Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($)
1 2 5 8 10
Probability 0.35 0.2 0.1 0.2 0.15
Expected Value = [? ]
Round to the nearest hundredth.
Enter

Answer:

J) [tex]18cm^2[/tex]

Step-by-step explanation:

a square inscribed in a circle means that the radius of the circle is the same thing as a line drawn from the center of the square to a corner.

this will give you the side measurements for a triangle (look at the attached picture). now use the Pythagorean theorem to find the hypotenuse aka the side length of the square. then multiply it by itself.

Answer: H

Step-by-step explanation:

If we draw a line through a diagonal of the square, two triangles are formed. The angle opposite the diagonal is 90°, as all angles are 90° in a square. One of the properties of a circle state that the angle in a semicircle is always 90°, which means that the diagonal formed a semi-circle.

A semi-circle only forms when a diameter is drawn in a circle, making the diagonal a diameter. This will be useful information, as we can calculate the side length of a square using the length of its diagonal.

A diameter is just twice the length of a radius, so the diagonal of the square would be 6 cm.

[tex]2*3=6[/tex]

The diagonal also splits the square into two 45-45-90 triangles. These triangles have a special property that their hypotenuse is √2 times each leg, and all legs are the same length.

Therefore, we can calculate the length of a leg by dividing the hypotenuse by √2.

[tex]\frac{6}{\sqrt{3}}[/tex]

The length of one side of the square is [tex]\frac{6}{\sqrt{3}}[/tex]

As we already know the length of one side, we can just square it to get the area.

[tex](\frac{6}{\sqrt{3}})^2[/tex]

[tex]\frac{6^2}{(\sqrt{3})^2}[/tex] [Properties of Exponents]

[tex]\frac{36}{3}[/tex]

[tex]12[/tex]

Hence, the area of the square is 12 cm².

Answer:

First, transform the given equation into the slope-intercept form, y = mx + b.

2x - 3y < 12

3y > 2x - 12

y > [tex]\frac{2}{3}[/tex]x - 4

Since the equation is y > [tex]\frac{2}{3}[/tex]x - 4, first draw the graph of y = [tex]\frac{2}{3}[/tex]x - 4 with a dotted line (because it is >, not ≥) and shade the area above the dotted line.

Using it's concept, any function with domain [tex]x \geq 0[/tex] has the same domain as [tex]y = 2\sqrt{x}[/tex].

The domain of a function is the set that contains all possible input values for the function.

Function [tex]y = 2\sqrt{x}[/tex] is defined for [tex]x \geq 0[/tex], hence any function with domain [tex]x \geq 0[/tex] has the same domain as [tex]y = 2\sqrt{x}[/tex].

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The total number of notes is 32

Let the number of notes be x

$50 = x

$20 = x

$10 = x

$5 = x

Total number of notes = 4x

Let's find 'x'

50x + 20x + 10x + 5x = 680

85x = 680

x = 680/ 85

x = 8

We know that;

Total number of notes = 4x = 4 × 8 = 32 notes

Thus, the total number of notes is 32

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area = pi * r^2

here, the radius is 2 as its the diameter/2.

so the area is 4pi.

circumference = 2*pi*r.

so the circumference is 4pi as well.

The point (12, 190) means that the temperature after 12 hours is 190 degrees Celsius

To do this, we make use of the following points

(12, 190), (14, 201), (15, 301), (16, 305), (18, 350), (20, 40), (25, 450)

Where x represents the number of hours and y represents temperature

See attachment for the scatter plot.

To do this, we make use of the point (12, 190)

This means that the temperature after 12 hours is 190 degrees Celsius

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Answer:

4a²*(9a + 3)

Step-by-step explanation:

Prime factorize 32 and 12. Then find GCF.

 32a³ = 2 * 2 * 2 * 2 * 2  * a³

12a²  = 2 * 2 *  3 * a²

GCF = 2 * 2 * a² = 4a²

32a³ + 12a² = (4a²*9a) + (4a²*3)

                   =4a²*(9a + 3)

Answer:

8/3 or 2(2/3) Textbooks to storybooks

Step-by-step explanation:

Textbooks:  (8 books)*(12 rupees/book) = 96 rupees

Storybooks:  (4 books)*(9 rupees/book) = 36 rupees

Total is 132 rupees

Ratio:  Textbook/Storybook = 96/36

96/36 = 8/3 or 2(2/3) Textbooks to storybooks

Answer: -2

Step-by-step explanation:

Substituting into the slope formula,

[tex]\frac{y-1}{3-9}=\frac{1}{2}\\\\y-1=-3\\\\y=-2[/tex]

The reasons Travis can use to prove both triangles are congruent by the SAS congruency theorem are:

The SAS congruency theorem states that two triangles are congruent when they both have two pairs of corresponding congruent sides and a pair of corresponding congruent included angles.

