100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

The decimal 0.36 can be represented as a fraction in simplest form as 9/25. It can also be expressed as a repeating decimal using a variable.

a) 0.36 can be represented as a fraction in simplest form by using place value to identify the denominator. The number 3 is in the hundredths place value position.

Thus, the denominator is 100. 36 is in the numerator position.

Therefore, 0.36 in fraction form is 36/100 which simplifies to 9/25.

b) 0.36 can be represented as a fraction in simplest form by identifying the denominator based on place value.

In this case, 6 is in the thousandths place value position, so the denominator is 1000. 36 is in the numerator position. Thus, 0.36 in fraction form is 36/1000 which can be simplified to 9/250.

c) To write 0.36 as a fraction in simplest form, the place value of each digit needs to be considered. 3 is in the tenths place value position and 6 is in the hundredths place value position.

Therefore, 0.36 in fraction form is 36/100 which simplifies to 9/25.The decimal 0.36 can be represented in fraction form as 36/100 or 9/25.

To determine the fraction in simplest form, the denominator must be reduced to its lowest possible value without changing the numerator. The decimal 0.36 with a line on top of 3 and 6 represents a repeating decimal.

To express this number as a fraction, a variable is used.

In this case, the variable x is equivalent to 0.36. By setting up a proportion and solving for x, the answer can be found.

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It should be noted that there will always be two people in attendance who have the same number of friends at the party using the pigeonhole principle.

The pigeonhole principle states that if you have n pigeons and m pigeonholes, and n > m, then at least one pigeonhole must contain more than one pigeon.

In this case, we have n people at the party, and there are m = n - 1 possible numbers of friends that a person can have. This is because a person can either know 0, 1, 2, ..., or n - 1 other people.

Since n > m, the pigeonhole principle tells us that at least two people at the party must have the same number of friends.

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A graph that represents the absolute function f(x) = |x + 4| - 3 is shown on the coordinate plane attached below.

In Mathematics and Geometry, an absolute value function is a type of function that contains an expression, which is placed within absolute value symbols, and it measures the distance of a point on the x-axis to the x-origin (0) of a graph.

By critically observing the transformed absolute value function f(x) = |x + 4| - 3, we can reasonably infer and logically deduce that the parent absolute value function g(x) = |x| was vertically shifted (translated) downward by 3 units and horizontally shifted (translated) to the left by 4 units, in order to produce it as follows;

g(x) = |x|

f(x) = |x + h| - k

f(x) = |x + 4| - 3

In conclusion, we would use an online graphing tool to plot the given absolute value function f(x) = |x + 4| - 3 as shown in the graph attached below.

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The measure of angle D of the given Kite is: 127°

From the diagram, the figure represents a kite.

Properties of a kite are:

- Two pairs of adjacent sides are equal.

- Two diagonals intersect each other at right angles.

- The longer diagonal bisects the shorter diagonal.

- The angles opposite to the main diagonal are equal.

Thus:

The angle B = the angle D

The sum of all angles of a quadrilateral = 360

Given: ∠A = 36 and ∠C = 70

Thus:

2∠D = 360 - (36 + 70)

2∠D = 254

∠D = 127°

So, the measure of angle D = 127°

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a.

The estimated total cost of the grocery items is $36.

b.

The actual total cost of the grocery items is $35.82.

for part a.

We will round each price to the nearest dollar:

$5.12 =  $5

$3.07 = $3

$7.11 = $7

$1.67 = $2

$13.18=  $13

$5.67 = $6

Summing them up, we have:

$5 + $3 + $7 + $2 + $13 + $6 = $36

the estimated total cost of the grocery items is $36.

for part b.

We will calculate the actual total cost of the grocery items by using a calculator:

$5.12 + $3.07 + $7.11 + $1.67 + $13.18 + $5.67 = $35.82

In conclusion, we will find the  actual total cost of the grocery items as $35.82.

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Using cosine Rule, the value of the requested angle is 33.12°

Since the three sides are given, we use the Cosine rule :

Hence,

CosA = (10²+4²-7²) / (2 × 10 × 4)

Cos A = 67/80

Cos A = 0.8375

A = [tex] {cos}^{ - 1} (0.8375)[/tex]

A = 33.12

Therefore, the value of the missing angle is 33.12

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The measure of the angle B is 32. 0 degrees

To solve the given triangle, we need to know the different trigonometric identities and their ratios.

We have that these identities are;

From the information given, we have that;

Opposite side of angle B = 5

Hypotenuse side = 9.43

Using the sine identity, we get that;

sin B = 5/9.43

Divide the values, we have;

sin B= 0.5302

Find the inverse value of the sine identity and then substitute

B = 32. 0 degrees

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Answer:

12 km (565m)

Step-by-step explanation:

Answer:

0.339, or approximately 33.9%

Step-by-step explanation:

We can solve this problem using Bayes' theorem. Let F denote the event that the selected student is female, and J denote the event that the selected student is taking Japanese classes. We want to find the probability of F given J, which we can write as P(F|J).

Using the law of total probability, we can decompose the probability of J as follows:

P(J) = P(J|F)P(F) + P(J|M)P(M)

where M denotes the event that the selected student is male. We can calculate the probabilities on the right-hand side of this equation as follows:

P(J|F) = 0.1 (from the problem statement)

P(F) = 0.51 (from the problem statement)

P(J|M) = 0.2 (from the problem statement)

P(M) = 0.49 (from the problem statement)

Plugging in these values, we get:

P(J) = 0.10.51 + 0.20.49 = 0.149

Now we can use Bayes' theorem to find P(F|J):

P(F|J) = P(J|F)P(F) / P(J)

Plugging in the values we calculated earlier, we get:

P(F|J) = 0.1*0.51 / 0.149 = 0.339

Therefore, the probability that the selected student is female given that they attend Japanese classes is 0.339, or approximately 33.9%.

Hope this helps!

The graph has: A. order 2 rotational symmetry about the origin.

In Mathematics and Geometry, the order of rotational symmetry of any geometrical shape can be defined as the number of times in which the geometrical shape can be rotated around a full (complete) circle and still look the same.

As a general rule in geometry, a geometrical shape with number of sides (n) has "n" lines of symmetry and its order of rotational symmetry is equal to "n."

Based on this rule, we can reasonably infer and logically deduce that the order of rotational symmetry for this graph is equal to 2.

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Answer:

446.95m²

Step-by-step explanation:

10+9+13.45=32.5

32.5x11=356.95

9x10=90

356.95+90=446.95

To create a graph, label the horizontal axis from 0 to 8 cm (1 cm = 0.5 m) and the vertical axis from 0 to 2 cm (1 cm = 500). Plot the points (2m, 400) as (4 cm, 1.6 cm) and (4m, 200) as (8 cm, 0.8 cm), then connect them with a line.

To create a graph with the provided scale, follow these steps:

1. Establish the horizontal axis: Label the axis from 0 to 8 cm, where each mark represents 1 meter. This means that 2 cm on the graph corresponds to 1 meter.

2. Set up the vertical axis: Label the axis from 0 to 2 cm, where each mark represents 500. This implies that 2 cm on the graph corresponds to 500.

3. Convert the given data points to fit the graph's scale:

For the point (2m, 400):

On the horizontal axis, 2 meters will be represented by 4 cm.

On the vertical axis, 400 will be represented by (400/500) * 2 cm = 1.6 cm.

For the point (4m, 200):

On the horizontal axis, 4 meters will be represented by 8 cm.

On the vertical axis, 200 will be represented by (200/500) * 2 cm = 0.8 cm.

4. Plot the converted points on the graph:

Place a point at (4 cm, 1.6 cm) to represent the point (2m, 400).

Place a point at (8 cm, 0.8 cm) to represent the point (4m, 200).

5. Connect the points with a line:

Draw a straight line to connect the two plotted points.

By following these steps, you will create a graph that visually displays the relationship between the given data points, adhering to the specified scale. Remember to provide appropriate titles and labels for the graph axes.

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Given statement solution is :- To find the area of the shaded region, we first need to determine the shapes involved and their respective areas.  A general process that you can apply to various scenarios, Identify the shapes , Break down the region, Calculate individual areas.

To find the area of the shaded region, we first need to determine the shapes involved and their respective areas. Without a specific diagram or description, I'll provide a general process that you can apply to various scenarios.

Identify the shapes: Examine the diagram and determine the shapes that make up the shaded region. These shapes can include rectangles, triangles, circles, or combinations of them.

Break down the region: If the shaded region consists of multiple shapes, break it down into simpler, recognizable shapes. This step is crucial for accurately calculating the total area.

Calculate individual areas: Determine the area of each shape by using the appropriate formulas. Here are some common formulas:

Rectangle: Area = length × width

Triangle: Area = (base × height) / 2

Circle: Area = π × radius²

Sum the individual areas: Add up the areas of all the individual shapes to find the total area of the shaded region.

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Based on the information, the minimum value is 15, and the maximum value is 30.

To find Q1: Calculate the position of Q1 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (25).

Position = (22 + 1) * (25 / 100) = 5.75 (rounded to 6)

Take the average of the values at positions 6 and 7 to find Q1.

Q1 = (18 + 19) / 2 = 18.5

To find Q2 (the median): Calculate the position of Q2 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (50).

Position = (22 + 1) * (50 / 100)

= 11.5 (rounded to 12)

The value at position 12 is the median.

Q2 = 21

To find Q3: Calculate the position of Q3 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (75).

Position = (22 + 1) * (75 / 100) = 16.5 (rounded to 17)

Take the average of the values at positions 17 and 18 to find Q3.

Q3 = (28 + 29) / 2 = 28.5

The minimum value is 15, and the maximum value is 30.

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Answer:

24m

Step-by-step explanation:

If we imagine this situation as a right angled triangle, 25m is the hypotenuse, 7m is the height and we need the base length

so by Pythagoras thorium we can say that [tex]\sqrt[2]{25^2 -7^2}[/tex]= base length

which is= 24

Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

To determine the range of the number of RVs that need to be sold each month for the company to make a profit, we need to consider the profit function and find the values of x that result in a positive profit.

The profit function is given by P(x) = -50x + 20,000x - 1,500,000.

To make a profit, the value of P(x) must be greater than zero (P(x) > 0). We can set up the inequality:

-50x + 20,000x - 1,500,000 > 0.

Combining like terms, we have:

19,950x - 1,500,000 > 0.

Now, let's solve this inequality for x:

19,950x > 1,500,000.

Dividing both sides by 19,950, we get:

x > 1,500,000 / 19,950.

Simplifying the right side, we have:

x > 75.

The range of the number of RVs that need to be sold each month for the company to make a profit is x > 75.

Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

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Answer:

To find the values of the other three angles in a pentagon given that the sum of all angles is 450 degrees and one angle is 150 degrees, we can use the fact that the sum of the angles in any polygon with n sides is (n-2) * 180 degrees.

Let's denote the other three angles as A, B, and C.

The sum of the angles in a pentagon is given as 450 degrees, so we have:

150 + A + B + C = 450

We know that the sum of the angles in a pentagon is (5-2) * 180 = 540 degrees, so we have another equation:

A + B + C = 540

Now we have a system of two equations with two variables. We can solve this system to find the values of A, B, and C.

The correct subtraction should be:

(150 + A + B + C) - (A + B + C) = 540 - 450

Simplifying the equation, we have:

This equation is not valid, which means that the values given for the sum of angles and one angle are inconsistent with a pentagon. The sum of the angles in a pentagon should be 540 degrees. Please ensure the accuracy of the provided values.

The Sine, Cosine and Tangent of the angles are sin(28) = 0.4695, cos(28) = 0.8829 and tan(28) = 0.5318

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

The triangle

Where, we have

tan(28) = 21/x

This means that

x = 21/tan(28)

Evaluate

x = 39.49

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

tan(28) = 21/39.49

tan(28) = 0.5318

Also, we have

sin(28) = 21/√(39.49² + 21²)

sin(28) = 0.4695

Lastly, we have

cos(28) = 39.49/√(39.49² + 21²)

cos(28) = 0.8829

Hence, the Sine, Cosine and Tangent of the angles are sin(28) = 0.4695, cos(28) = 0.8829 and tan(28) = 0.5318

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Answer:

:)

Step-by-step explanation:

This is a calculus problem that involves using differentials to estimate the maximum error in the area of a circle given the error in its radius. According to 1, the errors are related by ΔA=drdAΔr=2πrΔr

Therefore, Δr=2πrΔA

If the radius is 21 cm correct to the nearest cm, then the possible error in the radius is ±0.5 cm. Using this value in the formula above, we get ΔA=2π(21)(0.5)≈65.97 cm2

This is the possible maximum error when calculating the area of a circle with radius 21 cm correct to the nearest cm.

For question 3.) The three ratios for the marked angle would be =9.45:sin90°, 5:sinB, 8:sinA

For question 3.)

To determine the three ratios, the sine rule needs to be obeyed and the formula is written below as follows;

Sine rule:

a/sinA = b/sinB = c/sinC

where;

a = 8

A = sinA

b = 5

B = SinB

c = 9.45

C = Sin 90°

The three ratios;

= 9.45:sin90°; 5:sinB; 8:sinA

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The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

The actual bearing of the flight would be N 16.38° W.

North: 420 mph * cos(15) = 406.6 mph

West: 420 mph * sin(15) = 108.8 mph

The wind's velocity vector, when decomposed into north and west components, would be:

North: -15 mph * cos(25) = -13.6 mph (negative because it's in the south direction)

West: 15 mph * sin(25) = 6.3 mph

Now, add the corresponding components of the airplane and wind vectors:

North: 406.6 mph - 13.6 mph = 393 mph

West: 108.8 mph + 6.3 mph = 115.1 mph

Finally, to get the actual bearing, we can calculate the inverse tangent of the west component over the north component, but in this case, we need to consider the fact that we are dealing with bearings, which are usually measured from the North, moving in a clockwise direction.

Let's calculate the angle:

θ = atan(West/North) = atan(115.1/393) = 16.38°

So, the actual bearing of the flight would be N 16.38° W.

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Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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Answer:

To find the sum of x₁ and x₂, we need to solve the system of equations:

y = x² ...(1)

y = 1,002x - 2,000 ...(2)

Since both equations are equal to y, we can set them equal to each other:

x² = 1,002x - 2,000

To solve this quadratic equation, we can rearrange it into standard form:

x² - 1,002x + 2,000 = 0

Now, we can factorize the equation:

(x - 2)(x - 1,000) = 0

Setting each factor equal to zero, we get two solutions:

x - 2 = 0 => x = 2

x - 1,000 = 0 => x = 1,000

The sum of distinct solutions x₁ and x₂ to the system of equations y = x² and y = 1,002x - 2,000 is 1,002.

The problem here involves finding the solutions to the system of equations. Those equations are y = x² and y = 1,002x - 2,000. To solve this system of equations, we can set the two equations equal to each other, because they both equal y.

So, we have: x² = 1,002x - 2,000. Rearranging, we get x² - 1,002x + 2,000 = 0. This is a quadratic equation, and we can solve for x using the quadratic formula: x = [1,002 ± sqrt((1,002)² - 4*1*2,000)] / (2*1). This will yield 2 solutions for x, let's call them x₁ and x₂.

The question asks for the sum of x₁ and x₂. In a quadratic equation ax² + bx + c = 0, the sum of solutions is given by -b/a. Here, a = 1 and b = -1,002, so the sum of solutions x₁ and x₂ is -(-1,002)/1 = 1,002.

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Answer: 600000

Step-by-step explanation: just multiply it man

The expression 3j + 21 represents the sum of triple the number "j" and 21. It accounts for multiplying "j" by 3 and then adding 21 to the product. This equation allows us to calculate the desired sum when the specific value of "j" is known.

To find the sum of triple the number "j" and 21, we need to multiply "j" by 3 and then add 21 to the result.

Let's break it down step by step:

Multiply "j" by 3: This can be represented as 3 * j, or simply 3j.

Add 21 to the result: We take the product from step 1 (3j) and add 21 to it, resulting in 3j + 21.

In summary, the expression 3j + 21 represents the sum of triple the number "j" and 21. It accounts for multiplying "j" by 3 and then adding 21 to the product. This equation allows us to calculate the desired sum when the specific value of "j" is known.

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Answer: it stand for 3 million or 3,000,000

Step-by-step explanation:

Answer:

million

Step-by-step explanation:

millions always have six 0's behind it

Assuming that you want this to be expanded, simply multiply each term in the first set of parentheses with each term in the second parentheses:

(-2x + 10) (-9x + 5)

18x^2 - 10x - 90x + 15

18x^2 - 100x + 15

If the question, instead, is asking you to find the x-intercepts, set the expression to zero and solve:

0 = (-2x + 10) (-9x + 5)

0 = -9x + 5 <- divide -2x+10 on all sides

5/9 = x

OR

0 = -2x + 10

5 = x

Answer:

(-2x + 10) (-9x + 5) is a polynomial expression that represents the product of two binomials. To solve this expression, you can use the FOIL method, which stands for First, Outer, Inner, Last.

FOIL method:

First: multiply the first terms of each binomial (-2x and -9x) to get 18x^2

Outer: multiply the outer terms of each binomial (-2x and 5) to get -10x

Inner: multiply the inner terms of each binomial (10 and -9x) to get -90x

Last: multiply the last terms of each binomial (10 and 5) to get 50

Then, combine like terms to get the final expression:

(-2x + 10) (-9x + 5) = 18x^2 - 100x - 90x + 50 = 18x^2 - 190x + 50

Step-by-step explanation:

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The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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