Find the volume of the cylinder.
Either enter an exact answer in terms of t or use 3.14 for T

The exponential function that relates the mass of the substance to the number of years since 2005 is: [tex]y = 600 \times e^(-0.048t)[/tex]  . [Where t is a number of years since 2005, and y is mass of the substance in milligrams at that time.]

An exponential function is a mathematical function of the form[tex]f(x) = a^x,[/tex] representing a rapid increase or decrease in value as x increases or decreases.

It represents a rapid growth or decay in value as the independent variable changes, and is used to model many natural phenomena such as population growth, compound interest, and radioactive decay.

The radioactive decay of the substance follows an exponential decay model. The formula for exponential decay is:

[tex]y = a * e^(-rt)[/tex]

Where:

y - amount of substance at time t.

a - initial amount of the substance.

r - decay rate per unit of time.

t - time elapsed since the start of the decay.

In this case, we know that the initial mass of the substance in 2005 was 600 milligrams. We also know that the substance decays by [tex]4.8[/tex]  % each year, which means that the decay rate per year is [tex]0.048[/tex]  (4.8% expressed as a decimal).

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It can be stated that there exist 63,360 ternary sequences of digits selected from {0, 1, 2} with a length of twelve, which contain precisely three 1s and two 0s.

The problem is asking us to find out how many ternary sequences of digits are there that are chosen from {0, 1, 2} of length twelve, and have exactly three 1's and two 0's.

Therefore, there will be a total of 7 digits (12 - 3 - 2 = 7) that could be 1 or 2. So, let's solve it in steps.

Step 1: The number of ways we can choose 3 positions out of 12 for 1s is C (12,3).

Step 2: The number of ways we can choose 2 positions out of 9 (because there are already 3 1s and 2 0s) for 0s is C (9,2).

Step 3: We have three digits left that can be either 1 or 2. So, there will be 2 options for each of these digits, and the total number of options will be

2 × 2 × 2 = 8.

Step 4: So, the total number of sequences will be obtained by multiplying the results of Steps 1, 2, and 3. i.e.

C (12,3) × C (9,2) × 8

⇒ ¹²C₃ × ⁹C₂ × 8

⇒ 220 × 36 × 8 = 63360.

Therefore, there are 63,360 ternary sequences of digits chosen from {0, 1, 2} of length twelve that have exactly three 1s and two 0s.

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According to the solving this to the nearest naira, the amount credited to his account is 580,163 Nigerian naira.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.

The Nigerian visitor changed N70200 to rupees at a rate of 3 nairas to 35 rupees. Therefore,

70200 Nigerian naira = 70200 * 35 / 3 = 819500 Indian rupees

He spent 224,000 rupees, so the amount he invested at 41.5% per annum was:

819500 - 224000 = 595500 rupees

The simple interest he earned after 8 months at a rate of 41.5% per annum is:

595500 * (41.5/100) * (8/12) = 129702.5 rupees

So, the total amount he had after 8 months was:

595500 + 129702.5 = 725202.5 rupees

He then transferred this amount to his account in the Modern Bank of Nigeria at a rate of 21 rupees to 2 naira. Therefore,

725202.5 rupees = (725202.5 / 21) * 2 = 580162.5 Nigerian naira

this to the nearest naira, the amount credited to his account is 580,163 Nigerian naira.

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Answer:  b<-7/4

Step-by-step explanation:

Let's collect numbers with same variables to the same side:

-3-4>9b-5b

-7>4b

b<-7/4

Answer:

The correct option is A. x = -1, x = 3, x = ±√5.

We found the zero x = -1 through synthetic division, and then we factored the cubic polynomial using the Rational Root Theorem and synthetic division to obtain (x + 1)(x^3 - 3x^2 - 6x + 15). We found that the remaining zeros of the polynomial function are the roots of the quadratic factor x^2 - 3x - 5, which are x = (3 ± √29))/2.

Therefore, the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3, x = (3 + √(29))/2, and x = (3 - √(29))/2, which simplifies to x = (3 ± √(5))/2.

Option A lists all of these zeros, so it is the correct option. Options B and C do not list all of the zeros of the polynomial function.

STEPS: Here are the steps to find all the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15:

Write the polynomial function in descending order of degree: f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15.

Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±3, ±5, ±15.

