Let R = Z[i] and let A = {a + bi : a, b element of 2Z}. Show
that R is a subring but not an ideal of R.

Answer:

what am i supposed to answer?

Step-by-step explanation:

Step-by-step explanation:

5 +0.24 = 5 + 24 = 12 = 6

100 50 25

= 5 6

25

After 3 hours, approximately 318.5 mg of the painkiller remains in the body.

The function for the amount of painkiller remaining in the body after h hours can be described :

A(h) = A0 * \(e^{-kt}\)

Where:

A(h) is the amount of painkiller remaining in the body after h hours

A0 is the initial amount of painkiller (in this case, 450 mg)

k is the decay constant, which can be determined from the half-life of the painkiller using the formula

k = ln(2)/t1/2, where t1/2 is the half-life

t is the time elapsed in hours

Using the given half-life of 8 hours, we can calculate the decay constant:

k = ln(2)/8 = 0.0866

So the function for the amount of painkiller remaining after h hours is:

A(h) = 450 * \(e^{-0.0866h}\)

To find out how much remains after 3 hours, we simply plug in h=3:

A(3) = 450 * )\(e^{-0.0866*3}\) = 318.5 mg (rounded to one decimal place)

Therefore, after 3 hours, approximately 318.5 mg of the painkiller remains in the body.

know more about exponential function visit :

https://brainly.com/question/14355665

#SPJ1

(a) The probability of enough sleep and not enough exercise is 0.14.

(b) The probability of not enough sleep and enough exercise is 0.11.

(c) The probability of not enough sleep and not enough exercise is 0.47.

To find the probabilities of the given events, we can use set theory and the principle of inclusion-exclusion.

Let's define:

A = event of getting enough sleep

B = event of getting enough exercise

Given information:

P(A) = 0.42 (probability of getting enough sleep)

P(B) = 0.39 (probability of getting enough exercise)

P(A ∩ B) = 0.28 (probability of both getting enough sleep and enough exercise)

(a) Event of enough sleep and not enough exercise:

P(A ∩ B') = P(A) - P(A ∩ B)

= 0.42 - 0.28

= 0.14.

The probability of enough sleep and not enough exercise is 0.14.

Rule used: We used the subtraction rule, which states that the probability of event A occurring and event B not occurring is equal to the probability of event A minus the probability of both A and B occurring.

(b) Event of not enough sleep and enough exercise:

P(A' ∩ B) = P(B) - P(A ∩ B)

= 0.39 - 0.28

= 0.11.

The probability of not enough sleep and enough exercise is 0.11.

Rule used: We used the subtraction rule.

(c) Event of not enough sleep and not enough exercise:

P(A' ∩ B') = 1 - P(A ∪ B) (by the complement rule)

= 1 - [P(A) + P(B) - P(A ∩ B)] (by the inclusion-exclusion principle)

= 1 - [0.42 + 0.39 - 0.28]

= 1 - 0.53

= 0.47.

The probability of not enough sleep and not enough exercise is 0.47.

Rule used: We used the inclusion-exclusion principle.

To learn more about probability here:

https://brainly.com/question/31828911

#SPJ4

The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

To learn more about factor click here

brainly.com/question/26923098

#SPJ11

Answer:

$3.02

Step-by-step explanation:

You just subtract 97.98-94.96.

Answer:

3.02

Step-by-step explanation:

you subtract 94.96 from 97.98

Hey there! :)

Answer:

The polygon has 8 sides.

Step-by-step explanation:

Use the sum of interior angles formula to solve.

The sum of the interior angles is equal to (n-2)180. If 135° is one angle, we can simply set up an expression to represent this situation:

135 = (n-2)· 180 / n

Multiply both sides by n:

135n = (n-2) · 180

Distribute the 180:

135n = 180n - 360

Subtract 180n from both sides:

-45n = -360

Divide both sides by -45:

n = 8. The polygon has 8 sides.

Answer:8 sides

Step-by-step explanation:

Answer:

So You have to minus $39.50-$61.25 to getnegative 11.75

Based on the monthly expenses breakdown, getting a car loan to cut down on monthly car repair cost would be a good move.

Using the parameters given :

Total income : $705.00

Total Expenses : $510.00

Amount saved = $225.00

The amount saved from Last month's income is quite okay. However, looking at the breakdown of her expenses, we can see that she spent quite a lot on car repairs.

