Choose the proportion that is true.
3/8=15/40
12/13=2/3
9/13=27/36
16/49=4/7

The radius of the quadrant whose perimeter is 52cm is 14.56cm.

A quadrant is 1/4th of a circle, consisting of two radii, perpendicular to each other.

So, the perimeter of a quadrant consists of two radii and an arc, which is 1/4th the perimeter of a circle.

Therefore, the perimeter of the quadrant = 2r + (1/4)*(2πr) = 2r + (πr/2).

Now, we are given the perimeter of the quadrant = 52cm and are asked to find its radius.

We suppose the radius to be r cm.

Therefore, we can say that:

52 = 2r + (πr/2).

or, 52 = (4r + πr)/2

or, 52*2 = r(4 + π)

or, r = 104/(4 + π) = 14.56.

Therefore, the radius of the quadrant whose perimeter is 52cm is 14.56cm.

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Answer:

25 hours.

Step-by-step explanation:

Let the hours worked be x

2/5x = 10

2x = 50

x = 25

She has to work 25 hours to spend 10 hours doing paperwork.

Answer:

  647

Step-by-step explanation:

The divisibility rule for 9 can be used to find the unknown number.

A number is divisible by 9 if the sum of its digits is divisible by 9.

The number 3D8 will be divisible by 9 when 3 + D + 8 = <multiple of 9>. Since D is a single digit, we must have ...

  11 +D = 18

  D = 7 . . . . . . . subtract 11

The number 3D8 is 378.

Now we know that the difference is ...

  ABC -3D8 = ABC -378 = 269

  ABC = 269 +378 = 647

ABC represents the number 647.

Here are the awnsers

1. D ⅔

2.C 60%

Answer: a

Step-by-step explanation:

[tex]z_0=-1-2i\\\\z_1=2(-1-2i)+(3-2i)=-2-4i+3-2i=1-6i[/tex]

This eliminates all the options except for a.

The function which represents the annual salary for total sales of x dollars, where x is greater than $250000 is 0.025x+29750.

Given basic salary=3000 p.m. , bonus 2.5% of total sales above $250000.

We have to make a function which shows the annual salary for total sales of x dollars where x is greater than $250000.

Function is a relationship between two or more variables which have each y values corresponding to x values.

According to question

Total basic salary of whole year=3000*12=$36000

We have been given total sales be x.

Sales above $250000 is x-250000

Bonus on sales=2.5%(x-250000)

Function f(x)=36000+2.5%(x-250000)

=36000+0.025x-0.025*250000

=36000+0.025x-6250

=0.025x+29750

Hence the function which shows the annual salary for total sales of x dollars is f(x)=0.025x+29750.

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Answer:

=======================

Use circumference formula to find the tire circumference:

Find the distance by multiplying the number of revolutions by circumference:

Convert the inches to feet, or yards, considering 12 in = 1 foot and 3 feet = 1 yard:

The value of x in the equation 1/2x = -1/2x when 4 is subtracted from both sides is 0(not defined)

Subtraction of fraction

Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction

1/2x = -1/2x

1/2x - 4 = -1/2x - 4

(x-8) / 2 = (-x-8) / 2

(x - 8) / 2 = (-x-8) / 2

2(x - 8) = 2(-x - 8)

2x - 16 = -2x - 16

2x + 2x = -16 + 16

4x = 0

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Answer:c

is the answer

Step-by-step explanation:

The arcs intersected by these chords are not congruent.

Given that two circles with different radii have chords AB and CD, such that AB is congruent to CD.

Let r₁ and r₂ be the radii of two different circles with centers O and O' respectively.

Assuming that the each of the ∠АОВ  and ∠CO'D is less than or equal to π.

Then, we have isosceles triangle AOB and CO'D such that,

AO = OB = r₁,

CO' = O'D = r₂,

Let us assume that r₁< r₂;

We can see that arc(AB) intersected by AB is greater than arc(CD), intersected by the chord CD;

arc(AB) > arc(CD)      .......(1)

Indeed,

arc(AB) = r₁ angle (AOB)

arc(CD) = r₂ angle (CO'D)

So, we have to prove that ;

∠AOB >∠CO'D       ......(2)

Since each angle is less than or equal to π, and so

∠AOB/2  and ∠CO'D/2 is less than or equal to π

it suffices to show that :

tan(AOB/2) >tan(CO'D/2) ......(3)

From triangle AOB :

tan(AOB/2) = AB/(2*r₁)

tan(CO'D/2) = CD/(2*r₂)

Since AB = CD and r₁ < r₂ (As obtained from the result of (3) ), therefore, arc(AB) > arc(CD).

Hence, for two circles with different radii have chords AB and CD, such that AB is congruent to CD but the arcs intersected by these chords are not congruent.

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Answer:

Step-by-step explanation:

Solution

Interesting question.

The formula for the sum of the interior angles is

(n - 2)*180 = x

In this case, x = 1260

(n - 2)*180 = 1260                            Divide both sides by 180

(n -2 )* 180/180 = 1260/180

( n - 2) = 7                                         Remove the brackets

n - 2 = 7                                            Add 2 to both sides

n - 2 + 2 = 7 +2                                 The 2s on the left cancel

n = 9

Answer: Nonagon

The polygon with an interior angle sum of 1260° is the nonagon as per the concept of interior angles.

To find the sum of the interior angles of a polygon, we can use the formula:

Sum of interior angles = (n - 2) × 180°

where "n" is the number of sides of the polygon.

To achieve an interior angle sum of 1260°, we would need to consider a polygon with fewer sides.

For example, a nonagon (9 sides) would have an interior angle sum of 1260°:

Sum of interior angles = (9 - 2) × 180°

Sum of interior angles = 7 × 180°

Sum of interior angles = 1260°

So, a nonagon (a polygon with nine sides) has an interior angle sum of 1260°.

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The correct statement regarding the limit, using asymptotes, is:

The function [tex]f(x) = \frac{28x - 10x^2}{4x^2 - 1}[/tex] has a horizontal asymptote at [tex]y = -\frac{5}{2}[/tex].

In this problem, we have a limit, which is associated with a horizontal asymptote. The limit is:

[tex]\lim_{x \rightarrow \infty} \frac{28x - 10x^2}{4x^2 - 1}[/tex]

x goes to infinity, hence we consider only the highest exponents.

[tex]\lim_{x \rightarrow \infty} \frac{28x - 10x^2}{4x^2 - 1} = \lim_{x \rightarrow \infty} -\frac{10x^2}{4x^2} = -\frac{10}[4} = -\frac{5}{2}[/tex]

Hence the correct statement is:

The function [tex]f(x) = \frac{28x - 10x^2}{4x^2 - 1}[/tex] has a horizontal asymptote at [tex]y = -\frac{5}{2}[/tex].

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The solution of the graph can be located at the point of intersection of the two lines. The solution, approximated to the tenths place will be (0.4, 2.8)

The solution of a system of two linear equations can be calculated by determining the point of intersection.

Therefore, the solution = the coordinates of the point of intersection (x-coordinate, y-coordinate).

Given graph shows the system of equations in two lines:

The solution of the graph can be located at the point of intersection of the two lines, the x-coordinate against the y-coordinate.

The integers that the x-coordinate of the point of intersection is in between are 0 and 1.

The y-coordinates of the point of intersection lie between the integers 2 and 3.

The solution, approximated to the tenths place will be (0.4, 2.8)

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Answer:

199.5 ft^3

Step-by-step explanation:

to find your answer you simply multiply all the measurements together

19 * 1.5 * 7 is your equation

19 * 1.5 * 7 = 199.5

it is 199.5 ft^3

Answer:

262 passengers can have both headphones and blankets .

Step-by-step explanation:

I hope it will help you

Answer:

Answers are below.

Step-by-step explanation:

1) 60 centimeters

2) Perimeter = 48, Area = 144

3) Circumference = 20π, Area = 100π

4) 180 feet

5) 75 meters

6) 15 yards

Hope this helps!

The 3-D figure and combination of shapes that Scarlett can use is A. Equilateral triangle prism with two equilateral triangles and three rectangles

This refers to the solid figure or shape that has defined dimensions of length, width, and height.

Therefore, based on the fact that a 3-D figure is made up of six equal squares, option A is the best answer because it contains a total of six squares.

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Answer:

Graph Number 2

Step-by-step explanation:

Use the horizontal line test: If you can draw a horizontal line at any point and it only intersects the line once, then it's a one-to-one function.

The equation for ΔFON is sin F = 9/18.

Hence, option B) sin F = 9/18 is the correct answer.

This question is incomplete, the complete question is;

Which equation is correct for ∆FON?

Answers:

A.) cos F= 9/18

B.) sin F 9/18

C.) sin F=18/9

D.) cos F=18/9

From the diagram, we have a right angle triangle.

Note that; sinθ = Opposite / Hypotenuse

Therefore, for angle F

sin F = Opposite / Hypotenuse

sin F = 9/18

The equation for ΔFON is sin F = 9/18.

Hence, option B) sin F = 9/18 is the correct answer.

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Answer:

A ∩ C = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}

A ∩ B = {3, 1, 2, 4, 5}

Step-by-step explanation:

Given that A = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}

B = the set of all Natural numbers

C= the set of all Rational numbers

So set C contains numbers that can be expressed as the ratio of two integers. Since numbers in A can be expressed as follows:

0 = 0/1,  3 = 3/1,  1 = 1/1, 1.3 = 13/10, 2 = 2/1,  4 = 4/1, 5 = 5/1

Then, A ∩ C = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}.

A ∩ B = {3, 1, 2, 4, 5}, since B contains only Natural numbers = {1, 2, 3, ...}.

The expression [tex]10^{t^2+2t-3}[/tex] is equivalent to the expression [tex](10^{t+3})^{t-1[/tex]

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

Given the expression:

[tex]10^{t^2+2t-3}\\\\=10^{t^2+3t-t-3}\\\\=10^{[t(t+3)-1(t+3)]}\\\\=10^{(t-1)(t+3)}[/tex]

The expression [tex]10^{t^2+2t-3}[/tex] is equivalent to the expression [tex](10^{t+3})^{t-1[/tex]

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The solution of Tx" + (4t - 2)X' + (13t - 4)X = 0, If X(0) = 0 is mathematically given as

[tex]&n \times(S)=\frac{c}{\left((s+2)^{2}+9\right)^{2}}[/tex]

Generally, the equation for is mathematically given as

[tex]&t x^{\prime \prime}+(4 t-2) x^{\prime}+(13 t-4) x=0, \quad x(0)=0\\\\&\Rightarrow \quad t x^{\prime \prime}+4 t x^{\prime}-2 x^{i}+13 t x-4 x=5\\[/tex]

By taking Laplace to transform,

[tex]&L\left\{t x^{13}\right\}+L\left\{4 t x^{\prime}\right\}-L\left\{2 x^{\prime}\right\}+L\{13 t x\}-L\{4 x\}=0\\\\\\&-25 x(s)-s^{2} x^{1}(5)-4 x(s)-45 x^{\prime}(s)-25 x(s)-13 x^{\prime}(5)-4 x(s)=0\\[/tex]

[tex]&\Rightarrow \quad-\left(5^{2}+45+13\right) x^{4}(5)-4(5+2) x(5)=0\\\\\\&\Rightarrow \quad\left(s^{2}+45+13\right) x^{1}(5)+4(5+2) x(5)=0\\\\\\&\Rightarrow\left(s^{2}+4 s+13\right) x^{\prime}(s)=-4(s+2)^{x}(s)\\\\\\&\Rightarrow \frac{x^{\prime}(s)}{x(s)}=-\frac{4(s+2)}{s^{2}+4 s+13}\\\\\[/tex]

In conclusion, By integrating both sides

The solution is

[tex]&x(s)=\frac{c}{\left(s^{2}+4 s+13\right)^{2}}\\[/tex]

[tex]&n \times(S)=\frac{c}{\left((s+2)^{2}+9\right)^{2}}[/tex]

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The coefficient are as follows:

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

1. 12s + 4t

Variables: s, t

Coefficient: 12, 4

2. 46rs + 10x

Variables: r, s, x

Coefficient: 46, 10

3. 12q + 14x

Variables: q, x

Coefficient: 12, 14

4. 10x + 10y

Variables: x, y

Coefficient: 10, 10

5. 17rs + 32x

Variables: r, s, x

Coefficient: 17, 32

6. 5x + 7y - 12z

Variables: x, y, z

Coefficient: 5, 7, -12

7. 36ab + 70m

Variables: a, b, m

Coefficient: 36, 70

8. 3r + 19a + 10m

Variables: r, a, m

Coefficient: 3, 19, 10

9. 7k + 16m

Variables: k, m

Coefficient: 7, 16

10. 8r + 5s

Variables: r, s

Coefficient: 8, 5

11. 9h + 120m

Variables: h, m

Coefficient: 9, 120

12. 12k + m

Variables: k, m

Coefficient: 12, 1

13. 7g + 15h + w

Variables: g, h, w

Coefficient: 7, 15 , 1

14. 4c - 8d + 12f

Variables: c, d, f

Coefficient: 4, -8, 12

15. 6t + 17r - 35j

Variables: t, r, j

Coefficient: 6, 17, -35

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Round

8724 to the nearest whole number is 8720

Based on the calculations, the slope of line YZ in simplest form is equal to 2.

Mathematically, the slope of a straight line can be calculated by using this formula;

[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Since points X, Y, and Z are collinear, we can deduce that the line passes through line Z at 6 units form the origin and 3 units for Y from the origin.

Substituting the parameters into the formula, we have;

[tex]Slope, m = \frac{6\;-\;0}{3\;-\;0}[/tex]

Slope, m = 6/3

Slope, m = 2.

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The volume of volume of the rectangular prism is=240cm³ while the surface area of cylinder =225.04cm²

The volume of rectangular prism

= l×w×h

= 10× 6× 4

= 240cm³

The surface area of cylinder,

= 2πrh+2πr²

= 2× 3.14× 2.8 × 10 + 2×3.14×2.8²

= 175.84 + 49.2

= 225.04cm²

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Answer:

4x

Step-by-step explanation:

[tex]\frac{500x^{4} }{(5x)^{3} }[/tex] = [tex]\frac{500x^{4} }{125x^{3} }[/tex] = [tex]4x[/tex]

Explanation:

The first step is to add up all the values given:

11.01 + 10.50 + 5.70 + 14.67 + 9.50 + 12.54 + 8.90 + 13.56 + 11.23 + 6.80 + 3.00 + 10.55 = 117.96

Then we divide this sum over n = 12 since this is the sample size given (i.e. the number of customers)

117.96/n = 117.96/12 = 9.83