Evaluate the line integral, where C is the given curve.∫C xyds, C:x = t^2,y = 2t, 0 ≤ t ≤ 3

Grace can use the fraction 3 / 5 of the distance from point A and 2 / 5 of the distance from point B to determine the x coordinate of point C.

Herein we find the case of a point partitioning a line segment by observing a given ratio. The equation that observes this fraction is shown below:

AC / BC = 2 / 3

AC / AB = 2 / 5

Vectorially speaking, this is equivalent to the following equation:

C(x, y) - A(x, y) = (2 / 5) · [B(x, y) - A(x, y)]

C(x, y) = (3 / 5) · A(x, y) + (2 / 5) · B(x, y)

If we know that A(x, y) = (3, 2) and B(x, y) = (6, 11), then the coordinates of point C are, respectively:

C(x, y) = (3 / 5) · (3, 2) + (2 / 5) · (6, 11)

C(x, y) = (9 / 5, 6 / 5) + (12 / 5, 22 / 5)

C(x, y) = (21 / 5, 28 / 5)

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Approximately 34% of observations in a normal distribution lie above one standard deviation below the mean.

In a normal distribution, approximately 68% of observations fall within one standard deviation of the mean. This means that approximately 34% of observations lie below one standard deviation below the mean and 34% of observations lie above one standard deviation above the mean.

The standard normal distribution (also known as the Z-distribution) is a normal distribution with a mean of 0 and a standard deviation of 1. So if you have a normal distribution with a mean of "mu" and a standard deviation of "sigma", you can standardize it by (X - mu)/sigma to obtain the Z-score.

In a standard normal distribution, 34% of observations fall below -1 standard deviation and 34% fall above +1 standard deviation. So, 34% of observations in a normal distribution lie above one standard deviation below the mean.

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Answer:

[tex] \sf \: 9(x + 2)[/tex]

Step-by-step explanation:

Given expression,

→ 9x + 18

Let's factorise the expression,

→ 9x + 18

→ (9 × x) + (9 × 2)

→ 9(x) + 9(2)

→ 9(x + 2)

Hence, the factor is 9(x + 2).

The transformation for the graph f(x) to h(x) is a vertical transformation of 2 units.

The graph is given below.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

f(x) = x

h(x) = x + 2

h(x) = f(x) + 2

Now,

f(x) → h(x)

The transformation from f(x) to h(x) is a vertical translation of 2 units.

i.e

f(x) → f(x) + 2

The graph is given below.

The blue line is the function.

The red line is the parent function.

Thus,

The transformation of the function is f(x) → f(x) + 2.

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A function f for f'(0) = 3 it means that the slope of the line tangent to the point x = 0 is 3.

Function:

In mathematics, a function from a set X to a set Y assigns each element of X to exactly one element of Y.  The set X is called the domain of the function and the set Y is called the codomain of the function

As a set of inputs with one output for each, a function is defined as a relationship between them. A function, expressed simply, is an association between inputs where each input is connected to one and only one output.

when it says something like f(1) = 0 it means that when x = 1, y = 0

so we know one point on the graph is (0,0)

When it says something like f'(0) = 3 it means that the slope of the line tangent to the point x = 0 is 3

Complete Question:

Sketch the graph of a function f for which f(0)=0, f'(0)=3, f'(1)=0, f'(2)=-1

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The point-slope form of the horizontal line (-6,0) is y = 0.

Here given point (-6,0).

If the line is horizontal, the slope is zero.

Then the formula in slope-point form, ( y - y 1 ) = m ( x - x 1 )

By substituting,

This is equivalent to y - 0  = 0 ( x - (-6)).

y - 0 = 0

y = 0

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The difference in values of the two houses when they are each 15 years old is given as follows:

$22,000.

The home values are modeled using linear functions, which in slope-intercept form are given as follows:

y = mx + b.

In which the parameters are given as follows:

For House A, the points are given as follows:

(3,150) and (8, 180).

Then the slope is given as follows:

m = (180 - 150)/(8 - 3)

m = 6.

Hence:

y = 6x + b

When x = 3, y = 150, hence the intercept b is given as follows:

150 = 18 + b

b = 132.

Then the function for the value of the home after x years is given as follows:

y = 5x + 132.

Meaning that the value of the home after 15 years is given as follows:

y = 5(15) + 132

y = $222,000.

For House B, the points are given as follows:

(1,130) and (5, 150).

Then the slope is given as follows:

m = (150 - 130)/(5 - 1)

m = 5.

Hence:

y = 5x + b

When x = 1, y = 130, hence the intercept b is given as follows:

130 = 5 + b

b = 125.

Then the function for the value of the home after x years is given as follows:

y = 5x + 125.

Meaning that the value of the home after 15 years is given as follows:

y = 5(15) + 125

y = $200,000.

The difference is then given as follows:

$222,000 - $200,000 = $22,000.

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The fraction 1/9 is greater than the fraction 1/11.

Comparing fractions involves a set of rules related to the numerator and the denominator. When any two fractions are compared, we get to know the greater and the smaller fraction.

To compare unlike fractions:

Step 1: Observe the denominators of the given fractions: .

Step 2: Now, let us convert them in such a way that the denominators become the same.

Step 3: Compare the fractions:

Step 4: The fraction with the larger numerator is the larger fraction.

The given fractions are 1/9 and 1/11.

Here, LCM of denominator 9 and 11 is 99

Then, fractions becomes 11/99 and 9/99

11/99>9/99

1/9>1/11

Therefore, the fraction 1/9 is greater than the fraction 1/11.

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Answer:

where t is in hours since midnight and f(t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 30e^cos(/2)a) Define a new function, a(t), that would represent the amount of untreated water inside the plant, at any given time, t.b) Find a′ (t).c) Determine the critica

yes

the two shortest lengths are longer than the longest lenght

when added

5+3=8

8>6

Answer:

565.004, 565.040, 565.4

Step-by-step explanation:

Answer:

N/A

Step-by-step explanation:

1. subtract 3 from both sides to isolate the square root and its coefficient

5√(5-x) = - 10

2. divide both sides by 5 to isolate the square root

√(5-x) = -2

this means that the square root of something would be negative, which is not possible

Answer: 1478 = Pedro
1196 = Ricky

Step-by-step explanation: 2674-282 = 2392/2 = 1196 = Ricky
1196+282 = 1478 = Pedro

The 95% confidence interval for the population proportion is (0.88, 0.98).

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally employed. The confidence interval is the range of values within which you expect your estimate to fall a given proportion of the time if you repeat your experiment or re-sample the population in the same manner.

Here,

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.93.

The standard error of the proportion is:

σ=√(p(1-p)/n)

=√((0.93*7)/100)

=0.0255

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

=1.96*0.0255

=0.05

Then, the lower and upper bounds of the confidence interval are:

LL=0.93-0.05

=0.88

UL=0.93+0.05

=0.98

The population proportion's 95% confidence interval is (0.88, 0.98).

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The zeros of the quadratic function are: x = -3 or x = -4.

The quadratic function is:

f(x) = 2x² + 14x + 24

Set the function equal to 0

2x² + 14x + 24 = 0

Common 2 from the left side,

⇒2(x² + 7x +12) = 0

Factorize the left side

⇒2(x + 3)(x + 4) = 0

Set factors equal to 0 and we get

  x + 3 = 0 or, x + 4 = 0

⇒x = 0-3 or, x = 0-4

⇒x = -3  o, x = -4

Thus,

The zeros of the quadratic function are: x = -3 or x = -4.

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The value of Double integral will be [tex]\mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}[/tex]

A two-dimensional region can be integrated using double integrals. They enable us to, among other things, calculate the volume beneath a surface.

The integrals of a function in two variables over a region in R2, or the real number plane, are referred to as double integrals in mathematics. It is possible to write the double integral of a function of two variables, such as f(x, y), over a rectangular region as: R f (x, y) d A = R f (x, y) d x d y.

We know that by the property of integral [tex]$\int u \mathrm{udv}=u v-v \int d u$[/tex]

[tex]$$\begin{aligned}& \mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}=\left[\mathrm{x} \ln (1+\mathrm{x})-\int \mathrm{x} \frac{.1}{1+\mathrm{x}} \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4\left[\mathrm{x} \ln (1+\mathrm{x})-\int\left(1-\frac{1}{1+\mathrm{x}}\right) \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4[\mathrm{x} \ln (1+\mathrm{x})-\mathrm{x}+\ln |1+\mathrm{x}|]_0^4 \\& \mathrm{I}=[4 \ln (5)-4+\ln (5)]-[0-0+0] \\& \mathrm{I}=4[5 \ln 5-4] \\& \mathrm{I}=20 \ln 5-16\end{aligned}$$[/tex]

We have to evaluate the given double integral

[tex]$$\iint_{\mathrm{R}} \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dA} \text { where } \mathrm{R}=[0,4] \times[0,1]$$[/tex]

[tex]$$\begin{aligned}& \mathrm{I}=\int_0^4 \int_0^1 \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dydx}=\int_0^4 4 \mathrm{x}\left[\frac{|1+\mathrm{xy}|}{\mathrm{x}}\right]_0^1 \mathrm{dx} \\& \mathrm{I}=\int_0^{44}[\ln |1+\mathrm{x}|-0] \mathrm{dx}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}\end{aligned}$$[/tex]

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The equation statement 2(3 + 5x) = 6 + 5x is false

The statement is true if the values in the left hand side of the equation is equal to the value in the right hand side of the equation

The left hand side of the equation is simplified as follows

= 2(3 + 5x)

expanding to open the parenthesis

= 6 + 10x

6 + 10x is not equal to 6 + 5x hence we say that the sides are not equal

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Answer:

The y value of the point (x, y) is known as the ordinate.

Step-by-step explanation:

It represents the vertical or perpendicular distance of the point from the origin or from the x-axis. The point at which a line intercepts the x-axis is called the x-intercept, and the point at which it intercepts the y-axis is called the y-intercept.

Jon is painting a box like a rectangular prism with dimensions of 15 by 8 by 12 inches. Total surface area of the box that he has to paint is 792 square inches.

Let:

w = width of the rectangular prism

l = length of the rectangular prism

h =height of the rectangular prism

Then, the surface area can be calculated as:

surface area = base area + top area + left side area + right side area + front side area + back side area.

surface area = 2 (w x l) + 2 (l x h) + 2 (w x h)

Substitute:

w = 8 inches

l = 15 inches

h = 12 inches

Surface area = 2 (8 x 15) + 2 (15 x 12) + 2 (8 x 12)

                     = 2 x (120 + 180 + 96)

                     = 792

Hence, Jon has to paint 792 sq. in.

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The rate of change in feet per minute for each of the balloons, can be found to be :

The rate of change in feet per minute is dependent on the change in altitude given and the change in time in minutes.

For Midnight Express balloon, the change in feet per minute would be:

= Change in altitude / Change in time

= - 2, 700 / 135

= - 20 ft per minute

For Neon Lights balloon, the change in feet per minute is:

= 480 / 30

= 16 ft per minute

For Star Wonder, the change in feet per minute is:

= - 1, 500 / 60

= - 25 ft per minute

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The predicted number of sit ups each person can do in 12 seconds, using a proportional relationship model are;

Janet 18 sit ups

Paulo 10 sit ups

Shah 9 sit ups

A proportional relationship is one in which the values of the output variable are a constant multiple of the values of the variables in the set of the input values.

The data for the number of sit ups each person can do with time are as follows;

1. Janet does 3 sit ups in 2 seconds

2. Paulo does 5 sit ups in 6 seconds

3. Shah does 3 sit ups in 4 seconds

The rates at which each person does sit ups, using a proportional relationship between the number of sit ups and time and the the constant of proportionality in the proportional relationship is the rate of sit ups per person which are;

Rate = (Number of sit ups)/(Time)

The rate at which Janet does sit ups = (3 sit ups)/(2 seconds), m = 1.5 sit ups/second

Rate at which Paulo does sit ups = (5 sit ups)/(6 seconds), m = (5/6) sit ups/second

Rate at which Shah does sit ups = (3 sit ups)/(4 seconds), m = (3/4) sit ups/second

The number of sit ups each person can do, n, in a specified time, t, can be found using the formula;

n = m × t

Where;

n = The number of sit ups

m = The rate at which the person does sit ups

t = The time duration

Therefore, the number of sit ups each person can do in 12 seconds are therefore;

The number of sit ups Janet can do in 12 seconds is; n = 1.5 × 12 = 18

Janet can do 18 sit ups in 12 seconds

Number of sit ups Paulo can do in 12 seconds is; n = (5/6) × 12 = 10

Paulo can do 10 sit ups in 12 seconds

Number of sit ups Shah can do in 12 seconds is; n = (3/4)×12 = 9

Shah can do 9 sit ups in 12 seconds

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The markup from cost to sale price is $108.

The pricing system in which a commodity's (goods or services) price is lower than its listed price is referred to as a "discount." Simply put, "discount" refers to a percentage of the advertised price. A discount is a type of price reduction on products that are seen in consumer transactions.

Given,

the selling price of an item = $520

Markdown = 10% = discount

markdown  ​=  percent markdown * selling price

= 10%*520

=  0.10*520

markdown = $52

To find the sale​ price, subtract the markdown from the selling price.

sale/price ​=  selling price - markdown

= 520 - 52

sale price = $468

to find the markup.

cost of item after markdown = $360

mark up cost  ​=  sale price - cost

mark up = 468 - 360

mark up = $108

Therefore,  the markup from cost to sale price is ​$108.

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The table that shows the value of the input and output values of g(x) is shown below where x is for the input values and the output values is g(x)

x       g(x)

2       4

1        2

0        0

1         2

2         4

The values are solved by substituting the values of f(x) in the formula as shown in the problem, the formula is

g (x) = 2f (x)

The values of f(x) which is the input values for g(x) are

2 1 0 1 2

this values are substituted in to the function g (x) = 2f (x) to get

4 2 0 2 4

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Conversing the conditional statement we get the answer as, if x is odd, then x+ 1 is even.

Two pieces make up a conditional statement: an assumption in the "if" clause and a conclusion in the "then" clause. Conversing, changes the hypothesis and conclusion to create the conditional statement's opposite.

The converse of the first conditional statement is:

If x is odd, then x + 1 is even.

If x is not odd, then x + 1 is not even.

If x + 1 is even, then x is odd.

If x + 1 is not even, then x is not odd.

Hence, in converse of the conditional statement we switch the hypothesis and the conclusion of the statements.

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Answer:

8.15

Step-by-step explanation:

halfway means the middle value. Therefore the mean.

(8 + 8.3)/2

= 8.15

Answer:

At the beginning, the box has 12 ounces of cereal.

Sue eats 1/6 of the box which is 12*(1/6) = 2 ounces.

Glen eats 2/3 of the box which is 12*(2/3) = 8 ounces.

So, the total ounces that they have eaten is 2+8 = 10 ounces.

Therefore, 12-10 = 2 ounces are left in the box.

Answer: From the information provided, it can be inferred that the graph represents a piecewise function, which is a function defined by multiple smaller functions that apply to different parts of the domain.

Based on the information given, we can see that the function is constant for an input of 1. So the output value of 2 is not in the domain of the function.

It's also important to note that a function can only have one output value for a given input value, and the value of 2 is not on the graph of the function provided.

Step-by-step explanation:

The solutions for the equation are b = 0, 3.

What is the cubic equation?

A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. Polynomials are referred to as cubic polynomials if they have a degree of three. The opposite of cubing an integer is finding the cube root of that number. It can be determined by first determining how the given integer can be divided into prime factors, and then by using the cube root formula.

To find the solution for the equation 5/3b³ - 2b² - 5, we can factor it or use the quadratic formula.

One way to factor it is to note that it is a cubic equation in terms of b, and can be written as:

5/3b³ - 2b² - 5 = (5/3b³ - 2b²) - 5 = (5/3b³ - 2b²- 5b) + (5b)

= (5/3b)(b² - 3b) + 5

So, b=0 is one solution, but we can also factor the remaining quadratic equation (b² - 3b) = 0,

b=0 and b=3 are the solutions for the equation.

Hence, the solutions for the equation are b = 0, 3.

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Answer:

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are coefficients and x is the variable.

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Given that the roots of the quadratic equation are (3+√5) and (3-√5), we can set the quadratic equation equal to zero and substitute the roots for x:

ax^2 + bx + c = 0

(x - (3+√5))(x - (3-√5)) = 0

(x - 3 - √5)(x - 3 + √5) = 0

(x - 3 - √5)(x - 3 + √5) = (x-3)^2 - (√5)^2 = (x-3)^2 - 5 = 0

x^2 - 6x + 9 - 5 = 0

x^2 - 6x + 4 = 0

So the quadratic equation whose roots are (3+√5) and (3-√5) is x^2 - 6x + 4 = 0

Step-by-step explanation: