You have learned that pi is the ratio of the circumference of any circle to its diameter. The decimal value of pi is shown below

Pi= 3.1415926535897932

Step-by-step explanation:

To know how many eighths you have in two bars, simply divide 2 by 1/8

2/1 ÷ 1/8

Ans 2÷ ⅛

Answer: x=14

Step-by-step explanation:

Add 5 to both sides to get the x alone and get your answer.

Paul's monthly payment is $142.

What is the monthly payment?

What you pay each month to the lender to pay back your loan is known as your monthly payment. Your mortgage loan's terms will determine how much you pay each month. This includes both the loan's interest and principal, which is the actual amount owed.

Here, we have

The price of the TV is £1600 plus 20% VAT and he deposited £500 and the balance in ten equal monthly payments.

We have to calculate each monthly payment.

By applying monthly payment formula, we get

Price of the TV = $1600

20% VAT = $(1600 ×(1+ 20/100))

= $1920

He pays a £500 deposit.

So, balance = $(1920 - 500) = $1420

When this balance is paid in ten equal monthly payments, then the amount of each payment is $(1420/10)  = $142

Hence, Paul's monthly payment is $142.

To learn more about the monthly payment from the given link

https://brainly.com/question/25599836

#SPJ1

Answer:

I think 58% I’m not 100% sure but yea

Step-by-step explanation:

I divided the number of votes for printed 71 by the total number of votes 122 so 71/122=.58 58%

Answer:

1. i^20 X (2+i^22)

2. i² X (i¹¹-1) X (i²² + i¹¹ + 1) X (i^66 + i³³ + 1)

Step-by-step explanation:

1) 2i^20 + i^42

factor out i^20

i^20 X (2 + i^22)

2) i^101 - i²

i²X(i^99-1)

i²X(i³³-1)X(i^66+i³³+1)

Using a³-b³=(a-b)(a²+ab+b²)

i²X(i¹¹-1)X(i²²+i¹¹+1)X(i^66+i³³+1)

i²X(i¹¹-1)X(i²²+i¹¹+1)X(i^66+i³³+1)

I almost gave up typing. Quite stressful, but its fine

Answer:

A”(-3, -18) B” (0, -27) C” (-12, -30)

Step-by-step explanation:

Two transformations have been listed beneath the graph. Complete them in order to get the solution.

The first transformation is a translation. A translation involves moving the shape across the graph without altering its form. To receive the coordinates for this. Add the <-3, -8> given to coordinates A, B, and C. Which should result in the following: A (-1, -6) B (0, -9) C (-4, -10)

Now complete the second transformation, which is a dilation. Dilations happen when a shape is either made smaller or larger by a set number. To complete the second transformation: take the number given: “3” and multiply each number in the coordinate sets you got after the first transformation by this number.

Which should result in: A”(-3, -18) B” (0, -27) C” (-12, -30)

The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

To learn more about logarithm click here: brainly.com/question/30226560

#SPJ11

Answer:

0.5625:1

Step-by-step explanation:

unit rate has a denominator of 1

Answer:

$107.60

Step-by-step explanation:

100 [1 + (0.076 * 1)] = 107.6

= $107.60

Answer:

c

Step-by-step explanaticcon:

Answer:

C. 13/35

Step-by-step explanation:

Step 1: Write expression

4/5 - 3/7

Step 2: Find common denominator

5(7) = 35

7/7(4/5) - 5/5(3/7)

28/35 - 15/35

13/35

Answer: 12.50= 2x + 3y,

5.50= 2x+y,

5=x+Y

Step-by-step explanation: Use a graphing calculator bro

Answer:

y = 2x - 3

Step-by-step explanation:

We want to write the equation as y = ax + b, where a is the slope and b is the y-intercept.

Answer:

It's D.

Step-by-step explanation:

Answer:

:P

Step-by-step explanation:

Answer: Positive correlation

Step-by-step explanation:

As you go up and along the graph the values go up.

Both have to be increasing basically.

The secret is s=(4,5,7,2,3,6). Throughout this question, we will be working in mod11. Consider the problem of sharing a secret among n people such that at least k≤n of them must collude to retrieve it. We will do so by method of intersecting hyperplanes. The dealer's algorithm for distributing the secret can be outlined as:-

Select a point (s0,s1,…,sn) that is secret.- For 1≤i≤k and 0≤j≤n, set arbitrary values for aij and find ci such that ci≡sn−(∑j=0n−1aijsj)(mod11)- Define the ith hyperplane as −ci≡(∑j=0n−1aijxj)−xn(mod11)- Distribute the hyperplanes to each of the n participants.

Retrieving the secret is then trivially equivalent to solving the corresponding matrix problem. Compute an actual example of the dealer's algorithm along with secret extraction with n=6,k=3.

For this problem, we have k=3 and n=6. We need to select a secret point s0,s1,…,sn which is a secret.

For this problem, let us take secret point s0=4, s1=5, s2=7, s3=2, s4=3, and s5=6. That is s=(4,5,7,2,3,6).

Now, we need to select the arbitrary values of aij for 1≤i≤k and 0≤j≤n.

We have k=3, n=6, therefore i=1,2,3 and j=0,1,2,3,4,5.

Let's take the arbitrary values of aij as shown below:

a11=1,a12=1,a13=0,a14=0,a15=0,a16=0a21=1,a22=0,a23=1,a24=0,a25=0,a26=0a31=0,a32=1,a33=1,a34=0,a35=0,a36=0

From the above, we need to find the values of ci. We can write the equation as below:

ci≡sn−(∑j=0n−1aijsj)(mod11)For i=1,2,3 and j=0,1,2,3,4,5.

Let's calculate ci as shown below:

c1= 4(1) + 5(1) = 9c2= 4(1) + 7(1) = 2c3= 5(1) + 7(1) = 0

Thus, we have c=(9,2,0).For the ith hyperplane, we can write the equation as below:

-ci≡(∑j=0n−1aijxj)−xn(mod11)For i=1,2,3 and j=0,1,2,3,4,5.

Let's calculate the ith hyperplane as shown below:H1: −9≡x0+x1(mod11)H2: −2≡x0+x2(mod11)H3: 0≡x1+x2(mod11)

The above are the hyperplanes, we can distribute these hyperplanes to each of the n participants and retrieving the secret is then trivially equivalent to solving the corresponding matrix problem.

We can write the above system of equations as below:x0=−9−x1(mod11)x0=−2−x2(mod11)x1=−x2(mod11)

Now, let's find the values of x1 and x2 as shown below:x1=−x2(mod11)x0=−2−x2(mod11)=−2−x1(mod11)=−2−(−x2)(mod11)=−2+x2(mod11)So, we get x2=10, x1=1, and x0=0.Thus, the secret is s=(4,5,7,2,3,6).

Let p be the actual number of people in collusion - prove by suitable mathematical argument that for p

Learn more about dealer's algorithm - https://brainly.com/question/16283725

#SPJ11

Answer:

less than

this is 100% correct

Answer:

x = 7

Step-by-step explanation:

The proportion is

14/6 = 21/(3x - 12)                 Cross Multiply

14*(3x - 12) = 6*21                 Remove the brackets and combine

42x - 168 = 126                     Add 168 to both sides

42x = 126 + 168

42x =  294                           Divide by 42

x = 294/42

x = 7

Answer:

1/81

Step-by-step explanation:

\((-1/3) ^4\\\\\mathrm{Apply\:exponent\:rule}:\\\quad \left(-a\right)^n=a^n,\:\quad \mathrm{if\:}n\mathrm{\:is\:even}\\\\\left(-\frac{1}{3}\right)^4=\left(\frac{1}{3}\right)^4\\\\\mathrm{Apply\:exponent\:rule}:\\\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}\\\\\left(\frac{1}{3}\right)^4=\frac{1^4}{3^4}\\\\1^4=1\\3^4=81\\\\=\frac{1}{81}\)

The value of \(\((-1/3)^4\)\) using property of exponents is \(\(\dfrac{1}{81}\)\).

To simplify the expression \(\((-1/3)^4\)\), calculate the power of the numerator and the denominator separately.

\(\((-1/3)^4 = \left(\dfrac{-1}{3}\right)^4\)\)

Now, let's simplify each part:

\(\(\left(\dfrac{-1}{3}\right)^4 = \dfrac{(-1)^4}{3^4}\)\)

Using the exponent property

\((\dfrac{a}{b} )^4 = \dfrac{a^4}{b^4}\)

\(\(\dfrac{(-1)^4}{3^4} = \dfrac{1}{3^4}\)\)

The denominator \(\(3^4\)\) means 3 raised to the power of 4, which equals 81.

\(\(\dfrac{1}{3^4} = \dfrac{1}{81}\)\)

Therefore, \(\((-1/3)^4\)\)simplifies to  \(\(\dfrac{1}{81}\)\).

Learn more about exponent and power here:

https://brainly.com/question/28515493

#SPJ6

Answer:

Two zeros are 17 and -5

Step-by-step explanation:

Given:

f(x) = x² - 12x - 85

Find:

Zeros of the function

Computation:

f(x) = x² - 12x - 85

f(x) = x² - (17 - 5)x - 85

f(x) = x² - 17x + 5x - 85

f(x) = x(x - 17) + 5(x - 17)

f(x) = (x - 17) (x + 5)

So,

x - 17 = 0 , x + 5 = 0

So,

x = 17 , x = -5

Two zeros are 17 and -5

Answer:

3 x X - 14

Step-by-step explanation:

Is your algebra expression.

Answer:

3x-14

Step-by-step explanation:

Product of 3 and number is 3*x

For " 14 fewer than.." we simply subtract 14.

So we get 3x-14

Answer:

A) 12

Step-by-step explanation:

Notice that \(\int\limits^5_1 {f(x)} \, dx=-\int\limits^1_5 {f(x)} \, dx\) by the exchange-of-limits property of integrals, so  \(-\int\limits^1_5 {f(x)} \, dx=-1\)

We also know that \(\int\limits^1_{-1} {f(x)} \, dx+\int\limits^5_1 {f(x)} \, dx=\int\limits^5_{-1} {f(x)} \, dx\) by the additivity property of integrals, which means that:

\(\int\limits^1_{-1} {f(x)} \, dx+\int\limits^5_1 {f(x)} \, dx=\int\limits^5_{-1} {f(x)} \, dx\\\\\int\limits^1_{-1} {f(x)} \, dx-\int\limits^1_5 {f(x)} \, dx=\int\limits^5_{-1} {f(x)} \, dx\\\\5-1=\int\limits^5_{-1} {f(x)} \, dx\\\\4=\int\limits^5_{-1} {f(x)} \, dx\)

Therefore, \(3\int\limits^5_{-1} {f(x)} \, dx=3(4)=12\)

Answer:

6π

24π

54π

96π

Step-by-step explanation:

Cone 1:

Height, h= 18 meters

Radius, r = 1

Volume of cone 1 = πr²h/3

= (π * 1² * 18)/3

= (π * 1 * 18)/3

= 18π/3

= 6π

Cone 2:

Height, h= 18 meters

Radius, r = 2

Volume of cone 2 = πr²h/3

= (π * 2² * 18)/3

= (π * 4 * 18)/3

= 72π/3

= 24π

Cone 3:

Height, h= 18 meters

Radius, r = 3

Volume of cone 3 = πr²h/3

= (π * 3² * 18)/3

= (π * 9 * 18)/3

= 162π/3

= 54π

Cone 4:

Height, h= 18 meters

Radius, r = 4

Volume of cone 4 = πr²h/3

= (π * 4² * 18)/3

= (π * 16 * 18)/3

= 288π/3

= 96π

If a is an integer, when is a/b always equal to an integer

= b<1

We will have the following:

*First: We determine the measure of angle L:

So, the measure of angle L is 23°.

*Second: We will use the measure of MN and the angle of L to determine the length of the hypotenuse:

So, the length of the hypotenus is approximately 20.5 units.

Here is the graph that shows the scenario:

The solution to the initial-value problem is y(t) = sin(t) - [e^(-πt) - e^(-2πt)] × u(t-π)/2, 0 ≤ t < ∞.

To solve this initial-value problem using Laplace transform, we will apply the Laplace transform to both sides of the differential equation and use the initial conditions to find the Laplace transform of y.

Taking the Laplace transform of both sides of the differential equation, we get

Ly'' + Ly = Lf(t)

Using the properties of Laplace transform, we can find Ly' and Ly as follows

Ly' = sLy - y(0) = sLy - 0 = sLy

Ly'' = s^2Ly - s*y(0) - y'(0) = s^2Ly - 1

Substituting these expressions into the differential equation, we get:

s^2Ly - 1 + Ly = Lf(t)

Simplifying, we get

Ly = Lf(t) / (s^2 + 1) + 1/s

Now we need to find the Laplace transform of f(t). Using the definition of Laplace transform, we get

Lf(t) = ∫[0,π] 0e^(-st) dt + ∫[π,2π] 1e^(-st) dt + ∫[2π,∞) 0*e^(-st) dt

= 1/s - (e^(-πs) - e^(-2πs))/s

Substituting this expression into the equation for Ly, we get

Ly = [1/s - (e^(-πs) - e^(-2πs))/s] / (s^2 + 1) + 1/s

Now we need to find y(t) by taking the inverse Laplace transform of Ly. We can use partial fraction decomposition to simplify the expression for Ly

Ly = [(1/s)/(s^2 + 1)] - [(e^(-πs) - e^(-2πs))/s]/(s^2 + 1) + 1/s

Using the inverse Laplace transform of 1/(s^2 + 1), we get

y(t) = sin(t) - [e^(-πt) - e^(-2πt)]*u(t-π)/2

where u(t) is the unit step function.

Learn more about Laplace transform here

brainly.com/question/14487937

#SPJ4