The floor of a rectangular banquet hall has an area of 3,600 3 m 3 (cubic meters). The length is 90 meters. A. What is the width of the banquet hall?

The number of boats needed for 1491 people are 20.

What is the cross-product?

The cross product, also known as the vector product in mathematics, is a binary operation on two vectors in a Euclidean vector space that is oriented in three dimensions. It is represented by the symbol times.

We have,
134 people decided to go scuba diving,
523 people decided to neither scuba dive nor go on a boat tour,

So, people go to boat tour = 2148 -(134 + 523)
= 2148 - 657
= 1491
now, since each boat holds 78 people.

[tex]\frac{1491}{78} = 19\frac{3}{26}[/tex]

= 20 boats.
Hence, the number of boats needed for 1491 people are 20.

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Complete Question
The 2148 guests at a hotel have the. the choice to either go on a boat tour or go scuba diving.  134 people decided to go scuba diving.  523 people decided to neither scuba dive nor go on a boat tour. Each boat holds 78 people. How many boats are needed? Explain your reasoning.

[tex]72x^{2}+3x+3[/tex]Answer:

Step-by-step explanation:

[tex]1. (4x^{2}+34x^{2} +34x^{2} )+(x+x+x)+3\\ 2. 72x^{2} +3x+3[/tex]

Answer:

[tex]\textsf{D.} \quad 5^9=x[/tex]

Step-by-step explanation:

Given logarithmic equation:

[tex]\log_5x-\log_525=7[/tex]

[tex]\textsf{Apply the quotient log law}: \quad log_ax - \log_ay=\log_a \left(\dfrac{x}{y}\right)[/tex]

[tex]\implies \log_5\left(\dfrac{x}{25}\right)=7[/tex]

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies 5^7=\dfrac{x}{25}[/tex]

Multiply both sides by 25:

[tex]\implies 25 \cdot 5^7=x[/tex]

Rewrite 5 as 5²:

[tex]\implies 5^2 \cdot 5^7=x[/tex]

[tex]\textsf{Apply exponent rule}: \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 5^{2+7}=x[/tex]

[tex]\implies 5^9=x[/tex]

Multiply the fraction's bottom numbers with the top numbers in the two fractions.

The two fractions' top numbers should be multiplied, as should the bottom numbers.

Find the fraction of the following two fractions, for instance:

2/3, and 4/5

= 2/3 × 4/5

= (2×4)/(3×5)

= 8/15

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. 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 factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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[tex] \frac{1}{2} x - 4 < 3 \\ [/tex]

Add both sides 4

[tex] \frac{1}{2} x - 4 + 4 < 3 + 4 \\ [/tex]

[tex] \frac{1}{2} x < 7 \\ [/tex]

Multiply both sides by 2

[tex]2 \times \frac{1}{2} x < 2 \times 7 \\ [/tex]

[tex]x < 14[/tex]

_____________________________________________

[tex]7 \leqslant 3x + 5[/tex]

[tex]3x + 5 \geqslant 7[/tex]

Subtract both sides minus 5

[tex]3x + 5 - 5 \geqslant 7 - 5[/tex]

[tex]3x \geqslant 2[/tex]

Divide both sides by 3

[tex] \frac{3x}{3} \geqslant \frac{2}{3} \\ [/tex]

[tex]x \geqslant \frac{2}{3} \\ [/tex]

Each side of quadrilateral A changed by a factor of 1/4

When quadrilateral A was reduced the size of each angle remain unchanged

The dimensions of quadrilateral A are 16, 10, 6, 20

The dimensions of quadrilateral B are  4, 2.5, 1.5, 5

comparing the two dimensions

Let the factor be r

4r = 16

r = 16/4

r = 4

2.5r = 10

r = 10/2.5

r = 4

1.5r = 6

r = 6/1.5

r = 4

5r = 20

r = 20/5

r = 4

Therefore we can conclude that quadrilateral B was increased by 4, similarly, quadrilateral A was reduced by a factor of 1/4

16 * 1/4 = 4

10 * 1/4 = 2.5

6 * 1/4 = 1.5

20 * 1/4 = 5

since the reduction are similar quadrilateral A is similar to quadrilateral B

and the size of each angle were not affected

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Examples of one variable polynomial:

• Zero polynomial: 3

The degree of the polynomial is not defined

• Constant polynomial: f(x)= 3

The degree of the polynomial is 0

• Linear polynomial: f(x)= 3x

The degree of the polynomial is 1

• Quadratic polynomial: f(x)= 2x^2+3-1

The degree of the polynomial is 2

• Cubic polynomial: f(x)= 3x^3-5x+2

The degree of the polynomial is 3

• Quartic polynomial: f(x)= 5x^4-6x^2+2x+3

The degree of the polynomial is 4

Example of multiple variable polynomial:

Polynomial:  f(x)= 5x^4y^2z^3+3x^2yz+2xz

The degree of the polynomial is 9.

Degree of the polynomial:

The highest or greatest power of a variable in a polynomial equation is referred to as the degree of the polynomial.   The degree denotes the polynomial's highest exponential power.  

Types of polynomial:

• Zero polynomial

• Constant polynomial

• Linear polynomial

• Quadratic polynomial

• Cubic polynomial

• Quartic polynomial

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Hence, the graph of [tex]g[/tex] is upward than the graph of [tex]f[/tex].

What is the function?

Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.

Here given that,

The functions are

[tex]f(x)=2^x\\g(x)=f(x)+6\\g(x)=2^x+6[/tex]

Draw the graphs of both the equation

The graph of the [tex]g[/tex] is differ from [tex]f[/tex] because in the graph of [tex]g[/tex] it is upward than the graph of [tex]f[/tex].

Hence, the graph of [tex]g[/tex] is upward than the graph of [tex]f[/tex].

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Answer:

C

Step-by-step explanation:

15÷-3=15÷-3

15÷-3=-5

-15÷3=-5

The common denominator of 1/a + 1/b in the complex fraction (1/a - 1/b) / (1/a + 1/b) is ab

The given complex fraction is

(1/a - 1/b) / (1/a + 1/b)

The complex fraction is defined as the fraction that consisting fraction on the numerator or denominator or both. The top term is called numerator and the bottom term is called denominator

Here the given complex fraction is

(1/a - 1/b) / (1/a + 1/b)

Cross multiply the terms of the complex fraction

(b - a) / ab / (b + a) / ab

The denominator of the complex fraction became equal

Hence, the common denominator is ab

I have answered the question is general, as the given question is incomplete.

The complete question is:

What is the common denominator of 1/a + 1/b in the complex fraction (1/a - 1/b)/(1/a + 1/b)?

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The number that should be multiplied by 2/3 to get a product 1 is 3/2

What is the Reciprocal of two numbers?

One of two numbers that, when multiplied together, equals to 1 is known as a reciprocal or multiplicative inverse.

Transposing the numerator and denominator will allow you to get the reciprocal if you can reduce the number to a fraction.

Let the number that would result in product 1 be "x"

So, According to the question:

=> x × 2/3 = 1

Solving for x,

Dividing by 3/2 both sides

⇒x = 3/2 which is the reciprocal of 2/3

Hence,

The number that should be multiplied is 3/2

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The length of the shadow is 8. 06m

The Pythagorean theorem states that the square root of the hypotenuse is equal to the sum of the squares of the other two sides

This is expressed as;

a² = b² + c²

Where;

33² = 32² + c²

1089 = 1024 + c²

collect like terms

c² = 1089 - 1024

c² = 65

Find the square root

c = √65

c = 8. 06m

Hence, the value is 8. 06m

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All the inequalities that model the given situation are;

x + y ≥ 25

x > 10

y > 0

We are told that;

x represents the number of apples.

y represent the number of oranges.

Now, Mia needs to bring at least 25 pieces of fruit to the school picnic. Thus, the inequality is expressed as;

x + y ≥ 25

She is bringing both apples and oranges, and was told to be sure to bring more than 10 apples. Thus, the inequality is expressed as;

x > 10

Since we are not told the maximum number of oranges, then we can say it must be more than zero and as such we have the third inequality as; y > 0

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On solving the given question, we got Area of the base prism = bh/2 = (4.819 X 51)/2 = 122.89 cm2

A prism is a polyhedron in geometry that has an n-sided polygonal basis, a second base that is a shifted version of the first base, and n additional faces—necessarily all parallelograms. Connect the matching sides of the two bases.

h = 51 cm

a = 2cm

therefore,

volume of a Triangular Prism = (½) abh cubic cm

245.8 = [tex]\frac{1}{2}[/tex] X 2 X b X 51

[tex]= > b = \frac{245.8 X 2}{2 X 51}[/tex]

[tex]= > b = \frac{491.6}{102}[/tex]

[tex]= > b = 4.819[/tex]

Now Area of base of prism

Area of the base prism = bh/2 = (4.819 X 51)/2 = 122.89 cm2

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The amount of lavender oil y is proportional to the amount of jojoba oil x

Two quantities are said to be linearly proportionate if change in one quantity produce proportionate amount of change in the other quantity, or the ratio of the two quantities is fixed.

Given,

In the first case, 20 drops of lavender oil and 8 teaspoons of jojoba oil.

In second case, 50 drops of lavender and 20 teaspoons of jojoba oil.

Ratio in first case:

x:y  =  20:8

      = 5:2

Ratio in second case:

x:y  =  50:20

      = 5:2

Since ratio is fixed in both the cases, the amount of lavender oil y is proportional to the amount of jojoba oil x.

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Answer:

graph A

Step-by-step explanation:

If you use a graphing calculator to solve this you just swap the x and y so:

[tex]y=5\sqrt{x+3}-2\implies x=5\sqrt{y+3}-2[/tex] and then choose whichever aligns with the graph most accurately (graph A). I attached an image using desmos.

If you want to solve for y, you first add 2

[tex]x+2=5\sqrt{y+3}[/tex]

divide both sides by 5

[tex]\frac{x+2}{5}=\sqrt{y+3}[/tex]

square both sides

[tex](\frac{x+2}{5})^2=y+3[/tex]

subtract 3 from both sides

[tex](\frac{x+2}{5})^2-3=y[/tex]

distributing the exponent we get:

[tex](\frac{(x+2)^2}{25})-3=y[/tex]

move the 1/25 infront

[tex]\frac{1}{25}(x+2)^2-3=y[/tex]

we actually have the vertex since it's in vertex form (-2, -3) and you may be asking why this is important, well in an inverse function the domain and range are swapped, and in original function it had a range of y values greater than or equal to -2, so this is the domain of the new function... this conveniently happens at the vertex where this function goes from decreasing to increasing and continues to increase on the rest of the domain. This means the inverse function is increasing for all values of x and only graph A has this property, so it's the only plausible answer

The cartons of food and clothing that should be sent to maximize the number of people assisted are 300 and 400 respectively.

In order to determine the required number of cartons of food and clothing, we would have to first of all write a system of equations that models the situation.

Additionally, we would assign variables to the carton of food box and number of accessories sold, and then translate the word problem into algebraic equation as follows:

Therefore, translating the word problem into algebraic equation, we have the following:

20x + 30y ≤ 18000      ......equation 1.

40x + 10y ≤ 16000      ......equation 2.

Dividing both equations 1 and 2 by 10, we have:

2x + 3y ≤ 1800

4x + y ≤ 1600

Next, we would solve the system of equations simultaneously as follows:

2x + 3(1600 - 4x) ≤ 1800

2x + 4800 - 12x ≤ 1800

-10x ≤ -3000

x ≤ 3000/10

x ≤ 300

For the value of y, we have:

y ≤ 1600 - 4(300)

y ≤ 1600 - 1200

y ≤ 400

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Complete Question:

An agency wants to ship food and clothing to hurricane victims in Louisiana. Commercial carriers have volunteered to transport the​ packages, provided they fit in the available cargo space. Each ​20ft³ box of food weighs 40 lb and each ​30 ft³ box of clothing weighs 10 lb. The total weight cannot exceed​ 16,000 lb, and the total volume must be at most​ 18,000 ft³. Each carton of food will feed 8 ​people, while each carton of clothing will help 8 people.

How many cartons of food and clothing should be sent to maximize the number of people assisted?

Her son mowed the most lawn

35%of the lawn meeds to be mowed

Answer:

x = 8

Step-by-step explanation:

0.6x = 4.8

Divide both sides by 0.6

0.6x / 0.6 = x

4.8 / 0.6 = 8

x = 8

We will see that the base is between 0 and 1, so the function is an exponential decay.

A general exponential function is written as:

f(x) = A*(b)^x

Where A is the initial value, and b is the base.

if b > 1, we have an exponential growth.

if 0 < b < 1, we have an exponential decay.

Here the function is:

f(x) = 25*e^(-2x)

We can rewrite this as:

f(x) = 25*(e^-2)^x

If we solve it for the base, we have that:

b = e^-2 = 1/e^2 = 0.14

Then we can write the exponential function as:

f(x)=  25*(0.14)^x

So this is an exponential decay.

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Answer: ([tex]\frac{-3}{5}[/tex], 1) and ([tex]\frac{-3}{5}[/tex], 3) are two you could use, but there are countless possibilities.

Step-by-step explanation:

   To solve this question, we will first isolate the variable x.

       -5x = 3

       [tex]\displaystyle \frac{-5x}{-5} =\frac{3}{-5}[/tex]

       x = [tex]\frac{-3}{5}[/tex]

   Next, we will find points that satisfy the equation. Any value in the y-coordinate will work as long as x = [tex]\frac{-3}{5}[/tex]. Some examples:

([tex]\frac{-3}{5}[/tex], 1)

([tex]\frac{-3}{5}[/tex], 6)

([tex]\frac{-3}{5}[/tex], -4)

([tex]\frac{-3}{5}[/tex], [tex]\frac{1}{2}[/tex])

([tex]\frac{-3}{5}[/tex], 0)

     Etcetera.

   I have attached a graph with two of the examples to further show. This graph uses ([tex]\frac{-3}{5}[/tex], 1) and ([tex]\frac{-3}{5}[/tex], 6). Negative three-fifths is equal to -0.6.

A method for deriving facts is to multiply by 10 or to add using 10. This means that before using the make-ten strategy, kids need to know some facts by hear. Use of a make 10 strategy requires knowing that 8+2=10 and 9+1=10. In order to use the make 10 strategy, add 8 and 5, then decompose 5 into 2 and 3.

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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The solution for m in the inequality expression is m  < -139

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

m+14<−125

Subtract 14 from both sides of the inequality

So, we have

m + 14 - 14 <−125 - 14

Evaluate the like terms

This gives

m  < -139

Hence, the solution is m  < -139

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The complete table of values of the linear equation y = -3x - 4 is

x     y

-1     -1

0     -4

1     -7

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

y = -3x - 4

Also, we have the following table of values

x     y

-1

0

1

The above table of values mean that the x values are

x = -1, 0 and 1

Substitute x = -1, 0 and 1 in the equation y = -3x - 4

So, we have the following representation

When x = -1

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

When x = 0

y = -3(0) - 4 = -4

When x = 1

y = -3(1) - 4 = -7

So, we have the following ordered pairs

(-1, -1), (0, -4) and (1, -7)

When represented on the table of values, we have

x     y

-1     -1

0     -4

1     -7

The above represents the complete table of values

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Answer:

A

Step-by-step explanation:

the x of each point is moved by three units to the left, while the y is moved by 6 units upstairs

Exponential decay graph looks like see the given image attached.

The process of diminishing an amount by a constant percentage rate over time is known in mathematics as exponential decay. The quantity drops gradually, followed by a dramatic decline in the rate of change and growth over time.

A linear function reduces the original number by the same amount each time, but exponential decay reduces the original amount by a constant percentage over time. Exponential decay differs from linear decay in this way: the decay factor depends on a percentage of the original quantity.

The exponential decay formula is used to determine this decline in growth.

Formula of exponential decay is given by

Its graph is given by

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The number of minutes for 20 bacteria be left is 439minutes. The decay constant is 0.0081

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

The No of bacteria left at a particular time t is given as N(t)= Noe^-kt

where No= initial number of bacteria

k= decay constant and t = time

after 13 minutes

630= 700e^-13k

divide both sides by 700

630/700= e^-13k

0.9= e^-13k

ln0.9= -13k

k= ln0.9/-13 = -0.1054/-13 = 0.0081

time for 20 bacteria to be left =

20= 700e^-0.0081t

= 20/700=e^-0.0081t

0.0286= e^-0.0081t

ln0.0286= -0.0081t

-3.554= -0.0081t

divide both sides by -0.0081

t= -3.554/-0.0081= 439 minutes ( nearest minutes)

therefore the time for the bacteria to be left is 439minutes

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How to find a parabola's equation using its Vertex Form

Step 1: use the (known) coordinates of the vertex, (h,k), to write the parabola's equation in the form: y=a(x−h)2+k. ...

Step 2: find the value of the coefficient by substituting the coordinates of point P into the equation written in step 1 and solving for a.