Which of the following equations represents an exponential relationship?

y=3(-1)^x

Y =3x-1

y = 3x^2

y= x^3-1

Answer:

204

Step-by-step explanation:

Hello!

If y varies directly with x, that means y is a result of multiplying a number by x.

When x is 5 and y is 60, x is being multiplied by 12 to get y. That means, the direct variation equation is y = 12x.

Replace 17 with x to find y.

The value of y when x is 17 is 204.

Darryl should add 8 gallons of water to the 8-gallon 10% bleach solution to make a 5% bleach solution.

Darryl should add 8 gallons of water to the 8-gallon 10% bleach solution to make a 5% bleach solution .The correct equation that Darryl can use to find x, the number of gallons of water he should add, is:

0.8 / (8 + x) = 5/100

Let's break down the equation and explain each part:

The numerator 0.8 represents the amount of bleach in the original 8-gallon solution.

The denominator (8 + x) represents the total volume of the new solution after adding x gallons of water.

5/100 represents the desired concentration of the new solution, which is 5% bleach.

By setting up this equation, we equate the amount of bleach in the original solution (0.8 gallons) to the amount of bleach in the new solution (5% of the total volume, which is (8 + x) gallons).

Simplifying the equation:

0.8 / (8 + x) = 5/100

To solve for x, we can cross-multiply:

0.8 * 100 = 5 * (8 + x)

80 = 40 + 5x

Subtracting 40 from both sides:

80 - 40 = 5x

40 = 5x

Dividing both sides by 5:

40 / 5 = x

8 = x

Therefore, Darryl should add 8 gallons of water to the 8-gallon 10% bleach solution to make a 5% bleach solution.

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using standard z value, 20% of sandwiches are less than 10.58 inches.

In the given question,

Subway sells foot long sandwiches that have a mean of 11 inches and a standard deviation of 0.5 inches.

20% of sandwiches are less than...............inches.

The cumulative standardized normal distribution table indicates a z value of -0.84 for 20%.

From the question we know that

Mean(μ) = 11 inches

Standard Deviation(σ) = 0.5 inches

We have to find less than of 20% of sandwiches for z value of -0.84

P(ƶ<z) = 20%

We can write it as

P(ƶ<-0.84) = 20/100

P(ƶ<-0.84) = 0.20

Since z = -0.84

X-μ/σ = -0.84

Now putting the value

X-11/0.5 = -0.84

Multiply by 0.5 on both side

X-11/0.5 *0.5= -0.84*0.5

X-11= -0.42

Add 11 on both side

X-11+11= -0.42+11

X = 10.58

Hence, 20% of sandwiches are less than 10.58 inches.

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Right question is here

Subway sells foot long sandwiches that have a mean of 11 inches and a standard deviation of 0.5 inches. 20% of sandwiches are less than ................. inches. (The cumulative standardized normal distribution table indicates a z value of -.84 for 20%)

(a) 11.500

(b) 11.42

(c) 10.58

(d) cannot be determined from the information given

Answer:

The net amount received is 7,120,000

Step-by-step explanation:

The computation of the net amount received is shown below:

= Sale value of the house - real agent commission - expenses

= 8,000,000 - 8,000,000 × 5% - 8,000,000 × 6%

= 8,000,000 - 400,000 - 480,000

= 8,000,000 - 880,000

= 7,120,000

Hence, the net amount received is 7,120,000

The same is relevant

Answer:

$2,611.9.

Step-by-step explanation:

To find the operating cost for the lowest 2% of the airplanes, we need to find the corresponding z-score from the standard normal distribution using a z-table.

Using the formula:

z = (x - μ) / σ

where x is the cost we are interested in, μ is the mean cost, and σ is the standard deviation.

For the lowest 2% of airplanes, the z-score can be found by looking up the area to the left of z in the z-table. This area is 0.02.

Looking up 0.02 in the z-table gives a z-score of approximately -2.05.

So we have:

-2.05 = (x - 3403) / 398

Solving for x, we get:

x = -2.05 * 398 + 3403 = $2,611.9

Therefore, the operating cost for the lowest 2% of the airplanes is approximately $2,611.9.

A. The fundamental matrix for the homogeneous system is given by:Φ(t) = [1 e^(-t) cos(√3t), 1 e^(-t) sin(√3t);-1+i√3, -1-i√3] / 2.

