19:36 Trigonometry 90° + X 5 8.1 Prove that QS = 5 tan x. 8.2 Prove that the length of QT = 10 sin x. 8.3 Calculate the area of ATQR if TÔR = 70° and x = 25º. PLAY X R 20 P > - 14 E (3) (5) (2) [10]​

Banach Fixed Point Theorem, we can prove that the integral equation I1ƒ(x) = ₁ (1+s)(¹+ƒ(s))² * ds has a unique solution f in RI([0, 1]).

1. First, we define a mapping T: RI([0, 1]) → RI([0, 1]) as follows:

  T(ƒ)(x) = I1ƒ(x) = ₁ (1+s)(¹+ƒ(s))² * ds

2. To prove the existence and uniqueness of a solution, we need to show that T is a contraction mapping.

3. Consider two functions ƒ₁, ƒ₂ in RI([0, 1]). We can compute the difference between T(ƒ₁)(x) and T(ƒ₂)(x):

  |T(ƒ₁)(x) - T(ƒ₂)(x)| = |I1ƒ₁(x) - I1ƒ₂(x)|

4. Using the properties of integrals, we can rewrite the above expression as:

  |I1ƒ₁(x) - I1ƒ₂(x)| = |∫[0, x] (1+s)(¹+ƒ₁(s))² * ds - ∫[0, x] (1+s)(¹+ƒ₂(s))² * ds|

5. Applying the triangle inequality and simplifying, we get:

  |I1ƒ₁(x) - I1ƒ₂(x)| ≤ ∫[0, x] |(1+s)(¹+ƒ₁(s))² - (1+s)(¹+ƒ₂(s))²| * ds

6. By expanding the squares and factoring, we have:

  |I1ƒ₁(x) - I1ƒ₂(x)| ≤ ∫[0, x] |(1+s)(ƒ₁(s) - ƒ₂(s)) * (2 + s + ƒ₁(s) + ƒ₂(s))| * ds

7. Since 0 ≤ s ≤ x ≤ 1, we can bound the term (2 + s + ƒ₁(s) + ƒ₂(s)) and write:

  |I1ƒ₁(x) - I1ƒ₂(x)| ≤ ∫[0, x] |(1+s)(ƒ₁(s) - ƒ₂(s)) * K| * ds

8. Here, K is a constant that depends on the bounds of (2 + s + ƒ₁(s) + ƒ₂(s)). We can choose K such that it is an upper bound for this term.

9. Now, we can apply the Banach Fixed Point Theorem. If we can show that T is a contraction mapping, then there exists a unique fixed point ƒ in RI([0, 1]) such that T(ƒ) = ƒ.

10. From the previous steps, we have shown that |T(ƒ₁)(x) - T(ƒ₂)(x)| ≤ K * ∫[0, x] |ƒ₁(s) - ƒ₂(s)| * ds, where K is a constant.

11. By choosing K < 1, we have shown that T is a contraction mapping.

12. Therefore, by the Banach Fixed Point Theorem, the integral equation I1ƒ(x) = ₁ (1+s)(¹+ƒ(s))² * ds has a unique solution f in RI([0, 1]).

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Answer:

Step-by-step explanation:

Answer:

If each side of tangle is increased by 25 %, then find the percentage increase or decrease in area

Step-by-step explanation:

Answer:

c and d

Step-by-step explanation:

Answer:

C AND D

Step-by-step explanation:

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Answer:

25 square inches

Step-by-step explanation:

just divide your base by 2 and then multiply it by the height

Answer:

The associative property

Step-by-step explanation:

:/ wait its u again lol

Answer:

you should pay attention in class.

Step-by-step explanation:

To develop a binomial probability distribution, you need to know the probability of success and the number of trials.

A binomial probability distribution is used to model the probability of obtaining a specific number of successes in a fixed number of independent Bernoulli trials. In order to develop this distribution, two essential pieces of information are required: the probability of success and the number of trials.

Firstly, you need to know the probability of success, which represents the likelihood of a specific event or outcome occurring in each individual trial. This probability is denoted by "p" and must be a value between 0 and 1.

Secondly, you need to know the number of trials, which refers to the total number of independent experiments or events being conducted. This value is denoted by "n" and must be a positive integer.

With these two pieces of information, you can calculate the probability of obtaining a specific number of successes, ranging from 0 to n, using the binomial probability formula. This formula takes into account the probability of success, the number of trials, and the desired number of successes.

Overall, the probability of success and the number of trials are the key elements needed to develop a binomial probability distribution, enabling you to calculate the probabilities of various outcomes in a given set of independent trials.

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The algebraic expression is C(5) =2.5 * 5 + 1.4 and the total cost is $13.9

From the question, the equation of the total sales amount is given as

Equation = 2.3q + 1.4

Where q represents the number of days

Rewrite as

Cost = 2.3q + 1.4

Express the equation as a cost function

So, we have the following representations

C(q) = 2.3q + 1.4

When the number of days is 5, we have

q = 5

Substitute the known values in the above equation So, we have the following equation

C(5) =2.5 * 5 + 1.4

Evaluate the products

C(5) = 12.5+ 1.4

Evaluate the sum

C(5) = 13.9

Hence, the total cost for the 5 days is $13.9

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Answer:

108°

I hope it's helps you

Answer:

\(2x + 3x = 5x = 180 \\ x = \frac{180}{5} = 36 \\ rqs = 36 \times 3 = 108\)

Answer:

62, since positive doesn't change to negative.

Answer:

the length of the rope gives the circumference of the tree trunk. the tree trunk is in the shape of a circle. the circumference of a circle = πD. the inches would be converted to foot and the diameter would be determined from the length of the  rope.

7 foot

Step-by-step explanation:

Here is the full question :

A group of students wants to find the diameter of the trunk of a young sequoia tree. The students wrap a rope around the tree trunk. the length is 21 feet 8 inches

Explain how they can use the length to determine the diameter of the tree trunk to the nearest half foot

What is the diameter of the tree trunk

the circumference of a circle = πD

π = 22/ 7

D = diameter

we need to convert 21 feet 8 inches to foot

1 inch = 0.0833333 foot

8 x 0.0833333 = 0.667

0.667 + 21 = 21.667 foot

21.667 = 22/7 x diameter

diameter = 21.667 x 7/22 = 6.89 foot

The nearest half foot of 6.89 is 7.

7 foot

Answer:

10.5

Step-by-step explanation:

\(2(x + 4) = 50 \)

\(4x + 8 = 50 \)

\(4x = 50 - 8\)

\(4x = 42\)

\(x = 42 \div 4\)

\(x = 10.5\)

Answer:

Simplifying

2(x + 4) = 50

Reorder the terms:

2(4 + x) = 50

(4 * 2 + x * 2) = 50

(8 + 2x) = 50

Solving

8 + 2x = 50

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.

8 + -8 + 2x = 50 + -8

Combine like terms: 8 + -8 = 0

0 + 2x = 50 + -8

2x = 50 + -8

Combine like terms: 50 + -8 = 42

2x = 42

Divide each side by '2'.

x = 21

Simplifying

x = 21

This took a long time to type and i think it is wrong but hope this helps. hint, hint.

Answer:

y= -1

Step-by-step Explanation:

3(5y +2)-y=2(y-3)

Distribute-  15y +6-y=2y -6

Combine variables-  15y-2y-y=-6-6

Add everything together-  12y= -12

Divide-  y= -1

Answer:

y = -1

Step-by-step explanation:

Step 1. Expand the brackets.

3(5y + 2) - y = 2(y - 3)

(3 x 5y) + (3 x 2) - y = (2 x y) - (2 x 3)

15y + 6 - y = 2y - 6

Step 2. Simplify the expanded brackets (not always necessary but is in this case).

15y + 6 - y = 15y - y + 6 = 14y + 6

So

14y + 6 = 2y - 6

Step 3. Solve the equation.

14y + 6 = 2y - 6

+ 6 to both sides

14y + 12 = 2y

- 14y from both sides

12 = -12y

÷ 12 on both sides

1 = -y

flip the negative

-1 = y

Step 3. Write your answer.

y = -1

All parties involved in the supply chain must work together to reduce losses and improve the supply chain's efficiency.

The supply chain is responsible for moving materials through various parties. Each party is accompanied by a loss or defect rate that can have a significant impact on the overall supply chain. The loss or defect rate associated with each party of the supply chain is listed below:

A. Suppliers: 1.0% of all materials delivered are unacceptable for use. This means that the suppliers are responsible for the quality and delivery of raw materials. Suppliers should ensure that the materials provided are of the required standard, meet the manufacturer's specifications, and are delivered on time.

B. Manufacturing: 0.9% of items produced are defective and are thus not shipped. The manufacturer should ensure that products are manufactured to meet quality specifications, and that product defects are identified and corrected.

C. Distribution: 1.1% of the items shipped are lost, stolen, or damaged in transit. The distribution parties are responsible for moving the products from the manufacturing plant to the retail stores. They are responsible for ensuring that the product is delivered to the right location at the right time, and that it is in the right condition.

D. Retail Store: 1.2% of items are stolen/damaged and thus unavailable for sale. Retailers are responsible for ensuring that products are on the shelves and in the right condition, with the right pricing, in the right quantity, at the right time. They must ensure that products are protected from damage or theft.

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Step-by-step explanation:

0.000672, 6.72×10⁵, 67.2×10‐⁴, 672×10⁴

Scientific notation is a way of writing numbers that looks like the following:

\(a\times10^n\)

For instance, we can write 2930 in scientific notation.

First, write all the given values in scientific notation:

Now, let's compare the values of n, and organize the numbers from least to greatest:

\(6.72\times10^{-4}\)

\(6.72\times 10^{-3}\)

\(6.72\times10^5\)

\(6.72\times 10^6\)

Finally, rewrite all the numbers as their given format:

\(0.000672\)

\(67.2\times 10^{-4}\)

\(6.72\times10^5\)

\(672\times 10^4\)

\(0.000672\)

\(67.2\times 10^{-4}\)

\(6.72\times10^5\)

\(672\times 10^4\)

Answer:

-4

Step-by-step explanation:

-12x+18=-16x+2

+16x       +16x

4x+18=2

    -18   -18

4x=-16

/4     /4

x=-4

Answer:

x=‒4

Step-by-step explanation:

‒6(2x‒3)=‒2(8x‒1)

‒12x+18=‒16x+2

‒12x+16x=2‒18

4x=‒16

4x/4=‒16/4

x=‒4

i hope it helps you.

The probability that between 31.2% and 50.4% of the students in the sample will be minority students is approximately 0.7154, or 71.54%.

To solve this problem, we can use the normal approximation to the binomial distribution, assuming that the sample size is large enough. The mean (μ) of the binomial distribution is given by n * p, where n is the sample size and p is the probability of success. In this case, the sample size is 100 and the probability of success is 0.36.

μ = n * p = 100 * 0.36 = 36

The standard deviation (σ) of the binomial distribution is given by the square root of n * p * (1 - p).

σ = √(n * p * (1 - p)) = √(100 * 0.36 * (1 - 0.36)) ≈ 4.16

To calculate the probability between 31.2% and 50.4%, we need to convert these percentages into z-scores using the formula:

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

For 31.2%:

z1 = (31.2 - 36) / 4.16 ≈ -1.06

For 50.4%:

z2 = (50.4 - 36) / 4.16 ≈ 3.37

Next, we need to find the cumulative probabilities associated with these z-scores using a standard normal distribution table or calculator. The cumulative probability can be interpreted as the area under the normal curve up to a given z-score.

P(31.2% ≤ x ≤ 50.4%) = P(-1.06 ≤ z ≤ 3.37)

Using a standard normal distribution table or calculator, we can find the corresponding cumulative probabilities:

P(-1.06 ≤ z ≤ 3.37) ≈ 0.8577 - 0.1423 ≈ 0.7154

Therefore, the probability that between 31.2% and 50.4% of the students in the sample will be minority students is approximately 0.7154, or 71.54%.

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Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Step-by-step explanation:

31, (25/2) (or 12.5)

26, 10

21, (15/2) (or 7.5)

16, 5

11, (5/2) (or 2.5)

The probability that at least one of five randomly selected 40-year-old males will not live to be 41 years old is approximately 0.01214 or 1.214%.

a) To find the probability that two randomly selected 40-year-old males will live to be 41, we can multiply the individual probabilities together since the events are independent:

P(both live to be 41) = P(live to be 41) * P(live to be 41)

= 0.99757 * 0.99757

≈ 0.99514

Therefore, the probability that two randomly selected 40-year-old males will live to be 41 is approximately 0.99514.

b) Similarly, to find the probability that five randomly selected 40-year-old males will live to be 41, we can multiply the individual probabilities together:

P(all live to be 41) = P(live to be 41) * P(live to be 41) * P(live to be 41) * P(live to be 41) * P(live to be 41) = \(0.99757^5\)results to 0.98786.

