Given the distance covered and the time elapsed, Ryashkina's average walking rate is approximately 3.97 meters per second.
What was Ryashkina's average walking rate?Rate or speed is expressed as distance walked or traveled per unit time.
R = s/t
Given the data in the question;
Distance covered s = 10,000mTime elapsed t = 41 minutes 56.23 secondsRate r = ?First convert 41 minutes to seconds.
⇒ 41min = ( 41 × 60 )s = 2460sec
Now, Elapsed time t = 2460s + 56.23s = 2516.23 second
Next, we determine the rate.
R = s / t
R = 10000m / 2516.23 s
R = 3.97m/s
Given the distance covered and the time elapsed, Ryashkina's average walking rate is approximately 3.97 meters per second.
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[tex] \rm\sum \limits_{n = 2}^{ \infty } \frac{1}{( {n}^{2} - 1 {)}^{2} } \\ [/tex]
Partial fractions:
[tex]\displaystyle \frac1{(n^2-1)^2} = \dfrac14 \left(\frac1{n+1} - \frac1{n-1} + \frac1{(n+1)^2} + \frac1{(n-1)^2}\right)[/tex]
Now evaluate the sums. The first two terms form a telescoping sum,
[tex]\displaystyle \sum_{n=2}^\infty \left(\frac1{n+1} - \frac1{n-1}\right) = \sum_{n=1}^\infty \left(\frac1{n+2} - \frac1n\right) \\\\ ~~~~~~~~ = \lim_{N\to\infty} \sum_{n=1}^N \left(\frac1{n+2} - \frac1n\right) \\\\ ~~~~~~~~ = \lim_{N\to\infty} \left(\frac1{N+2} + \frac1{N+1} - 1 - \frac12\right) \\\\ ~~~~~~~~= -\frac32[/tex]
The others are flavors of [tex]\zeta(2)[/tex].
[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n+1)^2} = \sum_{n=3}^\infty \frac1{n^2} \\\\ ~~~~~~~~~~~~~~~~~ = \sum_{n=1}^\infty \frac1{n^2} - 1 - \frac1{2^2} \\\\ ~~~~~~~~~~~~~~~~~ = \frac{\pi^2}6 - \frac54[/tex]
[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n-1)^2} = \sum_{n=1}^\infty \frac1{n^2} \\\\ ~~~~~~~~~~~~~~~~~ = \frac{\pi^2}6[/tex]
It follows that
[tex]\displaystyle \sum_{n=2}^\infty \frac1{(n^2-1)^2} = \frac14 \left(-\frac32 + \left(\frac{\pi^2}6 - \frac54\right) + \frac{\pi^2}6\right) = \boxed{\frac{\pi^2}{12} - \frac{11}{16}}[/tex]
21-B Book Street Books sells about 1100 books each month. The circle graph displays the most popular book categories, by percentage, each month.
science fiction 38 %
Categories of Books Sold
children's fiction 13%
nonfiction 24%
sports 10%
romance 15 %
Step 1 of 5: Find the number of nonfiction books sold each month. Round your answer to the nearest integer.
well, we know they sell a total of about 1100 books monthly, and that nonfiction is 24% of that, what's 24% of 1100?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{24\% of 1100}}{\left( \cfrac{24}{100} \right)1100}\implies 264[/tex]
POSSIBLE POINTS: 5.88
A rectangular playground is to be fenced in using a wall on one side and 210 meters of fencing for the other three sides. The area A(z) in square
meters of the playground is a function of the length z in meters of the side parallel to the wall.
Write an expression for A(z)
The function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)
How to write a function of the length z in meters of the side parallel to the wall?The given parameters are:
Perimeter = 210 meters
Let the length parallel to the wall be represented as z and the width be x
So, the perimeter of the fence is
P = 2x + z
This gives
210 = 2x + z
Make x the subject
x = 1/2(210 - z)
The area of the wall is calculated as
A = xz
So, we have
A = 1/2(210 - z) * z
This gives
A = z/2(210 - z)
Rewrite as
A(z) = z/2(210 - z)
Hence, the function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)
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if two intersecting lines are not perpendicular, then they form which two types of angles
HELP ME WITH THISSSS
Using it's concept, the probability that a randomly selected boy attended the dance is:
7/9.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
From the table, we have that:
There are 49 + 14 = 63 boys.Of those, 49 attended the dance.Hence the probability that a randomly selected boy attended the dance is given as follows:
p = 49/63 = 7/9.
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What is the simplest form of the expression below?
Answer:
A. (2x+4)/x
Step-by-step explanation:
the graph of function y
[tex]y = x ^{2} [/tex]
p^2+3p+1=0 using completing the square method
Answer:
Answer is in the picture attached
∠A and \angle B∠B are vertical angles. If m\angle A=(5x+5)^{\circ}∠A=(5x+5)
∘
and m\angle B=(6x-8)^{\circ}∠B=(6x−8)
∘
, then find the value of x.
Each of the pairs of opposite angles made by two intersecting lines are called a pair of vertical angles. The value of x is 13.
What are vertical angles?Each of the pairs of opposite angles made by two intersecting lines are called a pair of vertical angles.
Given that ∠A and ∠B are vertical angles. Therefore, the measure of the two of the given angle will be equal to each other. Thus, we can write the measure of the two angles as,
∠A = ∠B
(5x + 5)° = (6x - 8)°
5x + 5 = 6x - 8
Bring the like terms on the same side of the equation,
5 + 8 = 6x - 5x
13 = x
x = 13
Hence, the value of x is 13.
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At Dapper Dave's annual end-of-season sale, every necktie in the shop gets marked down. Dillon purchased 6 neckties during the sale. Each necktie cost $5 less than its full price. He paid a total of $162. What is the cost of each necktie at full price?
$32 is the cost of each necktie at full price.
Given that
At Dapper Dave's annual end-of-season sale, every necktie in the shop gets marked down.
Dillon purchased 6 neckties during the sale. Each necktie cost $5 less than its full price.
He paid a total of $162.
To find
What is the cost of each necktie at full price ?
So, according to the question
we have,
On that end-of-season sale
Total purchased neckties = 6
Discount on each neckties = $5
Amount paid by him = $162
Let's assume the full price of one neckties is $x.
So,
The price of one neckties after discount = x - 5.
So the price of one neckties after discount = 6(x-5)
He paid $162 for 6 neckties,
So we can say that
the price of one neckties after discount = $162
So,
6(x-5) = 162
x-5 = 162/6
x-5 = 27
x = 27+5
x = 32
The cost of each necktie at full price is $32.
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What solution value satisfies the compound inequality 4 < 3x∕2 + 1 < 7?
Question 12 options:
A)
x = 0
B)
x = 4
C)
x = 3
D)
x = 6
Answer:
C) x = 3
Step-by-step explanation:
To find the solution value that satisfies the inequality 4 < 3x∕2 + 1 < 7, you must plug every x value into the x and see which one works.
Plug 0 into x
4 < 3(0)∕2 + 1 < 7
4 < 0∕2 + 1 < 7
4 < 0 + 1 < 7
Combine like terms
4 < 1 < 7
This is false, 1 is not greater than 4.
Plug 4 into x
4 < 3(4)∕2 + 1 < 7
4 < 12∕2 + 1 < 7
4 < 6 + 1 < 7
Combine like terms
4 < 7 < 7
This is false, 7 is not less than 7.
Plug 3 into x.
4 < 3(3)∕2 + 1 < 7
4 < 9∕2 + 1 < 7
4 < 4.5 + 1 < 7
Combine like terms
4 < 5.5 < 7
This is true, 5.5 is greater than 4 and less than 7.
Plug 6 into x.
4 < 3(6)∕2 + 1 < 7
4 < 18∕2 + 1 < 7
4 < 9 + 1 < 7
Combine like terms
4 < 10 < 7
This is false, 10 is not less than 7.
C) x = 3 is the only true solution that works, so that is your answer.
I hope that helped and have a lovely rest of your day! :)
Calculus 1 question
explain why the statement x < 3 or > 5 cannot be written 5 < x < 3
Answer:
This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.
Step-by-step explanation:
x < 3 or x > 5
This means, x is less than 3, but greater than 5.
Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.
PLEASE HELP ASAP!
What is the upper bound of the function?
f(x)= 3x^4 -7x^3 +5x -3
( ^4 and ^3 are exponents)
The term of highest degree is given as 3x⁴,and it has a positive coefficient. The upper bound is +∞.
What is the degree of a polynomial ?To determine the degree of a polynomial just observe the highest power of the given variable.
We have polynomial given by f(x) = 3x⁴ - 7x³ +5x -3
Here we can see that it is a polynomial in of degree 4.
We know that a polynomial of degree has n number of roots so it is obvious a polynomial of degree 4 has 4 roots.
The function that tends to infinity as x goes in both the positive and negative directions.
The term of highest degree is given as 3x⁴,and it has a positive coefficient.
The upper bound is +∞.
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Convert 1/2 into a fraction whose denominator is 10. Then write the corresponding decimal number
Answer:
• 5/10
• 0.5
Step-by-step explanation:
1.) if you multiply the numerator by 5 and the denominator by 5 you are left with a fraction of 5/10.
2.) the fraction line represents division. So 5 ÷ 10 = 0.5.
Which would increase an object’s temperature
Temperature is a physical quantity that expresses the hotness of matter or radiation. The heat increases an objects temperature.
What is temperature?
Temperature is a physical quantity that expresses the hotness of matter or radiation.
The temperature of the object increases due to the absorbed part of the heat. An object decreases its temperature by releasing energy in the form of heat to its surroundings. And an object increases its temperature by gaining energy in the form of heat from its surroundings.
So the temperature changes according to the heat of the surrounding.
Therefore the heat increases an objects temperature.
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Use the diagram to find the following measures
A) triangle angle sum equation
B) value of x = ———- degrees
Answer:
x = 71°
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180°.
The measure of two angles out of three is given, we will use the following equation to find the value of the missing angle:
82 + 27 + x = 180 add like terms
109 + x = 180 subtract 109 from both sides
x = 71
what are the slope and the y intercept of the linear function represented by the equation y=9x-2
Answer:
the slope is 9 and the y-intercept is -2
Which shape has at least one pair of perpendicular sides?
please help me. I will give extra points and a Brainly.
Answer:
All I can think of is ¨pattern¨
rofessor Frank Nabarro insists that all senior physics majors take his notorious physics aptitude test. The test is so tough that anyone not going on to a career in physics has no hope of passing, whereas 55% of the seniors who do go on to a career in physics still fail the test. Further, 75% of all senior physics majors in fact go on to a career in physics. Assuming that you fail the test, what is the probability that you will not go on to a career in physics? (Round your answer to four decimal places.)
The probability that you will not go on to a career in physics is 0.215.
How to calculate the probability?From the information, the test is so tough that anyone not going on to a career in physics has no hope of passing, whereas 55% of the seniors who do go on to a career in physics still fail the test and 75% of all senior physics majors in fact go on to a career in physics.
Therefore, the probability that you will not go on to a career in physics will be:
= (1 - 0.75) / (0.75 × 0.55) + (0.75)
= 0.25 / (1.1625)
= 0.215
Therefore, the probability that you will not go on to a career in physics is 0.215.
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Panchito walks 9.75 kilometers in 90 minutes what is the unit rate in kilometers per hour
Answer:
6.5 kilometers per hour
Step-by-step explanation:
90 minutes is 1 1/2 hours.
to find the unit rate you would divide the distance by the time so you would divide 9.75 by 1.5 (1.5 is the decimal version of 1 1/2) which would give you 6.5 kilometers per hour
solve the problem
(4 1/3) (-2) (5/13)
The solution of the given expression (4 1/3) (-2) (5/13) is -130/13.
According to the given question.
We have an expression (4 1/3) (-2) (5/13).
Here, we have to solve the given expression.
So, the solution of the expression (4 1/3) (-2) (5/13) is given by
(4 1/3) (-2) (5/13)
= (13/3)(-2)(5/-13) (by converting the mixed fraction into improper fraction)
= (-26/13)(5/13)
= -130/13
Hence, the solution of the given expression (4 1/3) (-2) (5/13) is -130/13.
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If f(x)=−7ex, find f(2) rounded to the nearest tenth.
Answer:
Step-by-step explanation:
f(x)=-7ex
f(2)=-7e(2)
f(2)=-10
Each shape in the diagram below stands for a number.
000
Work out the value of each shape.
50/51 Marks
Total 90
-Total 66
The value of the circle is 20 while the triangle is 35
How to determine the values of each shape?From the figure, we have
Three circles and Two triangles
Such that:
Three circles = 60
One circle and Two triangles = 90
Represent the circle with x and the triangle with y
So, we have
3x = 60
x + 2y = 90
The above forms a system of linear equations
Divide 3x = 60 by 3
x = 20
Substitute x = 20 in x + 2y = 90
20 + 2y = 90
This gives
y = 35
So, we have
Circle = 20
Triangle = 35
Hence, the values of the shapes are 20 and 35, respectively
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Which of these could be an option after high school for Jon, an active person, who is interested in higher education but who doesn't want to take out student loans?
O Sign up for the military
O Apply for college
O
Take a reflection year
Attend a technical school
The option after high school for Jon, an active person, who is interested in higher education but who doesn't want to take out student loans is to take a reflection year.
How to illustrate the information?It should be noted that based on the information, the inference has to do with the conclusion that one gets from the information or evidence that is given earlier.
In this instance, it should be mentioned that Jon, an energetic individual interested in further education but unwilling to take out student debt, has the choice to take a reflection year following high school.
In conclusion, the correct option is C.
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What is an integer between -5. And -6
Answer:
does not exist
Step-by-step explanation:
You want an integer between -5 and -6.
IntegersThe integers -5 and -6 are consecutive integers. There are no integers between these values. (That's what "consecutive" means.)
What is 96-8c=20-12
Answer:
c = 11
Step-by-step explanation:
96 - 8c = 20 - 12 , that is
96 - 8c = 8 ( subtract 96 from both sides )
- 8c = - 88 ( divide both sides by - 8 )
c = 11
help with theses answer please
Answer: correct me if I’m wrong
Step-by-step explanation:
Can you please help with this.
Answer:
1. 11/12 2. 3/20 3. 18/4 or 4 1/2
Step-by-step explanation: