Marcus is taking part in a charity run. He has received $250 in fixed pledges, and he will receive $25 more in pledges for each mile he runs. Write an equation for the amount of money P Marcus will earn in terms of the distance d he runs, measured in miles

The function g(x) = x - (f(x) / f'(x)) has a point c in (a, b) where g'(c) = 0. This is proven using the Mean Value Theorem applied to g(x) on the interval [a, b].

Given a non-degenerate closed interval [a, b] in the real numbers (R), and a function f : [a,b] → R that is twice differentiable, with f(a) < 0, f(b) > 0, f'(x) ≥ c > 0, and 0 ≤ f''(x) ≤ m for all x ∈ (a, b), we need to show that there exists a point c in (a, b) where g'(c) = 0, where g(x) = x - (f(x) / f'(x)) by using Mean Value Theorem.

To prove that there exists a point c in (a, b) where g'(c) = 0, we can use the Mean Value Theorem. First, we define the function g(x) = x - (f(x) / f'(x)). Since f is twice differentiable and f'(x) > 0 for all x in (a, b), g(x) is well-defined on [a, b].

Applying the Mean Value Theorem to g(x) on the interval [a, b], we obtain g'(c) = (g(b) - g(a)) / (b - a), where c is some point in (a, b). Now, substituting the expression for g(x), we have g'(c) = (b - a - (f(b) - f(a)) / (f'(c)(b - a)), where f'(c) > 0.

Since f(a) < 0 and f(b) > 0, we know that f(b) - f(a) > 0. Additionally, f'(x) ≥ c > 0 for all x in (a, b). Hence, g'(c) = (b - a - (f(b) - f(a)) / (f'(c)(b - a)) > 0.

Therefore, we have shown that g'(c) > 0 for all c in (a, b), indicating that there exists a point c in (a, b) where g'(c) = 0.

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The probability that two red balls are chosen from the vase would be = 1/9

Probability is defined as the concept that proves that an event may occur or not.

The number of red balls = 7

The number of black balls = 2

The number of green balls = 9

The total number of balls in the vase = 18

The probability of getting 2 red balls = 2/18 = 1/9

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Answer:

πr²=22/7×49

=22×7

=154

hope it helps

Mark me brainliest

The linear function for this problem is defined as follows:

y = 8x - 20.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

The graph crosses the y-axis at y = -20, hence the intercept b is given as follows:

b = -20.

When x increases by 10, from x = 0 to x = 10, y increases by 80, from y = -20 to y = 60, hence the slope m is given as follows:

m = 80/10

m = 8.

Hence the equation is:

y = 8x - 20.

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Answer:

- 7

Step-by-step explanation:

5 + (- 12)

5 - 12

- 7

Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Answer:

d. \(x=a(1-\frac{y}{b})\)

Step-by-step explanation:

\(\frac{x}{a} + \frac{y}{b} = 1\)

\(\frac{x}{a} = 1 - \frac{y}{b}\)

\(x = a(1 - \frac{y}{b})\) <----- This is your answer

Hope this helps!

Answer:

The function x=−1 means that for all values of y , the value of x=−1 . This is represented by a vertical line at x=−1

Step-by-step explanation:

Answer:

Theres an mnemonic device: HOY/VUX

H - horizontal  

O - 0 slope

Y-axis

-

V-vertical

U- undefined slope

X-axis

So in this question, x=-1 would be a vertical line at x=-1

It should be noted that z^4 will be -32 in rectangular form.

Based on the information, z = r(cos θ + i sin θ), and provided positive integer n, then it is implied that:

z^n = r^n (cos nθ + i sin nθ)

In this instance, we need to solve for z^4 in rectangular form when z = -2 - 2i. Firstly, we must calculate |z| and arg(z):

|z| = √((-2)^2 + (-2)^2) = 2√2

arg(z) = arctan(-2/-2) = π/4

Leveraging De Moivre's theorem, we can effectively deduce the value of z^4 as:

z^4 = (2√2)^4 (cos (4π/4) + i sin (4π/4))

= 32 (cos π + i sin π)

= -32

Concludedly, z^4  resolved in rectangular form is -32.

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Answer:

Step-by-step explanation:

You want to know which of several equations have x=3 as a solution. The equations are ...

The value x=3 will be a solution if it satisfies the equation. Substituting that value into the given equations, we find ...

The value x = 3 is a solution to ...

To find the MEAN of Natural numbers, such as  1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, a + b + c3 is the sum of the three numbers a, b, and c. Therefore, 5.5 is the MEAN of the first 10 natural numbers.

Firstly The Given set of numbers Represents Natural numbers,

A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc.

Therefore, the first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

And the mean of three numbers a, b, c is a + b + c3

Then the mean of 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is:-

⇒1+2+3+4+5+6+7+8+9+1010

Adding and dividing we get the value of the above term as,

⇒1+2+3+4+5+6+7+8+9+1010=5510=5.5

Hence, the mean of the first 10 natural numbers is 5.5.

Note: To solve this problem, you must understand that the integers greater than zero are natural numbers and that the mean of the three numbers a, b, and c equals a + b + c3. Knowing how to calculate the average number of elements and being familiar with natural numbers can help you arrive at the correct conclusion.

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The value of the integral is 15/512.

An integral is the continuous equivalent of a sum in mathematics, where sums are used to compute areas, volumes, and their generalizations. One of the two fundamental operations in calculus, the other being differentiation, is integration, which is the act of computing an integral.

We can use integration by parts to solve the integral:

∫x³ dx = x⁴/4 + C

Using the given values, we have:

∫8² 2x³ dx = (8⁴/4 - 2⁴/4) - (8⁴/4 - 2⁴/4) = 240

∫8² 2x dx = 2(8² - 2²)/2 = 90

∫8² dx = 8² - 2² = 60

Now, we can use these values to solve the final integral:

∫8² 1/(4x³) dx = -1/(8x²)|2⁸ = -1/512 + 1/64 = 15/512

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The volume of the solid in cubic units is 216. Antoine fit 54 unit cubes inside the solid below without any gaps or overlaps.

If we assume that all unit cubes are identical and have edge length 1, then the solid can be decomposed into a rectangular prism with dimensions 6 x 3 x 3 and a smaller rectangular prism with dimensions 2 x 2 x 1. This is illustrated in the attached diagram.

To see why this decomposition works, note that the larger rectangular prism contains 54 unit cubes, which implies that its volume is 54 cubic units. Furthermore, the only way to fill this rectangular prism with unit cubes without any gaps or overlaps is to stack 9 layers of 6 unit cubes each. Each layer has dimensions 6 x 3, and the height of each layer is 1, so the dimensions of the larger rectangular prism are indeed 6 x 3 x 3.

The smaller rectangular prism is formed by removing a 2 x 2 x 1 block from one corner of the larger rectangular prism. This block consists of 4 unit cubes, so its volume is 4 cubic units. Subtracting this volume from the volume of the larger rectangular prism gives us the volume of the solid:

Volume of solid = Volume of larger rectangular prism - Volume of smaller rectangular prism

= 54 - 4

= 50

Therefore, the volume of the solid in cubic units is 50. However, this is not the final answer, since we need to account for the fact that the unit cubes have edge length 1. To do this, we simply multiply the volume by (1 unit cube / 1 cubic unit) to get the answer in cubic units:

Volume of solid in cubic units = 50 x (1 unit cube / 1 cubic unit)

= 50

Hence, the volume of the solid in cubic units is 216.

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The ratio of the number of students who joined the class to the number of students who were initially in the class is 2:1.

Age ratio refers to the comparison of the number of individuals in different age groups in a population. It is often expressed as a ratio or percentage of the number of people in a particular age group to the total population or the number of people in another age group.

Given by the question.

Now, when the group of students with an average age of 16 years joins the class, the average age of all the students becomes 17 years. This means that the total age of all the students in the class would now be 17 times the total number of students.

Let "y" be the number of students who joined the class. Then, the total number of students in the class after they joined would be x + y.

So, we have two equations:

18x = 17(x+y) (because the total age of all the students remains the same before and after the group joins)

16y = (x+y)*1 (because the average age of the new group is 16)

Simplifying the above equations, we get:

x = 17y

x = 34y

Equating both the equations, we get:

17y = 34y

y = 2

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Answer:

30

Step-by-step explanation:

also brainly is for learning not getting answers you couldve done with on your fingers

The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation is given below.

y = - 3x + 2.5

The value of the equation at x = 1 will be given as,

y = - 3 × (1) + 2.5

y = - 3 + 2.5

y = - 0.5

The value of the equation at x = - 1.5 will be given as,

y = - 3 × (-1.5) + 2.5

y = 4.5 + 2.5

y = 7

The value of the equation at x = 8.5 will be given as,

y = - 3 × (8.5) + 2.5

y = - 22.5+ 2.5

y = - 20

The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

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Complete question:

Answer:

60°

Step-by-step explanation:

just in case if line AC and BD are straight lines,

angle EGD will be 180-90-30=60

and EGD will equal to x°becoz they are just in opposite

Answer:

The Answer is 60

Step-by-step explanation:

If you look at E B and F those make up a 180-degree angle if you look across from B then you will see that it is a 90-degree angle so you can assume that B is also a 90-Degree angle so if you add up 30 + 90 = 120

You then can subtract 180 - 120 to get the answer 60

So therefor the answer is 60

The approximate area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] using 4 subintervals is XXXX.

To approximate the area under the given graph, we can use the method of numerical integration known as the Trapezoidal Rule. This method involves dividing the interval into subintervals, approximating each subinterval as a trapezoid, and summing up the areas of these trapezoids.

In this case, we are given 4 subintervals within the interval [5,13]. To calculate the width of each subinterval, we can divide the total width of the interval by the number of subintervals: (13 - 5) / 4 = 2.

Next, we evaluate the function f(x) at the endpoints of each subinterval and calculate the area of each trapezoid. Using the Trapezoidal Rule formula, the area of each trapezoid is given by (h/2) * (f(x₁) + f(x₂)), where h is the width of the subinterval, f(x₁) is the function value at the left endpoint, and f(x₂) is the function value at the right endpoint.

By calculating the area of each trapezoid for the 4 subintervals and summing them up, we can approximate the total area under the graph.

Performing the necessary calculations, the approximate area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] using 4 subintervals is XXXX (replace with the numerical result).

It's important to note that this approximation will become more accurate as we increase the number of subintervals.

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Answer:

X=6

Step-by-step explanation:

1. 6(2x-10)+22=3x+16

2. 12x-60+22=3x+16

Is that the answer you are looking for

The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

Answer:

the second option

Step-by-step explanation:

the limit coming to x = 4 from the left (the '-' side) is -4.

the limit coming to x = 4 from the right (the '+' side) is 2.

it does not matter that the point itself is excluded. but the tendency of the function coming from the right is clear and defined.

the one-sided limit would not exist, if the function violently oscillates at the limit point.

or if the limit is infinite. then officially it does not exist, but we can write ±infinite.

for the case of the violent oscillation there is nothing else we can write but DNE.

The probability that the molecules will have a total energy of 6 kJ is 1/9 or approximately 0.111.

To find the probability that the two indistinguishable molecules will have a total energy of 6 kJ, we need to consider all the possible energy level combinations they can occupy.
There are a total of 3 possible energy levels for each molecule, which means there are 3 x 3 = 9 possible energy level combinations for the two molecules. We can list these combinations as follows:
- 1 kJ + 1 kJ = 2 kJ
- 1 kJ + 2 kJ = 3 kJ
- 1 kJ + 3 kJ = 4 kJ
- 2 kJ + 1 kJ = 3 kJ
- 2 kJ + 2 kJ = 4 kJ
- 2 kJ + 3 kJ = 5 kJ
- 3 kJ + 1 kJ = 4 kJ
- 3 kJ + 2 kJ = 5 kJ
- 3 kJ + 3 kJ = 6 kJ
Out of these 9 possible combinations, only one combination has a total energy of 6 kJ, which is the last one in the list. Therefore, the probability that the probability will have a total energy of 6 kJ is 1/9 or approximately 0.111.
This calculation is based on the assumption that each energy level is equally likely to be occupied by each molecule. If there are any other factors that affect the probability of probability each energy level, the calculation may be different.

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Answer:

you can do the normal operation

or use a calculator

The speed of the current of the river will be 4.47 km per hour.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A riverboat goes at a normal of 14km each hour in still water. the riverboat voyages 110km east up the Ohio waterway and 110km west down a similar stream in a sum of 17.5 hours.

Let 'y' be the speed of the current of the river. Then the equation is given as,

T = T₁ + T₂

17.5 = [110 / (14 + y)] + [110 / (14 - y)]

17.5 / 110 = (14 - y + 14 + y) / (196 - y²)

196 - y² = 176

y² = 20

y = 4.47 km per hour

Then the speed of the current of the river will be 4.47 km per hour.

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False. The value of the sample mean is not static and can change with different data sets.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

False.

The value of the sample mean is calculated based on the data in the sample, and it can change if the data set from which the sample is drawn changes.

For example, suppose we have a population with a certain mean and take a random sample from that population to calculate the sample mean. If we take a different sample from the same population, we may get a different sample mean. Similarly, if we take a sample from a different population with a different mean, we will get a different sample mean.

Therefore, the value of the sample mean is not static and can change with different data sets.

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Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

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Answer:

6n^2 - 5n + 3

Step-by-step explanation:

To find the nth term rule for the given quadratic sequence, we need to determine the pattern or relationship between the terms. Looking at the sequence:

4, 22, 52, 52, 94, 148,...

We can observe that the first term is 4, the second term is 22 (which is 18 more than the first term), and the third term is 52 (which is 30 more than the second term).

To find the nth term rule, we will first find the differences between consecutive terms:

1st difference: 18, 30, 0, 42, ...

We notice that the 2nd difference (the differences between the differences) is constant, which suggests that the sequence follows a quadratic pattern.

2nd difference: 12, -30, 42, ...

Now, to find the nth term rule, we can use the general form of a quadratic sequence:

an = dn^2 + en + f

By substituting the values of the terms into the equation, we can find the coefficients d, e, and f.

Let's use the first three terms to form three equations:

For the 1st term (n = 1):

4 = d(1)^2 + e(1) + f

4 = d + e + f ...(1)

For the 2nd term (n = 2):

22 = d(2)^2 + e(2) + f

22 = 4d + 2e + f ...(2)

For the 3rd term (n = 3):

52 = d(3)^2 + e(3) + f

52 = 9d + 3e + f ...(3)

Solving these three equations simultaneously will give us the values of d, e, and f.

Subtracting equation (1) from equation (2):

18 = 3d + e ...(4)

Subtracting equation (1) from equation (3):

48 = 8d + 2e ...(5)

Now, subtracting equation (4) from equation (5):

30 = 5d

d = 6

Substituting the value of d into equation (4):

18 = 3(6) + e

e = -5

Substituting the value of d into equation (1):

4 = 6 + (-5) + f

f = 3

Therefore, the nth term rule for this quadratic sequence is:

an = 6n^2 - 5n + 3