22. a. In 1990, Nadezhda Ryashkina set the record for the 10,000 m race-walking event. She finished this race in 41 minutes 56.23 seconds. What was Ryashkina's average walking rate, in meters per second?​

The function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)

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)

Read more about functions at

https://brainly.com/question/1415456

#SPJ1

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! :)

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

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.

$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.

To learn more about Discount and Cost, please click on the link:

https://brainly.com/question/26563760

#SPJ9

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

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]

Answer:

1. 11/12 2. 3/20 3. 18/4 or 4 1/2

Step-by-step explanation:

Answer:

the slope is 9 and the y-intercept is -2

Answer:

All I can think of is ¨pattern¨

The value of the circle is 20 while the triangle is 35

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

Read more about linear equations at

https://brainly.com/question/4074386

#SPJ1

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.

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.

Find out more inofrmation about expression here:

https://brainly.com/question/11382848

#SPJ1

Using it's concept, the probability that a randomly selected boy attended the dance is:

7/9.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

From the table, we have that:

Hence the probability that a randomly selected boy attended the dance is given as follows:

p = 49/63 = 7/9.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

Step-by-step explanation:

f(x)=-7ex

f(2)=-7e(2)

    f(2)=-10

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]

Temperature is a physical quantity that expresses the hotness of matter or radiation. The heat increases an objects 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.

To learn more on temperature click:

https://brainly.com/question/11464844

#SPJ1

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

The probability that you will not go on to a career in physics is 0.215.

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.

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Answer:

A. (2x+4)/x

Step-by-step explanation:

Answer:

 does not exist

Step-by-step explanation:

You want an integer between -5 and -6.

The integers -5 and -6 are consecutive integers. There are no integers between these values. (That's what "consecutive" means.)

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.

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.

Learn more about Vertical Angles here:

https://brainly.com/question/24460838

#SPJ1

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.

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.

Learn more about inference on:

brainly.com/question/25913650

#SPJ1

Answer: correct me if I’m wrong

Step-by-step explanation:

Answer:

Answer is in the picture attached

The term of highest degree is given as 3x⁴,and it has a positive coefficient. The upper bound is +∞.

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 +∞.

Learn more about polynomials here :

brainly.com/question/15465256

#SPJ1