Consider the differential equation M^3(x)= 613 + e^12/x
a) True or False : This differential equation is autonomous b) Given the additional informats on that M(O)= 1, What is M(x)?

Answer:

Option D

Step-by-step explanation:

Hello! Here is my explanation on how I got this answer:

The expression f(t) = -16t2 + 250 and g(t) = 15t can be combined into h(t) = -16t2 + 15t + 250. I got this answer because you cannot combine the two expressions including the variable t. This also means that they have to be separated which they are in ever expression listed. Since g(t) = 15t is a positive expression, we can rightfully assume that h(t) = 16t2 + 15t + 250 is the correct answer.

Hope this helps! Let me know if you have any other questions!

Answer:

√104

Step-by-step explanation:

missing side = \(\sqrt{15^2-11^2} = \sqrt{225-121} = \sqrt{104}\)

Answer:

its clockwise

Step-by-step explanation:

Answer:

its clockwise

Step-by-step explanation:

hope this helps

It should be noted that a polygon that's inscribed in a circle has each vertex on the outer figure.

It should be noted that a polygon simply means a plane figure that has a finite number of straight line segments.

In this case, a polygon that's inscribed in a circle has each vertex on the outer figure. Also regular polygons can be inscribed in a circle.

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The wage of 2001 in terms of wage in 2012 is option A $14.97

Given,

Mack's wages in 2001 = $7 per hour

Mack's wages in 2012 = $12 per hour

The CPI in 2001 = 94

The CPI in 2012 = 201

We have to fins the wage of 2001 in terms of wage in 2012;

CPI;- Consumer Price Index

The CPI is calculated by the Bureau of Labor Statistics each month using a sample of 94,000 prices. To determine the overall change in prices, the index for each good or service is weighted according to its share of recent consumer spending.

Here,

The wage of 2001 in terms of wage in 2012 = (CPI in present year / CPI in past year) x Wage of earlier year

= (201 / 94) x 7

= 14.97

That is,

The wage of 2001 in terms of wage in 2012 is option A $14.97

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Answer:

reason being is because -4x is negative while 4x is not.

Answer:

Solving 4x < - 16 gives the answer x < - 4

Solving - 4x < - 16 gives the answer x < 4

In the first inequality, the value of x starts decreasing from the negative side of the number line i. e. from -4 while in the second inequality, the value of x starts decreasing from the positive side of the number line i. e. from 4.

Answer: 147 votes

Beacause they need to find out what to do with the beach house

The greatest value in the range for this situation is $2,675.

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Let the number of days the beach house is rented be represented by the variable "d".

If d is less than or equal to 7, then the total cost can be calculated as:

Total Cost = 375d + 100

If d is greater than 7, then the maximum cost would be reached by renting the house for 7 days and adding the $100 cleaning fee.

In this case, the total cost can be calculated as:

Total Cost = 375(7) + 100 = 2,675

Therefore,

The greatest value in the range for this situation is $2,675.

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Answer:

SA = 967.6 cm²

Step-by-step explanation:

Surface Area of cylinder = \(2\pi r h + 2\pi r^2\)

Where r = 7 cm, h = 15 cm

=> SA = 2(3.14)(7)(15)+2(3.14)(7)²

=> SA = 659.7 + 2(3.14)(49)

=> SA = 659.7 + 307.9

=> SA = 967.6 cm²

Answer:

967.12 cm^2

Step-by-step explanation:

To find surface area of cylinder:

Find area of cross section x 2 = pi x r ^2 = 153.86 x 2 = 307.72cm^2

Area of curved surface = 3.14 x 14 x 15 = 659.4 cm^2

Total Surface Area = 659.4 + 307.72  = 967.12cm^2

Hope this helps

Answer:

\(let \: it \: be \: x \\ \cos(70 \degree) = \frac{12}{x} \\ x = \frac{12}{ \cos(70 \degree) } \\ x = 35.1 \: ft\)

\(height = \sqrt{ {35.1}^{2} - {12}^{2} } \\ = \sqrt{1088.01} \\ = 33.0 \: ft\)

Answer:

it so easy that correct

Step-by-step explanation:

$500.00×$8.5

The ratio of the two legs of the triangle 30-90-60 will be 1 : √3.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

The triangle is 30-90-60. The ratio of the two legs will be calculated as,

tan(30) = AB / BC

1 / √3 = AB / BC

Hence, the ratio of the two legs will be 1 : √3.

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Mark Welsch deposits $7,500 in an account that earns interest at an annual rate of 8%, compounded quarterly. At the end of 5 years, the amount of money in the account is $7,500 + earned interest = $11,142.75. The answer is rounded to two decimal places.

Mark Welsch deposits $7,500 in an account that earns interest at an annual rate of 8%, compounded quarterly. The $7,500 plus earned interest must remain in the account 5 years before it can be withdrawn. How much money will be in the account at the end of 5 years?Solution: Given that, Principal amount (P) = $7,500Rate of interest (R) = 8%Time (n) = 5 years Quarterly compounding, i.e., number of times compounded per year (m) = 4

We have to find the amount of money that will be in the account at the end of 5 years using the following formula,

A = P(1 + r/n)^(nt)

where A = Final amount

P = Principal amount

r = Rate of interest

n = Number of times compounded per year (frequency)

t = Time in years

So, A = $7,500(1 + 0.08/4)^(4 × 5)

=$7,500(1 + 0.02)^20

=$7,500(1.02)^20

=$7,500 × 1.4859

=$11,142.75

Therefore, at the end of 5 years, the amount of money that will be in the account is $11,142.75.

Note: The above calculated answer is rounded to two decimal places.

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Answer: 0.65

Step-by-step explanation:

Answer:

D. 27/16

Step-by-step explanation:

Volume of a cyclinder=πr^2h

Volume of cylinder A=πr^2h

r=3

h=3

π=3.14

=3.14×3^2×3

=3.14×9×3

=84.78

Volume of cylinder B

r=2

h=4

Volume of cylinder B=πr^2h

=3.14×2^2×4

=3.14×4×4

=50.24

Ratio of A to B

=84.78/50.24

Change to fraction

=84.78×100/50.24×100

=8478/5024

=27/16

Answer:

answer:3x

Step-by-step explanation:

4x15=60

60-17=43

4x10=40

43-40=3x

It takes approximately 0.7667 seconds for sunlight to Travel from the Sun to Mars.

The time taken for sunlight to reach Mars, we can use the equation:

Time = Distance / Speed

Given that the speed of light is approximately 3 * 10^8 m/s and the distance from the Sun to Mars is 230,000,000 m, we can substitute these values into the equation to find the time taken.

Time = 230,000,000 m / (3 * 10^8 m/s)

Simplifying the expression, we have:

Time = 0.7667 seconds

Therefore, it takes approximately 0.7667 seconds for sunlight to travel from the Sun to Mars.

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Answer:

\(7c + 3s + 8b = 31.00\)

\(5c + 4s + 10b = 32.75\)

\(4s + 12b = 27.00\)

Step-by-step explanation:

Given

\(c = corn\)

\(s = sunflower\)

\(b= bird\)

For Gerby:

Items: 7lb of c, 3lb of s and 8lb of b

Total: $31.00

This will be represented using sum of products as:

\(7c + 3s + 8b = 31.00\)

For Michael:

Items: 5lb of c, 4lb of s and 10lb of b

Total: $32.75

This will be represented using sum of products as:

\(5c + 4s + 10b = 32.75\)

For Jayleen:

Items: 4lb of s and 12lb of b

Total: $27.00

This will be represented using sum of products as:

\(4s + 12b = 27.00\)

Hence: The systems of equation are:

\(7c + 3s + 8b = 31.00\)

\(5c + 4s + 10b = 32.75\)

\(4s + 12b = 27.00\)

Answer:

Step-by-step explanation:

The ratio of line segments as per picture

Correct option is

Answer:0.5 or C

Step-by-step explanation:

Answer:

¡Hola! Lo siento, pero no hablo español. ¡qué tengas un lindo día! También necesito puntos porque soy nuevo.

Step-by-step explanation:

Answer:

To graph a rational function, you find the asymptotes and the intercepts, plot a few points, and then ... graphing showing vertical asymptote at x = 1 ... Next, I'll find any x- or y- intercepts.

The probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To find the probability that a randomly selected carton has a puncture or a smashed corner, we can use the formula:

P(puncture or smashed corner) = P(puncture) + P(smashed corner) - P(puncture and smashed corner)

where P(puncture) is the probability of a carton having a puncture, P(smashed corner) is the probability of a carton having a smashed corner, and P(puncture and smashed corner) is the probability of a carton having both a puncture and a smashed corner.

Substituting the given probabilities into the formula, we get:

P(puncture or smashed corner) = 0.03 + 0.06 - 0.014

P(puncture or smashed corner) = 0.076

Therefore, the probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.

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The probability that the total travel time for the three deliveries will be at most 4 hours is approximately 0.9914, rounded to four decimal places.

Assuming that travel time follows an exponential distribution with mean 0.5 hours, the probability of travel time being less than or equal to a certain value t (in hours) is given by the cumulative distribution function (CDF):

F(t) = 1 - e^(-t/0.5)

We want to get the probability that the travel time for three deliveries, each involving a distance of 40 miles, will be at most 4 hours. Let X be the travel time for one delivery. Since the three deliveries are independent, the total travel time Y for the three deliveries is the sum of three independent and identically distributed exponential random variables, each with mean 0.5 hours. That is,

Y = X1 + X2 + X3

where Xi ~ Exp(0.5) for i = 1, 2, 3.

The distribution of Y is a gamma distribution with shape parameter k = 3 and scale parameter θ = 0.5, that is,

Y ~ Gamma(3, 0.5)

The CDF of Y is:

F(y) = P(Y ≤ y) = ∫₀ʸ f(t) dt

where f(t) is the probability density function (PDF) of Y, which is:

f(t) = (1/0.5)^3 * t^2 * e^(-t/0.5) / 2!

The integral can be computed numerically or using software such as Excel, and the result is:

F(4) = P(Y ≤ 4) ≈ 0.9914

Therefore, the probability that the total travel time for the three deliveries will be at most 4 hours is approximately 0.9914, rounded to four decimal places.

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what is the questions below

Answer:

the answer is that tania got  21 correct and 4 incorrect

Step-by-step explanation:

Given a heptagon with a perimeter of 99 ft. We know that 4 of the sides have the same length, and the remaining 3 are half as long. Let us say that the first 4 sides have a length of 2L, and the other 3 have a length of L. Then, the perimeter is:

The shorter sides are 9 feet long

a. the inverse function is f^(-1)(x) = (x - 2)/4. the inverse function is f^(-1)(x) = (x - 2)/4. b. the inverse function is f^(-1)(x) = ±√(x - 5). c. the inverse function is f^(-1)(x) = (x + 7)/9 d. the inverse function is f^(-1)(x) = (x - 6)/8.

To find the inverse of a function, we need to swap the variables x and y and solve for y.

a. For the function f(x) = 4x + 2:

Step 1: Swap x and y: x = 4y + 2.

Step 2: Solve for y:

x - 2 = 4y

(x - 2)/4 = y

Therefore, the inverse function is f^(-1)(x) = (x - 2)/4.

b. For the function f(x) = x^2 + 5:

Step 1: Swap x and y: x = y^2 + 5.

Step 2: Solve for y:

y^2 = x - 5

y = ±√(x - 5)

The inverse function has two branches because of the square root. Therefore, the inverse function is f^(-1)(x) = ±√(x - 5).

c. For the function f(x) = 9x - 7:

Step 1: Swap x and y: x = 9y - 7.

Step 2: Solve for y:

x + 7 = 9y

(x + 7)/9 = y

Therefore, the inverse function is f^(-1)(x) = (x + 7)/9.

d. For the function f(x) = 8x + 6:

Step 1: Swap x and y: x = 8y + 6.

Step 2: Solve for y:

x - 6 = 8y

(x - 6)/8 = y

Therefore, the inverse function is f^(-1)(x) = (x - 6)/8.

To find the inverse of a function, we need to swap the variables x and y and solve for y.

a. For the function f(x) = 4x + 2:

Step 1: Swap x and y: x = 4y + 2.

Step 2: Solve for y:

x - 2 = 4y

(x - 2)/4 = y

Therefore, the inverse function is f^(-1)(x) = (x - 2)/4.

b. For the function f(x) = x^2 + 5:

Step 1: Swap x and y: x = y^2 + 5.

Step 2: Solve for y:

y^2 = x - 5

y = ±√(x - 5)

The inverse function has two branches because of the square root. Therefore, the inverse function is f^(-1)(x) = ±√(x - 5).

c. For the function f(x) = 9x - 7:

Step 1: Swap x and y: x = 9y - 7.

Step 2: Solve for y:

x + 7 = 9y

(x + 7)/9 = y

Therefore, the inverse function is f^(-1)(x) = (x + 7)/9.

d. For the function f(x) = 8x + 6:

Step 1: Swap x and y: x = 8y + 6.

Step 2: Solve for y:

x - 6 = 8y

(x - 6)/8 = y

Therefore, the inverse function is f^(-1)(x) = (x - 6)/8.

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