what is the sum of the measures of the interior angles of this polygon?​

1.

[tex]|\Omega|=15^2=225\\|A|=5\cdot4=20\\\\P(A)=\dfrac{20}{225}=\dfrac{4}{45}[/tex]

2.

[tex]|\Omega|=15^2=225\\|A|=6\cdot5=30\\\\P(A)=\dfrac{30}{225}=\dfrac{2}{15}[/tex]

Answer:

Option D (20 ≤ x ≤ 70; Rodney needs to make at least 20 more hamburgers but no more than 70).

Step-by-step explanation:

The given inequality is 30 ≤ x + 10 ≤ 80 . There are basically two inequalities. One is 30 ≤ x + 10 and x + 10 ≤ 80. x is the number of hamburgers that are to be made, 10 is the number of hamburgers already made, 30 is the lower limit of the hamburgers required, and 80 is the upper limit of the hamburgers required. The question requires to solve the inequality. To solve this, the inequality will be separated as done above.

1)

30 ≤ x + 10.

20 ≤ x.

2)

x + 10 ≤ 80.

x ≤ 70.

Now combining the two inequality gives:

20 ≤ x ≤ 70. So Rodney needs to make at least 20 more hamburgers but no more than 70. Therefore, Option D is the correct answer!!!

Answer:

20 ≤ x ≤ 70; Rodney needs to make at least 20 more hamburgers but no more than 70

Step-by-step explanation:

Let

x ----> the numbers of hamburgers that Rodney needs to make

we know that

[tex]x+10\geq 30[/tex] ----> inequality A

[tex]x+10\leq 80[/tex] -----> inequality B

Solve the inequality A

[tex]x\geq 30-10[/tex]

[tex]x\geq 20\ hamburgers[/tex]

Solve the inequality B

[tex]x\leq 80-10[/tex]

[tex]x\leq 70\ hamburgers[/tex]

so

The solution of the system of inequalities is the interval

[20,70]

[tex]20 \leq x \leq 70[/tex]

All whole numbers greater than or equal to 20 hamburgers and less than or equal to 70 hamburgers

therefore

Rodney needs to make at least 20 more hamburgers but no more than 70.

Answer:

[tex]8g+16h=8(g+2h)[/tex]

Step-by-step explanation:

The given expression is

[tex]8g+16h[/tex]

To factor this polynomial, we just need to extract the common factor. Or you can see as the greatest common factor.

What is the greatest common factor between 8 and 16?

16: 1, 2, 4, 8, 16.

8: 1, 2, 4, 8.

You can observe that the greatest common factor is 8, so we extract it from both numbers

[tex]8g+16h=8(g+2h)[/tex]

Notice that we placed the GCM in the front as a product, if we don't do that, it would be completely wrong, because we can change the equivalence of the expression. Now, notice that each variable have different coefficients, that is because if you extract the GCM, you need to placed its quotients as coefficients.

Therefore, the factor of the polynomial is

[tex]8g+16h=8(g+2h)[/tex]

For this case we have that by definition, a direct variation is given by:

[tex]y = kx[/tex]

Where:

k: It is the constant of proportionality of the variables.

On the other hand, we have that the inverse variation is given by:

[tex]y = \frac {k} {x}[/tex]

Where:

k: It is the constant of proportionality of the variables.

In this way, the correct option is: [tex]y = \frac {9} {x}[/tex]

ANswer:

Option A

Answer: Option A

[tex]y = \frac{9}{x}[/tex]

Step-by-step explanation:

It is said that two variables x and y vary inversely if the increase of one of the variables causes the other to decrease.

This is represented by the following equation

[tex]y = \frac{k}{x}[/tex]

Where k is known as variation constant

To answer this question, identify among the options given that the form has

[tex]y = \frac{k}{x}[/tex]

The answer is the option A. with k = 9

Answer:

  cos(A) = (4√97)/97

Step-by-step explanation:

The cosine is related to the sine by ...

  cos(A)² = 1 - sin(A)²

  cos(A)² = 1 - (9/√97)² = 1 - 81/97 = 16/97 . . . . substitute for sin(A), simplify

Make the denominator a square:

  cos(A)² = (16·97)/97²

  cos(A) = (4√97)/97 . . . . . square root

The exact value of cos A can be determined using the Pythagorean identity. In this case, cosA = 4√97/97, which is the exact value of cos A in simplest radical form with a rational denominator.

In mathematics, the exact value of cos A can be determined using the Pythagorean identity, sin²A + cos²A = 1.

According to the problem, sinA = 9/√97, which when squared gives 81/97. Using the Pythagorean identity, we can substitute the value of sin²A to get cos²A. Hence, cos²A = 1 - sin²A = 1 - 81/97 = 16/97. The exact value of cos A, then, is the square root of 16/97. As A is in Quadrant I where cosine is positive, this will be √(16/97).

