Please refer to picture

The surface area of the cone is  282.6 [tex]in^2[/tex].

What is surface area of cone?

  The region that a cone's surface occupies in three dimensions is known as the surface area of a cone. The whole area a cone's surface covers is known as the cone's surface area. The overall surface area will include the cone's lateral and base surfaces. A three-dimensional solid construction with a circular base is referred to as a cone. A cone can be thought of as a collection of irregularly shaped circular discs that have been stacked on top of one another while maintaining a constant ratio between the radii of the adjacent discs. It is the total of the cone's lateral area and base area.

Here the given ,

=> Height h= 12in

=> Radius r = 5 in

Using surface area of cone formula,

=> Surface area SA = [tex]\pi[/tex]r(r+ [tex]\sqrt{r^2+h^2}[/tex]) square unit.

=> surface area SA = 3.14*5(5+[tex]\sqrt{12^2+5^2}[/tex])

=> surface area SA = 15.7(5+[tex]\sqrt{144+25}[/tex])=15.7(5+13)

=> surface area SA = 15.7*18=282.6 [tex]in^2[/tex]

Therefore surface area of the cone 282.6 [tex]in^2[/tex].

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Rewriting all numbers in base 5

1000 = 13000

1001 = 13001

1002 = 13002

2000 = 31000

The base 5 number whose digits have least sum are 13000 and 31000

The decimal notation of the numbers are 1000 and 2000

Define unit number.

The rightmost point in a number or the number one are both acceptable definitions of the word "unit" in mathematics. A unit can also be an item or a person that is seen as distinct and whole but is actually a component of a whole or group. An identification number for a unit in a declaration is referred to as a unit number.

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The dimensions of this rectangular tank that has the minimum surface area are 42 feet and 21 feet.

First of all, we would determine the surface area of this rectangular tank with a square​ base by using this formula:

h = V/s²

Where:

For the surface area of this rectangular tank with a square​ base, we have:

Surface area, A = base area + 4(lateral area)

Surface area, A = s² + 4(s × h)

Surface area, A = s² + 4(s × V/s²)

Surface area, A = s² + 4V/s

Next, we would take the first derivative of the surface area as follows:

A' = 2s - 4V/s²

Substituting the given parameters into the formula, we have;

A' = 2s - 4(37044)/s²

For the minimum surface area dimension, the first derivative of the surface area would be equated to zero:

2s - 148,176/s² = 0

148,176/s² = 2s

148,176 = 2s³

s³ = 74,088

s = ∛74,088

s = 42 feet.

For the height, we have:

Height, h = V/s²

Height, h = 37044/42²

Height, h = 37044/1764

Height, h = 21 feet.

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Answer:

A fruit seller buys 712 fruits of which 3/4 are apples. The apples that he bought 1/3 were found to be rotten if he sold all the good apples at Rs.5 1/4 each.

Step-by-step explanation:

If FG = 10x − 10, GH = x + 4, and FH = 16, FG is 10

information given in the question include

FG = 10x − 10

GH = x + 4

FH = 16

The problem is solved using substitution. this involves replacement of a variable with another that are same.

An instance of this a line FH having points FG and GH

FH contains FG and GH, hence adding both FG and GH gives FH

FH = FG + GH

plugging in the values

16 = 10x - 10 + x + 4

collecting like terms

16 = 11x - 6

16 + 6 = 11x

22 = 11x

rearranging the equation

11x = 22

x = 2

FG = 10x − 10

substituting the value of x

FG = 10 * 2 − 10

FG = 20 - 10

FG = 10

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After using the property of power, the expressions as a power of the number a is [tex](a^3)^{-2} = a^{-6}[/tex] , [tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex] and [tex]((a^2)^{-2})^2=a^{-8}[/tex] .

In the given question we have to solve the given expressions as a power of the number a where a≠0.

The first given expression is [tex](a^3)^{-2}[/tex].

Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

Simplifying the expression.

[tex](a^3)^{-2} = a^{3*(-2)}[/tex]

[tex](a^3)^{-2} = a^{-6}[/tex]

The second expression is [tex](a^{-1}\cdot a^{-2})^{-3}[/tex]

Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(-1)\times(-3)}\cdot a^{(-2)\times(-3)}[/tex]

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{3}\cdot a^{6}[/tex]

Using the property of sum of power [tex]a^m\cdot a^n=a^{m+n}[/tex]

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(3+6)}[/tex]

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex]

The third expression is [tex]((a^2)^{-2})^2[/tex].

Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

[tex]((a^2)^{-2})^2=((a^2)^{(-2)\times2})[/tex]

[tex]((a^2)^{-2})^2=(a^2)^{-4}[/tex]

Again using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

[tex]((a^2)^{-2})^2=a^{2\times(-4)}[/tex]

[tex]((a^2)^{-2})^2=a^{-8}[/tex]

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The value of the number 9.15 x 10° written in standard form is equal to 9.15.

As given in the question,

Given number is equal to :

9.15 x 10°

Given number 9.15 x 10°  is written in standard form.

The value of the given number 9.15 x 10°  written in standard form is given by:

9.15 x 10°

Here 10° = 1

Using property of number: Any number raise to zero is always equal to 1.

9.15 x 1

Using Multiplicative identity , number multiply to 1 remain number itself.

= 9.15

Therefore, the value of the number 9.15 x 10° written in standard form is equal to 9.15.

The complete question is:

What is the value of 9.15 x 10° written in standard form?​

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The statement that accurately describes the difference between short-term and long-term capital gains in terms of taxes is A. Long-term capital gains are from investments that have been held for more than one year and are taxed at a lower rate than short-term capital gains.

A capital gains tax is a tax levied on profits made from the sale of a non-inventory asset. Capital gains from the sale of stocks, bonds, precious metals, real estate, and property are the most common.

Short-term capital gains are profits made from selling assets held for a year or less. Long-term capital gains, on the other hand, are gains from assets held for more than a year.

In conclusion, based on the information illustrated, the correct option is A.

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( 60+12x )/5 fish fisherman will catch in 5+x days .

The unit method is a method of solving a problem by first obtaining the value of a single unit,  then multiplying the value of the single unit to obtain the necessary value.

Assume you go to the market to buy six apples. The shopkeeper told you that he sells 10 apples for 100 rupees. In this case, the apple is the unit and the apple price is the value. Knowing the units and values ​​is important when solving problems using unitary methods.

For simplicity, always write what you calculate on the right and what you know on the left. In the problem above, we know the amount of apples, but we don`t know the value of the apples. Note that the concept of ratio and ratio is used for problems related to this method.

5 days ------------> 12 fish

1 day --------------> 12/5 fish

5 + x days --------------> 12/5 x (5+x)

                                   = ( 60+12x )/5 fish

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The table of the equivalent ratios is:

Toss     Dollars  

5             2

30           12

45           18

The points are plotted in the diagram below.

Applying the knowledge of ratios we can create a table of equivalent ratios, given that it cost $12 to toss 30 rings.

Therefore, the ratio of dollars to toss is: 12:30 = 2:5.

Number of toss = x

Amount in dollars = y

Substitute k = 2/5 into y = kx to derive an equation to use to create a table of equivalent ratios:

y = 2/5x.

Therefore, wheny = 2:

2 = 2/5(x)

10 = 2x

x = 5 toss

When x = 45:

y = 2/5(45)

y = 18 dollars

The table of equivalent ratios is completed as:

Toss     Dollars  

5             2

30           12

45           18

(5, 2), (30, 12), and (45, 18), which are the points of the equivalent ratio table are plotted as shown in the diagram below.

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Answer:

765

Step-by-step explanation:

The graph of the linear equation can be seen in the image at the end.

Here we have the linear equation:

y = -2x - 1

To graph this, we need to evaluate from x = -2 to x = 2, this means replacing the value of x by the correspondent number.

if x = -2, then:

y = -2*(-2)  - 1 = 4 - 1 = 3

So we have the point (-2, 3)

if x = -1

y = -2*-1 - 1 = 2 - 1 = 1

We have the point (-1, 1)

If x = 0

y = -2*0 - 1 = -1

We have the point (0, -1)

If x = 1

y = -2*1 - 1 = -3

We have the point (1, -3)

If x = 2

y = -2*2 - 1 = -5

We have the point (2, -5)

Now we just need to graph these 5 points on a coordinate axis and then connect them with a line, the graph of the linear equation can be seen below.

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The regular price of the tally set is $300.

From the information Illustrated, Great by is reducing by 250% the regular price of a tally set selling it for $225.

Let the regular price be represented by x.

Therefore, x - (25% × x) = 225

x - 0.25x = 225

0.75x = 225

Divide

x = 225 / 0.75

x = 300

The price is $300.

Note that the above percentage in the question is 25% and not 250%.

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Answer:

See below

Step-by-step explanation:

You can pull  one y   and 6 n's out to start

then   4/5 = 24/30     and 5 / 6 = 25/30

and you can factor out a   -1

- y n^6 /30  ( 24  + 25 y^3n^2 )

Examining the figure, the correct options are

Two angles are said to be congruent when they are equal to each. The symbol to represent congruency is ≅

The following angles are congruent in the figure

Corresponding angles refers to angles that are in a position that are in matching position to another angle.

Corresponding angles are said to be equal when there are parallel lines intersected across by a line called transversal line.

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4

Step-by-step explanation:

[tex]{ \tt{ \frac{5}{1} \times \frac{4}{5}}} [/tex]

[tex]{ \tt{ \frac{5 \times 4}{5}}} [/tex]

[tex]{ \tt{ = \frac{20}{5}}} [/tex]

[tex] = { \green{ \boxed{ \pink{ \sf{4}}}}}[/tex]

Answer: y= (2/3)x - 2

Step-by-step explanation:

The biggest way to remember equations like these is to know rise over run which means however many times it goes up until it intersects with both x and Y will be on the top of the fraction and however many times it goes to the right until it intersects with both x and y will be on the bottom of the fraction. So since it hits (0, -2) then intersects at (3,0) it will be 2/3x and the Y is where X equals zero so it would be -2. Hope that helps!

Answer:

y  =  [tex]\frac{2}{3}x - 2[/tex]

Step-by-step explanation:

Step 1:

Choose two points on the graph, (x1, y1) and (x2, y2), to find the slope.

Find the ratio between change in y-values and change in x-values.

m = (y2 - y1) / (x2 - x1)

Points I picked:

(x1, y1) = (0, -2)

(x2, y2) = (3, 0)

Then,

m = (0 - (-2)) / (3 - 0)

m = 2/3

Step 2 :

Find the y-intercept from the graph. That is the point at which the line intersects the y-axis.  

The y-intercept is -2.

b  =  -2

Step 3 :

Use the slope (m) and y-intercept (b) to write the equation in slope-intercept form:

y = mx + b

Substitute m = 2/3 and b = -2

y  =  2/3 x - 2

The populations, considering an exponential function, are given as follows:

An increasing exponential function is modeled according to the rule presented as follows:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which the variables of the function are:

In this problem, the parameters are given as follows:

A(0) = 16, r = 0.2.

Hence the function, written as P(t), is:

[tex]P(t) = 16(1.2)^t[/tex]

The numeric values are found replacing the lone instance of t by the value at which we want to find the numeric value, hence:

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1/[tex]a^{6}[/tex] is the required number.

Numbers, symbols and operators (such as and times) grouped together that show the value of something.

Given an expression (a³)^-2

(a³)^-2 = [tex]a^{-6}[/tex] = 1/[tex]a^{6}[/tex]

Hence, 1/[tex]a^{6}[/tex] is the value of the expression (a³)^-2

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The equation of the line is ,y= -9x+5.

Acc to our question-,

We should use the slope-intercept formula to solve this problem.

The point-slope formula states:= [ y = mx + c]

Where m is the slope and c is the y-intercept for the point (0,y1)

Substituting the information provided we get the equation: y= -9x+5.

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The measure of CBA is 44° , the measure of CAB is 46° and the sum of the three interior angles of the triangle is 180°.

According to the question,

We have the following information:

Angle CAB = 2x

Angle CBA = 3x-20

And the given triangle is a right-angled triangle which means that one of its angle is 90°.

Now, we know that the sum of three angles of a triangle is 180°.

So, we have the following expression:

2x+3x-20+90 = 180°

5x+70 = 180

5x = 180-70

5x = 110

x = 110/5

x = 22°

Now, putting the value of x in given angles:

Angle CAB = 2x

Angle CAB = 2*22

Angle CAB = 44°

Angle CBA = 3x-20

Angle CBA = 3*22-20

Angle CBA = 66-20

Angle CBA = 46°

Hence, the measure of CBA is 44° , the measure of CAB is 46° and the sum of the three interior angles of the triangle is 180°.

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The percentage of card  which is not divisor of 45 is 23.077%

Always write the things that need to be estimated on the right side and the variables that are known on the left side to simplify the task. In the important in the current, the number of apples is known, but it is unclear what they are worth. It should be highlighted that issues with this method are addressed using the concepts of ratio and proportion.

What does the term "percent" mean?

A fraction of one hundred is used to express a quantity or ratio as a percentage. The acronyms "pct," "pct," and occasionally "pc," as well as the percent symbol, "%," are also frequently used.

A % is a numeric expression that lacks both dimensions and a measurement system. The formula to determine the proportion of one number to another is percentage = (Original number/Another number) x 100.

In mathematics, a percentage is a number or ratio that represents a portion of 100. In percentages, 100% is meant. It contains no units.

A %, also known as a decimal or a fraction, is a figure that indicates how many out of 100 we are discussing. For example, "three for the price of one" is a percentage.

Given That:

In the deck of 52 cards You pick randomly 5 , 6 , 7 , 8
so each card has 4 variant
now for getting probability of not getting a divisor of 45 is
total outcomes = 52
observable outcomes = 4+4+4 = 12
its because 5 is a divisor so we didn't include it
hence the probability is 12/52
Percentage of this probability is 0.23077 x 100 = 23.077%

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The coordinates of G(4, 4) , H (0, 2),  J(8, 0)

In order to construct the three sets of relationships between the coordinates of each triangle's three sides' ends and the shared midpoint, we must first set up the three sets of relationships.

G(x(G), y(G))

K(2, 3) (2, 3)

M(6, 2) (6, 2)

H(x(H) and y(H))L (4, 1)

J(x(J), y(J))

K(2, 3) at the midway of side GH

According to the x-component:

x(H) = x(G - x(H))/2

x(G)-[x(H)-x(G)] = 2*x(H)

x(H) + x(G) = 4

x(H) = 4 - x(G) (G)

According to the y-component:

y(H) plus [y(G) - y(H)]/2 = 3.

2*y(H) plus [y(G-y(H)] = 6

y(H) + y(G) = 6

y(H) = 6 - y(G) (G)

Midpoint L(4) and side JH(1):

According to the x-component:

(x(H) + [x(J) - x(H)]/2) equals four.

2*x(H) plus [x(J)-x(H)] = 8

x(H) + x(J) = 8

x(H) = 8 - x(J) (J)

According to the y-component:

y(H) = y(J - y(H)]/2 + y(J) = 1

y(J) - y(H) = 2*y(H)

y(H) + y(J) = 2

y(H) = 2

Side GJ with M(6, 2) as the midpoint:

For the x - component, the formula is: x(J) = [x(G) - x(J)]/2 = 6 2*x(J) = [x(G)- x(J)] = 12 x(J) = 12 - x (G)

y(J) + [y(G) - y(J)]/2 = 2 2*y(J) + [y(G)- y(J)] for the y-component. = 4 y(J) = 4 - y + y(G) = 4 y(J) (G)

The x and y coordinates may now be easily separated, and we can use algebra to isolate each one and determine its location.

x(H) = 4 - x(G), 8 - x(J), and 12 - x(J) (G)

Because x(H) = x (H)

4 - x(G) = 8 - x(J) (J)

8 - x(J) - 8 - x(G) - 4 = -x(J) x(J) x(J) = 4 + x (G)

Using 1.c above and this relationship now x(J) = x(J), so:

-2 * x(G) = -8 x(G) =, 4 12 - x(G) = 4 + x(G) 12 - x(G) - x(G) - 12 = 4 + x(G) - x(G) - 12

Given that x(J) = 4 + x(G) above, x(J) = 4 + 4 = 8 and x(H) = 4 - x(G) = 4 - 4 = 0 respectively.

Let's now perform the identical procedure using the y-coordinates.

y(H) = 6 - y(G), y(H) = 2 - y(J), y(J) = 4 - y(G),

and since y(H) = y(H), 6 - y(G) = 2 - y(J), -y(G) = 2 - y(J) - 6 = -y(J) - 4 y(G) = y(J) + 4 Now that y(J) = 4 - y,

we may substitute (G).

y(H) = y(G) - 2 and y(H) + 4 - y(G) = 2

and y(H) + 4 - y(G) = 2 - 4 and y(G)

Since y(H) = 6 - y(G)

according to 1. above, y(H) = y(G) - 2 + 6 - y(G) 2 * y(H) = 4 y(H) = 2 y(H) = 2 - y(J) 2 = 2 - y(J) y(J) = 4 - y(G) 0 = 4 - y(G) y(G)

H(x(H), y(H)), G(x(G), y(G)), and J(x(J), y(J)) are the results.

To determine the coordinates of the angles or triangle's tips, we used the midpoints of each side.

The coordinates are: H (0, 2) G(4, 4) J(8, 0)

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He earned $71.5 if he earn $11 /hr. I worked for 6 and a half hrs yesterday.

An hour (symbol: h; also abbreviated as hr) is a measure of time that is traditionally thought of as one-fourth of a day and that, according to science, lasts between 3,599 and 3,601 seconds, depending on how quickly the Earth rotates. There are 24 hours in a day and 60 minutes in an hour. 60 minutes is one of the 24 equally spaced out segments of a day.

Given,

Earns $11/hr

Worked for 6 hours and 30 minutes

Multiplying:

$11 × 6.5 hours

$ 71.5

He earned $71.5 if he earn $11 /hr. I worked for 6 and a half hrs yesterday.

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Answer:

b= -2

Step-by-step explanation:

This is written in the y=mx+B form. This means that x is our slope, and -2 is our y-intercept (b). This meakes b= -2

-Hope this helped

Answer: x=6.

Step-by-step explanation: First go to the Algebra Calculator.

The value of x will be= 90 degress.

acc to our question-

hence,The value of x will be= 90 degress.

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The linear equation we need to solve is:

$25.50*w = $309.99 - $131.49

And the solution is w = 7.

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $131.49, and save another $25.50 per week, then the amount you have after w weeks is:

f(w) = $131.49 + $25.50*w

So the linear equation we need to solve is:

$131.49 + $25.50*w = $309.99

To solve this we need to isolate w.

$131.49 + $25.50*w = $309.99

$25.50*w = $309.99 - $131.49

w = ($309.99 - $131.49)/$25.50 = 7

So they can buy the chair after 7 weeks.

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