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A pool is filled with 2,980 quarts of water. How many gallons of water are in the pool?

A. 4 gallons
B. 745 gallons
C. 2,980 gallons
D. 11,920 gallons

The first ten terms of the Lucas sequence are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843.

The Lucas sequence or Lucas series are an integer sequence named after the mathematician francois Edouard Lucas, which are similar to the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediate previous terms, thereby forming a fibonacci integer sequence.

Now, the sequence of first 10 numbers of Fibonacci series are-

0, 1, 1 ,2, 3, 5, 8, 13, 21, 34

which are defined as set of integers that starts with zero, followed by a one,then by another one and then by series of steadily increasing numbers,The sequence follow the rule that each number is equal to the sum of preceding two numbers.

And the sequence of Lucas sequence is -

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843.

which is definedas  the sum of its two immediate previous terms.

The Lucas number may thus be defined as follows;

Ln =    \(\left \{ {{2} ; if n= 0 \atop {1}; if n = 1} \right.\)

Here we can see that Lucas series starts with 2 and 1 whereas Fibonacci series starts with 0 and 1.

Hence,The first ten terms of the Lucas sequence are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843.

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The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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The missing number to complete the linear equation is 89 and the equation that gives the rule for this table is; y = x + 89

The equation of a line in slope intercept form is expressed as;

y = mx + c

where;

m is slope

c is y-intercept which is the point at which x = 0

From the table given, we see the coordinates as;

(1, 90), (2, 91), (3, 92), (4, 93)

Thus, we can easily say that the coordinate that precedes (1, 90) must be (0, 89)

Thus, the y-intercept is 89 and since the slope is 1, the equation of the line is; y = x + 89

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Step-by-step explanation:

2 is the answer because:

72/2=36

108/2=54

Answer:

2

Step-by-step explanation:

Well divisible means the lowest numbers it can be divided by.

So we can make a chart.

72 -  1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

108 - 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

So besides 1, 2 is the lowest divisible number between 108 and 72.

Answer: Equilateral

Step-by-step explanation:

It's equilateral because it says that each side of the triangle is 4cm. In simple words, all the sides of triangle are equal. Such a triangle is called an equilateral triangle.

Hope you understood.

Answer: 14.

Step-by-step explanation:

Answer: We can set up the following pair of simultaneous equations:

a + c = 6.70 (equation 1) (the total amount of money they have is ₹6.70)

a = c + 1.70 (equation 2) (Alan has ₹1.70 more than Conner)

We can substitute equation 2 into equation 1 to eliminate a:

(c + 1.70) + c = 6.70

Simplifying and solving for c:

2c + 1.70 = 6.70

2c = 5.00

c = 2.50

So Connor has ₹2.50.

We can substitute this value into equation 2 to find the value of a:

a = c + 1.70

a = 2.50 + 1.70

a = 4.20

Therefore, Alan has ₹4.20.

The average weight of 13 fruits will therefore be more than 262 grams 12% of the time.

What is percentile ?

In statistics, a percentile is a metric that shows the value beneath which a specific proportion of information in a group of data falls. It allows you to evaluate each value in relation to the others in the group. A student who performs at the upper quartile on a test, for instance, has did best than 80% among the remaining test-takers. Similar to this, if a person is taller than 75% of people their age and gender, they are said to be at the 75th percentile for height. When comparing an employee's performance to that of a larger group of test-takers, percentiles are frequently utilised in standardized examinations like the SAT or GRE.

given,

Finding the z-score for the 88th percentile (100% - 12% = 88%) will help us identify the weight that occurs more frequently than 12% of the time.

The z-score corresponding to the 88th percentile, according to a normal distribution table or calculator, is around 1.18.

The formula to translate a z-score into a real value is as follows:

x = μ + zσ/√n

where n is the sample size, is the standard deviation, z is the z-score, and is the mean. In place of the values we hold:

x=248 + 1.18*34/13 = 262 grams

The average weight of 13 fruits will therefore be more than 262 grams 12% of the time.

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Answer:

A

Step-by-step explanation:

The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

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Answer:

3

Step-by-step explanation:

23

Answer:

  A(-4, 1)

Step-by-step explanation:

The parts being equal means ...

  A - P = P - B

  A = 2P - B . . . . . . . . useful to remember for P being the midpoint of AB

  A = 2(-1, 4) -(2, 7) = (-2-2, 8-7)

  A = (-4, 1)

Answer: 105ft^3

Step-by-step explanation:

Answer:

\(105ft^{3}\)

Step-by-step explanation:

V(h) = h(–h + 10)(–h + 8)

Apply the distributive property to the right side and simplify.

V(h) = h(–h + 10)(–h + 8)

V(h) = {h(-h) + h(10)}(-h+8)

V(h) = (-h²+10h)(-h+8)

V(h) = (-h²)(-h) + (-h²)(8) + (10h)(-h) + (10h)(8)

V(h) = -8h² -10h² + 80h

V(h) =  -18h² + 80h

Plug in the value of h from 1 to 9 (since 0<h<10) into the function V(h)   =  -18h² + 80h and create a table

h | V(h)

1  | 63

2 | 96

3 | 105 <------maximum volume is the highest y-value

4 | 96

5 | 75

6 | 48

7 | 21

8 | 0

9 | -9

The maximum volume for the domain 0<h<10 is 105 cubic feet.

If circle with center N with m∠MNP=124 ∘ and MN=13,  the area of sector MNP is approximately equal to 194.86 square units.

To find the area of a sector of a circle, we need to use the formula:

Area of sector = (central angle/360°) x πr²

Where r is the radius of the circle.

In this problem, we know that the central angle m∠MNP is 124° and MN, which is also the radius of the circle, is 13. So we can substitute these values into the formula:

Area of sector = (124/360) x π(13)²

Area of sector ≈ 194.86

Therefore, the area of sector MNP is approximately equal to 194.86 square units.

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Answer:

Respuesta: B

Step-by-step explanation:

Patrones de secuencia

Consiste en una serie de elementos conectados entre sí por una regla fija, de tipo numérica, lógica o de razonamiento.

La primera figura de la imagen muestra un rectángulo con un círculo sin rellenar dentro. La segunda figura muestra dos cambios claramente visibles:

* La figura externa ahora es interna y viceversa.

* La figura interna estaba sin relleno y ahora lo tiene

La tercera figura muestra una cruz con un círculo sin rellenar dentro. Si aplicamos la misma regla, la siguiente figura debería tener:

* Una cruz dentro de un círculo

* La cruz debe estar rellena

Sólo la figura B cumple con estas condiciones.

Respuesta: B

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

no

Step-by-step explanation:

Given:

Radius of circle is 6 dm

Perimeter of circle is:

Perimeter of half circle is:

If 4 half circle then perimeter is:

Radius = 6 dm

So perimeter of circle is:

The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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Answer:

B. 864 mm³

Step-by-step explanation:

Volume = area base x height

Area base = 48

Height = 18

Multiply:

48 x 18 = 864

Units are mm³

Answer = 864 mm³

If my answer is incorrect, pls correct me!

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-Chetan K

The volume of the prism is 864 cubic units.

To calculate the volume of a prism, we use the formula: Volume = Area of Base x Height. In this case, the area of the base is given as 48 square units, and the height is given as 18 units.

To find the volume, we multiply the area of the base by the height:

Volume = 48 x 18 = 864 cubic units.

Therefore, the volume of the prism is 864 cubic units. Since the base area is given in square units and the height is given in units, the volume is expressed in cubic units. In this case, the units are mm³ (cubic millimeters).

Thus, the proper calculation yields a volume of 864 mm³.

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Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

First product:

\(AB=\begin{bmatrix}3&-3\\-7&0\\2&4\end{bmatrix}\begin{bmatrix}1&0\\0&1\end{bmatrix}=\begin{bmatrix}\begin{bmatrix}3&-3\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}3&-3\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\\\begin{bmatrix}-7&0\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}-7&0\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\\\begin{bmatrix}2&4\end{bmatrix}\begin{bmatrix}1\\0\end{bmatrix}&\begin{bmatrix}2&4\end{bmatrix}\begin{bmatrix}0\\1\end{bmatrix}\end{bmatrix}=\begin{bmatrix}3&-3\\-7&0\\2&4\end{bmatrix}\)

Notice how multiplying A by B produces A again, because B is an identity matrix.

The second product cannot be carried out because A has more columns that B has rows.

The third product also cannot be computed because A is not a square matrix.

Answer: 21.15 ft²

Step-by-step explanation:

We can use the formula for the area of a triangle:

(b×h)/2

In this case, the base is 9 and the height is 4.7.

So, we substitute the variables with the numbers in this problem.

(9 × 4.7)/2

9 × 4.7 = 42.3

42.3/2 = 21.15

So, our final answer is 21.15 ft²

Answer:

42 Pages

Step-by-step explanation:

7x5=35

7+35=42

For the initial fee, Bob charges less than Ginny.

A unit rate means a rate for one of something.

Given that Ginny charges by uses the function f(x)=60x+80 where x represents the number of hours of labour.

Ginny initial charge = $80

Bob initial charge =$60

Hence, For the initial fee, Bob charges less than Ginny.

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Answer:

0 = 0 means that there are infinite solutions.

Step-by-step explanation:

Equation is -5(-4+2n)=-10(n-2)

1. Distribute the -5 and -10

20 -10n = -10n + 20

2. Subtract 20 from one side to the other to get only 1 variable on 1 side.

-10n = -10n

3. divide -10 to separate the variable from the constant.

n = n

This means there are infinite solutions.

Answer:

X = 9

Step-by-step explanation:

The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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