B. The inverse is Φ^(-1)(t) = (1/ie^(t/2)(√3e^(√3t) + 1))[(-1-i√3)/2, 1/2;1+i√3, -1-i√3]/e^t.

C. y(t) = Φ(t)c(t) = ∫Φ(t)Φ^(-1)(t)g(t) dt - ∫Φ(t)Φ^(-1)(t)Φ'(t)∫Φ^(-1)(t)g(t) dt dt

D. y(t) = [(√3e^(-t) + 1)(-3c^(-1) - e^(-t));(-3c^(-1) - e^(-t))(-1-i√3)/2 + (1/2)e^(-t)sin(√3t)] + [∫0^t (1/2) e^(-s) sin(√3s) (-3c^(-1) - e^(-s)) ds; ∫0^t (1/2) e^(-s) sin(√3s) (-1-i√3)/2 + (1/2)e^(-s)sin(√3s) (-3c^(-1) - e^(-s)) ds]

To write a fundamental matrix for the associated homogeneous system.

The homogeneous system of the given non-homogeneous system is obtained by removing the constant term from the non-homogeneous system.

That is, the homogeneous system for this non-homogeneous system is given by: y' = Ay.

Here, A is the matrix obtained by removing the constant terms from the non-homogeneous matrix.

Thus, the matrix A is: A = [2 2; -5 -4]..

Now, the fundamental matrix for this system is given by the formula: Φ(t) = [v1 e^(λ1 t), v2 e^(λ2 t)], where λ1 and λ2 are the eigenvalues of matrix A, and v1 and v2 are the corresponding eigenvectors.

To find the eigenvalues of matrix A, we solve the characteristic equation det(A-λI) = 0, where I is the identity matrix.

This yields: det(A-λI) = (2-λ)(-4-λ) + 10 = λ^2 + 2λ + 2 = 0.

Using the quadratic formula, we obtain:λ1,2 = -1 ± i√3.

Thus, the eigenvalues are complex. To find the eigenvectors, we solve the equation (A-λI)v = 0, where v is the eigenvector.

This yields two eigenvectors:v1 = [1, -1+i√3]t, v2 = [1, -1-i√3]t.

Therefore, the fundamental matrix for the homogeneous system is given by:Φ(t) = [1 e^(-t) cos(√3t), 1 e^(-t) sin(√3t);-1+i√3, -1-i√3] / 2

B. Compute the inverse.

To compute the inverse of Φ(t), we first find its determinant:

det(Φ(t)) = (1 e^(-t) cos(√3t))(1 e^(-t) sin(√3t) + (1 e^(-t) cos(√3t))(-1-i√3)/2

= (e^(-t)/2)(2i√3e^(√3t) + 2i)e^(-t)

= ie^(t/2)(√3e^(√3t) + 1)

Thus, the inverse of Φ(t) is given by:Φ^(-1)(t) = (1/det(Φ(t))) adj(Φ(t)), where adj(Φ(t)) is the adjugate of Φ(t), which is the transpose of the matrix of cofactors of Φ(t).

Thus, we have:Φ^(-1)(t) = (1/ie^(t/2)(√3e^(√3t) + 1))[(-1-i√3)/2, 1/2;1+i√3, -1-i√3]/e^t.

C. Multiply by g⃗ g→ and integrate.

Now, we need to find the particular solution to the non-homogeneous system: y' = Ay + g.

We can use the method of variation of parameters to find the particular solution.

The method involves assuming that the solution has the form: y(t) = Φ(t)c(t), where c(t) is a vector of unknown coefficients.

Substituting this into the equation, we get:

Φ'(t)c(t) + Φ(t)c'(t) = AΦ(t)c(t) + g(t)Φ'(t)c(t)

= g(t) - Φ(t)c'(t)

Multiplying both sides by Φ^(-1)(t), we obtain: c'(t) = -Φ^(-1)(t)Φ'(t)c(t) + Φ^(-1)(t)g(t).

Thus, to find c(t), we need to integrate both sides of this equation.

That is, we have: c(t) = ∫(Φ^(-1)(t)g(t) - Φ^(-1)(t)Φ'(t)c(t)) dt.

Multiplying both sides by Φ(t), we obtain: y(t) = Φ(t)c(t) = ∫Φ(t)Φ^(-1)(t)g(t) dt - ∫Φ(t)Φ^(-1)(t)Φ'(t)∫Φ^(-1)(t)g(t) dt dt.

D. Give the solution to the system.

Now, we substitute the values of Φ(t), Φ^(-1)(t), and g(t) into the formula above to obtain the solution to the system:

y(t) = [(√3e^(-t) + 1)(-3c^(-1) - e^(-t));(-3c^(-1) - e^(-t))(-1-i√3)/2 + (1/2)e^(-t)sin(√3t)] + [∫0^t (1/2) e^(-s) sin(√3s) (-3c^(-1) - e^(-s)) ds; ∫0^t (1/2) e^(-s) sin(√3s) (-1-i√3)/2 + (1/2)e^(-s)sin(√3s) (-3c^(-1) - e^(-s)) ds]

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Answer:

Step-by-step explanation:

x^10

25% discount means we pay 100% - 25% = 75% of the original price.

Relationship between sale price and regular price?

SalePrice = (1 - 25/100) × RegularPrice

Sale price is 75% of regular price.

Answer:

B) 16 x 8

Step-by-step explanation:

Just look at the units on each line, all the way to the left edge of the box, it is on the point -8, and on the right edge it's at 8, so you figure out how far apart those two points are, which is 16

Then for the other side you take the top point 2, and the bottom point -6, and find how far apart they are which is 8

then you get your dimensions of 16 x 8

hope this helped

Answer:

Step-by-step explanation:

Sales tax = 21.80 - 20 = $ 1.80

\(Tax \ percentage=\dfrac{tax}{listed \ price}*100\\\\\\=\dfrac{1.80}{20}*100\\\\\\=1.80*5\)

= 9%

Answer:

b

Step-by-step explanation:

Answer: Radius=19.2 diameter=38.39

Step-by-step explanation: :DDD

We have linearized the given ODE to: \(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\). This is the linearized equation.

To linearize the given ordinary differential equation (ODE) \(\( \frac{{dy}}{{dt}} = 5 \sqrt{x} \)\), we need to rewrite it in a linear form. One common approach is to introduce a new variable that relates to the derivative of \(\( y \)\).

Let's define a new variable \(\( v = \sqrt{x} \)\). Taking the derivative of both sides with respect to \(\( t \)\), we have:

\(\[ \frac{{dv}}{{dt}} = \frac{{d}}{{dt}} \left( \sqrt{x} \right) \]\)

Using the chain rule, we can express \(\( \frac{{dv}}{{dt}} \)\) in terms of \(\( \frac{{dx}}{{dt}} \)\):

\(\[ \frac{{dv}}{{dt}} = \frac{1}{{2 \sqrt{x}}} \cdot \frac{{dx}}{{dt}} \]\)

Now, we need to substitute \(\( \frac{{dx}}{{dt}} \)\) using the given equation \(\( \frac{{dy}}{{dt}} = 5 \sqrt{x} \)\):

\(\[ \frac{{dv}}{{dt}} = \frac{1}{{2 \sqrt{x}}} \cdot \left( 5 \sqrt{x} \right) \]\)

Simplifying the right-hand side:

\(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\)

Thus, we have linearized the given ODE to: \(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\)

The linearized equation is much simpler compared to the original non-linear equation.

Note: The complete question is:

Linearize the ODE below;

\(\(\frac{{dy}}{{dt}} = 5\sqrt{x}\)\)

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Answer:

mhm

Step-by-step explanation:

Answer:

sure

Step-by-step explanation:

Two numbers are in the ratio 4: 7. If their L.C.M. is 168,The numbers would be 56 and 98.

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm) in mathematics and number theory. It can also be referred to as the lowest common multiple (lcm), or the smallest common multiple of two numbers (a and b).

The given ratio is 4:7, which can be written as 4/7.

To find the individual numbers, we can use the formula:

Number1 = LCM × Ratio1/ (Ratio1 + Ratio2)

Number2 = LCM × Ratio2/ (Ratio1 + Ratio2)

Therefore,

Number1 = 168 × 4/ (4 + 7) = 56

Number2 = 168 × 7/ (4 + 7) = 98

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Step-by-step explanation:

4x^2 + 16x -4       factor out a '4'

4 ( x^2 + 4x -1)     Done.  

                  There isn't anything else you can factor out of the three terms

Berners-Lee's hypertext system revolutionized the way information was accessed, shared, and connected.

The hypertext system developed by Tim Berners-Lee, known as the World Wide Web, differed from earlier hypertext systems in several important ways:

1. Universality: Berners-Lee's hypertext system aimed to be universal and accessible to anyone with an internet connection. Unlike earlier proprietary hypertext systems that were limited to specific platforms or networks, the World Wide Web was designed to be platform-independent and accessible from any computer connected to the internet.

2. Decentralization: The World Wide Web was designed as a decentralized system, allowing anyone to create and publish webpages without requiring central control or approval. This stood in contrast to earlier systems that often had centralized control, where content creation and publishing were tightly controlled by a single organization or entity.

3. Hyperlinks: The concept of hyperlinks was fundamental to the World Wide Web. Berners-Lee's system introduced the idea of using hyperlinks, which are clickable connections between different webpages or resources, to navigate and explore the web. This interconnectedness through hyperlinks enabled users to seamlessly move between related information and explore different topics, forming the basis of the web's navigational structure.

4. Markup Language (HTML): Berners-Lee developed the Hypertext Markup Language (HTML) as a simple markup language to structure and format web documents. HTML allowed content creators to define the structure, layout, and presentation of webpages, making it easier to create and share information in a standardized format across different platforms and browsers.

5. HTTP Protocol: Berners-Lee also developed the Hypertext Transfer Protocol (HTTP) as a standard protocol for transferring data over the web. HTTP facilitated the communication between web browsers and web servers, enabling users to request and retrieve webpages and resources from remote servers.

Overall, Berners-Lee's hypertext system revolutionized the way information was accessed, shared, and connected. Its universality, decentralization, use of hyperlinks, HTML markup language, and HTTP protocol paved the way for the widespread adoption and growth of the World Wide Web as we know it today.

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Answer:

369

Explanation:

Calculate each of the groups mentioned. You will derive that 360 students and bilingual and 9 of the teachers are bilingual. Add them together and you got your answer!

- Hope this helped.

Answer:

360 students and 9 teachers

Step-by-step explanation:

30/100 x 1200=360 students

15/100 x 60=9 teachers

Answer:

Option A

Step-by-step explanation:

From the triangle given in the picture,

By applying sine rule,

sin(60)° = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)

\(\frac{\sqrt{3} }{2}=\frac{a}{7}\)

a = \(\frac{7\sqrt{3} }{2}\)

Similarly, by cosine rule,

cos(60)° = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)

\(\frac{1}{2}= \frac{b}{7}\)

b = \(\frac{7}{2}\)

Therefore, Option A will be the correct option.

The distance from Durham to Cary on the second map is 75 km

The scale of the first map:

1 cm = 2 km

The scale of the second map:

1 cm = 5 km

Map scale: A distance on a map and its corresponding distance on the planet are related by a scale. The equivalent of a map scale can be expressed, typically using different units. or visually, using a bar scale.

Distance from Durham to Cary = 15 cm

Distance from Durham to Cary on the second map = Scale of the second map * Distance from Durham to Cary

= 5*15

= 75 km

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Answer:

I think its D

Step-by-step explanation:

because 564÷71 is 7.9 and if u round that you will get 8

Step-by-step explanation:

11+11+9 equals 30 just do the math it simple

A binomial probability distribution with p = 0.3 is c. positively skewed.

A binomial probability distribution with p = 0.3 is positively skewed. This means that the distribution is skewed to the right. In a binomial distribution, the skewness is determined by the value of p, which represents the probability of success in each trial. When p is less than 0.5, as in this case (p = 0.3), the distribution tends to be positively skewed.

The correct answer is c. positively skewed.

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Step-by-step explanation:

Here f(x) = x² - 2x instead of f(x) = x². (typing error)

When (f + g)(x) = 0,

f(x) + g(x) = x² + 4x + 4 = 0.

Therefore (x + 2)² = 0, we have

x = -2.

Answer:

C50   X  n

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

24÷2=16×1=16÷2=8

am not sure I think the answer is also 16 so look at other people answer

Paul should buy 3 gallons

Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.

Thus, unit price of something is price of 1 thing.

Thus, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.

There are 16 cups in a gallon, and if each person will eat 2 cups, and there are 24 people, multiply 24 by 2 to get the number of cups.

24 x 2 = 48.

Then, divide that by 16 (the number of cups in a gallon) to how many gallons.

48 ÷ 16 = 3

Therefore, he needs 3 gallons.

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The polar form is 2∠(π/3). The exponential form is obtained by using Euler's formula: z = re^(iθ).

The given complex number, -1 - √3i, can be expressed in polar form as r∠θ, where r is the magnitude and θ is the argument. To find r, we calculate the magnitude using the formula r = √(a² + b²), where a and b are the real and imaginary parts respectively. In this case, a = -1 and b = -√3.

r = √((-1)² + (-√3)²) = 2. To find θ, we use the formula θ = arctan(b/a), where b and a are as defined above.

In this case, θ = arctan((-√3)/(-1)) = arctan(√3) = π/3. Thus, the polar form is 2∠(π/3). The exponential form is obtained by using Euler's formula: z = re^(iθ). Substituting the values, we have 2e^(iπ/3) as the exponential form.

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The interest rate your friend is charging you for the $20,000 loan is 20% per year.

The simple interest is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is the interest rate and t is time.

Given that;

The Principal P = $20,000

Accrued amount A = $40,000

Elapsed time t = 5 years

Interest rate r =?

Plug these values into the above formula and solve for the interest rate r:

\(A = P( 1 + rt )\\\\r = \frac{1}{t}( \frac{A}{P} -1 ) \\\\r = \frac{1}{5}( \frac{40000}{20000} -1 ) \\\\r = \frac{1}{5}( 2 -1 ) \\\\r = \frac{1}{5}\\\\r = 0.2 \\\\\)

Converting r decimal to R a percentage

Rate R = 0.2 × 100%

Rate r = 20% per year

Therefore, the interest rate is 20% per year.

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