Therefore, the probability that five randomly selected 40-year-old males will live to be 41 is approximately 0.98786.

c) To find the probability that at least one of five 40-year-old males will not live to be 41, we can use the complement rule. The complement of "at least one" is "none." So, the probability of at least one not living to be 41 is equal to 1 minus the probability that all five live to be 41:

P(at least one does not live to be 41) = 1 - P(all live to be 41)

= 1 - 0.99757^5  which gives value of 0.01214.

Therefore, the probability that at least one of five randomly selected 40-year-old males will not live to be 41 years old is approximately 0.01214 or 1.214%.

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The theorem is shown in a pythagoras theorem is c² = a² + b²

The theorem shown in the Pythagorean theorem is "a² + b² = c²". This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it.

The Pythagorean theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Mathematically, we can express this as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (called the legs) of the right-angled triangle.

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\(g(f(\text{x})) = -3\text{x}^2+3\)

\(g(f(2)) = -9\)

=======================================================

Explanation:

Let's compute g(f(x))

We do this by starting with the outer function g(x). Then replace every x with f(x). Then plug in the definition of f(x) as shown below.

\(g(\text{x}) = \text{x}-1\\\\g(f(\text{x})) = f(\text{x})-1\\\\g(f(\text{x})) = 4-3\text{x}^2-1\\\\g(f(\text{x})) = -3\text{x}^2+3\\\\\)

At this point, we then plug in x = 2 so we can find that...

\(g(f(\text{x})) = -3\text{x}^2+3\\\\g(f(2)) = -3(2)^2+3\\\\g(f(2)) = -3(4)+3\\\\g(f(2)) = -12+3\\\\g(f(2)) = -9\\\\\)

The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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Using a system of equations, we have that:

1. The table is completed on the image given at the end of the answer.

2. The equation is: 35w + 25t = 1600.

A system of equations is a set of equations in the context of a problem, and solving these equations, the numeric value of each variable in the context of the problem is found.

The variables in this problem are defined as follows:

A jug of drinking water weighs 35 pounds and a case of paper towels weighs 25 pounds. The truck can carry 1,600 pounds of cargo altogether. Hence the equation is:

35w + 25t = 1600.

When w = 10, the numeric value of t is obtained as follows:

35(10) + 25t = 1600

t = (1600 - 350)/25

t = 50.

When w = 30, the numeric value of t is obtained as follows:

35(30) + 25t = 1600

t = (1600 - 1050)/25

t = 22.

When t = 8, the numeric value of w is obtained as follows:

35w + 25(8) = 1600

w = 1400/35

w = 40.

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The growth rate for the linear function y=mx+b will be m or slope. the correct option is A.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

The equation of a line is given as below:-

y = mx + c

Where m is the slope and c is the y-intercept.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope of the line actually determines the rate of change of the function.

Therefore, the growth rate for the linear function y=mx+b will be m or slope. the correct option is A.

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The set of all points equidistant from the points A(-2, 4, 4) and B(5, 2, -3) forms a plane. This plane can be described by an equation that represents the locus of points equidistant from A and B.

To find the equation of the plane, we can first calculate the midpoint M between points A and B, which is given by the coordinates (x₀, y₀, z₀) of M, where x₀ = (x₁ + x₂)/2, y₀ = (y₁ + y₂)/2, and z₀ = (z₁ + z₂)/2.
Midpoint M:
x₀ = (-2 + 5)/2 = 3/2
y₀ = (4 + 2)/2 = 3
z₀ = (4 - 3)/2 = 1/2
Next, we calculate the direction vector D from A to B, which is obtained by subtracting the coordinates of A from those of B.
Direction vector D:
dx = 5 - (-2) = 7
dy = 2 - 4 = -2
dz = -3 - 4 = -7
Using the midpoint M and the direction vector D, we can write the equation of the plane as follows:
(x - x₀)/dx = (y - y₀)/dy = (z - z₀)dz
Substituting the values we calculated earlier, the equation becomes:
(x - 3/2)/7 = (y - 3)/(-2) = (z - 1/2)/(-7)
This equation represents the set of all points equidistant from points A(-2, 4, 4) and B(5, 2, -3), and it describes a plane in three-dimensional space.

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