What is the definition of the sine ratio in a right triangle?.

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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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%.

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

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

Hence the total percentage is of:

0.95 x 50 + 0.997 x 50 = 97.35%.

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correct answer must be (a) acute and Isosceles but not equilateral because triangle has two equal side and all angle is less than right angle 90°

answer - (A)

The sampling distribution of the sample mean for samples of size 16 is made up of V3.2 pets, which is the same as the average number of pets owned by the population of high school students.

We use sampling distribution because...

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The possible lengths( in whole elevation) for the third side is

9 elevation< x< 45 elevation, i.e in between 9 and 45 elevation.

 For the below question, we've a rule from the properties of triangle, the sum of the length of any two  sides of the triangle must be lesser than the length of the third side.

Hence

She has two sides of length 18 elevation and 27 elevation

Let the third side = x

Hence

a) 18 27> x

45> x

b) 18 x> 27

x> 27- 18

x> 9

thus, the possible lengths( in whole elevation) for the third side is

elevation< x< 45 elevation

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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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The adult tickets sold were 409.

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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Answer in the photo!!

hope it's right

Answer:

Domain:

[tex] - \infty < x < \infty [/tex]

Range:

[tex] - 1 \le \: y < \infty [/tex]

Step-by-step explanation:

The Domain of a function is x values which are included in the graph. Sometimes x values will not be included because they cannot be defined at that point, but in this case the graph indicates that the graph continues to the right and left with no indication that there is an asymptote or it is undefined beyond the graph so we can assume it's defined for all real numbers. We can represent this in interval notation as:

[tex] - \infty < x < \infty [/tex]

Since if you plug in any real number, this inequality should be true.

The range of a function is defined as y values which are on the graph, this is restricted when certain y values are not on the graph... but we can usually tell because functions will have a minimum/maximum. By looking at the graph it appears to reach a minimum at y = -1 and then on the right and left side is increasing, never going below this value, so the range can be defined as:

[tex] - 1 \le y < \infty [/tex]

Since the y values vary between -1 (including -1) and infinity... well that really just means there's no upper bound and it just keeps increasing and increasing.

Answer:

Step-by-step explanation:

The simple percent interest per year is calculated by dividing the interest earned by the original amount invested, then multiplying by 100 to express the answer as a percentage.

In this case, Kevin earns $42.80 - $40 = $2.80 in interest.

So, the simple percent interest per year is ($2.80 / $40) * 100 = 7%

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.

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

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

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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Answer:

21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

28 - 25%=21

An inequality that shows how much faster Elanor can drive without going over the speed limit is 43.5 + s ≤ 55.

Elanor can increase her speed by 2.

In order to write and solve an inequality that represents how much faster Elanor can drive without going over the speed limit, we would take note of the following important information;

Now, we can write an inequality that represents the value of s for which the speed of Elanor is still safe as follows;

43.5 + s ≤ 55

By subtracting 43.5 from both sides of the inequality, we have the following:

43.5 - 43.5 + s ≤ 55 - 43.5

s ≤ 11.5

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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

The value that will 8(-4x+3) equivalent to -14x+ _+(18x) is 24

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).

for example 2+ 3 and 4 + 1 are equivalent. The both have a value of 5.

Similarly;

8(-4x+3) , when the parentheses is opened, = -32x +24

Also

-14x -18x = -32x

Therefore the value of x that will make the two equation equivalent is 24

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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.

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

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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.

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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Answer:

To calculate the speed of the car's tires turning, you need to first calculate the circumference of the tire. If the tire has a 25 inch diameter, multiply 25 by 3.1416 to find the tire circumference, which is 78.54 inches. Now, divide 63,360 inches per mile by the tire circumference (78.54) to find the revolutions per mile, which is 803.6. Finally, multiply 803.6 by 29 (the speed of the car in mph) to get the revolutions per minute, which is 23,253.6. Therefore, the car's tires are turning at a rate of 23,253.6 revolutions per minute.

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 °

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

It is called a "congruent" angle.

A full rotation, or a complete revolution, is 360 degrees. Therefore, an angle of 360 degrees is called a "full rotation" or a "complete revolution." It is also sometimes called a "congruent" angle.

A full rotation is known as a circle. A circle is a round-shaped figure that has no corners or edges.

In geometry, a circle can be defined as a closed, two-dimensional curved shape.

The entire circle completes a total of 360 degrees as it completes one rotation or what we call a complete revolution.

A circle is a congruent angle.

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

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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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).

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[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]

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.

Answer:

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

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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An algebraic expression with more than 03 terms is known as Multinomial.

Multinomial Distribution:

In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, model the probability of counting on each side of a k-sided die n tosses. For n independent trials, each succeeds in exactly one of the k categories, and each category has a certain fixed probability of success. A multinomial distribution gives the probability for each particular combination of numbers of successes in different categories.

If k is 2 and n is 1, the multinomial distribution is Bernoulli. If k is 2 and n is greater than 1, the distribution is binomial. If k is greater than 2 and n is 1, the distribution is categorical. The term "multinoulli" is sometimes used for categorical distributions to emphasize this four-way relationship (hence n determines the prefix and k determines the suffix).

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