In order to write this value with a rational denominator, multiply and divide by the square root of the denominator (√97). Hence, cosA = 4√97/97, which is the exact value of cos A in simplest radical form with a rational denominator.

https://brainly.com/question/31837053

#SPJ2

Answer:

[tex]\dfrac{18}{5}<x<4\\ \\3.6<x<4[/tex]

Step-by-step explanation:

The picture shows three isosceles tirangles with the same legs. The base of each triangle is 12 units, 5x-3 units and 17 units.

Since the angles at vertex of each isosceles triangles are 27°, 28° and 29°, then the lengths of the bases satisfy the double inequality

15<5x-3<17

Add 3 to this inequality

15+3<5x-3+3<17+3

18<5x<20

Divide it by 5:

[tex]\dfrac{18}{5}<x<4\\ \\3.6<x<4[/tex]

Answer:

this message for guys... Guys who's interesting in fking girls? because I want someone 2 fk me from my psy soo hot

Answer:

(11 , -7)

Step-by-step explanation:

Note that x = 9, y = -9. Plug in the corresponding numbers to the corresponding variables.

(x + 2, y + 2)

(9 + 2, -9 + 2)

Simplify.

(11, -7)

(11 , -7) is your image point.

~

The probability of drawing a second green marble, given that the first marble is green is:

                    [tex]\dfrac{3}{8}[/tex]

Let A denote the event that first marble is green.

B denote the event that the second marble is green.

A∩B denote the event that both the marbles are green.

Let P denote the probability of an event.

We are asked to find:

                      P(B|A) i.e. probability of drawing a second green marble, given that the first marble is green.

We know that:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

Probability of drawing one green marble is 2/5  i.e.

          [tex]P(A)=\dfrac{2}{5}[/tex]

The probability of drawing two green marbles from the urn without replacement is 3/20 i.e.

[tex]P(A\bigcap B)=\dfrac{3}{20}[/tex]

Hence, we have:

[tex]P(B|A)=\dfrac{\dfrac{3}{20}}{\dfrac{2}{5}}\\\\\\i.e.\\\\\\P(B|A)=\dfrac{3\times 5}{20\times 2}\\\\\\P(B|A)=\dfrac{3}{8}[/tex]

Answer:

3/50

Step-by-step explanation:

Answer:

$532.50 / (number of members)

Step-by-step explanation:

Let m represent the number of members.

The net income (after subtracting the cost of the popcorn) was $532.50.

Thus, the amount of $ raised per member of the club was $532.50/m

Answer

(627.50-95)/m

Step-by-step explanation:

got 100%

Answer:

A. y = 3 cos (1/2) x.

Step-by-step explanation:

The y-intercept is 3  so it will contain 3 cos x (because  y = cos x passes through (0, 1).

The graph of 3 cos x has been stretched horizontally  by a factor 2 ( 3 cos x would pass through (π/2, 0) whereas the given graph passes through  (π, 0).

So the equation is 3 cos(1/2) x

The function which represents the graph is  A. y = 3 cos (1/2) x.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The y-intercept is 3  so it will contain 3 cos x (because y = cos x passes through (0, 1).

The graph of 3 cos x has been stretched horizontally by a factor of 2 ( 3 cos x would pass through (π/2, 0) whereas the given graph passes through  (π, 0).

Therefore the function which represents the graph is  A. y = 3 cos (1/2) x.

To know more about graphs follow

https://brainly.com/question/25020119

#SPJ2

Answer:

23ºC to 25ºC (74° F - 77° F)

Answer:

The height does not lie on the base because it is perpendicular to the base.

Step-by-step explanation:

Jalen's error is that the height of a cone does not lie entirely at the base of the cone. Only the diameter and the radius lie entirely on the base of a cone.

A cone is a three-dimensional object that  tapers smoothly from a flat circular base to its vertex. The diameter of a circle is a straight line that touches two points on the circumference of a circle and also passes through the center. The radius is half of the diameter.

To learn more about a cone, please check: https://brainly.com/question/13705125

#SPJ2

Answer: It moves the graph down by 1/4

Step-by-step explanation:

I used demos and the graph had a change making it lower coordinates by a fourth.

Answer:

22.3 km²

Step-by-step explanation:

you are given the diameter is 5[tex]\frac{1}{3}[/tex] km

radius = 1/2 x 5[tex]\frac{1}{3}[/tex] = 2.667 km

area = π * radius² = 3.142 * 2.667² = 22.3 km²

See attachment for solution steps and answer.

Answer:

C.

Step-by-step explanation:

To solve for x you have to move the -5y to the other side of the equals sign.  Since the opposite of subtracting is adding, we will add 5y to both sides to get

x = 5y + 6

Choice C

The value of x − 5y = 6 is x = 5y + 6.

Given:

x − 5y = 6

To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Solve the value of x, then

x - 5y = 6

Simplifying the above equation, we get

x = 6 + 5y

Therefore, the correct answer is option C) x = 5y + 6.

To learn more about the value of x

https://brainly.com/question/25151198

#SPJ2

Answer:

x < 7

Step-by-step explanation:

Simplify ...

6x -12 -4x +7 < 9

2x < 14 . . . . . . . . . . . add 5

x < 7 . . . . . . . . . . . . . divide by 2

Answer:

Y= 19.86 - 0.42b

Step-by-step explanation:

Step 1: Write the formula

Regression Line: Y = a + bx

a=(Total Y) x (Total X^2) - (Total X) x (Total XY)

                    n x (total X^2) - (Total X)^2

b= n x (Total XY) - (Total X) x (Total Y)

             n x (total X^2) - (Total X)^2    

Step 2: Make a table to find all values

X  Y          X^2    Y^2               XY

5 17.19 25 295.4961       85.95

6 19.12 36 365.5744       114.72

7 16.75 49 280.5625      117.25

8 15.58 64 242.7364       124.64

9 16.21 81 262.7641        145.89

10 14.14 100 199.9396        141.1

11 14.97 121 224.1009        164.67

12 16.2         144 262.44            194.4

68 130.16     620  2133.614       1088.62              TOTAL

Step 3: Substitute all values in the equation to find a and b

a=(Total Y) x (Total X^2) - (Total X) x (Total XY)

                    n x (total X^2) - (Total X)^2

a= (130.16 x 620) - (68 x 1088.62)

                     8 x (620) - (68)^2

a = 80699.2 - 74026.16

                336

a = 19.86

b = n x (Total XY) - (Total X) x (Total Y)

             n x (total X^2) - (Total X)^2    

b = 8 x (1088.62) - (68 x 130.16)

             8 x (620) - (68)^2

b = 8708.96 - 8850.88

                336

b = -0.42

Step 4 : Apply values of a and b in the formula of the regression line.

Regression Line: Y = a + bx

Y= 19.86 + b (-0.42)

Y= 19.86 - 0.42b

The regression line is calculated using the 'least squares method'. The formula is Y=a+bX, where a is the Y-intercept and b is the slope. These are calculated from the X and Y data values using specific formulas.

To calculate the regression line from the given X (year) and Y (high temperature) values, we first need to know the specific data. Unfortunately, the data isn't provided in the question. However, I can explain the process to you.

A regression line, also known as the line of best fit, is a straight line that best represents the data on a scatter plot. This line can be calculated using the 'least squares method'. This method minimizes the sum of the squares of the residuals (the differences between the actual and predicted Y values).

The formula for the regression line is Y=a+bX, where:

You can plug in your X and Y data values into these equations to find your regression line.

https://brainly.com/question/29753986

#SPJ2

Answer: 1/20, or 0.05

Step-by-step explanation: What we have to do is figure out how many times the blue shades area goes into the total area. Horizontally, it would be 5/10 squares, or 1/2. Vertically, it is 5/50 squares, or 1/10.  Multiplying 1/2 and 1/10 gives us 1/20, or 0.05 as your answer.

Answer:

65.52 square feet

Step-by-step explanation:

to find area of a rhombus with the diagonals multiply them together and divide by two.

10.4 x 12.6 = 131.04

131.04/2 = 65.52 square ft

Answer:

Approximately 7 deaths per minute.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The cubic equation ...

  (x -3)(x -1)(x +5) = 80

has one real root: x = 5. Using that value for x, the dimensions become ...

  length = 5 - 3 = 2

  width = 5 - 1 = 4

  height = 5 + 5 = 10

The dimensions are (length, width, height) = (2, 4, 10).

_____

We cannot tell the thrust of the problem, since it has only one solution. Perhaps you're supposed to write the cubic in standard form and use the Rational Root theorem to find possible values of x. That form can be found to be ...

  (x -3)(x -1)(x +5) -80 = 0

  x³ +x² -17x -65 = 0

Descartes' rule of signs tells you there is one positive real root. The rational root theorem tells you possible rational roots are factors of 65:

  1, 5, 13, 65

We know that x must be greater than 3 (so all dimensions are positive). Thus possible values of x are 5, 13, 65, and we're pretty sure that 65 is way too large.

According to the SMART goals method, goals should be clearly defined, aligning with the "Specific" attribute of the SMART acronym. This means having a clear and direct aim for the goal, which is essential for effective goal-setting.

According to the SMART goals method, goals should be clearly defined. SMART is an acronym that stands for Specific, Measurable, Attainable, Relevant, and Time-bound. Each of these attributes plays a crucial role in the formulation of effective and actionable goals.

Specific means the goal should be clear and direct, detailing exactly what is expected to be achieved. A goal that is Measurable has quantifiable criteria to indicate progress or completion. Attainable refers to the goal being realistic and possible to achieve given current resources and constraints.

Being Relevant means the goal aligns with broader objectives and makes sense within the greater plan. Lastly, Time-bound means there is a specific deadline or period within which the goal should be accomplished.

Therefore, the correct choice is A. Clearly defined, as a SMART goal must be specific and this inherently means the goal should have a clear definition.

Answer:

  $110

Step-by-step explanation:

Let a, b, and c represent the earnings of Alan, Bob, and Charles. The problem statement tells us ...

  a + b + c = 480 . . . . . . the combined total of their earnings

  -a + b = 40 . . . . . . . . . . Bob earned 40 more than Alan

  2a - c = 0 . . . . . . . . . . . Charles earned twice as much as Alan

Adding the first and third equations, we get ...

  (a + b + c) + (2a - c) = (480) + (0)

  3a + b = 480

Subtracting the second equation gives ...

  (3a +b) - (-a +b) = (480) -(40)

  4a = 440 . . . . . . . . simplify

  a = 110 . . . . . . . . . . divide by the coefficient of a

Alan earned $110.

_____

Check

Bob earned $40 more, so $150. Charles earned twice as much, so $220.

The total is then $110 +150 +220 = $480 . . . . as required

Answer:

1950 cubic units

Answer:

[tex]1040[/tex] cubic units

Step-by-step explanation:

The volume of any oblique geometric shape is equal to the product of area of its base and the height from which its top extends to its bottom base.

Mathematically, it can be represented as -

[tex]V = (Area_{base} * height)\\[/tex]

Substituting the given values in above equation, we get -

[tex]V = (10 * 13) * 8 \\V = 1040\\[/tex] cubic unit.

Answer:

The correct answer is last option

5/7

Step-by-step explanation:

It is given that, eight white balls and twenty black balls are in a bag

To find the probability

From the above data we get,

number of white balls = 8

Number of black balls = 20

total number of balls = 8 + 20 = 28

Probability of getting black ball = number of black ball/Total number of balls

 = 20/28 = 5/7

The correct answer is last option

5/7

Answer:

12.85 inches

Step-by-step explanation:

Angle ACP = Angle DPB = 92 degrees

because they are vertical angles

We are finding arc length, which is circumference

C = 2* pi *r

but we are only find 92 degrees of the 360 in a circle

C = 2 * pi * r * 92/360

  = 2 * pi *8 *92/360

  = 4.09 pi inches

 = 12.84562329

 = 12.85 inches

Answer:

Last answer

4.09 π

Step-by-step explanation:

Assuming CD and AB are straight lines and P is the center of the circle,

∠BPD = ∠CPA = 92°

r = 8 in

Minor Arc Length BD,

= (92/360) * 2πr

= (92/360) * 2π(8)

= 4.09 π

Answer:

10.4 cm

Step-by-step explanation:

In this question apply the formulae for volume of a pyramid

General formulae for volume of a pyramid is = l*w*h /3 where l is base length, w is base width and h is height.

In this question l=w= 6cm, v=120 cm³ and h=? ,

Apply the formulae

[tex]V= l*w*h /3\\\\120=6*6*h/3\\\\120=12h\\\\120/12 =h\\\\10cm=h[/tex]

Slant height

The length = 6cm-----------------divide by 2 to get half the legth

a=6/2=3cm

h=b= 10cm

c=?

apply the Pythagorean relationship

a²+b²=c²

3² + 10²= c²

9+100=c²

√109=c²

c=10.44

slant height =10.4 cm

Answer:

Slant height of pyramid = 10.4 m

Step-by-step explanation:

Points to remember

Volume of square pyramid = a²h/3

Where 'a' is the side of base and h is the height of pyramid

To find the height of pyramid

It is given that volume of square pyramid = 120 cm³ and

base a = 6 cm

a²h/3 = 120

h = (120 * 3)/a²

 = (120 * 3)/6²

 =10 cm

Therefore h = 10 cm

To find the slant height of pyramid

By using Pythagorean theorem we can write,

slant height ² = (base/2)² + height²

l² = (a/2)² + h²

 = (6/2)² + 10²

 = 3² + 10²

 = 9 + 100

 =109

l = √109 = 10.44 ≈ 10.4

Answer: 48cm2

Step-by-step explanation:

area = base x height

a = 8 x 6

a = 48

Answer:

y=2x-3

when two lines are parallel, they have the same slope.

in the formula y=mx+b, m=slope of the line

we know 2 will be the slope for the line passing through (4,5)

next plug in (4,5) into the formula with 2 as the slope

4=x 5=y

next 5=2(4)+b

and you end up with

y=2x-3 when you simplify