A tank is filling with water. After 2 minutes, it contained 12 gallons. After 5 minutes, it contained
30 gallons. What is the constant rate of change?
F 6 gallons per minute
G 10 gallons per minute
H7 gallons per minute
J 5 gallons per minute

9514 1404 393

Answer:

  8 1/4

Step-by-step explanation:

If you want the result as a mixed number, you can get there two ways:

a) convert the integer to an improper fraction, add, then convert the result to a mixed number:

  4 +17/4 = 16/4 + 17/4 = 33/4 = 8 1/4

b) convert the improper fraction to a mixed number and add:

  4 + 17/4 = 4 + 4 1/4 = 8 1/4

__

Further explanation

Of course, the conversion to an improper fraction involves multiplying by a suitably chosen version of 1.

  4 = 4(4/4) = 16/4

The conversion from an improper fraction involves finding the quotient and remainder when the numerator is divided by the denominator.

  33/4 = (8·4 +1)/4 = 8(4/4) +1/4 = 8 1/4 . . . . . that is, 33÷4 = 8 r 1

Answer:

91 adult tickets

Step-by-step explanation:

Algebra is really useful here:

Let a = number of adult tickets sold and c = number of child tickets sold.

Thus, we can say that

a + c = 153 (number of tickets)

6.40c + 9.60a = 1270.4. (cost of all of the tickets)

Solving,

c = 153 - a

6.40(153 - a) + 9.60a = 1270.4

979.2 - 6.40a + 9.60a = 1270.4

3.20a = 291.2

a = 91

(a) The value of #C(5) = 13.

(b) In the brute-force method, all binary strings of length n are listed and those that contain consecutive 1s are rejected. So a brute-force approach used to compute #C(5).

(c) Using the Theorem of Induction, we proved that #C(C) = #C(l – 1) + #C(l – 2) for l ≥ 2.

Let #C(l) denote the number of binary strings with length l that have no consecutive occurrences of a 1.

For example #C(3) 5; we can list all binary strings of length 3 and determine by inspection that only the strings 000, 001, 010, 100, and 101 have no consecutive occurrences of a 1.

(a) We have to compute #C(5).

All binary strings with length five include:

00000, 00001, 00010, 00100, 00101, 01000, 01001, 01010, 10000, 10001, 10010, 10100, 10101

Strings that don't have successive 1s in them.

So #C(5) = Total number of binary strings with length five

#C(5) = 13

(b) We have to describe why a brute-force approach used to compute #C(5).

In the brute-force method, all binary strings of length n are listed and those that contain consecutive 1s are rejected. The complexity is at least exponential, thus even for modest values of n (like 40 or 50), it will take a long time to process the number of binary strings of length n = 2n.

(c) We have to show that #C(C) = #C(l – 1) + #C(l – 2) for l ≥ 2 and derive a recursive algorithm to compute #C(C).

No empty string contains two consecutive ones.

So #C(0) = 1,

#C(1) = 2 ( 0 and 1)

Base Case : For l = 2,

#C(2) = |{00, 10, 11}|

#C(2) = 3

#C(2) = #C(1) + #C(0)

Consequently, the recurrence is true, for l = 2.

Number of strings with the character 0 = 2 = #C (1)

Theorem of Induction

Assume that the recurrence holds for every l < k and the quantity of strings with 0 = #C(l-1)

Induction Step :

For l = k+1,

#C(k+1): Only those strings of length k that do not include consecutive 1s will be the first string in such strings. These strings will never result in consecutive 1s when a 0 is added.

Thus, the number of strings that end in 0 = #C(k)

Only strings of length k that finish in 0 can be added to.

The number of such strings, by induction = #C(k-1)

Hence, #C(k+1) = #C(k) + #C(k-1)

Recursive Algorithm:

NoCon1(n)

{

1. if n < 0 : return 0

2. if n == 0 : return 1

3. if n==1 : return 2

4. return NoCon1(n-1) + NoCon1(n-2);

}

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Answer:

1. ×2+10x2+25

=(×+5)(×+5)

2. 4x2+16+

=(2×+4)(2×+4)

Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

The statement is False. The entire group of individuals we want information about is called the population, not sample.

In statistics, a sample is a subset of individuals or observations taken from a larger population, which is used to estimate characteristics or parameters of the population.

The goal of statistical analysis is often to make inferences about a population based on information gathered from a representative sample. Therefore, it is important to carefully select a sample that is truly representative of the population of interest.

The sample is a subset of the population that is selected for analysis in order to make inferences about the population.

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The complete question is : The entire group of individuals we want information about is called the sample.

a. True

b. False

Answer:

factor:

x^2+2x+2x+4

x(x+2)+2(x+2)

(x+2)(x+2)

100x^2+20x+1

100x^2+10x+(10x+1)

10(10x+1)+(10x+1)

(10x+1)(10x+1)=(x+2)(x+2)

Hope this helps you

Answer:

1/9, (-3)/11

Step-by-step explanation:

Both the left and right side are perfect squares,

                                         (x + 2)^2 = (10x + 1)^2

In order for the squares to be equal, we must have the inner expressions equal to each other or negations of each other:

                                         (x + 2) = \(\pm\) (10x + 1)

or

                                         x + 2 = -10x - 1

Simplifying the first equation gives 9x = 1 so 1/9 and simplifying the second equation gives 11x = -3, so (-3)/11

Answer:

2 /5

Step-by-step explanation:

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

The right answer is A (x=2,y=-1)

The height of the kite from the ground when the angle is 50 degrees is 232 feet.

The study of the correlations between triangles' sides and angles is the focus of the mathematic branch known as trigonometry. To link the angles of a right triangle to the lengths of its sides, it makes use of trigonometric functions like sine, cosine, and tangent.

Numerous industries, including physics, engineering, and navigation, use trigonometry. It can be used, for instance, to determine a building's height or the separation between two locations on a map, as well as to examine how waves and oscillations behave.

To find the height of the kite above the ground we use the trigonometric identity of tangent.

Thus, we have:

tan(50°) = h/200

Now, using cross multiplication:

h = 200 tan(50°) ≈ 232 feet

Hence, the height of the kite from the ground when the angle is 50 degrees is 232 feet.

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Answer:

81

Step-by-step explanation:

4 x 18 =72 + 9 =81

The skier's distance to the east of the center of the ski trail is

x = 1.25cosθ

The skier's distance to the north of the center of the ski trail is

y = 1.25sinθ

When radius 'r' and the angle θ are given, the coordinates (x,y) as shown

x = east direction

y = north direction

In this case we get,

x = r cosθ

y = r sinθ

Given r = 1.25 km

We get,

x = 1.25 cosθ in east direction

y = 1.25 sinθ in north direction

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Answer:

By multiple by 2

Step-by-step explanation:

1 multiplied by 2 = 2

3 multiplied by 2 = 6

In that case they equivalent due to the number 2.

Answer:

210

Step-by-step explanation:

35x3x2=210

The area of the shaded part is 20m²

The space enclosed by the boundary of a plane figure is called its area. The area of a rectangle is length × width It is measured in square units like cm² and m².

To find the area of the square, we need to find the side length.

The side length is found by using Pythagoras theorem

each box is 1m, then 4 boxes is 4m and 2 boxes is 2m

therefore;

l= √ 4²+2²

l = √ 16+4

l = √20 = 2√5

area a square is l²

A = (2√5)²

A = 4× 5

A = 20m²

therefore the area of the shaded part is 20m²

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Answer:

Equation: \(y=-\frac{5}{4} x\)

Slope: \(-\frac{5}{4}\)

Point: \((-4,5)\)

Step-by-step explanation:

To find the slope, you need two points \((-4,5)\) and \((0,0)\).

Then use the Slope Formula to Identify the slope.

M = Slope

M = \(\frac{y2-y1}{x2-x1}\)         Second y being subtracted by the first y / the second x being subtracted by the first x.

M = \(\frac{0-5}{0--4}\)          Plot the x and y values (In order) Then subtract

M = \(\frac{-5}{4}\)             Move the negative sign

M = \(-\frac{5}{4}\)

Slope = \(-\frac{5}{4}\)

Then the Equation has to be written in Slope-Intercept Form (y=mx+b)

y = \(-\frac{5}{4} x\)

The multiplication fact that can help you find 24 divided by 4 is 4 x 6.

The recursive rule is f(n) = f(n - 1) * 2; f(1) = 9 and the explicit rule is f(n) = 9(2)^n-1

The recursive rule

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

The table

The table definitions imply that we simply multiply 2 to the previous term to get the current term

This means that

f(n) = f(n - 1) * 2

Where

f(1) = 9

The explicit rule

The table definitions imply that we simply multiply 2 to the previous term to get the current term

a = 9

r = 2

So we have

f(n) = a * r^n-1

This gives

f(n) = 9(2)^n-1

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Answer:

The magnitude of the vector is 9.165 and it's direction is 40.6°

Step-by-step explanation:

A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.

Magnitude of vector v is given by

|v| = √6²+7²

= √36+49

= √84

= 9.165

Direction of vector v is obtained by:

\( \tan( \theta) = \frac{x}{y} \)

\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)

\(\theta = {40.6°}\)

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For (2,6) the 2 is the x value which is the left/right position and 6 is the y value which is the up/down position.

Moving 2 units to the right, you would add 2 to the x value. Moving 3 units down you would subtract 3 from the y value.

The answer would be (4,3)

Answer:

64

Step-by-step explanation:

It’s directly adjacent to the other angle.

The equation of the line given by the function table is expressed as:

y = ¹/₃x + 1

The formula for the equation of a line with two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

From the given function table, we will take the coordinates:

(3, 4) and (6, 5)

Thus, we have:

(y - 4)/(x - 3) = (5 - 4)/(6 - 3)

(y - 4)/(x - 3) = 1/3

(y - 4) = ¹/₃x - 3

y = ¹/₃x - 3 + 4

y = ¹/₃x + 1

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Answer:

E stands for the power of ten the number is multiplied by

I thonk

Answer:

Your answer will be $240

Using the pattern, n can represent the the increase of dots according to step.

In the given question we have to find what values make sense for n in this situation.

n is representing the number.

As we can see that there is a pattern given.

In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.

So if we see the pattern then according to number of step the dots increasing accordingly.

As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.

So, n can represent the the increase of dots according to step.

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The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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