Answers
The sum diverges (integral test). We have
\(\displaystyle \sum_{n=2}^\infty \frac3{2n} \ge \int_2^\infty \frac3{2x}\,\mathrm dx\)
and the integral diverges, so the sum also diverges.
\(\displaystyle\int_2^\infty\frac3{2x}\,\mathrm dx = \lim_{x\to\infty}\frac32\ln|x| - \frac32\ln(2) = \infty\)
Related Questions
Robert took a math test and got 36 correct and 14 incorrect answers. What was the percentage of correct answers?
Answers
Answer:
72% correct
Step-by-step explanation:
Question 8 of 10
Simplify (7 + 1)2 – (11 + 32) - 4.
Answers
Answer:
Does anyone watch shaurya aur anokhi ki on star plus an Indian serial you'll love it I guarantee
b. y =
Choose the equation for the graph
below.
2x-6
a. y =
x+4
3
4x+8
5x+10
C. y =
x²-1
–3x²
2x+6
- 2x2
e. y =
x²_9
d.y=
Answers
Answer:
2 4 23
Step-by-step explanation:
1. Mr. Griffith is ordering a whole new set of basketballs for the basketball teams at KIPP Infinity.
Modell's charges $50.50 for shipping and $7 per ball.
Sports Authority charges $18.50 for shipping and $11 per ball.
If he wants to spend as little money as possible, how should Mr. Griffith make a decision about which
company to buy the basketballs from?
Answers
To spend less money, it is better to buy from Sports authority if the number of balls are less than 8 and it is better to buy from Modell if the number of of balls are greater than 8
Consider the Modell's charges
The sipping charge = $50.50
The price per ball = $7
Consider the number of balls as x and the total cost y
Then the equation will be
y = 50.50 + 7x
Consider the Sports Authority charges
The shipping charge = $18.50
The price per ball = $11
The equation will be
y = 18.50 + 11x
The shipping charge of Modell is greater than Sports authority, but the cost of the ball of Sports authority is grater than Model. Therefore the total price depends on the number of balls
Consider
18.50 + 11x = 50.50 + 7x
11x - 7x = 50.50 - 18.50
4x = 32
x = 32/4
x = 8
Hence, to spend less money, it is better to buy from Sports authority if the number of balls are less than 8 and it is better to buy from Modell if the number of of balls are greater than 8
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Cual es la distancia que recorrió luis en su bicicleta rodada 20p (2.54) después que las llantas dieran 50 vueltas completas
porfaaa
Answers
Luis traveled approximately 31,736.8 inches on his bicycle.
We have,
To find the distance that Luis traveled on his bicycle, we need to calculate the circumference of the tires and then multiply it by the number of complete turns.
Given:
Radius of the tires (r) = 20p (2.54) inches
Number of complete turns (n) = 50
The circumference of a circle can be calculated using the formula:
Circumference = 2πr
Substituting the given radius into the formula, we have:
Circumference = 2π * (20p) inches
Now we can calculate the distance traveled (d):
Distance = Circumference x Number of complete turns
Distance = 2π x (20p) x 50 inches
To simplify the calculation, we can approximate π as 3.14:
Distance ≈ 2 x 3.14 x (20 x 2.54) x 50 inches
Calculating this expression, we find:
Distance ≈ 31736.8 inches
Therefore,
Luis traveled approximately 31,736.8 inches on his bicycle.
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The complete question.
What is the distance that Luis traveled on his bicycle rolled 20p (2.54) after the tires gave 50 complete turns
(a) Write down the angle between the vector i + j and the vector i- j.
(6) Calculate the angle between the vector 2i + 5j and the vector 4i.
(2)
(c) Two forces, A = (14i +2j) N and B = (2i - 6j) N, act on a ball.
Show that the magnitude of A is Root k times larger than the magnitude of B, where k is
an integer
(3)
Answers
(i + j) • (i - j) = ||i + j|| ||i -j|| cos(θ)
We also recall that for any vector x,
||x||² = x • x
We have
(i + j) • (i - j) = (i • i) + (j • i) + (i • (-j)) + (j • (-j))
= (i • i) + (j • i) + (i • (-j)) + (j • (-j))
= ||i||² + (i • j) - (i • j) - ||j||²
= 1 + 0 - 1
= 0
and
||i + j|| = √(1² + 1²) = √2
||i - j|| = √(1² + (-1)²) = √2
So,
0 = 2 cos(θ)
cos(θ) = 0
θ = arccos(0) = 180°
(b) By the same process, we find
(2i + 5j) • 4i = 8
||2i + 5j|| = √(2² + 5²) = √29
||4i|| = 4
Then if θ is the angle between 2i + 5j and 4i, we have
8 = 4√29 cos(θ)
cos(θ) = 2/√29
θ = arccos(2/√29) ≈ 68.1986°
(c) Compute the magnitudes:
||A|| = √(14² + 2²) = √200 = 10√2
||B|| = √(2² + (-6)²) = √40 = 2√10
Now we can write
||B|| = 2√10 = 2 √(5 × 2) = 2√5 × √2 = 1/√5 × 10 √2 = 1/√5 ||A||
or
||A|| = √5 ||B||
so that k = 5.
description of set D={3,6,9,12,15}
Answers
Answer:
The set D has 5 elements - 3, 6, 9, 12, and 15, all of which are multiples of 3.
juan is passionate about movies and dreams of going to film school. His goal for the next year is to
Answers
Answer:
completa la oracion!!!
etaStep-by-step explanation:
Robin Hartman earns $600 per week plus 3% of sales over $6,500. Robin's week sales are $14,000. How much does Robin earn
Answers
Answer:
$825
Step-by-step explanation:
Given that :
Weekly earning = $600 plus 3% of sales over $6500
If weekly sales = $14000
How much will Robin earn
Robin's earning will be:
Flat weekly pay + 3% of amount over 6500
$600 + 3%(weekly sales - 6500)
$600 + 0.03(14000 - 6500)
$600 + 0.03(7500)
$600 + $225
= $825
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
NEED HELP ASAP!
Samantha says that 5x and 5y are like terms. Is she correct? Explain.
Answers
Answer:
No
Step-by-step explanation:
They are not because since 5 is being multiplied by x, that is not the same thing as 5 being multiplied by y. Don't get confused by the 5. Have a wonderful day! <3
Help please!!!!!!!!!!!!!!!
Answers
Answer:
y=8x-3y=-2x-1y=-x-1y=4x+5y=3y=7x+0 or y=7xy=10x+4y=-6x+9the equation for the graph:
y=2x-2
use the y-intercept ((0,-2))
and the for the slope you do y1-y2/x1-x2
0-(-2)/1-0= 2
The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?
Answers
There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.
First, we can standardize the problem by using the z-score formula:
z = (x - μ) / σ
Where:
x = the weight value we want to find the probability for (345 g in this case)
μ = the mean weight (350 g)
σ = the standard deviation (4 g)
Substituting the values into the formula:
z = (345 - 350) / 4 = -1.25
Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.
The probability of obtaining a z-score less than -1.25 is approximately 0.1056.
However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.
The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.
Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
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What are the steps for using a compass and straightedge to construct a square?
Drag and drop the steps in order from start to finish.
Answers
Answer:
for future students, this is the answer. I dont know why the other guy made it so hard
Step-by-step explanation:
Is x = 3 a solution to the equation x + 7 = 11?
A. No, because 3+ 7 = 11 is true.
B. No, because 3 + 7 = 11 is not true.
C. Yes, because 3 + 7 = 11 is true.
D. Yes, because 3+ 7 = 11 is not true.
SUBMIT
Answers
Answer:
NO, because 3+7=11 is not true
Step-by-step explanation:
x+7=11
collect like terms
x=11-7
x=4
therefore x is not equal to 3 because 7+3=10 and not 11
27. What is the reflection image of (5, –3) across the y-axis? (–5, 3) (–5, –3) (–3, 5) (5, 3)
Answers
The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).
Solve for t.
4 (t + 1/4) = 3
Answers
Answer:
t=1/2
Step-by-step explanation:
In outer space, the distant an object travels varies directly with the amount of time it travels. If an asteroid travels 3000 miles in 6 hours, how far could the asteroid travel in 9 hours?
Answers
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
3000 miles = 6 hours
4500 miles = 9 hours
The distance asteroid travel in 9 hours is 4500 miles
What is a unit rate?Unit rate is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
3000 miles = 6 hours
Divide both sides by 6.
500 miles = 1 hour
Multiply 9 on both sides.
9 x 500 miles = 9 hours
9 hours = 4500 miles
Thus,
The distance asteroid travel in 9 hours is 4500 miles
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What is the most important thing to know when working with circle
theorems?
a) identifying the theorem by looking at the information provided
b) identify the angles
c) identifying arcs
d) B and C Only
Answers
Identifying the theorem is the most important step while working with circle theorems.
What is a circle?Circle is a round plane figure whose boundary (circumference) consists of points equidistant from a fixed point (centre). The general equation of the circle is -x² + y² = r²
Given are the points about circle theorems.
While working with circle theorems, identifying the theorem by looking at the information provided is the most important step.
Therefore, identifying the theorem is the most important step while working with circle theorems.
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Combine like terms.
9 + 12t – 6t
Question 3 options:
9 – 12t
21
21t
9 + 6t
Answers
The expression can be simplified to obtain as 9 + 6t.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given algebraic expression is 9 + 12t – 6t.
It can be simplified as follows,
9 + 12t – 6t
Here 9 is a constant.
And, the terms 12t and 6t have the same variable t.
Which implies they are like terms.
Since the like terms in an expression can be added to subtracted, the given expression can be simplified as below,
9 + 12t – 6t
⇒ 9 + 6t
Hence, the simplification of the given expression results as 9 + 6t.
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The measure of one small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles
Answers
Answer:
x + x - 45 = 90
2x - 45 = 90
2x = 135
x = 67.5, so x - 45 = 22.5
The other two angles measure 22.5° and 67.5°.
which of the following functions represent the graph g(x) above
Answers
The function represented by the graph given is equivalent to -
g(x) = (x - 4)².
The function plotted represents a quadratic equation. A quadratic equation has a degree of 2. The given function is shifted to the left by 4 units. This means that the following transformation will take place on the x - coordinate of each and every point lying on the graph -
f(x, y) → f(x - 4, y)
So, we can write the function as -
g(x) = (x - 4)²
So, the function represented by the graph given is equivalent to -
g(x) = (x - 4)²
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Use a system of linear equations with two variables and two equations to solve. A number is 9 more than another number. Twice
the sum of the two numbers is 30. Find the two numbers. Let the two numbers be represented by x and y. Let y represent the
larger number. Write your answer as an ordered pair (x, y).
Answers
9514 1404 393
Answer:
(x, y) = (3, 12)
Step-by-step explanation:
Using the given variable definitions, we can write the equations ...
y = x + 9
2(x +y) = 30
__
Solving the second equation for y, we have ...
y = 15 -x
Substituting this into the first equation gives ...
15 -x = x +9
6 = 2x . . . . . . . . . add x-9
3 = x . . . . . . . . . . divide by 2
y = 3+9 = 12 . . . . substitute into the first equation
The numbers are (x, y) = (3, 12).
Kenny wants to buy as many toy car sets as he can and he has a total of $38. If one care set costs 5 how much money will Kenny have left over?
Answers
Answer:
tbh I think the answer is 3
Step-by-step explanation:
first u divide $38 and 5
then the answer u will get is 7
then take away 38 and 35 since 7×5=35
you get $3
ANSWER=$3
THEREFORE: Kenny has $3 left over
a⃗ =⟨−3,−2⟩ and b⃗ =⟨2,4⟩ .
Represent a⃗ −b⃗ using the head-to-tail method.
Use the Vector tool to draw the vectors, complete the subtraction by the head-to-tail method, and draw a⃗ −b⃗ .
To use the Vector tool, select the initial point and then the terminal point.
Answers
The resultant of the subtraction by the head-to-tail method, is determined as 7.81.
Head-to-tail method of vector subtraction
The head-to-tail method of vector subtraction is done by adding the negative of the second vector to the first.
The diagram can be found in the image uploaded.
Resultant vectorThe resultant vector is determined as follows;
Vertical distance from 4 to negative 2 = 4 - (-2) = 6Horizontal distance from 2 to negative 3 = 2 - (-3) = 5R² = 6² + 5²
R² = 61
R = √61
R = 7.81
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List the terms of the polynomial. Give the coefficient of the second term. -4y5 + 6x4 +9w³ - 4w - 1 Separate terms using commas. Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c . Make sure your variables match those in the question. Terms Coefficient
Answers
The coefficient of the second term, 6x⁴, is 6.
The terms of the polynomial are:
-4y⁵, 6x⁴, 9w³, -4w, -1
The coefficient of the second term, which is 6x⁴, we look at the number in front of the variable term.
The coefficient is 6.
Therefore, the list of terms is:
-4y⁵, 6x⁴, 9w³, -4w, -1
Each term represents a separate component of the polynomial, where the variable is raised to a certain power and multiplied by its coefficient.
The coefficients indicate the scalar value by which each term is multiplied.
The polynomial's terms are -4y5, 6x4, 9w3, -4w, and -1.
Looking at the number in front of the variable term, we can determine the second term's coefficient, which is 6x4.
There is a 6 coefficient.
As a result, the terms are as follows: -4y5, 6x4, 9w3, -4w, and -1.
Each term represents a different part of the polynomial, where the variable is multiplied by its coefficient and raised to a given power.
The scalar value by which each phrase is multiplied is shown by the coefficients.
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Help please!
S = 180m
How many strides would a runner take during a 1-hour run (60 min)
Answers
The number of strides the runner will make during 1 hour run will be =
10,800.
How to calculate the total number of strides made by the runner in a hour?To calculate the distance or number of strides made by the runner in an
hour, the graph given above is considered as follows;
The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.
From the graph
20 minutes= 3600 strides
60 minutes = X strides
make X the subject of formula;
x= 3600×60/20
= 216000/20
= 10,800
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need help with geometry
Answers
To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:
Volume = π * r² * h
Substituting the given values, we have:
\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)
To solve for h, we divide both sides of the equation by 153.86:
h = 1500 / 153.86
h ≈ 9.75
Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.
Therefore, the height of the cylinder is 9.75 inches.
Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.
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Which function is the inverse of ƒ(x) = 4x3 – 2?
// its not A
Answers
Answer:
C) \(g(x)=\sqrt[3]{\frac{x+2}{4}}\)
Step-by-step explanation:
\(f(x)=4x^3-2\)
\(y=4x^3-2\)
\(x=4y^3-2\)
\(x+2=4y^3\)
\(\frac{x+2}{4}=y^3 \)
\(\sqrt[3]{\frac{x+2}{4}}=y \)
\(f^{-1}(x)=\sqrt[3]{\frac{x+2}{4}}\)
\(g(x)=\sqrt[3]{\frac{x+2}{4}}\)
PLEASEEE HELPPPP!!!
50 high school students were asked how many hours they study per day. The mean was 1.5 hours, with a standard deviation of 0.5 hours. Using a 5% level of significance, what could we claim about the mean study time of the entire population of high school students so that the hypothesis will fail to be rejected?
A. 1.3 hrs
B. 1.2 hrs
C. 1.6 hrs
D 1.7 hrs
Answers
Considering the desired result of the hypothesis test, we the closest mean time to 1.5 hours, hence the correct option is:
C. 1.6 hrs
What should be the mean?The closer the mean is to the sample mean, the less likely we are to reject the null hypothesis.
In this problem, the sample mean is of 1.5 hours, hence, the closest value, considering the absolute value of the difference, is of 1.6 hours, hence option C is correct.
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