The formula for calculating the volume of a cone is V=1/3(pi)r(to the third power)h. Solve this formula for h.​

The sequence partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 is -10, -7.5, -5, -2.5, …

Given recursive formula is f(n+1) = f(n)+2.5, n ≥ 1.

So the first term of the sequence is f(1) since n ≥ 1.

Given options for the sequences are:

a. 2.5, 6.25, 15.625, 39.0625, …

b. 2.5, 5, 10, 20

c. -10, -7.5, -5, -2.5, …

d. -10, -25, 62.5, 156.25

We compare the first term of each sequence with the given recursive formula.

a.  2.5, 6.25, 15.625, 39.0625, …

In this sequence, the first term, f(1) = 2.5

Using recursive formula, f(2) = f(1) + 2.5 = 2.5 +2.5 = 5.

But the second term in the given sequence is 6.25. So the recursive formula does not match with this sequence.

b.2.5, 5, 10, 20

Here, f(1) = 2.5

By the recursive formula, f(2) = f(1) + 2.5 = 5

f(3) = f(2) + 2.5 = 5 +2.5 = 7.5, which does not match with the third term of the given sequence. So this sequence is not defined by the recursive formula.

c. -10, -7.5, -5, -2.5, …

Here, f(1) = -10

Using recursive formula, f(2) = f(1) + 2.5 = -10 + 2.5 = -7.5

f(3) = f(2) + 2.5 = -7.5 +2.5 = -5

f(4) = f(3) +2.5 = -5 +2.5 = -2.5

So far the recursive formula matches with the given sequence. So the sequence defined partially by the recursive formula, f(n+1) = f(n)+2.5, n ≥ 1 is -10, -7.5, -5, -2.5, …

d.  -10, -25, 62.5, 156.25

Here the first term is, f(1) = -10.

But the sequence which matches with the recursive formula and starting with -10 is option c. So this sequence does not need to be verified.

The question is incomplete. Find out the complete question below:

Which sequence could be partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 ?

a. 2.5, 6.25, 15.625, 39.0625, …

b. 2.5, 5, 10, 20

c. -10, -7.5, -5, -2.5, …

d. -10, -25, 62.5, 156.25

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Variable - These are the unknown quantities that expected to estimate it as an output.

Example:- In an optimization model for labor scheduling, the number of nurses to employ during the morning shift in an emergency room may be a Decision variable.

Constraints - the restrictions on the variable open linear programming problem are called constraints.

The conditions x ≥ 0, y ≥ 0 called non negative restrictions.

Objective equation - the objective equation should be specified in a quantitative way.

It is of the form Z = ax + by

where x and y are decision variable.

Z is to be maximized or minimized to find the solution.

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The equation that has no solution is 24x+32-2.1x = 20.9x+30+x-2

Part A

24x+32-2.1x = 20.9x+30+x+2

Add like terms

24x-2.1x-20.9x-x = 30+2-32

0x = 0

Infinitely many solutions

Part B

24x+32-2.1x = 20.9x+30+x-2

Add like terms

24x-2.1x-20.9x-x = 30-2-32

0x = -4

There is no solution

Part C

24x+32-2x = 20.9x+30+x-2

Add like terms

24x-2x-20.9x-x = 30-2-32

0.1x = -4

x = (-4)/0.1

x = -40

It has only one solution

Part D

24x+32 = 20.9x+30

Add like terms

24x-20.9x = 30-32

3.1x = -2

x= (-2)/3.1

x = -0.64

It has only one solution

Hence, the equation that has no solution is 24x+32-2.1x = 20.9x+30+x-2

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If Jim is running a race against his best friend Ryan and Jim runs at a rate of 18 miles in 3 hours while Ryan runs at a rate of 11 miles in 2 hours, then Jim can run 0.5 miles further compared to his friend Ryan.

If Jim runs at a speed of 18 miles in 3 hours, it can be represented as,

Speed = distance / time = 18 miles / 3 hours = 6 miles per hour

As Ryan runs at a rate of 11 miles in 2 hours, it can be given as,

Speed = distance / time = 11 miles / 2 hours = 5.5 miles per hour

To determine how much further Jim can run in an hour compared to his friend Ryan,

Distance ( Jim ) = speed x time = 6 x 1 = 6 miles

Distance ( Ryan) = speed x time = 5.5 x 1 = 5.5 miles

The distance that Jim can run further in an hour can be calculated by subtraction.

Distance ( Jim ) - Distance ( Ryan) = 6 - 5.5 = 0.5 miles

Thus, Jim can run 0.5 miles further in an hour compared to his friend Ryan.

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If AB = 6y - 14, BC = 10 - 2y then the value of AC = 8.

In geometry, the midpoint is the point in the middle of a line segment. It is equidistant from both endpoints and serves as the segment and endpoint centroid. It cuts the segment in half.

Given: AB = 6y - 14, BC = 10 - 2y

Since B is the midpoint of AC, AB = BC then

6y - 14 = 10 - 2y

Add 14 on both sides of the equation, and we get

6y - 14 + 14 = 10 - 2y + 14

6y = - 2y + 24

Add 2y on both sides of the equation

6y + 2y = - 2y + 24 + 2y

simplifying the above equation, we get

8y = 24

y = 24/8

y = 3

Substitute the value of y in AC then we get

AC = 2(6(3) - 14)

= 2(4)

AC = 8

Therefore, the value of AC = 8.

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How many terms are there in the surface area formula below?2(lw + wh + hl) 3 terms.

What are the three terms ?

The total surface area of a cuboid= 2(lw + wh + hl)

Here, w= width, h= height, l= length

Thus, there are 3 terms in the surface area formula.

What is a total surface area?

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13.5 cm²   is the surface area of the cube  .

What is surface area of cuboid?

If the edge of a cube have a length =  a unit

then, the surface area of the cube = 6a² unit

here, the edge of a cube have length  a = 1.5 cm

Therefore , the surface area of the cube 6a² = 6 × 1.5²

                                                                          = 13.5 cm²

The area of each face = ( the length of the edges)²

The surface area of whole cube = 6 × the area of one face

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Answer:

.002 or

2x10^-3

Step-by-step explanation:

make sure the exponents match

8 x 10^-3 =

.008 × 10^-3

(.008 × 10^-6) ÷ (4 x 10^-6)

10^-6 cancels out

.008 ÷ 4 = .002

or

2x10^-3

a) The square that does not touch one of the perimeter squares is the square 3C.

b) The area is 10 units.

The perimeter squares are the outer squares of the image. So, the only square that does not touch one of the perimeter squares is the central one. To identify it, you need to first see in which row it is, and you can see that it is row 3.

Then you need to identify the column, the central square is in column C.

Then the square that does not touch one of the perimeter squares is the square 3C.

What is the combined area of rows 4 and 5?

Let's say that each square has an area of one unit. Now, we have 5 columns, then each row has 5 squares, then the area of each row is 5 units.

So, if we have two rows, the area will be: 2*5  units = 10 units.

The area is 10 units.

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According to the solving the slope of the ramp = 0.175.

shows the steepness of an inclination The slope is just the ratio of the rise over the run, or the change there in vertical out over change in the horizontal, as seen below:

find the coordinates of two points on the line. Calculate the difference in y-coordinates between these two places (rise). Determine the x-coordinate difference between these two places (run). Divide the y-coordinate difference by the x-coordinate difference (rise/run or slope).

The given values are indeed the heights of a two beams and indeed the distance between them, which are:

Y₁ = 3.5ft

Y₂ = 10.5 ft

ΔX = 40 ft

To get the slope of both the ramp, enter the following values into the slope formula:

m = (Y₂ - Y₁)/ΔX

  = (10.5 - 3.5)/40

  = 7/40

= 0.175

According to the solving the slope of the ramp = 0.175

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Answer:

1000

Step-by-step explanation:

The closest 1000 to 598 is 1000.

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

for our rectangle here that means

2×(5x) + 2×(x - 3) = 42

10x + 2x - 6 = 42

12x - 6 = 42

12x = 48

x = 4

length = 5x = 5×4 = 20 in.

width = x - 3 = 4 - 3 = 1 in.

Answer:

190

Step-by-step explanation:

Similar to the handshake problem, if every student must talk with another person, each student will talk to 19 other students. However, a conversation consists of two people, so we must divide the number of ways we can rearrange the two people. Therefore, our answer is 190

The value of top angle x will be 104° for the given isosceles triangle.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

In a triangle, the sum of all three angles is 180°

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

Given the roof as an isosceles triangle with a base angle of 38°.

Since in an isosceles triangle two sides and two angles are equal.

Since the sum of all angles of a triangle is 180 degrees.

So,

x + 38 + 38 = 180

x + 76 = 180

x = 104°.

Hence "The value of top angle x will be 104° for the given isosceles triangle".

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exact form:

decimal form:

mixed number form:

Answer:

-11/3

Step-by-step explanation:

Convert −4 5/9 to improper fraction -41/9 and do the math.

-41/9 + 8/9

-33/9

-11/3

If Martina has 16 cars available to rent, and if c is the number of cars she would have left after renting r of them, then the equation relating c to r will be c = 16 - r, and the number of cars she would have been left with after renting 14 of them is calculated to be 2.

An algebraic expression is a type of expression consisting of both numerals and letters.

If Martina has a total of 16 cars available to rent, then the equation or algebraic expression relating c to r is,

c = total number of cars available to rent - r

c = 16 - r

After renting 14 of the total cars available, then the number of cars left can be calculated using this equation,

c = 16 - r

c = 16 - 14

c = 2

Thus, the number of cars she would have been left with is calculated to be 2.

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The distance between points F and G is 15 units.

The length of the line segment connecting two points on a plane is known as the distance between the points. The formula for distance between two points ([tex]x_{1}[/tex],[tex]x_{2}[/tex]) and ([tex]y_{1}[/tex],[tex]y_{2}[/tex]) is given by

distance between two points =[tex]\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2 } }[/tex]

The equation can be used to calculate the distance between any two locations on an x-y plane or coordinate plane.

The point F is (-9,14) and point G is (1,-19)

distance between F and G

=[tex]\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2 } }[/tex]

=[tex]\sqrt{(-9-1)^2+(-14-(-19))^2 } }[/tex]

=[tex]\sqrt{(-9-1)^2+(-14+19)^2 } }[/tex]

=[tex]\sqrt{(-10)^2+(5)^2 } }[/tex]

=[tex]\sqrt{100+25}[/tex]

=[tex]\sqrt{125}[/tex]

=15 units.

Distance between point F and G is 15 units.

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Answer:

Step-by-step explanation:

x=5

The absolute value equation used to solve this problem: | x - 82 | = 12, where x = grade.

Now,

Given:

Let 'x' be the value that gives the value of grades.

The absolute value equation to find the grades will be given by: | x - 82 | = 12

=> x - 82 = ± 12

For maximum value of the grades, x - 82 = 12

=> x = 82 + 12

=> x = 94.

For minimum value of the grades, x - 82 = -12

=> x = 82 - 12

=> x = 70.

Hence, The absolute value equation used to solve this problem: | x - 82 | = 12, where x = grade.

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Answer: factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

Step-by-step explanation:

According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the midpoint of the sides.

The coordinates of the centroid (P) are (3 + 2, 6) or (5, 6).

The centroid method is an agglomerative clustering method in which the similarities (or dissimilarities) between clusters are defined in terms of the centroids (i.e., the multidimensional means) of the clusters on the clustering variables.

According to the centroid theorem, the triangle's centroid is located 2/3 of the way between the vertex and the midpoint of the sides.

The triangle has a balance point at the centroid.

Find the centroid of the triangular coffee table.

Use the centroid formula [tex](x_1+x_2+x_3/3, y_1+y_2+y_3/3)[/tex]

The centroid of the triangle is (3 + 5 + 7/3, 6 + 2 + 10/3) or(5, 6).

Let the points be A(3, 6), B(5, 2), and C(7, 10). The midpoint D of BC is  (5 + 7/2, 2 +10/2) OR (6, 6).

Note that AD is a line that connects the vertex A and D, the midpoint of BC. The distance from D(6, 6) to A(3, 6) is 6 – 3 or 3 units.

If P is the centroid of the triangle ABC, then So, the centroid is 2/3(3) or 2 units to the right of A.

The coordinates of the centroid (P) are (3 + 2, 6) or (5, 6).

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Answer:

what

Step-by-step explanation:

Using it's formula, the average rates of change are given as follows:

a) 30 meters per second.

b) -10 meters per second.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given by the following equation:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For item a, taking the data from the table, we have that:

Hence the rate is given as follows:

r = (138 - 0)/(4.6 - 0) = 30 meters per second.

For item b, taking the data from the table, we have that:

Hence the rate is given as follows:

r = (0 - 23)/(11.5 - 9.2) = -10 meters per second.

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The standard equation for the given slope is y - 2 = 0

These are two methods for finding the equation of a line given a point and slope. Create the equation y = mx + b.

We just solved using the m given in the problem and the b. Point-slope form = y-y1 = m (x-x1), where (x1, y1) is the specified point and m is the specified slope. "x" and "y" remain as variables.

Putting (0,2) for (x1, y1) and m=0, we get

y-2=0(x-0)

(y-2) =

y-2=

+y-2=0

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   The equation of the parabola that has vertex at (0,0 ) and focus (-1, 0) is

  A parabola is a quadratic function that can move on any axis, it is composed of:

   The equation that defines a parabola can be given by:

(x - h)² = 4p(y - k)

(y - k)² = 4p(x - h)

  This will depend on its aperture

  Since the vertex and the focal axis are on the same axis, we analyze that:

(y - 0)² = 4p(x - 0)

f = (0 + p, 0)

0 + p = -1

p = 0 - 1

p= -1

(y - 0)² = 4*-1(x - 0)

(Y)² = -1(X)

x = -y²

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Answer:

Well 40% of 15 is 6

Step-by-step explanation:

It depends on how many shots it takes to win a prize

Answer:

[tex]x=-\frac{42}{31}[/tex]

Step-by-step explanation:

2 ( 5 - 10x ) + 8x = 19x + 52

→ Expand brackets

10 - 20x + 8x = 19x + 52

→ Simplify

10 - 12x = 19x + 52

→ Minus 19x from both sides

10 - 31x = 52

→ Minus 10 from both sides

-31x = 42

→ Divide both sides by -31

[tex]x=-\frac{42}{31}[/tex]

The seventh term of the given geometric progression is: 729.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Now,

Given GP: 1, -3, 9, .....

Here, a₁ = 1

a₂ = a₁ (r)

=> 3 = 1 (r)

=> r = 3

Thus, a₇ = a₁ (r⁷⁻¹) = 1 (3⁶) = 729.

Hence, The seventh term of the given geometric progression is: 729.

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Answer:

1.)

[tex]\frac{3a}{4} =\frac{1}{4} \\[/tex]

cross multiply

[tex]12a=4\\\frac{12a}{12} =\frac{4}{12} \\a=\frac{1}{3}[/tex]

2.)[tex]\frac{7}{2} =\frac{c}{\frac{8}{7} }[/tex]

cross multiply

[tex]c=\frac{7}{2} *\frac{8}{7} \\c=\frac{56}{14} \\c=4[/tex]

3.)[tex]\frac{6}{5} =\frac{h}{\frac{3}{8} } \\[/tex]

cross multiply

[tex]\frac{6}{5} *\frac{3}{8} =h\\h=\frac{18}{40} \\h=\frac{9}{20}[/tex]

4.)[tex]\frac{-2}{9} =\frac{-3m}{2} \\[/tex]

cross multiply

[tex]-2(2)=9(-3m)\\-4=-27m\\\frac{-4}{-27}=\frac{-27m}{-27} \\m=\frac{4}{27}[/tex]

5.)[tex]\frac{7}{6} =\frac{7p}{3} \\42p=21\\ \frac{42p}{42} =\frac{21}{42} \\p=\frac{1}{2}[/tex]

6.)[tex]\frac{x}{\frac{1}{7} } =-\frac{4}{7} \\x=\frac{1}{7} *\frac{-4}{7} \\x=\frac{-4}{49}[/tex]

7.)[tex]\frac{n}{\frac{4}{9} } =\frac{10}{9} \\n=\frac{10}{9} *\frac{4}{9} \\n=\frac{40}{81}[/tex]

8.)[tex]\frac{5}{3} g=-\frac{8}{3}\\ g=-\frac{8}{3} /\frac{5}{3} \\g=\frac{-8}{3}*\frac{3}{5} \\ g=\frac{-24}{15} \\g=\frac{-8}{5}[/tex]