Question 13 < > 0.75/1 pt 95 97 Details The amount of trash, in tons per year, produced by a town has been growing exponentially, and is projected to continue growing according to the formula P(t) = 52 + 5e0.3t Set up a definite integral for the total trash that will be produced over the next 10 years by interpreting the integral as an area under a curve, and use a calculator to evaluate it. The definite integral is 5° f(t) dt where a. a = and b = b. f(t) = tons. c. The total trash over the next 10 years is (Round the answer to four decimal places.) Submit Question

Answer:

$2696.63

Explanation:

The future value A and the present value P are related by the following equation

A = P(1 + rt)

Where r is the interest rate and t is the time.

Now, we need to convert 9 months to years as follows

9 months x 1 year / 12 months = 0.75 years

Then, replacing A = 3000, r = 15% = 0.15 and t = 0.75, we get:

3000 = P(1 + 0.15(0.75))

3000 = P(1 + 0.1125)

3000 = P(1.1125)

Now, we can solve for P

P = 3000/1.1125

P = 2696.63

Therefore, the present value is $2696.63

The statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

Let {v₁, v₂, ...., vp} be a set of p vectors in Rⁿ, then the following are equivalent statements:

1. The set of vectors is linearly dependent.

2. There exist constants c₁, c₂, ... cp, not all of them zero, such that:

c₁v₁+c₂v₂+...+cpvp = 0 (zero vector)

For the above to be possible, the following must hold true: p≥n

Because in Rⁿ, each vector has n components.

So, the total number of unknowns is p, while the total number of equations that we have is n.

Hence p≥n for the system of linear equations above to have a non-zero solution.

Hence, the statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

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To find the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2, we can use the following formulas:

New x-coordinate = -2 * old x-coordinate

New y-coordinate = -2 * old y-coordinate

Let's apply these formulas to each point in triangle ABC:

Point A: (-3, 4)

New x-coordinate of A = -2 * (-3) = 6

New y-coordinate of A = -2 * 4 = -8

New coordinates of A: (6, -8)

Point B: (1, 1)

New x-coordinate of B = -2 * 1 = -2

New y-coordinate of B = -2 * 1 = -2

New coordinates of B: (-2, -2)

Point C: (5, -2)

New x-coordinate of C = -2 * 5 = -10

New y-coordinate of C = -2 * (-2) = 4

New coordinates of C: (-10, 4)

Therefore, the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2 are:

A: (6, -8)

B: (-2, -2)

C: (-10, 4)

Answer:

57/100

Step-by-step explanation:

27/100 = 0.27

3/10 = .3

.27 + .3 = .57

.57 = 57/100

Answer:

57/100

Step-by-step explanation:

make the denominators the same

lcm of 10, 100= 100

27/100+30/100=57/100

Step-by-step explanation:

3a + 6 + 5a - 2

8a + 4

4(2a+1)

or

Easy

3a + 6 + 5a - 2

8a +4

Answer:

\((87 - 7) \div 42\)

Step-by-step explanation:

80÷42=1.9047619048

Answer:

1.90476190476 or 1.90

Step-by-step explanation:

PEMDAS

Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

first you would do anything inside the parenthesis

(87 − 7) ÷ 42 =

80÷ 42 =

next you would do any Exponents but in this case we dont have to so you would do any Multiplication/Division whichever comes first

80÷ 42 = 1.90476190476

now you could round it to 1.90

Answer:

A hexagon

Step-by-step explanation:

A hexagon - - - the allen wrench has 2 hexagonal heads. See attached pic.

The geometric shape that forms the hole that fits an allen wrench is a hexagon, which is a six-sided polygon with straight sides and angles.

The geometric shape hexagon-shaped hole in an allen wrench, also known as a hex key, is designed to fit tightly over the hexagonal socket of a screw or bolt head. A hexagon is a six-sided polygon, meaning it has six straight sides and angles. In the case of an allen wrench, the hexagon has internal angles of 120 degrees and opposite sides that are parallel.

The hexagonal shape of the hole in the wrench allows for a tight and secure fit onto the corresponding hexagonal socket of the screw or bolt head. This design ensures that the wrench can apply a significant amount of torque to the fastener without slipping, which is essential for many applications in construction, mechanics, and other industries.

The use of a hexagonal shape also allows for greater precision and control when turning the screw or bolt, making it easier to achieve the desired level of tightness. Overall, the hexagon is an ideal shape for the hole in an allen wrench due to its strength, stability, and precision.

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Answer:

Let x be your original weight.

The weight loss of 4-8 kg can be represented as a range: 4 kg ≤ x ≤ 8 kg.

We also know that this weight loss is equal to 6% of your original weight:

6% of x = 4 kg

To find the lower end of the range, we use 4 kg:

0.06 * x = 4 kg

Solving this equation for x:

x = 4 kg / 0.06

x ≈ 66.67 kg

Therefore, your original weight was approximately 66.67 kg.

The scarf discounted by 60%.

What is discount?

Discount is a term that describes a sum or a percentage subtracted from a product's usual selling price. Make sure you need all of the items you plan to buy before waiting until after the holiday when you can frequently find them at a significant discount. Discount is a term that refers to a reduction in the cost of a commodity or service.

Given:

Janette buys a scarf with an original price of $30, but is on clearance for $18.

Suppose x be the discount on the scarf.

⇒ x = \(\frac{18}{30} (100)\)

x = 60%

Hence, the discount on the scarf is 60%.

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Answer:

15.8 ft

Step-by-step explanation:

The inclined plane, the base of and the shelving unit form the shape of a right angled triangle.

The hypotenuse is the length of the inclined plane, h.

The base of the triangle is 15 ft.

The height of the triangle is 5 ft.

To find the hypotenuse, h, we have to use Pythagoras rule:

\(h^2 = a^2 + b^2\)

where a = height of the triangle

b = base of the triangle

Therefore:

\(h^2 = 5^2 + 15^2\\\\h^2 = 25 + 225 = 250\\\\h = \sqrt{250}\\ \\h = 15.8 ft\)

The inclined plane is 15.8 ft long.

Answer:

King Leopold became the monarch of Belgium in 1865

The numeric value of ms within is = 19.

To find the numeric value of ms within:

Given: Swithin = 70, sample size = 17 and number of groups = 3.

So, 17 × 3 = 51

70 - 51 = 19

Therefore, the numeric value of ms within is = 19.

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To find the probability that the mean weight of 19 fish is between 16.1 and 20.6 lb, you would need to know the distribution of the weights of the individual fish. If the weights of the fish are normally distributed with a mean of 18.4 lb and a standard deviation of 2.5 lb, then you can use a normal distribution to find the probability that the mean weight of the 19 fish falls in the specified range.

How does probability work exactly?

Probability is calculated by dividing the total possible outcomes by the number of outcomes that are theoretically possible. Probability differs from odds in this regard. Calculating odds involves dividing the likelihood of a particular event by the likelihood that it won't occur.

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Answer: sphere

Step-by-step explanation:

For cone,

Radius = 9 in.

height = 12 in.

Volume = \(\dfrac{1}{3}\pi r^2h\)

Then, Volume = \(\dfrac{1}{3}(3.14)(9)^2(12)=1017.36\ \text{cubic inches}\)

For cylinder,

Radius = 9 in.

height = 12 in.

Volume = \(\pi r^2h\)

Then, volume = \((3.14)(9)^2(12)=3052.08\text{ cubic inches}\)

For sphere,

Radius = 9 in.

Volume = \(\dfrac{4}{3}\pi r^3\)

Then, volume = \(\dfrac{4}{3}(3.14)(9)^3=3052.08\text{ cubic inches}\)

For best buy, we require highest volume but lowest cost.

Thus, Volume of cone < Volume of cylinder and volume of sphere.

Volume of cylinder = volume of sphere.

But the cost of the sphere < cost of cylinder as $28<$30.

So, the sphere would be the best buy as it has the greatest volume but low cost.

The value of the expression given as (3x + 2.05) + (-x + 1.09) + (2x) + (x) is 5x  + 3.14

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(3x + 2.05) + (-x + 1.09) + (2x) + (x)

Start by opening the brackets

(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 3x + 2.05 - x + 1.09 + 2x + x

Next, we collect the like terms

(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 3x - x + 2x + x  + 2.05 + 1.09

Next, we evaluate the like terms

(3x + 2.05) + (-x + 1.09) + (2x) + (x) = 5x  + 3.14

Hence, the value of the expression is 5x  + 3.14

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Possible question

What is (3x + 2.05) + (-x + 1.09) + (2x) + (x)

There are infinitely many even integers that are divisible by 5.

By considering how any even integer can be represented as 2m, where m is an integer, it becomes evident that if 2m happens to be divisible by 5, then m will also have this quality because 5, which is a prime number, cannot divide into 2.

As a result, all even integers that aredivisible by 5 can be expressed in the format of 10n, with any n being acceptable. Examples of such numbers include:

0 (from 10 x 0 = 0)

10 (from 10 x 1 = 10)

-10 (through 10 x -1 = -10)

20 (by evaluating 10 x 2 = 20)

And similarly when exploring negative values:  

-20 (since 10 x -2 = -20), and so on.

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You cannot use the product of powers rule to simplify 34 · 28.

The product of powers rule states that when you multiply two powers with the same base, you can add the exponents. For example, 23 · 25 = 28 because 2+3=5 and 5+3=8.
In the expression 34 · 28, the bases are different. 34 means 3 raised to the power of 4, and 28 means 2 raised to the power of 8. Since the bases are not the same, you cannot simplify the expression using the product of powers rule.

Hence, The product of powers rule only applies when the bases of the powers are the same, so it cannot be used to simplify expressions with different bases, such as 34 · 28.

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The Maclaurin series for cos(x) is given by:

cos(x) = Σ (-1)^n * (x^(2n)) / (2n)!, for n = 0 to ∞

Now, we need to find the Maclaurin series for f(x) = 12x * cos(12x). We can substitute x with 12x in the Maclaurin series for cos(x):

cos(12x) = Σ (-1)^n * (12x)^(2n) / (2n)!, for n = 0 to ∞

Now, multiply the series by 12x:

f(x) = 12x * cos(12x) = 12x * Σ (-1)^n * (12x)^(2n) / (2n)!, for n = 0 to ∞

Simplify the expression:

f(x) = Σ (-1)^n * 12^(2n + 1) * x^(2n + 1) / (2n)!, for n = 0 to ∞

This is the Maclaurin series for the given function f(x) = 12x * cos(12x).

You should be concise and not provide extraneous amounts of detail. You should not ignore any typos or irrelevant parts of the question. Here is the solution to the given problem.Student question: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = 12X COS 12x cos(12)Step 1:We are required to find the Maclaurin series for a function involving cos(x). Let's recall the Maclaurin series for cos(x).cos(x) = Σ(-1)^(n)/(2n)!  (n=0)The same equality would be true for any variable, and in particular for u = x^2.x^2/2! = 1/2!x^4/4! = 1/4! x^6/6! = 1/6!Therefore, the Maclaurin series for cos(x^2) isx^4nΣ(-1)^(n)/n!(2n)!  (n=0)Step 2:Now we can use this to find the Maclaurin series of the given function, treating the term 12x as a constant and using the rule can=canf(x) = 12x cos(12x cos(1+2)) = 12x cos((12x)cos(1+2))= 12xΣ(-1)^(n)/(2n)! [12x cos(1+2)]^(2n) =Σ(-1)^(n)/(2n)!  (24nx)^(2n) =Σ(-1)^(n)/(2n)!  24^(2n) x^(4n+1) (n=0)Therefore, the required Maclaurin series of the given function is Σ(-1)^(n)/(2n)!  24^(2n) x^(4n+1) (n=0).

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Answer:

8x +6    is the expression.....

when x=5

8(5) + 6 = 46

Step-by-step explanation:

hope this helps :3

Answer: Interval notation. When using interval notation, domain and range are written as intervals of values. For f(x) = x 2, the domain in interval notation is: D: (-∞, ∞) D indicates that you are talking about the domain, and (-∞, ∞), read as negative infinity to positive infinity, is another way of saying that the domain is "all real numbers." The range of f(x) = x 2 in interval notation is: R: [0, ∞) R indicates that you are talking about the range.

Step-by-step explanation:

Answer:

540 sec

Step-by-step explanation:

Step 1: Find conversion

1 minute = 60 seconds

Step 2: Use Dimensional Analysis

9 min · (60 sec/1 min)

540 sec

Answer:

1

Step-by-step explanation:

assuming your points are (0,3) and (-3,0) you would "rise" 3 and "run" 3 to get from one point to the next on a graph, making your rise over run (aka slope) 3/3 which is equal to 1.

Since ∠2 and ∠3 are complementary, we know that their sum is equal to 90 degrees. Thus, we can say that m∠3 = 90 - m∠2 = 90 - 28 = 62 degrees.

Also, since ∠1 ≅ ∠4, they have the same measure. Therefore, we can say that m∠1 = m∠4.

Now, we can use the fact that the sum of the measures of the angles in a triangle is 180 degrees. In triangle ABC, we have:

m∠1 + m∠2 + m∠3 = 180

Substituting the values we know, we get:

m∠1 + 28 + 62 = 180

Simplifying the equation, we get:

m∠1 = 90

Therefore, each of ∠1 and ∠4 has a measure of 90 degrees.

To justify our work, we used the following theorems:

Complementary angles theorem: If two angles are complementary, their sum is equal to 90 degrees.

Triangle angle-sum theorem: The sum of the measures of the angles in a triangle is equal to 180 degrees.

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The simplest form of an algebraic expression is when it cannot be simplified further. The simplest form of the equation \(\frac{4}{y} - 2y-\frac{1}{2}\) is \(\frac{4y^{2}+y-8 }{2y}\).

Here's a step-by-step explanation:

Start with the equation: \(\frac{4}{y} - 2y-\frac{1}{2}\).

Making the denominator of all terms  \(2y\), multiply each term by (\(2y\) divided by their respective denominators )

We get,

\(\frac{4*2}{2y}-\frac{2y(2y)}{2y} -\frac{1}{2y}(y)\)

\(=\frac{8-4y^{2}-y }{2y}\)

\(=\frac{-4y^{2}-y+8 }{2y}\)

On multiplying by \(-1\), we get

\(\frac{4y^{2}+y-8 }{2y}\)

So, the simplest form is \(\frac{4y^{2}+y-8 }{2y}\).

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Answer:

I’m pretty sure it’s B

Step-by-step explanation:

Answer:

C (the rate of change of f(x) is -1/2 and g(x) if 1/2

Step-by-step explanation:

i cant be 100% sure so take this with a grain of salt but if x was 1, f(x)'s rate of change (another word for slope) would be -1/2 whilst g(x)'s slope would be 1/2.

Answer:

8

Step-by-step explanation:

We can use triangle inequality, let AC = x:

x+4 > 5

x+5 > 4

9 > x

Simplifying:

x>1

x>-1

9>x

Thus: 9>x>1

So the Largest whole number is 8

Answer:

The indifference point is 10 miles.

Step-by-step explanation:

Giving the following information:

Beth:

$5 per mile

Tonya's:

registration fee of $20

$3 per mile

First, we need to structure the income formulas:

Beth= 5x

Tonya= 20 + 3x

x= miles

Now, to determine the indifference point, we equal both formulas and isolate "x":

5x = 20 + 3x

2x= 20

x=10

The indifference point is 10 miles.

Beth= 5*10= $50

Tonya= 20 + 3*10= $50

Step-by-step explanation:

I just sketched all of them

integer solution= -1