In a drawing, there are three circles, four stars, and three triangles. What is the ratio of stars to the total number of shapes? Simplify your answer. ​

The probability helps us to know the chances of an event occurring. Pooja's expected value of playing this game is 0.3077.

The probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

There are 12 face cards, therefore, the probability of the getting a face card can be written as,

[tex]\text{Probability of face card }= \dfrac{12}{52} = 0.2308[/tex]

Also, the winning prize for drawing a face card is $6. Therefore, the expected value will be,

[tex]\text{Expected Value(Face)} = \$6 \times 0.2308= $1.3846[/tex]

There are 4 ace cards, therefore, the probability of the getting an ace card can be written as,

[tex]\text{Probability of ace card }= \dfrac{4}{52} = \dfrac{1}{13} = 0.077[/tex]

Also, the winning prize for drawing an ace card is $4. Therefore, the expected value will be,

[tex]\text{Expected Value(Ace)} = \$4 \times 0.077 = $0.3077[/tex]

There are 36 normal cards, therefore, the probability of the getting a normal card can be written as,

[tex]\text{Probability of normal card }= \dfrac{36}{52} = 0.6923[/tex]

Also, the losing prize for drawing a normal card is -$2. Therefore, the expected value will be,

[tex]\text{Expected Value(Normal)} = (-\$2) \times 0.6923 = -$1.3846[/tex]

Thus, Pooja's expected value of playing this game can be written as,

[tex]\rm Expected\ Value = 1.3846 + 0.3077-1.3846 = 0.3077[/tex]

Hence, Pooja's expected value of playing this game is 0.3077.

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Answer:

Permutation is an arrangement of things where order of arrangement matters. The position of each thing in a permutation matters. Thus, Permutation can be associated with Position.

Combination is grouping/selection of things where order does not matter. Permutation can be considered as an ordered combination.

Answer:

x ≈ 14.4 cm

Step-by-step explanation:

the third angle of the triangle = 180° - 40° - 46° = 94°

Using the Sine rule in the triangle

[tex]\frac{x}{sin46}[/tex] = [tex]\frac{20}{sin94}[/tex] ( cross- multiply )

x × sin94° = 20 × sin46° ( divide both sides by sin94° )

x = [tex]\frac{20sin46}{sin94}[/tex] ≈ 14.4 cm ( to the nearest tenth )

Answer:

14 cm (rounded to nearest whole number)

Step-by-step explanation:

Law of Sine:

[tex]\displaystyle \large{\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c} = 2R}[/tex]

Given angles are:

Definition of Euclidean Triangle:

Find another angle:

So another angle is 94°.

To find:

Determine:

Therefore:

[tex]\displaystyle \large{\dfrac{\sin 46^{\circ}}{x} = \dfrac{\sin 94^{\circ}}{20}}[/tex]

Multiply both sides by 20x:

[tex]\displaystyle \large{\dfrac{\sin 46^{\circ}}{x} \cdot 20x = \dfrac{\sin 94^{\circ}}{20} \cdot 20x}\\\displaystyle \large{20\sin 46^{\circ}= x\sin 94^{\circ}}[/tex]

Divide both sides by [tex]\displaystyle \large{\sin 94^{\circ}}[/tex]:

[tex]\displaystyle \large{\dfrac{20\sin 46^{\circ}}{\sin 94^{\circ}} = \dfrac{x\sin 94^{\circ}}{\sin 94^{\circ}}}\\\displaystyle \large{\dfrac{20\sin 46^{\circ}}{\sin 94^{\circ}} = x}[/tex]

Evaluate the expression, hence:

[tex]\displaystyle \large{x = 14.42...}[/tex]

Round to nearest whole number:

[tex]\displaystyle \large{x = 14}[/tex]

Therefore, the value of x is 14 cm.

Answer:

In radian :

[tex]\frac{\pi }{4} \ \text{and}\ \frac{5\pi }{4}[/tex]

In degree :

45° and 225°

Step-by-step explanation:

the x and y coordinate on the unit circle exactly the same at the angles :

In radian :

[tex]\frac{\pi }{4} \ \text{and}\ \frac{5\pi }{4}[/tex]

In degree :

45° and 225°

At those angles :

[tex]\left( x,y\right) =\left( \frac{\sqrt{2} }{2} ,\frac{\sqrt{2} }{2} \right) \ or\ \left( x,y\right) =\left( -\frac{\sqrt{2} }{2} ,-\frac{\sqrt{2} }{2} \right)[/tex]

Answer:

[tex]y=-\frac{1}{4}x+2[/tex]

Step-by-step explanation:

We will use the point slope formula: [tex]y=mx+b[/tex]

We will start by finding the slope([tex]m[/tex]).
The formula for slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

So if we just choose 2 random points on the line:

I choose (0,2) and (4,1), we get:

[tex]\frac{1-2}{4-0} = \frac{-1}{4}[/tex]

That's our slope.

Next we need to find the y-intercept([tex]b[/tex]). We can find that by looking at the graph. It is where x=0. So in this case y=2 when x=0.

So in point-slope form the equation is:

[tex]y=-\frac{1}{4}x+2[/tex]

Answer:

First number = 9

Second number = 7

Step-by-step explanation:

Let x be the first number and y be the second.

2x + y = 25

3x - y = 20

1) Add them together.

5x = 45

x = 9

2) Solve for y.

2(9) + y = 25

y=7

3) Check your work on the other equation.

3(9) - (7) = 20

27 - 7 = 20

20 = 20

Therefore the first number is 9 and the second number is 7.

I think this might helpful

Answer:

A. is NOT the function.

Step-by-step explanation:

In a function, 1 input (the 3) can not have two differnt ouputs (8 and 9) meaning that this is NOT a dunction.
I hope this helps! :)

Answer:

$3.50

Step-by-step explanation:

add up all the x's and distribute them starting from the outside until you get to the middle. if there is an odd number of x's (which there isn't), the last x to be placed will be on the spot that is the median. If there is an even number of x's, and they both land on the same spot, that spot will be the median, and if they are next to each other, the median will be between them.

Answer:

y = -3x -1

Step-by-step explanation:

Hi there!

We are given a line on a coordinate grid, with 2 marked points, (-1, 2) and (1, -4)

We can use these points to help find the equation of the line, which we can write in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, we need to find the slope of the line
The formula for the slope calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have everything we need to find the slope, but let's label the values of the points to help avoid confusion.

[tex]x_1=-1\\y_1=2\\x_2=1\\y_2=-4[/tex]

Now substitute these values into the formula to find the slope

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-4-2}{1--1}[/tex]

Simplify

m=[tex]\frac{-4-2}{1+1}[/tex]

m=[tex]\frac{-6}{2}[/tex]

Divide

m= -3

The slope of the line is -3

We can substitute this into the formula.
Here's our line so far:

y = -3x + b

Now we need to find b

As the equation passes through the points (-1, 2) and (1, -4), we can use either one to find the value of b

Taking (-1, 2) for example:

Substitute -1 as x and 2 as y.

2 = -3(-1) + b

multiply

2 = 3 + b

Subtract 3 from both sides

-1 = b

Substitute -1 as b.

y = -3x - 1

Hope this helps!

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Answer:

a

Step-by-step explanation:

looked it up if u dondon't like the answer sorry

The size of the sample space would be  { H-1 H-2 H-3 H-5 H-6 T-1 T-3 T-4 T-5 }.

Sample space is the set of all possible outcome the considered random experiment can result to.

Thus, suppose we toss a coin, then tossing a coin is a random experiment, and the sample space is {'head', 'tail'}.

We ignore other outcomes like slant coin, or standing coin by assuming that coin is very thin to stand and always falls down.

Ella rolls a die and then flips a coin. The sample space for this compound event is represented in the table (H is heads and T is tails).

Die 1 2 3 4 5 6

Coin: heads H-1 H-2 H-3 H-5 H-6

         tails T-1 T-3 T-4 T-5

The size of the sample space

= { H-1 H-2 H-3 H-5 H-6 T-1 T-3 T-4 T-5 }

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Answer:

hope this works for u

Step-by-step explanation:

Mee

increase 31 kg by 100%

Answer:

Step-by-step explanation:

Since you did not include what the point is that you are trying to label, I can only tell you which quadrant is which. The quadrants go from 1 to 4 in a counterclockwise direction, starting from the top right quadrant (or the +,+ quadrant). One easy way to remember which direction the quadrants go in is the letter C, as they follow the same path as that letter.

I included a diagram to help.

Hope this helps! :)

Answer:

Hence, the security camera be adjusted in order to have the lens aimed at point. P. on the ground at an angle of depression of. x∘=30∘

Step-by-step explanation:

Answer:

Y+3=-6(x+9)

Step-by-step explanation:

Got it right on usa test prep

Answer: 0.47 is equal to 47/100

Step-by-step explanation:

1.00=100 Is like pennies, if you have a hundred of them you have 1 dollar but since there’s only 47 it’s out of a hundred

Answer:

0.47 as a fraction equals 47/100

Step-by-step explanation:

Write 0.47 as  

Multiply both the numerator and denominator by 10 for each digit after the decimal point.

[tex]\frac{0.47}{1}[/tex] = [tex]\frac{0.47 x 100 } {1x100}[/tex] = [tex]\frac{47}{100}[/tex]

So, 0.47 as a fraction  in simpliest form equals 47/100

Answer:

3x km

Step-by-step explanation:

Answer:

$1952.62

Step-by-step explanation:

1,800(1+.0275)^3

= 1952.62

The graphs and their functions/equations are all illustrations of quadratic functions.

The zeros of a function of a graph are the points where the line or curve of the graph crosses the x-axis

The axis of symmetry of a graph is the line that divides the graph into equal  halves

The vertex of a function is the minimum or the maximum point on the graph

The vertex of a quadratic function is minimum if it opens upward, otherwise the vertex is maximum

Using the above definitions, the solutions to the worksheet are:

Graph 1

Graph 2

Graph 3

Graph 4

Graph 5

Graph 6

Graph 7

Graph 8

Graph 9

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Answer:

Step-by-step explanation:

A variable is an undetermined number represented by a letter.

K is a variable.

The addition of more than is not a subtraction.

I hope this helps. Let me know if you have any questions.

A geometric series is the sum of an unlimited number. The common ratio of the geometric sequence is 3.

A geometric series is the sum of an unlimited number of terms with a fixed ratio between them.

Given the value of a₁ is 10, while the value of a₅ is 810, therefore, the common ratio can be written as,

[tex]\dfrac{a_5}{a_4} \times \dfrac{a_4}{a_3} \times \dfrac{a_3}{a_2}\times \dfrac{a_2}{a_1} = r \times r \times r \times r\\\\\\\dfrac{a_5}{a_1} = r^4\\\\\\dfrac{810}{10} = r^4\\\\\sqrt[4]{81} = r\\\\r = 3[/tex]

Hence, the common ratio of the geometric sequence is 3.

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The expression that is equivalent to [(4a + 4)/2a] * [a²/(a + 1)] after simplification is; 2a

We want to simplify the expression;

[(4a + 4)/2a] * [a²/(a + 1)]

This expression can be further reduced to;

[(4a + 4)/2] * [a/(a + 1)]

Factorizing the numerator to get;

[(4(a + 1)/2] * [a/(a + 1)]

(a + 1) will cancel out to get;

2a

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Answer:

Step-by-step explanation:

variance = (S.D)^2

=3.2^2

=10.24

=10

therefore , varience of a distribution is 10

Answer:

176 cubic cm

Step-by-step explanation:

[tex](2 \times 8 \times 2) + (3 \times 6 \times 8) = 32 + 144 = 176[/tex]

Answer:

The answer with calculator would be 2.16096

Answer:

A

Step-by-step explanation:

the graph is mostly going in an upward direction therefore both x and y are increasing.

Answer:

It is not symmetric and has a peak at $2.00

Step-by-step explanation:

$2.00 has 4 dots while the others have less

in order for it to be symmetric:

it is also not clustered from $1.00 to $5.00 because $1.00 has no amount

There are no gaps as $1.00 has no amount

Answer:

It is not symmetric and has a peak at $2.00

Step-by-step explanation:

hope i helped you very much

Answer:

The Letter E has 1 line of symmetry. (Horizontal)

Step-by-step explanation:

Yes, because if you fold it in half (horizontally), both halves match up.