Please help will mark brainiest!!!

1.) Rowan graphs the function f (x) = 7x + 1 and then transforms the function by horizontally translating it 5 units to the right. What is the newly transformed function, g (x)?

(a) The differential equation that is satisfied by y is:

\(\frac{dy}{dt} = ky(1-y)\)

(b) To solve the differential equation, we separate the variables and integrate both sides:

\(\frac{dy}{y*(1-y)} = k*dt\)

Integrating both sides, we get:

\(\frac{lnly}{1-y} = k*t +c1\)

where C1 is an arbitrary constant of integration.

We can rewrite the equation in terms of y:

\(\frac{y}{1-y} = e^{(k*t+c1)}\)

Multiplying both sides by (1-y), we get:

\({y} = e^{(k*t+c1)} *(1-y)\)

\(y= \frac{C}{(1+(c-1)e^{-kt} }\)

where C = y(0) is the initial fraction of the population who have heard the rumor.

(c) In this case, the initial fraction of the population who have heard the rumor is y(0) = \(\frac{100}{1300}\) = 0.077. At noon, half the town has heard the rumor, so y(4) = 0.5.

Substituting these values into the equation from part (b), we get:

\(0.5= \frac{0.077}{1+(0.777-1) e^{-k4} }\)

Solving for k, we get:

\(k= ln(\frac{12.857}{4} )\)

Substituting this value of k into the equation from part (b), and setting y = 0.9 (since we want to find the time at which 90% of the population has heard the rumor), we get:

\(0.9= \frac{0.077}{1+(0.777-1) e^{-ln(12.857}*\frac{t}{4} }\))

Solving for t, we get:

t = 8.7 hours after the beginning (rounded to one decimal place)

A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).

Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.

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Answer:

10 ^ 1.50  = 31.622776601683793319988935444327

answer is c

please mark brainliest i need it to level up

Answer:

x = log(31.62)

Step-by-step explanation:

10^x = 31.62

is equivalent by taking the 10-logarithm from each side as both numbers are the same:

x = log(31.62) ≈ 1.4999618655961902407156407924264

Answer:

\(7^{x}\) or "7 to the power of x"

Step-by-step explanation:

Ok! So an exponential function is a function with a variable as an exponent.

                                         x                             y        

                                         0                             1

                                         1                              7

                                         2                            49

                                         3                           343

                              An example exponential function is \(2^{x}\)

Now! Let's look at what number multiplies by each of our "y" values to get the following "y" value. 7!

Now let's see if we can put 7 to the power of x (\(7^{x}\)) to get the rest of our table.

                                                       \(7^{0}\) = 1

                                                       \(7^{1}\) = 7

                                                      \(7^{2}\) = 49

                                                      \(7^{3}\) = 343

                      Now, we know our exponential function is \(7^{x}\)

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

slope = 1

y-intercept = 5

Step-by-step explanation:

change in y-values = 1

change in x-values = 1

slope = 1/1 or 1

to find the y-intercept ('b'), select an ordered pair:  (1, 6)

use the slope-intercept formula and solve for 'b':

6 = 1(1) + b

6 = 1 + b

5 = b

slope = 1

y-intercept = 5

Step-by-step explanation:

a) The dependent variable is the velocity of the scooter, and the independent variable is time.

b) Using the kinematic equation v = u + at, where u is the initial velocity, a is the acceleration, t is time, and v is the final velocity, we can find the velocity as a function of time for t ≤ 6 seconds:

v = u + at = 1.0 + (a × t)

c) The graph of velocity as a function of time for the scooter would be a straight line with a positive slope, starting at (0,1.0) and ending at (6,4.0). The x-axis would be labeled "Time (s)" and the y-axis would be labeled "Velocity (mph)".

d) We can find the acceleration of the scooter by rearranging the equation from part (b) to a = (v - u) / t, where v = 4.0 mph, u = 1.0 mph, and t = 6 seconds:

a = (4.0 - 1.0) / 6 = 0.5 mph/s

We can label the acceleration as 0.5 mph/s on the graph.

e) The initial velocity of the scooter is 1.0 mph, which we can label on the graph.

f) To find the distance traveled by the scooter between 0 and 6 seconds using the graphical method, we can calculate the area under the velocity-time graph. The graph forms a trapezoid with a base of 6 seconds, a height of 3 mph (the difference between the final and initial velocities), and a top length of 1.0 mph. The distance traveled is therefore:

distance = 0.5 × (1.0 + 4.0) × 6 = 15.0 miles

g) To find the distance traveled by the scooter between 0 and 6 seconds using the kinematic equations, we can use the equation s = ut + 0.5at^2, where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is time. Since the acceleration is constant, we can use the average velocity (2.5 mph) to find the distance traveled:

s = 1.0 × 6 + 0.5 × 0.5 × 6^2 = 15.75 miles

The result from the kinematic equation is slightly larger than the result from the graphical method. This is likely due to rounding errors and the approximation of the trapezoidal area under the velocity-time graph. Overall, both methods provide a good estimate of the distance traveled by the scooter between 0 and 6 seconds.

When we make inferences about the difference of two independent population proportions, we assume that it is a random sample, and the number of successes and failures are at least 15 in each group.

Two independent proportions tests involve comparing the proportions of two unrelated datasets.

For these two datasets to be regarded as an independent population, the following must be true or assumed to be true

Hence, the above highlights are the assumptions of two independent population proportions.

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Answer:

the answer is A.

Step-by-step explanation:

hope it help

Answer:

19/9

Step-by-step explanation:

16/27^2/3=19/9

hope this is helpful! brainly deleted my last response for some reason

By counting the table entries, we can see that there are 10 different options for a 3-topping pizza.

The different toppings ought on a pizza are:

As a general rule of thumb, I recommend selecting three to five toppings for each pizza you create.

Because mozzarella is a basic component of every pizza I prepare, it does not qualify as a topping.

Other cheeses that can be used as toppings are goat cheese, feta, and smoked gouda.

The most common supreme toppings are pepperoni, link, immature bell pepper, ebony olives, and red onions.

Sautéed mushrooms or even hot peppers are frequently incorporated.

Even though the sauce and cheese should almost always go on the bottom, the toppings themselves usually require the greatest attention.

Regardless of how many layers your pizza has, the top layer will receive the most heat.

Thus, by counting the table entries, we can see that there are 10 different options for a 3-topping pizza.

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The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Answer: 64/35

Step-by-step explanation:

8/7 and then divide by 5/8 and you get 1 29/35. 35x1= 35 then add the numerator, 29 and you get 64. so the answer would be 64/35

A long-term movement up or down in a time series is called a trend. A trend represents the general direction of a time series over a longer period of time. It helps to identify the overall pattern or behavior of the data.

For example, let's say we are analyzing the sales of a product over several years. If the sales consistently increase over time, we can say there is an upward trend. On the other hand, if the sales consistently decrease, there is a downward trend.

Trends are important because they can help us understand and predict future behavior of the time series. By identifying trends, we can make informed decisions and forecasts. Trends can also be useful in identifying cycles and seasonality in the data.

In summary, a long-term movement up or down in a time series is called a trend. It represents the overall direction of the data over a longer period of time and helps in making predictions and forecasts.

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Answer:

W is the point of intersection of the lines 'a' and 'b'.

Step-by-step explanation:

Three points lying on line 'b' are points Y, Z and W.

Similarly, three points on line 'a' are points V, X and W.

Common point lying on both the lines 'a' and 'b' is W.

Therefore, point of intersection of the lines 'a' and 'b' is W.

Answer:

Straight along the horizontal axis

Step-by-step explanation:

Hope this helped :)

Answer: -6x^7

Step-by-step explanation:

 2x^3 × (-3x^4)

=(2×-3) · (x^3 × x^4) ⇔ multiply the like terms

=-6 × [x^(3+4)] ⇔ the multiplication of exponents works as addition if same base

=-6x^7

Answer:

\(-6x^7\)

Step-by-step explanation:

So when doing this equation, you multiply the numbers, which is 2 × -3, and add the exponents, which is 3 + 4, so then you get the answer, and that is \(-6x^7\).

Answer: Parallel lines

Step-by-step explanation:

These lines are Parallel due to the fact that they will never cross each other. Since they are both perfectly lined up with each other, this makes them Parallel.

Answer: Jas is 9, and Sandeep is 11.

Step-by-step explanation: 9 + 11 = 20

Answer:

I think it is 13 and increasing

Answer: -12 and decreasing.

Step-by-step explanation: The rate of change of the function represented in the table is  -12 . For the given x- and y-values, the function is  decreasing .

According to the conversation we can infer that the information focused on the conversation of two people; one of them is studing for an exam.

To identify what is the conversation about we have to consider who is talking and what are the ideas that they share. In this case, we can infer that the main idea of this conversation is that one of them is studying for an exam this week.

Also, the second person is apologizing because he considered that he is distracting the other person. So, the correc information about de conversation is a short conversation about study.

Note: This question is incomplete. Here is the complete information:

Conversation:
Hello

Hello, How are you?

I am fine, and you?

i am fine too, What are you doing?

I am studing for an exam this week.

Oh, sorry I won´t distract you.

Don´t worry.

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the answer is 17.5

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here we have,

4/7 = 10/x

2x=35

x=17.5

That the answer.

hence, the answer is 17.5 .

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Answer:

Step-by-step explanation:

The slope field shown in the question is that of a differential equation of the form y'= f(x,y).

The solutions of this equation are the curves in the slope field that emanate from each point and that have the same slope as the line at that point. Thus, for each point (x,y) in the slope field, it is possible to calculate the particular solution that passes through that point.

The first statement is false because it involves the second derivative of the particular solution, which cannot be determined from the slope field. The second statement is false because a concave up graph requires that the derivative of the solution be increasing at x=0, but the slope field does not indicate the sign of the derivative of the particular solution. The third statement is false because a concave up graph requires that the derivative of the solution be decreasing at x=-1, which cannot be determined from the slope field. The fourth statement is false because a concave down graph requires that the derivative of the solution be increasing at x=0, which cannot be determined from the slope field.

In summary, none of the statements can be determined to be true or false from the slope field shown.

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Answer:

-4d - 6

Step-by-step explanation:

-1/3(12d+18)

-4d - 6

That is the simplest we can simple the function

So, the answer is -4d - 6

On a graph, the absolute value of a number is always non-negative.

The absolute value of a number is defined as the distance of that number from zero on the number line. Since the distance can never be negative, the absolute value of a number is always non-negative.

This is reflected in the graph of an absolute value function. The graph of an absolute value function, |x| is a V-shape that opens upward, with the vertex of the V being the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line. The coordinates of the vertex (0,0) and the graph is always non-negative.

It's important to note that although the absolute value is always non-negative on a graph, the input value (x) can be both positive and negative. The output of the absolute value function (|x|) will always be positive.

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Therefore, the lateral surface area of the rectangular prism is 35 square feet, and the total surface area is 47.5 square feet.

A prism is a solid object made of glass, plastic, or another transparent material, with flat, polished surfaces that are angled relative to one another. When light enters the prism, it is refracted or bent, causing the light to spread out into its component colors, creating a spectrum. This effect is due to the fact that different colors of light have different wavelengths, and these wavelengths are bent by different amounts as they pass through the prism.

Given by the question.

The lateral surface area of a rectangular prism is the sum of the areas of all its faces excluding the top and bottom faces, which are identical. The lateral surface area can be found by multiplying the height of the prism by the perimeter of its base.

The total surface area of a rectangular prism is the sum of the areas of all its faces. This can be found by adding the area of the base (which is a square) to the lateral surface area, and then doubling the result (since there are two identical faces).

Given that the base of the prism has a side length of 2 1/2 feet and the height is 3 1/2 feet, we can calculate the lateral and total surface areas as follows:

Lateral surface area = height x perimeter of base

= 3 1/2 feet x (2 1/2 feet + 2 1/2 feet + 2 1/2 feet + 2 1/2 feet)

= 3 1/2 feet x 10 feet

= 35 square feet

Total surface area = 2 x (area of base) + lateral surface area

= 2 x (2 1/2 feet x 2 1/2 feet) + 35 square feet

= 2 x 6.25 square feet + 35 square feet

= 12.5 square feet + 35 square feet

= 47.5 square feet

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Answer:

false

Step-by-step explanation:

the constant term is 3 not 8

hope this helps

Answer:

I think d is a one on one function while c is a function but a multiple relation function, sorry if im wrong

Answer:

Step-by-step explanation:

On Monday, Nora read ¼ of the book, therefore she is left with ¾ of the original book.

Then on Tuesday, she read 2/5 of what was left on Monday therefore she is left with 3/5 of ¾ of the original book. This is equal to:

(3/5) (3/4) = 9/20

She still needs to read 9/20 of the book or 0.45 or 45% of the book.