\( \frac{ \zeta(2)}{2} - \frac{ \zeta(3)}3 + \frac{ \zeta(4)}{4} - \frac{ \zeta(5)}{5} + \cdots \cdots \\ \)​

Rollaway Skates is cheaper when the number of people is less than or equal to 4. For example, the cost for 2 people at Rollaway Skates is $10, while the cost for 2 people at Wheelie's Skates and Stuff is $106.

Wheelie's Skates and Stuff is cheaper when the number of people is greater than or equal to 5. For example, the cost for 6 people at Rollaway Skates is $30, while the cost for 6 people at Wheelie's Skates and Stuff is $118.

I hope this helps! Do you have any other questions?

Pythagoras property geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Example :

\( \red{ \star} \: h^2 = b^2 + p^2\)

Answer: 540

Step-by-step explanation: because if he pays 45 bucks a month and a year equals 12 then ya do 45x12 and ya get 540

Answer:

Carl spends $540 per year on car insurance

Step-by-step explanation:

Carl pays $45 per month. There are 12 months in 1 year.

All we need to do is multiply the rate per month by the number of months to get our answer.

\(45*12=540\)

Answer:

The answer is A. 34556

Step-by-step explanation:

The 5th term of the sequence would be a{5} = 10334.

Sequence : A sequence is defined as an arrangement of numbers in a particular order.        

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is the sequence -

1, 45, 104, 1034

We can write the next term as -

a{n} = 10a{n - 1} - 6

So, we can write -

a{5} = 10 x 1034 - 6

a{5} = 10340 - 6

a{5} = 10334

Therefore, the 5th term of the sequence would be a{5} = 10334.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ5

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer: A(t) = (6.4 ft^2/min)*t

Step-by-step explanation:

We know that Emily paints at a constant rate, and she can paint 32 ft^2 in 5 minutes.

Then if we take the quotient of these two quantities, we will find the amount she can paint in one minute, this is:

32ft^2/5min = (32/5) ft^2/min = 6.4 ft^2/min.

Then if she paints for t minutes, the area that she can cover can be written as:

A(t) = (6.4 ft^2/min)*t

This is the linear equation we wanted to find.

Answer:

(0, 1/3)

Step-by-step explanation:

To find the centroid of a triangle with vertices A, B, and C, we can use the following formula:

centroid = (x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices A, B, and C, respectively.

In this case, we have A = (-3, 1), B = (-2, 4), and C = (5, -2), so the centroid of the triangle is:

centroid = ((-3) + (-2) + 5) / 3, (1 + 4 + (-2)) / 3 = (0, 1/3)

Therefore, the coordinates of the centroid of ABC are (0, 1/3).

Answer:

7 rounds

Step-by-step explanation:

After the 5th round, 8 divide by 2 equals 4. After the 6th round, 4 divided by 2 equals 2. After the 7th round, 2 divided by 2 equals 1 determining a winner. After every round, the number of people is decreased by dividing by 2.

Hope this helps!!! PLZ MARK BRAINLIEST!!! GG’s

The statements that are true about the graph of y < 2x+1 include the following:

C. The area below the line is shaded.

D. A solution to the inequality is (2, 3).

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided, we have the following equation (inequality);

y < 2x + 1

The slope of the above equation (inequality) is 2 and the y-intercept of the boundary line is (1, 0). Additionally, the area below the dashed line must be shaded because the inequality symbol is less than (<).

Read more on inequality here: brainly.com/question/27976143

#SPJ1

Answer:

Step-by-step explanation:

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

From the question, we have the following ordered pairs

x intercepts = (6,0) and (18, 0)

Vertex = (12, -36)

Points (21, 41.25)

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is the calculated using

m = [f(21) - f(18)]/[21 - 18]

This becomes

m = [f(21) - f(18)]/3

Substitute the known values in the above equation

m = [41.25 - 0]/3

Evaluate the difference

m = 41.25/3

Evaluate the quotient

m = 13.75

Approximate

m=14

Hence, the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

Read more about average rate of change at

https://brainly.com/question/8728504

#SPJ1

Complete question

The graph below shows the value of Edna's profits f(t), in dollars, after t months:

What is the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month?

