Please help ASAP will give 5 stars and brainliest if possible!!

6th terms of given geometric progression whose common ratio is 3/2 and first term is 4  is 243/8 using the farmula ar^(n-1).

What is a geometric sequence?

A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers. Learn development in mathematics here as well. Here, each phrase is multiplied by the common ratio to generate the subsequent term, which is a non-zero value. A geometric series with a common ratio of 2 is 2, 4, 8, 16, 32, 64, etc.

Geometric Progression takes the following general form: a, ar, ar^2, ar^3, ar^4,..., ar^(n-1).

a = First term where

The common Ratio is r.

nth term = ar^(n-1)

6th terms ar^(6-1) = ar^5.

given is that r =3/2. a = 4.

6th term = 4 * (3/2)^5

= 4 * 3^5/2^5

=4*243/4*8

=243/8.

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The cone should have its maximum volume. V=1/*3r2h is the formula for calculating the volume V of a cone with height h and radius r.

The cone has a volume of

V=πr2h/3

Therefore, we must calculate the values of r and h in terms of R. R is the diameter of the cone's top-circular circle, and h is the cone's height.

R is the cone's slant height, and it serves as the hypotenuse of a right triangle.

R2 = h2 + r2, or r2 = R2-h2.

So V = (1/3)π

[R2-h2]

h = (π/3)[R2h-h3]

You must take the derivative of the cone's volume, set it to zero, then solve for h to determine the cone's maximum volume.

dV/dh=(π/3)[R2-3h2]

R2-3h2=0 --> h2=R2/3 -> h = R/√3

Now we can determine r:

r2=R2-R2/3 = (2/3)R2

The volume formula with r and h substituted:

V = (π/3)

r2h = (π/3)(2R2/3)

(R/√3)

V(R)=2πR3/(9√3)

The complete question is:

A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup (Your answer may depend on R).

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Answer: uhm...

Step-by-step explanation:

2...?

No, I'm not agree with Noah. Because the equation 1. 20(d+5)=42 is a mathematical equation and can be false depending on the value of the variable d.

The equation 1. 20(d+5)=42 is a mathematical equation that contains a variable d. The equation states that when you multiply 20 with (d+5) the result should be 42.

The equation is true if there is a value of d that makes the equation true. For example, if d=1, then 20(1+5)=20(6)=120 which is not equal to 42, so this value of d does not make the equation true.

On the other hand, if d=-7, then 20(-7+5)=20(-2)= -40 which is equal to 42, so this value of d makes the equation true.

Therefore, the equation can be true or false depending on the value of the variable d. In general, without knowing the specific context or situation in which the equation is being used, it is impossible to determine if the equation accurately represents a situation or not.

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The final answer after solving the given equation could be 14.

What is Linear Equation ?

Linear Equation can be defined as the equation in which the highest degree of the variable is one. Linear equations are generally three types , they are standard form , slope intercept form , point slope form and linear equation is also called as the equation of straight line.

Given,

Given equation,

2x + 6 = 3x -8

separating the value into a similar term:

2x-3x = -8 - 6

subtracting the equation:

-x = -14

remove negative sign:

x = 14

Therefore , the final answer could be 14.

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the answer to your question is 36

Answer:

3/2

Step-by-step explanation:

3/2 is in the simplest form; it can't be decreased any more.

In 7th grade math, students learn basic algebra, ratios and proportions, geometry, graphing, probability, equation and statistics.

In 7th grade math, students typically learn basic algebraic principles, including linear equations, variables, and functions. They also learn about ratios, proportions, and percents. Geometry is typically introduced, with topics such as angles, lines, triangles, and circles. Additionally, students may be taught more advanced topics such as graphing, probability, and statistics.In 7th grade math, students learn basic algebra, ratios and proportions, geometry, graphing, probability, and statistics.

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The next operation that should be done when evaluating this expression 9-12+-2+3(-3) is A. 3(-3)=-9

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, it should be noted that the expression given is written as 9-12+-2+3(-3). In PEDMAS, the first operation is parentheses. Therefore, the number on parentheses will be solved first.

