Which of the following fraction pairs is equivalent?
6/12 and 8/20. 16/20 and 20/35. 2/6 and 7/21. 8/24 and 8/20

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The total cost of the pair of headphones is $23.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/200 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

105 = 10/100 = 1/10

We have,

Original price of the headphones = $50

60% of $50

= 60/100 x 50

= $30

The price of the headphones after the discount.

= $50 - $20

= $20

The amount of sales tax.

= 15% of $20

= 15/100 x 20

= $3

The total cost.

= $20 + $3

= $23

Thus,

The total cost of the pair of headphones is $23.

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Given:

The equation is:

\(x^2-64=0\)

One solutions is 8.

To find:

The other solution of the given equation.

Solution:

We have,

\(x^2-64=0\)

It can be written as:

\(x^2-8^2=0\)

\((x-8)(x+8)=0\)              \([\because a^2-b^2=(a-b)(a+b)]\)

Using zero product property, we get

\(x-8=0\) and \(x+8=0\)

\(x=8\) and \(x=-8\)

It is given that the one solutions is 8.

Therefore, the other solution is -8.

The statement holds for n=k+1.

By mathematical induction, we have proven that 1·1!+2·2!+···+n·n!=(n+1)!−1 for all positive integers n.

What are integers?

Integers are a set of numbers that include whole numbers (positive, negative, or zero) as well as their opposites.

We will use mathematical induction to prove the statement.

Base case: Let n=1. Then the left-hand side of the equation is 1·1!=1 and the right-hand side is (1+1)!=2!-1=1. Therefore, the statement holds for n=1.

Induction hypothesis: Assume that the statement holds for some positive integer k, i.e., 1·1!+2·2!+···+k·k!=(k+1)!−1.

Inductive step: We need to show that the statement also holds for k+1, i.e., 1·1!+2·2!+···+(k+1)·(k+1)!=(k+2)!−1.

We have:

1·1!+2·2!+···+k·k!+(k+1)·(k+1)!=k!+1·1!+2·2!+···+k·k!+(k+1)·(k+1)!=k!+(k+1)!−1+(k+1)·(k+1)!=k!(k+1+1)+(k+2)!−1=(k+1)!(k+2)−1=(k+2)!−1,

where we have used the induction hypothesis in the second step and simplified in the fourth step.

Therefore, the statement holds for n=k+1.

By mathematical induction, we have proven that 1·1!+2·2!+···+n·n!=(n+1)!−1 for all positive integers n.

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Answer:

f(x)=-3x+6

Step-by-step explanation:

because y=6

slope is rise/run so -3 down by 1 right

-3/1=-3

mx+b=y

-3x+6=f(x)

If this has a constant, it would travel 13.5 miles in an hour, therefore it would travel 6.75 miles in a half hour.

The cycle of summer Olympics is 4 years while the cycle of the USA Census is 10 years. If these events happen in 2000, the year they both will happen again is 2020. Here's the explanation:

Cycle of summer Olympics 4: The summer Olympics is an international multi-sport event that happens every four years. It is organized by the International Olympic Committee (IOC). The first summer Olympics was held in Athens, Greece, in 1896. Since then, it has been held every four years. So, if it happened in 2000, the next cycle would be in 2004, then 2008, 2012, 2016, and finally 2020. So, the year summer Olympics will happen again is 2020.Cycle of USA Census10: The USA Census is a population count that happens every 10 years. It is conducted by the United States Census Bureau. The first census was conducted in 1790, and since then, it has been conducted every ten years. So, if it happened in 2000, the next cycle would be in 2010 and then 2020. So, the year the USA Census will happen again is 2020.Therefore, if both events happened in 2000, the year they both will happen again is 2020.

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The linear regression equation for estimating tip amount is y = 0.174x + 1.971, where x is the total bill amount and y is the estimated tip amount.

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The derivative of F(x) is \(F'(x) = x^{(1/3)\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] \(t^{(1/3)} dt\)

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\)   [applying the chain rule to the upper limit]

Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.

\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)

\(F'(x) = x^{(1/3)\)

Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).

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click the photo there is the answer

The series converges for x in the interval [-1, 1), with the left end included and the right end not included.

To find all the values of x for which the given series converges, we will use the Ratio Test. The series is given by:

\(\sum_{n=1}^\infty \frac{(4 x)^n}{n^{8}}\)

Let's apply the Ratio Test:

\(\lim_{n \to \infty} \frac{\frac{(4 x)^{n+1}}{(n+1)^{8}}}{\frac{(4 x)^n}{n^{8}}} = \lim_{n \to \infty} \frac{n^8 (4x)^{n+1}}{(n+1)^8 (4x)^n}\)

Simplify the expression:

\(\lim_{n \to \infty} \frac{4x n^8}{(n+1)^8}\)

Now, we need to find the values of x for which this limit is less than 1, as the Ratio Test states that the series converges if this limit is less than 1.

\(\frac{4x}{(1+\frac{1}{n})^8} < 1\)

Divide both sides by 4:

\(x < \frac{1}{(1+\frac{1}{n})^8}\)

As n approaches infinity, the term \(\frac{1}{n}\) approaches 0:

\(x < \frac{1}{(1+0)^8} = \frac{1}{1}\)

So, for the series to converge, x must be less than 1.

The series is convergent from x = -1, left end included (Y) to x = 1, right end not included (N).

Your answer: The series converges for x in the interval [-1, 1), with the left end included and the right end not included.

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Answer:

Tai will burn 6 calories in 1 minute while biking

Step-by-step explanation:

45-----270

1-------x

45x = 270

x = 270/45

x = 6

Answer:

There is only one solution and it is the point of intersection

Step-by-step explanation:

Answer:

Option 4

125 × 125

Step-by-step explanation:

5⁶ = 5 × 5 × 5 × 5 × 5 × 5 = 125 × 125

Thus, 5⁶ = 125 × 125

-TheUnknownScientist

A line has an interval of measurable distance between pre-established points. It can be limited or shallow or extended or deep in design.

A line is a geometric object that extends infinitely in both directions and has an interval of measurable distance between two pre-established points. It can be characterized by its length, which can vary from being limited or shallow to being extended or deep in design.

A line serves as the foundation of geometry, representing the most basic element of spatial measurement and direction. It provides a framework for measuring and comparing distances, angles, and shapes, and plays a fundamental role in various mathematical and scientific disciplines, as well as practical applications in architecture, engineering, and design.

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Answer:

156

Step-by-step explanation:

its perimeter i think

Answer and explanation:

Surface area of a rectangle = length * width

Surface area of a square = a² where a is length of a side

To find total surface area of the the five pieces of paper, we add up all the areas of all the shapes

Given that length of rectangle =3.5

And width = 2

Area of rectangle =3.5*2=7

Area of 3 rectangles given they are all equal = 7*3=21

Since width of rectangle equal to width of square and all sides of square are equal

Area of square = 2 *2 =4

Area of the two squares =4*2=8

Total surface area of the five plane shapes = 21+8= 29

Answer:

4

Step-by-step explanation:

The degree of a polynomial is the highest power of its variables. For example, in the polynomial 4x^3 + 2x^2 - 5x + 7, the degree is 3 because x^3 is the term with the highest degree. The degree of a constant polynomial, such as 7, is 0. In general, if a polynomial has n terms, its degree is the degree of its leading term (the term with the highest degree).

Answer:

None

Step-by-step explanation:

-18-2 would be equal to -20

-12+(-3) would be equal to -15

-10-5 would be equal to -15

0-8(-4) would be equal to 32

Is that the letter "O" or the number "0"?

Is all of this information given to you for this question here?

Answer:

(a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1) b^1 + C(n, 2)a^(n-2) b^2 + ... + C(n, n-1)a^1 b^(n-1) + C(n, n)a^0 b^n

The binomial expansion of (2x - 3y)^5 is:

32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5

The binomial expansion of the given expression is 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵.

The given expression is (2x-3y)⁵.

In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial.

(2x)⁵+⁵c₁(2x)⁴(3y)¹+⁵C₂(2x)³(3y)²+⁵C₃(2x)²(3y)³+⁵C₄(2x)(3y)⁴+⁵C₅(3y)⁵

= 32x⁵+5(16x⁴)(3y)+10.(8x³)(9y²)+10(4x²)(27y³)+5(2x)(81y⁴)+243y⁵

= 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵

Therefore, the binomial expansion of the given expression is 32x⁵+240x⁴y+720x³y²+1080x²y³+810xy⁴+243y⁵.

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Answer:

B. d = sin2e

Step-by-step explanation:

Use the following identity: 2cos(x)sin(x)=sin(2x)

Therefore

d = 2sine cose

can be written as

d=sin(2e)

However, if you want step by step (for example if your teacher does not give you formula sheets with identities let me know.

The horizontal distance of the hop can also be written as d = sin 2e,  the correct option is B.

A trigonometric identity is used to solve a trigonometric Equation, it is based on the six trigonometric Ratios.

The horizontal distance of a hop by a frog is given by

d = 2 sine cose

By the trigonometric Identity sin 2x = 2 sinx cosx

From the above Identity, the horizontal distance of the hop can also be written as

d = sin 2e

Therefore, the correct option is B.

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Answer:

C: 2^2 x 3^2 x 7

Step-by-step explanation:

2x2=4

3x3=9

4x9=36

36x7=252

Answer:

C)

Step-by-step explanation:

252/2 = 126

126/2 = 63

63/3 = 21

21/3 = 7

7/7 = 1

252 = 2² × 3² × 7

Answer: C)

Answer:

the awnser is:30° yup it is

Answer:

30°

Step-by-step explanation:

We Know

(4x - 2) + (20x - 10) = 180°

4x - 2 + 20x - 10 = 180

24x - 12 = 180

24x = 192

x = 8

Find m∠EBD

∠ABC is a vertical angle to ∠EBD, meaning they will equal it.

4(8) - 2

32 - 2

30°

So, m∠EBD is 30°

Answer:

11

Step-by-step explanation:

Based on the given information and relationships in the diagram, the three true relationships are:

□AACF AECF by HL

DACBF ACDF by SSS

ACFD AEFD by SSS

Given the information Geometry in the question and assuming appropriate triangle arrangements, the possible true statements based on congruence postulates might include: ∆ACF≅∆ECF by HL, ∆ACB≅∆DFC by SSS, and ∆BFA≅∆DFE by SAS.

The provided question appears to pertain to geometric proofs, specifically in relation to triangles and the principles of congruency. Without a proper diagram, it's somewhat difficult to clarify, but based on the clues given, we can touch on some general principles.

Given that ZBCD is a right angle, BC=DC, DF=BF, FA = FE, the most applicable congruence postulates could be Hypotenuse-Leg (HL), Side-Side-Side (SSS), or Side-Angle-Side (SAS). These are all used to prove that triangles are congruent.

So, if we presume the statements to be: ∆ACF≅∆ECF by HL, ∆ACB≅∆DFC by SSS, and ∆BFA≅∆DFE by SAS, these could possibly be correct given the appropriate conditions in the diagram.

Remember: HL can only be applied in right triangles whereas SSS and SAS can be applied without the right angle requirement. All require the triangles to share at least one side or angle.

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Answer:

Step-by-step explanation:

45000 x %22 = 9900 per year

9900/12=825 per month

Answer: Its a whole number. It is a composite number.

Step-by-step explanation:

Answer:

$875

Step-by-step explanation:

take the 700 mulitple it by.25. you should get the answer 175. add 175 to 700 and you get your whole which is 875.

Step-by-step explanation:

The answer is as follows

p+20=14

p=-6

Answer:

Step-by-step explanation:

I will help you if you help me look at my question in my profile

Answer:

15-20mile/h

Step-by-step explanation:

d=speed*time

100mile=speed*(5.5 to 6)

100/5.5 to 6=speed

speed= 18.18 to 16.67 mile/h

it is between 15-20mile/h