Given the image below, we have the following proof with the statement and reasons in bracket:

WZ ≅ XY [given]

WY ≅ WY [reflexive property]

∠ZWY ≅ ∠XYW [by the alternate interior ∠s theorem]

△WZY ≅ △YXW [by the SAS congruency theorem]

Therefore, the reasons Travis can use are:

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Answer:

A. ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem;  

B. WY ≅ WY by the reflexive property;  & E. WZ ≅ XY by the given.  

Step-by-step explanation:  Trust Me!  Answer is correct on Edge.  

Good Luck! :)

Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.

Answer:

4x^04x^04x^04x^1 which equals 256

Step-by-step explanation:

The 4 outside of the parentheses says take what you have outside of the parentheses and multiply it by itself that may times.

x raised to the zero is 1, so you are just left with 4x4x4x4 or 256

The equation in function form is f(x)=-4x+80.

What is linear function?

A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.

We can find the equation in function form as shown below:

We have given two points (5,60) and (10,40)

Slope of line

m = (40-60)/ (10-5)

m=-20/5

m=-4

Equation in slope intercept form

(y-y1) =m(x-x1)

(y-60) =-4(x-5)

y-60=-4x+20

y=-4x+20+60

y=-4x+80

y=f(x)

f(x)=-4x+80

Hence, the equation in function form is f(x)=-4x+80.

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Yes, the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of the arc is 9.6 feet

As we can see that at the mid value, for x=4, the value of f(x)=9.4

It means that the maximum height occurs at mid of the arc where it is height is 9.6 feet above the ground.

It means that the planner has met the minimum height, as the minimum height was 9 feet and the maximum height of arc is 9.6 feet

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Step-by-step explanation:

Simplifying 8a = 2xy + b

Reorder the terms: 8a = b + 2xy

Solving 8a = b + 2xy

Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right.

Divide each side by '8'. a = 0.125b + 0.25xy

Simplifying a = 0.125b + 0.25xy

Answer:

The answers are in the image

Step-by-step explanation:

The solutions are in the image

Answer:

95 - 20[tex]\sqrt{15}[/tex]

Step-by-step explanation:

(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )²

= (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )(5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] )

each term in the second factor is multiplied by each term in the first factor, that is

5[tex]\sqrt{3}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) - 2[tex]\sqrt{5}[/tex] (5[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{5}[/tex] ) ← distribute parenthesis

= 75 - 10[tex]\sqrt{15}[/tex] - 10[tex]\sqrt{15}[/tex] + 20 ← collect like terms

= 95 - 20[tex]\sqrt{15}[/tex]

Answer:

95 - 20√15

Step-by-step explanation:

I assume the expression is (5√3 − 2√5)^2 (?).

(5√3 − 2√5)*(5√3 − 2√5)

25√3^2 - 20√15 + 4√5^2

25*3 - 20√15 +4*5

75 - 20√15 +20

95 - 20√15

Answer:

110/11

A

Step-by-step explanation:

divide the bill by 11 people.

Answer:

D. 110/11

Step-by-step explanation:

110 Dollars

11 people to split it with

110/11 to find the total for each person

9a). The measure of segment GH from the given information can be evaluated as one-fourth of the perimeter; 48/4 = 12 cm.

9b). The measure of <EJF is 90° as the angle EJF is a right angle made at the intersection of the rhombus diagonals.

9c). The measure of <EHG is 60° as the opposite angles in a rhombus are congruent and <EHG = 2 × <EHJ = 2 × 30 = 60°.

10a). The sides labelled in the rectangle are congruent by the rectangle diagonal congruence concept; it therefore follows that the required value of x is; 9x+ 20 = 10x +8; and x = 12.

10b). The angle measures as labelled in the rhombus are congruent as this follows from the fact that the diagonal is an angle bisector. Hence, 2x +15 = 5x +3; and x = 4.

The concept of congruence describes a similarly between 2 or more geometric figures or elements.

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Ms. Sanchez paid 150 dollars more than Mr. Roland.

Let's say that the electrician worked for x hours in Mr. Roland's home, then worked for (x + 2) hours in Ms. Sanchez home.

Then we need to find the difference between the linear equations:

C(x + 2) - C(x) = (75*(x + 2) + 125) - (75*x + 125)

If we simplify that, we get:

75*x + 75*2 + 125 - 75*x - 125

= 75*2 = 150

This means that Ms. Sanchez paid 150 dollars more than Mr. Roland.

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The true statement for f(x) = 2(3)^x is the y-intercept is (0, 2).

The function is given as:

f(x) = 2(3)^x

Set x = 0 to determine the y-intercept

f(0) = 2(3)^0

Evaluate

f(0) = 2

This means that the y-intercept of f(x) = 2(3)^x is (0,2)

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Answer: 39 units

Step-by-step explanation:

Using the distance formula, we get that:

[tex]PT=\sqrt{10^2 + 4^2}=\sqrt{116}\\\\TS=\sqrt{7^2 + 0^2}=7\\\\SR=\sqrt{7^2 + 1^2}=\sqrt{50}\\\\RQ=\sqrt{6^2 + 5^2}=\sqrt{61}\\\\PQ=\sqrt{2^2 + 6^2}=\sqrt{40}[/tex]

So, the perimeter is

[tex]\sqrt{116}+7+\sqrt{50}+\sqrt{61}+\sqrt{40} \approx 39[/tex]

Stratified random sampling is used to subdivided into groups by volume of sales.

According to the statements

Manufacturers are subdivided into groups by volume of sales. and for this Stratified random sampling is used.

Stratified random sampling is the technique used divide the population can be partitioned into subpopulations.

Thus, Stratified random sampling is used to subdivided into groups by volume of sales.

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Answer:

AB-46 cm

Step-by-step explanation:

Use law of cosines

AB^2 = 24^2 + 26^2 - 2 (24)(26)cos 134

AB= 46 cm

The probability of at least one of them being a physics instructor is 120 ways to form the committee.

Sometimes, simply the occurrence of the event at least once matters when computing independent events. The "At Least One" Rule is used to describe this. The complement of the probability of the event never occurring will be used to calculate the probability of the event occurring at least once.

There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected.

Starting with 6, choose two because we require at least two professors. Let's move on to the remaining 8 individuals (there were initially 10, but now there are just 8): and select 3.

6 select 2; 8 select 3

15×56 =840

We then chose 5 individuals from a group of 10, at least 2 of whom were lecturers.

(9) = 20 options for selecting the professors. 3

(3) = 6 options for selecting the professors.

(9) (¹) = 20 × 6 = 120 ways.

Therefore, 120 ways to form the committee.

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Complete question:

There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor?

Answer: A

Step-by-step explanation:

See attached image.

Answer:

  c.  Substitute

Step-by-step explanation:

A graph of the function on the left shows the parabola touches the x-axis at x = -8/3. That is, the vertex is on the x-axis. It crosses the y-axis at y = 64.

A given solution to an equation can be verified by substituting that value into the equation an showing the result is a true statement. Here, the value x=-8/3 is a root of the given equation because that value makes the equation true.

  [tex]9\left(-\dfrac{8}{3}\right)^2+48\left(-\dfrac{8}{3}\right)+64=0\\\\9\left(\dfrac{64}{9}\right)-\left(\dfrac{48\cdot8}{3}\right)+64=0\\\\64-\dfrac{3\cdot2\cdot8\cdot8}{3}+64=0\\\\64-2\cdot64+64=0\\\\0=0\qquad\text{True}[/tex]

Answer:

24000 ft²

Step-by-step explanation:

          b = base = PR = 240 ft

      2AS = 240 ft

       [tex]\sf AS = \dfrac{240}{2}\\\\ AS = 120 \ ft[/tex]

         h  = height = AS  = 120 ft

      [tex]\sf \boxed{\bf \ Area \ of \ triangle = \dfrac{1}{2}b*h}[/tex]

                                       [tex]\sf =\dfrac{1}{2}*240*120\\\\ = 120 * 120\\\\ = 14400 \ ft^2[/tex]

          b = PR = 240 ft

     3BQ = 240 ft

        [tex]\sf BQ = \dfrac{240}{3}\\\\ BQ = 80 \ ft[/tex]

[tex]\sf Area \ of \ triangle \ PRQ = \dfrac{1}{2}*240*80[/tex]

                                 = 120 * 80

                                 = 9600 ft²

Area of the quadrilateral PQRS = area of ΔPRS + area of ΔPRQ

                                                    =  14400 + 9600

                                                    = 24000 ft²

Answer:

The answer would be 36cm².

Step-by-step explanation:

⇒ Two prisms are similar.

⇒ Scale factor = 3:8

⇒ The ratio of the surface area is 9:64.

⇒ So S₁ : S₂ = 9:64

⇒ S₁ : 256 = 9:64

⇒ S₁ = 36cm²

This would mean that the answer is 36 centimeters ² (squared).