Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3)

The mean number of candy bars needed to find a golden ticket is 1/p, and the variance is (1-p)/p^2.

To find the mean and variance of the number of candy bars you need to eat to find a golden ticket, we need to use the concept of a geometric distribution. The geometric distribution models the number of trials it takes to achieve a success, where each trial has the same probability of success.

The mean of a geometric distribution is given by μ = 1/p, where p is the probability of success. In this case, p represents the probability of finding a golden ticket. Therefore, the mean number of candy bars needed to find a golden ticket is 1/p.

The variance of a geometric distribution is given by σ^2 = (1-p)/p^2. This represents the spread or variability in the distribution. Using the given value of p, you can calculate the variance of the number of candy bars needed to find a golden ticket.

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Answer:

total tax is = 14685 pound

Step-by-step explanation:

Given data:

For first year -  

earning is 11000 pound

for second year

income is = 43000 - 11000 = 32000 pound

tax rate = 20%

for third year

income is = 150000 - 43000 = 107000 pound

tax rate = 40%

for fourth year

income is = 158900 - 150000 = 8900 pound

tax rate = 45%

As it is given there is no tax on first year

Tax in 2nd year  = 0.20 × 32000 = 6400 pound

Tax in 3rd year  = 0.40 × 107000 = 42800 pound

Tax in 4th year  = 0.45 × 8900 = 4005 pound

The function f(g(x)) is ((x^10+1)^(9/2), the derivative f'(u) is (9/2)u^(7/2), the derivative f'(g(x)) is (9/2)(x^10+1)^(7/2), the derivative g'(x) is 10x^9, and the derivative (f ∘ g)'(x) is the product of g'(x) and f'(g(x)) which equals to 10x^9 * (9/2)(x^10+1)^(7/2).

The functions are defined as f(u)=u9/2 whereas g(x)=x10+1.

To find f(g(x)), input g(x) into the f function. Thus, f(g(x))=((x10+1)9/2.

Next, the derivative of f(u) would be: f'(u)= (9/2)u7/2.

For f'(g(x)), replace u with g(x) in f'(u): f'(g(x))=(9/2)(x10+1)7/2.

The derivative of g(x) is: g'(x)=10x9.

Lastly, to find (f ∘ g)'(x), use the chain rule which states that (f ∘ g)'(x) = g'(x) * f'(g(x) : (f ∘ g)'(x) = 10x9 * (9/2)(x10+1)7/2.

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The percentage decrease in a price is 37 percent.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, in January 2015 the price of gas was on average $2.05 per gallon this was $1.20 cheaper than a year.

Cost of gas per gallon = 2.05+1.20

= $3.25

Now, Percentage decrease = (Original Price - New Price)/Original Price ×100

= (3.25-2.05)/3.25 ×100

= 1.20/3.25 ×100

= 0.3692×100

= 0.37×100

= 37%

Therefore, the percentage decrease in a price is 37 percent.

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Answer:

D They must have common denominators.

Step-by-step explanation:

Rational expressions are fractions formed by two polynomials, one in the numerator and other in the denominator.

The numerator is the polynomial that is at the top of the fraction and denominator is the polynomial that is at the bottom of the fraction.

To add any fractions it is necessary that they have the same denominator, this applies to rational expressions, to add them it is required that they have the same polynomial in the denominator.

Answer:

I think A

Step-by-step explanation:

Answer:

[tex]7ab^3[/tex]

Step-by-step explanation:

the greatest common factor of [tex]42a^5b^3[/tex], [tex]35a^3b^4[/tex], and [tex]42ab^4[/tex]

LEts write the factors for each expression

[tex]42a^5b^3=6*7*a*a*a*a*a*b*b*b[/tex]

[tex]35a^3b^4=5*7*a*a*a*b*b*b*b[/tex]

[tex]42ab^4=6*7*a*b*b*b*b[/tex]

From all the terms we have common factors

7, 'a'  and b^3

So GCF is [tex]7ab^3[/tex]

Answer:

A. [tex](-1,-2)[/tex]

D. [tex](-6,0)[/tex]

E. [tex](-5,-1)[/tex]

Step-by-step explanation:

We have been given an inequality [tex]x+3y\geq -8[/tex]. We are asked to find the ordered pairs that are solution to the given inequality.

Let us check each ordered pair by substituting in the given inequality.

A. [tex](-1,-2)[/tex]

[tex]-1+3(-2)\geq -8[/tex]

[tex]-1-6\geq -8[/tex]

[tex]-7\geq -8[/tex]

Since the given inequality holds true, therefore, ordered pair [tex](-1,-2)[/tex] is a solution for the inequality.

B. [tex](-16,2)[/tex]

[tex]-16+3(2)\geq -8[/tex]

[tex]-16+6\geq -8[/tex]

[tex]-10\geq -8[/tex]

Since the given inequality is not true, therefore, ordered pair [tex](-16,2)[/tex] is not solution for the inequality.

C. [tex](0,-3)[/tex]

[tex]0+3(-3)\geq -8[/tex]

[tex]0-9\geq -8[/tex]

[tex]-9\geq -8[/tex]

Since the given inequality is not true, therefore, ordered pair [tex](0,-3)[/tex] is not solution for the inequality.

D. [tex](-6,0)[/tex]

[tex]-6+3(0)\geq -8[/tex]

[tex]-6+0\geq -8[/tex]

[tex]-6\geq -8[/tex]

Since the given inequality holds true, therefore, ordered pair [tex](-6,0)[/tex] is a solution for the inequality.

E. [tex](-5,-1)[/tex]

[tex]-5+3(-1)\geq -8[/tex]

[tex]-5-3\geq -8[/tex]

[tex]-8\geq -8[/tex]

Since the given inequality holds true, therefore, ordered pair [tex](-5,-1)[/tex] is a solution for the inequality.

Academic integrity is essential for a fair and genuine educational experience, emphasizing honesty and accountability in all academic endeavors. It is crucial for building trust, equity, and facilitating real learning outcomes, necessitating a collective effort from the academic community to maintain these values. The widespread issue of academic dishonesty further highlights the need for strict adherence to integrity principles.

Academic integrity is the cornerstone of a meaningful educational experience, emphasizing the value of honesty and fairness within the academic community. It involves the commitment to avoid cheating, plagiarism, and any form of deception or fraud in academic work, ensuring that all academic activities, from research to examination, are conducted in a manner that is fair, respectful, and accountable. The importance of academic integrity lies not only in the cultivation of a fair and trustworthy academic environment but also in fostering genuine learning and understanding, thereby empowering students to achieve authentic success that extends well beyond their academic careers.

Despite the challenges posed by technological advancements and digital resources, which have made cheating more accessible and harder to detect, maintaining academic integrity is crucial. It builds trust, understanding, equity, and facilitates real, meaningful learning outcomes. Faculty, administrators, and students alike bear the responsibility of upholding these principles to ensure that the academic community remains a space where fairness prevails and genuine knowledge acquisition is celebrated.

According to the International Center for Academic Integrity, a significant number of students have admitted to engaging in dishonest behaviors, which underscores the ongoing battle against academic dishonesty. Highlighting the importance of maintaining integrity, these statistics serve as a reminder of the collective effort needed to nurture an academic culture that values honesty above all.

Answer:

6,7,7,8,9 both have 7 for mode and median

Step-by-step explanation:

Final answer:

The student should invest $60,000 in the CD at 7% annual interest and $80,000 in the mutual fund at 10% to earn a total interest of $12,200 in one year. This is determined by setting up and solving a system of linear equations.

Explanation:

The student asked how much money should be invested in a CD at 7% annual interest and a mutual fund with a three-year average annual interest of 10%, given a total investment of $140,000, to earn a total of $12,200 in one year. We can set up a system of equations to solve for X (the amount invested in the CD) and Y (the amount invested in the mutual fund).

Let X be the amount invested in the CD and Y be the amount invested in the mutual fund. We then have the following system of equations:

Solving this system, we subtract the first equation from the second equation multiplied by 0.07:

Subtract the second equation from the first we get:

0.03Y = $2,400

Dividing both sides by 0.03 gives:

Y = $80,000

Substitute Y in the first equation:

X + $80,000 = $140,000

X = $140,000 - $80,000 = $60,000

Therefore, $60,000 should be invested in the CD and $80,000 in the mutual fund to obtain a total interest of $12,200 in one year.

Answer: [tex]y=500(1.05)^x[/tex]

Step-by-step explanation:

We know that the general exponential equation to find the value after x years is written as :-

[tex]y=Ab^x[/tex], where A is the initial value and b is the multiplicative rate of change and x is the time period.

Given : The initial amount of a product = $500

After 2 years, the item is worth $551.25.

Substitute A = 500, x=2 and y= 551.25 in the above equation we get

[tex]551.25=500b^2\\\\\Rightarrow\ b^2=\dfrac{551.25}{500}\\\\\Rightarrow\ b^2=1.1025\\\\\Rightarrow\ b=\sqrt{1.1025}=1.05[/tex]

Now, substitute b= 1.05, A = 500 in the general exponential equation, we get the equation represents y, the value of the item after x years as :-

[tex]y=500(1.05)^x[/tex]

Answer:

The value of x is 11.

Step-by-step explanation:

The given number is 0.27272727..., and it is converted to the fraction as

[tex]0.272727...=\frac{3}{x}[/tex]                 ..... (1)

Multiply both sides by 100.

[tex]0.272727...\times 100=\frac{3}{x}\times 100[/tex]

[tex]27.272727=\frac{300}{x}[/tex]            .... (2)

Subtract equation (1) from equation (2),

[tex]27.272727-0.272727...=\frac{300}{x}-\frac{3}{x}[/tex]

[tex]27=\frac{300-3}{x}[/tex]

Multiply both sides by x.

[tex]27x=297[/tex]

Divide both sides by 27.

[tex]x=\frac{297}{27}[/tex]

[tex]x=11[/tex]

Therefore the value of x is 11.

The value of the variable "x" in the fraction 0.27... = 3/x is x = 11.

To find the value of "x" in the fraction 0.27... = 3/x, we use algebraic techniques to solve for x,

Let us represent the repeating decimal 0.27... as a variable, say y,

y = 0.27...

To eliminate the repeating decimal, we multiply both sides of equation by a power of 10. In this case, we multiply by 100 to shift decimal point two places to right,

100y = 27.27...

Now, we subtract original equation from this new equation to eliminate the repeating part:

100y - y = (27.27...) - (0.27...),

Simplifying the equation:

99y = 27

y = 27/99

The fraction 27/99 is simplified further by dividing both the numerator and the denominator by their greatest common divisor, which is 9,

y = 3/11

Therefore, the required value of "x" is 11.

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Corresponding sides in similar figures match up. The person's shadow in the small triangle corresponds to the shadow of the Flag Pole in the large triangle. The longest side of the large triangle corresponds to the Longest side of the small triangle.

Corresponding sides in similar figures are the sides that match up.

In the given diagram of two similar triangles, the person's shadow in the smaller triangle corresponds to the shadow of the Flag Pole in the larger triangle.

The longest side of the large triangle corresponds to the Longest side of the small triangle.

The Area of the rectangle is 45 square feet.

The perimeter of a form is the space surrounding its edge. To Find the perimeter of various forms by summing the lengths of their sides.

Given, The length of a rectangle is 4 ft longer than its width. If the perimeter of the rectangle is 28 ft.

Let "l" be the length of the perimeter

Thus, width = l - 4

From the general formula of perimeter:

perimeter = 2*(length + width)

In our case

Perimeter = 2* (l + l -4)

Perimeter = 4l - 8

Since the perimeter is given 28 ft

thus,

4l - 8 = 28

4l = 36

l = 9 ft

thus width = 9 - 4 = 5 ft

Since,

Area = Length * width

Area = 9 * 5

Area of rectangle = 45 square feet.

therefore, The Area of the rectangle is 45 square feet.

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The inequality 834 + 14s > 978 - 10s can represent a situation involving saving and spending money over time. To solve it, you perform a series of operations to isolate variable 's', which in this case results in s > 6, indicating more than six weeks required for savings to exceed spending.

A real world situation that can be modelled by this inequality 834 + 14s > 978 - 10s could be a scenario involving saving and spending money. Say you start with $834 and each week you save $14 (s represents the number of weeks). On the other hand, you have $978 and you spend $10 each week. You want to figure out how many weeks it will take for the amount you have from saving to be more than the amount left from spending.

Now, to solve the inequality: subtract 834 from both sides which gives 14s > 144 - 10s, then combine like terms to get 24s > 144. Finally, divide both sides by 24 to solve for s: s > 6. Therefore, it will take more than six weeks for the money you save to exceed what remains from your starting amount of $978 after spending $10 each week.

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