In gambling, the chances of winning are often written in terms of odds rather than probabilities. The odds of winning is
the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2:3 (read "2 to 3") or 2/3


(Note: if the odds of winning are 2/3, the probability of success is 2/5)

The odds of an event occurring are 1:4. Find (a) the probability that the event will occur and (b) the probability that the event will not occur

Answers

Answer 1

a) The probability of event occur is  [tex]\frac{1}{5}[/tex].

b) The probability of event not occur is  [tex]\frac{4}{5}[/tex].

What is probability?

The likelihood of an event happening is gauged by probability. It is difficult to provide a complete prediction for many events. We can only anticipate the likelihood of an event occurring by using it. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

Here The ratio of the odds of an event occurring are 1:4.

Then probability of that the event will occur is ,

=>P(event will occur = [tex]\frac{1}{4+1}[/tex] = [tex]\frac{1}{5}[/tex]

Now the probability of that event not will occur is ,

=> P(event will not occur) = 1 -[tex]\frac{1}{5}[/tex] = [tex]\frac{5-1}{5}[/tex] = [tex]\frac{4}{5}[/tex]

Hence the answers are a) [tex]\frac{1}{5}[/tex] and b) [tex]\frac{4}{5}[/tex].

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Related Questions

he weight of an organ in adult males has a​ bell-shaped distribution with a mean of 310 grams and a standard deviation of 35 grams. Use the empirical rule to determine the following. ​(a) About 99.7​% of organs will be between what​ weights? ​(b) What percentage of organs weighs between 240 grams and 380 ​grams? ​(c) What percentage of organs weighs less than 240 grams or more than 380 ​grams? ​(d) What percentage of organs weighs between 240 grams and 415 ​grams?

Answers

a) About 99.7​% of organs will be between 205 grams and 415 grams.

b) The percentage of organs weighing between 240 grams and 380 grams is of 95%.

c) The percentage of organs less than 240 grams or more than 380 grams is of 5%.

d) The percentage between 240 grams and 415 grams is of: 97.35%.

What is defined by the Empirical Rule?

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

68% of the measures within one standard deviation of the mean.95% of the measures within two standard deviation of the mean.99.7% of the measures within three standard deviation of the mean.

The first three questions are quite straight forward, while for the fourth we consider the symmetry of the normal distribution, as follows:

95% of 50% of the measures are between 240 grams and 310 grams.99.7% of 50% of the measures are between 310 grams and 415 grams.

Hence the total percentage is of:

0.95 x 50 + 0.997 x 50 = 97.35%.

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What is the product of 64?.

Answers

The product of 64 are 1, 2, 4, 8, 16, 32, 64 and its factors in pairs are (1, 64), (2, 32), (4, 16), and (8, 8).

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

The set of integers that can be divided evenly by 64 is called the factorization of 64. Overall, there are 7 components that make up 64: 1, 2, 4, 8, 16, 32, and 64, with 64 being the largest. The prime factors for the number 64 are 1, 2, 4, 8, 16, 32, and 64. Its factors in pairs are 1, 64, 2, 32, 4, and 16. (8, 8).

Factors of 64: 1, 2, 4, 8, 16, 32 and 64Negative Factors of 64: -1, -2, -4, -8, -16, -32 and -64Prime Factors of 64: 2Prime Factorization of 64: 2 × 2 × 2 × 2 × 2 × 2 = 26Sum of Factors of 64: 127

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A flu epidemic has hit a local day care facility.
The population of sick children is represented
in the equation below where P is the number
of sick children, and t is the number of days
since the first child was diagnosed. How
many days will it take for 50 children to catch
the flu?
P =
110
1+7e-0.22t

Answers

It will take 8 days for 50 children to catch the flu

How to determine the number of days?

The given equation states as follows:

P = 110/(1+7e⁻⁰²²ⁿ     (Where n stands for t)

P = 110/(1+7e⁻⁰²²ⁿ = 2.2

7.e⁻⁰²²ⁿ = 2.2 - 1

7.e⁻⁰²²ⁿ = 1.2/7

0.22n = In (12/7)

n= 8.02

Recall that n=t

Therefore t = .02

Therefore time = 8 days

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What is the distance between − 2 − 3 and − 4 − 5 )?.

