The following sequence of steps shows why you can square binomial the short way. For each step, name the definition or property that justifies the step.

(a+b)²
a. = (a+b)(a+b)
b. = (a +b)(a) + (a+b)(b)
c. = a² + ba + ab + b²
d. = a² + 2ab + b²

Answer:

1 tube of paint is $2.25.

Step-by-step explanation:

We can set this as an equation first. Since we know that the canvas is $6.95 and the total is $24.95, those are the values that we will work with to determine the tube price. We can set the tube price as 8x, x being the tube price, and 8 being the number of tubes Ishi plans to buy. Now, we can set an equation:

6.95 + 8x = 24.95

8x = 18

x = 18/8 (simplified is 9/4, or 2.25)

Answer:

$ 2.25

Step-by-step explanation:

A= $6.95

B= (Cost of each tube) x 8

C= $24.95

A+B = C

The Area and perimeter of the triangle is given by 75m² and 33.02 m respectively.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: A right triangular garden with base 10m and  height 15 m

We know the area of a triangle is given by A=1/2×b×h where b=base and h=height. And the perimeter of a triangle is given by sum of all sides.

Thus Area of triangular Garden =1/2×10×15

                                                    =75 m²

And the perimeter the triangle is given by=10+15+[tex]\sqrt{10^2+15^2}[/tex]

                                                                      =10+15+18.02

                                                                      =33.02 m

Hence, The Area and perimeter of the triangle is given by 75m² and 33.02 m respectively.

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He used [tex]$=1 \frac{7}{8} \mathrm{lb}$[/tex] . An algebraic equation, often known as a polynomial equation

Determine the number of pounds used

To solve this, we simply multiply the fraction of tomato used by the total;

[tex]Used $=$ Fraction $*$ Total[/tex]

Used[tex]=\frac{5}{8} * 3 l b$[/tex]

Used[tex]=\frac{5 * 3}{8} l b$[/tex]

Used = 15/8 lb

Convert to mixed number

Used [tex]$=1 \frac{7}{8} \mathrm{lb}$[/tex]

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The measure of ∠ADB is equivalent to 90°.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

Given is a geometrical image as shown.

We can write -

∠ADC = ∠ADB + ∠BDC

(- 3c + 120°) + (- 10 c + 145°) = 135°

- 3c + 120° - 10c + 145° = 135°

- 13c + 265° = 135°

265° - 135° = 13c

13c = 130

c = 10

Now -

∠ADB = (- 3c + 120) = 90°

∠ADB = 90°

Therefore, the measure of ∠ADB is equivalent to 90°.

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The answer is 9n²-48n+64

The sampling distribution is approximately normal.

What is the standard deviation?

Standard Deviation is calculated by first squaring the differences between the observations and the mean and then taking the square root of the sum of the squares of the differences divided by the number of observations - 1.

The Central Limit Theorem tells us that the sampling distribution for the population proportion is approximately normal.

The mean of the sampling distribution is equal to the true population proportion and the standard deviation of the sampling distribution is equal to the true population proportion times (1 - true population proportion) divided by the sample size.

So, the sampling distribution is approximately normal, with the true population proportion as its mean and the true population proportion times (1 - true population proportion) divided by the sample size as its standard deviation.

Hence, the sampling distribution is approximately normal.

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The minimum amount of paint needed to paint the walls of the room would be 2,2 gallon.

To calculate the amount of paint we need to paint the walls of the room we must calculate the area of each of the walls, in this case it would be 4 rectangles with the following dimensions:

According to the above, the area of the walls would be:

Based on the above, it can be inferred that 2.2 gallons of paint are needed to paint all the walls.

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Answer:

The derivative of the function f(x) = 3x² + 2√x - 4x at x=1 is

[tex]\boxed{f'(1) = 3}[/tex]

Step-by-step explanation:

We have f(x) = 3x² + 2√x - 4x

[tex]f'(x) = \dfrac{d}{dx}\left(3x^2+2\sqrt{x}-4x\right)\\\\=\dfrac{d}{dx}\left(3x^2\right)+\dfrac{d}{dx}\left(2\sqrt{x}\right)-\dfrac{d}{dx}\left(4x\right)\\\\[/tex]

[tex]\dfrac{d}{dx}\left(3x^2\right) = 6x\\\\[/tex]

[tex]\dfrac{d}{dx}\left(2\sqrt{x}\right) = 2\dfrac{d}{dx}\left(\sqrt{x}\right)\\\\=2\dfrac{d}{dx}\left(x^{\frac{1}{2}}\right)\\\\= =2\cdot \dfrac{1}{2}x^{\frac{1}{2}-1}\\\\\\=\dfrac{1}{\sqrt{x}}\\\\[/tex]

[tex]\dfrac{d}{dx}\left(4x\right)=4[/tex]

Therefore

[tex]f'(x) = 6x+\dfrac{1}{\sqrt{x}}-4\\\\f'(1) = 6(1) + \dfrac{1}{\sqrt{1}} - 4\\\\f'(x) = 6 + 1 - 4\\\\f'(x) = 3\\\\[/tex]

A concentration of the majority of  Muslim population of the country is on one island, leading to ethnic separatism.

Ethnic Separatism is the process by which a nation or ethnic group makes efforts to become more autonomous from the central government of a state, or even secedes, when it is unhappy with any combination of social, economic, and political conditions in the nation in which it is located.

When an ethnic group actively works to assert its rights and importance, ethnic nationalism is the result. When it serves the interests of the state, governments may support ethnic nationalism as a project; however, for a variety of reasons, ethnic nationalism may also pose a threat to the state. Separatism based on ethnicity is one of these causes. Find out what ethnic separatism is, some examples of it, and more by continuing to read.

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Full question:

THE PHILIPPINES, 2010

Total Population

Roman Catholic Population

Percent Roman Catholic

Muslim Population

Percent Muslim

92 million74 million

80.6%

5.1 million

5.6%

THE PHILIPPINE ISLAND OF MINDANAO, 2010

Total Population

Roman Catholic Population

Percent Roman Catholic

Muslim Population

Percent Muslim

18 million

10.9 million

60.9%3.7 million

20.4%Source: Philippines Statistics Authority

The cultural composition of the Philippines and its constituent islands affects the political stability of the country. Which of the following patterns is best explained by the data in the tables?

A. An even dispersal of Muslims around the country, leading to assimilation

B.An even dispersal of Muslims around the country, leading to ethnic separatism

C. An even dispersal of Muslims around the country, leading to irredentism

D. A concentration of the majority of the country’s Muslim population on one island, leading to assimilation

E. A concentration of the majority of the country’s Muslim population on one island, leading to ethnic separatism

A vector diagram showing the vector OE denoted by a + 2b is as attached.

Vector diagrams can be used to improve visualization and understanding of the magnitude and direction of vectors, and more importantly how multiple vectors interact.

For example, if Peter is pushing a heavy container towards the west, while John is pulling it in the northwest direction, in what direction does the container actually move?

A vector diagram is what will be useful in finding the answer.

Now, we see the vectors  OC and OD denoted by a + b and a − b in the attached diagram. Now, if we want to find a + 2b, we know that a + b will be a resultant but by use of vector analysis, we can plot a + 2b as seen in the first vector diagram attached.

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Answer: Yes

Step-by-step explanation:

Answer:

[tex] \sf \textbf{8.608} \: is \: a \: rational \: number[/tex]

Step-by-step explanation:

Rational Numbers: Any number that can be written as a ratio (or fraction) of two integers is a rational number.

Step-by-step explanation:

(b)

logx . logx = 2log x

logx = 2

so x = 100

(c)

2x + 3x= 10

5x = 10

so ×=2

The largest possible value for the probability of A4 is 0.2000

Since A1, A2, A3, and A4 are events from a common sample space, the sum of their probabilities must be less than or equal to 1.

So, the sum of the probabilities of the events can be expressed as:

P(A1) + P(A2) + P(A3) + P(A4) = 1

From the question, we have

P(A1) = P(A2) = P(A3) = 0.3

Also, we have that

Al and A2 occur simultaneously with a probability of 0.1

This means that the initial equation becomes

P(A1) + P(A2) - P(A1 and A2) + P(A3) + P(A4) = 1

Where

P(A1 and A2) = 0.2

So, we have

0.3 + 0.3 - 0.1 + 0.3 + P(A4) = 1

Evaluate the like terms

P(A4) = 0.2

Hence, the probability is 0.2

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The measure of r is 24°

The opposing angles created by the junction of two lines are known as vertically opposite angles or vertical angles. A pair of angles that are vertically opposed to one another is always equal.

Additionally, the vertical angle and its adjacent angle add up to 180° which is said to be a supplementary angle.

Here we have

3 straight lines are met at a point  

Let's name each name as l, m, and n as the given figure

From the line l  

=> ∠LOM + ∠MON + 122° = 180°  [ Pairs of Linear angles ]

=>  34° + ∠MON + 122° = 180°  

=> ∠MON = 180° - 122°- 34°

=>  ∠MON = 24°  

Here

∠MON and r are two vertically opposite angles

As we know vertically opposite angles are equal

=> r = 24°    

Therefore,

The measure of r is 24°

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the annual expenditure of the US federal government is 4 trillion dollars and dollar bill is 0.001m then, the length of four trillion dollars would be 4×[tex]10^{9}[/tex] m

Government spending or expenditure includes all government

consumption, investment, and transfer payments. In national income accounting, the acquisition by governments of goods and services for current use, to directly satisfy the individual or collective needs of the community, is classed as government final consumption expenditure.

Since we have given that annual expenditure = 4 trillion dollars,

1 dollar bill = 0.0001m

so, the thickness would be.

[tex]4*10^{12} *0.001\\\\=4*10^{12}*10^{-3}\\\\=4*10^{9}[/tex]

the length of 4 trillion dollars would be. 4×[tex]10^{9}[/tex]

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The height that the ladder reaches on the building is 10.7 feet

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

A 14-foot ladder is leaning against a building. The ladder makes a 50° angle with the ground. Let h represent the height of the building. Using trigonometric ratio:

sin(50) = h/14

h = 14 * sin(50)

h = 10.7 feet

The height is 10.7 feet

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1) y-coordinate of the vertex of y = x^2 + 2x - 1 is -1.

2) The statement "the vertex of quadratic function f is (-b/2a, f(-b/2a))" is true.

3) The equation y = -2x^2 - 12x - 17 has a maximum.

What is Quadratic Equation?

A quadratic equation is any equation in algebra that can be rearranged in standard form as where x represents an unknown value and a, b, and c represent known numbers.

1) y = x^2 + 2x - 1 is the equation of a parabola in vertex form.

In vertex form, the equation of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

So, to find the y-coordinate of the vertex, we can substitute the values of a, h and k into the equation and get the y-coordinate.

For the equation y = x^2 + 2x - 1, the vertex is (-1, -1), where -1 is the y-coordinate.

So, the y-coordinate of the vertex of y = x^2 + 2x - 1 is -1.

2) True.

The vertex of a quadratic function f(x) = ax^2 + bx + c is the point on the parabola that represents the graph of the function where the parabola changes direction from opening upward to opening downward or vice versa.

The x-coordinate of the vertex is given by (-b/2a), and the y-coordinate is given by f(-b/2a), where a, b, and c are constants.

So, the statement "the vertex of quadratic function f is (-b/2a, f(-b/2a))" is true.

3) maximum

The equation y = -2x^2 - 12x - 17 is a quadratic function, and it is in vertex form.

The leading coefficient is -2 which is negative, so the parabola opens downward, which means the vertex of the parabola represents the maximum point of the function. Therefore, the equation y = -2x^2 - 12x - 17 has a maximum.

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Answer:

The company's largest rug dimensions are either 18 ft by 27 ft Or 12 ft by 18 ft.

Step-by-step explanation:

Given:

Dimension of the smaller rug are 2 ft by 3 ft.

Also One side of the largest rug is 18 ft.

We need to find the possible dimension of largest rug.

Also Given:

Both the smaller rug and larger rugs are similar.

Now By Similar rectangles property which states that;

"When 2 rectangles are similar then their lengths are in proportion."

In this case there are 2 possibilities.

either the largest rug's 18 ft side is similar to the 2 ft side or the 3 ft side

Now let us consider the other side be 'x'.

Now when he largest rug's 18 ft side is similar to the 2 ft side we get;

Now when he largest rug's 18 ft side is similar to the 3 ft side we get;

Hence the company's largest rug dimensions are either 18 ft by 27 ft OR 12 ft by 18 ft.

Answer:37,396

Step-by-step explanation:

The obtained Z score for the following blood pressures =-2

Enter data in Excel work sheet and use the formulae

=VAR(A1:A6)  and =VAR(B1:B6)  to get the variance

Variance for

Men aged 20-29=42.97

Men aged 60-69=211.77

The variance is substantiaaly larger for the set of blood pressures of men aged 60-69

Enter the data in Excel worksheet and use =AVERAGE(A1:A15) to find mean and calculate is the mean

Mean=15833.33 and is to calculated for finding relative position

Z=38-(27*10)=-232Z=262.7-(200*57)=-11,137.3

Hence 262.7 has higher relative position

=[48-70]/11=-2

Z score=-2

The calculated Z score for the subsequent blood pressures is therefore = -2.

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The least common denominator or LCD of the given fractions  1/2x-6 and 2x/7x-21 is (2x-6)(7x-21)

A fraction can simply be defined in mathematics as the part of a whole variable or number.

Some types of fractions in mathematics are;

The least common denominator of a fraction is seen as the lowest or smallest number in all the common multiples of the denominator given.

Given the information, the fractions are;

1/2x-6 and 2x/7x-21

It is crucial to identify that the denominator of the two fractions are;

(2x-6)(7x-21)

They are in form of algebraic expressions, thus, the  least common denominator is the product of the expression.

Hence, the lowest common denominator is (2x-6)(7x-21)

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The estimation of the numbers given as 0.87 × 310 will give 270.

You must approximate (eliminate or round off) the decimals to obtain whole numbers before you can use the whole numbers to find the product of two decimals using estimation.

A figure is discovered through estimation.

A value, amount, or size that rounds off to the nearest whole number is said to be approximating.

The estimation of the numbers given as 0.87 × 310 will give:

= 0.9 × 300

= 270.

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The  95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount is 629 to 727

The variance of  a variate X is the arithmetic mean of the squares of all the deviations of X from the arithmetic mean of the observations and it is denoted by Var(X) or σ². The spread of statistical data is measured by the standard deviation. Distribution measures the deviation of data from its mean or average position. The positive square root of the variance of a variate X is known as the standard deviation.    

Given here: Sample mean x=678, Sample size n=500, Standard deviation σ=560

Standard error=σ.x=σ/√n

                               =560/√500

                               =25.044

Now for a 95% Class interval the value of z=1.960

The margin of error, E=Z×standard error

                             =49.08624

Lower bound=628.9147

upper bound=728.0854

∴ The 95% interval for population mean = 629 to 727

Hence, The  95% confidence interval for the true average dollar loss in burglaries rounded to the nearest dollar amount is 629 to 727

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It is in good conditions, the automobile travels at 57 mph.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

A scalar quantity known as distance measures "how much ground an object has traversed" while moving. The term "how far out of place an object is" is referred to by the vector quantity displacement, which is the object's overall change in position.

Simply draw a vector from your initial position to your destination and solve for the length of this line to determine displacement. In the case of a circular 5K path, where your beginning and ending positions are identical, your displacement is 0. Displacement in physics is denoted by s.

"A automobile moves 20 mph more slowly in heavy rain than in bright sunshine."

x - 19 = y

where "x" stands for speed in good weather and "y" stands for speed in bad weather.

"The same distance is covered by the car in two hours in the sun as it is in three hours in the rain."

2x = 3y

where "x" stands for speed in good weather and "y" stands for speed in bad weather.

The speed of the car in good weather, or "x," is what we are looking for. In the second equation, substitute the first equation's value for the variable "y."

x - 19 = y

2x = 3y

2x = 3 (x - 19)

Distribute:

2x = 3x - 57

3x off on both sides equals:

-x = -57

Give both sides a -1:

x = 57

It is in good conditions, the automobile travels at 57 mph.

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The new revenue can be calculated as R = q*p = 2,000*4 = $8,000.

R(q) is the revenue function for the school lunch program, which is given by the equation q*p, where q is the quantity and p is the price. According to Braley and Nelson's study, the city of Pittsburgh had an increase in price of school lunches. The revenue can be calculated by multiplying the quantity (q) of school lunches with the new price (p) after the increase. Therefore, the new revenue (R) can be calculated by R = q*p. As an example, if the quantity of school lunches is 2,000 and the price is increased to $4, then the new revenue can be calculated as R = q*p = 2,000*4 = $8,000.

R(q) is the revenue function for the school lunch program, which is given by the equation q*p, where q is the quantity and p is the price. According to Braley and Nelson's study, the city of Pittsburgh had an increase in price of school lunches. The revenue can be calculated by multiplying the quantity (q) of school lunches with the new price (p) after the increase. Therefore, the new revenue (R) can be calculated by R = q*p. As an example, if the quantity of school lunches is 2,000 and the price is increased to $4, then the new revenue can be calculated as R = q*p = 2,000*4 = $8,000.

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Since Zach isolated x^2 in the first equation and then substituted it into the second equation, the resulting equation is equal to: C. 25 - y^2/16 - y^2/9 = 1.

In Mathematics, an equation is sometimes referred to as an expression and it can be defined as a mathematical expression which shows that two (2) or more quantities are equal.

From the information provided above, we have the following system of equations;

x^2 + y^2 = 25 ....... equation 1.

x^2/16 - y^2/9 = 1   ....... equation 2.

By making x^2 the subject of formula in equation 1, we have the following:

x^2 = 25 - y^2     ....... equation 3.

By substituting equation 3 into equation 2, we have the following:

25 - y^2/16 - y^2/9 = 1

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Answer:

Rate : 1 page for every 4 students.  

Unit Rate: 500 pages per ream.40 pages for every blooket.15 pages for evry blooket

Neighter: 25 pages

Step-by-step explanation:

I hope this helps :)

The diffrence between unit rate and rate is the unit rate refers to those rates in which the numerator is 1. Rate would be like there is 1 person per car. Unit rate would mean There are 3 cars for each person.

The ordered pair is not solution to the system of equations.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Cameron determined that an ordered pair made a true statement when substituted into one of the equations but not in the other equation.

As, we know we enter the values of the variables into each equation to see if an ordered pair is a solution to the system of two equation. The system has a solution if the ordered pair proves both of the equations.

So, the ordered pair is not solution..

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Answer:

$902.36

Step-by-step explanation:

820.33 times 10% = 82.033

add 82.033 to 820.33

820.33 + 82.033 = 902.363

Answer:

-9 -6

Step-by-step explanation: