A bag contains 3 gold marbles, 7 silver marbles, and
28 black marbles. Someone offers to play this game:
You randomly select one marble from the bag. If it
is gold, you win $3. If it is silver, you win $2. If it is
black, you lose $1.
What is your expected value if you play this game?

In the given graph, the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

To find the equation of the quadratic function, we start by using the vertex form:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex. Plugging in the given vertex (4,-2), we get:

\(y = a(x - 4)^2 - 2\)

Next, we use the other two points to find two additional equations:

\(6 = a(8 - 4)^2 - 2 (plugging in (8,6))\\0 = a(2 - 4)^2 - 2 (plugging in (2,0))\)

Simplifying these equations, we get:

\(6 = 16a - 2\\8a = 4 -- > a = 1/2 \\0 = 4a - 2 \\4a = 2 -- > a = 1/2 \\\)

So the equation of the quadratic function is:

\(y = (1/2)(x - 4)^2 - 2\)

Now, we can answer the questions:

The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0 in the equation:

\(y = (1/2)(0 - 4)^2 - 2 = 6\)

So the y-intercept is (0,6).

To find the x-intercepts, we set y = 0 in the equation:

\(0 = (1/2)(x - 4)^2 - 2\)

Simplifying, we get:

\((x - 4)^2 = 4\\ - 4 = \pm 2 \\= 2, 6\)

So the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

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Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

What I understand you saying is you can't find the Ad Pop-up. But is this is a bad thing? No. It will speed up the process of you finishing your homework and you won't get stressed!

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Answer:

1 protractor 2 rulers

Step-by-step explanation:

is this wat u wanted or no?

Answer:

-18

Step-by-step explanation:

Hope This Helps :)

The common ratio of the resulting sequence is 1.4.

Given that, the three terms are 60, 100 and 180.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Let the same constant is added to the given number is x.

60+x, 100+x and 180+x

Now, the common ratio is

(100+x)/(60+x) = (180+x)/(100+x)

⇒ (100+x)(100+x)=(180+x)(60+x)

⇒ (100+x)²=10800+180x+60x+x²

⇒ 10000+200x+x²=10800+180x+60x+x²

⇒ 10000+200x=10800+180x

⇒ 20x=800

⇒ x=40

The three number are 100, 140 and 220

The common ratio is 140/100 =1.4

Therefore, the common ratio of the resulting sequence is 1.4.

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Answer:

the variance is 6.6

sry for not showing work

Answer:2.6

Step-by-step explanation:

Answer:

6 eggs per chicken

Step-by-step explanation:

hdjdjidbdudbddjow0s

Answer:

6

Step-by-step explanation:

We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

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Answer: The breaking point

Step-by-step explanation:

The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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The solution of the given inequality is -2(2/3) < c < 5 (1/3) which is the first option.

We are given the inequality:-

I3c - 4I < 12

We have to find the solution of the given inequalities.

Let 3c - 4 ≥ 0

Hence,

3c - 4 < 12

3c < 16

c < 16/3 = 5 (1/3)

c < 5 (1/3)

Let 3c - 4 < 0

Hence,

-3c + 4 < 12

-8 < 3c

-8/3 = -2(2/3) < c

-2(2/3) < c

Hence, we can write,

-8/3 = -2(2/3) < c

-2(2/3) < c < 5 (1/3)

Hence, the solution is Option A.

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Answer:

2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2

B is the correct answer.

Step-by-step explanation:

everything can be found in the picture

Answer:

x=5/8

Step-by-step explanation:

The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

For mileages greater than 75 miles, Company A will charge less than Company B.

It is given that Company A charges  $100 and allows unlimited mileage company B charges an initial fee of $55 and an additional charge of $0.60 per mileage.

No. of miles covered is m miles

Hence, the amount charged by Company A for m miles is

$100

The amount charged by Company B for m miles is

$55 + $0.60m

According to the problem we need to find the mileage for which company A charges less than B

Therefore the inequality will be,

$100 < $55 + $0.60m

Taking $55 to the LHS we get

$100 - $55 < $0.60m

or, $45 < $0.60m

Taking $0.60m to the LHS we get

$45/$0.60 < m

or, m > 75

Therefore, m is greater than 75 miles.

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The length FE in the circle is 6 units

The arc AE has a measure of 64 degrees

From the question, we have the following parameters that can be used in our computation:

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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Answer:

49

Step-by-step explanation:

because it is the middle

Distance cover in full rotation is 87.92 inches

Given that;

Radius of wheel = 14 inches

Find:

Distance cover in full rotation

Computation:

Distance cover in full rotation = Circumference of wheel

Distance cover in full rotation = 2πr

Distance cover in full rotation = 2(3.14)(14)

Distance cover in full rotation = (6.28)(14)

Distance cover in full rotation = 87.92 inches

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A rectangle and two semicircles make up this figure. The perimeter of this figure is 423.52m.

The complete length of a shape's boundary is referred to as the perimeter in geometry. The perimeter of a shape is determined by adding the lengths of all of its edges and sides. Linear measurements like centimeters, meters, inches, and feet are used to express its dimensions. The area around a form's edge is known as its perimeter. The perimeter of a shape is always calculated by summing the lengths of its sides.

Perimeter=2*1/2πd+2a

d=68, a=105

Perimeter = 2*1/2*3.14*68+2*105

423.52m

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The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer: 3= x-12.    

x=15 because all the money spent together equals 12 dollars and if he gets 3 dollars back you would add 12+3 to get x

The growth rate of the population, given the initial population and the population after 10 years is 12. 5 % every 10 years.

To find the percent change or growth rate of a quantity between two different values, you can use the formula:

Percent change = ( new value - old value ) / old value x 100%

The new value would be the population of the village after 10 years which is 450 people.

The old value is the initial population of the village which is 400

The growth rate of the population is:
= ( 450 - 400 ) / 400 x 100 %

= 12. 5 %

The growth rate for the village is therefore 12. 5 % every ten years.

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Answer:

Let's assume the original price of the stock was x.

When the company announced it overestimated demand, the stock price fell by 40%.

So, the new price of the stock after the first decline was:

x - 0.4x = 0.6x

A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.

So, the new price of the stock after the second decline was:

0.6x - 0.6(0.6x) = 0.24x

Given that the current stock price is $2.40, we can set up the equation:

0.24x = 2.40

Solving for x, we get:

x = 10

Therefore, the stock was originally selling for $10.

Answer:

1.2

Step-by-step explanation:

The number 27 when rounded to the nearest ten using the number line will give the number 30.

On the number line, the numbers are marked from 10 to 50.

So, the tens are 10, 20, 30, 40, and 50.

The number 27 has to be rounded to the nearest ten.

The one position will be 0.

Now, 27 lies in between the tens 20 and 30 on the number line.

Now, it is required to find which number is 27 closer to.

There are 7 units from 20 to 27.

But there are only 3 units far from 27 to 30.

So, 27 can be rounded to 30 to the nearest ten.

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Answer: 51.4°

Step-by-step explanation:

Use law of cosines:

(because you are trying to find angle B, you need to use Cos B)

Cos B = c² + a²-b²/ 2ca

Then, plug in your numbers:

 Cos B = 30²+64²-51²/ 2(30)(64)

Simplify:

Cos B = 0.6237

Next, to get rid of Cos B, so that we have just B, you need to do the Arccosine or 0.6237:

B = arccosine (0.6237)

Which gets you: 51.4°    

The measure of angle B is 51.41 degrees after applying the cos law of the triangle.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have given a triangle in the figure:

To find the measure of the angle B

We can apply cos law:

c² = a² + b² - 2ab cosB

The a, b, and c represents the side lengths of the triangle and the measures are:

a = 30

b = 64

c = 51

51² = 30² + 64² - 2(30)(64) cosB

3840CosB = 4996 - 2601

3840CosB = 2395

CosB = 2395/3840

CosB = 0.623

B = Cos⁻¹(0.623)

B = 51.41 degrees

Thus, the measure of angle B is 51.41 degrees after applying the cos law of the triangle.

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