Answers

The distance between points (2, 3) and (-4, 5) is 6.3 units.

As we know according to the distance formula the distance between points (x₁, y₁) and (x₂, y₂) is given by,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]

Here we have been given points (2,3) and (-4,5)

Let us assume that  (x₁, y₁) = (2, 3)

and (x₂, y₂) = (-4, 5)

Let d represents the distance between points (2,3) and (−4,5)

Using above distance formula the distance d between given points would be,

[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow d = \sqrt{[(-4 - 2)^2 + (5 - 3)^2]}\\\\\Rightarrow d = \sqrt{[(-6)^2 + (2)^2]}\\\\\Rightarrow d = \sqrt{36+4}\\\\\Rightarrow d = \sqrt{40}\\\\\Rightarrow d = 6.3~units[/tex]

Therefore, the distance is 6.3 units.

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The complete question is:

What is the distance between points (2,3) and (−4,5)  ?

Is 0 infinite or no solution?.

Answers

No, 0 is neither an infinite solution nor no solution.

The solution x = 0 implies that the value 0 satisfies the equation, so there is a solution. “No solution” implies that there is no value, not even 0, which would satisfy the given equation.

Let us take an example for a more reasonable interpretation,

An example is the equations

² + 1 = 0 and

− 3 = 2 − 3

Suppose that is real.

The first equation has no solution, while the second equation has a solution = 0.

Hence, 0 can be a solution to a system of equations.

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Solve for x...............
[tex]\bf 4x+6=14[/tex]

Answers

4x+6= 14
-6 -6
4x= 8
— —
4 4

x=2

How does the sum rule work?.

Answers

The formula for the sum rule is: P(A or B) = P(A) + P(B) - P(A and B)

The sum rule, also known as the addition rule of probability, states that the probability of any two events occurring together is the sum of the probability of each event occurring individually, minus the probability of them both occurring at the same time. The formula for the sum rule is:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are two events and P(A) and P(B) are the probabilities of each event occurring individually, and P(A and B) is the probability of both events occurring at the same time.

The sum rule is used when the two events are mutually exclusive, meaning that they cannot happen at the same time. In this case, P(A and B) = 0, so the formula becomes:

P(A or B) = P(A) + P(B)

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A fair die is rolled 5 times. What is the probability of having no 1 and no 2 among the rolls

Answers

Answer:

40%

Step-by-step explanation:

There are 5 options to roll: 1, 2, 3, 4, and 5.

This means you have a 1 out of 5 chance of rolling each number.

This question is asking for 1 AND 2, not just one number. So, we have a 2 out of 5 chance of rolling that, because 2 options are acceptable instead of just one number.

I'm not sure which form you are looking for, but 2 out of 5 is the same as saying 2/5. Most probability solutions are wanted as a percentage. To find that just solve 2/5, which is 0.4. Move the decimal to the right twice, and that is a 40% chance.

i need answer by today​

Answers

The total cost of the fence will be £841. The solution is obtained using the concept of perimeter of triangle.

What is perimeter of triangle?

Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.

We are given a right-angled triangle with one angle 59° and the adjacent side as 145 meters.

We know that tan θ = Opposite side/Adjacent side

⇒ tan 59° = Opposite side/145

⇒ 1.66 = Opposite side/145

241 meters(approx) = Opposite side

Now, using pythagoras theorem,

⇒Hypotenuse^2 = Base^2 + Perpendicular^2

⇒Hypotenuse^2 = 241^2 + 145^2

⇒Hypotenuse^2 = 58,081 + 21,025

⇒Hypotenuse^2 = 79,106

Hypotenuse = 281 meters(approx)

Perimeter of triangle = Sum of three sides

⇒ Perimeter = 145 + 241 + 281

⇒ Perimeter = 667 meters

The fence costs £ 1.26 per meter

Total cost of fence = 1.26 * 667 = £840.42 = £841

Hence, the total cost of the fence will be £841.

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Which pair of related inequalities can be graphed to find the solution set to 4*-7 <1?
O y<4*-7 and y < 1
Oy> 4*-7 and y < 1
O y<4*-7 and y> 1
O y> 4*-7 and y> 1

Answers

Answer:

The second one :( y> 4x - 7) and y<1

What is the value of k such that the following pair of equations have infinitely many solutions?.

Answers

For the value of k is equal to 6, the system of equations,

kx + 3y - (k – 3) = 0 and 12x + ky - k = 0 have infinitely many solutions

Here we have equations

kx + 3y - (k – 3) = 0

12x + ky - k = 0

For a system of 2 linear equations,

a₁x + a₂y + a₃ = 0

b₁x + b₂y + b₃ = 0

They will have infinitely many solutions if

a₁/b₁ = a₂/b₂ = a₃/b₃

here,

k = a₁,          3 = a₂          - (k – 3) = a₃

12 = b₁         k = b₂           - k = b₃

Hence

k/12 = 3/k = (3 - k)/(-k)

Taking up

3/k = (3 - k)/(-k)

we get

3 = k - 3

or, k = 6

hence for k = 6, the equations will have infinite solutions.

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Complete Question

What is the value of k such that the following pair of equations has infinitely many solutions?

kx + 3y - (k – 3) = 0

12x + ky - k = 0

question= 3 x + 2 / x + 7 ​

Answers

solved, 3x+2/x+7 = 3x²+21x+2/x+7

solution:

3x+2/x+7

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times x+7/x+7

we get,

3x(x+7)/x+7 + 2/x+7

since 3x(x+7)/x+7 and 2/x+7  have the same denominator, add them by adding their numerators.

we get,

3x (x+7) +2/x+7

Do the multiplications in 3x(x+7)+2.

we get, 3x²+21x+2/x+7

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For the following set of data, find the percentage of data within 2 population standard deviations of the mean, to the nearest 10th of a percent. 90, 40, 63, 62, 65, 67, 63, 68 90, 40, 63, 62, 65, 67, 63, 68

Answers

The percentage of data within 2 standard deviations of the mean is given as follows:

100%.

What are the mean and the standard deviation of a data-set?

The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.

Using a calculator, the measures for this problem are given as follows:

Mean: 64.75.Standard deviation: 12.65.

The bounds within two standard deviations of the mean are given as follows:

64.75 - 2 x 12.65 = 39.45.64.75 + 2 x 12.65 = 90.05.

All the measures in this problem are within these bounds, hence the percentage is of 100%.

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A scale on a blueprint drawing of a house shows that 10 centimeters represents 2 meters. what number of actual meters are represented by 18 centimeters on the blueprint?

Answers

The required number of actual meters represented by 18 centimeters on the blueprint is 3.6 meters.

What is the scale factor?

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
A scale on a blueprint drawing of a house shows that 10 centimeters represent 2 meters.

Scale factor,
10 centimeter: 2 meters = 1 centimeters : 0.2 meters

So,
18 centimeters = 18 × 0.2 meters = 3.6 meters.

Thus, the required number of actual meters represented by 18 centimeters on the blueprint is 3.6 meters.

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The theater sells two types of tickets: adult tickets for $11 and child tickets for $3.
Last night, the theater sold a total of 464 tickets for a total of $3520. How many adult tickets did the theater sell last night?

Answers

The adult tickets sold were 409.

What number of total adult ticket were sold?

11a + 3c = 3520

Where "a" is the number of adult tickets sold and "c" is the number of child tickets sold.

We also know that the theater sold a total of 464 tickets, so we can add the following equation:

a + c = 464

We can now use the first equation to solve for one of the variables, and then substitute it into the second equation:

11a + 3c = 3520

3c = 3520 - 11a

c = (3520 - 11a)/3

We know that:

a + c = 464

We can substitute the value of c into this equation:

a + (3520 - 11a)/3 = 464

a + (3520 - 11a) = 464*3

a + 3520 - 11a = 1392

12a = 4912

a = 4912/12

a = 409

So, the theater sold 409 adult tickets last night

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What’s 14x+14x

x= 1/2


Answer in simplest form please and thank you!

Answers


[tex]\huge\text{Hey there!}[/tex]


[tex]\mathsf{14x + 14x}\\\\\mathsf{= 14(\dfrac{1}{2}) + 14(\dfrac{1}{2})}\\\\\mathsf{= \dfrac{14}{1}\times \dfrac{1}{2} + \dfrac{14}{1} \times \dfrac{1}{2}}\\\\\mathsf{= \dfrac{14\times1}{1\times2} + \dfrac{14\times1}{1\times2}}\\\\\mathsf{= \dfrac{14}{2} + \dfrac{14}{2}}\\\\\mathsf{= 7 + 7}\\\\\mathsf{= 14}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{14}}\huge\checkmark[/tex]


[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]


~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

14x + 14x = 14

Step-by-step explanation:

Given expression,

→ 14x + 14x

Now we have to use,

→ x = 1/2

Let's simplify the expression,

→ 14x + 14x

→ 14(1/2) + 14(1/2)

→ (14/2) + (14/2)

→ 7 + 7

→ 14 => {final value}

Hence, required answer is 14.

HELP PLEASE THIS IS DUE IN 1 MINUTE!!!!!!!!
A sixth grade class is going on a field trip. The school is providing one sack lunch for each student. Each lunch has either a ham, turkey, or bologna sandwich along with either carrots or celery.


Identify which list below shows all the possible outcomes of sack lunches, and select the outcomes from that list that represent picking a ham or turkey sandwich with carrots if there are an equal number of each type of sack lunch and students are randomly selecting their lunch. Use this information to mark the probability on the number line.

Answers

The required probability has been shown on the number as illustrated in the figure.

What is probability?

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
There are two veggies (carrots, and celery) and three types of meat (ham, turkey, and bologna),

This results in 3*2 = 6 distinct combinations of meat and a vegetable. Here, we are limited to choosing just one of each kind. List 2 shows the 6 different combinations. List 1 is inaccurate because you can only take one vegetable at a time and not both.

List 2 alternatives that state "ham, carrots" and "turkey, carrots" should be circled. Two things have been circled. This is one of a total of six.

Probability is given as,
= 2/ 6
= 1/3

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Andrew and Michael went for a hike in the Great Smoky
Mountains. They drank 500 fluid ounces of water during
their hike. What possible combinations of water could
Andrew and Michael have each drank while they were
hiking?

Answers

Here are some suggestions to assist you make sure you are consuming enough liquids to keep your hydration levels at good levels.

How much water should you drink while walking?By multiplying the hourly sweat rate by 4, you may calculate how much to drink every 15 minutes. This becomes the recommended amount of fluid consumption every 15 minutes of walking or running.Every hour of hiking for adults typically requires 2 cups of water. For every hour of hiking, kids typically need 1-2 cups. However, depending on whether you can filter water along the journey, the weather, and your own level of thirst, you might require more or less than this.An excellent general advice is one half-liter of water for every hour of moderate activity in temperatures between 50 and 60 degrees. If the temperature and level of exercise increase, you might need to drink more.

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There are an infinite number of combinations of water that Andrew and Michael could have each drank as long as the sum is 500.

How to solve the equation?

Since Andrew and Michael drank a total of 500 fluid ounces of water, any combination of water that they drank must add up to 500 fluid ounces.

Let's call the amount of water Andrew drank as "a" and the amount of water Michael drank as "m". Then, we can write the equation: a + m = 500.

There are an infinite number of combinations of water that Andrew and Michael could have each drank as long as the sum is 500. Here are a few examples:

Andrew drank 250 fluid ounces and Michael drank 250 fluid ounces.

Andrew drank 200 fluid ounces and Michael drank 300 fluid ounces.

Andrew drank 100 fluid ounces and Michael drank 400 fluid ounces.

and so on.

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Solve using substitution.
x = –3
x + 7y = 18
(, )

Answers

The value of y in the expression x + 7y = 18 when x = - 3 is 3.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

We know Substitution in mathematics is when we replace some specific numerical values with variables according to our wants or given in the problem.

Given, x = - 3 and x + 7y = 18.

Replacing x with - 3 in x + 7y = 18.

- 3 + 7y = 18.

7y = 18 + 3.

7y = 21.

y = 21/7.

y = 3

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What is the result when the number 28 is decreased by 25%?

Answers

Answer:

21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

28 - 25%=21

Can it be true that a 10 year old child weighs 30%
more than a 6 year old child?

Answers

Answer:Kids grow at their own pace. Big, small, tall, short — there is a wide range of healthy shapes and sizes among children. Genetics, gender, nutrition, physical activity, health problems, environment, and hormones all play a role in a child's height and weight. And many of these things can vary widely from family to family.

Step-by-step explanation:

For each sequence below: (a) use a difference table to find a formula, then check your formula for a few values of n (b) use your formula to calculate the next three terms in the sequence. 3 14, 32, 60, 98, ...

helpp please​

Answers

The subsequent three words in the list. 3 14, 32, 60, 98, ... is 276 . In this case, the order is 3, 14, 32, 60, 98, and 276.

How do you find the nth term formula?(a)An arithmetic sequence's nth term is determined by a = a + (n - 1)d in step 1. As a result, enter the given values for a and d into the formula to determine the nth term. Step 2: Now, change the nth term in the equation to n = 5 to determine the fifth term. Consecutive integers in an arithematic sequence often differ from one another. Simply subtract the first term from the second term to discover it, or the second term from the third, and so forth. Our shared difference is thus eight.(b)the subsequent three words in the list. 3 14, 32, 60, 98, ... is 276 . In this case, the order is 3, 14, 32, 60, 98, and 276.

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The next three terms in the sequence are 79, 90, and 101.

What is sequence?An ordered group of numbers or items is referred to as a sequence.Since each element in a series has a particular place in the sequence, the order of the elements is crucial.Sequences can either have a finite or infinite number of words, meaning they can either end or continue eternally.A formula that can be used to determine any term in a series given its location can be used to characterize sequences.

a) To find a formula for the sequence, we can use a difference table.

First, let's write out the first few terms of the sequence:

3, 14, 32, 60, 98, ...

Next, we'll create a difference table:

n | Term | Difference

1 | 3 |

2 | 14 | 11

3 | 32 | 18

4 | 60 | 28

5 | 98 | 38

We see that the difference is increasing by 10 each time, so our formula can be written as:

Term = 11n + 3

To check the formula, we can plug in a few values of n and see if it matches the terms in the sequence:

n = 1, Term = 11(1) + 3 = 14

n = 2, Term = 11(2) + 3 = 32

n = 3, Term = 11(3) + 3 = 60

The formula matches the terms in the sequence, so it is correct.

b) To find the next three terms in the sequence, we can use our formula:

n = 6, Term = 11(6) + 3 = 79

n = 7, Term = 11(7) + 3 = 90

n = 8, Term = 11(8) + 3 = 101

So the next three terms in the sequence are 79, 90, and 101.

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What is the multiplicative inverse of − 3 − 8?.

Answers

The multiplicative inverse of 'a' is indicated by a-1 or 1/a. In other words, the multiplicative inverse of a number is explained as 1 divided by the number.

The multiplication inverse of 3 is 1/3.

The multiplication inverse of 8 is. 1/8.

The multiplicative inverse is defined as the reciprocal of a given number. It is used to clarify mathematical expressions.

The word 'inverse' infers something opposite/contrary in effect, position, order, or direction. A number when multiplied by its multiplicative inverse results in 1.

The multiplicative inverse formula is called that the product of a number and its reciprocal is 1.

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5. City B has constructed their own subway system. The Green Line and the Orange Line run parallel to each other and the purple line runs perpendicularly to the Green Line and the Orange Line. The Silver Line intersects with the purple line and the green line at the same station. Angles 1 and 6 have the same measure. What is the measure of angle 9?

Answers

Answer:

135°

Step-by-step explanation:

Angles 1 and 6 have the same measure and sum to a 90 degree angle

   so they are each 45°

Angles 1 and 4 are equal as well   45°

then angle 5 = 90 + 45 = 135 °

Angles 5  2  9 and 7 are all equal     angle 9 = 135 °

Can someone tell me what number on the number line is greater than -9 for an inequality?

Answers

Draw a circle over the number to begin plotting an inequality, such as x>9, on a number line (e.g., 9). If the sign also says equal to (or), then complete the circle.

What is inequality in math example?An inequality compares two values and indicates whether one is lower, higher, or just not equal to the other. It is implied by the expression a b that a and b are not equal. If a b, then a must be smaller than b. When a > b, an is greater than b.A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance.When resolving an inequality, you can either add or subtract the same amount from each side, or multiply or divide each side by the same positive amount. The inequality sign appears if each side is multiplied or divided by a negative number.

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The side length of the square is 11 cm. The diameter of the circle is 14 cm. Find the area of the shaded region. Use . A 153.86153.86153.86 cm2 B 94.98594.98594.985 cm2 C 32.8632.8632.86 cm2 D 615.44615.44615.44 cm2

Answers

Answer:

32.9 cm^2

Step-by-step explanation:

In the absence of a diagram, lets use the one shown in the attached worksheet.  The assumption is that the "blue areas" are the four sections of the circle that extend beyond the square boundaries.  The approach is to calculate areas for both the circle and the square.

Square = (11 cm)^2              =  121 cm^2

Circle = (3.14)*(14/2 cm)^2  =   153,9 cm^2

Subtract the square from the circle.  That removes all the circle area, except for the four sections outside the square.  The result is 32.9 cm^2

What is the solution to the system of equations y 2x 3. 5 and x 2y =- 14?.

Answers

The point (7, 10.5) is on the graph of both equations and satisfies the system of equations.

To find the solution to a system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

The system of equations is:

y = 2x - 3.5

x - 2y = -14

We can begin by solving one of the equations for one of the variables, for example, we can solve the first equation for y:

y = 2x - 3.5

Next, we can substitute this expression for y into the second equation:

x - 2(2x - 3.5) = -14

This gives us:

x - 4x + 7 = -14

-3x = -21

x=7

Now we can substitute this value of x back into the first equation to find the corresponding value of y:

y = 2(7) - 3.5

y = 10.5

So the solution to the system of equations is x = 7, y = 10.5.

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What type of function is Y =- 2x 3?.

Answers

The type of the function y = -2x + 3 is a linear function.

Function in math is known as a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.

Here we have given that the function y = -2x +3 and here we need to identify the type of the function.

As we all know that the type of function called linear function is defined as a function that has either one or two variables without exponents.

While we consider the definition we have identified that the given function is is the linear function because in the given function there is no exponents in it so it can fall under the category of the function called exponents.

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what is the following product? Assume x>0 3root x^2 times 4 root x ^3

Answers

the product of the given expressions will be x([tex]x^{5/12}[/tex])

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

[tex]x^{2/3}[/tex] * [tex]x^{3/4}[/tex]

= [tex]x^{2/3+3/4}[/tex]

=[tex]x^{17/12}[/tex]

=x([tex]x^{5/12}[/tex])

Hence the product of the given expressions will be x([tex]x^{5/12}[/tex])

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What is the axis of symmetry and vertex for the function /( x 3 x 2 2 4?.

Answers

The axis of symmetry is the y-axis and the vertex for the function

f(x) = 3(x - 2)²+ 4 is (2,4).

Given f(x) = 3(x - 2)² + 4

The graph will be symmetrical to the y-axis and since a> 0, the parabola opens up.

The axis of symmetry is the line that divides a parabola into two symmetrical parts. The vertex is the point where the axis of symmetry intersects the parabola.

The axis of the symmetry is x=2

The vertex form of a parabola is y = a (x - h)²+ k

The vertex is given by (h,k) coordinates.

In order to find the vertex, we need to compare the given equation to the vertex form of the parabola.

f(x) = 3(x - 2)²+ 4=0

a = 3, h = 2 and k = 4

Thus the vertex of the function is (2,4).

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