Help me please I’d really appreciate it

a. P(A) = 1/12, P(B) = 1/3, P(C) = 1/6 based on counting outcomes.

b. P(A|B) = 1/12, calculated using the definition of conditional probability.

c. P(B|C) = 1/3, calculated using the definition of conditional probability.

d. P(A|C) = 1/6, calculated using the definition of conditional probability.

e. A and B are not independent, B and C are not independent, A and C are independent based on the observations and calculations.

a. We have:

P(A): The only ways to get a sum of at least 10 are (4,6), (5,5), (6,4). Each of these outcomes has probability 1/36. So, P(A) = 3/36 = 1/12.

P(B): The only ways to get an odd sum are (1,2), (1,4), (1,6), (3,2), (3,4), (3,6), (5,2), (5,4), (5,6), (6,1), (6,3), (6,5). Each of these outcomes has probability 1/36. So, P(B) = 12/36 = 1/3.

P(C): The blue die has a probability of 1/6 of landing on 5, regardless of what the red die shows. So, P(C) = 1/6.

b. We have:

P(A|B) = P(A and B) / P(B)

To find P(A and B), we need to count the number of outcomes that satisfy both A and B. There are 6 outcomes that satisfy B: (1,2), (1,4), (1,6), (3,2), (3,4), and (5,4). Out of these, only (5,4) satisfies A as well. So, P(A and B) = 1/36.

Therefore, P(A|B) = (1/36) / (1/3) = 1/12.

c. We have:

P(B|C) = P(B and C) / P(C)

To find P(B and C), we need to count the number of outcomes that satisfy both B and C. There are only two such outcomes: (1,4) and (3,2). So, P(B and C) = 2/36 = 1/18.

Therefore, P(B|C) = (1/18) / (1/6) = 1/3.

d. We have:

P(A|C) = P(A and C) / P(C)

To find P(A and C), we need to count the number of outcomes that satisfy both A and C. Since C requires the blue die to show 5, there is only one outcome that satisfies both A and C: (5,5). So, P(A and C) = 1/36.

Therefore, P(A|C) = (1/36) / (1/6) = 1/6.

e. We have:

A and B are not independent, because knowing that the sum is odd affects the probability of the sum being at least 10 (it makes it impossible).

B and C are not independent, because knowing that the blue die shows 5 affects the probability of the sum being odd (it makes it even).

A and C are independent, because knowing that the blue die shows 5 does not affect the probability of the sum being at least 10.

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Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

4x - y = 13 Equation represents the line that passes through the point (3,-1) and is perpendicular to the graph of x+4y=11

According to the question,

Its given that

The required line is passing through (3, -1)

And is perpendicular to line x + 4y = 13

Let required line be (y-y') = m'(x - x') ----(1)

Where m' is slope of required line

The given line is  x + 4y = 13

Slope of this line be m =

=> 4y = 13 - x

=> y = 13/4 - x/4

m = -1/4

You should know that if two lines are perpendicular to each other than the product of their slope is always -1

Therefore , m × m' = -1

=> -1/4 × m' = -1

Multiplying by -4

=> m' = 4

Substituting the value in equation (1)

=> (y - (-1)) = 4 ( x - 3)

=> y + 1 = 4x - 12

=> 4x - y = 13 is our required equation

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The positive difference between the two probabilities is 11/35.

To calculate the probability that three distinct numbers chosen at random without replacement from the set would have an even sum, Jan would consider the number of ways to choose three even numbers (4 choose 3) and divide that by the total number of combinations of three numbers (7 choose 3).

To calculate the probability that three distinct numbers chosen at random without replacement from the set would have an even product, Judy would consider the number of ways to choose three numbers such that the product is even (3 choose 2) and divide that by the total number of combinations of three numbers (7 choose 3).

The positive difference between the two probabilities would be the difference between these two calculations. In this case, 11/35 is a positive difference, meaning that the probability of having an even product is 11/35 higher than the probability of having an even sum.

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The surface area of the cone provided would be 75.36 cm².

To find the surface area of a cone, we will use the formula A = πr(r + √h2+r2)

Now we will break down the dimensions as follows:

π = 3.14

r = 3 cm

h = 4 cm

l = 5 cm

Now we will substitute the variables into the equation

A = 3.14 * 3 cm( 3 cm + √4² + 3²)

A = 9.42 (3 cm + 5 cm)

A = 9.42(8 cm)

A = 75.36

So, the surface area of the cone  to the nearest hundredth is 75.36

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Answer:

0.13

Step-by-step explanation:

2/3×1/5 = 0.13

Answer:

Step-by-step explanation:

Touching angles have to equal  the full amount of degrees. This means oppisite angles are the same so 7/6, 5/8, 1/4, 2/3. This then means that 1/4 and 5/8 are the same. 3 and 5 would add up to the full amount of a flat line. 2 and 7 could as well, but diffrently (i dont remebr the terms lol). 6/8 would be supplementary, but wouldnt show that the lines are parrlele. Nether would D, as it is true but not helpful.  B seems the most likely at this point with a being a close second. I am so sorry I couldnt be more helpful

Answer:

The answer would be b ;0

Answer:

x = 51

Step-by-step explanation:

x = 180 - (2x - 8) - (180 - 153)

x = 180 - 2x + 8 - 27

3x = 180 - 27

3x = 153

x = 51

Answer:

80.5

Step-by-step explanation:

2x-8 + x =153

The charge per cubic foot is $0.05. The equation for the total cost of a resident's water is C(x) = 0.05x + 40. The number of cubic feet of water used that would lead to a bill of $130 is 2200.

We will use the given data to calculate the charge per cubic foot:Let x be the number of cubic feet of water used by a household and let y be the corresponding bill amount.

Case 1: When a household using 1000 cubic feet was billed $90.

Case 2: When one using 1600 cubic feet was billed $105.Subtracting case 1 from case 2, we get:$$105 - 90 = 15$$$$1600 - 1000 = 600$$So, the charge per cubic foot is:$$\frac{15}{600} = 0.025$$$$\implies 0.05 \text{ (for two decimal place)}$$ Hence, the charge per cubic foot is $0.05.

To write an equation for the total cost of a resident's water as a function of cubic feet of water used, we will use the given data:

$$\text{Fixed amount = } $40$$\text{Charge per cubic foot of water used = } $0.05$$\text{Number of cubic feet used = } x$$

Therefore, the equation for the total cost of a resident's water as a function of cubic feet of water used is:

$$C(x) = \text{(Charge per cubic foot of water used)}\times\text{(Number of cubic feet used)}+\text{(Fixed amount)}$$$$C(x) = 0.05x + 40$$

To find out how many cubic feet of water used would lead to a bill of $130, we will use the equation obtained above:

$$C(x) = 0.05x + 40

= $130$$$$\implies 0.05x

= $90$$$$\implies x

= \frac{90}{0.05}

= 1800$$

Therefore, the number of cubic feet of water used that would lead to a bill of $130 is 1800.

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15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

the radius of convergence (R) is ∞, and the interval of convergence (I) is (-∞, ∞).

To find the radius of convergence (R) and the interval of convergence (I) of the series given by:

∑ 7(-1)^(n-1) n^n x^n

We can apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is L as n approaches infinity, then the series converges absolutely if L < 1, diverges if L > 1, and the test is inconclusive if L = 1.

Let's apply the ratio test to the given series:

L = lim(n→∞) |(7(-1)^(n-1) (n+1)^(n+1) x^(n+1)) / (7(-1)^(n) n^n x^n)|

Simplifying and canceling out common factors:

L = lim(n→∞) |(7(n+1) x) / (n^n)|

Taking the absolute value:

L = lim(n→∞) |7(n+1) x / n^n|

Now, let's evaluate the limit:

L = |7x| lim(n→∞) (n+1) / n^n

The limit can be further simplified by applying the ratio test for the sequence:

lim(n→∞) (n+1) / n^n = 0

Therefore, the limit L simplifies to:

L = |7x| * 0 = 0

Since L = 0, which is less than 1, the ratio test indicates that the series converges absolutely for all values of x. Thus, the series converges for all x.

For a series that converges for all x, the radius of convergence (R) is infinite (∞), and the interval of convergence (I) is the entire real number line (-∞, ∞).

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The measure of the other leg of the right triangle to the nearest tenth is equal to 5.2 cm.

In mathematics, the Pythagorean theorem or Pythagoras theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

Given the following data:

To find the measure of the other leg, we would apply Pythagorean's theorem:

Mathematically, Pythagorean's theorem is given by the formula:

\(\sf Hypotenuse^2=opposite^2+adjacent^2\)

Substituting the given parameters into the formula, we have:

\(\sf 6^2=opposite^2+3^2\)

\(\sf 36=opposite^2+9\)

\(\sf Opposite^2=36-9\)

\(\sf Opposite^2=27\)

\(\sf Opposite=\sqrt{27}\)

\(\rightarrow \boxed{\boxed{\bold{Opposite = 5.19\thickapprox5.2 \ cm}}}\)

Thus, the measure of the other leg of the right triangle to the nearest tenth is equal to 5.2 cm.

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Answer:

88

Step-by-step explanation:

The actual volume is 87.965

To the nearest tenth would be 88 (the hundreths place would round up the tenths place and it is 9 so .9 is rounded up to 1)

Answer:

c

Step-by-step explanation:

15 divided by 10= 1.5

21 divided by 14= 1.5

Answer: C is correct

Step-by-step explanation:

If you put in the fractions into a calculator you will see that both ratios are equal to 1.5

Answer:

Step-by-step explanation:

5

The number of plants Ethan has are 5.

Two or more expressions with an Equal sign is called as Equation.

Let x be the number of plants Ethan has.

Ethan uses 3.5 ounces of water for each plant, so he will use a total of 3.5p ounces of water.

If he starts with 32 ounces of water and ends up with 14.5 ounces

Total of 32 - 14.5 = 17.5 ounces of water.

As given the amount of water used is equal to the amount of water per plant times the number of plants:

3.5x = 17.5

Divide both sides by 3.5

x=5

Hence, , Ethan has 5 plants.

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Answer:

do you still need this answered?

Step-by-step explanation:

If a computer suggests that det a = 1 and det a^(-1) = 3 for an n x n matrix a, then we cannot trust these answers without further investigation. This is because there is a contradiction between the two statements.

We know that det a is the determinant of matrix a, while det a^(-1) is the determinant of the inverse of matrix a. We also know that the determinant of a matrix and its inverse are related by the formula det(a) * det(a^(-1)) = 1.

So, if det a = 1, then det a^(-1) should be 1/det a = 1/1 = 1. However, the computer suggests that det a^(-1) = 3, which contradicts the above formula. Therefore, we cannot trust the answers given by the computer, and we should double-check the calculations or the data used by the computer to ensure that there are no errors.

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Answer:

14/9

Step-by-step explanation:

Answer:

The answer is 35!

Step-by-step explanation:

I got it wrong and it gave me the answer.

The cost of the plan for the limited talk and text is $50 with an additional cost of $22.99 for each gigabyte of data.

Generally, a mathematical function means a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables. It can take an input from many variables but will  always give the same output, unique to that function.

We are given that "H(g) = 22.99g + 50", where H represents the cost, in dollars, and g represents the number of gigabytes of data. The main answer is based on the given function where the constant term of 50 represents the cost of the plan for limited talk and text, and the coefficient of 22.99 represents the additional cost for each gigabyte of data used.

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Answer:

113.1

Step-by-step explanation:

A = πr²

A = π (6)²

A = π (36)

A = 113.09 = 113.1

Given:Expression to be checked whether it makes sense mathematically.15. Solution: Firstly, let us understand the terminologies used in this question. A set of numbers or terms that are related by addition and subtraction are called expressions.

Expressions may contain letters or variables, which represent numbers. Expressions can be simple or complex.Let's take each expression one by one.15. (a) u (v w)This expression makes sense mathematically. We can evaluate this expression by using the associative property of addition, which states that if a, b, and c are real numbers, then the sum of a and b, added to c, is the same as a added to the sum of b and c. Hence, u + (v + w) can be written as (u + v) + w and vice versa.(c) llu v This expression does not make sense mathematically as the operator ll is not defined in mathematics.

Therefore, this expression is invalid.(d) (u v)- u This expression makes sense mathematically. We can evaluate this expression by using the distributive property of subtraction, which states that if a, b, and c are real numbers, then the difference of a and b, multiplied by c, is the same as the difference of a times c and b times c. Hence, (u - u) + v can be written as 0 + v, which is equal to v.(a) lul-vThis expression does not make sense mathematically as the operator l is not defined in mathematics. Therefore, this expression is invalid.(b) (u v)-wThis expression makes sense mathematically. We can evaluate this expression by using the distributive property of subtraction, which states that if a, b, and c are real numbers, then the difference of a and b, multiplied by c, is the same as the difference of a times c and b times c. Hence, (u - v) - w can be written as u - (v + w) and vice versa.

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Answer:

A-> a(n)=a+(n-1)d

B-> Yes, I do agree

Step-by-step explanation:

A=   a+(n-1)d

where a=the first term

           n=the term's location

           d= the difference between two adjacent terms

B= I agree

a3=12+2d=4.........equation 1

          2d=-8

             d=-4

a10=12+9d=-24.....equation 2

            9d=-36

              d=-4

Hence, to find the next term of the sequence, add -4 to  the previous term.

{I hope this answers your question}

Answer:

50.6x + 75.9

Step-by-step explanation:

25.3(2x+3) = 50.6x+75.9

Answer:

24 represents 12 percent

Answer:

black

black

Step-by-step explanation:

Answer:

\( s = 14.1 \)

Step-by-step explanation:

Given:

<S = 31°

SQ = r = 9

SR = q = 21

s = ?

To find s, use the Law of Cosines:

s² = r² + q² - 2rs*cos(S)

\( s^2 = 9^2 + 21^2 - 2*9*21*cos(31) \)

\( s^2 = 81 + 441 - 378*0.8572 \)

\( s^2 = 522 - 324.02 \)

\( s^2 = 197.98 \)

\( s = 14.1 \) (nearest tenth)

Answer:

14) -123

15) 144

16) 3303

Step-by-step explanation:

The derivative of the function y = x(6x + 1)⁵ is: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴

To find the derivative of the given function, we can apply the rules of differentiation. Using the product rule, we differentiate each term separately and then add them together.

For the first term x, the derivative is simply 1.

For the second term (6x + 1)⁵, we apply the chain rule. The derivative of (6x + 1)⁵ with respect to x is 5(6x + 1)⁴ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get (6x + 1)⁵ * 6 = 6(6x + 1)⁵.

For the third term x(6x + 1)⁴, we again apply the product rule. The derivative of x is 1, and the derivative of (6x + 1)⁴ is 4(6x + 1)³ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get x * 4(6x + 1)³ * 6 = 24x(6x + 1)³.

Finally, we add the derivatives of each term to get the derivative of the entire function: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴.

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Complete question:

Use the rules of differentiation to find the derivative of the function y= x(6x + 1)⁵

(6x + 1)⁵ + 30x(6x + 1)⁴

(6x + 1)⁴ (36x + 1)

x-1/6

No correct answer provided.