Shawna's sister drank gallon of water after running a marathon. If she ran four races and drank the same amount of water after each race, how many gallons of water would she drink?

Given data set: Mean: 65.8Median: 63.5Mode: 65Range: 11 Standard Deviation: 3.9To find the mean, median, mode, range, and standard deviation when each value of the data set is increased by 8, we need to add 8 to each data value.

Mean: 65.8 + 8 = 73.8Median: 63.5 + 8 =  there are no changes in the frequency of numbers, the mode will remain the same.Mode: 65Range: 11 Standard Deviation: 3.9 The standard deviation of a data set is not affected by adding or subtracting a constant from every value in the data set.

Therefore, the standard deviation remains the same.Standard Deviation: 3.9Answer:Mean: 73.8Median: 71.5Mode: 65Range: 11Standard Deviation: 3.9.Mean: 65.8 + 8 = 73.8Median: 63.5 + 8 = 71.5Since there are no changes in the frequency of numbers, the mode will remain the same.Mode: 65Range: 11 Standard Deviation: 3.9

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To calculate the number of cones that need to be sold in order to break even, we need to use the formula, Break-even point = Fixed costs / (Selling price per unit - Variable cost per unit).

Here, the fixed cost is the cost of the freezer which is $200. The variable cost per unit is the cost of making each single-scoop ice cream cone which is $0.45. The selling price per unit is $1.25.Substituting the values in the formula, we get, Break-even point = $200 / ($1.25 - $0.45) = $200 / $0.8 = 250 cones Therefore, 250 cones need to be sold in order to break even.

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The range of the function g(x) = x^2 - 2, when the domain is {-2, -1, 1, 3}, is C. {-7, -2, -1, 1}.

To find the range of the function g(x) = x^2 - 2, we need to substitute each value from the given domain into the function and observe the corresponding outputs.

For x = -2, g(-2) = (-2)^2 - 2 = 4 - 2 = 2.

For x = -1, g(-1) = (-1)^2 - 2 = 1 - 2 = -1.

For x = 1, g(1) = (1)^2 - 2 = 1 - 2 = -1.

For x = 3, g(3) = (3)^2 - 2 = 9 - 2 = 7.

Thus, when the domain is {-2, -1, 1, 3}, the corresponding range values are {-7, -2, -1, 1}. Therefore, the correct option is C. {-7, -2, -1, 1}.

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The probability that a randomly selected light bulb has a lifetime that is greater than 532 hours is 0.10027

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

Normal distribution, where, we have

Mean = 500

Standard deviation = 25

So, the z-score is

z = (x - mean)/SD

This gives

z = (532 - 500)/25

z = 1.28

So, the probability is

P = P(z > 1.28)

Using the table of z scores, we have

P = 0.10027

Hence, the probability is 0.10027

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Paula made a scale drawing of the auditorium, which is a replica of the actual auditorium, but smaller in size. The scale drawing shows measurements of the actual auditorium at a reduced size.

Paula needs to determine the scale used to draw the auditorium. The scale is the ratio of the lengths of the corresponding sides of the actual auditorium and the scale drawing. We can use the following formula to find out the scale of the drawing:

Scale = (Length of the corresponding side of the actual object) / (Length of the corresponding side of the scale drawing)First, we have to convert 56 feet to inches:1 foot = 12 inches56 feet = 56 x 12 = 672 inchesNow, we can find the scale of the drawing as follows:

Now, we can use the scale to determine the length of other parts of the auditorium. For example, if a door in the auditorium is 32 inches long on the drawing, its actual length would be 32 x 8 = 256 inches or 21.3 feet. Therefore, the missing value in the ratio 3 inches : ____ feet is 2.333 feet. (This is obtained by dividing 84 inches by 36 inches, which is equivalent to 3 feet. Then multiplying the result by 3 inches, which gives 7/12 or 0.5833 feet or 7 inches. This can be written as 2.333 feet.)

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There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.

There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.

To calculate the percent change, we'll use the following formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

Let's calculate the percent change for each statistic:

1. Number of people living with the disease:

  Percent Change = ((27.3 million - 31.6 million) / 31.6 million) * 100

                ≈ (-4.3 million / 31.6 million) * 100

                ≈ -0.136 * 100

                ≈ -13.6%

Conclusion: There was a decrease of approximately 13.6% in the number of people living with the disease from 2005 to 2015.

2. Number of deaths from the disease:

  Percent Change = ((1.2 million - 2.4 million) / 2.4 million) * 100

                ≈ (-1.2 million / 2.4 million) * 100

                ≈ -0.5 * 100

                ≈ -50%

Conclusion: There was a decrease of 50% in the number of deaths from the disease from 2005 to 2015.

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The equation x^2 = p has 0 real number solution when p is less than or equal to 0. This is because the square of any real number is always non-negative. Therefore, if p is less than or equal to 0, then there is no real number x such that x^2 = p.

For example, if p = -1, then the equation x^2 = -1 has no real number solutions. This is because the square of any real number is always non-negative. Therefore, there is no real number x such that x^2 = -1.

However, if p is greater than 0, then there are two real number solutions to the equation x^2 = p. These solutions are x = sqrt(p) and x = -sqrt(p).

For example, if p = 4, then the equation x^2 = 4 has two real number solutions. These solutions are x = 2 and x = -2.

In conclusion, the equation x^2 = p has 0 real number solution when p is less than or equal to 0. This is because the square of any real number is always non-negative.

The approximate form of the expression for all values of t is simply

To find an approximate form of the expression [tex]3(1.25)^{t/5}[/tex] for all values of t, we can simplify it by evaluating the exponent.

First, let's simplify

= [tex]3(1.25)^{t/5}[/tex]

= [tex]3 \sqrt[5]{1.25} ^{t}[/tex]

= 3 * (1.05)ˣ (Assuming x = t)

Now, let's rewrite the expression:

3(1.05)ˣ

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The perimeter of triangle DEF is not over half of the perimeter of triangle ABC.This is proven below.

Given: Triangle ABC is acute with heights AD, BE, and CF.

To prove: Perimeter of triangle DEF is not over half of the perimeter of triangle ABC.

1. Let the side lengths of triangle ABC be a, b, and c.

2. Then the lengths of the heights are h1 = a/2, h2 = b/2, and h3 = c/2.

3. The perimeter of triangle ABC is a + b + c.

4. The perimeter of triangle DEF is h1 + h2 + h3 = a/2 + b/2 + c/2.

5. 1/2 < 1, so a/2 + b/2 + c/2 < a + b + c.

6. Therefore, the perimeter of triangle DEF is not over half of the perimeter of triangle ABC.

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The cost of a carton of milk is a) $0.35.

To find the cost of a carton of milk, we can set up a system of equations based on the given information.

Let's assume the cost of a hamburger is "h" and the cost of a carton of milk is "m".

From the information given, we can create the following equations:

Equation 1: 2h + 1m = 2.85 (from Monday's purchase)

Equation 2: 3h + 2m = 4.45 (from Tuesday's purchase)

We can solve this system of equations to find the value of "m", the cost of a carton of milk.

Multiplying Equation 1 by 2 and Equation 2 by 1, we can eliminate "h" and solve for "m":

4h + 2m = 5.70

3h + 2m = 4.45

Subtracting Equation 2 from Equation 1, we get:

(4h + 2m) - (3h + 2m) = 5.70 - 4.45

h = 1.25

Now, we can substitute the value of "h" back into Equation 1 or Equation 2 to find the value of "m":

2(1.25) + 1m = 2.85

2.50 + m = 2.85

m = 2.85 - 2.50

m = 0.35

Therefore, the cost of a carton of milk is $0.35.

The correct answer is option a) $0.35.

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The correct answer is:p = 3 × 4

Let's write the equation for the given statement:

Randy baked 4 pies

Let the number of pies that Liza baked be p

Liza baked 3 times as many pies as Randy.

Thus, the equation for the above statement can be written as:

p = 3 × 4Simplifying the above equation we get:p = 12Thus, Liza baked 12 pies.

So, the equation that can be used to find how many pies Liza made is:

p = 3 × 4The equation can be simplified to p = 12.

Therefore, the correct answer is:p = 3 × 4

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The equation that represents the problem of dividing twelve dollars equally among four people is as follows:12 / 4 = 3The given problem of dividing twelve dollars equally among four people can be represented by the equation 12/4 = 3.

Here, 12 represents the total amount of money that is being divided and 4 represents the number of people among whom the money is being divided .In this problem, we divide the total amount of money by the number of people to find out how much money each person will get. As there are four people to divide the money among, we divide the total amount of $12 by 4 to get $3 as the share of each person. Therefore, the equation that represents this problem is 12/4 = 3.

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In calculus, there are different ways to differentiate the tangent to a curve. The first principle is one of the ways to differentiate the tangent to a curve.

Differentiation is the foundation of calculus, and it's used to find rates of change, maxima and minima, and the behavior of functions in general.The first principle of differentiation.

The first principle is the fundamental approach to finding derivatives, which involves finding the limit of the difference quotient, or f(x + h) – f(x) / h as h approaches zero. This difference quotient represents the slope of the line tangent to the curve at the point (x, f(x)).

The first principle formula for differentiation is given by:lim h → 0 [f(x + h) – f(x) / h]To differentiate the tangent to the curve y = 2x² – 5x + 3 at the point where x = 2 using the first principle, we need to find the slope of the line tangent to the curve at x = 2. We start by finding the equation of the tangent line and then calculate its slope using the first principle.To find the equation of the tangent line, we differentiate the given function, y = 2x² – 5x + 3:dy/dx = 4x – 5At x = 2, dy/dx = 4(2) – 5 = 3.

Thus, the slope of the tangent line at x = 2 is 3.

Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line:

y – f(2) = m(x – 2)y – (2(2)² – 5(2) + 3) = 3(x – 2)y – 4 = 3x – 6y = 3x – 2

This is the equation of the tangent line to the curve

y = 2x² – 5x + 3

at the point where x = 2. The slope of the tangent line is 3.

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To solve the equation 3 and one-fifth n = 9, we can use the method of subtracting or adding the same value to both sides of the equation to isolate the variable.

In this case, we can subtract 3 and one-fifth from both sides or add 3 and one-fifth to both sides of the equation.

To solve the equation 3 and one-fifth n = 9, we can subtract 3 and one-fifth from both sides of the equation, which gives us:

3 and one-fifth n - 3 and one-fifth = 9 - 3 and one-fifth.

Simplifying the left side of the equation, we get:

n = 9 - 3 and one-fifth.

Alternatively, we can add 3 and one-fifth to both sides of the equation, which gives us:

3 and one-fifth n + 3 and one-fifth = 9 + 3 and one-fifth.

Simplifying the left side of the equation, we get:

n = 9 + 3 and one-fifth.

In either case, we have isolated the variable n and obtained the solution by either subtracting or adding the same value to both sides of the equation.

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Answer:

To calculate the time it takes for Thor to travel 2 miles at a speed of 24 miles per hour, we can use the formula:

Time = Distance / Speed

Given:

Distance = 2 miles

Speed = 24 miles per hour

Plugging these values into the formula, we have:

Time = 2 miles / 24 miles per hour

Calculating this, we get:

Time = 0.08333 hours

Rounding to the nearest tenth, the time it takes for Thor to travel 2 miles is approximately 0.1 hours.

Therefore, it takes Thor approximately 0.1 hours (or 6 minutes) to travel 2 miles at a speed of 24 miles per hour.

The 11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.

Jillian is trying for the cross country team. To make it she must run 3 1/2 miles in less than 40 minutes.

To find out if Jillian will make the cross country team, we must check if she can run 3 1/2 miles in less than 40 minutes. The time required for Jillian to run one mile is found by dividing 40 minutes by 3.5:40 / 3.5 = 11.43Jillian must complete one mile in 11.43 minutes to be eligible for the cross country team.

Since ,11.43 minutes is less than 12 minutes, Jillian has a good chance of making the team. Therefore, Jillian might make the cross country team.

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The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = −(1/2)x + b

The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = 2x + b.

Explanation: The given equation of line is 2x − y = 7.

We can rearrange the given equation of line in slope-intercept form, y = mx + b ,

where m is the slope of the line and b is the y-intercept of the line.

Rewrite the given equation of line, 2x − y = 7, in slope-intercept form:

First, add  y  to both sides of the equation to isolate the variable y:

2x − y + y = 7 + y

Simplify to get: 2x = y + 7

Then, subtract 7 from both sides to isolate y.

So, 2x − 7 = y or y = 2x − 7

We now have the slope-intercept form, where m = 2 is the slope and b = −7 is the y-intercept of the line.

Thus, the slope of the line 2x − y = 7 is m = 2.

Now, to find the equation of line that is perpendicular to 2x − y = 7, we need to flip the sign of the slope and switch the places of m and n (as the product of slopes of two perpendicular lines is −1).

Therefore, the slope of the line that is perpendicular to the line 2x − y = 7 is m = −1/2 (flip the sign of the slope) and

the equation of the line can be written as: y = −(1/2)x + b.

So, the answer is: The equation represents a line that is perpendicular to the line represented by 2x − y = 7 is y = −(1/2)x + b.

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Based on the information given, the combination of loaves of zucchini bread and banana bread that Hayley can make is option D: 4 loaves of zucchini bread and 6 loaves of banana bread.

To determine the possible combinations, we need to ensure that Hayley has enough sugar and butter for each loaf. Let's analyze the options:

Option A: 8 loaves of zucchini bread and 4 loaves of banana bread

This combination requires a total of 8 cups of sugar and 8 sticks of butter, which exceeds Hayley's available supply.

Option B: 6 loaves of zucchini bread and 8 loaves of banana bread

This combination requires a total of 14 cups of sugar and 12 sticks of butter, which exceeds Hayley's available supply.

Option C: 2 loaves of zucchini bread and 12 loaves of banana bread

This combination requires a total of 16 cups of sugar and 16 sticks of butter, which exceeds Hayley's available supply.

Option D: 4 loaves of zucchini bread and 6 loaves of banana bread

This combination requires a total of 12 cups of sugar and 10 sticks of butter, which can be accommodated within Hayley's available supply.

Hence, option D is the correct combination based on the given quantities of sugar and butter.

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To identify the beverage that consistently yielded the highest profit according to the Smith's BBQ Report, we need to compare the profit margins of liquor, beer, and wine. By analyzing the profit margins over time, we can determine which beverage consistently had the highest margin, indicating the highest profit.

To determine which beverage consistently yielded the highest profit, we need to analyze the data provided in the Smith's BBQ Report. The report likely includes information on the sales and profits generated from liquor, beer, and wine. By comparing the profit margins of each beverage over a period of time, we can identify the one that consistently yielded the highest profit.

1. Analyzing profit margins: To determine the beverage with the highest profit, we examine the profit margins for liquor, beer, and wine. Profit margin is calculated by subtracting the cost of goods sold (COGS) from the revenue and dividing the result by the revenue. By comparing the profit margins of each beverage, we can identify which one consistently had the highest margin.

For example, if the profit margin for beer is consistently higher than that of liquor and wine across different time periods, it suggests that beer consistently yielded the highest profit. The profit margin analysis would provide insights into the beverage that generated the most profit for Smith's BBQ consistently.

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There would be 318 grams of sugar in a 3-liter bottle of soda. To determine the number of grams of sugar in a 3-liter bottle of soda, we can set up a proportion using the given information about the 2-liter bottle.

Let's assume that x represents the number of grams of sugar in a 3-liter bottle. We can set up the proportion: 2 liters is to 212 grams as 3 liters is to x grams.

Using cross-multiplication, we have 2 * x = 3 * 212. Solving for x, we get: x = (3 * 212) / 2 = 636 / 2 = 318 grams.Therefore, there would be 318 grams of sugar in a 3-liter bottle of soda.

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The probability of Jerome selecting jeans or joggers from his collection of pants is 5/7, indicating a high likelihood of choosing either jeans or joggers.

Jerome has a total of 3 pairs of jeans and 2 pairs of joggers. Since the question asks for the probability of selecting jeans or joggers, we need to consider the favorable outcomes, which are the jeans and joggers, and the total number of possible outcomes, which is the total number of pants.

The total number of pants Jerome has is 3 (jeans) + 2 (joggers) + 1 (black pants) + 1 (khaki pants) = 7. Out of these 7 pants, the favorable outcomes are the jeans and joggers, which total 3 (jeans) + 2 (joggers) = 5.

Therefore, the probability of Jerome selecting jeans or joggers can be calculated as the favorable outcomes divided by the total number of outcomes: P(jeans or joggers) = 5/7.

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A catalytic ozone destruction cycle requires no atomic oxygen and it incorporates the photochemical decomposition of ClONO₂ to Cl and NO₃, and photochemical decomposition of the later to NO and O₂. The overall reaction is NO + O₃ → NO₂ + O₂

In the lower stratosphere, a proposed mechanism for ozone destruction in the late spring over northern latitudes begins with the photochemical decomposition of ClONO₂ to Cl and NO₃. This reaction is catalyzed by sunlight in the lower stratosphere. The photodissociation of NO₃ is the next step in the cycle, and it results in the production of NO and O₂.

The NO then reacts with O₃ in the following reaction: NO + O₃ → NO₂ + O₂The NO₂ that is produced then reacts with atomic oxygen to form NO₃, and the cycle starts again with the photodissociation of ClONO₂. The NO that is produced during the reaction between NO₂ and O₃ can also react with atomic oxygen to form NO₂, which can then go on to form NO₃.However, the catalytic cycle that has been proposed requires no atomic oxygen to be present. The NO that is produced during the reaction between NO₂ and O₃ reacts with more O₃ to form NO₃ and O₂: NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂The NO₃ that is produced in this reaction can then go on to react with more O₃, starting the cycle over again. Thus, the overall reaction for the catalytic ozone destruction cycle is:NO + O₃ → NO₂ + O₂NO₂ + O₃ → NO₃ + O₂NO₃ + O₃ → NO + 2O₂The cycle continues as long as the necessary reactants are available.

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Emma is using x fence panels along the width of her garden. We need to find expressions for f(x), the width of her garden in feet, and g(x), the length of her garden in feet.

To find an expression for f(x), the width of Emma's garden, we need to determine how the number of fence panels (x) relates to the width. Assuming each fence panel has a fixed width, we can express f(x) as:

f(x) = x * width of each fence panel

The width of each fence panel may vary depending on the specific measurements provided. For example, if each fence panel has a width of 4 feet, then the expression for f(x) becomes:

f(x) = 4x

To find an expression for g(x), the length of Emma's garden, we need additional information or assumptions. The given information does not specify how the number of fence panels along the width relates to the length of the garden. Without this information, we cannot determine a specific expression for g(x).

In summary, we can express the width of Emma's garden, f(x), by multiplying the number of fence panels (x) by the width of each fence panel. However, we cannot determine a specific expression for the length of her garden, g(x), without additional information or assumptions.

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Complete question:

Emma wants to enclose her rectangular garden with fence panels. If she uses x fence panels along the width of her garden, find an expression for f(x), the width of her garden in feet.

f(x) = ?

"Next, find an expression for g(x), the length of her garden, in feet.

g(x) = ?

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To build the frame of the rectangle long jump pit with a length of 9.54 meters and a width of 2.75 meters, a total of 24.58 meters of wood is needed.

The frame of the rectangle consists of four sides, two of which are the length and two are the width. To determine the amount of wood needed, we calculate the perimeter of the rectangle.

The perimeter of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.

Substituting the given values, we have P = 2(9.54) + 2(2.75) = 19.08 + 5.50 = 24.58 meters.

Therefore, to build the frame of the rectangle long jump pit, a total of 24.58 meters of wood is needed.

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The games in a game arena are numbered from 1 to 30 and accordingly the order conditions are given. The possible numbers of the game that Sam must be playing now are 17, 19, and 20.

Since Sam earned 4 bands, he must have won 4 sets of 4 games in a row. Each set of 4 games consists of consecutive game numbers.

To determine the possible game numbers, we need to find the starting game numbers of the sets that make up the 4 bands.

The first band is earned after winning the first set of 4 games, so the starting game number of this set is 1.

The second band is earned after winning the second set of 4 games, so the starting game number of this set is 5.

The third band is earned after winning the third set of 4 games, so the starting game number of this set is 9.

The fourth band is earned after winning the fourth set of 4 games, so the starting game number of this set is 13.

Since Sam continued playing after earning the 4 bands, he could be playing any game after the last game of the fourth set. Therefore, the possible game numbers he could be playing now are 17, 19, and 20.

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The 27th term of the arithmetic sequence with the first term [tex]\(a_1 = -13\)[/tex] and a common difference of 4 is 91.

To find the 27th term of an arithmetic sequence, we can use the formula:

[tex]\[a_n = a_1 + (n - 1)d\][/tex]

where [tex]\(a_n\)[/tex] represents the [tex]\(n\)[/tex]th term, [tex]\(a_1\)[/tex] is the first term, [tex]\(d\)[/tex] is the common difference, and [tex]\(n\)[/tex] is the term number.

Given that [tex]\(a_1 = -13\)[/tex] and the common difference [tex]\(d = 4\)[/tex], we will simply substitute these values into the given formula:

[tex]\[a_{27} = -13 + (27 - 1) \cdot 4\][/tex]

Simplifying the equation, we have:

[tex]\[a_{27} = -13 + 26 \cdot 4\][/tex]

Calculating the expression, we get:

[tex]\[a_{27} = -13 + 104\][/tex]

Finally, evaluating the sum, we find:

[tex]\[a_{27} = 91\][/tex]

Therefore, the 27th term of the arithmetic sequence with the first term [tex]\(a_1 = -13\)[/tex] and a common difference of 4 is 91.

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We can use the formula for compound interest: after 7 years, Ed will have approximately $617.

To determine how much money Ed will have after 7 years of investing $500 at an annual interest rate of 3% compounded quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (expressed as a decimal)

n = the number of times interest is compounded per year

t = the number of years

In this case, P = $500, r = 3% (or 0.03), n = 4 (quarterly compounding), and t = 7. Plugging these values into the formula, we can calculate the final amount:

A = 500(1 + 0.03/4)^(4*7)

Simplifying the equation, we get:

A = 500(1.0075)^(28)

Calculating the expression within the parentheses, we find:

A = 500(1.234)

Finally, we can compute the final amount:

A = $617

Therefore, after 7 years, Ed will have approximately $617.


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A polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.

A polynomial in standard form with a degree of 6 is written as P(x) = a₆x⁶ + a₅x⁵ + a₄x⁴ + a₃x³ + a₂x² + a₁x + a₀, where a₆ ≠ 0 and a₀, a₁, a₂, a₃, a₄, a₅, and a₆ are coefficients.

To ensure that the polynomial has only complex solutions, we need to make sure that all of its roots are complex numbers.

Complex numbers have the form a + bi, where a and b are real numbers and i is the imaginary unit (√(-1)).

By factoring the polynomial into linear factors, we can ensure that each factor (x - zᵢ) contributes a complex root.

Here, z₁, z₂, z₃, z₄, z₅, and z₆ represent complex numbers.

Since the polynomial has a degree of 6, we need six complex factors to form the polynomial.

The product of these factors will give us the desired polynomial with complex solutions.

Therefore, the polynomial in standard form with a degree of 6 and only complex solutions can be represented as P(x) = (x - z₁)(x - z₂)(x - z₃)(x - z₄)(x - z₅)(x - z₆), where z₁, z₂, z₃, z₄, z₅, and z₆ are complex numbers.

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The solution to the problem is that Omar has 16 apples and 14 bananas. the first row satisfy the condition that Omar has four times as many apples as bananas.

To solve this problem, we are given that Omar has four times as many apples as bananas and a total of 30 pieces of fruit.

Let's represent the number of apples as 'a' and the number of bananas as 'b'.

We know that a + b = 30, as the total number of fruits is 30.

From the given information, we are also told that Omar has four times as many apples as bananas, which can be expressed as a = 4b.

To find the values of 'a' and 'b', we can use the table provided:

Types of Fruit  | a | b | a + b |

-------------------------------

16 apples and 14 bananas

20 apples and 10 bananas

22 apples and 8 bananas

24 apples and 6 bananas

We can observe that in the first row, a = 16 and b = 14. Let's check if these values satisfy the given conditions.

If we add the number of apples and bananas, we get 16 + 14 = 30, which matches the total number of fruits given.

We can also verify that a = 4b: 16 = 4 * 14.

Therefore, the solution to the problem is that Omar has 16 apples and 14 bananas.

It's worth noting that the other rows in the table represent different combinations of apples and bananas that sum up to 30, but only the values in the first row satisfy the condition that Omar has four times as many apples as bananas.

In conclusion, Omar has 16 apples and 14 bananas, as per the given information and by checking the values in the table.

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The area of the figure is given by 34cm²

The figure is made up of  triangle and a square.

The area of the figure is given by area of the square + area of the triangle

The area of a triangle is the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 b h. This formula is applicable to all types of triangles, whether it is a scalene triangle, an isosceles triangle, or an equilateral triangle

area of triangle = 1/2bh

Area of triangle = 1/2*10*6

Area = 30 com²

But the area of the square is S²

Where s = side

Area of square = 2*2 = 4cm²

therefore area of the shape is( 4+30)cm² = 34cm²

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