It would be advisable of Lianna could get a good car which would allow her to cut down on repair cost because in the long run, it could eat up her savings as well.

Hence, Lianna should opt for a car loan to cut down on repair cost.

Learn more on savings :https://brainly.com/question/25787382

#SPJ1

Answer:

b

Step-by-step explanation:

just add x values and numbers

None of the expressions is an identity

The expressions are given as:

I. y=x

II. 4 = 3x^2 + 2

III. x=x

In algebra, there are three identities; and they are

None of the given expression take the above forms

Hence, none of the expressions is an identity

Read more about expressions at:

https://brainly.com/question/723406

#SPJ1

Answer:

Sides = 3.2

Diagonals = 4.5

Shape = Square

Step-by-step explanation:

a) i) Distance from P to Q= 3.162278 which is approx 3.2.

So to calculate your answer you use the distance formula. The formula is the square root of (x2 - x1) + (y2 - y1).

So all sides of the shape have a length of 3.2 because the shape is a square.

DIAGONALS:

QS = 4.472136 approx 4.5

For:

(X1, Y1) = (-3, -2)

(X2, Y2) = (-1, 2)

We use the same formula for distance.

B) The shape is a square

I REALLY HOPE THIS HELPED

To find the Laplace transform of a function, we apply the definition of the Laplace transform and use known transform pairs. The Laplace transform of a function f(t) is denoted as F(s) and is given by the integral of f(t) multiplied by\(e^(-st),\) where s is the complex frequency variable.

a) For the equation t³ + 5t - 2, we apply the linearity property of the Laplace transform and calculate the transform of each term separately. The Laplace transform of\(t^n\) (n is a positive integer) is n!/s^(n+1). Therefore, the Laplace transform of t³ is 3!/s^4. The Laplace transform of 5t is 5/s, and the Laplace transform of -\(2 is -2/s^0\). Combining these terms, we have F(s) =\(3!/s^4 + 5/s - 2.\)

b) For the equation (t² + 1)e²t - e^-³t sin(t), we again apply the linearity property and calculate the transforms of each term. The Laplace transform of\(t^2 is 2!/s^3\), the Laplace transform of 1 is 1/s, the Laplace transform of\(e^at\) is 1/(s - a), and the Laplace transform of sin(t) is\(1/(s^2 + 1).\)Combining these terms and applying the shifting property for the exponential term, we have F(s) = \((2!/s^3 + 1/s) * (1/(s-2)) - 1/(s+3)^2 + 1/(s^2 + 1).\)

c) For the differential equation y" - \(2y' - 4y = 2te^-t\), we apply the Laplace transform to both sides of the equation and use the transform pairs for derivatives and the multiplication property. The Laplace transform of y" is s^2Y(s) - sy(0) - y'(0), the Laplace transform of y' is sY(s) - y(0), and the Laplace transform of y is Y(s). Using these transforms and the known transform pairs for\(e^at\) and t, we can solve for Y(s). The final Laplace transform equation will involve Y(s), the initial conditions, and the Laplace transform of \(2te^-t.\)

Learn more about Laplace transform here:

https://brainly.com/question/14487937

#SPJ11

Given limits are lim x→3-5 , lim (x + 7) , lim x² x-10 , lim (4- 3.x²) 1112 , lim 4 1-1 f. lim 2 X-3. To solve these limits, we need to simplify each limit and substitute the value of x.

Let’s calculate the given limits one by one.

lim (x + 7) as x → -7

When x → -7, the given limit becomes

lim (x + 7)= -7 + 7= 0

Therefore, the limit equals to 0.

lim x → 3x²/x - 10

We need to apply the L'Hopital's rule to solve the above limit.

The rule says that if f(x) and g(x) are differentiable at x = a and g(a) ≠ 0, thenlim x → a f(x)/g(x) = lim x → a f '(x)/g '(x)

Applying this rule to the above limit, we getlim x → 3x²/x - 10= lim x → 3 (2x)/1= 6

Therefore, the limit equals to 6.

lim x → 1- 3x²/1 - x1 - x= -1

When x → 1-, the given limit becomes lim x → 1- 3x²/1 - x= lim x → 1- 3x²/ -(x - 1)= lim x → 1- (3x + 3)/-1= 0

Therefore, the limit equals to 0.d)lim x → ∞(4 - 3x²)/1112

Here, x is tending towards infinity. Therefore, the limit becomes lim x → ∞(4 - 3x²)/1112= lim x → ∞ - 3x²/1112= -∞

Therefore, the limit is negative infinity.e)lim x → 14 1-1= lim x → 1(4-1)= 3

Therefore, the limit equals to 3.f)lim x → 3(2x - 6)= 2(3) - 6= 0

Therefore, the limit equals to 0.Thus, the limits are given as follows;lim x → 3-5 = Not defined lim x → -7(x + 7) = 0

lim x → 3x²/x - 10 = 6

lim x → 1- 3x²/1 - x = 0

lim x → ∞(4 - 3x²)/1112 = -∞

lim x → 14 1-1 = 3

lim x → 3(2x - 6) = 0

Hence, we have calculated the given limits by using different rules and concepts of calculus.

To know more about L'Hopital's rule visit:

brainly.com/question/29279014

#SPJ11

Answer:

9

Step-by-step explanation:

i can not really tell what letters are on the picture but i think it is 9

The customer should conclude that the GEM Fund is being sold at a premium, as its POP is higher than its NAV. Conversely, the ABC Fund is being sold at a discount, as its POP is lower than its NAV.

The Net Asset Value (NAV) represents the value of a mutual fund's assets per share. It is calculated by dividing the total value of the fund's assets by the number of shares outstanding. The Public Offering Price (POP), on the other hand, is the price at which new shares of the mutual fund are being sold to investors.

In the given scenario, the GEM Fund has an NAV of $12 and a POP of $12.50. Since the POP is higher than the NAV, it indicates that investors are required to pay a premium of $0.50 per share to purchase the GEM Fund. This premium can be seen as an additional cost or fee associated with buying into the fund.

On the other hand, the ABC Fund has an NAV of $11.50 and a POP of $10.98. Here, the POP is lower than the NAV, suggesting that investors can purchase shares of the ABC Fund at a discount of $0.52 per share compared to its underlying asset value.

Therefore, based on the provided information, the customer can conclude that the GEM Fund is being sold at a premium, while the ABC Fund is being sold at a discount.

Learn more about Net Asset Value (NAV) here:

https://brainly.com/question/29988660

#SPJ11

Answer:

6 trials

Step-by-step explanation:

The number of rats that run the maze incorrectly after t trials ;

N(t) = 100e^-0.14t

Initial number of rats = 100

45% of rats to run the maze incorrectly ; 45% * 100 = 45 rats

N(t) = 45

N(t) = 100e^-0.14t

45 = 100e^-0.14t

45/100 = e^-0.14t

0.45 = e^-0.14t

Take the In of both sides :

In(0.45) = In(e^-0.14t)

- 0.798507 = - 0.14t

Divide both sides by -0.14

- 0.798507 / - 0.14 = - 0.14t / - 0.14

5.7036 = t

To the nearest whole number :

Number of trials, t = 6 trials

Answer:

D

Step-by-step explanation:

I checked it on desmos and also the shift is 1 up that means subtracting from a larger number

Answer: d

Step-by-step explanation:

The area of the regular octogon is 196.15 square inches.

For a regular octogon with apothem A and side length L, the area is given by:

area =(2*A*L) * (1 + √2)

Here we know that:

A = 7in

L = 5.8 in

Replacing these values in the area for the formula, we will get the area:

area = (2*7in*5.8in) * (1 + √2)

area = 196.15 in²

Learn more about area at:

https://brainly.com/question/24487155

#SPJ1

Answer:

670.21 inches^3

Step-by-step explanation:

To find the volume of the spheres, all you need to know is the formula for the volume of a sphere, which you've included in your problem. From the problem, you also know that r = 2. From here, you calculate the volume of 1 of the spheres, which turns out to be:

V = 33.51032

Since there are 20 spheres in this box, you multiple the volume of a single sphere by 20 to get the total volume occupied by the spheres.

V = 20 * 33.51032

V = 670.2064

If you round to 2 decimal places, this becomes 670.21.

\( \binom{ 1/3}{-2/3} \binom{1/3}{-1/6} \)

The probability that both marbles are blue is 1/4.

Since the marble is put back into the bag before the second draw, the probability of drawing a blue marble on the first draw is 3/6 or 1/2, and the probability of drawing a blue marble on the second draw is also 3/6 or 1/2.

The probability of both events happening together (drawing a blue marble on the first and second draws) is equal to the product of the probabilities of each event occurring separately, since the two events are independent of each other:

P(Blue on first draw AND Blue on second draw) = P(Blue on first draw) x P(Blue on second draw)

= 1/2 x 1/2

= 1/4

Therefore, the probability of drawing two blue marbles in a row with replacement is 1/4 or 25%.

To learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

Answer:

Solve.

Step-by-step explanation:

make the 2 3 and 1 then turn them into 20 30 and 10 then you need to add them together to get the answer divide that by thirty and if its more than half yes, less than half no.

So the total amount received by Sohail is 100 * y². To get the precise amount, we must first determine the value of x.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Let's call the number of days Sohail was in town and cleaned the house "y". Then we can write:

y = x - 8 (since he was out of town for 8 days)

And the amount he was promised per day is 10, so the total amount promised is:

10 * y = 10 * (x - 8)

At the end of the break, his mother decided to square the amount due to him, so the final amount he received is:

(10 * y)² = (10 * (x - 8))²

Expanding the square and simplifying, we get:

100 * y²= 100 * (x - 8)²

So the final amount Sohail received is 100 * y². To find the exact value, we need to know the value of x.

To know more about expression,

https://brainly.com/question/30091997

#SPJ1

It takes Bill approximately 6.5 hours to clean the house alone. Since it takes Billy one hour longer, it takes him approximately 7.5 hours to clean alone.

Let's denote the time it takes Bill to clean the house alone as "x" hours. According to the given information, it takes Billy (the son) one hour longer to clean alone than it takes his dad. Therefore, it takes Billy "x + 1" hours to clean alone. When they work together, they can clean the house in 4 hours. We can set up the following equation based on their combined work rate:

1/x + 1/(x + 1) = 1/4

[(x + 1) + x] / (x * (x + 1)) = 1/4

(2x + 1) / (x * (x + 1)) = 1/4

Cross-multiplying, we have:

4(2x + 1) = x * (x + 1)

\(8x + 4 = x^2 + x\\x^2 - 7x - 4 = 0\)

Now we can solve this quadratic equation. Using the quadratic formula, we get:

x = (-(-7) ± √((-7)² - 4 * 1 * (-4))) / (2 * 1)

x = (7 ± √(49 + 16)) / 2

x = (7 ± √65) / 2

Since the time taken cannot be negative, we consider the positive root:

x = (7 + √65) / 2

≈ 6.5

To know more about longer,

https://brainly.com/question/7638593

#SPJ11

The year-2 CPI is 102, and the rate of inflation from year 1 to year 2 is 2%.

To calculate the rate of inflation and the Consumer Price Index (CPI) change from year 1 to year 2, we need to follow these steps:

Step 1: Calculate the inflation rate:

Inflation Rate = (Year 2 CPI - Year 1 CPI) / Year 1 CPI

Step 2: Calculate the Year 2 CPI:

Year 2 CPI = (Year 2 Basket Price / Year 1 Basket Price) * 100

Let's calculate the values:

Year 1 Basket Price = $25.00

Year 2 Basket Price = $25.50

Step 1: Calculate the inflation rate:

Inflation Rate = ($25.50 - $25.00) / $25.00

Inflation Rate = $0.50 / $25.00

Inflation Rate = 0.02 or 2%

Step 2: Calculate the Year 2 CPI:

Year 2 CPI = ($25.50 / $25.00) * 100

Year 2 CPI = 1.02 * 100

Year 2 CPI = 102

Therefore, the year-2 CPI is 102, and the rate of inflation from year 1 to year 2 is 2%.

For such more questions on CPI and Inflation Calculation

https://brainly.com/question/31995570

#SPJ8

The probability that the marble is red or blue is 0.6923 or 69.23% if the bag contains five red marbles, four blue marbles, and four yellow marbles. You randomly pick a marble.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

We have the total number of marbles = 5+4+4 =13

Total number of red and blue marble = 5+4 = 9

The probability that the marble is red or blue = 9/13 = 0.6923 or

= 69.23%

Thus, the probability that the marble is red or blue is 0.6923 or 69.23% if the bag contains five red marbles, four blue marbles, and four yellow marbles. You randomly pick a marble.

Learn more about the probability here:

brainly.com/question/11234923

#SPJ2

Answer:

Step-by-step explanation: