points a ,b and c ate plotted on the unit circle .
which if the coordinates is equal to cos (3pi/4)?

To solve this problem let's draw a picture.

We must compare ratios between the two rectangles. Like this.

For the first rectangle we may write:

12 / 5

For the second one we get:

24 / 15

But we can simplify that. Divide numerator and denominator by 3. We have:

24 / 15 = 8 / 5

Comparing both fractions:

12 / 5 ≠ 8 / 5

Answer: The new rectangle won't be proportional to the original.

To find the measure of an angle in a triangle that is isosceles, you can use the fact that the two equal sides of the triangle are congruent to each other.  The measure of each of these angles can be found by subtracting the measure of the third angle from 180 degrees.

Determine which two sides of the triangle are equal in length (these are called the "congruent sides").

Find the measure of the angle opposite one of the congruent sides. This angle is called the "base angle."

Subtract the measure of the base angle from 180 degrees. This will give you the measure of the other two angles in the triangle (since the three angles in any triangle must add up to 180 degrees).

For example, if the measure of the base angle is x degrees, then the measure of the other two angles would be (180-x) degrees.

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The measure of angles in an isosceles triangle can be found using the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in any triangle is 180 degrees. Therefore, if you know two of the angles in the triangle, you can find the third angle by subtracting the sum of the two known angles from 180.

To find the measure of an angle in a triangle isosceles, you can use the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in any triangle is 180 degrees. Therefore, if you know two of the angles in the triangle, you can find the third angle by subtracting the sum of the two known angles from 180.

Let's look at an example. Suppose you have an isosceles triangle and you know that two of its angles measure 50 degrees and 60 degrees. To find the measure of the third angle, you would subtract 110 (the sum of the two known angles) from 180. This gives you 70 degrees as the measure of the third angle.

In addition to the Triangle Angle Sum Theorem, you can also use the Isosceles Triangle Theorem to find the measure of an angle in an isosceles triangle. The Isosceles Triangle Theorem states that the angles opposite the two equal sides of an isosceles triangle are equal. This means that if you know one of the angles in the triangle, you can determine the measure of the other two angles, since they will both be equal to the measure of the known angle.

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A)  The coordinates (225, 0) and (0, 150) represent the combinations of pork and carbohydrates that Tonyo can purchase with his grocery budget.

B) Quantity of carbohydrates (Qc) = 136.36 units

A) Graph Budget line on year 2021, considering pork and carbohydrates:

To graph the budget line for year 2021, we need to calculate the quantity combinations of pork and carbohydrates that Tonyo can purchase with his allotted budget. Given that Tonyo allocates 15% of his salary to groceries and his salary is 30,000 PHP, his grocery budget for 2021 would be:

Grocery budget for 2021 = 0.15 * 30,000 PHP = 4,500 PHP

Let's assume that Tonyo spends all of his grocery budget on either pork or carbohydrates.

Assuming he spends all on pork:

Quantity of pork (Qp) = Grocery budget for 2021 / Price of pork = 4,500 PHP / 20 PHP = 225 units

Assuming he spends all on carbohydrates:

Quantity of carbohydrates (Qc) = Grocery budget for 2021 / Price of carbohydrates = 4,500 PHP / 30 PHP = 150 units

We can now graph the budget line with pork on the x-axis and carbohydrates on the y-axis. The coordinates (225, 0) and (0, 150) represent the combinations of pork and carbohydrates that Tonyo can purchase with his grocery budget.

B) Graph Budget line on year 2022, considering pork and carbohydrates:

In year 2022, prices of groceries increased by 10%. To calculate the new prices for pork and carbohydrates, we multiply the original prices by 1.10.

New price of pork = 20 PHP * 1.10 = 22 PHP

New price of carbohydrates = 30 PHP * 1.10 = 33 PHP

Using the same budget of 4,500 PHP, we can now calculate the new quantity combinations:

Quantity of pork (Qp) = Grocery budget for 2021 / New price of pork = 4,500 PHP / 22 PHP ≈ 204.55 units

Quantity of carbohydrates (Qc) = Grocery budget for 2021 / New price of carbohydrates = 4,500 PHP / 33 PHP ≈ 136.36 units

We can now graph the budget line for 2022, using the new quantity combinations.

C) Graph the budget line on year 2023, considering fish and carbohydrates:

In year 2023, Tonyo decided to shift from pork to fish. Let's assume that the price of fish remains the same as in 2022, while the price of carbohydrates increases by 10%.

Price of fish = 15 PHP

New price of carbohydrates = 33 PHP * 1.10 = 36.30 PHP

With a 10% increase in salary, Tonyo's new salary in 2023 would be:

New salary = 30,000 PHP * 1.10 = 33,000 PHP

Using the same grocery budget of 15% of his salary:

Grocery budget for 2023 = 0.15 * 33,000 PHP = 4,950 PHP

Let's calculate the new quantity combinations:

Quantity of fish (Qf) = Grocery budget for 2023 / Price of fish = 4,950 PHP / 15 PHP ≈ 330 units

Quantity of carbohydrates (Qc) = Grocery budget for 2023 / New price of carbohydrates = 4,950 PHP / 36.30 PHP ≈ 136.27 units

We can now graph the budget line for 2023, using the new quantity combinations.

Please note that the actual graphing of the budget lines would require plotting the points based on the calculated quantity combinations and connecting them to form the budget line. The computed quantities provided here are approximate and should be adjusted according to the specific graphing scale and precision desired.

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The critical value that corresponds to a confidence level of 90 % [1.34503037 , ∞ ).

Given:

you intend to estimate a population mean with a confidence interval. you believe the population to have a normal distribution. your sample size is 15. find the critical value that corresponds to a confidence level of 90%.

sample size n = 15

confidence interval ci = 90

we know that,

Degrees of freedom df = n - 1

here n = 15

df = n - 1

= 15 - 1

= 14

Using the graphical t value calculator:

with df = 14 significance level = 1 - 0.90 = 0.10

so t = [1.34503037 , ∞ )

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We cannot determine which account has a greater principal from the information given, but we know that your account has a greater balance than your sister's account after 10 years.

To determine which account has a greater principal, we need to know the initial investment of each account. However, we have not been provided with this information in the problem. The equation for the balance of each account is given, but we cannot determine the initial investment from these equations.

To determine which account has a greater balance after 10 years, we can use the given equation for the balance of the account:

A = 3800e^0.07t

We can substitute t = 10 into this equation to find the balance after 10 years for each account:

- For your account: A = 3800e^(0.07*10) = 9146.81 dollars

- For your sister's account: A = 2000e^(0.08*10) = 4892.21 dollars

Therefore, your account has a greater balance after 10 years, with a balance of approximately 9146.81 dollars compared to your sister's account with a balance of approximately 4892.21 dollars.

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Answer:

\(\sqrt{59}\)

Step-by-step explanation:

7^2 is 49 and 8^2 is 64, which means the square root of any number between 49 and 64 (exclusive) will be in between 7 and 8, and it's also going to be irrational, because it's not a perfect square.

One number between 49 and 64 is 59, so \(\sqrt{59}\) is an irrational number between 7 and 8

The given scenario of rolling a fair die repeatedly until we see the number four appear, and then we stop, is an example of a geometric distribution. The probability that we need at most 3 rolls is 91/216

This can be calculated as follows:

Given that we roll a fair die repeatedly until we see the number four appear and then we stop.

Let X be the number of times the die is rolled until we see the number four. Then X is a geometric random variable with the parameter p = 1/6.

The probability that we need at most 3 rolls is the probability that we get a four on the first, second, or third roll.

P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

The probability of getting a four on the first roll is:

P(X = 1) = (1 - p)^(1-1) * p = (5/6)^0 * 1/6 = 1/6

The probability of getting a four on the second roll is:

P(X = 2) = (1 - p)^(2-1) * p = (5/6)^1 * 1/6 = 5/36

The probability of getting a four on the third roll is:

P(X = 3) = (1 - p)^(3-1) * p = (5/6)^2 * 1/6 = 25/216

Therefore, P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3) = 1/6 + 5/36 + 25/216 = 91/216

The probability that we need at most 3 rolls is 91/216.

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Answer:

2x^(3) - 4x^(2) - 4x - 4.

Step-by-step explanation:

2x^(3)-3x^(2)-3x^(2)+2x^(2)-4x-9

Bring like terms together:

= 2x^(3) - 3x^(2) - 3x^(2) + 2x^(2) - 4x + 5 - 9

Now simplify:

= 2x^(3) - 4x^(2) - 4x - 4.

Answer:

\(2x^3-4x^2-4x-4\)

Step-by-step explanation:

Subtract the numbers

\(2x^3-3x^2+5-3x^2+2x^2-4x-9\)

\(2^3-3^2-4-3^2+2^2-4\)

Combine like terms

\(2x^3-3x^2-4-3x^2+2x^2-4x\)

\(2^3-4^2-4-4\)

Rearrange terms

\(2x^3-4x^2-4-4x\)

\(2^3-4^2-4-4\)

Solution:

\(2x^3-4x^2-4x-4\)

The symbolic notation are;

a. Atlanta is the capital of Georgia, or there are 3 feet in a yard.

2. ⇒ p ∧ q

b. Atlanta is the capital of Georgia and there are not 3 feet in a yard.

6. ⇒ p ∨ ~ q

c. Atlanta is not the capital of Georgia, or there are 3 feet in a yard.

5. ⇒ ~ p ∧ q

d. Atlanta is the capital of Georgia, and there are 3 feet in a yard.

1. ⇒ p ∨ q

What is Symbolic notation?

Symbolic notation is a way of representing the counting numbers by writing a simple symbol.

Now,

For the false statement we use the symbol ( ~ ).

If in the statement the word ''or'' is present then we use the symbol ''∧'' and for the word ''and'' we use the symbol ''∨''.

Hence,

For the statement;

a. Atlanta is the capital of Georgia, or there are 3 feet in a yard.

Both are truth and with the word ''or'', then the symbolic notation,

⇒ p ∧ q

For the statement;

b. Atlanta is the capital of Georgia and there are not 3 feet in a yard.

One statement is truth and second is false , then the symbolic notation,

⇒ p ∨ ~ q

For the statement;

c. Atlanta is not the capital of Georgia, or there are 3 feet in a yard.

First statement is false and second is truth , then the symbolic notation,

⇒ ~ p ∧ q

For the statement;

d. Atlanta is the capital of Georgia, and there are 3 feet in a yard.

Both are truth and with the word ''and'', then the symbolic notation,

⇒ p ∨ q

So, The symbolic notation are;

a. Atlanta is the capital of Georgia, or there are 3 feet in a yard.

2. ⇒ p ∧ q

b. Atlanta is the capital of Georgia and there are not 3 feet in a yard.

6. ⇒ p ∨ ~ q

c. Atlanta is not the capital of Georgia, or there are 3 feet in a yard.

5. ⇒ ~ p ∧ q

d. Atlanta is the capital of Georgia, and there are 3 feet in a yard.

1. ⇒ p ∨ q

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Answer:

804.25 m^2

Step-by-step explanation:

diameter= 36m

radius=36/2=18m

Area= πr^2

= π*18*18

=256π

=804.25 m^2

Answer:

Area equals to 1017.88

Step-by-step explanation:

A=1/4πd 2=1/ 4·π·362≈1017.87602

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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Answer:

h=-18

Step-by-step explanation:

Here you go mate

Step 1

55 – -26h = -413  Question

Step 2

55 – -26h = -413

26h+55=-413

Step 3

26h+55=-413  Subtract 55

26h=-468

Step 4

26h=-468  Divide sides by 26

Answer

-18

(a) The derivative of y = \((3x^2 - 5) / (2x + 3)\) with respect to x is given by:

dy/dx = \([(6x)(2x + 3) - (3x^2 - 5)(2)] / (2x + 3)^2\)

Simplifying this expression yields:

\(dy/dx = (12x^2 + 18x - 6x^2 + 10) / (2x + 3)^2\\dy/dx = (6x^2 + 18x + 10) / (2x + 3)^2\)

(b) The derivative of y = √(1 + √x) with respect to x can be found using the chain rule. Let's denote u = 1 + √x. Then y = √u. The derivative dy/dx is given by:

dy/dx = (dy/du) * (du/dx)

To find dy/du, we apply the power rule for derivatives, resulting in 1/(2√u). To find du/dx, we differentiate u = 1 + √x, which gives du/dx = 1/(2√x).

Combining these results, we have:

dy/dx = (1/(2√u)) * (1/(2√x))

dy/dx = 1 / (4√x√(1 + √x))

(c) The equation \(x^2y - (y^2/3) - 3 = 0\) can be rewritten as \(x^2y - y^{2/3} = 3\). To find dy/dx, we differentiate both sides with respect to x using the product rule and chain rule.

Using the product rule, we get:

\(x^2(dy/dx) + 2xy - (2/3)y^{-1/3}(dy/dx) = 0\)

Rearranging the equation and isolating dy/dx, we have:

\(dy/dx = -(2xy) / (x^2 - (2/3)y^{-1/3})\)

This is the derivative of y with respect to x for the given equation.

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Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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The best estimate for the percent equivalent of 7 15 is Approximate 46%.

What is a percentage in math?

Given : 7/15

To convert a number in to percentage we multiply it by 100.

\(\frac{7}{15} = \frac{7}{15} * 100\)

\(\frac{7}{15} = \frac{700}{15}\)

\(\frac{7}{15} =\)   46 %

Therefore, Approximate 46%.

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The probability that none of the 4 light bulbs work is 0.0256, or approximately 2.56%.

Since each light bulb works independently of the others, we can treat the outcome of each bulb as a Bernoulli trial with a probability of success (working) p = 0.6 and a probability of failure (not working) q = 0.4.

To find the probability that none of the 4 light bulbs work, we need to find the probability of having 0 successful trials out of 4. This can be calculated using the binomial distribution:

P(X=0) = (4 choose 0) * (0.6)^0 * (0.4)^4 = 0.4^4 = 0.0256

Where (4 choose 0) is the number of ways to choose 0 successful trials out of 4, which is 1.

In summary, we can use the binomial distribution to find the probability that none of the 4 light bulbs work, since each bulb works independently of the others. Using this method, we find that the probability is 0.0256 or approximately 2.56%.

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Therefore , the solution of the given problem of angle  comes out to be  the sharp angle cos(892°) equals cos(172°) = -cos(8°).

In Euclidean geometry, the wall's top and bottom separate two circle faces, which make up of both a tilt's sides. A junction point can occur when two rays come together. Another result of two things interacting is an angle. They most closely resemble dihedral forms. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.

Here,

This implies that the given angle can have multiples of 360° subtracted or added without altering the angle's cosine value.

Find an angle between 0° and 360° that has the same cosine value as 892° by doing so first.

For this, we can continually subtract 360 degrees from 892 degrees to obtain an angle between 0 degrees and 360 degrees:

=> 892° - 360° - 360° - 360° = 172°

=> Cos(892°)

therefore has the same number as cos(172°).

Since the final side of 172° and the x-axis in the second quadrant form an acute angle, we know that this angle serves as the reference angle.

We can deduce this reference angle by deducting 172° from 180°:

=> 180° - 172° = 8°

As a result, the sharp angle cos(892°) equals cos(172°) = -cos(8°).

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Answer:

21 cm squared

Step-by-step explanation:

The area of a triangle is base times height divided by 2, or

a = base time height/2

The base here is 7cm and the height is 6cm.

7 times 6 is 42.

42 divided by 2 is 21

Answer:

Step-by-step explanation:

The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;

a is the first term of the geometric sequence

r is the common ratio

n is the number of terms

If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;

T₁₂ = ar¹²⁻¹

T₁₂ = ar¹¹

Given T₁₂ = -12,288 and r = 2, we can calculate the first term a

-12,288 = a2¹¹

a = -12,288/2¹¹

a =  -12,288/2048

a = -6

Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;

Tₙ = -6(2)ⁿ⁻¹

Tₙ = -6 * 2ⁿ * 2⁻¹

Tₙ = -6 * 2ⁿ * 1/2

Tₙ = -3(2)ⁿ

Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ

Two non-functions could be (a,a) -> a and (a,b) -> a and (a,a) -> b and (a,b) -> b, meaning that both inputs can result in either a or b.

A set is a collection of distinct objects, which can be anything, such as numbers, letters, or even other sets.

The set-roster notation is a way to write a set by listing its elements inside curly brackets {}.

(a) To write the set (XXX) XY, we need to repeat the set X three times, which would be X = {a,a,a}.

Then we can join it with the set Y to form (XXX) XY = {a,a,a,a,b}.

(b) To find two functions and two non-function relations from X x Y to Y, we need to understand what a function and a relation are. A function is for every element in the domain (X x Y), there is exactly one corresponding element in the codomain (Y) where as a non-function, or a relation, is a set of ordered pairs where the same input can have different outputs.

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In a process with rework, we find the bottleneck as the resource with the highest implied utilization.

The above statement is True.

Bottleneck:

A bottleneck is a process in a process chain where the performance of the entire chain is degraded due to limited capacity. Bottlenecks lead to downtime, excess inventory, customer pressure and low employee morale.

Another example is a surface mount board assembly line with multiple pieces of equipment lined up. A common-sense strategy in general is to set and move the bottleneck until the end of the process, leading the better and faster machines to keep the printed circuit board (PCB) powered at all times, and preventing the slower machines from coming to a complete halt. Strategies that can lead to detrimental (or destructive) significant overall process drawbacks.

The product with the highest usage (again, the resource with the lowest capacity is not always the case) is the bottleneck. Defines the bottleneck as the resource with the highest specified usage in a process that involves rework. Better predictions can be identified by simply averaging the prediction errors. In the manufacturing process, each flow unit must have the same output. The recycling process requires only one turnaround time.

Rework also has a processing time different from that of a typical flow unit.

Complete Question:

In a process with rework, we find the bottleneck as the resource with the highest implied utilization. T/F?

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Answer:  The amount of grain it can hold can also be called it's volume. 423.9

The formula for volume is PI × Raduis² × Height

And for the radius we divide the diameter by 2.

Answer:

Option A.

V = π × r(9)² × 15 ≈ 3,817.04

Which rounds closest to

3,815.10 inches

The data in the table of values can be used to find the line of best fit after plotting the graph

a. Please find attached the graph of the data showing the next two points on the table, which are (9, 9.8), (7, 11)

b. Linear correlation

c. Please find attached the graph of the data showing the line of best fit created with MS Excel

A line of best fit is a line that passes through a set of scatter plot, which most precisely reflects the relationship between the points.

a. Please find attached the graph of the data in the table, including the plot of the next two points (9, 9.8), and (7, 11), created with MS Excel

b. The type of correlation on the graph which consists of a straight line that is drawn across the points such that the distance between the line and the points on the graph is minimized, is a linear correlation.

c) The line of best fit, can be obtained adding the Trendline chart element on MS Excel, which can be obtained as follows;

Please find attached the graph of the Number of hours sleep to the Age of the children, showing the line of best fit, created with MS Excel

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Answer:

A fraction bar separates the numerator and denominator of a fraction. It indicates that a division of the numerator by the denominator will be performed.

Step-by-step explanation:

In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions. Fraction bars or fraction strips are a part-to-whole representational model. Each part of a fraction bar represents one unit out of a whole.

Answer:To separate the top and bottom numbers.

Step-by-step explanation:In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions.

Answer:

2 m/s or 7.2 km/h

Step-by-step explanation:

Time = 50 seconds

Distance = 100 meters

Velocity = distance/time = 100/50 = 2 m/s or 7.2 km/h

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Answer:

point g is the correct answer

Step-by-step explanation:

The midpoint of Line segment A B is Option B; Point G.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

Midpoint, means the point which lies in the middle of something.

Midpoint of a line segment means a point which lies in the mid of the given line segment.

Given the graph at the right, the midpoint of A and B

AB = 14 units (by counting).

The midpoint is 7 units from either endpoints.

Thus, the midpoint of Line segment A B is Option B; Point G.

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Answer:

1133.3 liters of water after leakage.

Step-by-step explanation:

x*.30=340

x=340/.30

x=1133.33