Use synthetic division to test each possible zero. We start with x = -1:

-1 │ 1 -2 -8 10 15

│ -1 3 -5 -5

└───────────────

1 -3 -5 5 10

x = -1 is a zero of the polynomial function. We can write f(x) as:

f(x) = (x + 1)(x^3 - 3x^2 - 5x + 10)

Use the Rational Root Theorem and synthetic division to factor the cubic equation x^3 - 3x^2 - 5x + 10:

3 │ 1 -3 -5 10

│ 3 0 -15

└─────────────

1 0 -5 -5

x = 3 is not a zero of the polynomial function.

-3 │ 1 -3 -5 10

│ -3 24 -57

└────────────

1 -6 19 -47

x = -3 is not a zero of the polynomial function.

The only remaining possible rational zeros are ±1/1 and ±5/1, but testing these values using synthetic division does not yield any more zeros.

Solve for the remaining zeros of the polynomial function by factoring the quadratic equation x^2 - 3x - 5 using the quadratic formula or factoring by grouping:

x = (3 ± √(29))/2

These are the remaining zeros of the polynomial function.

Therefore, the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3, x = (3 + √(29))/2, and x = (3 - √(29))/2, which simplifies to x = (3 ± √(5))/2.

Option A lists all of these zeros, so it is the correct option.

Hope this helps! I'm sorry if it doesn't! :]

Answer:

[tex]\huge\boxed{\sf 14 \ km}[/tex]

Step-by-step explanation:

7 hours = 98 km

Divide both sides by 7

7/7 hour = 98/7 km

[tex]\rule[225]{225}{2}[/tex]

Answer:

$274,526

Step-by-step explanation:

Answer: "An irrational number is a number that cannot be expressed as a ratio between two integers and is not an imaginary number.

Since 4.284 is not the square root of a negative number, it is not imaginary

Since 4.284 is a rational number from above, 4.284 is not an irrational number"

Step-by-step explanation: /\ I looked at a calculator for irrational numbers. Should be right, considering how it's well explained. Just search for "irrational number calculator". Dont rely on that. But it's there if

you need it! :)

No

It is a rational number since it is a fraction/decimal that isn't non-terminating, not is it pi or

The probability of choosing an odd prime number from 1 to 20 is 0.35

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The odd prime numbers between 1 and 20 are 3, 5, 7, 11, 13, 17, and 19. There are 7 odd prime numbers in this range.

The total number of possible choices is 20 (since there are 20 numbers in the range 1 to 20).

Therefore, the probability of choosing an odd prime number is:

number of odd prime numbers / total number of possible choices

= 7 / 20

= 0.35

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Answer: A ‍♀️

Step-by-step explanation:

Answer:

chocolate = $1.25

soft drink = $1.85

Step-by-step explanation:

Given price of chocolate is c and price of soft drink is s

Olivia: 5c + 2s = 9.95

Taylor: 6c + 6s = 18.60

6c + 6s = 18.60

divided by 6, we have

c + s = 3.1

=> s = 3.1 - c

Substitute s = 3.1 - c into

5c + 2s = 9.95

5c + 2(3.1 - c) = 9.95

5c + 6.2 - 2c = 9.95

3c = 9.95 - 6.2

3c = 3.75

c = 3.75/3 = 1.25

s = 3.1 - c = 3.1 - 1.25 = 1.85

Answer:

Probability of drawing an odd number.

Number of odd numbers = 5

Number of numbers in the set = 10

So it's a 5 in 10 chance or 1 in 2 chance.

Probability of drawing a multiple of 3.

Multiples of 3 in the set = 3, 6 and 9 = 3 multiples of 3

Number of numbers in the set = 10

So it's a 3 in 10 chance

The area of each part of the figure and then the whole figure, can be found to be :

The area of Triangle A would be :

= 1 / 2 x  Base x height

= 1 / 2 x ( 2 + 2 + 6 ) x 4

= 1 / 2 x 10 x 4

= 20 units ²

The area of Triangle D is :

= 1 / 2 x base x height

= 1 / 2 x 6 x 2

= 6 units ²

The area of the whole figure would then be:

= 20 + 2 + 4 + 6

= 32 units ²

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If a lorry travels 320km and uses 40 litres of petrol, the average rate of petrol usage for the lorry is 8 km per liter.

To find the average rate of petrol usage for the lorry, we need to divide the total distance traveled by the amount of petrol used. This will give us the number of kilometers traveled per liter of petrol.

In this case, the lorry traveled 320 km and used 40 liters of petrol, so we can calculate the average rate of petrol usage as follows:

Average rate of petrol usage = Total distance traveled / Amount of petrol used

= 320 km / 40 litres

= 8 km/litre

This means that for every liter of petrol used, the lorry can travel an average of 8 kilometers. This metric can be useful in comparing the fuel efficiency of different vehicles or in calculating the cost of a particular journey based on the price of petrol per liter.

In summary, calculating the average rate of petrol usage involves dividing the distance traveled by the amount of petrol used, resulting in a unit of km per liter.

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Answer:

a = 12.56637061

Step-by-step explanation:

a= 4 · π · r²

a= 4 · π · 1²

a= 4π

a= 12.56637061

a= 12.57

The discounted price of the camera is $270 and the price of the camera after the 40% increase is $378.

When the store offered a 40% discount on the original price of $450, the discounted price of the camera can be calculated as follows:

Discounted price = Original price - Discount

Discounted price = $450 - 40% x $450

Discounted price = $450 - $180

Discounted price = $270

Therefore, the discounted price of the camera is $270.

After the sale, the discounted price of the camera was increased by 40%. We can calculate the new price of the camera as follows:

New price = Discounted price + 40% x Discounted price

New price = $270 + 40% x $270

New price = $270 + $108

New price = $378

Therefore, the price of the camera after the 40% increase is $378.

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Answer:

The machine can make 9 parts in 2.8 hours.

To find the rate of production, we can divide the number of parts by the time: 9 parts / 2.8 hours = 3.214 parts per hour.

Now that we know the machine's rate of production, we can use it to answer the question:

In 28.0 hours, the machine will produce: 3.214 parts per hour x 28.0 hours = 89.9 parts.

Therefore, the machine can make 89.9 parts in 28.0 hours at the given rate. We can round this to 90 parts.

Step-by-step explanation:

The ladder slipped down the wall by approximately 296 cm to the nearest 1 cm.

We can use the Pythagorean theorem to solve this problem.

Let the distance the ladder slips down the wall be represented by x (in cm).

Then, at the start of the day, we have a right triangle formed by the wall, the ground, and the ladder, with the ladder being the hypotenuse.

The length of the ladder is 3m = 300cm, and the distance from the foot of the ladder to the wall is 50cm.

Therefore, we have:

(300)² = x² + (50)²

Simplifying this equation, we get:

90000 = x² + 2500

Subtracting 2500 from both sides, we get:

87500 = x²

Taking the square root of both sides, we get:

x = √87500

x = 295.8 cm

x ≈ 296 cm

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The solution to the given homogenous differential equation dy/dx = y² + x² / x^2 is y² = -x(y³ / 3 + Cy³ - 3Cx)

The given differential equation is: dy/dx = y² + x² / x^2

To solve this, we can first separate the variables by bringing all the y-terms on one side and all the x-terms on the other side:

(1/y²)dy = (x² / x² + y²)dx

Next, we can integrate both sides:

∫(1/y²)dy = ∫(x²/x² + y²)dx

Using the substitution u = y/x, we can simplify the integrals:

∫(1/y²)dy = ∫(1 + u²)dx

-1/y = x + (1/3)u³ + C

where C is the constant of integration.

Substituting back u = y/x, we get:

-1/y = x + (1/3)(y/x)³ + C

Multiplying both sides by -y³, we get:

y² = -x(y³ / 3 + Cy³ - 3Cx)

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By speed formula, it would take Franklin 2 hours and 30 minutes (or 150 minutes) to shovel the driveway alone.

What is speed?

Speed is defined as the distance travelled by an object in a given amount of time. Speed is a scalar quantity, meaning that it has magnitude but no direction.

Mathematically, speed is calculated as follows:

speed = distance / time

where "distance" is the distance travelled by the object, and "time" is the time it takes for the object to travel that distance.

Let's assume that Angela's shoveling rate is "a" and Franklin's shoveling rate is "f" (measured in driveways per hour). We can use the formula:

time = distance / rate

where "distance" is the length of the driveway (which we can assume to be 1 driveway) and "rate" is the shoveling rate (in driveways per hour).

According to the problem, Angela can shovel the driveway in 2 hours, so her shoveling rate is:

a = 1/2

When Franklin joins her, they can finish the driveway in 54 minutes, or 9/10 of an hour. Therefore, their combined shoveling rate is:

(a + f) = 1 / (9/10) = 10/9

We can now set up a system of equations to solve for "f".

First, we know that Angela and Franklin can finish the driveway in 9/10 of an hour:

1/2 + f = 1 / (9/10)

Multiplying both sides by 10/9, we get:

5/9 + (10/9)f = 1

Simplifying, we get:

(10/9)f = 4/9

f = (4/9) * (9/10)

f = 4/10

f = 2/5

Therefore, Franklin's shoveling rate is 2/5 of a driveway per hour. To find how long it would take him to shovel the driveway alone, we can use the formula:

time = distance/rate

time = 1 / (2/5)

time = 5/2

time = 2 1/2 hours

Therefore, it would take Franklin 2 hours and 30 minutes (or 150 minutes) to shovel the driveway alone.

