Iodine-131 has a half-life of days. How much would be left of an original g sample after days?

Answer: M=1/3

Step-by-step explanation: We know how to find the slope by using the formula: y2-y1/x2-x1

Then we get 3-1/3--3=2/6=

1/3

Answer:

a. 8 years

b. $49.20

Step-by-step explanation:

The computation is shown below:

a. The mark age is

Given that

232 is 8 times of the sum of mark and his sister ages

And, his sister is 21

So,

Let us assume the mark age be x

now

8(x + 21) = 232

x + 21 = 29

x = 29 -21

x = 8

b. The original price of the socks is

As each pair get $3 off

And she bought 6 pairs for $31.20

= $31.20 + 6 × $3

= $31.20 + 18

= $49.20

The solution to the linear congruence 2x + 6 ≡ 4 (mod 8) is x ≡ 3 (mod 8).To solve the linear congruence 2x + 6 ≡ 4 (mod 8), we need to find the values of x that satisfy the congruence equation.

First, let's simplify the equation:

2x + 6 ≡ 4 (mod 8)

Subtracting 6 from both sides:

2x ≡ 4 - 6 (mod 8)

2x ≡ -2 (mod 8)

Next, we can simplify -2 (mod 8) by adding 8 to it:

-2 ≡ 6 (mod 8)

Now the congruence equation becomes:

2x ≡ 6 (mod 8)

To solve for x, we need to find the multiplicative inverse of 2 modulo 8. The multiplicative inverse of 2 is 4, as 2 * 4 ≡ 1 (mod 8).

Multiplying both sides of the congruence equation by 4:

4 * 2x ≡ 4 * 6 (mod 8)

8x ≡ 24 (mod 8)

Simplifying the equation:

8x ≡ 24 (mod 8)

x ≡ 3 (mod 8)

Therefore, the solution to the linear congruence 2x + 6 ≡ 4 (mod 8) is x ≡ 3 (mod 8).

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Answer:

(x+1)(x+9)

Step-by-step explanation:

Hope this helps!

Answer:

581

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Answer:

1. True

2. True

3. True

angle 1 = 90°

angle 2 = 90°

angle 3 = 90°

angle 4 = 90°

angle 5 = 90°

angle 6 = 90°

angle 7 = 90°

Answer:

All of them are 90 degrees.

Step-by-step explanation:

Using the known Maclaurin series expansion for e^x: e^x = 1 + x + (x^2 / 2!) + (x^3 / 3!) + ...

We can obtain the Maclaurin series for the function f(x) = xe^(7x) by multiplying the Maclaurin series for e^x by x:

f(x) = x(1 + 7x + (7x)^2 / 2! + (7x)^3 / 3! + ...)

Simplifying further:

f(x) = x + 7x^2 + (49x^3 / 2!) + (343x^4 / 3!) + ...

Therefore, the Maclaurin series expansion for f(x) is:

f(x) = x + 7x^2 + (49x^3 / 2!) + (343x^4 / 3!) + ...

The associated radius of convergence, R, can be determined by applying the ratio test. In this case, we have an infinite power series with terms involving powers of x. The ratio test states that if the limit of |a_(n+1) / a_n| as n approaches infinity is L, then the radius of convergence is R = 1 / L.

In our case, applying the ratio test yields a limit of 0 as n approaches infinity. Therefore, the radius of convergence R is infinite, indicating that the Maclaurin series for f(x) converges for all values of x.

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Yes, the given matrix A is diagonalizable.

Let the matrix A be given by A = [−2 2 1 0 0 2].

To determine if this matrix is diagonalizable, we need to check whether A has enough linearly independent eigenvectors. If there are enough such eigenvectors, then A will be diagonalizable. Otherwise, A will not be diagonalizable.

To find the eigenvalues and eigenvectors of the matrix A, we solve the equation Ax = λx, where λ is a scalar (eigenvalue) and x is the corresponding eigenvector. This gives: (A - λI)x = 0, where I is the identity matrix.To solve for the eigenvalues, we need to find λ such that det(A - λI) = 0. This gives us the characteristic equation:

(−2 − λ)(2 − λ)(1 − λ) − 4(2 − λ) = 0, which simplifies to λ^3 − λ^2 − 10λ − 12 = 0.

To find the eigenvectors, we solve for x in the equation (A - λI)x = 0, using each eigenvalue λ obtained from the characteristic equation.To solve for λ, we need to solve the characteristic equation. Factoring it gives (λ - 4)(λ + 1)^2 = 0, which has eigenvalues λ1 = 4 and λ2 = −1 (multiplicity 2).

Since we have two distinct eigenvalues (λ1 = 4 and λ2 = −1), we know that A is diagonalizable if and only if it has two linearly independent eigenvectors corresponding to each eigenvalue.To find the eigenvectors corresponding to λ1 = 4, we need to solve the system (A - 4I)x = 0.

This gives the matrix equation:

[−6 2 1 0 0 −2][x1 x2 x3 x4 x5 x6] = [0 0 0 0 0 0]

Solving this system gives x1 = -x3/6 - x6/2, x2 = x2, and x4 = x4. We can choose any two of these variables (for example, x3 and x6) and solve for the other three variables in terms of them.

Doing so gives:

x1 = -1/6

x3 - x6/2x2 = x2x4 = x4x5 = 0

So, the eigenvectors corresponding to λ1 = 4 are of the form [x1 x2 x3 x4 x5 x6] = [−1/6t  −2s  t  0  0  −2t], where t and s are arbitrary constants.To find the eigenvectors corresponding to λ2 = −1, we need to solve the system (A + I)x = 0.

This gives the matrix equation: [−1 2 1 0 0 2][x1 x2 x3 x4 x5 x6] = [0 0 0 0 0 0]

Solving this system gives x1 = -x3 + 2x6, x2 = x2, and x4 = -2x6. We can choose any two of these variables (for example, x3 and x6) and solve for the other three variables in terms of them. Doing so gives: x1 = 2t - s, x2 = x2, x4 = -2t ,x5 = 0

So, the eigenvectors corresponding to λ2 = −1 are of the form [x1 x2 x3 x4 x5 x6] = [2t − s  0  t  −2t  0], where t and s are arbitrary constants.Since we have four linearly independent eigenvectors (two corresponding to each eigenvalue), we can diagonalize the matrix A by forming the matrix P whose columns are these eigenvectors.

The matrix P is given by P = [−1/6 −2 2 0 0 2][0 1 0 0 0 0][1 −2 0 0 0 0][0 0 0 1 0 0][0 0 1 0 0 0][−2 0 0 0 0 1]

Hence A is diagonalizable.

Answer: Yes, the given matrix A is diagonalizable.

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Answer:

-18 C

Step-by-step explanation:

we have to do this operation

5 - 23

we can proceed like this

if we do 5-5 we reach the 0

23 - 5 = 18

now we have to do 18 steps to the left of the zero, that it means reach -18, that is the answer of the question

Answer:

The first is (-1, 1) and the second is (2, -2)

Step-by-step explanation:

Answer:

9 hours.

Step-by-step explanation:

$357 / 17 = $21. ($21 per hour.)

$189/$21 = 9. BOOM

Answer: It would be option D :)

Step-by-step explanation: the formula for volume in a cylinder is π r squared times height. You plug those in and that’s your answer!

Answer: Since her art and music sections each only had half the number of sheets of paper as a core subject, together the two sections had the same amount of paper as a core subject. Therefore, it is almost like her notebook had five core subjects, rather than four core subjects and two electives. If she divided the 200 sheets equally among the five core subjects, there would be 200 ÷ 5 = 40 sheets in each section. Now we can see that art would actually have half of this amount, or 20 sheets of paper.

Answer:

1. 7

2. 3

3. 2 and 2

Step-by-step explanation:

first is 7

second is 3

third is 2 and 2

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Answer:

4 pounds 12 ounces

Step-by-step explanation:

there are 16 ounces in 1 pound so 76/16 = 4.75 and .75 is equal to 12 ounces.

76 ounces is equal to 4 pounds and 12 ounces.

To convert 76 ounces to pounds and ounces, we need to consider that 1 pound is equal to 16 ounces.

Here's how to proceed:

Divide the total number of ounces by 16 to find the number of pounds:

76 ounces ÷ 16 ounces/pound = 4.75 pounds

Since 4 pounds = 4 x 16 pounce/ pound

= 64 ounces ,we subtract this amount from the total of 76 ounces to determine the remaining ounces:

= 76 ounces - 64 ounces

= 12 ounces

Therefore, 76 ounces is equal to 4 pounds and 12 ounces.

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Answer: a

Step-by-step explanation: A plane is a 2d surface so if it ever intersects a 3d object the cross-section will be a 2d figure, in this case, a rectangle.

Answer:

20

Step-by-step explanation:

Answer:

2 2/5

Step-by-step explanation:

2.4 = 2 4/10 = 2 2/5 (all you had to do is divide by 2)

The answer would be 2 2/5 (could also be 1.2 as a decimal)

Hopefully this helps :3 sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

-Bee~

Step-by-step explanation:

The

2

is in the ones place, and the

4

is in the tenths place.

2.4

means two and four tenths. So in fraction form it is 2 4/10

Answer link

Answer:

3x+y=13

+2x-y=12

SOlve it like what you would normally do

3x+2x=5x

y+(-y)=0

13+12=25

Basically

5x+0=25

Bring down all appropiate signs

Now solve that

5x=25

x=5

Now to find “y”

Plug in The “x”

3*5=15

15+y=13 now solve that and you’d get -2

If you plug it into the other one, it would be the same thing

2*5=10

10-y=12

-y=2

y= -2

x=5

y= -2

that's the correct answer!

Answer:

3(y +8) (d+e) /4

Step-by-step explanation:

I gotta get to class too soon so my explanation here is just to get this sent. hopefully it does. I tried my best. could be wrong

Answer: What percentage is 15 out of 75?

20

Percentage Calculator: 15 is what percent of 75? = 20.

Answer:

5%

Step-by-step explanation:

Answer:

40 cups of food

Step-by-step explanation:

First, you would multiply 2/3 by 2, which gives you 4/3. That means the beagle will eat 1 and 1/3 of a cup a day. If you multiply that by 30, you get 40.

Answer:D

Step-by-step explanation:

Answer:

4.046 m

Step-by-step explanation:

Answer:

hope this helps

you will find all answer in the photo i sent

Answer:

B

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

You're welcome.