What is the decimal equivalent of 2
- ?
3​

Answer:

the general Question

which repersents the nth term of the sequence {2,-1,-4,-7,...}formula for the nth term in an arithmetic sequence is: an = a0 + d(n-1) where a0 is the first term, n is nth, d is the difference for our problem a0 is -2, d is 3

Step-by-step explanation:

helloineedmppiontsthe general formula for the nth term in an arithmetic sequence is: an = a0 + d(n-1) where a0 is the first term, n is nth, d is the difference for our problem a0 is -2, d is 3

The geometric series defined by 6 + 5 + 25/6 + 125/36 +....., is a convergent series. The sum of convergent series is equals to the 36.

An infinite geometric series is which one of the following form \(∑a{r}^{n−1} \); where, n varies from 1 to ∞. Then it converges only when the absolute value of the common ratio is less than 1, i.e., |r|<1. When the series converges, sum formula for series is Sum = a/(1−r)

where, a --> first term and

r -->constant ratio of every two successive terms

We have a geometric series defined as 6 + 5 + 25/6 + 125/36 +.....

First term of series, a = 6

Common ratio of series, r = 5/6 < 1

We have to determine if the series converges or diverges. As we see the constant ratio, r = 0.82, which is less than 1. So, from the geometric series test this series is convergent series. Now, the formula for the sum to infinity of a geometric progression, S = a/(1 - r)

= 6/( 1 - 5/6)

= 6 × 6

= 36

Hence, required sum of series is 36.

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Complete question:

determine whether the geometric series is convergent or divergent, 6 + 5 + 25/6 + 125/36 +.....convergent divergent correct: your answer is correct. if it is convergent, find its sum. (if the quantity diverges, enter diverges.) incorrect: your answer is incorrect.

Answer:

The expression;

represents how much more Elena spent than Taniy

Explanation:

Let the variable p to represent the price per pound of cherries.

Given that Elena buys a watermelon for $6.55 and 3 pounds of cherries.

The total cost Elena spent is;

Taniy buys a pineapple for $4.35 and 2 pounds of cherries.

The total cost Taniy spent is;

The amount Elena spent more than Taniy is;

Therefore, The expression;

represents how much more Elena spent than Taniy

Answer:

T=7

Step-by-step explanation:

(T-8) x (-t+15)

Then 15-8

T= 7

Distributive Property.

In a research experiment, the variable that is measured by the experimenter is: dependent variable.

Therefore, in a research experiment, the variable that is measured by the experimenter is: dependent variable.

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The relative frequency of class D is 0.35.

The number of times an event occurs is called a frequency. Relative frequency is an experimental one, but not a theoretical one. Since it is an experimental one, it is possible to obtain different relative frequencies when we repeat the experiments.

The ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes gives the value of relative frequency.

Consider the given partial relative frequency distribution.

  Class            Relative frequency

    A                         0.22

    B                         0.18

    C                         0.43

    D                            

Then,

We need to find the relative frequency of class D

We know that,

Sum of relative frequency is equal to one.

that is.

\($0.22+0.18+0.25+$\) relative frequency of class D=1

0.65 + relative frequency of class \($\mathrm{D}=1$\)

relative frequency of class D=1-0.65

=0.35

We get,

Relative frequency of class D Is 0.35

Therefore, the relative frequency of class D is 0.35

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The dimensions of the rectangle such that the rectangle have the greatest area is length  = 8 and width = 4   .

In the question ,

it is given that ,

a rectangle is inscribed with its base on the x axis , and its upper corner on the parabola y = 12 − x²  ,

let the coordinate of the upper right corner be P(x,y) ,

and A be the area of the rectangle .

the point P lies on the parabola , given y = 12 − x² ,

So,  P = P(x,12−x²)

Due to symmetry of the rectangle,  the width of rectangle is half the distance between P and the y axis ,

that means width = 2x   and length = y .

Area of the rectangle = width × Length

= 2x * y

= 2x (12 − x²)

= 24x - 2x³

To maximize the area we differentiate Area with respect to x ,

we get ,

dA/dx = 24 - 6x²

for critical point dA/dx = 0 ,

24 - 6x²  = 0

6x² = 24

x² = 4

x = ±2 ,

since length cannot be negative ,

So , x = 2 .

to check for maximum and minimum ,we differentiate Area with respect to x,

we get

d²A/dx² = -12x

substituting , x = 2 ,

we get -12 < 0, So , the area is maximum .

hence the width = 2*2 = 4

and length = 12 - 4 = 8

and the maximum area is 32 .

Therefore , The dimensions of the rectangle such that the rectangle have the greatest area is length  = 8 and width = 4   .

The given question is incomplete , the complete question is

A rectangle is inscribed with its base on the x axis and its upper corners on the parabola y = 12 − x² . What are the dimensions of such a rectangle with the greatest possible area ?

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Answer:

1. (any number less than 10) < 10

2. 520 (division)

   520

➗     2

   260

3. (any number less than 3 *1 or 2*) < 3

4. (any number greater than 1) > 1

5. (Subtraction - A number subtracting two and the result is less than 10) < 10  

Step-by-step explanation:

1. The symbol "<" shows greater than. It is facing the number "10",

So, we need to get any number below 10. As example: 1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9. The numbers I mentioned there are what you can use for question 1.

-----------------------------------------------------------------------------------------------------------------

2. The number 520' is what I find to be multi-result but I would do division. Number 520 is part of the addition, subtraction, multiplication, and division but I am doing division.

Divison:

   520

➗     2

   260

Multiplication:

    260

  x     2

    520

Addition:

  500

+  20

  520

Subtraction:

 550

-   30

 520

These are the examples that you can try for number 2.

-----------------------------------------------------------------------------------------------------------------

3. First, you can see that there is the greater symbol here again, "<".

But this time, it's pointing to 3. Which means the number is less than 3.

The only numbers that are less than 3 is 1 and 2 so those are the 2 options you can choose.

-----------------------------------------------------------------------------------------------------------------

4. This time, the symbol is less. It's now pointing at 1, so you can pick any number that is greater than 1.

Example:

5 > 1

Like that! You can pick any number that is greater than 1 for this question!

-----------------------------------------------------------------------------------------------------------------

5. the equation "-2 < 10" is about a number subtracting 2 but than the results come in being less than 10. Since we have spotted the greater symbol as "<", and the subtraction symbol as "-".

Now, first we find a number that can subtract 2 but less than 10 in the result.

The options we have are:

1. 2 (2-2=0 ; 0 < 10)

2. 3 (3-2=1 ; 1 < 10 )

3. 4 (4-2=2 ; 2 < 10 )

4. 5 (5-2=3 ; 3 < 10 )

And so on until you reach number 9 as the result!

-----------------------------------------------------------------------------------------------------------------

Hope this helped you! I tried my best to help you. But have a good day!

The domain of the  f(x)=3x-2 form a graph is -∞ < x<∞. See the attached graph. The interval notation is given as (-∞, ∞)

It is to be noted that the domain of a function is the set of input or argument values for which the function is real and defined. Note from the graph that the function has no undefined points nor domain constraints. Hence, the domina is expressed as the notation:

-∞ < x < ∞.

If one were to solve for x,

Then

y = 3x -2

=

3x -2 = y [Flipping the eqation]
3x -2 + 2 = y + 2 {Added two to both sides]

Hence,

3x = y +2

Divide both sides by 3 to get:

3x/3 = (y+2)/3
x = [1/3y] + [2/3]

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The dimensions of the sheet metal are 10 inches by 2.86 inches.

To find the dimensions of the sheet metal, we need to use the formulas for the area and volume of a cylinder.

The formula for the volume of a cylinder is:
\(V = πr^2h\)
where V is the volume, r is the radius, and h is the height.

Since we want the volume of the stovepipe to be 900 in^3, we can plug in the values and solve for the height:
\(900 = πr^2h\)
\(h=\frac{900}{πr^{2} }\)

Now, the formula for the lateral surface area of a cylinder is:
A = 2πrh
where A is the lateral surface area.

We know that the sheet metal has an area of 1800 in^2, so we can set up an equation:
1800 = 2πrh

Substituting h from the first equation, we get:
\(1800=2πr(\frac{900}{πr^{2} } )\)

Simplifying, we get:
r = 10
So the radius of the cylinder is 10 inches.

Substituting this value of r into the equation for h, we get:
\(h=\frac{900}{π(10^{2}) }\)
h =2.86

So the height of the cylinder is approximately 2.86 inches.

Therefore, the dimensions of the sheet metal are 10 inches by 2.86 inches.

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Our standard linear slope equation is:

mx + b = y

We're told our slope is 1/2, so that's our m value.

When x = 0 our value is 5. If you need this visualized, then:

1/2 * 0 +b = 5

0 + b = 5

b = 5

So our equation looks like:

x/2 + 5 = y

The reduction of the fraction is (y-3)/4.

Suppose the fraction is proper (the numerator is smaller than the denominator).

Let it be \(\dfrac{a}{b}\)

Then, we can interpret it as:

\(\dfrac{a}{b}\)= a parts out of b parts of a thing.

There is a fraction, containing numerator(upper value) and denominator(lower value).

When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction.

A proper fraction is also called fraction which is less than 1.

And an improper fraction is ≥ 1

A mixed fraction contains a sum of whole number and a proper fraction.

Given;

=y^2-9/4y+12

=y^2-3^2/4(y+3)

=(y+3)(y-3)/4(y+3)

=y-3/4

Therefor, the answer of fraction will be (y-3)/4

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Answer:

160 females 96 males

Step-by-step explanation:

find multiples of 256

multiply 5/3 by those multiples

40/24 times 8/8= 160/96

add=

256

Answer:Formular for simple interest is

I = P X R XT

————

100

where P is the amount borrowed or loan , Rate is the percentage of interest in P while T is the Time range for the loan

Now to find the Principal, we now change the original subject of the formula to suit or reflect P.
P = I X 100

———-

R X T

= 11, 178

———

6 X 9

=. 11, 178

——

54

=. $20,700

Step-by-step explanation:

Answer:

$20,700

Step-by-step explanation:

Simple Interest Formula

I = Prt

where:

Given:

Substitute the given values into the formula and solve for P:

\(\implies \sf 11178=P(0.06)(9)\)

\(\implies \sf 11178=0.54P\)

\(\implies \sf P=\dfrac{11178}{0.54}\)

\(\implies \sf P=20700\)

Therefore, the principal amount is $20,700.

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Answer:

The polynomial has degree 4 and 2 terms.

Step-by-step explanation:

The degree is 4 because it is the highest degree among the terms (\(5x^4\) has degree 4 and \(12\) has degree 0). There are 2 terms (\(5x^4\) and \(12\)).

Hope this helps :)

u = [2, -2]. The orthogonal complement W⊥ of W is the set of all vectors orthogonal to W. In this case, a basis for W⊥ is {[2, -2]}.

Rewrite the equation in standard form for vectors

The given equation is 2x - y = 0. We can rewrite it as y = 2x

Find a vector in W
We can choose any value of x and compute the corresponding y value to find a vector in W. Let x = 1, then y = 2(1) = 2.

So, one such vector in W is v = [1, 2].

Find a vector orthogonal to v

To find a vector orthogonal to v, we need to find a vector u = [a, b] such that the dot product of v and u is zero (v • u =

0). So, [1, 2] • [a, b] = 0. This translates to 1a + 2b = 0.

Find a basis for W⊥

Solve the equation 1a + 2b = 0 for a and b. We can set a = 2 and solve for b: 2(2) + 2b = 0, which gives b = -2.

Therefore, u = [2, -2].
The orthogonal complement W⊥ of W is the set of all vectors orthogonal to W. In this case, a basis for W⊥ is {[2, -2]}.

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Answer:

15 minutes

Step-by-step explanation:

2 and a half hours is the same as 150 minutes. There are ten rows, so if you divide 150 by 10, you get 15. The farmer spent 15 minutes in each row.

Answer:

15

Step-by-step explanation:

2 hours and 30 minutes equals 150 minutes. Divide by the 10 rows equals 15 minutes each.

The side length of the large frame is 4 inches longer than the side length of the small frame.

To find the difference in side lengths between the small square frame and the large square frame, we need to find the length of the sides of each frame.

Let x be the length of the side of the small square frame. Then, we know that the area of the small frame is 16 square inches.

Area of small frame = side length of small frame x side length of small frame = 16
\(x^2 = 16\)

Taking the square root of both sides, we get:
\(x = 4 inches\)

So, the length of the side of the small square frame is 4 inches.

Now, let y be the length of the side of the large square frame. We know that the area of the large frame is 64 square inches.

Area of large frame = side length of large frame x side length of large frame = 64
\(y^2 = 64\)

Taking the square root of both sides, we get:
y = 8 inches

So, the length of the side of the large square frame is 8 inches.

To find the difference in side lengths, we subtract the length of the small frame from the length of the large frame:
\(y - x = 8 - 4 = 4\)

Therefore, the side length of the large frame is 4 inches longer than the side length of the small frame.

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A 2.5-foot-radius sand mandala's surface area is 19.63 square feet.

A Tibetan Buddhist practise known as "sand mandala" involves building and tearing down mandalas composed of different coloured sand. The ritualistic breakdown of the sand mandala is followed by ceremonies and viewing when it is finished to represent Buddhism's doctrine on the fleeting nature of material life.

Here is how to calculate a circle's area:

Circle area is equal to  πr² (where r is the radius of the circle)

We can use the radius value that has been provided to solve for the area using the following formula:

The sand mandala's size is πr²= π(2.5)²= π(6.25)= 19.63 square feet.

Hence, the sand mandala has a 19.63 square foot surface area.

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Answer:

C.)  -4/5

Step-by-step explanation:

First find two points where the line directly meets points on the map, I used (0,2) and (5,-2).You start with rise-over-run, because this has a negative rise  is -4 (numerator). The run is 5 (denominator). so -4/5

Answer:

It should be -4/5.

Step-by-step explanation:

if you take two points that are obvious, like the two intercepts, you can then use the formula (y2-y1)/(x2-x1) and plug in the points.

y intercept = (0,2)

x intercept = (2.5, 0)

(0-2)/(2.5-0)= -2/2.5 = -0.8 = -4/5

Answer:

The answer is A.

Step-by-step explanation:

B cannot be correct, as S did not represent the total amount paid.

C and D cannot be correct, since they never mentioned the "first sock"

The area οf the shaded regiοn is  24 square units

The amοunt οf space οccupied by a twο-dimensiοnaI figure is referred tο as its area. In οther wοrds, it is the quantity that cοunts hοw many unit squares cοver the surface οf a cIοsed figure.

The area οf the shaded regiοn is equaI tο the subtractiοn οf the tοtaI area tο the area οf the twο smaII squares and οne big square.

AII οf the quadriIateraIs in the shape beIοw are squares.

Then the area οf the shaded regiοn wiII be

The area οf the shaded regiοn is equaI tο the subtractiοn οf the tοtaI area tο the area οf the twο smaII squares and οne big square.

Area = 9 ×9  - 7 × 7 - 2 × 2 - 2× 2

= 81-49-4-4

= 24

The area οf the shaded regiοn is  24 square units

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Answer:

a

Step-by-step explanation:

Answer:

110

Step-by-step explanation:

you would have to place the values in a line in ascending order and cancel numbers on both sides until you only have one left in the center. If you have two left because the number of variables is even then add both and divide by two. That was the case here. Both middle numbers were 110

so...

110+110/2

220/2

110

The volume if the solid generated is 12.32 cubic units.

The volume of the solid generated by revolving the region bounded by the curves y = sin^-1(x/13), x = 0, and y = pi/12 about the y-axis can be calculated using the method of cylindrical shells.

First, we need to find the limits of integration for y. From the equation y = sin^-1(x/13), we can solve for x to get x = 13 sin(y). Since y ranges from 0 to pi/12, we know that x ranges from 0 to 13 sin(pi/12).

Next, we need to find the height of each cylindrical shell. This is simply the difference between the upper and lower curves, which is pi/12 - sin^-1(x/13).

Finally, we integrate the expression for the volume of a cylindrical shell over the range of y to obtain the total volume:

V = ∫[0, pi/12] 2πx(pi/12 - sin^-1(x/13)) dy

V = π/6 ∫[0, pi/12] (13sin(y))^2 (pi/12 - y) dy

V = π/6 ∫[0, pi/12] 169sin^2(y) (pi/12 - y) dy

V = π/6 [169(1/2)(pi/12)^2 - 169∫[0, pi/12] ysin^2(y) dy]

V ≈ 12.32 cubic units

Therefore, the volume of the solid generated by revolving the region bounded by the curves y = sin^-1(x/13), x = 0, and y = pi/12 about the y-axis is approximately 12.32 cubic units.

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Answer:

57,600 ft

Step-by-step explanation: