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Brian and Colin are marking exam papers. Each set takes Brian 43 minutes and Colin 1 hour.


Express the times Brian and Colin take as a ratio in its simplest form.


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what is the answer?

To make each pair of radicals similar by reducing the radicand, we need to simplify the radicands to their lowest terms. Simplifying radicals involves finding the largest perfect square factor of the number under the radical sign and rewriting it. Let's take an example:

Pair 1: √50 and √32

To make these radicals similar, we simplify the radicands:

√50 = √(25 × 2) = 5√2

√32 = √(16 × 2) = 4√2

Now, both radicals have the same simplified radicand, which is √2. The pair becomes 5√2 and 4√2, making them similar.

Similarly, you can apply the same process to any other pairs of radicals, simplifying the radicands to their lowest terms and making the pairs similar by having matching simplified radicands.

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The area of triangle OBC in terms of r and θ is (1/2) * r^2 * sin(θ), which simplifies to (1/2) * r^2.

To find the area of triangle OBC in terms of r and θ, we can utilize the formula for the area of a triangle: Area = (1/2) * base * height. In this case, the base of the triangle is the side BC, which has a length equal to r, and the height is the perpendicular distance from point O to side BC.

Considering that point O is the origin (0,0) and point B is located on the positive x-axis, the distance from the origin to the line BC is equal to the radius r. Thus, the height of the triangle is r.

To find the angle θ between the positive x-axis and the line BC, we can use trigonometry. Since the line BC forms an angle of θ with the positive x-axis, the perpendicular from point B to the x-axis creates a right triangle. Therefore, sin(θ) can be determined by dividing the height of the triangle (r) by the hypotenuse (also r), resulting in sin(θ) = r/r = 1.

Substituting the values into the formula for the area of a triangle, we have Area = (1/2) * r * r * 1 = (1/2) * r^2.

Therefore, the area of triangle OBC in terms of r and θ is (1/2) * r^2 * sin(θ), which simplifies to (1/2) * r^2.

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A cube has a volume of 1433 inch^3, and we are to identify which equation represents the side length of the cube. Let's use the formula for the volume of a cube:V = s³Where;V = Volume of the cubes = 1433 in³s = side length of the cube.

To obtain the side length of the cube, we can rearrange the formula thus: s = ³√VTherefore, the equation that represents the side length of the cube is: s = ³√1433 in which is option C.If we solve for s:s = ³√1433 in≈ 11.13 in (rounded to two decimal places)Therefore, the side length of the cube is approximately 11.13 in.

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Two cyclists meet at the library and then go for a bike ride. The distance each person has traveled from her home at x hours from the start of the ride is linear, as shown.

Let's assume that cyclist A and B start at a distance x and y, respectively, from the library. Further, let's assume that cyclist A starts at t = 0. Then, the distance from the library for cyclist A at t hours after the start of the ride is represented by x + rt. The distance from the library for cyclist B at t hours after the start of the ride is represented by y + st.As the question says, the distance each person has traveled from her home at x hours from the start of the ride is linear. Thus, we can write their distances from the library as:dA(x) = x + rtdB(x) = y + st, where dA and dB represent the distance covered by cyclists A and B respectively.Now, if we want to find out the distance between the two cyclists at x hours after the start of the ride, we can use the following formula:distance between the two cyclists = dB(x) - dA(x)= (y + st) - (x + rt) = (y - x) + (s - r)tSince s and r are constants, the expression (y - x) + (s - r)t is linear with respect to t. Hence, the statement "The distance between the two cyclists is a linear function of x" must be true.

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The number of weeks required to have same amount in the Candace and Spencer account is equal to 5 weeks.

Amount in the bank account = $700

Amount spent per week = $35

To find the number of weeks it will take for Candace and Spencer to have the same amount of money in their accounts,

Set up the following equation,

$700 - $35w = $450 + $15w

$35w represents the amount Candace spends after w weeks,

and $15w represents the amount Spencer saves after w weeks.

By equating the amounts in their accounts,

solve for the number of weeks, w, it will take for them to have the same amount of money.

To solve the equation,

$700 - $35w = $450 + $15w

Simplifying the equation,

$700 - $450 = $15w + $35w

⇒$250 = $50w

Next, divide both sides of the equation by $50 to isolate the variable w,

⇒$250 / $50 = w

⇒5 = w

Therefore, it will take 5 weeks for Candace and Spencer to have the same amount of money in their accounts.

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The sequence that best represents the relationship between DNA and the traits of an organism is: DNA base sequence -> Amino acid sequence -> Protein function -> Protein shape -> Trait.

1. DNA base sequence: The DNA molecule contains genetic information in the form of a sequence of nucleotide bases (adenine, thymine, cytosine, and guanine). This sequence acts as a template for protein synthesis.

2. Amino acid sequence: The DNA base sequence is transcribed into mRNA, which is then translated into a sequence of amino acids. The sequence of amino acids determines the primary structure of a protein.

3. Protein function: The specific sequence of amino acids in a protein determines its function. Proteins perform various roles in cells, such as enzymatic activity, structural support, and signaling.

4. Protein shape: The sequence of amino acids determines the folding and three-dimensional structure of a protein. The shape of a protein is crucial for its proper function.

5. Trait: Proteins play a fundamental role in the expression of traits. Traits are characteristics of an organism that result from the combined effects of various proteins and their functions.

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The upthrust on the object would be 5N.

Given data:

One quarter of the object is submerged under water, the volume of water displaced is one quarter of the object's total volume.

According to Archimedes' principle, the upthrust is equal to the weight of the water displaced.

Weight of the fluid displaced = (1/4) * Weight of the object

= (1/4) * 20N

= 5N.

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The angles at which the fences of the three sides will meet are approximately: 39.919°, 45.305° and 94.776°

To determine the angles at which the fences of the three sides will meet in Brian's triangular plot of farm land, we can use the Law of Cosines. The Law of Cosines relates the side lengths and angles of a triangle and can be used to find an angle when the lengths of the three sides are known.

In this case, the lengths of the three sides of the triangle are given as follows:

a = 1.1 miles

b = 1.5 miles

c = 2.2 miles

Using the Law of Cosines, we can calculate the angles:

Angle A:

cos(A) = (b^2 + c^2 - a^2) / (2 * b * c)

cos(A) = (1.5^2 + 2.2^2 - 1.1^2) / (2 * 1.5 * 2.2)

cos(A) = (2.25 + 4.84 - 1.21) / (3.3)

cos(A) = 5.88 / 3.3

cos(A) ≈ 1.778

Angle B:

cos(B) = (a^2 + c^2 - b^2) / (2 * a * c)

cos(B) = (1.1^2 + 2.2^2 - 1.5^2) / (2 * 1.1 * 2.2)

cos(B) = (1.21 + 4.84 - 2.25) / (2.42)

cos(B) = 3.8 / 2.42

cos(B) ≈ 1.571

Angle C:

Since the sum of the angles in a triangle is always 180 degrees, we can calculate Angle C by subtracting the sum of Angle A and Angle B from 180 degrees:

Angle C = 180 - (A + B)

Angle C = 180 - (acos(1.778) + acos(1.571))

Calculating the arccosine values using a calculator:

Angle C ≈ 180 - (39.919° + 45.305°)

Angle C ≈ 94.776°

Therefore, the angles at which the fences of the three sides will meet are approximately:

Angle A ≈ 39.919°

Angle B ≈ 45.305°

Angle C ≈ 94.776°

These angles determine the meeting points of the fences in Brian's triangular plot of farm land.

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b = -15.

Thus, for any value of a = 6 and b = -15, any value of x would be a solution of the equation 3(2x-5) = ax + b.

To find the values of a and b for which any value of x would be a solution of the equation 3(2x-5) = ax + b, we need to consider the properties of the equation.

In the equation 3(2x-5) = ax + b, the left side represents a linear expression that simplifies to 6x - 15. We can equate this to the right side, ax + b.

So, we have the equation 6x - 15 = ax + b.

For any value of x to be a solution, the left side and the right side of the equation should always be equal, regardless of the value of x.

To achieve this, we need the coefficients of x to be equal on both sides of the equation. This means that the coefficient of x on the left side (which is 6) should be equal to the coefficient of x on the right side (which is a).

Therefore, a = 6.

Additionally, the constant term on the left side (-15) should be equal to the constant term on the right side (which is b).

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When a store advertises sales on different combinations of goods, they are engaging in price discrimination. In this case, the holiday store is practicing second-degree price discrimination because it has different prices for different quantities of bows and wrapping paper.

According to the signs in the store, there are two different deals on bows and rolls of wrapping paper. One sign says that one bow and one roll of wrapping paper can be purchased for $6.00. This means that the store is offering a bundle deal that gives a discount if you purchase both items together. The second sign offers five bows and one roll of wrapping paper for $10.00.

This means that the store is offering an even larger discount for customers who purchase a larger quantity of bows.The fact that the store is offering different prices based on the quantity of goods purchased is an example of price discrimination. Specifically, the store is practicing second-degree price discrimination because it is offering different prices for different quantities of goods.

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The unit price of the pecans is $0.815 per ounce (rounded to three decimal places).

To calculate the unit price, we divide the total cost of the item by the quantity purchased. In this case, Averi bought a 6-ounce can of pecans for $4.89.

To find the unit price, we divide the total cost ($4.89) by the quantity purchased (6 ounces):

Unit price = Total cost / Quantity purchased

= $4.89 / 6 ounces

To simplify the unit price, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4.89 and 6 is 3.

Dividing both the numerator and denominator by 3, we get: Unit price = ($4.89 / 3) / (6 ounces / 3)

= $1.63 / 2 ounces

Therefore, the unit price of the pecans is $0.815 per ounce (rounded to three decimal places). This means that Averi paid approximately $0.815 for each ounce of pecans she purchased.

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The question asks about the recovery time for a randomly selected patient from a surgical procedure. This recovery time follows a normal distribution with a mean of 4 days and a standard deviation of 1.9 days.

To answer questions about probabilities or specific values of the recovery time, we can use the properties of the normal distribution.

Standardize the variable: Convert the recovery time value (X) into a standard score or z-score using the formula: z = (X - μ) / σ, where μ is the mean and σ is the standard deviation.

Use the standard normal distribution table or a calculator to find the corresponding probability or value associated with the standardized z-score.

For example, if you want to find the probability that a randomly selected patient has a recovery time less than a certain number of days (X), you would calculate the z-score, look up the corresponding probability in the standard normal distribution table, and round the answer to four decimal places.

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There is more dispersion relative to the mean in the distribution of GPA compared to the distribution of age of the students.

The coefficient of variation (CV) is a measure of relative dispersion, which compares the standard deviation to the mean of a dataset. A higher CV indicates greater dispersion relative to the mean, while a lower CV indicates less dispersion.

If the distribution of GPA has a higher coefficient of variation compared to the distribution of age, it means that there is more dispersion relative to the mean in the GPA distribution. This suggests that there is greater variation or diversity in GPA scores among the students compared to their ages. In contrast, if the distribution of GPA had a lower coefficient of variation compared to the distribution of age, it would indicate less dispersion relative to the mean in the GPA distribution, implying less variation or more uniformity in GPA scores.

Therefore, we can interpret that there is more dispersion relative to the mean in the distribution of GPA compared to the distribution of age of the students.

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The function that represents the amount of money the student saves after x months is y = 12x + 15.

In the given scenario, the student initially has $15. Every month, the student saves an additional $12. This means that the amount of money saved after x months can be calculated by multiplying the number of months (x) by the monthly savings of $12 and adding the initial amount of $15. Therefore, the function y = 12x + 15 represents the amount of money (y) the student saves after x months. For example, after 3 months, the student would have saved $12 * 3 + $15 = $51. The function allows for easy calculation of the savings based on the number of months elapsed.

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Myron received $43.20.

We have,

To determine how much Myron received, we need to find the proportion of the job he completed compared to the total work done by all three workers.

First, let's calculate the total number of days worked by all three workers:

Total days worked = Josiah's days + Nathaniel's days + Walden's days

Total days worked = 7 + 5 + 3

Total days worked = 15

Next, we'll calculate the proportion of the job that Myron completed:

Myron's proportion = Myron's days / Total days worked

Myron's proportion = 3 / 15

Myron's proportion = 1/5

Finally, we'll determine how much Myron received:

Myron's payment = Myron's proportion x Total payment

Myron's payment = (1/5) x $216.00

Myron's payment = $43.20

Therefore,

Myron received $43.20.

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To determine the distance between the blimp and the stadium, we can use trigonometry.

In this case, we have an angle of depression of 8° and an altitude of 420 meters. We want to find the horizontal distance (the distance between the blimp and the stadium).

Using trigonometric ratios, we can use the tangent function to find the horizontal distance. The tangent of the angle of depression is equal to the opposite side (altitude) divided by the adjacent side (horizontal distance).

Tangent(8°) = opposite/adjacent

tan(8°) = 420/adjacent

To solve for the adjacent side (horizontal distance), we rearrange the equation:

adjacent = opposite / tan(8°)

adjacent = 420 / tan(8°)

Using a calculator, we find that tan(8°) is approximately 0.1405.

adjacent ≈ 420 / 0.1405 ≈ 2986.54

Rounding to the nearest meter, the blimp is approximately 2987 meters from the stadium.

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The equation representing the number of candy bars Khalil has sold can be written as n(t) = 20 + 6(t/8), where n(t) is the number of candy bars sold and t represents the number of hours since the initial sale of 20 bars.

Initially, Khalil sold 20 candy bars. After that, he sold an additional 6 bars every 8 hours. To represent this situation with an equation, we can use the function n(t), where n is the number of candy bars sold and t is the number of hours since the initial sale.

Since Khalil sold 20 candy bars initially, we start with that as the base value. Then, for every 8 hours that pass, he sells an additional 6 bars. We can represent this using the equation n(t) = 20 + 6(t/8), where t/8 represents the number of 8-hour intervals that have passed since the initial sale.

By substituting different values of t into the equation, we can calculate the number of candy bars Khalil has sold at different points in time. For example, if t = 8, it means 8 hours have passed since the initial sale, and Khalil would have sold 20 + 6(8/8) = 26 candy bars.

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the ∠VRI = ∠TRI and ∠VWI = ∠URI (vertically opposite angles). Also, ∠VRI + ∠WRI = 180° (Linear pair angles). The two lines TU and VW intersect at the point R.

Here, R is the common point of the two lines, and V and W are on one side of the line RS, whereas T and U are on the other side of the line RS.

Let's analyse the given diagram and draw the conclusions.According to the given diagram:∠VRI + ∠WRI = 180°(Linear pair angles)

∠TRI and ∠URI ar

e supplementary angles because T, R, and U lie on the same line.∠VWI and ∠VRI are supplementary angles because V, R, and W lie on the same line.∠VRI = ∠TRI and ∠VWI = ∠URI (vertically opposite angles)

Let's understand this with the help of a few examples.If two parallel lines are intersected by a third line, then the corresponding angles are congruent to one another.

For example, consider the two parallel lines, l and m, and a third line, n, intersecting them as shown below:In the above figure, the lines l and m are parallel, while the line n intersects them.

Corresponding angles are those angles formed when a third line intersects two parallel lines.

For example, ∠1 and ∠5, ∠2 and ∠6, and so on. As per the theorem, all the corresponding angles are equal.In the above figure, ∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8 because the lines l and m are parallel.

This is the reason why the corresponding angles theorem is also known as the same-side interior angles theorem.

Therefore, from the given diagram, we can conclude that the ∠VRI = ∠TRI and ∠VWI = ∠URI (vertically opposite angles). Also, ∠VRI + ∠WRI = 180° (Linear pair angles). The two lines TU and VW intersect at the point R.

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To subtract 1/4 from 11/24, you need to find a common denominator for both fractions. The least common multiple (LCM) of 4 and 24 is 24. Convert 1/4 to an equivalent fraction with a denominator of 24 by multiplying the numerator and denominator by 6. This gives you 6/24. Now, subtract 6/24 from 11/24, which equals 5/24. Therefore, 11/24 - 1/4 simplifies to 5/24.

To subtract fractions, you need to have a common denominator. In this case, the denominators are 24 and 4. To find a common denominator, you can use the least common multiple (LCM) of the two denominators.

The LCM of 4 and 24 is 24. To convert 1/4 to an Summary:

To subtract 1/4 from 11/24, you need to find a common denominator for both fractions. The least common multiple (LCM) of 4 and 24 is 24. Convert 1/4 to an equivalent fraction with a denominator of 24 by multiplying the numerator and denominator by 6. This gives you 6/24. Now, subtract 6/24 from 11/24, which equals 5/24. Therefore, 11/24 - 1/4 simplifies to 5/24.

To subtract fractions, you need to have a common denominator. In this case, the denominators are 24 and 4. To find a common denominator, you can use the least common multiple (LCM) of the two denominators.

The LCM of 4 and 24 is 24. To convert 1/4 to an equivalent fraction with a denominator of 24, you can multiply the numerator and denominator by 6. This gives you (1 * 6) / (4 * 6) = 6/24.

Now that both fractions have a common denominator of 24, you can subtract them:

11/24 - 6/24 = (11 - 6) / 24 = 5/24.

Therefore, 11/24 - 1/4 simplifies to 5/24. with a denominator of 24, you can multiply the numerator and denominator by 6. This gives you (1 * 6) / (4 * 6) = 6/24.

Now that both fractions have a common denominator of 24, you can subtract them:

11/24 - 6/24 = (11 - 6) / 24 = 5/24.

Therefore, 11/24 - 1/4 simplifies to 5/24.

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The entrance measures 6 feet wide and 8 feet long, and the hallway is 3 feet wide and 14 feet long. We need to calculate the area of both and then multiply by $2.40. We can do that as follows:

Entrance area = 6 feet x 8 feet

= 48 square feet

Hallway area = 3 feet x 14 feet

= 42 square feet

Total area = 48 + 42

= 90 square feet

The cost of the carpet, we can multiply the total area by the cost per square foot: $2.40/square foot x 90 square feet = $216.00

It will cost Zac $216.00 to carpet the entrance and hallway of his house if he selects the carpet that sells for $2.40 a square foot.

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The possible values for x that make the statement true are x = -1 or x = 1.5.

Let's solve the equation step by step to find the possible values for x. We start with the given equation:

5.6 = 3.1 - 12.5|1 - 0.8x|

We can begin by isolating the absolute value expression:

2.5 = -12.5|1 - 0.8x|

Next, divide both sides of the equation by -12.5:

-0.2 = |1 - 0.8x|

Now we have two cases to consider, one where the absolute value is positive and another where it is negative.

Case 1: 1 - 0.8x is positive:

-0.2 = 1 - 0.8x

Solving this equation:

-0.8x = -1.2

x = 1.5

Case 2: 1 - 0.8x is negative:

-0.2 = -(1 - 0.8x)

Solving this equation:

0.2 = 1 - 0.8x

-0.8x = -0.8

x = -1

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The blimp will be directly overhead of Ethan in 9.94 minutes.

To determine how long it will take for the blimp to be directly overhead of Ethan, we can use the information about the blimp's altitude and speed.

First, let's find the horizontal distance covered by the blimp in the time it takes to be directly overhead. Since the blimp is moving at a speed of 15 mph, we need to convert this to feet per minute:

15 mph * (5280 ft / 1 mile) * (1 hour / 60 minutes) = 1320 ft/minute

So, the blimp is moving at a rate of 1320 feet per minute horizontally.

Now, let's calculate the vertical distance the blimp needs to cover to be directly overhead of Ethan. This is equal to the altitude of the blimp, which is given as 1150 feet.

Since Ethan is looking up at an angle of 5 degrees, we can use trigonometry to find the horizontal distance covered by the blimp when it reaches the altitude of 1150 feet.

tan(5 degrees) = vertical distance / horizontal distance

We want to solve for the horizontal distance, so rearranging the equation:

horizontal distance = vertical distance / tan(5 degrees)

horizontal distance = 1150 ft / tan(5 degrees)

Using a calculator, we find:

horizontal distance ≈ 13129.01 ft

Now, we can determine the time it takes for the blimp to cover this horizontal distance at a rate of 1320 feet per minute:

time = horizontal distance / rate

time = 13129.01 ft / 1320 ft/minute

Calculating this, we get:

time ≈ 9.94 minutes

Therefore, the blimp will be directly overhead of Ethan in approximately 9.94 minutes.

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Rounded to the nearest tenth of a gram, the amount of the original sample that is still radioactive after half an hour is approximately 17.7 grams.

To model the decay of carbon-11 over time, we can use the exponential decay formula A = A₀ * (1/2)^(t/h), where A is the amount remaining, A₀ is the initial amount, t is the time elapsed, and h is the half-life. In this case, the initial amount is 50 grams and the half-life is 20 minutes. Using this model, we can determine the amount of carbon-11 remaining after a half-hour (30 minutes). Using the exponential decay model A = A₀ * (1/2)^(t/h), we can calculate the amount of carbon-11 remaining after a certain time. For a half-life of 20 minutes, the equation becomes A = 50 * (1/2)^(t/20). To find the amount remaining after half an hour (30 minutes), we substitute t = 30 into the equation:

A = 50 * (1/2)^(30/20)

A = 50 * (1/2)^(3/2)

A = 50 * (√1/2)^3

A = 50 * (√1/8)

A = 50 * (1/2√2)

A = 25/√2

To determine the decimal value of the amount remaining, we can approximate √2 as 1.414. Therefore:

A ≈ 25/1.414 ≈ 17.68 grams

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Equation x + 2 = 3y, which represents a relation between acute angles x,y in a right triangle. To find values, we need more information.With such information, we could apply trigonometric functions.

The equation x + 2 = 3y relates the angles of a right triangle, but it is not sufficient to determine the specific values of x and y. The relationship between the acute angles in a right triangle is given by the trigonometric ratios, such as sine, cosine, or tangent. However, without any additional information or equations, we cannot solve for the exact values of x and y.

To determine the values of x and y, we would need either the lengths of the sides of the right triangle or additional equations or relationships between the angles. With such information, we could apply trigonometric functions or use geometric properties of right triangles to find the values of x and y.

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To meet the demand and minimize total costs, Fancy Pineapple should produce 18,000 pints of pineapple juice and 3,600 cans of pineapple rings.

By producing this quantity, the company can meet the demand for 36,000 pints of pineapple juice and 3,600 cans of pineapple rings while using the minimum number of pineapples and minimizing costs.

To determine the optimal production quantity, we need to consider the requirements for each product and the costs associated with production.

Since each pint of pineapple juice requires 2 pineapples and each can of pineapple rings requires 1 pineapple, the total number of pineapples needed for both products is 39,600 (36,000 pints + 3,600 cans).

Given that the company anticipates using at least 72,000 pineapples, this quantity is sufficient to meet the demand.

Next, we consider the costs. Each pint of pineapple juice costs 16¢ to produce, while each can of pineapple rings costs 40¢ to produce. To minimize costs, the company should produce the product with the lower cost per unit.

In this case, producing pineapple juice is more cost-effective as it costs 16¢ per pint compared to 40¢ per can of pineapple rings. Therefore, Fancy Pineapple should produce 18,000 pints of pineapple juice to meet the demand.

In summary, Fancy Pineapple should produce 18,000 pints of pineapple juice and 3,600 cans of pineapple rings to meet the demand for 36,000 pints of pineapple juice and 3,600 cans of pineapple rings while minimizing costs.

This production quantity ensures the optimal use of pineapples and takes into account the lower production cost per unit for pineapple juice compared to pineapple rings.

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The probability of 82.3% is the chance that the subject is physics if an assignment is submitted on time. The answer is Option A: 82.3%.

Given the probabilities by subject of on-time assignment submission and on-time arrival to class.

Find the probability of the subject being Physics if an assignment is submitted on time.

From the table, we see that the probability of on-time assignment submission in Physics is 89.7%.

If an assignment is submitted on time, the probability of the subject being Physics is 89.7%.

However, in the provided answer options, the probability of 82.3% corresponds to the on-time arrival to class in Physics, not the probability of the subject being Physics given an on-time assignment submission. Therefore, the answer provided is incorrect.

To find the correct probability of the subject being Physics if an assignment is submitted on time, we need additional information, such as the overall probability of on-time assignment submission across all subjects.

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Amy compared the fractions 4/2 and 5/8 by converting each fraction into a whole number.

To compare fractions, Amy converted each fraction into an equivalent form with a common denominator of 1. For 4/2, she multiplied both the numerator and denominator by 2 to get 8/4. Then, she simplified it to 2/1, since both the numerator and denominator are divisible by 4. Similarly, for 5/8, she multiplied both the numerator and denominator by 8 to get 40/64. Amy then simplified it to 5/8 by dividing both the numerator and denominator by their greatest common divisor, which is 8.

Comparing the two fractions, Amy found that 2/1 is greater than 5/8. This means that 4/2 is greater than 5/8 when comparing the fractions as whole numbers. It is important to note that comparing fractions by converting them to whole numbers may not always provide an accurate comparison. Other methods, such as finding a common denominator and comparing the fractions directly, are more reliable.

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The point where you end after moving is (4, 5)

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

Start = (-3, 5)

Direction: 1 unit left and 8 units right

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

New point = (-3, 5) + (-1 + 8, 0)

So, we have

New point = (-3 - 1 + 8, 5 + 0)

Evaluate

New point = (4, 5)

Hence, the point where you end is (4, 5)

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In the desert community, 19% of the total area is desert, while the remaining area is occupied by houses. No squares represent houses, shops, or parks in the grid.

In the given desert community, the total area is represented by a 100x100 grid, with each square representing an equal portion of the community. The prompt states that 19% of the area is desert, so 19 squares in the grid would represent the desert region.

Since the rest of the area is occupied by houses, we need to find the number of squares that would represent houses. The prompt does not provide this information, so we cannot place any squares on the grid for houses.

Similarly, no squares can be placed for shops or parks, as the prompt states that 0% of the area is occupied by them. Therefore, the grid remains empty for these features.

To summarize, the grid representation of the desert community would consist of 19 squares for the desert region, while no squares would be allocated for houses, shops, or parks, as their percentages are mentioned as 0%.

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the value of f is 70, g is 50 and h is 30. So, correct option is

c

We know that sum of all angles of a triangle is 180°.

So, h + 20 + 130 = 180

h + 150 = 180

h = 180 - 150

h = 30

We know that straight line make an angle of 180°

130 + g = 180

g = 180 - 130

g = 50

g + f + 60 = 180

50 + f + 60 = 180

f + 110 = 180

f = 180 - 110

f = 70

Therefore, the value of f is 70, g is 50 and h is 30. So, correct option is

c

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Given question is incomplete, the complete question is below

Find the values of angles h, f, and g