In this case, the number in parentheses will be 3(-3). Therefore, the correct option is A.

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The area of the circle is  1256.64 square inches.

All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

One of the most fundamental curvilinear geometric forms, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its basis in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

The diameter of the cylindrical barrel is 20 in

So the diameter of the circular base is 20 in = 10 inches in radius.

Area of the circle = [tex]\pi\ r^{2}[/tex] =  π*20*20 = 1256.64 square inches.

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The process of simplify the equation is explained below.

The term equation is known as a mathematical statement that defines the equality between two expressions.

Here we have to define the process of simplifying the equation.

The first and foremost step is to remove parentheses and brackets by multiplying factors.

And then we have to use the exponent rule to remove grouping if the terms contain exponents.

Then we have to combine like terms by adding or subtracting coefficients.

Finally, we have to Combine the constants.

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Answer:

v=πr²h

divide both sides by πh

v/πh=r²

r²=v/πh

square root both sides

r=√v/√πh

I hope this helps

The value of p is 12.322

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as: For x > 0 , a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.

Given here p=-log(2.1×10¹²)

                  p= - ( log(2.1) +12 log10)

                  p= -(0.322+12)

                  p=12.322

Hence, the value of p is 12.322

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Answer:

[tex] \sf \: h(-3) = 13[/tex]

Step-by-step explanation:

Given information,

→ h(a) = a² + 4

The value of h(a) when a is -3,

→ h(a) = a² + 4

→ h(-3) = (-3)² + 4

→ h(-3) = 9 + 4

→ [ h(-3) = 13 ]

Hence, required answer is 13.

Answer:

Step-by-step explanation: i'd say jus divide

Answer:

He got 32 candy, he give each person , 3,50. or give only tree each person. and he live 8 candy.

The factors of 2[tex]x^{2}[/tex] + 7x + 3 are ( x + 3) and (2x + 1)

Now, According to the question:

The given function is :

f(x) = [tex]2x^2+7x+3[/tex]

To find the factors of  [tex]2x^2+7x+3[/tex] we need to split the middle term, that is, 7x.

7x = 6x + x

Therefore, 2[tex]x^{2}[/tex] + 7x+ 3 can be written as 2[tex]x^{2}[/tex] + 6x + x + 3 .

On taking '2x' common from first two terms and +1 from next two terms we get

2x (x + 3) +1 (x + 3)

(x + 3) (2x + 1)

Thus, the factors of 2x2 + 7x + 3 are (x+3) and (2x+1)

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The complete question is this:

What are the factors of 2x^2+7x +3?

Answer:

0.0005

Step-by-step explanation:

this is a binomial experiment -- they are either cured or not, and the outcome is random

probability = n choose r * p^r * q^(n-r)

here, n = number of trials, r = number of successes desired, p = probability event occurs, and q = probability event doesn't occur

probability = n choose r * p^r * q^(n-r) = 6 choose 3 * 0.97^3 * 0.03^(6-3)

= 0.00049284342 rounding to 0.0005

The Constraints of the inequality are

x ≤ 2y + 500

22500  < √ 35x + 50y

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

The Company A (x) at most 500 more than twice then unit by B(y).

So, x ≤ 2y + 500

Now, the square of Company Profit will be equal to 35x + 50y

Then, the constraints will be

1. x ≤ 2y + 500

2. Company Profit² < 35x + 50y

Company Profit < √ 35x + 50y

22500  < √ 35x + 50y

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Answer:

120 cm.

Step-by-step explanation:

The perimeter of a rectangle is found by adding up the length of all four sides. In this case, the length is 36 cm and the breadth is 24 cm. Therefore, the perimeter of the rectangular table-top is

2 (length + breadth) = 2 (36 + 24) = 2 × 60 = 120 cm.

The perimeter of the rectangle, given the area and the segment from R ( 6, -16) to S (14, - 1 ) is 88 units

To find the perimeter, first find the distance between  R ( 6, -16) to S (14, - 1 ) which will allow you to find the length of one side. This distance can be found by the formula :
= √((x2 – x1)² + (y2 – y1)²)

= √((14 – 6)² + (-1 – (-16))²)

= 17 units

This means that one side of the rectangle measures 17 units so the other side would be:

Area = Length x Width

459 = 17 x Width

Width = 459 / 17

Width = 27 units

The perimeter of the rectangle is:

= Length + Width + Length + Width

= 17 + 27 + 17 + 27

= 88 units

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Answer:

5.5

Step-by-step explanation:

7*8=56

42-8=34

56-34=22

22/4=5.5

The probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes is 59.81%

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. Look up all the related responses.

The likelihood that an event will happen is quantified by probability. An event's likelihood is determined by how frequently it will occur over the long run. Probabilities are all digits that fall between 0 and 1, inclusive—that is, all digits that fall between 0 and 1.

Let the equation of Z score be:

z = (raw score - mean) / standard deviation

Given mean of 36 minutes and a standard deviation of 3 minutes.

If x = 32:

z = (32 - 36)/3 = -1.33

and x = 37:

z = (37 - 36)/3 = 0.33

P(-1.33 < z < 0.33) = P(z < 0.33) - P(z < -1.33)

= 0.6179 - 0.0198

= 0.5981

A consumer selected at random has a 59.81% chance of having to wait between 32 and 37 minutes.

The complete question is:

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 36 minutes and a standard deviation of 3 minutes. What is the probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes, to the nearest thousandth?

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The equation of the line will be y = -2/3x + 5.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the line passes through points (9, -1) and (6, 1).

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 1 - (-1) / ( 6 - 9 )

Sloe = - 2 / 3

The y-intercept will be calculated as,

y = mx + c

-1 = (-2/3) x 9 + c

c = 5

The equation of the line,

y = mx + c

y = -2/3x + 5

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A given set of expressions are known as equivalent expression if and only if the result after evaluating those expression is the same number.

Example,

3 + 2 = 5

4 + 1 =  5

5 + 0 = 5

These three are equivalent as because the sum of all of them is same , i.e., 5.

An equivalent expression is an expression which consists of variables, coefficients, constants, and mathematical functions such as addition, subtraction, multiplication, and division.

In general, if two objects are identical, they are then called as identical.

These expressions are also known as duplicates of each other though they look different but they are same.

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Answer:

2,570 meters

Step-by-step explanation:

110% of what number is 2827

1.1x = 2827  Divide both sides by 1.1

[tex]\frac{1.1x}{1.1}[/tex] = [tex]\frac{2827}{1.1}[/tex]

x = 2570

The value of expression -x³+3x²+5x+1 is -1235 when x is 12

An expression is combination of variables, numbers and operators.

Given polynomial is -x³+3x²+5x+1

We need to find the value of the polynomial when x is 12.

To find this we just need replace x with 12

-(12)³+3(12)²+5(12)+1

Minus twelve cube plus three times of twelve square plus five times of twelve plus one

-1728+3(144)+5(12)+1

-1728+432+60+1

-1728+493

-1235

Hence, the value of expression -x³+3x²+5x+1 is -1235 when x is 12

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The graph from the function is a linear graph

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

g(x)=(x+2)(x−1)−x 2

Express properly

So, we have the following representation

g(x) = (x + 2)(x − 1) − x²

Next, we set x = 0, 1, 2 and 3 to determine the table of values

g(0) = (0 + 2)(0 − 1) − (0)² = -2

g(1) = (1 + 2)(1 − 1) − (1)² = -1

g(2) = (2 + 2)(2 − 1) − (2)² = 0

g(3) = (3 + 2)(3 − 1) − (3)² = 1

So, the table is

x        0         1        2        3

g(x)     -2      -1        0        1

From the table above, we can see that as x increases by 1, y constantly increase by 1

This means that the function is a linear function

See attachment for the graph

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Based on the information given, the number of students from Florida will be; 9000 students.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that At Florida A&M University, the ratio of students from Florida to students not from Florida is about 3 : 1

The Total number of students = 12000

Fraction from Florida = 3/4

Fraction of students not from Florida = 1/4

Therefore, the students from Florida will be:

= 3/4 × 12000

= 9000

Hence, the number of students from Florida is 9000.

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