5. Sean has 56 bills in his pockets. The bills are only fives and tens.
If the value of the bills adds up to $495, how many of each bill does
he have?

The linearized equation around its equilibrium position is given as;f(x) = -4.8(x - 1.39)

The given equation is x² + 2x* + 2x² - 12x + 10 = 0.

It needs to be linearized around its equilibrium position.

Linearizing the given equation around its equilibrium position x0, we have;

f(x) = f(x0) + f'(x0)(x - x0)

Where f(x) = x² + 2x* + 2x² - 12x + 10

The equilibrium position is the point where f(x) = 0.

Hence, f(x0) = 0.

Thus, x² + 2x* + 2x² - 12x + 10 = 0⇒ 3x² - 6x = -10⇒ x² - 2x + (2.33) = 0(x-1)² = 0.77x - 0.77 or

x = 1 + (0.77)/(2) or x = 1.39

Hence, the equilibrium position x0 = 1.39.

Substitute x0 = 1.39 in the equation and simplify to get f'(x0):

f(x) = x² + 2x* + 2x² - 12x + 10

f(x) = 3.84 - 8.34 + 10

f'(x0) = f'(1.39) = -4.8

Therefore, the linearized equation around its equilibrium position is given as;f(x) = -4.8(x - 1.39)

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Answer:

D. direct variation; y = 1.5x

Step-by-step explanation:

9/6 = 1.5

12/8 = 1.5

answer is C Direct variation, y = 1.5x

...............................................................................................................................................

The answer is c. Direct variation; y=1.5x

Step-by-step explanation:

Answer:

51 degrees

Step-by-step explanation:

m<A = 11x+13

m<B=9x-24

Right angle = 90 degrees

11x+13=90

11x=77

x=7

To find m<B:

plug in x:

9(7)-24

m<B=39 degrees

Difference in the two angles: m<A - m<B

= 90-39

51 degrees

Slope's second run took 5 minutes. Slope's second run took 5 minutes.  To solve the problem, we need to first understand what is being asked. We know that Slope's second run was 1 3 minutes faster than his first run, and we also know that his first run took 6 minutes.

Therefore, we need to find the time of his second run.

To do this, we can start by finding out how much time 1 3 minutes is in seconds. There are 60 seconds in a minute, so 1 3 minutes is equal to 20 seconds.

Next, we can subtract 20 seconds from the time of his first run, which was 6 minutes or 360 seconds.

360 seconds - 20 seconds = 340 seconds

So Slope's second run took 340 seconds or 5 minutes and 40 seconds. However, the question asks for the time of his second run in minutes, so we need to convert 340 seconds to minutes.

340 seconds ÷ 60 seconds/minute = 5 minutes and 40 seconds ÷ 60 seconds/minute = 5 minutes

Therefore, Slope's second run took 5 minutes.

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Sarah scored 82 points on her first test of the year. On the second test,

82%

On the Second Test, She scored 77 points

77%

82

-77

=5

The Percent of Change is 5%

or -5% Because The second test Is lower than her first test

Answer:

5%

Step-by-step explanation:

82% - 77%=5%

82%

77%

so there fore the answer is 5%

Answer:

468

Step-by-step explanation:

8/4*234=2*234=468

Answer:

468

Step-by-step explanation:

5+3/ 4 =2

2*234=468

Answer:

6√6

Step-by-step explanation:

√6 * √6 * √6 = ?

√6*√6 = √36, which can be square rooted down into 6.

6 * √6 = 6√6, cannot simplify further.

The equation x2 + y2 = z2, with (x, y, z) = 1 and y being odd, can be proven using the Pythagorean Theorem.

The Pythagorean Theorem states that in any right triangle, the sum of the squares of the two legs (the sides of the triangle adjacent to the right angle) is equal to the square of the hypotenuse (the side opposite the right angle).

In this case, let the side of length x be a, the side of length y be b, and the side of length z be c.

Since x2 + y2 = z2, a2 + b2 = c2. Additionally, since (x, y, z) = 1 and y is odd, a = 1, b is odd, and c is also odd.

Therefore, since the sum of the squares of the two legs is equal to the square of the hypotenuse, and the two legs are both equal to 1 and the hypotenuse is an odd number, the equation x2 + y2 = z2 is proven.

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Answer:

Graph g(x) = 2x - 3

Step-by-step explanation:

Plug in (x+1) to f(x) = 2x - 5:

g(x) = 2(x+1) - 5 = 2x + 2 - 5

g(x) = 2x - 3

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

Diagram

Step 02:

a.

Big Rectangle Area = s²

= 7 cm * 5 cm

= 35 cm²

Triangle Area = (b * h) / 2

= (3 cm * 4 cm) / 2

= 12 cm² / 2 = 6 cm²

probability = Triangle Area / Big Rectangle Area

= 6 cm² / 35 cm² = 6 / 35 = 0.171

b.

Small Rectangle Area = s²

= 2 cm * 2 cm

= 4 cm²

Shaded region Area = Big Rectangle Area - Triangle Area - Small Rectangle Area

Shaded region Area = 35 cm² - 6 cm² - 4 cm² = 25 cm²

probability = Shaded region Area / Big Rectangle Area

= 25 cm² / 35 cm² = 25 / 35 = 5 / 7 = 0.714

The answer is:

a. probability = 6 / 35 = 0.171

b. probability = 5 / 7 = 0.714

Answer:

I think its -4.

Answer:

B. D. E

Step-by-step explanation:

The range of f(x) is y> 0 and the y-intercept is (0, 1). Therefore, options B, D and E are the correct answers.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=(3/5)ˣ.

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (−∞,∞),{x|x∈R}

Range: (0,∞),{y|y>0}

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): None

y-intercept(s): (0,1)

Therefore, options B, D and E are the correct answers.

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Answer:

238000

Step-by-step explanation:

hope I did this right!!

Answer:

The total profit the company would make over the course of its first 14 years of operation is approximately $2,562,841.

Step-by-step explanation:

The profit of the company increased at a constant 20% per year. We can use the formula for the future value of an investment to calculate the profit for each year, where:

FV = PV x (1 + r)^n

FV is the future value of the investment

PV is the present value of the investment

r is the annual interest rate

n is the number of years

Using this formula, we can find the profit for each year:

Year 1: $140,000

Year 2: $168,000

Year 3: $201,600

Year 4: $241,920

Year 5: $290,304

Year 6: $348,364

Year 7: $418,037

Year 8: $501,644

Year 9: $601,972

Year 10: $722,367

Year 11: $866,840

Year 12: $1,040,208

Year 13: $1,248,250

Year 14: $1,497,900

To find the total profit over the course of the first 14 years, we can simply add up the profits for each year:

Total profit = $140,000 + $168,000 + $201,600 + $241,920 + $290,304 + $348,364 + $418,037 + $501,644 + $601,972 + $722,367 + $866,840 + $1,040,208 + $1,248,250 + $1,497,900

Total profit = $2,562,841 (rounded to the nearest whole number)

The area of the rectangle is 43.75 square centimeters, and we get that by using the area formula:

A = L*W

A rectangle is defined only by two dimensions, which are length and width if we define the variables:

L = length of the rectangle

W = width of the rectangle

Then the area of the rectangle is given by the formula:

A = L*W

Here we know that the dimensions of the rectangle are 12.5 cm and 3.5 cm, so we can define:

L = 12.5cm

W = 3.5cm

Replacing that in the formula for the area we get:

A = (12.5cm)*(3.5cm) = 43.75 cm^2

That is the area of the rectangle.

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The probability that the sum of the numbers shown will be 6 when rolling two is equals to the 1/80. So, the correct answer is option (a).

The probability of a simple event happening is defined as the number of times the event can happen, divided by the number of possible event. The probability of occurrence of the event A is P(A) = n/N. We have a twenty sided die has each side showing numbers from 1-20. Let us consider an event A , A : the event of getting sum of 6 when two dice are rolled. Also, Assume that it is fair dice, we have all the outcomes to be equally likely. We have, to determine the probability of occurrence of the event A, P(A)= No. of favourable outcomes/total num of outcomes = n/N

Thus the favourable outcomes for event A, n = {(1,5),(5,1),(2,4),(4,2),(3,3)} = 5

On rolling a die, total possible outcomes

= 20 so, on rolling two dice, we have total number of outcomes as, N = 20× 20= 400.

Thus the probability of occuring of event A, P(A) = n/M = 5/400 = 1/80.

Hence, required probability is 1/80.

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Complete question:

On a 20-sided die, each side shows a number from 1-20. What is the probability that the sum of the numbers shown will be 6 when rolling two?

a. 1/80

b. 1/6

c. 395/400

d. 1/400

The correct response is C. 0.0036 Square degrees The field of vision of the Hubble Space Telescope is only 0.006 degrees, which is around 100 times less than that of the Micro Observatory telescopes. But it has a 100 times better angular resolution!

Skywatchers can readily view planets with just a modest or medium-sized telescope. How much of our solar system is visible will wow you! Additionally, you don't need a completely dark sky to see all of the planets in our solar system; a telescope can still make Venus, Mars, Jupiter, and Saturn easily visible even when viewed in a city. From $100 to well over $10,000, a telescope can be purchased. In 2022, you can anticipate that a good telescope for visual observing will start around $300 and a telescope capable of deep-sky astrophotography would start around $800. With a 25x telescope, even the tiniest telescope should be able to see Saturn's rings.

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Large telescopes often have small fields of view. For example, the Hubble Space Telescope's (HST's) advanced camera has a field of view that is roughly square and about 0.06 degree on a side. Calculate the angular area of the HST's field of view in square degrees.

A. 0.006 Square degrees

B. 0.36 Square degrees

C. 0.0036 Square degrees

D. 0.06 Square degrees

The probability of seven baseballs having straight stitching is relatively high which is 0.309, so the company does not need to stop the production line.

As per the given information in the question:

Probability of baseball having straight stitching

= 87.6%

= 0.876

Probability of baseball not having straight stitching

= 1-0.876

= 0.124

We need to find out whether the company should stop the production line if exactly seven of the eleven have straight stitching or not.

P(X=7) = (\(C^{11}_7\)) × 0.876⁷ × 0.124⁴

= (330) × (0.377) × (0.0025)

= 0.309

Therefore, the probability of exactly seven baseballs having straight stitching is 0.309.

The company should only stop the production line if the probability of baseballs having straight stitching is very low.

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The method of periodization that an athlete performs is  traditional periodization method.

Given,

An athlete perform five sets of five repetitions at 90% of 1rm on the first day of the week, five sets of fourteen repetitions at 85% of 1rm on the next training day, and five sets of two repetitions at 62.5%of 1rm on the last training day of the week;

Here,

The example above, where the percentage of one-repetition maximum (1RM) decreases as the training day progresses, is essentially a traditional periodization method.

As a result, during the course of the training cycle, the athletes' completed work gradually grows. As a result, as the load increases over time, there is a corresponding decrease in volume.

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Answer:

the slope is 1

Step-by-step explanation:

you could just leave it as x in the equation

To find the length of the polar curve \(r = 3e^(6θ)\) from Ф =0 to Ф= 2π, we use the formula for arc length in polar coordinates. the length of the polar curve from θ = 0 to θ = 2π is \((1/2)(3√130)(e^(12π) - 1).\)

\(L = ∫[a,b] sqrt[r(θ)^2 + (dr/dθ)^2] dθ\)

where a and b are the initial and final values of θ\([e^(6θ)]_\).

In this case, we have: \(r(θ) = 3e^(6θ)\)

\(dr/dθ = 18e^(6θ)\)

So, the arc length is:

\(L = ∫[0,2π] sqrt[(3e^(6θ))^2 + (18e^(6θ))^2] dθ\)

= ∫\([0,2π] 3e^(6θ) sqrt[1 + 36^2] dθ\)

= \(3√130 ∫[0,2π] e^(6θ) dθ\)

=\((3√130/6)\)

\(=0^(2π)\)

\(= (1/2)(3√130)(e^(12π) - 1)\)

Therefore, the length of the polar curve from θ = 0 to θ = 2π is \((1/2)(3√130)(e^(12π) - 1).\)

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Answer: Simplifying ratios is just like simplifying fractions. Think of ratios as fractions. You divide a number that both numerator and denominator can be divided by.

Example

5/10 = 1/2

How did we get 1/2? Simple! You divide the numerator and denominator by 5.

5/10÷5/5=1/2

You do the same for ratios but the only difference is instead of putting a fraction bar (/) you put a colon (:)

Let's try another example but with a ratio!

Example

5:10 = 1:2

How did we get 1:2? Simple! Again we divided by 5 just like we did with the fraction example! So really ratios are just like fractions!

5:10÷5:5=1:2

Remember

The fraction bar is /

The ratio bar is :

Ratios are just like fractions but the symbol can sometimes trick people.

Using the law of cosines, it is found that the measure of angle Y is of 64º.

The problem is incomplete, hence we research it on a search engine, and we have that we have a triangle in which:

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 12, b = 17, c = 16, C = Y.

Hence:

c² = a² + b² - 2abcos(Y)

16² = 12² + 17² - 2(12)(17)cos(Y)

408cos(Y) = 177

cos(Y) = 177/408

Y = arccos(177/408)

Y = 64º.

The measure of angle Y is of 64º.

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Answer:

2/5

Step-by-step explanation:

Total=4+5+1=9+1=10

4/10=2/5

2/5 is the correct answer

The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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Answer:

600/50=12

12*19=228 people read one book per month

Step-by-step explanation:

Answer:

72% of the sample read at least 1 book. You can extimate that 432 people out of the 600 people read at least 1 book because 432 is 72% of 600

Step-by-step explanation:

brainliest please