I need help with my final

The 30-60-90 triangle is shaped like half of an equilateral triangle.

A special right triangle with angles 30°, 60°, and 90° is called a 30-60-90 triangle. Since 30° is the smallest angle in the triangle, the side opposite to the 30° angle is always the smallest.

The side opposite to the 60° angle is the longer leg, and finally, the side opposite to the 90° angle is the largest side of the right triangle, also known as the hypotenuse.

30°-60°-90° Triangle Rule:

In a 30-60-90 triangle, we can find the measure of any of the three sides by knowing the measure of at least one side in the triangle. This is known as the 30-60-90 triangle rule.

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The equations of the commissions are

From the question, we have the following parameters that can be used in our computation:

Also from the question, we have:

This means that:

Commission = Unit rate * Commission proportion * Number of pieces

Using the above as a guide, we have the following:

Sara: y = 25 * 60% * x

Ravi: y = 2000 * 25% * x

Evaluate

Sara: y = 15x

Ravi: y = 500x

See attachment for the graph of the commission equations

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Answer:

P = -6

Step-by-step explanation:

y2-y1 / x2-x1 = slope formula

p-2/10-6 =

p-2 over 4

P would be -6 since -6-2 = -8, and -8/4 = -2

Answer:

Hopefully this makes sense. All you're doing is inputting your X VALUES (or your inputs) and using those numbers to find our what your Y VALUES (or your outputs) are

x: -2     -1      0     1      2      3

y: 49     7       1     [tex]\frac{1}{7}[/tex]       [tex]\frac{1}{49}[/tex]      [tex]\frac{1}{343}[/tex]

The 3 horizontal line refers the equivalent relation.

The term horizontal line in math defined as a straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system.

Here have to find the meaning of 3 horizontal line.

As per the definition of horizontal line, the three horizontal line also known as triple line defines the equivalent relation of the term.

Here the equivalent that is not the same as 'equals'

Where the double bar is more common and generally implies equality on the other hand the triple bar or equal sign with three lines means congruent or, more generally, an arbitrary equivalence relation.

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Answer:

There are 5 choices for the first digit, 5 choices for the second digit, 4 choices for the third digit, 3 choices for the fourth digit, and 2 choices for the fifth digit.

Answer:

we get a required sample size of 122.

Step-by-step explanation:

We can use the following formula to calculate the required sample size:

n = (Z * sigma / e)^2

where:

n is the required sample size

Z is the z-score corresponding to the desired confidence level (e.g. for a 95% confidence level, Z = 1.96)

sigma is the standard deviation of the population

e is the maximum error allowed

Plugging in the given values, we get:

n = (1.96 * 0.6 / 0.08)^2 = 121.6

Rounding up to the next integer, we get a required sample size of 122.

Answer:

A . 17/21

B . 14/21

C . 7/14

D. 11/17

Step-by-step explanation:

Answer:

Answer is B: 14 to 21

Step-by-step explanation:

The ratio "2 to 3" was multiplied by 7 to get this ratio. All the other following are incorrect.

The factors of 2[tex]x^{2}[/tex] + 7x + 3 are ( x + 3) and (2x + 1)

Now, According to the question:

The given function is :

f(x) = [tex]2x^2+7x+3[/tex]

To find the factors of  [tex]2x^2+7x+3[/tex] we need to split the middle term, that is, 7x.

7x = 6x + x

Therefore, 2[tex]x^{2}[/tex] + 7x+ 3 can be written as 2[tex]x^{2}[/tex] + 6x + x + 3 .

On taking '2x' common from first two terms and +1 from next two terms we get

2x (x + 3) +1 (x + 3)

(x + 3) (2x + 1)

Thus, the factors of 2x2 + 7x + 3 are (x+3) and (2x+1)

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The complete question is this:

What are the factors of 2x^2+7x +3?

Answer:

0

Step-by-step explanation:

+ 1 + (-1)

1 + (-1)

1 - 1

Answer:

C 2003 and 2004

Step-by-step explanation:

Looking at the graph, you can see that the greatest incline occurs between 2002 to 2003 then 2003 to 2004.This means that the prices grew the most in 2003 and 2004

Answer:

54

Step-by-step explanation:

63 x 2 = 126

180 - 126 = 54

The wheel will travel 131.8cm in 3 rotations.

The radius of the wheel, r = 7cm

Number of rotations, n= 3

distance covered in 1 rotation= circumference of circle=2πr

distance covered in 3 rotation= 2πr x 3

where π=3.14(fixed)

=2 x 3.14 x 7 x 3

Distance=131.88cm

Therefore, the distance covered in 3 rotations is 131.88cm

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Answer:

132cm

Step-by-step explanation:

use formula 22/7 *diameter which is 7*2 getting the answer as 44.For three rotations multiply the answer by three

Answer:

What shape? i don't see no shape

Answer:

What shape? Can you add in a picture or something? That would be very helpful in trying to figure out what shape we're dealing with.

the total of 29 cheesecake and 2 slices of cheesecake will be making $703.

What is the arithmetic operation?

The four basic arithmetic operations are addition, subtraction, multiplication, and division of two or more quantities. They all fall under the umbrella of mathematics, and among them is the study of numbers, particularly the order of operations, which is crucial for all other branches of the subject, such as algebra, data organisation, and geometry. To solve the problem, you must be familiar with the fundamentals of mathematical operations.

A lacrosse team is raising money by selling cheesecakes.

The players plan to sell an entire cheesecake for 24. 00 each and slices of cheesecake for 3. 50 each.

A multiplier of 24 close to 700 is 29

So 29 cheesecake will cost 696.

Now they need more 4 dollars to raise so they have to sell 2 slices, which will be 7$.

So the total of 29 cheesecakes and 2 slices of cheesecake will be making $703.

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Answer:

4/3

Step-by-step explanation:

Answer:

12L/3L

4: 1

four litre of sparkling water for 1 liter juice

Answer:

[tex]area = 4 \times ( \frac{1}{2} \times base \times height) \\ =2 \times ( \frac{1}{2} \times 16.3 \times 42.7) + 2 \times ( \frac{1}{2} \times 16.3 \times 22.5) \\ = 696.01 + 366.75 \\ = 1062.76 \\ = 1063[/tex]

Answer:

Step-by-step explanation:

Answer:

4.5π[tex]cm^2[/tex] will be your answer!

Step-by-step explanation:

Oki... So the area of a circle is radius x radius x π

So.....

Lemme find what the radius's are

4.5 ÷ 2 = 2.25

2.25 - 1.5 = 0.75

2.25 x 2.25 x π = 5.0625π

0.75 x 0.75 x π = 0.5625π

And subtract.

5.0625π - 0.5625π = 4.5π

Answer: 14

Step-by-step explanation: 18 x 14 = 252

Answer:

14

Step-by-step explanation:

recall that area of figure, A= length x. breadth

and A=252

and b=18

therefore, 252= 18b

l= 252/18

l= 14

therefore p= 14

Answer:

see below

Step-by-step explanation:

9 is the difference of a number n and 7.

Let's break this down.

"is" represents the equal sign.

"the difference" represents subtraction.

9 = n - 7

Now let's solve the equation.

9 = n - 7

Add 7 to both sides.

16 = n

Hope this helps!

Answer:

x > [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Given

- 2 (8x - 4) < 2x + 5 ← distribute left side

- 16x + 8 < 2x + 5 ( subtract 2x from both sides )

- 18x + 8 < 5 ( subtract 8 from both sides )

- 18x < - 3

Divide both sides by - 18, reversing the symbol as a result of dividing by a negative quantity.

x > [tex]\frac{-3}{-18}[/tex] , that is

x > [tex]\frac{1}{6}[/tex]

Answer:

A

Step-by-step explanation:

The extreme value theorem can be applied on an interval if the function is continuous in the entire interval. Testing the continuity for each function, we get that the correct option is the third option.

Continuity:

A function f is continuous at an interval if all points in the interval are in the domain of the function, and, for each point of [tex]x^{\ast}[/tex], the limit exists and:

[tex]\lim_{x \rightarrow x^{\ast}} = f(x^{\ast})[/tex]

First function:

At [tex]x = 4[/tex], the denominator is 0, and so, the extreme value theorem cannot be applied.

Second function:

At [tex]x = 5[/tex], the denominator is 0, and so, the extreme value theorem cannot be applied.

Third function:

The only point there can be a discontinuity is at [tex]x = 4[/tex], where the definition of the function changes. First we have to find the lateral limits, and if they are equal, the limits exist:

To the left(-), it is less than 4, so we take the definition for x < 4.

To the right(+), it is more than 4, so we take the definition for x >= 4.

[tex]\lim_{x \rightarrow 4^{-}} h(x) = \lim_{x \rightarrow 4} \frac{9x}{10-x} = \frac{9*4}{10-4} = \frac{36}{6} = 6[/tex]

[tex]\lim_{x \rightarrow 4^{+}} h(x) = \lim_{x \rightarrow 4} x + 2 = 4 + 2 = 6[/tex]

The lateral limits are equal, so the limit exists, and it's value is 6.

The definition at [tex]x = 4[/tex] is [tex]h(x) = x + 2[/tex], so [tex]h(4) = 4 + 2 = 6[/tex].

Since [tex]\lim_{x \rightarrow 4} = h(4)[/tex], the function is continuous over the entire interval, and this is the correct answer.

Fourth function:

There can be a discontinuity at [tex]x = 5[/tex], so we test the limits:

[tex]\lim_{x \rightarrow 5^{-}} h(x) = \lim_{x \rightarrow 5} -x = -5[/tex]

[tex]\lim_{x \rightarrow 5^{+}} h(x) = \lim_{x \rightarrow 5} x^2 - 20 = 5^2 - 20 = 25 - 20 = 5[/tex]

Different limits, so the limit does not exist and the function is not continuous at [tex]x = 5[/tex], and the extreme value theorem cannot be applied.

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A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.

Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.

Part A:

The correlation coefficient of r = 0.51 is valid based on the provided scatter plot.

Part B:

The amount of fertilizer applied in connection to the kilograms of pumpkins harvested on the farm can be a scenario where a causal relationship exists.

Hence, A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

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Answer:

A. 58 square cm

Step-by-step explanation:

From the composite figure,

A1 = [tex]\frac{1}{2}[/tex] x base x height

   = [tex]\frac{1}{2}[/tex] x 2 x 3

   = 3 [tex]cm^{2}[/tex]

A2 = length x width

     = 8 x 2

     = 16 [tex]cm^{2}[/tex]

A3 = [tex]\frac{1}{2}[/tex] (a + b) h + [tex]\frac{1}{2}[/tex] x base x height

    = [tex]\frac{1}{2}[/tex] (10 + 12) 3 + [tex]\frac{1}{2}[/tex] x 2 x 3

    = [tex]\frac{1}{2}[/tex] (22) 3 + 3

    = 11 x 3 + 3

A3 = 33 + 3

     = 36 [tex]cm^{2}[/tex]

Total area = A1 + A2 + A3

                 = 3 + 16 + 36

                 = 58 [tex]cm^{2}[/tex]