7. What is the ratio of the interior angles of a pentagon and a decagon?​

The probability that s+d > 3 and sd > 3 is 0.03.

Plot the inequalities

The region -5 ≤ s,d ≤ 5 is the square shaded in grey.

The region s + d > 3 is the region Q shaded to the right of the straight line.

The region sd > 3 is the region R shaded to the right of the curve d = 3/s.

Find the intersection of the three regions

From the figure, the region satisfying all the above three inequalities is the region to the left of the curve d = 3/s, bounded by the square region, i.e. the region R.

Probability of region R

The required probability is the Geometric probability of the intersection region R. It is calculated as

P(R) = ar(region R) / ar(square region P).

Calculate the areas of the regions

ar(region R) = area of the rectangle to the right in the first quadrant formed by dropping a vertical from point F - area under the curve d = 3/s in the first quadrant

[tex]\[\Rightarrow \;\; \mathrm{ar(\mathbf{R}) =} \int_{3/5}^5\frac{3}{s}ds = 25-3-3\ln\frac{25}{3} = 15.64.\][/tex]

ar(region P) = 25 × 25 = 625.

Calculate P(R)

The probability of the region R, P(R) = 15.64 / 625 = 0.025.

Rounding it to the hundredth place of decimal, P(R) = 0.03.

The probability that s+d >3 and sd>3, where -5 < s,d < 5, is 0.03.

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Disclaimer: The question was incomplete. Please find the full content below.

What is the probability that s + d > 3 and sd > 3, where -5 ≤ s,d ≤5? Write your answer as a decimal rounded to the hundredth place.

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Answer:

x = 4

Step-by-step explanation:

7 * ( x-2) = 196/14

7x -14 = 14

7x = 28

x = 4

Answer:

050°

Step-by-step explanation:

The bearing of D from C is the angle between the north pole and the line joining C and D when moving in a clockwise direction.

From the diagram, the angle is 050°

Answer:

Step-by-step explanation:

A. Correct

B. Correct

C. Correct

D. False

2.

A. Correct

B. Correct

C. Correct

D. False

Hope I helped!

Answer:

0

Step-by-step explanation:0 times anything is still 0

Answer:

3.160

Step-by-step explanation:

You can solve for x using logarithm.

Rewrite in logarithm form

[tex]log_{6}4=2x\\\\x=\frac{log_64}{2}\\x=\frac{\frac{log4}{log6}}{2}\\x=\frac{log4}{log6} * \frac{1}{2}\\x=\frac{log4}{log6 * 2}\\x\approx0.386852807\\36^{6(0.386852807)-2} \approx3.160[/tex]

Answer:

[tex]\boxed {C. -2}[/tex]

Step-by-step explanation:

[tex]\textsf {Substitute x = 5 in the expression :}[/tex]

[tex]\longrightarrow \mathsf{\frac{15 - x}{x - 10}}[/tex]

[tex]\longrightarrow \mathsf{\frac{15 - 5}{5 - 10}}[/tex]

[tex]\longrightarrow \mathsf{\frac{10}{-5}}[/tex]

[tex]\longrightarrow \mathsf{-2}[/tex]

The length of CD will be option C. 3

From given diagram, triangle ABC and EDC meet at a common vertex C.

So, triangle ABC and EDC both are congruent to each other.

Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.

Therefore,

AB/ED = AC/EC = BC/CD

AC/EC = BC/CD

18/6 = (12 - x)/x

Simplifying the expression,

We get

18x = 6(12 - x)

Multiplicating the terms in right hand side,

18x = 72 - 6x

Solving 6x on both sides,

we get

18x + 6x = 72 - 6x + 6x

24x = 72

Dividing both the sides by 24, we get

24x/24 = 72/24

x = 3

Hence, the length of CD is 3.

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The correct option is option D: This is the graph of one to one function.

Function is a relationship between two sets X and Y where set X is domain and set Y is codomain.

If we draw a vertical line and it crosses the graph only once at all locations, the relation is a function and this relation will be one-one.

by checking all the options

Option A: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So it is a function with one-one relation. Therefore option A is incorrect.

Option B: Linear function is a function in which highest degree of variable is 1 and it also describes the straight line. From the graph, it is clear that it is not a straight line. Therefore option B is incorrect.

Option C: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So, it is surely a function. Therefore option C is incorrect.

Option D: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So, it is surely a one-one function. Therefore option D is correct.

The correct option is option D: This is the graph of one-to-one function.

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The answer is (-1,1) and (1,5)

Step-by-step explanation:

[tex] \sqrt{10} = 3.2 \\ then \: the \: sign \: there \: is \: = \\ \sqrt{10 } = 3.2 \\ \\ \: \sqrt{12} = 3.5 \\then \: the \: sign \: there \: is \: = \\ \: \sqrt{12} = 3.5 \\ \\ 6 \frac{1}{3} = 6.3 \: and \: \sqrt{40 } = 6.3 \\ therefore \: 6 \frac{1}{3} = \sqrt{40} \\ \\ 2 \frac{2}{5} = 2.4 \: and \: \sqrt{5.76} = 2.4 \\ then \: \: 2 \frac{2}{5} = \sqrt{5.76} \\ \\ 5 \frac{1}{6} = 5.16 \: and \: 516 \: \: therefore \: \\ 5 \frac{1}{6} = 5.16 \\ \\ \sqrt{6.2} = 2.5 \\ and \: 2.4 \: therefore \: \\ \sqrt{6.2} > 2.4[/tex]

The number represented by the arrow is 9 if each unit is represented by 1 option fourth is correct.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a number line shown in the picture.

As we can see each unit is represented by 1.

So after 2 there will be 3 and after 4 there will be 5 and so on.

So after 8, there will be 9 which is represented by the arrow.

Thus, the number represented by the arrow is 9 if each unit is represented by 1 option fourth is correct.

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Answer: 9

Step-by-step explanation:

The number line going from - 4 to + 12 represents the range of possible values for the dividend of the division expression. The arrow going from 0 to 9 indicates the actual value of the dividend. Therefore, the number represented by the arrow is 9.

Answer:

g(x) = x³ - 2

(option B)

Step-by-step explanation:

because the shape of the graph has not changed, we know that there was no direct change to x

(this would have looked like 2x³ instead of x³)

and because the graph was not shifted along the x-axis (left or right), we know that the change did not happen inside the parenthesis

(this would have looked like (x³ - 3) instead of (x³) )

we know that the only change that has happened to this graph was a downward shift along the y-axis  which can be expressed as

g(x) = x³ - 2

The equation of the red graph will be g(x) = x³ - 2.Option B is correct.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

We know that there was no immediate change to x since the graph's form has not altered. Instead of x³, this would have appeared as 2x³.

Thus we can be confident that the change did not occur inside the parenthesis since the graph was not moved down the x-axis.

We may infer that this graph's sole modification was a downward shift along the y-axis, which is written as;

g(x) = x³ - 2

The graph is also attached in the attachment.

The equation of the red graph will be g(x) = x³ - 2.

Hence option B is correct.

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A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.

En este problema tenemos un sistema formado por dos triángulos similares, la semejanza entre los dos triángulos se debe a la colinealidad entre los segmentos de línea AP' (triángulo pequeño) y AP'' (triángulo grande), así como de los lados AM y AB, así como los lados AN y AC, así como los mismos ángulos en la misma distribución. (Semejanza Lado - Ángulo - Lado)

En consecuencia, obtenemos las siguientes proporciones:

AP'/AP'' = MN/BC = 1/2     (1)

Finalmente, la proporción entre el triángulo AMN y el cuadrilátero BMNC es:

[tex]\frac{AMN}{ABC - AMN} = \frac{\frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)}{\frac{1}{2}\cdot (2\cdot a) \cdot h - \frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)} = \frac{\frac{1}{4}\cdot a\cdot h }{a\cdot h - \frac{1}{4}\cdot a \cdot h }[/tex]

[tex]\frac{AMN}{ABC - AMN} = \frac{\frac{1}{4} }{\frac{3}{4} } = \frac{1}{3}[/tex]

A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.

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Answer:

x=1

Step-by-step explanation:

20(3x-3/5) = 20(2x-2/4)

12x-12= 10x-10

12x-10x =12-10

x= 1

Answer:

Step-by-step explanation:

Solution

3x - 3       2x - 2

=====  =  ======                       Cross Multiply

5              4

4(3x - 3) = 5(2x - 2)                   Remove the brackets. Distributive Property

12x - 12 = 10x - 10                     Subtract 10 x from both sides

12x-10x - 12 = 10x-10x - 10       Combine

2x - 12 = - 10                             Add 12  to both sides

2x-12+12 = -10 + 12                   Combine  

2x = 2                                       Divide by 2

2x/2 = 2/2                                

Answer

x = 1

Answer:

it it a parallelogram

Step-by-step explanation:

it has 2 sets of 2 parallel lines

With the information given, we can not prove this quadrilateral is a parallelogram. Explanation is given.

A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

In order to prove, quadrilateral is a parallelogram:

We can prove either one of these following method;

1. Establish the congruence of the two pairs of opposing sides.

2. Show that the two opposing side pairs are parallel.

3. Show that one pair of opposed sides is parallel and congruent.

Here, we have AB = CD

And we have line AD and BC.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

AD and BC are at equal distance.

That means, AD II BC.

And to solve further, we do not have any statements.

Therefore, with given information, we can not prove this quadrilateral is a parallelogram.

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Answer:

(144)^1/2

(12^2)^1/2

12 is the answers

Step-by-step explanation:

please mark me as brainlest

Answer:

12

Step-by-step explanation:

Rewrite 144 as 12²

(12²)^1/2

Apply the power rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].

12^2(1/2)

Cancel the common factor of 2.

Cancel the common factor.

Rewrite the expression

12^1

Evaluate the exponent.

12

Answer: r = 121.92 cm

              Volume = 4/3 x 3.14 x [tex]121.92^{3}[/tex]

              7587404.65

Step-by-step explanation:

The radius is given. It's the distance from the center of the sphere to the end. The radius is 4 ft. 1 ft is 30.48cm so 4ft is 121.92cm  

(radius) r = 121.92 cm

Volume = 4/3 x 3.14 x [tex]121.92^{3}[/tex]

             = 4/3 x 3.14 x 1812278.18

             = 4/3 x 5690553.49

             = 7587404.65

Answer:

The standard deviation for the number of people with the genetic mutation in such groups of 1000 is 9.49.

Step-by-step explanation:

Standard deviation: It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

The given parameters are:

Proportion, p = 10%

Sample size, n = 1000

The standard deviation is calculated as:

σ=[tex]\sqrt{np(1-p}[/tex]

So, we have:

σ=[tex]\sqrt{1000*10%*(1-10%)}[/tex]*(1-10%)

Evaluate:

σ= 9.49

Hence, the standard deviation for the number of people with the genetic mutation in such groups of 1000 is 9.49.

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Answer:

64%

Step-by-step explanation:

Convert 16/25 to Percentage by Converting to Decimal

With this method, we first need to divide the numerator by the denominator:

16 ÷ 25 = 0.64

Once we have the fraction in a decimal format, the answer is then multiplied by 100 to get the correct percentage:

0.64 × 100 = 64%

We can see that this gives us the exact same answer as the first method: 16/25 as a percentage is 64%.

Note, the final percentage is rounded to 2 decimal places to make the answer simple to read and understand.

The expected value of the game is $2.00.

To Find: The fair price to pay to play the game of rolling a colored die with three red sides, two green sides, and one blue side

Now the question arises how to find the Fair Price

We are told that in the game of rolling the colored die;

A roll of a red loses.

A roll of blue pays 5.00 and A roll of green pays 2.00.

Now, the best game to get the fairest price is to play; RRRGGB  i.e (RED, RED, RED, GREEN, GREEN,BLUE)

Fair price = 2(3/6) + 6(1/6) + 0(2/6)

Fair price = $2

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Answer: 20

Step-by-step explanation:

Let [tex]f(y)=x[/tex]

[tex]x=\frac{1}{2}y+10\\\\x-10=\frac{1}{2}y\\\\y=h(x)=2x-\boxed{20}[/tex]

Answer:

The very last one is a function

Step-by-step explanation:

The last one is a function because there are no y values that repeat. For example, If the points on one graph are like this; (1, 3) (2, 3); then it cannot be a function, the y values cannot repeat if it is a function.

To make things easier, just try to imagine vertical drawing lines through each point in every graph, if this imaginary vertical line passes more than one point in any graph, then that graph is not a function.

I hope this helps!! :D

Answer:

The last graph represents a function.

Explanation:

A function cannot be one-to-many, i.e., one value of x cannot produce multiple values of y.

In the first graph, when x = 1, y = 3 and y= -2, so it is not a function.

In the second graph, when x = 2, y = 2 and y = -2, so it's not a function.

In the third graph, when x = -3, y = 2 and y = -2, so it's not a function.

∴ In all the graphs except the last, single values of x give multiple values of y on the graph, so they are not functions.

Answer:

the measure of line AD is 8

Step-by-step explanation:

lines AD and BC are equal, due to the markings on the lines
this means that if line BC is 8, than line AD is also 8

Answer:Angle C=68 degrees

Step-by-step explanation:

The solution is in the

Answer:

V= 48 in^2

Step-by-step explanation:

Formula

Since the base has a known area, we do not need the full volume formula. This formula is

V = B * h / 3

B is the area of the base and h is the height measured from the top of the pyramid to the base meeting the base at right angles.

Givens

B = 24 in^2

h = 6 in

Solution

V = B * h / 3

V = 24 * 6/3

V= 48 in^2

Answer:

Step-by-step explanation:

Answer:

how many times does 4.2 go into 14.7

1. 4.2

2. 8.4

3. 12.6

14.7-12.6=2.1 or one half of 4.2

3.5

Hope This Helps!!!

Answer:

51

Step-by-step explanation:

let's set the starting number as x

1. x times 2 = 2x

2. 2x- 138

3. result = 102

So, 2x-138 = 102

Now lets work backwards to solve for x.

1. 2x = 102

x = 51

So the starting number was 51.