What are some easy ways to find the value of
(2017^4−2016^4)/(2017^2+2016^2) without calculator

Answers

Answer 1

Answer:

4033

Step-by-step explanation:

An easy way to solve this problem is to notice the numerator, 2017^4-2016^4 resembles the special product a^2 - b^2. In this case, 2017^4 is a^2 and 2016^4 is b^2. We can set up equations to solve for a and b:

a^2 = 2017^4

a = 2017^2

b^2 = 2016^4

b = 2016^2

Now, the special product a^2 - b^2 factors to (a + b)(a - b), so we can substitute that for the numerator:

[tex]\frac{(2017^2+2016^2)(2017^2 - 2016^2)}{2017^2+2016^2}[/tex]

We can notice that both the numerator and denominator contain 2017^2 + 2016^2, so we can divide by [tex]\frac{2017^2+2016^2}{2017^2+2016^2}[/tex] which is just one, and will simplify the fraction to just:

2017^2 - 2016^2

This again is just the special product a^2 - b^2, but in this case a is 2017 and b is 2016. Using this we can factor it:

(2017 + 2016)(2017 - 2016)

And, without using a calculator, this is easy to simplify:

(4033)(1)

4033


Related Questions

A sample of students at a university took a test that diagnosed their learning styles as active or reflective and also as visual or verbal. Each student received a numerical score on the active/reflective style and also a numerical score on the visual/verbal style. The sample size was 39, and the sample correlation coefficient turned out to equal .273.a. State the hypotheses for testing whether there is a positive correlation between these variables in the population of all students at this university.b. Calculate the value of the test statistic.c. Determine the p-value as accurately as possible.d. State the test decision for the α= .10 and α= .05 significance levels, and summarize your conclusion in context.e. If the sample size was much larger, and the value of the sample correlation coefficient stayed the same, describe the impact on your test statistic, p-value, and conclusion.

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Sample size, n = 39

Correlation Coefficient, r = 0.273

The hypothesis test to examine if there is a positive correlation :

H0 : ρ = 0

If there is a positive correlation, then ρ greater than 1

H0 : ρ > 1

The test statistic :

T = r / √(1 - r²)/(n - 2)

T = 0.273 / √(1 - 0.273²)/(39 - 2)

T = 0.273 / 0.1581541

T = 1.726

The Pvalue using a Pvalue calculator can be be obtained using df = n - 2, df = 39 - 2 = 37

The Pvalue = 0.0463

α= .10 and α= .05

At α= .10

Pvalue < α ; Hence, we reject H0 and conclude that a positive correlation exists

At α= 0.05 ;

Pvalue < α ; Hence, we reject H0 and conclude that a positive correlation exists

The length of a rectangle is 3 cm more than its breadth. If the perimeter of the
rectangle is 46 cm, find the length and the breadth.

Answers

Answer:

breadth = 10 cm

length = 13 cm

Step-by-step explanation:

so,

perimeter = 46cm

2(l+b) = 46cm

or, 2(3+b+b) = 46cm ( because l = 3+b)

or, 2(3+2b) = 46cm

or, 6 + 4b = 46cm

or, 4b = 46cm - 6

or, 4b = 40cm

or, b = 40/4 cm

so, b = 10 cm

now,

l = 3cm + b

l = 3 cm + 10cm

= 13cm

Answer:

Let us assume the breadth of the rectangle be 'b' cm.

So length of the rectangle will be b+3 cm.

Now

Perimeter =46

[tex] \large \mid\orange {2(l + b) = 46}[/tex]

[tex] \large \mid\orange {2(b+3+b)=46}[/tex]

[tex] \large\mid \orange {2(2b+3) = 46}[/tex]

[tex] \large\mid \orange {4b + 6 = 46}[/tex]

[tex] \large \mid \orange{4b = 46 - 6}[/tex]

[tex] \large\mid \orange {4b = 40}[/tex]

[tex] \large \mid \orange{b = \frac{40}{4} }[/tex]

[tex] \large\mid \orange {b = 10}[/tex]

[tex] \large \orange{l=b+3= \:10 + 3 = 13 cm }[/tex]

Length = 13cm

Breadth = 10cm

Graph the image of trapezoid PQRS after a translation 9 units right and 10 units up.​

Answers

(X,Y)
Q (-1,10)
P (-1,6)
S (2,0)
R (3,6)

what is the answer?
(2a³b⁴)⁴=

Answers

Answer:

16a^12 b^16

Step-by-step explanation:

that's the answer. just multiply out the powers

Answer:

16*(a^12)*(b^16)

Step-by-step explanation:

In order to solve this problem, we can split these term into three separate terms.

[tex]{(2 {a}^{3} {b}^{4})}^{4} = {2}^{4} \times {( {a}^{3}) }^{4} \times {( {b}^{4} )}^{4} [/tex]

2 to the power of 4 is 16.

[tex] {2}^{4} = 16[/tex]

As for the terms a and b, the two exponents can multiply with each other.

[tex] {( {a}^{3} )}^{4} = {a}^{(3 \times 4)} = {a}^{12} [/tex]

[tex] {( {b}^{4} )}^{4} = {b}^{(4 \times 4)} = {b}^{16} [/tex]

Now, we can directly multiply the values together by combining into one term.

Hence, the final answer is

[tex]16 {a}^{12} {b}^{16} [/tex]

Need help ASAP hshehebsbeb

Answers

Answer:

I thing option A. all real numbers.

but IAM not exactly sure....

Answer:

all real numbers is correct answer

What statement is true about the following pair of rectangles

Answers

Answer:

The second choice

Step-by-step explanation:

For this, we can use the process of elimination. The first choice is crossed out, since they are mix and matching the numbers. The third choice is also crossed out since the second choice is correct. The second choice is correct because 9/11*3=27/33.

Answer:

They are similar because 9/11 = 27/33

Classify the graph as a linear function, nonlinear function, or relation (non-
function)

Answers

Answer: Nonlinear function

Step-by-step explanation:

find the derivatives of f(X)=25​

Answers

Answer:

The derivative of any constant number is 0.

So,

Differentiating with respect to "x",

d f(x)/dx

=d 25/dx

=0

Which phrase describes the linear relationship between the values of x and y shown in the table?

-- --
X|Y
12|8
13|9
14|10
-- --
A. y is 4 less than x
B. y is 4 more than x
C. y is 2/3 of x
D. x is 4 less than y

Answers

Answer:

the answer is C...i guess?

Answer: its a

explanation: trust me, i did this question just now and got it right.

also.... BRAINLIEST PLEASE

If the function m(x) has the point (1, 9) on its graph name a point that would be on the function 17n(x) + 2.

(1, 155)
(17, 11)
(2, 17)
(1, 11)

Answers

9514 1404 393

Answer:

  (1, 155)

Step-by-step explanation:

Let f(x) = 17n(x) +2, where n(1) = 9.

Then we have ...

  f(1) = 17n(1) +2 = 17×9 +2 = 153 +2

  f(1) = 155

A point on the new graph would be (1, 155).

A student measured the lead content of a paint sample 4 times. The standard deviation of the measurements was found to be 0.76% of the average. Calculate the confidence interval at the 90% confidence level.

Answers

Answer:

[tex]CI =0.894%[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=4[/tex]

Standard deviation [tex]\sigma=0.76\% of \=x[/tex]

Confidence level [tex]\mu =90\%=0.90[/tex]

Degree of Freedom [tex]Df=n-1=3[/tex]

Therefore

Test T from table is given

 [tex]t=2.353[/tex]

Generally the equation for Confidence interval CI is mathematically given by

 [tex]CI =t*\frac{\sigma}{\sqrt{n}}[/tex]

 [tex]CI =2.353*\frac{0.76}{\sqrt{4}}[/tex]

 [tex]CI =0.894%[/tex]

What number must be added to both the numerator and denominator of the fraction 2/5 to get 7/8?
a) 13
b) 15
c) 17
d) 19​

Answers

The answer is D.
Adding 19 to both 2 & 5 in 2/5 will equal 21/24. 21/24 can then be simplified to 7/8.

If two line segments have the same length, which of the following must be
true?
• A. They share an endpoint.
C
B. a They form a right angle.k

C. They
are congruent.
D. They are equal.

Answers

Step-by-step explanation:

oprion C is the answer. The two line are congruent

Sally wants to make a chocolate crunchy cake.
The recipe uses 16 biscuits and 22 squares of chocolate.
13
Sally wants to make her cake with 24 biscuits.
How many squares of chocolate will she need?

Answers

Answer:

33 squares of chocolate need

Answer:

33 Biscuits

Step-by-step explanation:

Uni method

How much biscuits do we need for 1 square of chocolate?

22/16 = 1.3

For 1 square of chocolate she needs 1.3 Biscuits.

So for 24 biscuits,

24 * 1.3

=33 biscuits

George bought a shirt and a pair of pants at a clothing store. The pants cost $5.33 more than the shirt, and he used a $10 off coupon to purchase the shirt. The equation below is used to determine the cost of the shirt before the coupon, s.

Answers

Answer:

15.99

Step-by-step explanation:

5.33+5.33+5.33

What are the coordinates of the vertices of the triangle under the translation (x, y) -> (x + 2, y + 3)?


(−4, 5), (3, 4), (0, 0)


(6, −5), (5, 2), (1, −1)


(5, −4). (4, 3), (−1, 2)


(−5, 6), (2, 5), (−1, 1)

Answers

9514 1404 393

Answer:

  (d)  (−5, 6), (2, 5), (−1, 1)

Step-by-step explanation:

No answer choices have any points in common, so we only need to find one translated point to determine the correct answer choice.

For the point on the y-axis, (0, 2), the translation is ...

  (x, y) ⇒ (x +2, y+3)

  (0, 2) ⇒ (0 +2, 2 +3) = (2, 5) . . . . matches choice D

What’s the solution

Answers

Answer:

x ≥ 12

Step-by-step explanation:

-3/4x +2 ≤ -7

Subtract 2 from each side

-3/4x +2-2 ≤ -7-2

-3/4x  ≤ -9

Multiply each side by -4/3, remembering to flip the inequality

-3/4x * -4/3 ≥ - 9 *(-4/3)

x ≥ 12

Answer:

x>=12

Step-by-step explanation:

-3/4x + 2<=-7

-3/4x <= -7 -2

-3/4x<=-9

cross multiply

-3x<=-36

dividing throughout by -3

x>=12

What does the digit 8 represent in 687,413?
Eight hundred thousand
Eight thousand
Eight hundred
O Eighty thousand

Answers

Answer:

Eighty thousand

Step-by-step explanation:

Look at the place value chart.

Find the product with the exponent in simplest
form. Then, identify the values of x and y.
6
X
- 64
.
6
X
y =
DONE

Answers

Answer:

[tex]\displaystyle 8^\bigg{\frac{8}{3}}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \bigg(8^\bigg{\frac{2}{3}} \bigg)^4[/tex]

Step 2: Simplify

Exponential Rule [Powering]:                                                                           [tex]\displaystyle 8^\bigg{\frac{2}{3} \cdot 4}[/tex]Multiply:                                                                                                             [tex]\displaystyle 8^\bigg{\frac{8}{3}}[/tex]

The frequency n of vibration of a stretched string is a function of its tension F, the length l and the mass per unit length m. From the knowledge of dimensions, prove that, n∝1/l √f/m
Pls fast

Answers

Answer:

n ∝ (1/l) (√F/m)

Step-by-step explanation:

Since frequency, n of vibration of a stretched string is a function of its tension F, the length l and the mass per unit length m, and has dimensions [T]⁻¹ where T = time, its dimension must be equal to that of the combination of F, L and m

Since n = f(F,L,m)

n = kFᵃLᵇmˣ

dimension of n = (dimension of F)ᵃ × (dimension of L)ᵇ × (dimension of m)ˣ

Since n = frequency, dimension of n = [T]⁻¹

F = Force, dimension of F = [M][L][T]⁻²

Also, L = length, dimension of L = [L] and

m = mass per unit length, dimension of m = [M][L]⁻¹

So, n = FᵃLᵇmˣ

[T]⁻¹  = ([M][L][T]⁻²)ᵃ( [L] )ᵇ([M][L]⁻¹)ˣ

[T]⁻¹  = ([M]ᵃ[L]ᵃ[T]⁻²ᵃ[L]ᵇ([M]ˣ[L]⁻ˣ

[M]⁰[L]⁰[T]⁻¹  = ([M]ᵃ ⁺ˣ)([L]ᵃ ⁺ ᵇ ⁻ˣ)([T]⁻²ᵃ)

equating the exponents on both sides, we have

a + x = 0  (1 )⇒ x = -a

a + b - x = 0 (2) ⇒

-2a = -1 (3) ⇒ a = 1/2

Substituting x into 2, we have

a + b -(-a) = 0

a + b + a = 0

2a + b = 0

b = -2a

b = -2 (1/2)

b = -1

x = -a = -1/2

So, substituting the variables into n, we have

n = kFᵃLᵇmˣ

n = kFᵃLᵇmˣ

[tex]n = kF^{\frac{1}{2} }L^{-1}m^{-\frac{1}{2} }[/tex]

n = k/l(√F/m)

n ∝ (1/l) (√F/m)

PLS HELP ASAP
Graph x+3y=6x

Answers

Answer:

Not sure what more you need, but here is an example of the graph on Desmos.

Answer:

Your graph should look like the one on the pic...

☆•☆•☆•☆•☆•☆

Hope it helps. .

Have a great day!!

NEED HELP ASAP

6 th grade mathematics question

Answers

Answer:

B, 8 (2a+3b).

Step-by-step explanation:

First, let's let A=1 and B=2. 16a+24b would equal 64, and so would B, which is 8 (2a+3b). Then lastly you solve, and you get 64 for both of them, which means B is equal to that expression.

Answer:

B

Step-by-step explanation:

8(2a) = 16a

8(3b) = 24b

16a + 24b

Photo attached!!!!!!!

Answers

Answer:

i cant see the photo

Step-by-step explanation:

Tính I = tích phân ( x^2 - 3xy) dx + ( x-y) dy với đường cung định hướng AB là ve tẻ nối điểm A ( 2,3 ) và B ( 1 , 1 )

Answers

izvzzhhhbhbugggtguguzvzuvutggutfztfutftzflsosskkxjissosos

Jim is the quarterback on his football team.
He was sacked 3 times during the game.
Each time he was sacked, the team lost 7
yards. What was the total number of yards
lost from the sacks?

Answers

Answer: 21 yards

Step-by-step explanation:

Multiply 3 by 7 to find the number of years lost from the sacks because he was sacked 3 times and each time he lost 7 yards.

He lost 7 yards per sack , so in three sacks  he will lose 21 yards.

3* 7 = 21

A ball is thrown vertically upward from the top of a building. The height (in meters) of the ball after t seconds is given by the function
s(t) = -(t-3)^2+ 14. Find the instantaneous velocity of the ball at t= 4 seconds by considering the average velocities over the intervals [3.5, 4],
[3.7.4]. [3.9,4]. [3.99, 4], [4, 4.01], [4, 4.1], [4, 4.3], and [4,4.5).
ОА.
1.50 m/sec.
OB.
2.00 m/sec.
Ос.
-2.00 m/sec.
OD. -1.50 m/sec.

Answers

9514 1404 393

Answer:

  C.  -2.00 m/sec

Step-by-step explanation:

The average velocity on the interval [a, b] is found by ...

  m = (s(b) -s(a))/(b -a)

One end of the interval remains constant here, so we can define 'd' so that the interval is [4, 4+d]. Then the average velocity is ...

  m = (s(4 +d) -s(4))/((4 +d) -4)

  m = (s(4+d) -s(4))/d

The attached table shows the average velocity values on the intervals required by the problem statement. Respectively, they are ...

  -1.5 m/s, -1.7 m/s, -1.9 m/s, -1.99 m/s, 2.01 m/s, 2.1 m/s, 2.3 m/s, 2.5 m/s

We expect the instantaneous velocity at d=0 to be the average of the values at d=-0.01 and d=+0.01. We estimate the instantaneous velocity at t=4 seconds to be -2.00 m/s.

HELPPPPPPPPPP

Which of the following is equivalent to the expression below ?

square root 8 minus square root 72 plus square root 50 ?

A. 13 square root 2
B. 7 square root 2
C. 3 square root 2
D. Square root 2

Answers

Answer:

a13 square root

..cv

..

..

The Punjab Highway department is studying traffic pattern on G.T. Road near Lahore. As part of previous study, population standard deviation is 680 number of vehicles per day. A random sample of 64 days gives mean of 5410 cars. Find a 90 percent confidence interval for population Mean (the average number of vehicles per day).

Answers

Answer:

for this we need 90 percent 5410

so we multiply 5410*0.9=4869

Hope This Helps!!!

A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful, however he cannot try more than 3 times or the phone will lock him out. Let S denote a successful attempt and F denote a failed attempt. What is the sample space for this random experiment

Answers

Answer:

(S, FS, FFS, FFF)

Step-by-step explanation:

According to the Question,

Given, A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful.however, he cannot try more than 3 times or the phone will lock him out.Let, S denote a successful attempt and F denote a failed attempt.

So, the sample space for this random experiment is

{S, FS, FFS, FFF}

The person stops trying when he successfully enters the code or when he has failed at all 3 attempts .

Mary wants to buy candies with an amount of money she has in her pocket.  we know that if she had $3.20 more money she could buy 120 candies. While if she had $2.40 less money she could buy 85 candies. What is the price per candy?

Answers

Answer:

the price per candy is $0.16

and she has $16.00 in her pocket.

Step-by-step explanation:

x = the money in her pocket.

y = the price per candy

x + 3.2 = 120×y

x - 2.4 = 85×y

y = (x - 2.4)/85

=>

x + 3.2 = 120×(x - 2.4)/85 = (24x - 57.6)/17

=>

(17x + 17×3.2)/17 = (24x - 57.6)/17

17x + 54.4 = 24x - 57.6

54.4 = 7x - 57.6

112 = 7x

x = 16

y = (16 - 2.4)/85 = 13.6/85 = 0.16

Other Questions
Based on the passage, what is Victors expectation for this school year? "All that is valuable in human society depends upon the opportunity for development accorded the individual." justify the statement with reasonable points. The Loud House Center of Chaos Calculate the simple interest on a loan of $9000 at an interest rate of 8% for 6 years? PLEASE HELP MEEE The math score for ten of Mrs. Moore's students are shown below. How many students made a score of more than 69 but less than 90? The gloom inside the house enveloped me as I stepped through the door. All around I could hear stealthy footsteps and ominous creaking. As an unearthly cry filled the room, I let out my own cry of dread.What is the purpose of this passage?to narrateto persuadeto informto describe Alicia wants to bake a cake with /10 grams of flour.However,she only has grams of flour she needs.How much does she have? prove that SinAtanA=cosA mong moi nguoi giup do Beth owns a corporate office park in Ohio. Her ownership rights include the right to sell or give away the property without restriction, as well as the right to commit waste, if she chooses. Beth's ownership interest is: Which angles are complementary? I'm not sure if its B. what is it when called when businesses produce goods and services that consumers do not want Ayyo help a girl out please-An object is pulled to the right using spring balance. The spring balance reads 20N. The object is moving with constant speed, so the net force acting on it is equal to zero. If we consider that the force of pull and the friction force are the only forces acting on the object, what will be the value of the friction force? Explain. Help me i need the answer now!!!!!:( Jamal works at a sporting goods store on the weekends. Suppose last weekend he worked 12.5 hours and earned $110. How much money does Jamal earn per hour? Step I: Write an equation you can use to solve the problem. Be sure to define the variable you use. NOTE: If you are paid hourly, you must multiply your hourly rate by the number of hours worked in a week to find the amount of money made. (4 Which answer does not describe the benefits to the industry-wide practice of localization?a) It is only used in the game industryb) It creates wide audience appealc) It is time-savingd) It is cost-effective Complete the solution of the equation. Find thevalue of y when x equals 0.6x - 2y = 14 Which aspect of a story is most likely to contribute to its theme?A. The reading levelB. The story's plotC. The story's lengthD. The reader's age Whats the word for this definition? The change in the Y values divided by the change in X values A German travel company considers its futureA German travel company decides to stop selling holidays in Italy and instead to offer holidays in a new destination. This is the Maldives, a group of islands in the Indian Ocean, famous for their long hours of sunshine and sandy beaches. Tourism is a fast growing industry. Not all families, however, are able to go on holiday whether at home or abroad. Most of those who take holidays would like to have more holiday breaks.a. What evidence is there in the passage of scarcity? (3)b. Using examples, identify three factors of production involved in providing holidays in the Maldives.(6)c. Explain the difference between an economic good and a free good.(4)d. Identify a free good from the passage.(1)e. Explain the relevance of opportunity cost for a travel firm in deciding how to use its resources.(6)