See attachment for graph

Answer: 5 inspections in 4 hours, because if its 8 hours it would be 10 inspections

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

10 ÷ 8 = 1.25

Answer:

The surface area is 98 square feet.

Step-by-step explanation:

7 x 4 = 28

28 x 3 = 84

4 x 3.5 = 14

14 / 2 = 7

7 x 2 = 14

84 + 14 = 98

Answer:

I think its C

Step-by-step explanation:

(17) The length of the arc is 39.27 in

(18) The length of the arc is 70.7 cm

(19) The area of the sector is 395.84 in²

(20) The area of the sector is 38.5 cm².

The area of each of the sector is calculated by using the following formula;

Area = πr² (θ/360)

Where;

The formula for length of arc is given as;

length of arc = 2πr (θ/360)

(17) The length of the arc is calculated as;

L = 2π (10 in) (225/360)

L = 39.27 in

(18) The length of the arc is calculated as;

L = 2π (15 cm) (270/360)

L = 70.7 cm

(19) The area of the sector is calculated as;

A = π(12)² (315/360)

A = 395.84 in²

(20) The area of the sector is calculated as;

A = π(7)² (90/360)

A = 38.5 cm²

Learn  more about area of sector here: https://brainly.com/question/22600628

#SPJ1

The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

More can be learned about transformations at https://brainly.com/question/28687396

#SPJ1

The function f(x) = \(-2(x+4)^2\) + 1 has a greater maximum.

1. The given function is f(x) = \(-2(x+4)^2\) + 1.

2. To find the maximum of the function, we need to determine the vertex of the parabola.

3. The vertex form of a quadratic function is given by f(x) = \(a(x-h)^2\) + k, where (h, k) represents the vertex.

4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.

5. The x-coordinate of the vertex is given by h = -4.

6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = \(-2(-4+4)^2\) + 1 = \(-2(0)^2\) + 1 = 1.

7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.

8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = \(-2(x+4)^2\) + 1 is greater than the maximum of g(x).

9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.

10. Hence, the function f(x) =\(-2(x+4)^2\) + 1 has a greater maximum.

For more such questions on maximum, click on:

https://brainly.com/question/29795588

#SPJ8

Answer:

the area of the rectangle is 35.25 square meters.

Step-by-step explanation:

To find the area of a rectangle, we multiply the length by the width.

First, we need to convert the mixed numbers to improper fractions to make the multiplication easier:

4 and 2/4 = 4 + 2/4 = 16/4 + 2/4 = 18/4

7 and 5/6 = 7 + 5/6 = 42/6 + 5/6 = 47/6

Now we can multiply the length and width:

Area = (18/4) * (47/6)

Area = (9/2) * (47/6) (canceling the common factor of 2 between 18/4 and 6 in 47/6)

Area = (9 * 47) / (2 * 6)

Area = 423/12

Area = 35.25

Therefore, the area of the rectangle is 35.25 square meters.

Answer:

  6 ft

Step-by-step explanation:

You want the length of the short side of a 30°-60°-90° triangle, given the longest side is 12 ft.

A 30°-60°-90° triangle has side lengths in the ratios ...

  1 : √3 : 2

Here, the longest side is given as 12 ft, so we can multiply this set of ratios by 6 ft to find the lengths of all of the sides:

  1 : √3 : 2 = (6 ft) : (6√3 ft) : (12 ft)

The shortest side has length ...

  k = 6 ft

__

Additional comment

You can also use trig functions to find the length k:

  k/(12 ft) = cos(60°) = 1/2, or

  k/(12 ft) = sin(30°) = 1/2

  k = (1/2)(12 ft) = 6 ft

Answer:

4.75 megabytes per second

Step-by-step explanation:

500-25 = 475

475 / 100 = 4.75

Answer:

Step-by-step explanation:

We know the the total of angles for a triangle is 180 degrees.

So in this case we'd want to set up adding all of our angles and setting them equal to 180

17 + 126 + b = 180

then solve for b

143 + b = 180

b = 37 degrees

So the answer would be 37 degrees for angle b

If you're looking for x, then:

2 = |x|-1

lxl-1 = 2

lxl-1+1=2+1

lxl=3

so x = -3, x=3

Using the simple interest formula it is seen that Mrs Jo saves an amount of $180 when she chooses option B over option A.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

To determine which option is better, we need to compare the total amount of interest paid for each option.

Option A -

The principal amount is $900 and the interest rate is 8%. The term is 5 years.

Using the formula for simple interest -

Interest = Principal × Rate × Time

Interest = $900 × 0.08 × 5

Interest = $360

Total amount paid = Principal + Interest

Total amount paid = $900 + $360

Total amount paid = $1260

Option B -

The principal amount is $900 and the interest rate is 10%. The term is 2 years.

Using the formula for simple interest -

Interest = Principal × Rate × Time

Interest = $900 × 0.10 × 2 = $180

Total amount paid = Principal + Interest

Total amount paid = $900 + $180

Total amount paid = $1080

Therefore, option B is the better option because it has a lower total amount paid by choosing option B.

Mrs. Jo will save -

$1260 - $1080 = $180

Therefore, Mrs. Jo will save $180 by choosing option B instead of option A.

To learn more about Simple Interest from the given link

https://brainly.com/question/2294792

#SPJ1

Answer:

9.95h + 5  ≤ 125

Step-by-step explanation:

let 'h' = number of hats

Answer:

x=-6

Step-by-step explanation:

g(-6)=3

f(-6)=3

Answer:

Step-by-step explanation:

Isolate the term of x from one side of the equation.

Rewrite the problem down.

⇒ 34x-1.72=-6.82

First, add by 1.72 from both sides.

⇒ 34x-1.72+1.72=-6.82+1.72

Solve.

⇒ -6.82+1.72=-5.1

Rewrite the problem down.

⇒ 34x=-5.1

Divide by 34 from both sides.

⇒34x/34=-5.1/34

Solve.

Divide the numbers from left to right.

⇒ -5.1/34=-0.15

⇒ x=-0.15

I hope this helps you! Let me know if my answer is wrong or not.

Here is the correct answer is this

Step-by-step explanation:

Answer:

Step-by-step explanation:

hope it helps you

Answer:

3 1/2

Step-by-step explanation:

4 3/5-1 1/10

4*5+3/5-1*10+1/10

23/5-11/10     LCD 10

46/10-11/10

35/10

7/2

3 1/2

Answer:

Question 7

Domain: (-2,3]

Range: (1,4]

Question 8

a) No

b) x=4 and x=-2

c) (0,3)

d) (3,0) and (-1,0)

Step-by-step explanation:

Question 7

Domain refers to the span of x-values that a function encompasses. We can see from the graph that the lowest x value is -2 and the highest one is 3, and we also note the open circle at x=-2 (meaning x=-2 itself isn't included, which we note using curved brackets) and the closed circle at x=3 (meaning x=3 itself is included, which we note using square brackets). This leaves us with a domain of (-2,3]

Range meanwhile refers to the span of y-values that a function encompasses. We can see from the graph that the lowest y value is 1 and the highest one is 4, and we also note the open circle at y=1 (meaning y=1 itself isn't included, which we note using curved brackets) and the closed circle at y=4 (meaning y=4 itself is included, which we note using square brackets). This leaves us with a range of (1,4]

Question 8

a)

If the point (1,-3) is on the graph, then subbing 1 in for x and -3 in for f(x) should equate:

f(x)=x²-2x-3

-3=1²-2(1)-3?

-3=1-2-3?

-3=-4?

Since this doesn't equate, we can say the point is not on the line.

b)

The condition is that (x,5) is on the graph, so let's sub 5 in for f(x):

f(x)=x²-2x-3

5=x²-2x-3

x²-2x-8=0

(x-4)(x+2)=0

x=4 and x=-2

c)

The y-intercept is the point(s) at which the graph crosses the y-axis, ie where x=0, so to find it we sub 0 in for x:

f(x)=x²-2x-3

f(0)=0²-2(0)-3=-3

Therefore the y-intercept is (0,3)

d)

The c-intercept is the point(s) at which the graph crosses the x-axis, ie where y=0, so to find it we sub 0 in for f(x):

f(x)=x²-2x-3

0=x²-2x-3

(x-3)(x+1)=0

x=3 and x=-1

Therefore the x-intercepts are (3,0) and (-1,0)