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1.  triangle = 180

7x7 = 49

180-49 = 131

2. 10x10 = 100 but since its a pyramid its degrees is 180

180-100=80

Julie is trekking to the Blue Ridge Mountains, therefore she is 10 1/12 miles from the beginning point M.

Distance in mathematics is a numerical representation of the actual area between two points. The shortest distance between those two points is how long the path is. The Pythagorean theorem, which asserts that in a right triangle, the sum of the squares of the lengths of the two legs (the sides perpendicular to one another) is equal to the square of the length of the hypotenuse, is used to determine the distance between two locations in a two-dimensional plane (the longest side, opposite the right angle).

given

We must determine Julie's total distance traveled before we can determine how far she is from the beginning location M. By combining the distances between each location, we may determine this:

3 3/8 miles from M to N

2 1/4 miles from N to P

P returning to M: 4 11/24 miles

We must identify a common denominator in order to aggregate these distances. Because it can be divided by 8, 4, and 3, we may pick 24 as the common denominator.

From M to N, the distance is 3 3/8 miles (or 27/8 kilometers). From N to P, it is 2 1/4 kilometers (or 9 kilometers).

We may now multiply the distances:

27/8 + 9/4 + 107/24 = (81 + 54 + 107) / 24

= 242/24

= 10 1/12

Julie is trekking to the Blue Ridge Mountains, therefore she is 10 1/12 miles from the beginning point M.

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The composition of the two translation rules is:

(x, y) → (x - 1, y - 6)

What is a translation rule?

A translation rule is a mathematical description of how to move each point in a geometric shape by a fixed distance in a certain direction. It is used to describe a transformation called a translation, which moves a shape without changing its size, shape, or orientation.

To find the composition of the two translation rules, we apply the second rule first and then apply the first rule to the result.

Let's consider a point (x, y). Applying the second rule (x, y) → (x - 5, y - 5) gives us a new point:

(x - 5, y - 5)

Now we apply the first rule (x, y) → (x + 4, y - 1) to this new point:

(x - 5 + 4, y - 5 - 1)

Simplifying:

(x - 1, y - 6)

Therefore, the composition of the two translation rules is:

(x, y) → (x - 1, y - 6)

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The area of the triangle with side lengths of 25 cm, 7 cm, and 15 cm is approximately 209.27 cm².

To calculate the area of a triangle with side lengths of 25 cm, 7 cm, and 15 cm, we can use Heron's formula, which is a formula for finding the area of a triangle when only the side lengths are known:

Area = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of its sides. The semi-perimeter is half the sum of the three sides:

s = (a + b + c) / 2

Substituting the given values, we get:

s = (25 + 7 + 15) / 2 = 23.5

Now we can use Heron's formula to calculate the area:

Area = √(23.5(23.5-25)(23.5-7)(23.5-15))

= √(23.5 * (-1.5) * 16.5 * 8.5)

= √(43,822.5)

≈ 209.27 cm²

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Therefore, the zeros of the function f(x) are x = 5 and x = -4.

A polynomial is a mathematical expression consisting of variables and coefficients, combined using the operations of addition, subtraction, multiplication, and non-negative integer exponents. It can have one or more terms, and the degree of a polynomial is the highest power of the variable in the expression.

Here,

To find the zeros of the function f(x) = x² - x - 20, we need to solve for x when f(x) = 0:

x² - x - 20 = 0

We can factor the left side of this equation as:

(x - 5)(x + 4) = 0

Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero. Therefore, we can set each factor equal to zero and solve for x:

x - 5 = 0 or x + 4 = 0

Solving for x in each equation gives us:

x = 5 or x = -4

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(a) The distribution of x is a binomial distribution with n=3 and p=0.41, where n is the number of trials (each of you playing level 4 one time) and p is the probability of success (defeating Bowser).

(b) The probability that only 1 of you defeats Bowser is given by the binomial probability formula:
P(x=1) = (3 choose 1)(0.41)^1(0.59)^2 = 0.411
(c) The variance of x is given by the formula:
Var(x) = np(1-p) = 3(0.41)(0.59) = 0.726
(d) The probability that you beat Bowser, regardless of whether your friends beat him or not, is simply the probability of success in one trial, which is 0.41.
(e) The distribution of y is a geometric distribution with p=0.41, where p is the probability of success (defeating Bowser).
(f) The probability that you play less than 3 times is given by the sum of the probabilities of playing 1 or 2 times:
P(y<3) = P(y=1) + P(y=2) = (0.41)^1(0.59)^0 + (0.41)^1(0.59)^1 = 0.651
(g) The expected number of times that you play is given by the formula:
E(y) = 1/p = 1/0.41 = 2.439

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Therefore, the density of the drink is approximately 1.04 grams per cm³.

Volume is a measure of the amount of space occupied by a three-dimensional object or substance. It is the amount of space inside an object or container and is usually measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

Given by the question.

To calculate the density of the drink, we need to first calculate the total mass of the drink, which is the sum of the masses of apple juice, fruit syrup, and sparkling water.

Mass of apple juice = volume of apple juice x density of apple juice = 35 cm³ x 1.04 g/cm³ = 36.4 g

Mass of fruit syrup = volume of fruit syrup x density of fruit syrup = 25 cm³ x 1.6 g/cm³ = 40 g

Mass of sparkling water = volume of sparkling water x density of sparkling water = 270 cm³ x 0.99 g/cm³ = 267.3 g

Total mass of the drink = mass of apple juice + mass of fruit syrup + mass of sparkling water

= 36.4 g + 40 g + 267.3 g

= 343.7 g

Now we can calculate the density of the drink by dividing the total mass by the volume of the drink:

Density of the drink = total mass of the drink / volume of the drink = 343.7 g / 330 cm³ = 1.04 g/cm³ (approx.)

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Answer:

The correct option is C. x=3, x=-2±√2/3.

Step-by-step explanation:

To find all the zeros of the polynomial function f(x) = 3x^3 - 5x^2 - 10x - 6, we can follow the steps outlined in the previous answer:

Write the polynomial function in descending order of degree: f(x) = 3x^3 - 5x^2 - 10x - 6.

Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±2, ±3, ±6, ±(1/3), ±(2/3).

Use synthetic division to test each possible zero. We start with x = 1:

1 │ 3 -5 -10 -6

│ 3 -2 -12

└─────────────

3 -2 -12 -18

x = 1 is not a zero of the polynomial function.

We continue testing the remaining possible zeros:

-1 │ 3 -5 -10 -6

│ -3 8 2

└────────────

3 -8 -2 -4

x = -1 is not a zero of the polynomial function.

2 │ 3 -5 -10 -6

│ 6 2 -16

└─────────────

3 1 -8 -22

x = 2 is not a zero of the polynomial function.

-2 │ 3 -5 -10 -6

│ -6 22 -24

└────────────

3 -11 12 -30

x = -2 is not a zero of the polynomial function.

3 │ 3 -5 -10 -6

│ 9 12 6

└─────────────

3 4 2 0

Since the remainder is zero, we have found a zero of the polynomial function at x = 3.

We can use synthetic division to factor the polynomial function:

3x - 1

(x - 3)(3x^2 + 13x + 2)

Now we can solve for the remaining zeros of the polynomial function by factoring the quadratic equation using the quadratic formula or factoring by grouping. Either way, we find that the remaining zeros are approximately x = -4.87 and x = -0.435.

Therefore, the zeros of the polynomial function f(x) = 3x^3 - 5x^2 - 10x - 6 are x = -4.87, x = -0.435, and x = 3.

It's C because we found the zero x = 3 through synthetic division, and then we used the quadratic formula to find the other two zeros. The quadratic formula gave us two solutions, which we simplified to x = -2 + sqrt(2)/3 and x = -2 - sqrt(2)/3.

If we substitute these solutions back into the original polynomial function f(x), we get:

f(-2 + sqrt(2)/3) = 3(-2 + sqrt(2)/3)^3 - 5(-2 + sqrt(2)/3)^2 - 10(-2 + sqrt(2)/3) - 6

≈ 0

f(-2 - sqrt(2)/3) = 3(-2 - sqrt(2)/3)^3 - 5(-2 - sqrt(2)/3)^2 - 10(-2 - sqrt(2)/3) - 6

≈ 0

Both of these values are approximately zero, which means that -2 + sqrt(2)/3 and -2 - sqrt(2)/3 are also zeros of the polynomial function.

Therefore, the zeros of the polynomial function f(x) = 3x^3 - 5x^2 - 10x - 6 are x = 3, x = -2 + sqrt(2)/3, and x = -2 - sqrt(2)/3, which matches option C.

Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]