Use the Binomial Theorem and substitution to expand each Binomial. Show your step.
A) (3x+y)^4
B) (x-2y)^6

On solving the provided question, we can say that the function is y = f(x) and (7.-6) and (7,3); nm = 3+6//-/7 => m = not defined

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

the function is

y = f(x)

and (7.-6) and (7,3)

m = 3+6//-/7

m = not defined

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Answer:

Um, answer my recently asked question l ol It's called"Their eyes were watching god" and im on ch 5.

Step-by-step explanation:

Answer:

answer my recently asked question please.

In order to solve for the missing sides of a right triangle, you need to use the Pythagorean Theorem.

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The bought amount of banana is less than 3 pounds, found from the conversion and this, it will not be enough.

As per the known information, 1 ounce is equivalent to 0.0625 pound. Based on this information, the amount of bought banana will be calculated.

So, the amount of banana = bought amount of bananas in ounces × value of one ounce

The amount of bought banana = 42 × 0.0625

Performing multiplication on the Right Hand Side of the equation

The amount of bought banana = 2.625 pounds

The bought amount of banana is less than the required amount. Therefore, the bought amount will not be enough.

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Answer: 42258

Step-by-step explanation:

multiply by 2 because if 1 hour is 21,189 feet 2 hours is 2 times more!

Hope this helps!

Answer:

1:5 or in decimal terms 0.2

Step-by-step explanation:

hope this help

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The required retail price is $44 for the markdown of 20% with an original price of $55.

The retail price is calculated by the formula,

retail price = original price - a markdown

Now markdown is calculated from the markdown percentage i.e.,

markdown = (original price) × markdown percentage

Calculation:

The given original price = $55

Markdown percentage = 20% = 0.2

So, the markdown value = $55 × 0.2 = $11

Then, the retail price = original price - a markdown

retail price = $55- $11 = $44

Therefore, the retail price is $44.

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Out of 100 observations, 10% of them were the number 3.

Percentage is a way of expressing a proportion or a fraction as a part of 100. It is a common method used in everyday life and in various fields, including finance, statistics, and education.

To determine the percentage of time a 3 was observed, you need to first find the number of occurrences of the number 3 in a given set of data. Let's say, you have a set of 100 observations and 10 of them are 3.

To find the percentage of time a 3 was observed, divide the number of occurrences of the number 3 (10) by the total number of observations (100) and multiply the result by 100.

Percentage = (10/100) * 100

Percentage = 10

Therefore, the percentage of time a 3 was observed is 10%.

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If line L passes through point (1, 2, 3) and is perpendicular to the xy-plane,  the coordinates of the points on the line which are at a distance 7 from the point P(3,-1, 5) are (1, 2, 11) or (1, 2, -1).

Equation of the xy - plane is z = 0. So, direction ratio perpendicular to xy - plane is (0,0,1)

So, the equation of line passing point (1, 2, 3) and is perpendicular to the xy-plane is:

          x-1/0 = y-2/0 = z-3/1 = t (say)

x = 1, y = 2 and z = t + 3

Let, (1, 2, t+3) be any point on the line that is at a distance 7 units from the point (3, -1, 5)

Then, ( (1 - 3)² + (2 + 1)² + (t + 3 - 5)²)^1/2 = 7

                                          4 + 9 + (t - 2)² = 49

                                                      (t - 2)² = 36

                                                         t - 2 = ± 6

                                                              t = 8, -4

Hence, the coordinates of the points on the line which are at a distance 7 from the point P(3,-1, 5) are (1, 2, 11) or (1, 2, -1).

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The separation between a 6.8 kg particle and a 3.7 kg particle in order for their gravitational attraction to have a magnitude of 2.9 ✕ 10^−12 N will be 24 m.

m₁ = 6.8 kg

m₂ = 3.7 kg

F = 2.9×10^−12 N

We want to determine the distance r between both particles. The gravitational force on particle 2 due to particle 1 has the same magnitude as the force on particle 1 but in the opposite direction. If a distance r separates two masses, then the magnitude of the gravitational force acting on each due to the presence of the other is given by

F = Gm₁m₂/r²     Eqn(1)

Where G is the gravitational constant and equals 6.6×10^−11 N⋅m²/kg².

By solving equation (1) for r, we get

r = √(Gm₁m₂/F)

Now we can plug our values for m₁, m₂ and G into equation (2) to get the separated distance r

r = √(Gm₁m₂/F)

= √{[(6.6×10^−11 N⋅m²/kg²)(6.8 kg)(3.7 kg)]/(2.9×10^−12 N)}

​= 24 m

The gravitational force is very small due to the small masses where this force is indistinguishable.

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In the given case-Equivalent ratios are created by multiplying or dividing the two terms of a ratio by the same number.

What are ratios used for?

The ratio is written as a/b when the ordered pair's second number, b, is not equal to 0. A ratio can be used to compare similar quantities or show relationships between them. We use ratios to contrast comparable items.

The ratio between two numbers when they are measured in different units is expressed using a rate. A ratio in mathematics depicts the quantity of smaller numbers that make up a larger number.

The equivalent ratios are linked to one another through the multiplication of a number. To create equivalent ratios, a ratio's two terms must be multiplied or divided by the same number.

8 : x = 2 : 1

x = 4 (hours)

8 : x = 1 : 4

x = 32 (hours)

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The amount of pounds of sweet potatoes that she uses to buy paper is 35/8.

To model the problem with a tape diagram, we can draw 5 boxes representing the 5 pounds of white potatoes, and then draw 7/8 of that number of boxes to represent the number of sweet potatoes.

[5 white potatoes]

[4 sweet potatoes (7/8 * 5 = 7/8)]

Hence, since Maribella bought 5 pounds of white potatoes

This becomes 5x7/8= 35/8

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The unit rate at which the barber cuts the hair is then 16:1.

What is meant by the ratio and rate?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

In contrast, a rate is a comparison of two quantities that may have different units. A rate is a unique ratio that differs somewhat from a ratio. It compares measures with other units. A rate having a denominator of 1 is known as a unit rate.

Given,

   number of haircuts in 2 days = 32

So the number of haircuts in 1 day = 32/2= 16

Therefore the unit rate at which the barber cuts the hair is then 16:1.

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Answer:

If 3 brownies require 3/4 cups of flour, then 12 brownies will require 12/3*(3/4) = 3 cups of flour.

Step-by-step explanation:

Answer:

3 cups of flour

Step-by-step explanation:

We know

3/4 cups of flour = 3 brownies

? = 12 brownies

12 brownies are 4 times 3 brownies, so we take 3/4 cups of flour times 4

3/4 times 4 = 3 cups of flour

So, you need 3 cups of flour for 12 brownies

This equation depicts all x values such that -3 x 2 is true. These values encompass every real figures within -3 and 2, but not the actual integers -3 and 2.

The concept of an equation in algebra is a statistical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A range of variables for x are represented by the inequality -9 4x + 3 11 in which they meet the inequality. We must first isolate x solely on a single side of the discrepancy before determining the variable x that cause the inequality to hold true.

First, subtract 3 from both sides:

-12 < 4x < 8

Next, divide both sides by 4:

-3 < x < 2

This solution represents all values of x such that -3 < x < 2. These values include all real numbers between -3 and 2, but do not include -3 and 2 themselves.

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The probability that we have picked exactly n cards by multiplying the probability of picking each card, which is [tex]$\frac{13}{52}[/tex]

Verified that, after taking summation over n = 1, 2, . . ., the sum of the probabilities above equals to 1.

(1) The probability of picking exactly n cards to cover all 4 shades can be calculated as follows:

For n = 1, the probability of picking exactly 1 card is 0, as it is not possible to pick only one card and cover all 4 shades.

For n = 2, the probability of picking exactly 2 cards is:

[tex]$=(\frac{13}{52})\times (\frac{12}{52} )\\\\= \frac{13\times12}{52\times 52}[/tex]

For n = 3, the probability of picking exactly 3 cards is:

[tex]$=(\frac{13}{52})\times (\frac{12}{52} )\times(\frac{11}{52}) \\\\= \frac{13\times12\times11}{52\times 52\times52}[/tex]

And so on, we can calculate the probability of picking exactly n cards by multiplying the probability of picking each card, which is [tex]$\frac{13}{52}[/tex].

(2) To verify that the sum of the probabilities is equal to 1 , we can add up the probabilities for all values of n from 1 to 52 :

[tex]$& \mathrm{P}=\left(\frac{13}{52}\right) \times\left(\frac{12}{52}\right)+\left(\frac{13}{52}\right) \times\left(\frac{12}{52}\right) \times\left(\frac{11}{52}\right)+\ldots+\left(\frac{13}{52}\right) \times\left(\frac{12}{52}\right) \times \ldots \times \frac{52-(\mathrm{n}-1)}{52} \\[/tex]

P = 1

This verifies that the sum of the probabilities is equal to 1.

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From a set of 52 poker cards (without 2 jokers), we keep taking cards randomly one by one with replacement, until all the cards taken by us can cover all 4 shades.

(1) Compute the probability that we have picked exactly n cards.

(2) Verify that, after taking summation over n = 1, 2, . . ., the sum of the probabilities above equals to 1.

The slope for the trend line for the scatter plot shown is option B: 3.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The first two data points obtained form the graph is -

(1,8) and (2,11)

The slope of a line can be found using the formula -

m = (y2 - y1) / (x2 - x1)

Substitute the values into the equation -

m = (11 - 8) / (2 - 1)

Apply the arithmetic operation of subtraction -

m = 3 / 1

Apply the arithmetic operation of division -

m = 3

Therefore, the slope value is 3.

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Answer:

So, Lake Erie is 3/8 the size of Lake Superior.

Step-by-step explanation:

To find the size of Lake Erie in comparison to Lake Superior, we need to first find the size of Lake Michigan in relation to Lake Superior. If Lake Michigan is about 7/8 the size of Lake Superior, we can say that:

Lake Michigan / Lake Superior = 7/8

Next, we need to find the size of Lake Erie in relation to Lake Michigan. If Lake Erie is about 3/7 the size of Lake Michigan, we can say that:

Lake Erie / Lake Michigan = 3/7

Now, we can use these two relationships to find the size of Lake Erie in relation to Lake Superior. To do this, we can cross-multiply and simplify:

Lake Erie / Lake Michigan = 3/7

(Lake Erie / Lake Michigan) * (Lake Michigan / Lake Superior) = (3/7) * (7/8)

Lake Erie / Lake Superior = (3/7) * (7/8) = 3/8

So, Lake Erie is 3/8 the size of Lake Superior.

The polygons that are congruent are as attached.

Congruent polygons are two or more polyggon shapes that have the same size and shape. In other words, they have the same number of sides, the same length of sides, and the same interior angles. If you were to superimpose one congruent polygon over the other, they would perfectly fit and cover each other.

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The map scale is printed in the map legend. It is given as a ratio of inches on the map corresponding to inches, feet, or miles on the ground. For example, a map scale indicating a ratio of 1:24,000 (in/in), means that for every 1 inch on the map, 24,000 inches have been covered on the ground.

The both integral and differential form of conservation law will be equivalent.

Differentiation and Integration are the two major concepts of calculus. Differentiation is used to study the small change of a quantity with respect to unit change of another.

On the other hand, integration is used to add small and discrete data, which cannot be added singularly and representing in a single value.

Integral and differential forms of the conservation law:

Both the farms are equivalent only. Integral form is applied to a region in spore (control volume). Differential form is formulated for an infinitesimal fluid particle.

Integral form:

for any control volume (Ω),

[tex]$$\begin{aligned}\frac{d}{d t} \int_{\Omega} u d v & =\text { Infher through } \partial \Omega \\& =\int_{\partial \Omega} \ \vec{f} (u) \cdot(-\vec{h}) d A+\int_{\Omega} g d \omega\end{aligned}$$[/tex]

Integrating and changing the above Equation,

We get,

[tex]\frac{\partial u}{\partial t}[/tex][tex]+\nabla \cdot f(u)=g[/tex]

By Divergence theorem,

[tex]$$\begin{gathered}\int_{\delta u} \frac{I}{f} \cdot \vec{n} d A=\int \nabla \cdot \bar{f} d v \\\frac{d}{d t} \int_{\Omega} u d w+\int_{\Omega} \nabla \cdot \bar{f} d v=\int_{\Omega} g d v \\\frac{\partial u}{\partial r}+\nabla \cdot \bar{f}(h)=g\end{gathered}$$[/tex](integral form)

Differential form: for can arbitrary control volume the integrand must be saw yielding the differential Equation.

[tex]& \frac{\partial}{\partial t} \int f \hat{\jmath}+\int P \tilde{v} \cdot d \vec{A} \\[/tex]

[tex]& \int \rho \vec{v} \cdot d \vec{A}=\left(-\left|\rho u-y / \partial x\left(f(x) \frac{d_2}{x}\right) d_y d_z\right|\right. \ )[/tex]

[tex]& \frac{\partial f}{\partial t} d_x d_y d_z=\left(\frac{\partial \beta_u}{\partial x}+\frac{\partial e v}{\partial y}+\frac{\partial e w}{d z}\right) d{_x}d_ y d_z} \\[/tex]

[tex]& 0=\frac{\partial f}{d t}+\frac{\partial P_u}{\partial x}+\frac{\partial P v}{\partial y}+\frac{\partial P w}{\partial z} \\[/tex]

[tex]& \vec{\nabla} \cdot \vec{F}=\frac{\partial A_x}{\partial x}+\frac{\partial A_1}{\partial y}+\frac{\partial A_2}{\partial_2} \\[/tex]

[tex]& \nabla \cdot(P \vec{v})=\frac{\partial P_n}{\partial}+\frac{\partial P_v}{\partial u}+\frac{\partial P_w}{\partial 2} \\[/tex]

[tex]& \left.\frac{\partial s}{\partial t}+\nabla \cdot(A \vec{v})=9\right)[/tex] (Differential form)

From the hint of two equations, we can evaluate that both integral and differential form of conservation law will be equivalent.

Therefore, both integral and differential form of conservation law will be equivalent.

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Answer:

Area = (1/2) x (12)(15)sin(92)

If we take a ride that goes around 5 times, we will travel for 502.86 feet. The result is obtained by using the formula for circumference.

Circumference is the perimeter of a circle. It can be calculated by the following formula.

C = 2πr

Where

A Ferri wheel has a radius of 16 feet. If you take a ride that goes around 5 times, determine the distance you traveled!

(Round answer to the nearest hundredth and for pi use π = 22/7)

The shape of the wheel is round (a circle). The distance traveled is the circumference multiplied by the number of rounds.

We have

Distance traveled

= C × n

= 2πr × 5

= 2(22/7)(16) × 5

= 502.86 feet

Hence, the distance traveled by the wheel is 502.86 feet.

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Answer: 16 meters

Step-by-step explanation:

1 cm         4cm

--------    =  ---------

4m             16m

No, because the slope of AB is 5/3 and the slope of CD is -3/4.

The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = 1/6 is a vertical line with a slope that is undefined.

A line's steepness may be determined by its slope. In measuring slopes mathematically, "rise over run" is being used (change in y divided by change in x).

The vertical difference between two places, known as the rise, and the horizontal difference between those same two points, known as the run, is known as the slope. It is referred to as the slope-intercept version of the equation if the equation of a line is expressed as y = mx + b. Slope is indicated by "m". And b is the value in the y-intercept point (0, b).

The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = 1/6 is a vertical line with a slope that is undefined.

Thus, the correct option is: C

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If the sequence is aₙ = n/2n²+1 then the process to show the sequence is monotone decreasing for n≥1 is shown below .

To show that the Sequence "aₙ = n/2n²+1"  is monotone decreasing for n ≥ 1, we need to prove that for any two consecutive terms of the sequence, the next is always less than or equal to the previous one .

Let's compare two consecutive terms of the sequence, aₙ and aₙ+1:

⇒ aₙ = n / 2n² + 1  

So , aₙ₊₁ = (n + 1)/2(n + 1)² + 1

we have to show that aₙ₊₁ ≤ aₙ, we can subtract aₙ from both sides:

⇒ aₙ₊₁ - aₙ = [(n + 1)/2(n + 1)² + 1] - [n/2n² + 1]  ;

We can simplify this expression and get ;

⇒ aₙ₊₁ - aₙ = (n+1-n)/2(n+1)²+(1-1)

⇒ aₙ₊₁ - aₙ = 1/2(n + 1)²

the fraction ,  1/2(n + 1)² > 0 for all n ≥ 1,
that means ⇒ aₙ₊₁ - aₙ > 0 ; ⇒  aₙ > aₙ₊₁ ;

Therefore,  the sequence " aₙ " is monotone decreasing for n ≥ 1.

The given question is incomplete , the complete question is

A Sequence is given by the formula aₙ = n/2n²+1 . Show the sequence is monotone decreasing for n≥1.

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If the length, width, and height of a right rectangular prism are halved, the surface area will be reduced by a factor of four.

The surface area of a right rectangular prism can be calculated by adding up the areas of all six of its faces.

To see why, consider that each of the original face's area was given by the product of two of the original dimensions. If each of those dimensions is halved, the area of each face is reduced to one-fourth of its original size. Because there are six faces, the total surface area is reduced by a factor of four.

In other words, if the original surface area was 2 * (44 cm * 22 cm + 44 cm * 77 cm + 22 cm * 77 cm) = 6176 square cm, the surface area of the halved rectangular prism would be 6176 square cm / 4 = 1544 square cm.

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In linear equation, $ 1300 is the cost for 80 employees.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.      

                             The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Given that cost of a company picnic varies directly as the number of employees attending the picnic

Let "c" be the company picnic cost

Let "n" be the number of employees attending the picnic

Therefore,

 cost ∝ number of employee attending picnic

       c ∝ n

   c = kn

Where "k" is the constant of proportionality

c = kn ---------- eqn 1

Given that company picnic costs $487.50 for 30 employees

Therefore substitute c = 487.50 and n = 30

   487.50 = k(30)

  k =   487.50/30

   k = 16.25

Substitute n = 80 and k = 16.25 in eqn 1

    c = 16.25(80)

    c = 1300

Thus $ 1300 is the cost for 80 employees.

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[tex]5(2x+7)=4x-3[/tex]

Distribute numbers outside of parentheses:

[tex](5)(2x)+(5)(7)=4x-3[/tex]

[tex]10x+35=4x-3[/tex]

Subtract 4x from both sides:

[tex]10x+35-4x=4x-3-4x[/tex]

[tex]6x+35=-3[/tex]

Subtract 35 from both sides:

[tex]6x+35-35=-3-35[/tex]

[tex]6x=-38[/tex]

Divide both sides by 6:

[tex]\dfrac{6x}{6} =\dfrac{-38}{6}[/tex]

[tex]\boxed{x = -\frac{19}{3} }\texttt{ or }\boxed{x =-6.33}[/tex]

Answer:

x = -19/3

Step-by-step explanation:

Given equation,

→ 5(2x + 7) = 4x - 3

Now the value of x will be,

→ 5(2x + 7) = 4x - 3

→ 10x + 35 = 4x - 3

→ 10x - 4x = -3 - 35

→ 6x = -38

→ x = -38/6

→ [ x = -19/3 ]

Hence, value of x is -19/3.

Considering Moses Road is 7 kilometres long, then that would take Moses roughly 21 minutes and 30 seconds to make the route at his top speed of 21 kilometres per hour.

Speed is referred to as the rate at which an object's location changes in any direction. Speed is defined as the ratio of distance travelled to time spent travelling. Because it has just one direction and no scale, speed is a scalar number.

Step 1: Determine the total distance travelled (7 km)

Step 2: Determine how long it takes to traverse the distance (7 km/21 km/h = 0.333 h = 20 min).

Step 3: Accounting for the half km/h, add 30 seconds to the overall time (20 minutes + 0.5 minutes = 20.5 minutes).

Step 4: To the closest minute, round the total time (20.5 minutes = 21 minutes).

As a result, at the maximum speed of 21 km/h, Moses will finish the route in around 21 minutes.

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