex]\sigma^2=30\%[/tex]
Generally going through the table the
Minimum sample size is
[tex]X=173[/tex]
find the composition of transformations that map ABCD to EHGF.
Reflect over the (y) -axis then translate
(x+?,y+?)
9514 1404 393
Answer:
(x, y) ⇒ (x +(-1), y +(-1))
Step-by-step explanation:
Reflection over the y-axis is the transformation ...
(x, y) ⇒ (-x, y)
After that reflection, the figure is translated left 1 and down 1. That transformation is ...
(x, y) ⇒ (x -1, y -1)
_____
Additional comment
The composition of the two transformations is ...
(x, y) ⇒( -x -1, y -1)
Answer: x-1, y-1
Step-by-step explanation:
Which choices are equivalent to the quotient below? Check All That Apply.
Answer:
Option C. √5/3
Step-by-step explanation:
We'll begin by simplifying √15 / 3√3. This can be obtained as follow:
√15 / 3√3
Rationalise
√15 / 3√3 × (√3 /√3)
(√15 × √3) / (3√3 × √3)
√45 / (3 × 3)
√45 / 9
Recall:
√45 = √(9 × 5) = √9 × √5 = 3√5
Thus,
√45 / 9 = 3√5 / 9
√45 / 9 = √5 / 3
Therefore,
√15 / 3√3 = √5 / 3
Thus, option C gives the right answer to the question.
A bag of 31 tulip bulbs contains 13 red tulip bulbs, 9 yellow tulip bulbs, and 9 purple tulip bulbs. Suppose two tulip bulbs are randomly selected without replacement from the bag. (a) What is the probability that the two randomly selected tulip bulbs are both red? (b) What is the probability that the first bulb selected is red and the second yellow? (c) What is the probability that the first bulb selected is yellow and the second red? (d) What is the probability that one bulb is red and the other yellow?
Answer:
36% on first
Step-by-step explanation:
Find the area of each figure one of the sides are 8.3cm it’s a square btw
Answer:
68.89 cm
Step-by-step explanation:
8.3 X 8.3 would equal 68.89 cm. We can see that one side is 8.3 cm, and the other sides don't say their sides, so the only number we will use for multiplying is 8.3, and all sides of the square will be 8.3. The equation is L X W, where L is the length, and W is the width. Since 8.3 is on all four sides, it will also be the length and the width on the equation. As a result, 68.89 cm would be the final answer.
Answer:
I don't real know if this is right, but I think its this:
68.89 cm2 is the area.
Answer pleaseeeeeeeeee
Answer:
[tex]y=-\frac{8}{7}x+4[/tex]
Step-by-step explanation:
A line is perpendicular to another if its slope is the negative reciprocal of the other.
Your lines are in slope intercept form here, y=mx+b, where m is the slope. We can see the given line has slope [tex]\frac{7}{8}[/tex]. The negative reciprocal of that is [tex]-\frac{8}{7}[/tex], which is the slope of the third answer choice.
for 0 degrees ≤ x < 360 degrees , what are the solutions to sin (x/2) + cos(x) - 1 =0
Recall the double angle identity for cosine:
cos(x) = cos(2×x/2) = 1 - 2 sin²(x/2)
Then the equation can be rewritten as
sin(x/2) + (1 - 2 sin²(x/2)) - 1 = 0
sin(x/2) - 2 sin²(x/2) = 0
sin(x/2) (1 - 2 sin(x/2)) = 0
sin(x/2) = 0 or 1 - 2 sin(x/2) = 0
sin(x/2) = 0 or sin(x/2) = 1/2
[x/2 = arcsin(0) + 360n ° or x/2 = 180° - arcsin(0) + 360n °]
… … or [x/2 = arcsin(1/2) + 360n ° or x/2 = 180° - arcsin(1/2) + 360n °]
x/2 = 360n ° or x/2 = 180° + 360n °
… … or x/2 = 30° + 360n ° or x/2 = 150° + 360n °
x = 720n ° or x = 360° + 720n °
… … or x = 60° + 720n ° or x = 300° + 720n °
(where n is any integer)
We get only three solutions in 0° ≤ x < 360° :
720×0° = 0°
60° + 720×0° = 60°
300° + 720×0° = 300°
Answer:
B: (0, 60, 300)
Step-by-step explanation:
right on edge
Tìm thể tích của khối bao bởi mặt z=5+(x−4)^2+2y và mặt x=3,y=4 và mặt phẳng tọa độ.
Step-by-step explanation:
ccxiddidificifificici i i ivi i i i i i i i iivvii iix9difi
2. Approximately what is the ratio of customers
from Zone 1 to customers from Zone 3?
UA. 3:5
B. 3:2
OÇ. 2:1
D. 1:2
The ratio of customers from Zone 1 to from Zone 3 is 1 : 2
This question appears to be incomplete.
Please find attached the graph required to answer this question
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
The graph is in the image is a bar graph
A bar graph is a pictorial representation of data. The rectangles measure the length of the data
Looking at the graph, the interval is 100
Looking at the rectangle that represents zone 1, it appears to be halfway between 400 and 500. It is concluded that the number of customers in zone 1 is 450
Looking at the rectangle that represents zone 3, it appears to lie on 900.
It can be concluded that there are 900 customers in zone 3
the ratio of zone 1 to 3
450 : 900
to convert to its simplest form, divide both side of the ratio by 450
1 : 2
For more information, please check : https://brainly.com/question/14894834?referrer=searchResults
Select the next item in the sequence.
10.172,10.983,10.994...
A. 10.972
B. 11.000
C.11.172
D.11.983
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Answer:
B. 11.000
Step-by-step explanation:
The function looks like a reflected and translated exponential function with a horizontal asymptote near y = 11.000. The rate of change is decreasing so fast that the next value is expected to be very near 10.994. The closest one among the answer choices is 11.000.
_____
First differences are 0.811 and 0.011. The latter is about 0.0136 times the former. At that rate of change, we expect the next first difference to be about 0.000149, which would make the next number in sequence be about 10.9941—very little change from 10.994.
Clearly, first differences are not constant, so the function is not linear. Ratios of the numbers are not constant, so this is not an exponential (geometric) sequence. A reflected exponential function of the type described is a good fit.
With only 3 points given, the rule is not at all obvious. The next term could legitimately be anything you like, and a rule could be made that would fit it.
g(x) = f(x+1) using f(x)= x to the power of 2
Answer:
g(x) = x² + 2x + 1
General Formulas and Concepts:
Algebra I
Terms/Coefficients
ExpandingFunctions
Function NotationStep-by-step explanation:
Step 1: Define
Identify
g(x) = f(x + 1)
f(x) = x²
Step 2: Find
Substitute in x [Function f(x)]: f(x + 1) = (x + 1)²Expand: f(x + 1) = x² + 2x + 1Redefine: g(x) = x² + 2x + 1PLSS HELPPPP WILL GIVE BRAINLESSS A 22-foot ladder is resting against the side of a building. The bottom of the ladder is 3 feet from the building. Find the measure of the angle the ladder makes with the ground. Round your answer to the nearest tenth of a degree.
Answer:
The answer is 82.2
Step-by-step explanation
hope this helps
Write an equation and solve it to answer each question. A pile of 55 coins consisting of nickels and dimes is worth $3.90. Find the number of each. I only need the equation plz. WILL MARK BRAINLIEST.
Answer:
0.05x + 0.1(55 - x) = 3.9
Step-by-step explanation:
There are 55 coins.
Let x = number of nickels.
The number of dimes is 55 - x.
The value of a nickel is $0.05, and the value of a dime is $0.10.
The value of x nickels is 0.05x
The value of 55 - x dimes is 0.1(55 - x)
The total value of the coins is 0.05x + 0.1(55 - x)
The total value of the coins is $3.90
0.05x + 0.1(55 - x) = 3.9
Please help im begging you
Find the domain of the function expressed by the formula:
y = 1/x - 7
Answer:
the domain is ALL reals numbers except ZERO
- ∞ < x < 0 ∪ 0 < x < ∞
Step-by-step explanation:
Answer:
(-∞,0) ∪ (0,∞), {x|x≠0}
Step-by-step explanation:
I think this is it. Im not completely sure though
50 money prize for solve
Answer:
-7.5
Alternatively,
-0.5(units^-1) + (-4(units^0)) + (-3(units))
Step-by-step explanation:
On graph, only clearly defined points:
1. x = -3 , y = 0
2. x = -3 , y = -8
3. x = 5 , y = -4
So for:
1. -3 = c ( + a×(0^2) + b×0)
And
2. -3 = a×((-8)^2) + b×(-8) + c = 64×a + (-8)×b + c
Since c = -3 ==> 64×a - 8×b = 0
Simplified ==> 8×a - b = 0 ==> b = 8×a
3. 5 = a×((-4)^2) + b×(-4) + c = 16×a + (-4)×b + c
Since c = -3 ==> 16×a - 4×b = 5 - (-3) = 8
Simplified ==> 4×a - b = 2
Since b = 8×a ==> 4×a - (8×a) = 2
Simplified ==> 2×a - 4×a = 1
==> -2×a = 1
==> a = -0.5
Since b = 8×a ==> b = 8×(-0.5) = -4
So...
c = -3
b = -4
a = -0.5
Then...
a + b + c = -0.5 - 4 - 3 = -7.5
A six-sided die is rolled ten times. What is the probability that the die will show an even number at most eight times?
P(even)=1/2. P(odd)=1/2. Let x= number of even in ten rolls
P(x<=8) = 1-P(x>=9) = 1-[C(10,9)(1/2)^9 *(1/2)^1 + C(10,10)(1/2)*(1/2)^0]
=1-[C(10,9)(1/2)^10 +C(10,10)(1/2)^10]
=1-(1/2)^10[10+1
=1–11/1024
=1013/1024
Please Help with this
Answer:
csc = 6/5= 1.2
cot = √(11)/5= 0.6633
sin = 5÷6= 0.83333
Living with parents: The Pew Research Center reported that 36% of American Millennials (adults ages 18–31) still live at home with their parents. A group of students wants to conduct a study to determine whether this result is true for students at their campus. They survey 300 randomly selected students at their campus and determine that 43% of them live at home with their parents. With this data, they test the following hypotheses. The P-value is 0.006.
H0: Of Millennial students at their campus, 36% live at home with their parents.
Ha: More than 36% of Millennial students at their campus live at home with their parents.
What can we conclude?
A. Nothing. The sample size is too small to represent students at their campus.
B. The evidence suggests that more than 36% of students at their campus live at home with their parents because 43% is greater than 36%.
C. The evidence suggests that more than 36% of students at their campus live at home with their parents because the P-value is less than the significance level.
D. The evidence does not suggest that more than 36% of students at their campus live at home with their parents because the difference between 43% and 36% is not statistically significant. A 7% difference could be due to random chance.
Answer:
C. The evidence suggests that more than 36% of students at their campus live at home with their parents because the P-value is less than the significance level.
Step-by-step explanation:
H0: Of Millennial students at their campus, 36% live at home with their parents.
Mathematically, [tex]H_0: p = 0.36[/tex]
Ha: More than 36% of Millennial students at their campus live at home with their parents.
[tex]H_a: p > 0.36[/tex]
The P-value is 0.006.
p-value is less than the significance level of 0.05, which means that there is enough evidence to accept the alternative hypothesis, that is, the proportion is more than 36%.
Thus, the correct answer is given by option C.
please help me with geometry
Answer:
CAD = 25°
Step-by-step explanation:
The angles are shown to be equal in the figure so BAC = CAD.
Find the Perimeter of the figure below, composed of a rectangle and two semicircles.
Round to the nearest tenths place.
15
10
WILL GIVE BRAINLIEST
Answer:
61.42 units
Step-by-step explanation:
Perimeter = sum of all sides of surrounding the figure = circumference of a circle + 2(length of the rectangle)
Note: two semicircles = 1 full circle
Perimeter = πd + 2(L)
Where,
Diameter of the circle (d) = 10
Length of rectangle (L) = 15
Plug in the values
Perimeter = π*10 + 2(15)
Perimeter = 10π + 30
≈ 61.42 units (approximated to nearest tenths)
find the HCF of 20 and 25 by listing all possible factor
Answer:
Check Internet
Step-by-step explanation:
Switch on your laptop, Open the Internet and then type your question there.
Hope this Helped You :D
How can you minimize the risk from your investments?
A.
by investing in a stock with the highest volatility
B.
by investing in a stock with maximum returns
C.
by investing in a variety of investment options
by common sense I can tell is C.) by investigating in a variety of investment options!
while doing business I rather have multiple options than one! but that is personal you may have your own thought!
Answer:
C. by investigating in a variety of investment options
Explanation:
diversification reduces investment risk
(it is obviously not a as volatility is high degree of variation which is negative)
expand the logarithm. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!
Answer:
d) log₉ (10) + log₉ (11) + 6 log₉ (3)Step-by-step explanation:
Use the following identities:
log (abc) = log a + log b + log clog aᵇ = b log aSolve the given:
log₉(10*11*3⁶) = log₉ (10) + log₉ (11) + log₉ (3⁶) = log₉ (10) + log₉ (11) + 6 log₉ (3)Correct choice is d
Matematykakdbebox
Jaggbn
Answer:
theres no question....
Step-by-step explanation:
???
There are 11 green marbles and 12 orange marbles in a bag. You randomly
choose one of the marbles. What is the probability of choosing a green marble?
[tex]\\ \Large\sf\longmapsto 11+12[/tex]
[tex]\\ \Large\sf\longmapsto 23[/tex]
[tex]\boxed{\Large{\sf P(G)=\dfrac{No\:of\:green\:marbles}{Total\:marbles}}}[/tex]
[tex]\\ \Large\sf\longmapsto P(G)=\dfrac{11}{23}[/tex]
Answer:
11/23
Step-by-step explanation:
11 green marbles and 12 orange marbles = 23 marbles
P(green) = green marbles / total marbles
= 11/23
An acre of land planted with sugar beet produces 550 gallons of ethanol from the sugar by fermentation. A car converted to run on E75 (a 75% ethanol, 25% petrol mixture) can do 40 miles per gallon. If you drive 20,000 miles per year, how many acres of sugar beet will be needed to produce the ethanol you need?
Answer:
Step-by-step explanation:
a
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