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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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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 number of Canadians who are at least 100 years old in 2001 is 3793.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Percentage of Canadians who live in British Columbia are at least 100 years old = 14%

The number of Canadians who live in British Columbia who are at least 100 years old in the 2001 census = 531

This means,

14% = 531

Now,

The number of Canadians who are at least 100 years old.

14% = 531

Multiply 100/14 on both sides.

100% = 100/14 x 531

100% = 3792.8

100% = 3793

Thus,

The number of Canadians who are at least 100 years old is 3793.

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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.

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 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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With the description of the parallel lines and the transversal line, the alternate exterior angles are angle 1 and angle 8 and they are equal

According to the description

angle 1 + angle 2 = 180 degrees (angles of a straight line)

angle 4 + angle 2 = 180 degrees (angles of a straight line)

subtracting will result to

angle 1 - angle 4 = 0

angle 1 = angle 4

the vertical angle theorem

because the line is parallel

angle 1 = angle 5 (corresponding angles)

angle 4 = angle 8 (corresponding angles)

Since angle 1 = angle 4 = angle 8 then applying transitive property

angle 1 = angle 8

This completes the prove that alternate exterior angles are equal.

Another pair of alternate exterior angles are angle 2 and angle 7

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yes

the two shortest lengths are longer than the longest lenght

when added

5+3=8

8>6

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: 1478 = Pedro
1196 = Ricky

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

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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Answer:

y = 2/3x + 4

Step-by-step explanation:

It intersects at (0, 4)

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 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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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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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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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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The balloons reached the same altitude after 30 seconds.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. 

Let's say you go to the store to buy six apples.

You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples. Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.

We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

Purple balloon altitude = 2.5 t+0 m = 2.5 t

Starting at a height of 15 meters above sea level, the gold balloon rose 2 meters every second.

Altitude of the gold balloon: 2 t + 15 m

Hence , The balloons reached the same altitude after 30 seconds.

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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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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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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:

Answer:

8.15

Step-by-step explanation:

halfway means the middle value. Therefore the mean.

(8 + 8.3)/2

= 8.15

1. Line AB is an angle bisector of DAC.

4. Angle ABD is congruent to angle ABC

5. Triangle DAB is congruent to triangle CAB

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given, Triangle DAC is isosceles with congruent sides AD and AC.

The statements that are sufficient to for proving triangle DBC is isosceles

are, Line AB is an angle bisector of DAC.

Angle ABD is congruent to angle ABC as the opposite sides are equal.

Triangle DAB is congruent to triangle CAB as they share a common side AB and sides AD and AC are equal in length.

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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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On solving the provided question we can say that by equation of the cost, 96 x 1.46 = $140.16 = total fencing cost

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

one fence is around the perimeter of the garden,

36/4  = 9  by 9  for the inner fence  

6 for the outer fence,  15 by 15

60 + 36 = 96 feet total fence

total fencing cost is 96 x 1.46 = $140.16

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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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So on solving the provided question, we can say that 121 and 1221 are palindrome numbers

A number that remains the same even after the digits are switched is known as a palindrome. With regard to the vertical axis, it is mirror symmetric. The word "palindrome" is derived from the word "palindrome," and it describes words whose spelling remains the same when the letters are switched. A palindromic number, also known as a numeric palindrome or numeric palindrome, is a number (such as 16461), in which the value is unaffected by the order of the digits. Therefore, the first palindromes are 0 and 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, which equals 121.

here the numbers are

33, 121, 1221, 23465

121 and 1221 are palindrome numbers

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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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