what is the difference between linear and non linear change

a. The mass remaining after t years, 130 is the initial mass, and 30 is the half-life of cesium-137.

b.  About 19.35 mg of the sample will remain after 100 years.

c.  After about 330 years, only 1 mg of the sample will remain

(a) The mass remaining after t years can be found using the formula:

\(y(t) = 130 * 2^(-t/30)\)

where y(t) represents the mass remaining after t years, 130 is the initial mass, and 30 is the half-life of cesium-137.

(b) To find how much of the sample remains after 100 years, we can substitute t = 100 into the formula:

\(y(100) = 130 * 2^(-100/30) = 19.35 mg\)

Therefore, about 19.35 mg of the sample will remain after 100 years.

(c) We need to solve the equation y(t) = 1 for t. Substituting y(t) and solving for t, we get:

\(1 = 130 * 2^(-t/30)\)

\(2^(-t/30) = 1/130\)

\(-t/30 = log2(1/130)\)

\(t = -30 * log2(1/130) = 330 years\)

Therefore, after about 330 years, only 1 mg of the sample will remain.

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a) The decay of cesium-137 can be modeled by the function \(y(t) = 130 * 2^{(-t/30)\)

b) after 100 years, only about 31.57 mg of the sample remains.

c) after about 207.1 years, only 1 mg of the sample will remain.

(a) The decay of cesium-137 can be modeled by the function \(y(t) = 130 * 2^{(-t/30)\), where t is the time in years and y(t) is the remaining mass of the sample in milligrams.

To find the mass that remains after t years, we simply plug in the value of t into the function:

\(y(t) = 130 * 2^{(-t/30)\)

(b) To find the amount of the sample that remains after 100 years, we plug in t = 100:

\(y(100) = 130 * 2^{(-100/30)\) ≈ 31.57 mg

So after 100 years, only about 31.57 mg of the sample remains.

(c) To find the time it takes for only 1 mg to remain, we set y(t) = 1 and solve for t:

\(1 = 130 * 2^{(-t/30)}\\\\2^{(-t/30)} = 1/130\)

Taking the natural logarithm of both sides, we get:

\(ln(2^{(-t/30)}) = ln(1/130)\)

Using the logarithmic identity \(ln(a^b) = b * ln(a)\), we can simplify the left side:

(-t/30) * ln(2) = ln(1/130)

Solving for t, we get:

t = -30 * ln(1/130) / ln(2) ≈ 207.1 years

So after about 207.1 years, only 1 mg of the sample will remain.

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Answer:

1 and 5 are corresponding angle

8 and 4 are corresponding angle

4 and 6 are alternate interior angle

2 and 8 are alternate exterior angle

7 and 3 are corresponding angle

2 and 6 are corresponding angle

3 and 5 are alternate interior angle

1 and 7 are alternate exterior angle

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

\(11\sqrt{797}\pi\)

Step-by-step explanation:

\(A=\pi r \sqrt{h^2+r^2}\)

the radius is 22/2 = 11 in

h is 26 in

substitute: \(\pi \left(11\right)\sqrt{\left(26^2\right)+\left(11^2\right)}\)

= \(11\sqrt{797}\pi\)

Answer:

286π in²

Step-by-step explanation:

The lateral area (A) of the cone is calculated as

A = πrs ( r is the radius and s the slant height )

Here r = 22 ÷ 2 = 11 and s = 26 , then

A = π × 11 × 26 = 286π in²

The number of people corresponds to are (a) 26, (b) 38, (c) 3, (d) 20, (e) 34, (f) 61 and (g) people who are correct but don't exercise regularly.

Venn diagram is a diagram of circles used to show the relationships of finite groups of things.

Here a Venn diagram relating the number of people who are correct and who exercise regularly are given.

Given,

Total number of people (Universal set), U = 49

Number of people who are correct = 18 + 20 = 38

Number of people who exercise regularly = 3 + 20 = 23

(a) Number of people who don't exercise regularly = 49 - 23 = 26

(b) Number of people who were correct = 38

(c) Number of people who were incorrect and exercise regularly = 3

(d) Number of people  who exercise regularly were correct = 20

(e) Number of people who were incorrect or exercise regularly = people who were incorrect + people who exercise regularly

= (49 - 38) + 23 = 11 + 23 = 34

(f) Number of people who were either correct or exercise regularly = people who were correct + people exercise regularly

= 38 + 23 = 61

(g) The 18 people in the left circle of diagram are people who are correct but don't exercise regularly.

Hence the number of people in all aspects are found.

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Set x<5 = sagutan mo apapapdifuv

The sequence is geometric with a common ratio of 1/5. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant number, which is known as the common ratio.

We can use the formula of the geometric sequence for finding the nth term:an=a1 * rn-1 where:an= nth terma1= first termr=common ratio (the constant number between consecutive terms)n= number of termsThe common ratio is given by: r= 40/200 = 1/5The first term is a1=200The nth term can be given by a(n) = 200 * (1/5)^(n-1)Therefore, the first five terms are:a1 = 200a2 = 200 * (1/5) = 40a3 = 200 * (1/5)^2 = 8a4 = 200 * (1/5)^3 = 1.6a5 = 200 * (1/5)^4 = 0.32Hence, the given sequence is geometric with a common ratio of 1/5.

A geometric sequence can be represented by the formula a, ar, ar^2, ar^3, ... , where a is the first term, r is the common ratio, and ar, ar^2, ar^3, ... are the successive terms. The common ratio can be calculated using any two consecutive terms in the sequence.To determine if a sequence is geometric or not, we need to check whether the ratio of successive terms is the same. In the given sequence, 200 is the first term, 40 is the second term, and 8 is the third term.

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Answer:

Since dilation is not mentioned in the answer options, thus, the correct option is 'None of the above'.

Step-by-step explanation:

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

The figure seems to have enlarged by a certain scale factor. Thus, the figure b is a result of dilation of the original figure by a certain scale factor.

Rotation, Reflection, and translation do not affect the size of the original figure.

Since dilation is not mentioned in the answer options, thus, the correct option is 'None of the above'.

Answer:

-3x = 7 .  

Step-by-step explanation:

-3x - 6 - 1 =

-3x - 7

Hope that helps!

Answer:

-3x-7

Step-by-step explanation:

Combine like terms

The number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

The payment of car washing per hour = $10

The payment for landscaping = $12

Total number of hours worked = 14  hours

Number of hours worked in car washing = x

Number of hours worked in landscaping = y

Then the first equation will be

x + y = 14

x = 14 - y

Total amount he earned = $152

Next equation will be

10x + 12y = 152
Here we have to use substitution method

10(14-y) + 12y = 152

140 - 10y +12y = 152

140 + 2y = 152

2y = 152 - 140

2y = 12

y = 12/2

y = 6 hours

Then

x = 14 - y

x = 14 -6

x = 8  hours

Hence, the number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

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Answer:

the measure of angle 4 is 52 degrees.

Step-by-step explanation:

The measure of angles 3 and 4 added together is 90 degrees. Angle 3 is 38 degrees. 90-38=54.

Answer:

∠ 4 = 52°

Step-by-step explanation:

The 3 angles lie on a straight line and sum to 180°, that is

90 + ∠ 3 + ∠ 4 = 180, substitute ∠ 3

90° + 38° + ∠ 4 = 180°

128° + ∠ 4 = 180° ( subtract 128° from both sides )

∠ 4 = 52°

Answer:

5 hours

Step-by-step explanation:

hope this helps ^^

Answer:

+ 9

Step-by-step explanation:

x²+ 6x

to complete the square

add ( half the coefficient of the x- term )² to x² + 6x

x² + 2(3)x + 3²

= x² + 6x + 9

= (x + 3)² ← a perfect square

The given expression e^ze^w= e^(z+w) has been proved.

What is complex number?

In mathematics, a complex number is a component of a number system that includes an element designated i, also referred to as the imaginary unit, and extends the real numbers while meeting the equation every complex number can be expressed as a + bi, where a and b are real numbers.

As per question given that,

Suppose that z = A + Bi and w = C + Di

From the property:

[e^a · e^b = e ^ (a + b)]

Proof that: e^ze^w= e^(z+w)

From Left hand Side of expression: e^z · e^w

Substitute values z = A + Bi and w = C + Di respectively,

e^z · e^w = e^(A + Bi) · e^(C + Di)

e^z · e^w = e^(A + Bi + C + Di)

e^z · e^w = e^(A + C + i(B + D))

Similarly, From Right hand Side of expression:: e^(z+w)

Substitute values z = A + Bi and w = C + Di respectively,

e^(z+w) = e^(A + Bi + C + Di )

e^(z+w) =e^(A + C + i(B + D))

Since, Left hand Side = Right hand Side.

Hence, the given expression e^ze^w= e^(z+w) has been proved.

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Answer:

Adjacent angles

Step-by-step explanation:

I can't see answer choice D in the photo provided, but the answer would be adjacent due to that fact that angles a and b are right next to each other, without forming a 90 or 180 degree angle.

Answer:

the answer is a

Step-by-step explanation:

all of the lines are vertical

The mean and the standard deviation of the sampling distribution of x are given as follows:

The mean and the standard deviation of the sampling distribution of x are defined according to the Central Limit Theorem, which states that:

The parameters for this problem are given as follows:

Hence the standard deviation for the sampling distribution of x is given as follows:

s = 60/sqrt(10) = 19 seconds.

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Answer:

A

Step-by-step explanation:

Answer:

Only LOKI is correct

Step-by-step explanation:

Elektra multiplied 8 with the inside parenthesis but it was wrong to do.

Green Goblin took 2x outside with negative sign but that is wrong

Morbius did the same mistake as Green Goblin at first step but then corrected it in the second step, still it's wrong

The windmill's blade measures 7 feet in length.

To find the measure of the windmill's blade:

Therefore, the windmill's blade measures 7 feet in length.

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The correct question is given below:

The equation h=7sin(pi/21t)+28 can be used to model the height, h, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, t, in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at t = 0, and that the windmill turns counterclockwise at a constant rate. 7 feet 14 feet 21 feet 28 feet

The magnetic force that the wire exerts on the point charge is in the negative z-direction.

When a current-carrying wire and a moving point charge are placed in a magnetic field, a magnetic force is exerted on the moving charge due to the interaction between the magnetic field and the charge's velocity. According to the right-hand rule, the direction of the magnetic force is perpendicular to both the velocity of the moving charge and the magnetic field created by the current-carrying wire.

In this scenario, the wire carrying current in the positive y-direction generates a magnetic field that circulates around the wire. The point charge moving along the x-axis in the positive x-direction experiences a magnetic force directed perpendicularly to both the velocity (positive x-direction) and the magnetic field (circulating around the wire). Applying the right-hand rule, the magnetic force is found to be in the negative z-direction, which is downward and perpendicular to the x and y axes.

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An indication of the inequality negative 2 over 3 > −1 about the positions of negative 2 over 3 and −1 on the number line is that: A. negative 2 over 3 is located to the right of −1.

A number line can be defined as a type of graph that is designed and developed with a graduated straight line containing both positive and negative numbers (numerical values), that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used for the comparison of two or more numbers such as -2/3 and -1. Also, a number line typically decreases in numerical value towards the left and increases in numerical value towards the right.

Note: negative 2 over 3 = -2/3.

By comparison, we have:

-2/3 > -1

In conclusion, the above inequality simply means that -2/3 is greater than -1 and it would be located to the left of 0 and right of -1 on a number line as shown in the image attached below.

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Answer:

slope is -2/3

Step-by-step explanation:

y = mx+b

m = slope

b = y-intercept

given: y = -2/3x

in this case we don't have a b so make it an automatic 0

now we have y = -2/3x +0

slope is m, so our slope is -2/3

Therefore, the equation for which g = 5 is not the solution is 4g = 20.

An equation is a mathematical statement that shows the equality between two expressions or values. It typically consists of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations can be used to solve problems or to describe relationships between quantities. They are commonly written in the form of "expression 1 = expression 2" or "expression 1 - expression 2 = 0", where the goal is to find the value(s) of the variable(s) that make the equation true.

To check for which equation g = 5 is not the solution, we can substitute g = 5 into each equation and see which ones result in a false statement.

\(8g = 40\)

Substituting g = 5 gives: 8(5) = 40, which is true. Therefore, g = 5 is a solution to this equation.

4g = 20

Substituting g = 5 gives: 4(5) = 20, which is false. Therefore, g = 5 is not a solution to this equation.

g - 2 = 3

Substituting g = 5 gives: 5 - 2 = 3, which is true. Therefore, g = 5 is not a solution to this equation.

2g = 25

Substituting g = 5 gives: 2(5) = 25, which is false. Therefore, g = 5 is not a solution to this equation.

Therefore, the equation for which g = 5 is not the solution is 4g = 20.

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Answer:

2/2=1

6/2=3

2/2=1 so the fractions are equivalent

2/6 = 1/3

Hope this helps

Step-by-step explanation:

In the early 1980s, hemophiliacs received reconstituted clotting factor concentrates derived from human blood, with each concentrate pooled from about 1000 donors.

With a hepatitis C prevalence of 1 in 1000 donors, the probability that a hemophiliac would contract hepatitis C from a single infusion can be calculated using the complementary probability.

First, find the probability of a donor not having hepatitis C: 1 - (1/1000) = 999/1000. Since the concentrates were pooled from 1000 donors, the probability that none of the donors had hepatitis C is (999/1000)^1000.

Since each lot of clotting factor concentrate contained blood from about 1000 donors, the probability of any given donor having hepatitis C would be 1/1000.

Therefore, the probability of a single lot of clotting factor concentrate containing hepatitis C would be the probability of at least one of the 1000 donors in the pool having hepatitis C.

To calculate this probability, we can use the complement rule, which states that the probability of an event occurring is equal to one minus the probability of the event not occurring.

So the probability that none of the 1000 donors in the pool have hepatitis C would be (999/1000)^1000, since each donor is independent and has a 999/1000 chance of not having hepatitis C.

Therefore, the probability that at least one donor in the pool has hepatitis C is 1 - (999/1000)^1000, which is approximately 0.632.

This means that the probability of a hemophiliac contracting hepatitis C from a single infusion of clotting factor concentrate would be approximately 0.632, assuming that the prevalence of hepatitis C in donor blood in the early 1980s was 1 in 1000.

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