Addition and subtraction of monomials

1) -3^5 + 2x^4 - 7x^2 + 8x + 9 + 5x^4 - 8x^3 + 10x^2 - 3x + 4

2) 9x^5 + 3x^2 - 6 + 2x^4 + 5x^3 - 4x^2

3) 3x^2 - 6 - 4x^2 + 7x^2 - 4x+11

4) -2x^2 + 10x^2 - 3x - 4x + 11

5) -19a + 7b - 8c + 5a - 32b + 23c - 22a + 5b - 20c

(PS: The ^ means that the number to the right of it is an exponent)

In a data set, the number of elements will always be the same as the number of observations.

An observation is a single measurement or record of a particular variable or event. In a data set, observations are typically organized into rows, with each row representing a single observation.

The number of observations in a data set corresponds to the number of times the data was measured or recorded.

On the other hand, a data point can refer to a single value within a data set, or a combination of values if the data set contains multiple variables.

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Answer:

there are 3 feet in one meter.

Step-by-step explanation:

12 inches = 1 foot.

39.3701 inches = 1 meter.

39.3701 ÷ 12 = 3.281.

3.281 is simplified to 3.

There are about 3 feet in 1 meter.

Hope this helped! Have a Good Day!

Answer:

[tex]\huge\boxed{\sf 9x}[/tex]

Step-by-step explanation:

= 3x + 3x + 3x

Take x as common factor

= x(3 + 3 + 3)

= x (9)

[tex]\rule[225]{225}{2}[/tex]

Answer:

x=-10, PR=10.

Step-by-step explanation:

(x+15)/(x+20)=1/2 => 2(x+15)=x+20 => x=-10. PR=20-10=10.

Answer: 60%

Step-by-step explanation:

In order to find the percentage, we need to find the sum of the espressos ordered.

57 + 38 = 95

95 will be our denominator, and since we are trying to find the percentage of the single-shot, our numerator is going to be 57 because that is how many sold.

57 / 95

Now we can divide 57 by 95 to get the percent of single shot espressos to get an answer of 60%

Answer: Santa Maria to Los Alamos is approximately 2,612,951.6 centimeters.

Step-by-step explanation:

To convert miles to centimeters, we need to use the following conversion factors:

1 mile = 160,934.4 centimeters

So, to find the distance from Santa Maria to Los Alamos in centimeters, we can use the following calculation:

16.25 miles x 160,934.4 centimeters/mile = 2,612,951.6 centimeters

Therefore, the distance from Santa Maria to Los Alamos is approximately 2,612,951.6 centimeters.

1 mile = 160,934 centimeters

16.25 miles = ?

16.25 * 160,934 = ?

16.25 miles = 2,615,184 centimeters

The area below the curve is equal to 10 - 3π / 2 square units. (Correct choice: B)

In this problem we need to determine the area below the curve for the interval x ∈ [- 4, 7]. Mathematically speaking, this area can be found by means of definite integrals. Given that we find a piecewise function formed by five expressions, the area is the sum of several subintervals.

The areas can be represented by using the following area formulas:

Triangle

A = 0.5 · w · l

Semicircle

A = 0.5π · R²

Rectangle

A = w · l

Where:

Please notice the area above the x-axis is positive and the area below the x-axis is negative. Finally, we find the net area below the curve:

A = 0.5 · 2 · 2 - 0.5π · 2² + 0.5 · 2 · 2 + 2 · 2 + 0.5π · 1² + 1 · 2

A = 2 - 2π + 2 + 4 + 0.5π + 2

A = 10 - 1.5π

A = 10 - 3π / 2

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In general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect sample mean. The correct option is (b) sample mean

The sample size is large, adding an extremely large outlier to a data set will not substantially affect the sample mean.

This is because the sample mean is a measure of central tendency that is influenced by all the values in the dataset, but it is more affected by the values that are closer to it in magnitude. When the sample size is large, the impact of any individual outlier on the overall mean is typically reduced, as the outlier will be more likely to be balanced out by the other values in the dataset.

However, the addition of an extremely large outlier may still have an impact on the sample standard deviation and median, depending on the magnitude and distribution of the other values in the dataset.

Therefore, the correct option is (b) sample mean

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It will take her 30 minutes if she walks to the school.

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

The time can be modeled as follows:

t = d/v.

Hence if the velocity decays by a factor of 1/3, the time is tripled, hence the time needed to get to the school walking is given as follows:

t = 10 x 3

t = 30 minutes.

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The area of the given composite figure is the sum of the areas of triangles and the area of the rectangle, which is 11 sq. units.

What is a composite figure?

Geometric figures can be combined from two or more separate geometric figures. A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. The total of the individual areas will represent the composite shape's area.

The given composite figure can be divided into the shapes given below.

There are 3 right triangles and one rectangle.

The sum of the areas of each shape makes the area of the given composite figure.

Δ ARC

base RC, b = 3

Height AC, h = 4

Area = 1/2 * b * h = 1/2 * 3 * 4 = 6 sq. units.

Δ RST

base RS, b = 2

Height ST, h = 2

Area = 1/2 * b * h = 1/2 * 2 * 2 = 2 sq. units.

Δ BCK

base BK, b = 1

Height BC, h = 2

Area = 1/2 * b * h = 1/2 * 1 * 2 = 1 sq. units.

Rectangle SCBT

length l = 2

Breadth b = 1

Area = 2 * 1 = 2 sq. units

Therefore the area of the given composite figure is = 6 + 2 + 1 + 2

                                                                            = 11 sq. units

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The area of the base is 0.7547 m², the curved surface area is 2.201 m², and the volume is 0.630 m³.

To calculate the area of the base, we use the formula for the area of a circle:

Area of base = πr²

where r is the radius of the circle.

Area of base = π(0.49m)²

Area of base = 0.7547 m²

To calculate the curved surface area, we first need to calculate the slant height of the poly tank. We can use the Pythagorean theorem to find this value:

Slant height = √(height² + radius²)

Slant height = √(0.9m² + 0.49m²)

Slant height = 1.05 m

Now we can use the formula for the curved surface area of a cylinder:

Curved surface area = 2πrh

where r is the radius of the cylinder and h is the height of the cylinder.

Curved surface area = 2π(0.49m)(0.9m)

Curved surface area = 2.201 m²

To calculate the volume of the poly tank, we use the formula for the volume of a cylinder:

Volume = πr²h

Volume = π(0.49m)²(0.9m)

Volume = 0.630 m³

Therefore, the area of the base is 0.7547 m², the curved surface area is 2.201 m², and the volume is 0.630 m³.

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Answer:

If there is a 25% chance that a customer who purchases milk will also purchase bread. the probability of a milk purchase is 70%.  the probability that a customer will purchase bread given that they purchase milk is 36%.

How to find the probability?

Using this formula to find the probability that a customer will purchase bread given that they purchase milk

P(B | M) = P(M / B) / P(M)

Let plug in the formula

P(B | M) = 0.25 / 0.70

P(B | M) = 0.3571 ×100

P(B | M) = 36% (approximately)

Therefore the probability is 36%.

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The height of 164.8 centimeter after conversion to feet is equivalent to  5.41 feet .

The various measurements units that are used in measuring the height of an object are , centimeter (cm) , meter (m) , feet , inches .

We have to convert the height of 164.8 cm to feet ;

we know that , 1 centimeter is = 0.0328 feet ;

So , we multiply the units given in centimeter by 0.0328 ,

On multiplying 164.8 cm by 0.0328 ;

We get ;

⇒ 164.8 centimeter = 164.8 × 0.0328 ;

⇒ 164.8 centimeter = 5.40544 feet ≈ 5.41 feet ;

Therefore , 164.8 cm is approximately equal to 5.41 feet .

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Answer:

A. (2,3)

Step-by-step explanation:

2,3 is a solution, because it is marked on the graph. We can also tell because they are solutions for both the marked lines.

Answer:

2,3 is the answer

Step-by-step explanation:

on graph

There are 2.47105 acres in 1 hectare.

An acre is a common unit of measurement in the United States and other countries. One acre equals 43,560 square feet (4,047 square metres).

In contrast, a hectare is a metric unit of area that is widely used in many countries. One hectare equals 10,000 square metres (2.47105 acres).

You can use the conversion factor of 1 acre = 0.4047 hectares or 1 hectare = 2.47105 acres to convert acres to hectares.

Simply multiply the number of acres by 0.4047 to convert from acres to hectares. Similarly, multiply the number of hectares by 2.47105 to convert the number of hectares to acres.

To convert a given number of acres to hectares using mathematical terms, you can use the formula:

Hectares = Acres × 0.4047

In this formula, "Acres" is the number of acres you want to convert to hectares, and "Hectares" is the equivalent area in hectares.

Similarly, to convert a given number of hectares to acres using mathematical terms, you can use the formula:

Acres = Hectares × 2.47105

In this formula, "Hectares" is the number of hectares you want to convert to acres, and "Acres" is the equivalent area in acres.

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The upper quartile of the data set is, 56.

The process for combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The values of 42, 44, 50, 54, and 56 are all marked by the box plot.

Hence, The value of upper quartile is,

⇒ Upper quartile = 3/4 (n + 1)

Where, n is number of terms.

Hence, We get;

⇒ Upper quartile = 3/4 (5 + 1)

                           = 3/4 × 6

                           = 4.5

                           ≈ 5th term

Thus, The value of Upper quartile = 56

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In order to expand and simplify an expression, we need to multiply out the brackets and then simplify the resulting expression by collecting the like terms. Expanding brackets is the process by which we remove brackets. It is the reverse process of factorization.

To expand and simplify a binomial, use the distributive property. The distributive property states that for any two binomials, the product of each term in the first binomial and each term in the second binomial should be added together to get the expanded form of the expression.

For example, the binomial (2x + 3)(4x + 7) can be expanded using the distributive property by multiplying each term of the first binomial with each term in the second binomial. This gives us:

(2x × 4x) + (2x × 7) + (3 × 4x) + (3 × 7)

And simplifying this expression yields 8x² + 14x + 21.

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Answer: Half the side of NL from the original figure.

Step-by-step explanation:

When it is a scale factor of 1/2 all the sides are halved there fore nl is halved.

In metric system distance measured by using kilometres and miles units. Thus, the conversion of one kilometre to mile is equals to the 0.62137119 miles.

To convert from one unit to another, multiply by a conversion factor. Typically, conversion from kilometers to miles is a conversion of distance from kilometers to miles. Kilometers and miles are used to measure the length from one point to another. In the metric system, the kilometer is a unit of length and is considered the International System of Units, while the mile is used as an English and US customary unit. One kilometer is abbreviated as "km" and one mile is abbreviated as "mi". These two measurements are mainly used to measure the geographical area of land. The following conversion values are used to convert distance measurements from kilometers to miles: 1 kilometer = 0.62137119 miles. A conversion factor is required to convert kilometers to miles. This means that 1 km is approximately equal to 0.62137119 miles.

Hence, required value is 0.62137119 miles.

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Answer: where do i answer where is the question?

Step-by-step explanation:

the contact force between the block and the plane is equal to the normal force, which is equal to the weight of the block (mg) multiplied by the cosine of the angle of inclination (θ). Therefore, the contact force between the block and the plane is mg cosθ.

The contact force between the block and the plane can be determined by analyzing the forces acting on the block.

First, we need to consider the forces acting on the block in the direction parallel to the inclined plane. Since the block is moving with uniform speed, the forces in this direction must be balanced. The forces in this direction are the force due to gravity acting down the inclined plane (mg sinθ) and the frictional force acting up the inclined plane (μmg cosθ). Therefore, we have:

mg sinθ = μmg cosθ

Simplifying this equation, we get:

μ = tanθ

This means that the coefficient of friction between the block and the plane is equal to the tangent of the angle of inclination.

Next, we need to consider the forces acting on the block in the direction perpendicular to the inclined plane. Since the block is not accelerating in this direction, the forces in this direction must also be balanced. The forces in this direction are the normal force acting up the inclined plane (N) and the force due to gravity acting vertically down (mg cosθ). Therefore, we have:

N = mg cosθ

So, the contact force between the block and the plane is equal to the normal force, which is equal to the weight of the block (mg) multiplied by the cosine of the angle of inclination (θ). Therefore, the contact force between the block and the plane is mg cosθ.

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Answer:

1,000,000,000,000 = 1,000,000,000 × 1,000

Step-by-step explanation:

One trillion equals a thousand billions, or a million millions.

Using the Pythagorean theorem we get the value of the missing leg BC in the triangle is 6 miles.

Since AC is the hypotenuse and AB is one of the legs of the right-angled triangle ABC, BC is the other leg. Using the Pythagorean theorem, we have:

BC² = AC² - AB²

When we replace the values in the problem, we obtain:

BC²= 10² - 8²

BC² = 100 - 64

BC² = 36

The result of taking the square root of both the sides is:

BC = 6

Therefore, the value of the missing leg BC in the triangle is 6 miles. The Pythagorean Theorem is a fundamental concept in mathematics that relates to right-angled triangles. This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it. The hypotenuse is the side of a right-angled triangle that is opposite the right angle. It is the longest side of the triangle and is always opposite the largest angle. The hypotenuse is important because it determines the size of the triangle and is used in many calculations involving right-angled triangles. The Pythagorean Theorem is used in various fields such  as engineering, physics, and construction. It is a basic tool for calculating distances and determining whether or not a triangle is a right-angled triangle.

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Step-by-step explanation:

Principal (P)=$7869

Rate (R)= 13%

Time (T)= 5 years

Compound Interest (CI)=?

We know that,

CI = P { (1+R/100)^T -1}

= $7869 {(1+13/100)^5 -1}

= $7869 {(113/100)^5 -1}

= $7869 {(1.13)^5 -1}

= $7869 {1.84-1}

= $7869 × 0.84

= $6609.96

Compound Amount= CI+p

= $6609.96+7869

= $14478.96

Therefore, he will have $14478.96 after 5 years.

The requried solution to the system of equations is x = 7, y = 6.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

To solve the system of equations:

4x - 2y = 16 - - --  - -(1)

2x + 3y = 32 - - - - - - (2)

We can use the method of substitution:
Solve one of the equations for one of the variables in terms of the other variable.
Let's solve the first equation for y:

4x - 2y = 16

-2y = -4x + 16

y = 2x - 8

Substitute the expression found in step 1 into the other equation 2.

2x + 3(2x - 8) = 32

Solve the resulting equation for the remaining variable.

2x + 6x - 24 = 32

8x - 24 = 32

8x = 56

x = 7

Substitute the value of x into one of the original equations to find the value of the other variable.

Using the first equation:

4x - 2y = 16

4(7) - 2y = 16

28 - 2y = 16

-2y = -12

y = 6

Therefore, the solution to the system of equations is x = 7, y = 6.

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One liter equals 1000 milliliters.

Answer:

One liter equals 1000 milliliters.

Step-by-step explanation:

A liter (L) and a milliliter (mL) are both units of volume in the metric system. One liter is defined as the volume of a cube with edges that are 10 centimeters in length, which is equivalent to 1000 cubic centimeters (cm^3). A milliliter, on the other hand, is equal to one-thousandth of a liter, which means there are 1000 milliliters in one liter.

In other words, if you have one liter of water in a container, you could pour it into a smaller container that measures in milliliters, and it would fill exactly 1000 mL.

To complete the square for the equation [tex]x^2 + 8x + 32 = (x - h)^2 + 16[/tex],

we need to choose h = -2.

To complete the square for the given equation

[tex]x^2 + 8x + 32 = (x - h)^2 + 16[/tex],

we need to express the left-hand side of the equation in the form

[tex](x - p)^2 + q[/tex], where p and q are constants.

We can start by expanding the right-hand side of the equation:

[tex](x - h)^2 + 16 = x^2 - 2hx + h^2 + 16[/tex]

Now we can compare the coefficients of [tex]x^2[/tex], x, and the constant term on both sides of the equation:

[tex]x^2 + 8x + 32 = (x - p)^2 + q[/tex]

=> [tex]p^2 = 0[/tex] (since the coefficient of [tex]x^2[/tex] is 1 on both sides)

=> -2hp = 8 (since the coefficient of x is 8 on the left-hand side)

=> h = -2 (solving for h)

=> q = [tex]h^2 + 16[/tex] = 20 (since the constant term on the right-hand side is 16)

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The complete question may be:

What value of h is needed to complete the square for the equation [tex]x^2+8 x+32=(x-h)^2+16[/tex] ?

A) The hiker traveled 6.0 miles on the first day.

B) [tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]

C)  The total number of miles the hiker will travel in 14 days≈168 miles.

Series and sequence are the basic ideas in mathematics. A sequence is an ordered group of elements where repetitions of any kind are allowed, as opposed to a series, which is the sum of all components.

The distances are organized geometrically, with the first term being a1 and the common ratio being (1 + 10%) = 1.10.

The sum of the seven terms in the series is...

 S7 = a1·(r^7 -1)/(r -1)

 56.923 = a1·(1.1^7 -1)/(1.1 -1)

 5.6923 = a1·0.9487171

Its value is obtained by dividing by the coefficient of a1:

 5.6923/0.9487171 ≈ 5.999997 ≈ 6.000

The hiker traveled 6.0 miles on the first day.

Equation for Sn,

[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]

where ,

a= first term

r=common ratio

n=number of terms

[tex]S_{14} =\frac{6(1.1^{14}-1)}{1.1-1} \\\\S_{14}=167.84[/tex]

The total number of miles the hiker will travel in 14 days≈168 miles

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Answer:

Step-by-step explanation:

csc and sin are inverses of one another, therefore, c is the correct statement.