Find the common difference and the next two terms of the arithmetic sequence.11,19,27,35The common difference isWrite the next two terms in the sequence:11,19,27,35,?,?

Answer:

basically the even twill not happen as the probability of that is 0

Answer

Area of the figure = 105.12 ft²

Explanation

The figure shown is a combination of a rectangle with length 10 ft. and width 8 ft., with a semicircle that has diameter 8 ft., which translates to a radius of 4 ft.

The area of the figure = (Area of the rectangle) + (Area of the semicircle)

Area of rectangle = L × W

L = Length = 10 ft.

W = Width = 8 ft.

Area of the rectangle = 10 × 8 = 80 ft²

Area of semicircle = Half of the area of a circle = ½ × πR²

π = pi = 3.14 (According to the question)

R = Radius of the semicircle = 4 ft.

Area of semicircle = ½ × 3.14 × 4² = 25.12 ft²

Area of the figure = 80 + 25.12 = 105.12 ft²

Hope this Helps!!!

The equation of parallel line is y = 2x + 3

Given,

The line below is the function y=2x-1.

From the figure,

Identify the equation of a parallel line.

Now, According to the question:

We are given that line a represented by the equation

y = 2x -1

and, We know that

Slope- intercept form of line is given by

y = mx + c

Where m=Slope of line a

c = y- intercept

Comparing it  with the given equation then, we get

Slope of line a = 2

We know that

When two lines are parallel then their slopes are equal.

Hence, Option (b) slope is equal to the given function

It means, y = 2x - 1 and y = 2x +3

Value of slope m = 2 = 2

Hence, The equation of parallel line is y = 2x + 3

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Answer:

y=13

Step-by-step explanation:

We will have that some of the principles that geometry works with, that are present in the image are:

Length, Area, Volume, Surfaces, Angles & Curves.

Given:

The quadratic equation ,

The solution of the given quadratic equation can be obtained as,

Hence, the solutions are,

Answer:

2(x-2)

Step-by-step explanation: distribute, add the numbers, common factor

Answer:

13

Step-by-step explanation:

The probability that a 3 will be rolled would be 0.125 and the expected number of 6's roll would be 68.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

The events' estimated probabilities are as follows, according to the exponential probability theory:

P(3) = 0. 125

P(6 in 500 rolls) = 68 rolls

Number of times event occurs / number of trials

A number of attempts = sum of frequency:

(12+35+11+23+7+12) = 88

So the probability that a 3 will be rolled as

⇒ number of 3's / number of attempts

⇒ 11/88 = 0.125

The number of 6's probable in 500 rolls

⇒ (12 /88) × 500

⇒ 68.18 = 68

Therefore, the expected number of 6's roll would be 68.

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Answer:

it is often known as the unequal variance t test. It assumes that both groups of data are drawn from Gaussian populations, but does not assume that their standard deviations are the same.

Let the total marks are 100.

And Bradely got 66% marks.

So the marks of Bradely are:

And Zevel got one third of Bradely's marks so:

Answer:

First number: 21

Second number: 84

Third number: 30

21 times 4 = 84 which checks out.

30 - 21 = 9 which also checks out

21 + 84 + 30 = 135 so they are correct!

Step-by-step explanation:

Hope it helps! =D

The inequality that represents having enough money to buy the gaming system is x ≥ 35.

The mathematical expression that represents the sentence " you charge $10 per dog" is x = 10 where x is the number of dogs.

x ≥ 35 means that the minimum number of dogs to wash is 35 to make $500.

It is a statement of an ordered relationship

- greater than,

- greater than or equal to,

- less than,

- less than or equal to between two numbers or algebraic expressions.

We have,

The cost of the gaming system = $500

Amount already saved = $150

Charges per dog = $10

The inequality that represents having enough money to buy the gaming system:

150 + 10x ≥ 500

10x ≥ 500 - 150

10x ≥ 350

x ≥ 35   where x is the number of dogs.

The mathematical expression that represents the sentence " you charge $10 per dog ":

x = 10 where x is the number of dogs.

x ≥ 35 means that the minimum number of dogs to wash is 35 to make $500.

Thus,

The inequality that represents having enough money to buy the gaming system is x ≥ 35.

The mathematical expression that represents the sentence " you charge $10 per dog" is x = 10 where x is the number of dogs.

x ≥ 35 means that the minimum number of dogs to wash is 35 to make $500.

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Given:

A table with the given values of the function y=g(x).

To find the function that represents g(x), we substitute a value of x into the given options.

For:

g(x =3+2x:,:

Let x=3

Based on the given table, the value g(x) is 24 when x=3. So g(x)=3+2x is not the function that represents g(x).

For

The value of g(x) =18 when x=3, so this is not the function.

For g(x)=3x^2:

Hence, this is not the function as well.

For g(x)=3(2)^x:

We can notice that when x=3, the value of g(x) =24 which is the same as the value of g(x) in the given table.

To double check this, we plug in the other values of x.

Therefore, the answer is:

Answer:

mixed: 2 and 1/4

improper: 9/4

Step-by-step explanation:

The  mixed number in picture is [tex]2\frac{1}{4}[/tex] and improper fraction represented in the picture 9/4.

Fractions are the components of a collection or whole. Two parts make up a fraction. The numerator is the number at the top of the line. It indicates the number of equal portions taken from the collection or whole. The number beneath the line is known as the denominator. It indicates the total number of identical parts that make up a collection or the total number of parts that make up the whole.

Given picture shows three circles each are divided in 4 equal parts,

circle 1 and 2 are completely filled it can be counted 1 for each,

1 + 1 = 2

but for third circle only one part is filled out of 4,

it is represented by 1/4

total value of 3 figures is 1 + 1 + 1/4 = 2 + 1/4 = 9/8

and of mixed fraction   [tex]2\frac{1}{4}[/tex] .

Hence the mixed fraction  [tex]2\frac{1}{4}[/tex]  and improper fraction 9/8.

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It is to be noted that the ONLY option that the customer can select from when purchasing the product is  "(M2, C2, A3)" Option C.

The above exercise is a test of logic, as it is with a simple calculation.

The study of formal logic within mathematics is known as mathematical logic. Mathematical logic research frequently focuses on the mathematical aspects of formal logic systems, such as their expressive or deductive capability.

Hence, from the above, we can see that:

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Full Question:

Apple has created a new i-Pad. There are 4 choices for memory size (M), 8 choices for color (C) and 3 apps (A) to select when you purchase the product. From the options below what is the ONLY option the customer can select?

(M1, C2, A4)

(M1, C9, A3)

(M2, C2, A3)

(M4, C2, A8)

Answer:

Part A is Figure D

Part B is 3 units left

The equation of the line is y = -1x + 3.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. In this essay, let's study more about parallel lines. No matter how far we extend a parallel line, it will never meet another parallel line.

The slope so rewrite the equation for the line as y = -x + 1.

The equation in “y = mx + b” form, the slope is always the number m in front of x.

The slope is -1.

First, by using “y = mx + b” form,

we know m is -1 so only need b.

To get b, plug in the (x, y) coordinates for the point (-1, 4)

(4) = -1×(-1) + b.

The y-coordinate 4 on the left side, and the x number -1 on the right.

b = 3.

Therefore, the equation of the line is y = -1x + 3.

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Answer:

$15 × .8 = $12

$12 × .75 = $9

The equation for the perpendicular bisector of the line segment whose endpoints are (-2, 4) and (-8,-6) is 3x + 5y + 20 = 0.

Given:

Endpoints of the line segment are (-2, 4) and (-8,-6).

Midpoint of the line segment = ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )

                                                 = [tex]\frac{-2 +(-8) }{2}[/tex] , [tex]\frac{4 +(-6) }{2}[/tex]

                                                =( [tex]\frac{-10}{2}[/tex] , [tex]\frac{-2}{2}[/tex] ) = (-5, -1)

Slope of the line segment =  [tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex]

                                            = [tex]\frac{(-6) - 4 }{(-8) - (-2) }[/tex]

                                            = [tex]\frac{-10}{-6}[/tex] = [tex]\frac{5}{3}[/tex]

The line perpendicular to the line segment will have a slope of the negative reciprocal of the line segment which is -3/5.

Therefore, the perpendicular bisector passes through (-5,-1) and has a slope of -3/5.

Equation of the line will be,

y - y₁ = m(x - x₁)

⇒ y - (-1) = -3/5(x -(-5))

⇒ 5( y + 1) = -3(x + 5)

⇒ 5y + 5 = -3x - 15

⇒ 3x + 5y + 20 = 0

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Ben must bowl 130 in his third game so that the average will be of at least 160.

Given that, Ben bowled 157 and 193 in his first two games. So, we have to calculate the average of his third bowl to have an average of at least 160.

Let the average of third bowl be x.

The average is known as the arithmetic mean which is the sum of all numbers in a collection, divided by the count of the numbers present in the collection. In other words, the average is the ratio of the sum of all given observations to the total number of observations. Hence, the average formula is:

Average = Sum of the Observations/Number of Observations

160 = 157+193+x/3

⇒ 160×3 = 157+193+x

⇒ 480 = 350+x

⇒ 480-350 = x

⇒  130 = x

Therefore, Ben must bowl 130 in his third game so that the average will be of at least 160.

Hence, 130 is the required answer.

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Answer:x=32°

y=35°

Step-by-step explanation:

23°+32°+y=90°

55°+y=90°

y=35°

35°+23°+x=90°

58°+x=90°

x=32°

Answer:

Angle AOE = angle FOB = 32° (vertically opposite angles)

x = 32°

Since GH is a straight line, angle COH = angle COG = 90°

Angle BOD = angle COA = y° (vertically opposite angles)

y = 90-32-23 = 35°

He drove for 2.3 hours.

The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity. 

A body's speed is the amount of distance it travels in one unit of time.

Therefore, the SI Unit for speed is the meter per second, abbreviated as m/s 

Formula

Speed = [tex]\frac{distance}{time }[/tex]

Time = [tex]\frac{distance}{speed}[/tex]

Given Data

Distance = 161km

Speed = 70km

Putting values in the formula

Time = [tex]\frac{161}{70}[/tex]

Time = 2.3

He drove for 2.3 hours.

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you get he common ratio by dividing a term by the previous term

so,

15/-5 = -3

common ratio = -3

Geometric seuqence has a general term of:

Wher

r is common ratio

a is first term

Given,

a = -5

r = -3

We have:

12th term is basically n = 12

So, we have:

Answer:

true

Step-by-step explanation:

We can tell the difference among linear, quadratic, and exponential functions just by looking at equation as Exponent functions are rapidly increasing or decreasing, and the highest power of variable for a linear function is 1. The highest power of variable for a quadratic function is 2.

Linear functions are functions that are used to model phenomena that increase or decrease at a constant rate. These types of functions are polynomial functions with a highest exponent of one on the variable. The graphs of these functions are in the shape of a straight line.

Exponential functions are functions that have the variable in the exponent. They increase or decrease slowly then quickly or quickly then slowly.

Quadratic functions are the functions that have the highest power of variables equal to 2.

For example,

Linear Equation : The population of a family of rabbits starts with 2 rabbits and doubles every month.

Expoential Equation : Compound interest is example of exponential function.

Quadratic Equation : When you throw a ball (or shoot an arrow, fire a missile or throw a stone) it goes up into the air, slowing as it travels, then comes down again faster and faster and a Quadratic Equation tells you its position at all times!

Therefore, we can conclude that linear function have highest power of variable as 1 , exponent functions are quickly increasing or decreasing, Quadratic functions have the power of variables equal to 2.

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The perimeter of the isosceles triangle whose base is 6 cm and two equal sides are 7.5 cm is 21 centi-meters.

What is isosceles triangle?

An isosceles triangle in geometry is one with at least two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception. The isosceles right triangle, the golden triangle, the faces of bipyramids, and some Catalan solids are all examples of isosceles triangles.

To calculate the perimeter of isosceles triangle, we use equation:

Perimeter = Base + 2(Two equal side)

Perimeter = 6 + 2(7.5)

Perimeter = 21 cm

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If this is an arithmetic sequence, each of the terms will have a common difference. Let's check.

As we can see, each of the terms does not have a common difference. The first one is -18 while the other one is -126. Therefore, this is not an arithmetic sequence.

Now, let's check if this is a geometric sequence. If it is, each of the terms will have a common ratio.

As we can see, each of the terms has a common ratio which is 1/7. Therefore, 147, 21, 3 is a geometric sequence and the common ratio is equal to 7.