find the expected vaulue of the random variable with the following probability distribution 2 3 4 5 6 7 8 9 10 11 12 1/36 1/18 1/12 1/9 5/36 1/9 1/12 1/18 1/36

The solution of the equation are y=9 and x=4

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

WE are given that the system of equation;

5x+6y=26 and 10x-6y=-2

5x+6y=50

-1(-x+6y=26)

X-6y=-26

Then Eliminate the y and combine evrything

6x=24

Divide 6 both sides

X=4

Then, substitute the x

-(4)+6y=50

-4+6y=50

Add 4 both sides

6y=54

y=9 and x=4

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Answer: To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the amount of money after the given time period

P = the principal (starting amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period (in years)

In this case, the principal is $6500, the annual interest rate is 2.8% (or 0.028 as a decimal), and the interest is compounded monthly (so n = 12). We want to find the amount after 2 years, so t = 2.

Plugging these values into the formula, we get:

A = 6500(1 + 0.028/12)^(12*2)

A ≈ $7,107.08

Therefore, the amount of money after 2 years is approximately $7,107.08.

Step-by-step explanation:

Therefore, Sam wrote a total of 38,789 digits. Therefore, the probability that Sam chooses a 0 is approximately 0.026. So the sum of all the digits in the numbers from 1000 to 9999 is: 4500.

In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and expressing how likely it is that a particular outcome will occur. Probability is calculated by dividing the number of outcomes that satisfy a certain condition (such as rolling a six) by the total number of possible outcomes. Probability theory is used in a wide range of fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It is used to model and analyze random phenomena, make predictions, and estimate the likelihood of certain outcomes.

Here,

(a) Sam writes down all the positive integers from 1 to 9999, inclusive. To find the total number of digits Sam wrote, we can count the number of digits in each number and add them up.

Numbers from 1 to 9 have one digit each, so there are 9 numbers with one digit, for a total of 9 digits.

Numbers from 10 to 99 have two digits each, so there are 90 numbers with two digits, for a total of 180 digits.

Numbers from 100 to 999 have three digits each, so there are 900 numbers with three digits, for a total of 2700 digits.

Numbers from 1000 to 9999 have four digits each, so there are 9000 numbers with four digits, for a total of 36000 digits.

Adding up these totals gives:

9 + 180 + 2700 + 36000 = 38789

Therefore, Sam wrote a total of 38,789 digits.

(b) Since Sam chose the digits 1 to 9999, there are 4 digits (0, 1, 2, and 3) that can appear in the thousands place, and 10 digits (0 to 9) that can appear in each of the other three places.

Therefore, the probability of choosing a 0 at random is the number of times 0 appears in the numbers divided by the total number of digits written down.

0 appears as the last digit in 1000 numbers (from 10 to 9990), and as the first digit in 9 numbers (1000, 10000, 2000, 20000, 3000, 30000, 4000, 40000, and 5000). So the total number of times 0 appears is 1000 + 9 = 1009.

The total number of digits Sam wrote is 38,789, so the probability of choosing a 0 at random is:

1009/38789 ≈ 0.026

Therefore, the probability that Sam chooses a 0 is approximately 0.026.

(c) We can find the sum of all the digits Sam wrote by adding up the sum of the digits in each number from 1 to 9999.

The sum of the digits in the numbers from 1 to 9 is 1+2+3+4+5+6+7+8+9=45.

The sum of the digits in the numbers from 10 to 99 can be found by observing that each of the digits from 0 to 9 appears in the tens place the same number of times (that is, 10 times each). Since there are 90 two-digit numbers, each digit appears a total of 10 x 90 = 900 times in the tens place. So the sum of the digits in the tens place is:

900(0+1+2+3+4+5+6+7+8+9) = 45,000

Similarly, each of the digits from 0 to 9 appears in the hundreds place the same number of times (that is, 100 times each). So the sum of the digits in the hundreds place is:

100(0+1+2+3+4+5+6+7+8+9) = 4500

Finally, each of the digits from 0 to 9 appears in each of the four places (thousands, hundreds, tens, and ones) the same number of times (that is, 1000 times each). So the sum of all the digits in the numbers from 1000 to 9999 is: 4500.

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The probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

What is probability?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.

a.

i. P(male) = number of males in the sample / total number in the sample = 154 / 306 ≈ 0.503

ii. P(hybrid) = number of hybrid cars purchased / total number in the sample = 99 / 306 ≈ 0.324

iii. P(hybrid|male) = number of males who purchased a hybrid / total number of males in the sample = 32 / 154 ≈ 0.208

iv. P(hybrid|female) = number of females who purchased a hybrid / total number of females in the sample = 67 / 152 ≈ 0.441

v. P(female|hybrid) = number of females who purchased a hybrid / total number of people who purchased a hybrid = 67 / 99 ≈ 0.677

b.

i. P(male) represents the probability of randomly selecting a male from the sample of 306 people who purchased a Honda Civic.

ii. P(hybrid) represents the probability of randomly selecting a car from the sample that has a hybrid engine.

iii. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male.

iv. P(hybrid|female) represents the probability of selecting a hybrid car given that the person selected is female.

v. P(female|hybrid) represents the probability of selecting a female given that the car selected has a hybrid engine.

c. No, P(hybrid|male) and P(male|hybrid) are not equal. P(hybrid|male) represents the probability of selecting a hybrid car given that the person selected is male, while P(male|hybrid) represents the probability of selecting a male given that the car selected has a hybrid engine. These probabilities are different because the sample is not necessarily representative of the entire population.

Hence, the probabilities are

i. P(male) ≈ 0.503

ii. P(hybrid) ≈ 0.324

iii. P(hybrid|male) ≈ 0.208

iv. P(hybrid|female) ≈ 0.441

v. P(female|hybrid) ≈ 0.677

P(hybrid|male) and P(male|hybrid) are not equal because the sample may not be representative of the entire population.

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The three vertices will give us the dilated figure.

First we find the slope of the line that would pass through the point of dilation, (-3, 0), and each vertex.

From (-3, 0) to (5, 4), the slope would be

m = (4-0)/(5--3) = 4/8

Since the scale factor is 1/2, this means each part of the slope would be multiplied by this scale factor:

(4(1/2))/(8(1/2)) = 2/4

This means from our point of dilation we count up 2 and over 4; this puts the new point at (-3+4, 0+2) = (1, 2).

From (-3, 0) to (3, 8) the slope is

m = (8-0)/(3--3) = 8/6

Multiplying the rise and run by 1/2, we have

(8(1/2))/(6(1/2)) = 4/3

This means the dilated point would be up 4 and over 3 from (-3, 0), putting it at (-3+3, 0+4) = (0, 4).

From (-3, 0) to (-5, 4), the slope is

m = (4-0)/(-5--3) = 4/-2.

Multiplying the rise and run by 1/2, we have

(4(1/2))/(-2(1/2)) = 2/-1

This means the dilated point would be up 2 and over -1 from (-3, 0), putting it at (-3+-1, 0+2) = (-4, 2).

These three vertices give us the dilated figure.

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The missing term in the sequence 5, 11, 17, ?, 31, 41 is B. 23.

We have been given the series 5, 11, 17, ?, 31, 41. We need to find the missing number out of the given sequence.

Let us write the prime numbers upto 50.

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47.

By looking into the above prime numbers we can make out our sequence. The series is formed by the alternate prime numbers. Thus we can complete the given sequence as,

5, 11, 17, 23, 31, 41.

Thus we got the missing number as 23 in the sequence 5, 11, 17, 23, 31, 41.

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Find the missing term in the sequence 5, 11, 17, ?, 31, 41.

Answer:

Step-by-step explanation:

-15

The total monthly payment of Ricky with an APR of 3.84 % is given by the equation M = $ 1,208.0523

The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. An APR is a number that represents the total yearly cost of borrowing money, expressed as a percentage of the principal loan amount.

The monthly payment [tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1][/tex]

where

M = Total monthly payment

P = The total amount of your loan

I = Your interest rate, as a monthly percentage

N = number of months for paying off your mortgage

Given data ,

Let the monthly payment be represented as M

Now , the number of years n = 20 years

The annual interest rate i = 3.84 %

The total loan amount P = $ 258,000

Now , the monthly payment [tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1][/tex]

On simplifying , we get

[tex]M = 258,000 [ ( \frac{ 0.0384}{12} ) ( 1 + \frac{ 0.0384}{12} )^{12*30} ] / [ ( 1 + \frac{ 0.0384}{12} )^{12*30} - 1 ][/tex]

[tex]M = 258,000 [ (0.0032 ) ( 1.0032 )^{360} ] / [ ( 1.0032 )^{360} - 1 ][/tex]

On further simplification , we get

M = 258,000 [ 0.0101078417 ] / [ 2.158700543922579 ]

M = 258,000 ( 0.00468237327729 )

M = $ 1,208.0523

Hence , the monthly payment of Ricky is $ 1,208.0523

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Answer: |ax-b| > c

c >= 0

Answer:

0.0376 or 3.76%.

Step-by-step explanation:

The probability of drawing a red marble on the first draw is 5/21 because there are 5 red marbles out of 21 total marbles in the bag.

After the first draw, there are only 20 marbles left in the bag, so the probability of drawing a red marble on the second draw, without replacement, is 4/20 or 1/5.

Similarly, after the second draw, there are only 19 marbles left in the bag, so the probability of drawing a red marble on the third draw, without replacement, is 3/19.

To find the probability of all three marbles being red, we need to multiply the probabilities of each individual draw together:

(5/21) x (1/5) x (3/19) = 15/399 or approximately 0.0376.

Therefore, the probability of drawing three red marbles in a row, without replacement, is about 0.0376 or 3.76%.

The proportional equation to graph is y= 5/3x + 10.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

From the graph we take two points as (6, 15) and (0,0).

So, the slope of line

= (0- 15)/ (0-6)

= -15 /(-6)

= 15/6

= 5/3

and, Equation of line is

y= mx+ b

15 = 5/3(6) + b

15 = 10 + b

b= 5

Thus, the proportional equation to graph is y= 5/3x + 10.

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All frumpable numbers are odd Suppose n is an even integer so n^2 + 2n = (2k)^2 + 2(2k) = 4k^2 + 4k = 4k(k+1)

Natural numbers are: 1, 2, 3, ....

Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )

Rational numbers are numbers which can be written in the form of \dfrac{a}{b} where a and b are integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.

Irrational numbers are those real numbers which are not rational numbers.

Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.

We are given that;

A integer n is frupable if n2 2n is odd

Now,

Suppose n is an even integer, so n = 2k for some integer k. Then:

n^2 + 2n = (2k)^2 + 2(2k) = 4k^2 + 4k = 4k(k+1)

Since k and k+1 are consecutive integers, one of them is even and the other is odd. Therefore, their product is even. This means that 4k(k+1) is even, and therefore, n^2 + 2n is even.

Since n^2 + 2n is even, it cannot be frumpable by definition. Therefore, if n is frumpable, n must be odd.

We have shown that if n is even, then n^2 + 2n is even and therefore, n cannot be frumpable.

Therefore, by the given numbers all frumpable numbers will be odd and n^2 + 2n = (2k)^2 + 2(2k) = 4k^2 + 4k = 4k(k+1)

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Pick a positive and a negative number: 15 and -1

Since the produce of a positive and a negative number is always negative, then x * y can't be greater than 13.

Answer:

The net profit would be 26-18=6 dollars per hour.

we need hours such that 8h≥264 =>h≥33 hours

Answer:

So, if we sell 150 flowers total, we can purchase 100 daisies and 50 roses for exactly $300.

Step-by-step explanation:

Let R be the number of roses and D be the number of daisies.

Now we can set the following equations to represent the cost and the total number of flowers,

Cost equation=3.50R + 1.25D

                       = 300

Number of flowers equation= R + D

                                              = 150

We need to find the number of roses and daisies that we can purchase, as according to question the total number of flowers is 150. To find R, we can put value of  the number of flowers in the equation for R in terms of D, and also put this expression for R in the cost equation,

R = 150 - D

3.50R + 1.25D

= 300

3.50(150 - D) + 1.25D

= 300

525 - 3.50D + 1.25D

= 300

-2.25D = -225

D = 100

Therefore, we can buy 100 daisies and the remaining 50 flowers must be roses.

The cost of 100 daisies is 100 × 1.25

= $125

The cost of 50 roses is 50 × 3.50

= $175.

Therefore, the total cost is $125 + $175

= $300.

So, if we sell 150 flowers total, we can purchase 100 daisies and 50 roses for exactly $300.

Answer:

13.5

Step-by-step explanation:

If y and x have a proportional relationship, we can write this relationship as:

y = kx

where k is the proportionality constant.

To find the value of k, we can use the information that "y = 9 when x = 2":

9 = k(2)

Solving for k, we get:

k = 9/2

Now we can use this value of k to find the value of y when x = 3:

y = (9/2)(3) = 27/2 = 13.5

Therefore, the value of y when x = 3 is 13.5.

The answer here would be D. In choice A, this would be incorrect because he would divide the millage cost before the passenger fee. In choice B, this would be incorrect because he would add the passenger fee, when it is required to subtract it. Choice C would be incorrect, because yet again, you are not supposed to add the passenger fee. This leaves choice D, which is correct.

Answer:

17

Step-by-step explanation:

60=4d-8

We move all terms to the left:

60-(4d-8)=0

We get rid of parentheses

-4d+8+60=0

We add all the numbers together, and all the variables

-4d+68=0

We move all terms containing d to the left, all other terms to the right

-4d=-68

d=-68/-4

d=17

The statement "  If n is odd,  then n³ +1 is even " can easily be proved by a direct proof

What is an integer?

A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8

Let the first Integer be x

Since the two numbers are consecutive

therefore the second number will be x+1

If n is odd, then its cube n³ is always odd

then n³ +1 is always even

So, the option"  If n is odd,  then n³ +1 is even " is correct

The statement "  If n is odd,  then n³ +1 is even " can easily be proved by a direct proof

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Answer:

Step-by-step explanation:

To express 799 cm² as a fraction of 0.13 m², we need to convert the units of one of the areas so that they are both in the same units.

1 cm = 0.01 m (since there are 100 cm in 1 meter)

So, we can convert 799 cm² to m² by dividing by (100 cm/m)²:

799 cm² = (799/10000) m²

Now, we can express 799 cm² as a fraction of 0.13 m²:

(799/10000) m² ÷ 0.13 m² = (799/10000) ÷ 0.13

Simplifying this fraction, we get:

(799/10000) ÷ 0.13 = 0.0799 ÷ 0.13

= 0.6138461538

Therefore, 799 cm² is equal to approximately 0.6138 of 0.13 m², or we can say:

799 cm² = (0.6138/1) × 0.13 m²

So, we can express 799 cm² as a fraction of 0.13 m² as:

799 cm² = 0.6138 × 0.13 m² (approximately)

or

799 cm² = 6138/10000 × 0.13 m²

or

799 cm² = 6138/100000 × m².

Randy had 20 touchdown passes and his deviation from the mean is 5.

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a small variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the values deviate from the mean. The most popular way to assess dispersion is standard deviation, which is based on all values.

Given that, mean touchdown passes=15.

Randy's touch down passes = 20.

The deviation of the touch down passes = 20 - 15 = 5.

Hence, his deviation from the mean is 5.

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Answer: the positive value of tan(1/2x) in simplest radical form with a rational denominator is √(2/3).

Step-by-step explanation:

Using the half-angle formula for tangent, we have:

tan(1/2x) = ±√((1-cos(x))/(1+cos(x)))

Substituting cos(x) = 1/5, we get:

tan(1/2x) = ±√((1-1/5)/(1+1/5))

= ±√(4/6)

= ±√(2/3)

Since we are looking for the positive value, we have:

tan(1/2x) = √(2/3)

Therefore, the positive value of tan(1/2x) in simplest radical form with a rational denominator is √(2/3).

Answer:

Step-by-step explanation:

sin(x)=sqrt(24)/5=2*sqrt(6)/5

tan(x/2)=sin(x)/(1+cos(x))

Thus, tan(x/2)=sqrt(6)/3

Answer:

48

Step-by-step explanation:

2*4*6

Another form of energy that is in the electromagnetic spectrum is X - rays

The electromagnetic spectrum is the range of all the electromagnetic waves.

Since electromagnetic spectrum contains more than just the visible light that you see, its range is given by the pneumonic RMIVUXG where

So, the frequencies of the electromagnetic waves increase as we go from top to bottom and its wavelength decreases as we go from top to bottom.

So, another form of energy that is in the electromagnetic spectrum is X - rays

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A linear graph passes through (0, 0) and (4, 1)  represent a proportional relationship.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Now, For the line passes through (0, 2.5) and (1, 4).

Equation of line is.

⇒ y - 2.5 = (4 - 2.5) / (1 - 0) (x - 0)

⇒ y - 2.5 = 1.5x

⇒ y = 1.5x + 2.5

Hence, It cannot represent a proportional relationship.

For the line passes through (0, 0) and (4, 1).

Equation of line is.

⇒ y - 0 = (1 - 0) / (4 - 0) (x - 0)

⇒ y = 0.25x

Hence, It represent a proportional relationship.

For the line passes through (0, - 1) and (1, - 1).

Equation of line is.

⇒ y - (- 1) = (- 1 - (- 1)) / (1 - 0) (x - 0)

⇒ y + 1 = 0

Hence, It cannot represent a proportional relationship.

For the line passes through (0, 3) and (1, - 2).

Equation of line is.

⇒ y - 3 = (- 2 - 3) / (1 - 0) (x - 0)

⇒ y - 3 = - 5x

⇒ y = - 5x + 3

Hence, It cannot represent a proportional relationship.

Thus, A linear graph passes through (0, 0) and (4, 1)  represent a proportional relationship.

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Answer:

R=47/pi

Step-by-step explanation:

If the of circumference of the circle is 94 cm, the diameter is 94/pi makin the radius 47/pi.

Answer:

w = 105° because 180 - (45 + 60) = 75 and 180 - 75 = 105.

Step-by-step explanation:

To find w, we first need to find z.

We can find z by setting up an equation. As we know, all angles in a triangle will add up to 180, we can say that z + 45 + 60 = 180.

We can also rewrite this as 180 - 45 - 60 = z, or 180 - (45 + 60) = z.

Solving this, we get z = 75.

We can also see that w and z are supplementary angles, meaning they will add up to 180.

Therefore, we can come to the conclusion that w + 75 = 180, or 180 - 75 = w.

Solving this we get:

w = 105

Therefore, w = 105°.

The expression that can be used to determine the average number of people that watch each free movie is -

y = - 81x⁴ - 405x³ - 216x² + 660x - 281x³ - 1485x² - 792x + 2420

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is that a movie website offers one free movie viewing to anyone that registers. The total number of people that register can be modeled by the function f(x) = - 27x³ - 135x² - 72x + 220, where x is the number of months passed since starting the website. The number of free movies available to choose from can be modeled as 3x + 11.

The expression that can be used to determine the average number of people that watch each free movie can be written as -

y = (- 27x³ - 135x² - 72x + 220)(3x + 11)

y = 3x(- 27x³ - 135x² - 72x + 220) + 11(- 27x³ - 135x² - 72x + 220)

y = - 81x⁴ - 405x³ - 216x² + 660x - 281x³ - 1485x² - 792x + 2420

Therefore, the expression that can be used to determine the average number of people that watch each free movie is -

y = - 81x⁴ - 405x³ - 216x² + 660x - 281x³ - 1485x² - 792x + 2420

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This set {σ ∈ S4 : σ(1) = 3} contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23) and  {σ ∈ S4 : σ(2) = 2} this set contains the following elements of S4: (12), (21), (13)(24), (24)(13).

The group S4 is the symmetric group on 4 elements and has 24 elements. We can list all of its subgroups as follows:

Now, let's consider the sets (a) and (b) and see if they are subgroups of S4:

(a) {σ ∈ S4 : σ(1) = 3}

This set contains the following elements of S4: (13), (23), (34), (24), (14), (12)(34), (13)(24), (14)(23). We can check that this set is not a subgroup of S4 because it is not closed under composition. For example, (13)(14) = (134) is not in the set.

(b) {σ ∈ S4 : σ(2) = 2}

This set contains the following elements of S4: (12), (21), (13)(24), (24)(13). We can check that this set is a subgroup of S4. It is closed under composition, inverses, and contains the identity element e. Therefore, it is a subgroup of S4 and is isomorphic to the cyclic group of order 2.

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Answer:

x = 3

y = 6

Step-by-step explanation:

2x - y = 0

3x - 2y = -3

-----------

2x-y = 0 ---> 2x = y ---> y = 2x ----> 3x - 2(2x) = -3 ---> 3x - 4x = -3 ---->

-----> -x = -3 ---> x = -3/-1 = 3 -----> x = 3

y = 2x ----> y = 2 (3) ----> y = 6