What is the value of x?

Answer:

Expected value = $8.89

Step-by-step explanation:

cost of playing game = $1

winning if sum is odd = $10

winning if sum is 4 or 8 = $5

winning if sum is 2 or 12 = $50

two dice rolled, possible outcomes =

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

total no. of outcomes = 36

now according to the table of outcome with respect to winning money, we can calculate expected value by multiplying the probability of each roll with winning amount associated with each roll. and subtract the amount that we paid for the game that is $1.

E(x) = 1/36*($50) + 1/18*($10) + 1/12*($5) + 1/9*($10) + 5/36*($0) + 1/6*($10) + 5/36*($5) + 1/9*($10) + 1/12*($0) + 1/18*($10) + 1/36*($50)

= 25/18 + 5/9 + 5/12 + 10/9 + 0 + 5/3 + 25/36 + 10/9 + 0 + 5/9 + 25/18

Expected value = $8.89

Subtract the amount that was paid to play the game that is $1.

$8.89 - $1 = $7.89

A profit of $7.89 is expected every-time the game is played.

Answer:

an = 5 + 2n

Step-by-step explanation:

Each time it increases by the same amount (2), so this is an arithmetic sequence:

an = a₁ + d (n - 1)

Given a₁ = 7 and d = 2:

an = 7 + 2 (n - 1)

an = 7 + 2n - 2

an = 5 + 2n

Check our answer:

n=1: a₁ = 5 + 2(1) = 7

n=2: a₂ = 5 + 2(2) = 9

n=3: a₃ = 5 + 2(3) = 11

n=4: a₄ = 5 + 2(4) = 13

The pattern represents the arithmetic progression and the explicit formula for the nth term is a(n) = 2n + 5

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a sequence:

7, 9, 11, 13…

The above pattern represents the arithmetic progression.

The first term a = 7

Common difference d = 2

nth term:

a(n) = 7 + (n - 1)(2)

a(n) = 2n + 5

Thus, the pattern represents the arithmetic progression and the explicit formula for the nth term is a(n) = 2n + 5

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Answer:

x < - 11

Step-by-step explanation:

Given

4 + 6x < 4x - 18 ( subtract 4x from both sides )

4 + 2x = - 18 ( subtract 4 from both sides )

2x < - 22 ( divide both sides by 2 )

x < - 11

Answer:

4

Step-by-step explanation:

4 squared equals 16 and 4 times 4 equals 16

Hello There!

The length of the hypotenuse is 10.

We know what 2 sides are 6 and 8.

To find the third side we use the formula a^2 + b^2 = c^2

So we multiply 6 by 6 which equals 36 and then multiply 8 by 8 which equals 64.

Next we add 64 and 36 together and we get 100.

Next, we square root 100 and get 10.

10 is the length of the hypotenuse.

343 will be your answer

Answer: Thus, Third option is correct.

Step-by-step explanation:

Since we have given that

[tex]1,\dfrac{1}{8},\dfrac{1}{27},\dfrac{1}{64},...............\dfrac{1}{n^3}[/tex]

So, we can see the pattern:

General term of the series is given as

[tex]\dfrac{1}{n^3}[/tex]

So, we just put the value of n = 7, to get the required denominator:

[tex]\dfrac{1}{7^3}=\dfrac{1}{343}[/tex]

Hence, the denominator of the seventh term is 343.

Thus, Third option is correct.

Answer:

A) y=4x-12

B) y-4x=-12

C) y+4=4(x-2)

Step-by-step explanation:

Sorry it took you so long to be answered, but I hope this helps! :D

Answer with explanation:

Coordinate of Point E and F are = (4,4) and (2,-4).

 Two Point form of line, that is equation of line Passing through two points is given by:

     [tex]\rightarrow \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}_x_{1}}\\\\\rightarrow \frac{y-4}{x-4} =\frac{4+4}{4-2}\\\\\rightarrow \frac{y-4}{x-4} =4\\\\ \rightarrow y-4=4 x-16\\\\\rightarrow 4 x-y -16+4=0\\\\\rightarrow 4 x -y-12=0[/tex]

Standard Form : 4 x-y-12=0

Slope-intercept form

  [tex]\rightarrow 4 x-y-12=0\\\\\rightarrow 4 x- y=12\\\\\rightarrow \frac{4 x-y}{12}=1\\\\\rightarrow \frac{4x}{12}-\frac{y}{12}=1\\\\\rightarrow \frac{x}{3} +\frac{y}{-12}=1[/tex]

Point-slope form

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

x= -4/3 + 2/3 square root of 13 or x= -4/3 + -2/3 square root of 13 !!

Answer:

Step-by-step explanation:

3x² + 8x = 12

3x² + 8x - 12 = 0

a=3, b=8, and c=-12.  Solving with quadratic formula:

x = [ -b ± √(b² - 4ac) ] / 2a

x = [ -8 ± √(8² - 4(3)(-12)) ] / 2(3)

x = (-8 ± √208) / 6

x = (-8 ± 4√13) / 6

x = -4/3 ± 2/3 √13

Answer:

D

Step-by-step explanation:

2/6 is litterally right there cause it has seven lines and tge 0 doesnt count

The answer would be 0.

you would add -4v on the left to -4v to the right to get 0. Then you would add -12 on the left to -12 on the right to get 0.

Answer:

D) 115

the inside angles of a triangle always (ALWAYS) add up to 180, add 75 and 40. You get 65. Then you know that a straight line means it is 180 degrees so you subtract 65 from 180. you get 115 degrees

Missing angle is 115

Answer:

It would take 4 men 37 hrs and 12 mins to complete the same task.

step-by-step explanation:

Let X be the time the four men would use to complete the task.

From the question, 6 men completed a task in 24 hrs and 48 mins

But

[tex]24 \: hrs \: 48 \: mins = 24(60mins) + 48 \: mins=1488 \: mins[/tex]

Using ratio and proportion

[tex]6 \: men:1488 \: mins[/tex]

[tex]4 men:x\:mins[/tex]

if more, less divides and if less, more divides.

4 men required more time to complete the task

Hence:

[tex]x = \frac{6}{4} \times 1488 \: mins[/tex]

[tex]x = 2232 \: mins[/tex]

x = 37 hrs 12 mins

The product could be either less than or greater than 67,124.

If you multiplied by a negative number, you would get a negative number, which is less than a positive number such as 67,124.

If you multiplied by zero, you would get zero, which is less than a positive number such as 67,124.

If you multiplied by one, you would get 67,124, which is equal to 67,124 since they are the same number.

If you multiplied by a positive number less than one, you would get a positive number greater than zero and less than 67,124.

If you multiplied by a positive number greater than one, you would get a positive number greater than 67,124.

Answer:

k=ab

Step-by-step explanation:

a=k/b

a(b)=(k/b)(b)---multiple b to both sides to isolate k

k=ab

Answer:

k is the constant of variation.

Step-by-step explanation:

In direct variation:

[tex]y\propto x[/tex]

[tex]y=kx[/tex]

In inverse variation:

[tex]y\propto \frac{1}{x}[/tex]

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

[tex]yx=k[/tex]

In both cases k is the constant of variation

The given equation is

[tex]a=\frac{k}{b}[/tex]

We need to find the value of k in this equation.

First we have to isolate k on one side of the equation.

Multiply both sides by b to isolate k on right side.

[tex]a\times b=\frac{k}{b}\times b[/tex]

Cancel out the common factors.

[tex]ab=k[/tex]

Interchange the sides of the equation.

[tex]k=ab[/tex]

It means a and b are inversely proportional.

Therefore, the k is the constant of variation.

Answer:

Choice C is correct

Step-by-step explanation:

We use the law of exponents in this problem;

[tex](a^{b})^{2}=a^{b}*a^{b}[/tex]

Therefore,

[tex](9^{\frac{1}{2} })^{2}=9^{\frac{1}{2} }*9^{\frac{1}{2} }[/tex]

Since the base is the same, that is 9, we simply add the exponents 1/2;

[tex]9^{\frac{1}{2}+\frac{1}{2} }[/tex]

one-half plus one-half is equal to unity and any number raised to one is simply equal to the given number;

[tex]9^{1}=9[/tex]

Answer: A) 13

Step-by-step explanation:

Mean - 1 SD: 20.2 - 2.4 = 17.8 --> (18)

Mean + 1 SD: 20.2 + 2.4 = 22.6 --> (23)

Now, find the values on the histogram for 18 through 23:

2 + 3 + 4 + 3 + 1 + 1 = 13

d. y=-2x+4

this is because in the formula used y=mx+b, b is represented as the the "y" intersept, which is 4. the slope, which is -2, is represented as x in this formula. therefore, D. y=-2x+4 is the correct answer

Answer:

the answer is A the square root of 80.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

B.

At the center of the inscribed circle of the park

Answer:

B

Step-by-step explanation:

that would be B.  This circle touches each side of the triangle and has a center which is equidistant from all of the sides.

I think it would be “B”

Answer:

Option B.

Step-by-step explanation:

Given information: [tex]m\angle A=48^{\circ},\angle E=90^{\circ},\angle EMS=59^{\circ}[/tex].

According to the angle sum property of a triangles, the sum of interior angles of a triangle is 180°.

Apply angle sum property on triangle AEJ.

[tex]\angle A+\angle E+\angle J=180^{\circ}[/tex]

[tex]48^{\circ}+90^{\circ}+\angle J=180^{\circ}[/tex]

[tex]138^{\circ}+\angle J=180^{\circ}[/tex]

Subtract 138 from both sides.

[tex]\angle J=180^{\circ}-138^{\circ}[/tex]

[tex]\angle J=42^{\circ}[/tex]

The measure of angle J is 42°.

According to exterior angle property, the sum of two interior angles of a triangle is equal to the third exterior angle.

Apply exterior angle property on triangle JMS.

[tex]\angle EJA+\angle JSM=\angle EMS[/tex]

[tex]42^{\circ}+\angle JSM=59^{\circ}[/tex]

Subtract 42 from both sides.

[tex]\angle JSM=59^{\circ}-42^{\circ}[/tex]

[tex]\angle JSM=17^{\circ}[/tex]

The measure of ∠JSM is 17°.

Therefore, the correct option is B.

There is 12 1/3-cups in 4 cups

To determine how many 1/3-cup servings are in 4 cups, you divide 4 cups by 1/3 cup per serving, resulting in 12 servings of 1/3 cup each.

The question asks how many 1/3-cup servings are in 4 cups. To find the answer, we divide the total number of cups by the size of each serving. Here, we have 4 cups total, and we want to know how many 1/3 cup servings that equates to.

To calculate:
4 cups ÷ (1/3 cup/serving) = 4 ÷ (1/3) = 4 × 3 = 12 servings.

Therefore, there are 12 servings of 1/3 cup in 4 cups.

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Answer:

325 sq. units

Step-by-step explanation:

top shape vol.: 5*5*5=25*5=125

bottom shap vol.:8*5*5=40*5=200

combined they are 325

Answer:

325 units ³

Step-by-step explanation:

Volume of cube = Length × Width × Height

Volume of cube  = 5 × 5 × 5

Volume of cube = 125 units ³

Volume of cuboid =  Length × Width × Height

Volume of cuboid = 8 × 5 × 5

Volume of cuboid = 200 units ³

Total volume = 125 + 200 = 325 units ³

The statements that are true about polygons are:

A closed polygonal chain of connected line segments makes up a polygon, a plane shape. The edges or sides of a closed polygonal chain are the individual pieces. The polygon's vertices or corners are the places where two edges converge.

Each side of a polygon is the same length, and each angle is the same size. For instance, in a square, every side is the same length and every angle is 90 degrees. There is at least one interior angle that is more than 180 degrees in a concave polygon. A concave polygon will have at least one point that is inside it if a side or diagonal is expanded.

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Answer:

0.75

Step-by-step explanation:

Z-score tells the no. of standard deviations a data point is from the mean.

the formula for z score is given by

z-score= (data value - mean) / standard deviation

Given:

mean=44

standard deviation= 8

data point=50

putting the values of mean(44), standard deviation(8) and given data value(50) in the above equation

z-score= (50-44)/8

           = 6/8

           =0.75 !

Answer: 1/8

Step-by-step explanation: There is 1/4 of a chance of spinning a red, and 1/2 of a chance of getting a heads. Multiply these numbers.

1/4 x 1/2 = 1/8

There is a 1/8 chance of this outcome.

Hi there! Here's the answer and how I got that answer!!

Answer:

11

The change in the Median would be 11 instead of 11.5 because the total amount of numbers became odd when the outlier is removed. This allowed for the step of having to solve for two middle numbers to be avoided and therefore only leave you with the answer simple as 11 instead of having to solve between two numbers!

Step-by-step explanation:

With all the numbers (including the outlier) the median would be 11.5.

Here's how:

First sort least to greatest and cancel out the numbers until you get to the one on the middle.

9, 9, 11, 12, 14, 28

If you have two middle numbers add them together and then divide by two.

11+12=23

23/2= 11.5

So your median with the outlier is 11.5.

Now if you take out the outlier, which in this case I'm assuming its 28. Let's re-look for the median once more!

First sort least to greatest and cancel out the numbers until you get to the one on the middle.

9, 9, 11, 12, 14

Now because there is an odd amount of numbers your left to only one middle number, 11.

This means if the outlier is removed the median would change to be 11.

I hope this helps, have a stupendous day!! ☆*:.｡.o(≧▽≦)o.｡.:*☆

Answer:

143 desks

62 desks

108.5 hours

=  

x desks

250 hours

15500 = 108.5x

142.8 = x

Round to 143

Step-by-step explanation:

Answer:

In 250 hours 143 seats can be assembled.

Step-by-step explanation:

62 desks can be assembled in 108.5 hours.

In 108.5 hours 62 desks can be assembled.

In 1 hour [tex]\dfrac{62}{108.5}[/tex] seats can be assembled.

In 250 hours [tex]\dfrac{62}{108.5}\times 250[/tex] seats can be assembled.

In 250 hours 142.86 seats can be assembled.

Hence, In 250 hours 143 seats can be assembled. (Round to nearest whole number)

Answer:

B. [tex]F(x)=(x+2)^4[/tex]

Step-by-step explanation:

The parent function is [tex]G(x)=x^4[/tex]

The given translation is of the form;

This shifts the graph of [tex]G(x+k)[/tex]  [tex]G(x)=x^4[/tex], k units to the left.

If this function is shifted 2 units to the left, its equation will now be

[tex]F(x)=(x+2)^4[/tex]

The correct choice is B. [tex]F(x)=(x+2)^4[/tex]

Answer:

C) 4 cm

Step-by-Step Explanation:

1. - Identify variables:

V = πr²h

V = 64π

r = 4

h = ?

2. - Substitute:

64π = π(4)²h

3. - Solve for h:

64π / π = 16hπ / π

64 = 16h

64 / 16 = 16h / 16

4 = h

4. - State your answer:

h = 4 cm

Hope this helps!