Twenty thousand raffle tickets are sold. One first prize of $3000, two second prizes of $750, and three third prizes of $200 each will be awarded, with all winners
f selected randomly. If you purchased one ticket, what are your expected gross winnings?
The expected gross winnings are

Using probability we get (a) P(1|A) = 1/2 and (b)P(1|B) =3/4 , hence P(1|A) ≠ P(1|B).

Probability is the study of chance . The part of mathematics known as probability deals with fractional representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, 0 denotes the event's impossibility and 1 denotes certainty.

Probability is calculated by the fraction possible outcomes ÷ total outcomes

a) The first spinner has the total 4 sections. so there are 4 total outcomes.

Favorable outcome = 1

Total number of favorable outcome=2

Probability P(1|A) = favorable outcome ÷ total outcome

∴ P(1|A) =2/4 or P(1|A) =1/2

b) The first spinner has the total 4 sections. so there are 4 total outcomes.

Favorable outcome = 1

Total number of favorable outcome=3

Probability P(1|B) = favorable outcome ÷ total outcome

∴ P(1|B) =3/4 or P(1|B) =3/4

c)Therefore P(1|A)≠P(1|B)  so the events A and B are dependent.

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Answewhats the number mason

Step-by-step explanation:

Answer:

your answr would be a 13

Step-by-step explanation:

Answer:

A) 13

Step-by-step explanation:

[tex]-5 + |-18|\\where\:|-a|=|a|\:\:\mathrm{if}\:a\neq 0\\|-18| = |18|\\= -5 + 18\\Inverse\:\:the\:\:expression\\= 18 - 5\\= 13[/tex]

Given

Tom got 72 marks in 8 tests.

Answer

[tex] \frac{72}{8} = 9[/tex]

he get 9 mark on average

Answer: i think you want y=125x+225

Step-by-step explanation:

the linear equation is created by sticking these two numbers into y=mx+b

so we start at 225 feet, which means that goes where b is, and the helicopter goes up 125 per whatever, which means we put 125 where m is

The required expression for the given statement is 4x + 1.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

The given statement is,

the difference between nine times a number and one more than five times the number

Let x be the number.

Thus, we have

nine times a number = 9x

one more than five times the number = 1 - 5x

Thus, the numerical expression we get is

9x + (1 - 5x)

Expanding we get

9x + 1 - 5x

Solving we get

4x + 1

this is the required expression

Thus, the required expression for the given statement is 4x + 1.

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Area of triangle ΔCDE  with the vertices C( -4 , 2 ), D( -3 , 7 ), and E( -7 , 6 ) is 9.5 square units.

We have a triangle ΔCDE with the vertices C( -4 , 2 ), D( -3 , 7 ), and E( -7 , 6 ). To calculate the area of triangle when its vertices are given we have the formula as shown below,

Area of triangle ΔCDE = [tex](1/2)(x_{1} (y_{2} - y_{3} ) + x_{2} (y_{3} -y_{1} ) + x_{3} (y_{1} -y_{2} ))[/tex]

Here, [tex]x_{1}[/tex] = -4 , [tex]x_{2}[/tex] = -3 ,[tex]x_{3}[/tex] = -7 , [tex]y_{1}[/tex] = 2 , [tex]y_{2}[/tex] = 7 and [tex]y_{3}[/tex] = 6

On substituting the above values in the formula of area of triangle , we will get

Area of triangle ΔCDE = (1/2)( -4 ( 7 - 6 ) + ( -3 ) ( 6 - 2) + (-7 ) ( 2 - 7 ))

Area of triangle ΔCDE = (1/2) ( - 4 - 12 + 35 )

Area of triangle ΔCDE = 19/2

Area of triangle ΔCDE = 9.5 square units

Area of triangle ΔCDE  with the vertices C( -4 , 2 ), D( -3 , 7 ), and E( -7 , 6 ) is 9.5 square units.

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Answer:

≈67.81

Step-by-step explanation:

Answer:

7x+y=3 is not a linear equation.

here hope this helps u

Answer:

4a.) 0.0005 = 5 x 10 to the exponent -4

4b.) 0.0025 = 2.5 x 10 to the exponent -3

5a.) 2 x 10 to the exponent -2 = 0.02

5b.) 16 x 10 to the exponent -4 = 0.0016

Tip:

The number being multiplied has to be less than or equal to 10. Count the places the decimal point moves from the end of the number to the number in the original equation.

Example: 0.05 = 5 x 10 to the exponent -2

0.05 has 2 spaces for the decimal point to move up to 5 going right. We use a negative decimal because 0.05 is less than 5. Here is an example where the exponent is positive:

5000 = 5 x 10 to the exponent 3

5000 has 3 spaces for the decimal point to move down to 5 going left.  

Answer:  2x-5/3=7

Tiger shows you, step by step, how to Isolate x (Or y or z) in a formula

Answer: 162 million

Step-by-step explanation:

147.4 million= 147,400,00

Make a proportion:

147,400,000   -  91%

          x             - 100%

Hence,

[tex]\displaystyle\\x=\frac{147,400,000*100}{91} \\\\x=\frac{14,740,000,000}{91} \\\\x\approx162,000,000\\\\x=162 \ million[/tex]

The experimental probability of next person to have Blue eyes is 3/7.

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

It is based on the possible chances of something to happen.

Probability (P) = Number of a Favourable outcome {n (E)} / Total number of outcomes {n (S)}  

Simply,  P = n (E) / n (S)

Given, Eye colors of the people

Green = 2

Blue    = 30

Brown = 38

To find the probability of next person to have blue eyes, first we will add the given eye colors

Total number of Eye Colors = 2 + 30 + 38 = 70

Number of Blue Eyes = 30

Then, Probability to have blue eyes P(blue) = Number of Blue Eyes / Total number of Eye Colors

                                                      = 30/70

                                                      = 3/7

So, there is 3/7 chances to next person to have blue eyes.

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Answer:

3/7

Step-by-step explanation:

The line which is perpendicular to the given line y = -x/8 + 3 is y - 8x =-2, there slopes are negative reciprocals of each other

Given data

line y = -x/8 + 3

The equation of a line is represented as y = mx + c where m represents the slope. The unique feature of perpendicular line is that the slopes are negative reciprocals of each other.

Hence we find the line that has same value of m which is the slope

using the second option: y - 8x = -2

y - 8x = 2

y = 8x - 2

y = 8x - 2

the slope here is m = 8 which is equal to the negative reciprocals of the slope in the given equation and hence the correct option

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Answer:

Step-by-step explanation:

add 99 and 36 together to get 135 degrees

Answer:

135°

Step-by-step explanation:

You add the two angles together.  

Answer:

4, 8, 12, 16, 20, 24, 28, 32, 36, and 40 are some multiples of 4 that are positive.

The points scored by Rodney is 20 points.

The points scored by Justin is 19 points.

x + y = 39 equation 1

x - y = 1 equation 2

Where:

x = points scored by Rodney

y = points scored by Justin

In order to determine the points scored by Justin, take the following steps:

Subtract equation 2 from equation 1 :

2y = 38

Divide both sides of the equation by 2

y = 38/2

y = 19 points

To determine the value of x, substitute for y in equation 2

x - 19 = 1

Combine similar terms: x = 19 + 1

Add similar terms together: x = 20

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The cost equation for Debra is given by 4x + 6y = 94 and for Heather is 5x + 3y = 77.

Linear equations in two variable have one, none, or infinitely many solutions, with the highest exponent order of 1 in each of the two variables. The standard form of a two-variable linear equation is ax + by + c = 0, where x and y are variables. Solutions can also be written in pairs, for example (x, y). A two-variable linear equation system is represented graphically by two straight lines that can intersect, parallelize, or coincide.

According to the given condition, we have 2 equations:

4x + 6y = 94
5x + 3y = 77

Now, multiply by 2 on both sides of the equation 5x + 3y = 77 to obtain:

10x + 6y = 154

Now, subtracting the equation 10x + 6y = 154 and 4x + 6y = 94.

[10x + 6y = 154] - [ 4x + 6y = 94]

6x + 0y = 60

x = 10

Putting the value of x = 10 in equation 4x + 6y = 94, we get

y = 9

So, the cost of 1 hammer is 10$ and tape is 9$.

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The solutions of the quadratic equation 5k² - 20k = 15 will be 4.65 and negative 0.65.

Let the equation be ax² + bx + c = 0.

Then the roots of the equation will be

[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}\\[/tex]

The quadratic equation is given below.

5k² - 20k = 15

Simplify the equation, then we have

k² - 4k = 3

k² - 4k - 3 = 0

Then the roots of the equation will be

[tex]\rm k = \dfrac{ -(-4) \pm \sqrt{(-4)^2 - 4 \times 1 \times (-3) }}{2 \times 1}\\\\k = \dfrac{4 \pm \sqrt {28}}{2}[/tex]

Simplify the equation, then we have

k = (4 ± 5.30) / 2

k = (4 + 5.30) / 2, (4 - 5.30) / 2

k = 4.65, -0.65

The solutions of the quadratic equation 5k² - 20k = 15 will be 4.65 and negative 0.65.

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The actual weight of the animal is between 450.2 and 426.2 pounds

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequality can be used to show that two variables or numbers are not equal to each other.

The weight of the larger animals can be off by 12 pounds. Let x represent the actual weight of the animal. If the scale reads 438.2 lbs, hence:

|x - 438.2| = 12

x - 438.2 = 12; or -(x - 438.2) = 12

x = 450.2; or x = 426.2

The actual weight of the animal is between 450.2 and 426.2 pounds

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Using it's concept, the average rates of change are given as follows:

a. 1264.03 soda per person per year.

b. 5851.89 soda per person per year.

c. 128010.89 soda per person per year.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For this problem, the function is given as follows:

f(x) = 5.852x^4 - 0.002x³ + 0.006x² + 0.029x + 47.855.

From 1990 to 1996, we have t = 0 to t = 6, hence:

Hence the rate is:

(7632.01- 47.855)/6 = 1264.03.

1264.03 soda per person per year.

From 1990 to 2000, we have t = 0 to t = 10, hence:

Hence the rate is:

(58566.75 - 47.855)/10 = 5851.89.

5851.89 soda per person per year.

From 2005 to 2010, we have t = 15 to t = 20, hence:

Hence the rate is:

(936354.84 - 296300.39)/5 = 128010.89.

128010.89 soda per person per year.

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The distance traveled by the ball as a function of time, s(t) = 16•t² ft., and the rate of change, based on calculus, gives;

(a) During the time interval [6, 6.5], the distance traveled is 100 feet

(b) In the interval, [6, 6.5], the average velocity is 200 ft/s

(c) The calculated average velocities in ft/s, for the respective time intervals are;

[6, 6.01]. 192.16

[6, 6.001]. 192.016

[6, 6.0001]. 192.0016

[5.9999, 6]. 191.9984

[5.999, 6]. 191.984

[5.99, 6]. 191.84

The instantaneous velocity at t = 6 is v(6) = 192 ft/s

The distance traveled as a function of time is s(t) = 16•t² ft.

(a) The distance traveled during the time interval [6, 6.5] is found as follows;

s(6) = 16 × 6² = 576

s(6.5) = 16 × 6.5² = 676

The distance traveled in the interval, [6, 6.5], ∆s(t) = 676 - 576 = 100

The distance traveled during the time interval [6, 6.5] = 100 feet

(b) Average velocity = ∆s(t)/∆t

∆t = 6.5 - 6 = 0.5

Therefore;

∆s(t)/∆t = 100/0.5 = 200

The average velocity = 200 ft./s

(c) The average velocities over the given time intervals, obtained using a graphing calculator, are;

Interval. Average velocity

[6, 6.01]. 192.16

[6, 6.001]. 192.016

[6, 6.0001]. 192.0016

[5.9999, 6]. 191.9984

[5.999, 6]. 191.984

[5.99, 6]. 191.84

Given that at t = 6, as the time interval approaches zero from the right and from the left, the average velocity approaches 192 ft./s, the instantaneous velocity at t = 6, v(6) is 192 ft./s

v(6) = 192 ft./s

Using calculus, differentiation, we have;

v(t) = ds/dt = 2×16 × t = 32•t

v(6) = 32 × 6 = 192

Therefore;

v(6) = 192 ft./s

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Answer:

6

Step-by-step explanation:

The diameter is half of the given radius, therefore, split the radius in half.

[tex]\frac{12\:in^2}{2} = 6\:in^2[/tex]

Answer:

Slope is 1

Step-by-step explanation:

From the general linear equation:

[tex]{ \rm{y = mx + c}}[/tex]

m is the slope

Comparing with the equation given:

[tex]{ \rm{y = { \green{1}}x - 3}}[/tex]

Let the Principle be 100.

P = 100, then A = 200 and SI will be 200 - 100 = 100

YES = 100 in 10 years

Rate = 100/10 = 10%.

∴ The interest rate is 10%.

Given:

Time period = 10 years

Formula used:

SI = (P × R × T)/100

A = P + SI

Where P = main amount, R = rate, T = time, SI = primary interest

Calculations:

Monetary amount 2P

YES = 2P - P

⇒ P = (P × R × 10)/100

⇒ 1 = R/10

⇒ R = 10%

∴ The interest rate is 10%

Answer:

Step-by-step explanation:

NO x=3

The average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.

It is a measure of how much the function changed per unit, on average, over that interval.

We have,

f(x) = x - 2√x

On the interval [1,9].

[1, 9] = [a, b]

The average rate of change:

= f(b) - f(a) / b - a

= f(9) - f(1) / 9 - 1

= [(9 - 2√9) - (1 - 2√1)] / 8

= [ (9 - 6) - (1 - 2) ] / 8

= (3 + 1) / 8

= 4 / 8

= 1/2

Thus the average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.

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Answer:

x = 24/5

Step-by-step explanation: