Find the unit vectors that are parallel to the tangent line to the parabola y = x2 at the point (6, 36).

Answer:

255

Step-by-step explanation:

Let's call the number of bags of popcorn sold by Team A as "x".

The total cost for the popcorn machine rental and supplies is $15 + 0.05x.

The revenue from selling the popcorn is 0.5x.

To reach their goal of $100, they need to satisfy the equation:

$100 = 0.5x - ($15 + 0.05x)

Expanding and solving for x:

$100 = 0.5x - $15 - 0.05x

$115 = 0.45x

x = $115 / 0.45 = 255 bags of popcorn

So, Team A needs to sell 255 bags of popcorn to reach their goal of $100.

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Answer:

Below

Step-by-step explanation:

n   = # nickels     value = 5n

(200-n) = # dimes     value = 10(200-n)

summed, these equal 1685

5n      +    10(200-n)   = 1685

5n + 2000 -10 n = 1685

-5n = -315

n = 63     then dimes = 137

The indefinite integral is   [tex]\frac{x^6}{3} +c[/tex].

What is indefinite integral?

An integral is considered to be indefinite if it has no upper or lower bounds.

The most generic anti-derivative of f(x) is known as an indefinite integral and denoted, in mathematics, by F(x), which is any anti-derivative of f(x).

[tex]\int[/tex]f(x) = F(x) + C

Here the given integral is [tex]\int{2x^5} dx[/tex]

=> [tex]\int{2x^5} dx[/tex]

=> [tex]2\int x^5 dx[/tex]

We know that [tex]\int x^n dx = \frac{x^{n+1}}{n+1}+c[/tex] where c is constant then,

=> [tex]2[\frac{x^{5+1}}{5+1} ]+c[/tex]

=> [tex]2\frac{x^6}{6} +c[/tex]

=> [tex]\frac{x^6}{3} +c[/tex]

Now take [tex]\frac{x^6}{3}[/tex] and differentiate to check the results then,

=> [tex]\frac{d}{dy}[\frac{x^6}{3} ][/tex]

=> [tex]\frac{1}{3} \frac{dx^6}{dy}[/tex]

We know that [tex]\frac{d}{dy} x^n = nx^{n-1}[/tex] then

=> [tex]\frac{1}{3}\times6x^{6-1}[/tex]

=> [tex]2x^5[/tex]

Hence the indefinite integral is  [tex]\frac{x^6}{3} +c[/tex].

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The required solution of the expression y = 8x + 8 at x = 3 3/4 is given as after simplification is 38.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
y = 8x + 8

We are given that to determine the solution of the given expression at x = 3 3/4, Since x = 3 3 /4 = 15 / 4

Now, put x = 15/4 in the given expression,
y = 8 (15/4) + 8
y = 30 + 8
y = 38

Thus, the required solution of the given expression is y = 38.

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The time it takes for the balance to reach $1000 depends on the frequency of compounding:

This is calculated using the formula for compound interest: A = P * (1 + r/n)^(nt), where P is the initial deposit, r is the annual interest rate, n is the number of times compounded in a year, and t is the number of years.

I calculated the time it takes for the balance to reach $1000 using the formula for compound interest:

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

where A is the final balance, P is the initial deposit ($100), r is the annual interest rate (6%), n is the number of times compounded in a year (annually, semi-annually, quarterly, or monthly), and t is the number of years.

I solved for t, keeping all other variables constant, by taking the natural logarithm of both sides of the equation and rearranging the terms:

t = (ln(A/P)) / (ln(1 + r/n) * n)

I used a mathematical software or calculator to perform the calculations and obtain the values for t for each given frequency of compounding.

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Answer:

To find the area of a triangle you got A=1\2×b×h

By  differentiable polynomial f(x) = 0 for some x such that a < X < b , A is correct

What is an example of a differentiable function?

If a function's derivative is present at every location inside its domain, the function is said to be differentiable. If a function f(x) is differentiable at x = a, in particular, then f′(a) exists in the domain.

                        Let's examine a few instances of differentiable polynomial and transcendental functions, such as f(x) = x4 - 3x + 5.

A is correct

F receives  two equal values in different places .

consider the line between them .

it cannot be in a coustant ascent nor descent, since it must return to the minimal value .

therefore, A, either coutant or has an surprising and descending area ,

thus from Fermat's rule the derivate must be equal to zero .

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The mean is the measure of the central tendency most likely to be affected by an outlier.

The following statement is correct.

The term "mean" is another synonym for "average." When there is an outlier in the data set, the mean suffers the most. The only measure of central tendency on which an outlier will always have an effect is the mean.

The mean is the only measure of central tendency that is affected by all values since it is calculated by dividing the total of the values by the number of observations.

The arithmetic mean is the average quantity in a given set of data. It is defined as the sum of all observations in the data divided by the total number of observations in the data. As a result, because it comprises all of the data in a series, the mean is influenced by the extreme values.

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The probability that the sum of the numbers rolled is even or greater than 9 is 25/36.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, two number cubes at the same time. Each cube has sides numbered 1 through 6.

There are six different possible outcomes for a dice, the set (S) of all the outcomes can be listed as follows:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Probability of getting sum as even number:

Number of favourable out comes = 18

Total number of outcomes = 36

Now, probability = 18/36

Probability of getting sum as greater than 9:

Number of favourable out comes = 7

Total number of outcomes = 36

Now, probability = 7/36

So, the probability of event is 18/36 + 7/36

= 25/36

Therefore, the probability that the sum of the numbers rolled is even or greater than 9 is 25/36.

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The area of the parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet is,

⇒ four hundred thirty-three and one-eighth ft²

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

A parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet.

Now, We know that;

Area of a parallelogram = Base × Height

Substitute the given values, we get;

⇒ Area of a parallelogram = Base × Height

⇒ Area of a parallelogram = 22 1/2 × 19 1/4

⇒ Area of a parallelogram = 45/2 × 77/4

⇒ Area of a parallelogram = 3465/8

⇒ Area of a parallelogram = 433 1/8 ft²

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Answer:

I finished

Step-by-step explanation:

B) P(t) increases as t increases toward positive infinity.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The population of winbug beetles after t years from 1990 is represented by the expression P(t) = 6,000 + 29,000(1 + 0.031)t.

We can see that when t grows, the exponential growth factor (1 + 0.031)t will eventually reach positive infinity. This implies that as t approaches positive infinity, the population of winbug beetles will similarly increase.

Consequently, the following is the best prediction of what will occur to the winbug beetle population in the years after 1990.

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After evaluating the given equation ∫(x²-4)dx, we get -32/3.

Integration is the process of finding the area of the region under the curve. This is done by drawing as many small rectangles covering up the area and summing up their areas. The sum approaches a limit that is equal to the region under the curve of a function. Integration is the process of finding the antiderivative of a function. If a function is integrable and if its integral over the domain is finite, with the limits specified, then it is the definite integration. If F(x) is a particular anti-derivative of f(x) on an interval I, then every anti-derivative of f(x) on I is given by ∫ f(x) dx = F(x) + C.

Here, ∫ f(x) dx represents the whole class of integral.

C is the arbitrary constant, and all the antiderivatives of f(x) on I can be obtained by assigning a particular value to C.

Here f(x) is the integrand,

The variable x in dx is called the integrator and the whole process of finding the integral is called the integration. The ∫ sign stands for the sum.

The given equation is:

∫(x²-4)dx for interval (-2,2).

Integrate the above equation, we get

∫(x²-4)dx = x³/3 -4x +c

Now, solving this for the interval (-2,2), we get

= (2³/3 - 4×2) - ((-2)³/3 - 4×-2)

= (8/3)-8 + 8/3 - 8 = -32/3

Thus, after evaluating the given equation ∫(x²-4)dx, we get -32/3.

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Answer:

a . a²-9

b.x²-y²

c.n²-25

d.z²-4

The domain of a function is the set of possible values that can be plugged into it.

Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while using a value for x to that end, then that selected x-value is said to belong to the domain of f.

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values. The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

The entire range of possible values for the independent variable make up the domain of a function. In layman's terms, this definition states that the domain is the collection of all x-values that could possibly cause the function to "work" and produce actual y-values.

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The local minimum of the of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(-1) = -1 and the local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(0) = 0.

The local minimum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 occurs when x = -1. This is because when x = -1, the value of the function is f(-1) = -1. This is the lowest the function can get since the function is decreasing for x < -1 and increasing for x > -1.

The local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 occurs when x = 0. This is because when x = 0, the value of the function is f(0) = 0. This is the highest the function can get since the function is increasing for x < 0 and decreasing for x > 0.

Therefore, the local minimum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(-1) = -1 and the local maximum of the function f(x) = {−x, x < −1} 2 − x2, x ≥ −1 is f(0) = 0.

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The probability that the selected pool has a ph level not considered safe is approximately 0.22 (or 22%). This can be calculated using the cumulative probability of a normal distribution with a mean of 7.5 and a standard deviation of 0.2.

1. Calculate the z-score for the lower limit of 7.2: (7.2 - 7.5) / 0.2 = -1.5

2. Calculate the z-score for the upper limit of 7.8: (7.8 - 7.5) / 0.2 = 1.5

3. Calculate the cumulative probability of the lower limit: P(-1.5) = 0.0668

4. Calculate the cumulative probability of the upper limit: P(1.5) = 0.9332

5. Calculate the probability that the selected pool has a ph level not considered safe: P(not safe) = 1 - (P(1.5) - P(-1.5)) = 0.22

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The answer to the question is no, there is not convincing evidence of a difference between the population proportions.

Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.

In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.

Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.

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The answer to the question is no, there is not convincing evidence of a difference between the population proportions.

Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.

In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.

Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.

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The number of those line segments which have endpoints of different colors is 40.5.

Given data :

There are 2 red, 5 green, and 3 blue points on a circle.

There are different colored endpoints on each line segment that starts at a red point and travels to either a green point or a blue point.

There are 2 red points and 7 segments from each of them, making a total of 14 segments.

There are different colored endpoints on each line segment that leaves at a green point and travels to either a red or blue point.

There are 5 green points and 8 segments from each, for a total of 40 segments.

There are different colored endpoints on each line segment that leaves at a blue point and travels to either a green point or a red point.

Each blue point has 9 segments, and there are a total of 3 blue points.

Add all the ways = 14 + 40 + 27

= 81 segments.

Number of segment = 81/2 = 40.5 Segments

Thus, the number of those line segments which have endpoints of different colors is 40.5.

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The total cost for the truck rental will be $495.75

The cost of the truck rental can be calculated using the formula:

Cost = Daily rate + Per mile rate * Total miles

where:

Daily rate = $39.95 per day

Per mile rate = 64 cents per mile = $0.64 per mile

Total days = 5 days

Total miles = 460 miles

Substituting the values in the formula, we get:

Cost = $39.95 * 5 + $0.64 * 460

Cost = $199.75 + $296

Cost = $495.75

Therefore, the total cost for the truck rental will be $495.75.

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The total cost for the truck rental will be $495.75

The cost of the truck rental can be calculated using the formula:

Cost = Daily rate + Per mile rate * Total miles

where:

Daily rate = $39.95 per day

Per mile rate = 64 cents per mile = $0.64 per mile

Total days = 5 days

Total miles = 460 miles

Substituting the values in the formula, we get:

Cost = $39.95 * 5 + $0.64 * 460

Cost = $199.75 + $296

Cost = $495.75

Therefore, the total cost for the truck rental will be $495.75.

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Answer:

43.4 m²

Step-by-step explanation:

side 1= 4+7 m=11m

side 2=3m

height = 6.2 m

we have

the area of the trapezoid = [tex]\frac{1}{2} height*(side1+side2)[/tex]

=[tex]\frac{1}{2} *6.2*(11+3)[/tex]

=[tex]\frac{1}{2} *6.2*14[/tex]

=43.4  m²

The terminal point of the vector for a length of 10 is (x, y) = (-15.8, 7).

The length of a vector can be calculated using the Pythagorean Theorem. The formula for calculating the length of a vector can be expressed as:

Length (vector) = √((x2 - x1)² + (y2 - y1)²).

In this case, the initial point is (x1, y1) = (-3, 1) and the terminal point is (x2, y2) = (x, y) = (x, 7). Substituting these values into the formula, we get:

Length = √((x - (-3))² + (7 - 1)²)

As we need the length of the vector to be 10, we can solve for x.

10 = √((x + 3)² + 6²)

100 = (x + 3)² + 36

164 = (x + 3)²

12.8 = x + 3

x = -15.8

Therefore, the terminal point of the vector for a length of 10 is (x, y) = (-15.8, 7).

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Answer: -2 (basement)

Step-by-step explanation:

20-13=7

7+10=17

17-19= -2

Answer:

the basement

20-13=7+10=17-19=-2

The multiplication problem that matches the model is, 3/5 x 3/10. So Option D is correct

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.

Given that,

Two models

One having,

3 blue color filled sections and 2 blank sections

Another one having,

3 blue color filled semi-sections and 7 blank sections

we have to make analogy between multiplication of ratio of filled to total sections and multiplications of numbers,

Total sections in model 1 = 5

Total semi-sections in model 2 = 10

Ratio in 1 = filled/total = 3/5

Ratio in 2 = filled/total = 3/10

Now multiplying both the ratio,

⇒  3/5 × 3/10

Hence, the analogy is 3/5 × 3/10

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Answer: 12

Step-by-step explanation:

Answer:

[tex] \sf \: x = 12[/tex]

Step-by-step explanation:

Given equation,

→ x - 9 = 3

Now the value of x will be,

→ x - 9 = 3

→ x = 3 + 9

→ [ x = 12 ]

Hence, the value of x is 12.

The solution to the given inequality, 10 ≤ 2x ≤ x+9, is 5 ≤ x ≤ 9

From the question, we are to solve the given inequality

The given inequality is

10 ≤ 2x ≤ x+9

Then,

We can write that

10 ≤ 2x and 2x ≤ x+9

First, solve the inequality 10 ≤ 2x

10 ≤ 2x

Divide both sides by 2

5 ≤ x

Now, solve

2x ≤ x + 9

2x - x ≤ 9

x ≤ 9

Thus,

5 ≤ x and x ≤ 9

5 ≤ x ≤ 9

Hence, the solution is 5 ≤ x ≤ 9

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The ordered pair (-2, 1) is not a solution

From the question, we have the following parameters that can be used in our computation:

6x + 5y = -7

2x - 4y = -8

The ordered pair is given as

(-2, 1)

Substitute the known values in the above equation, so, we have the following representation

6(2) + 5(-1) = -7 == false

The above equation is false

Hence, the ordered pair is not a solution

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The perimeter and area of a parallelogram can be determined if the length and width are known.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

Without additional information, it is not possible to determine the exact perimeter and area of each cookie. Assuming the length and width are given, we can use the formula for the perimeter of a parallelogram (2 times the sum of the length and width) and the formula for the area of a parallelogram (length times width) to find the desired quantities.

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The value of f(-1) is 9

The value of f(x+h) is 4x + 4h + 3

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

f(x) = 4x² - 3x + 2      Now replace x with -1.

f(-1) = 4(-1)² -3(-1) + 2

f(-1) = 4 + 3 + 2

f(-1) = 9

f(x) = 4x + 3         Now replace x with x + h.

f(x+h) = 4(x+h) + 3    

Distribute and simplify

        = 4x + 4h + 3

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39.5cm the diameter of the circular garden whose circumference is 124.03 cm.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object.

here, we have,

circumference is 124.03 cm.

i.e. pi*d= 124.03 cm.

we know,

pi = 3.14

i.e. d= 124.03/3.14

       =39.5cm

Hence, 39.5cm the diameter of the circular garden whose circumference is 124.03 cm.

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