Karen drove 387 miles using 18 gallons of gas. At this rate, how many miles would she drive using 11 gallons of gas?

The table that best shows the conditional relative frequency of rows for the data is as follows: Learn Salsa Do Not Learn Salsa Total Learn Ballet0.43 0.12 0.55Do Not Learn Ballet0.28 0.17 0.45Total0.71 0.29 1The conditional relative frequency of rows is determined by dividing the number of people in each cell by the total number of people in that row.

The number of people learning salsa and ballet is 23. The number of students learning only ballet is 15. The number of students who do not learn either salsa or ballet is 10.Therefore, there are 54 - 23 = 31 students who only learn salsa. There are 54 - 15 = 39 students who learn either salsa or ballet, or both. There are 54 - 10 = 44 students who learn either salsa or ballet but not both.

Hence, the conditional relative frequency of rows is obtained as shown in the table above. The total number of students is 77, which is the sum of the number of students who learn salsa and ballet, the number of students who learn only salsa, the number of students who learn only ballet, and the number of students who learn neither salsa nor ballet. Since 54 + 23 = 77, the table is accurate. Learn Salsa Do Not Learn Salsa Total Learn Ballet0.43 0.12 0.55Do Not Learn Ballet0.28 0.17 0.45Total0.71 0.29.

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the pressure of the water on the diver who is 100 feet below the surface is approximately 6818.18 pounds per square foot.To find the pressure of the water on the diver who is 100 feet below the surface, we can substitute the value of d = 100 into the given formula:

p = 15 * (15/33) * d

p = 15 * (15/33) * 100

Simplifying the expression, we have:

p = (2250/33) * 100

p ≈ 68.18 * 100

p ≈ 6818.18 pounds per square foot

Therefore, the pressure of the water on the diver who is 100 feet below the surface is approximately 6818.18 pounds per square foot.

None of the given answer choices (a, b, c, d) match the approximate value calculated.

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Let's represent the amount of money Justin has as [tex]\(x\).[/tex]

According to the given information, Trey has 3 times what Justin has, so Trey has [tex]\(3x\)[/tex] dollars.

Leila has 10 dollars more than Justin, so she has [tex]\(x + 10\)[/tex] dollars.

The sum of the amounts of money they have is 125 dollars:

[tex]\(x + 3x + (x + 10) = 125\)[/tex]

Combining like terms, we have:

[tex]\(5x + 10 = 125\)[/tex]

Subtracting 10 from both sides:

[tex]\(5x = 115\)[/tex]

Dividing both sides by 5:

[tex]\(x = 23\)[/tex]

So Justin has 23 dollars.

Trey has 3 times that amount:

[tex]\(3 \times 23 = 69\)[/tex]

Leila has 10 dollars more than Justin:

[tex]\(23 + 10 = 33\)[/tex]

Therefore, Justin has 23 dollars, Trey has 69 dollars, and Leila has 33 dollars.

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In the ancient city of Mohenjo-Daro, solid waste was collected in square brick pits located along the banks of the drains.

Mohenjo-Daro was an important urban settlement of the Indus Valley Civilization, which flourished around 2600 to 1900 BCE. The city featured a sophisticated system of drainage, with well-planned brick-lined channels or drains that were constructed to manage wastewater and rainwater runoff. Along these drains, square brick pits were strategically placed to collect solid waste.

These brick pits served as designated areas for waste disposal within the city. The square shape of the pits likely facilitated easy maintenance and cleaning. The waste would accumulate in these pits, and periodic cleaning and removal of the solid waste would help maintain the cleanliness and functionality of the drainage system.

The careful planning and implementation of waste management practices in Mohenjo-Daro reflect the advanced urban planning and sanitation systems of the Indus Valley Civilization. The square brick pits along the drains played a crucial role in effectively managing solid waste within the city.

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Question: In the ancient city of Mohenjo-Daro, a unique waste management system was observed. Solid waste was systematically collected in square brick pits positioned along the ______________ of the drains. Fill in the blank with the appropriate word.

Answer choices:

a) Banks

b) Sidelines

c) Middle

d) Corners

Based on Amadou's measurements, the height of the skyscraper is approximately 97.2 meters.

Amadou measures the angle of elevation from his eye to the top of the skyscraper as 44 degrees. To determine the height of the skyscraper, we can use trigonometry. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

In this case, the opposite side represents the height of the skyscraper, and the adjacent side represents the horizontal distance from Amadou to the base of the skyscraper. We are given that the adjacent side is 164 meters and the angle of elevation is 44 degrees.

Using the tangent function, we can set up the following equation:

tan(44 degrees) = height of skyscraper / 164 meters

To solve for the height of the skyscraper, we rearrange the equation:

height of skyscraper = tan(44 degrees) * 164 meters

Using a scientific calculator or trigonometric table, we find that tan(44 degrees) is approximately 0.9659. Multiplying this value by 164 meters gives us the height of the skyscraper:

height of skyscraper ≈ 0.9659 * 164 meters ≈ 97.2 meters

Therefore, based on Amadou's measurements, the height of the skyscraper is approximately 97.2 meters.

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In the question, it is asked whether the value 63.749 is less than 63.[].  On the other hand, if we take 9 in the box, we get:63.749 < 63.9This inequality is true because 63.749 is indeed less than 63.9.

Now, we will compare the value 63.749 with 63.[] and the answer will depend on the digit which is in the box. Let's try both the digits one by one. If we take 8 in the box, we get:63.749 < 63.8This is a false inequality because 63.749 is not less than 63.8.

Therefore, the answer to the given question is that the digit which should be in the box is 9 because 63.749 is less than 63.9 by the given inequality.What is an Inequality?An inequality is a mathematical statement that compares two values and shows their relationship to each other. It is represented by the symbols: > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).

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The sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.

To find the sum of a geometric series, we can use the formula:

S = a * (1 - r^n) / (1 - r)

Where:

S is the sum of the series,

a is the first term of the series,

r is the common ratio,

n is the number of terms in the series.

In this case, the first term (a) is 10, the common ratio (r) is 2, and the number of terms (n) is 12.

Plugging in the values into the formula, we have:

S = 10 * (1 - 2^12) / (1 - 2)

Simplifying further:

S = 10 * (1 - 4096) / (1 - 2)

S = 10 * (-4095) / (-1)

S = 10 * 4095

S = 40,950

Therefore, the sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.

The correct answer is D) 40,950.

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we would need a total of 5 buses to accommodate all the students and teachers on the trip.To determine the number of buses needed, we divide the total number of students and teachers by the capacity of each bus, which is 58 people.

238 students + 10 teachers = 248 people

To calculate the number of buses needed, we divide 248 people by 58 people per bus:

248 people ÷ 58 people/bus ≈ 4.276 buses

Since we cannot have a fraction of a bus, we round up to the nearest whole number. Therefore, we would need a total of 5 buses to accommodate all the students and teachers on the trip.

It's important to note that rounding up ensures that there are enough buses to accommodate all the individuals, even if there are some empty seats on each bus.

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A function is a relation where each input value (x) corresponds to exactly one output value (y). In other words, for every x-value, there should be only one y-value associated with it.

Let's consider some examples to determine which choice represents a function: The set of ordered pairs {(1, 2), (2, 4), (3, 6)}: This is a function since each input (x) has a unique output (y). For example, when x = 1, y = 2, and there are no other inputs with the same output. The set of ordered pairs {(1, 3), (2, 5), (1, 4)}: This is not a function because the input x = 1 has two different output values, y = 3 and y = 4. A function requires each input to have only one corresponding output. The equation y = x^2: This is a function because for every x-value, there is a unique y-value. No two x-values have the same y-value.

Based on these examples, the choice that represents a function is the first example: the set of ordered pairs {(1, 2), (2, 4), (3, 6)}.

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To calculate the perimeter, add the lengths of sides AB, BC, and AC. The area can be found using Heron's formula. To find the angles, use the law of cosines.

1. **Perimeter and area of triangle ABC**

To find the perimeter and area of triangle ABC, we need to use the given information about its sides and angles.

Let's assume that side AB has a length of "a", side BC has a length of "b", and side AC has a length of "c". The given angles are angle A, angle B, and angle C.

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter P of triangle ABC is given by: P = a + b + c.

To find the area of triangle ABC, we can use Heron's formula, which states that the area A of a triangle with side lengths "a", "b", and "c" is given by: A = √(s(s - a)(s - b)(s - c)), where s is the semi-perimeter of the triangle, given by: s = (a + b + c) / 2.

Once we have calculated the area, we can use the law of cosines to find the measures of the angles. The law of cosines states that for a triangle with side lengths "a", "b", and "c", and opposite angles A, B, and C, the following relationships hold:

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

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

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

Using these formulas, we can calculate the measures of the angles A, B, and C.

To find the exact values of the perimeter, area, and angles, we would need the specific lengths of the sides and the measures of the angles. Please provide those values, and I can assist you with the calculations.

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1/10 of the baker's total cost for 100 pounds of chocolate sprinkles is 10x dollars.

To find 1/10 of the baker's total cost for 100 pounds of chocolate sprinkles, we need to determine the cost per pound of chocolate sprinkles.

Let's assume the cost per pound of chocolate sprinkles is 'x' dollars.

Since it is mentioned that chocolate sprinkles cost as much per pound as sugar, we can assume that the cost per pound of sugar is also 'x' dollars.

Now, let's calculate the total cost for 100 pounds of chocolate sprinkles:

Total cost = Cost per pound * Number of pounds

Total cost = x * 100

Total cost = 100x dollars

To find 1/10 of the total cost, we multiply the total cost by 1/10:

1/10 of total cost = (1/10) * (100x)

1/10 of total cost = 10x

Therefore, 1/10 of the baker's total cost for 100 pounds of chocolate sprinkles is 10x dollars.

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The regression equation is given asp = 0.02b + 2366Where, p is the profit in dollars and b is the number of bulbs sold. It can be seen that the coefficient of b is 0.02 i.e., the profit per bulb is $0.02.

The problem states that the profit required is $3000, therefore,3000 = 0.02b + 2366b = (3000 - 2366)/0.02b = 31700Therefore, approximately 31,700 bulbs need to be sold to make a profit of $3000.The profit margin for Larry's Light Bulbs in 2006 can be determined using the regression equation p = 0.02b + 2366, where p is the profit in dollars and b is the number of bulbs sold. The coefficient of b is 0.02, which implies that the profit per bulb is $0.02.Let us assume that Larry's Light Bulbs requires a profit of $3000. This means that p = 3000. Using the regression equation, we get,3000 = 0.02b + 2366Solving for b, we get,b = (3000 - 2366)/0.02b = 31700Therefore, approximately 31,700 bulbs need to be sold to make a profit of $3000.Hence, option A, i.e., 32,000 is the closest option to the answer. Thus, the correct option is A, i.e., 32,000.

The regression equation p = 0.02b + 2366, where p is the profit in dollars and b is the number of bulbs sold is given. The profit required is $3000. The profit per bulb is $0.02. Therefore, approximately 31,700 bulbs need to be sold to make a profit of $3000. Since 31,700 is the closest option to 32,000, option A is the correct answer.

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To increase their win percentage from 70% to 80%, the basketball team needs to win a specific number of remaining games.

Let's first determine the number of games the team has won out of the 20 games played. Since they have won 70% of the games, we can calculate that as 0.7 * 20 = 14 games won.

Now, let's assume the team has to play 'x' remaining games to achieve an 80% win percentage. If they win all the remaining games, they will have a total of 20 + x games played and 14 + x games won.

To find the win percentage, we divide the total number of games won by the total number of games played and set it equal to 80% or 0.8:

(14 + x) / (20 + x) = 0.8

We can solve this equation to determine the value of 'x':

0.8 * (20 + x) = 14 + x

16 + 0.8x = 14 + x

0.8x - x = 14 - 16

0.2x = -2

x = -2 / 0.2

x = -10

Since we cannot have a negative number of remaining games, it is not possible for the team to increase their win percentage to 80% by winning all their remaining games.

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Rob has (1/2) * x - $25.75 of his earnings left from this week. This is obtained by subtracting the amount spent on bills and the cost of the video game from his total earnings.

To find out how much of his earnings Rob has left, we need to calculate the portion he spent and subtract it from his total earnings.

Given that Rob spends 1/2 of his earnings on bills, he has 1 - 1/2 = 1/2 of his earnings remaining.

If Rob buys a video game for $25.75, we can subtract this amount from his remaining earnings.

Let's say Rob's total earnings for the week were x dollars.

Amount spent on bills: (1/2) * x

Amount spent on the video game: $25.75

Remaining earnings: x - [(1/2) * x + $25.75]

Simplifying the expression, we have:

Remaining earnings: x - (1/2) * x - $25.75

Remaining earnings: (1/2) * x - $25.75

So, Rob has (1/2) * x - $25.75 of his earnings left from this week.

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The correct statement is given as follows:

The can of pringles has a z-score close to zero, which means it's more likely to happen.

The z-score formula is given as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

The z-score for pretzels is given as follows:

Z = (25 - 23)/1.2

Z = 1.67.

The z-score for pringles is given as follows:

Z = (40 - 34)/4

Z = 1.5. -> closer to zero -> more likely to happen.

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There are 32 ounces are in a quart

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

128 ounces in a gallon

Also, we have

4 quart in a gallon

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

128 ounces = 4 quart

Divide both sides by 4

So, we have

32 ounces = 1 quart

Hence, there are 32 ounces are in a quart

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The area is then calculated as (1/2) * base * height, resulting in approximately 39.375 square feet.

To find the area of the actual banner, we need to scale up the dimensions from the drawing to real-world measurements. We are given that 1 inch on the drawing is equivalent to 1.5 feet on the actual banner.

The base of the triangle on the drawing is 5 inches, so the base of the actual triangle will be:

5 inches * 1.5 feet/inch = 7.5 feet

Similarly, the height of the actual triangle will be:

7 inches * 1.5 feet/inch = 10.5 feet

Now that we have the base and height of the actual triangle, we can calculate its area using the formula for the area of a triangle:

Area = (1/2) * base * height

Area = (1/2) * 7.5 feet * 10.5 feet

Area ≈ 39.375 square feet

Therefore, the area of the actual banner will be approximately 39.375 square feet.

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Given that y is inversely proportional to the square root of x. When x = 64, y = 4.Therefore, y∝1/√x We need to find the value of x when y = 8.Substitute the given values in the above equation and get:y∝1/√xx1/4= k where k is a constant.

the equation becomes y = k/√x Given that x = 64 and y = 4 ⇒ 4 = k/√64 = k/8⇒ k = 4 × 8 = 32Therefore, the equation becomes y = 32/√x Now, we need to find the value of x when y = 8. Substituting the given value of y in the above equation, we get:8 = 32/√x⇒ √x = 32/8 = 4⇒ x = (4)² = 16Hence, the value of x when y = 8 is 16.

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To determine the probability that the average shoe size of five randomly chosen women is 9 or more, we need to calculate the z-score for this value and then find the corresponding probability using the Normal distribution.

In summary, we want to find the probability that the average shoe size of five randomly chosen women is 9 or more.

Now, let's explain the answer in more detail. The distribution of women's shoe sizes in the US follows a Normal distribution with a mean of 8 and a standard deviation of 1.5. To calculate the probability, we first need to find the z-score corresponding to a shoe size of 9 or more.

The z-score formula is given by z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation. In this case, the value of interest is 9, the mean is 8, and the standard deviation is 1.5. Plugging these values into the formula, we get z = (9 - 8) / 1.5 = 0.67.

Next, we use a standard Normal distribution table or a statistical calculator to find the probability corresponding to the z-score of 0.67. The probability of obtaining a z-score of 0.67 or higher represents the probability that the average shoe size of five randomly chosen women is 9 or more.

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The spinner spins for a total of 2.4 hours when Sam spins it 24 times at a speed of 10 mph.

If Sam spins the spinner 24 times at a speed of 10 mph, we can calculate the total time the spinner spins by dividing the distance traveled by the speed.

Let's assume that each spin of the spinner covers a distance of 1 revolution. The total distance covered by the spinner would then be 24 revolutions.

To calculate the time the spinner spins, we divide the distance by the speed:

Time = Distance / Speed

Distance = 24 revolutions

Speed = 10 mph

Time = 24 revolutions / 10 mph = 2.4 hours

Therefore, the spinner spins for a total of 2.4 hours when Sam spins it 24 times at a speed of 10 mph.

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The solution to the system of equations is (x, y) = (2, 1).

Given equations are,1. 1/4x + 1/2y = 5/82. 3/4x - 1/2y = 27/8 - 3/8

Now we will solve these two equations by elimination method:

Multiplying equation 1 by 3 and equation 2 by 2,3/4x + 3/2y = 15/8  -------------- (3)

3/2x - y = 6/8 -------------- (4)

Simplifying equation 3,3/4x + 3/2y = 15/8 -------------- (5)

Multiplying equation 4 by 3,4.5x - 3y = 3 -------------- (6)

Now, we will add equation 5 and equation 6,

3/4x + 3/2y = 15/8 -------------- (5)

4.5x - 3y = 3 -------------- (6)

______________15/4x + 0y = 39/8

Therefore, x = 2.Now, substituting x=2 in equation 4,3/2(2) - y = 6/8-3y = -3/8

Therefore, y = 1.

Hence, the solution to the system of equations is (x, y) = (2, 1).

We are given 2 equations as follows:1/4x + 1/2y = 5/8 ...(i)3/4x - 1/2y = 27/8 - 3/8 ...(ii)

Multiplying equation (i) by 3 and equation (ii) by 2,3/4x + 3/2y = 15/8...(iii)3/2x - y = 6/8 ...(iv)We can write equation (iii) as follows: y = (3/2x - 6/8)/-1 = 3/2x - 6/8Now we substitute this value of y in equation (i)1/4x + 1/2(3/2x - 6/8) = 5/8Simplifying,3/4x - 3/8 = 5/8 => 3/4x = 5/8 + 3/8 => 3/4x = 1 => x = 4/3

Now we substitute this value of x in equation (iv):y = 3/2(4/3) - 6/8 = 2/1 = 2

Therefore, the solution to the system of equations is (x, y) = (4/3, 2).

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To find the amount of the payment that goes towards interest at the 12th payment, you should multiply the balance at the 12th payment by the interest rate which is 8%.

The balance of the loan after 12 payments is $4159.90.

Thus the amount of the payment that goes towards interest at the 12th payment is:

4159.90 × 0.08 = $332.79

The principal amount paid at the 12th payment is the difference between the monthly payment of $187.80 and the amount of interest paid of $332.79.

The principal amount paid at the 12th payment

= $187.80 − $332.79

= −$144.99

The negative answer means that the amount paid is the interest.

To find the balance of the loan after the 35th payment, we will subtract the monthly payment from the balance after the 34th payment.

Therefore, the balance of the loan after the 35th payment is:

380.60 − 187.80 = $192.80

To find the amount of the payment that goes towards interest at the 35th payment, you should multiply the balance at the 35th payment by the interest rate which is 8%.

The balance after the 34th payment is $380.60, so the interest payment at the 35th payment is:

380.60 × 0.08 = $30.44

The principal amount paid at the 35th payment is the difference between the monthly payment of $187.80 and the amount of interest paid of $30.44.

The principal amount paid at the 35th payment

= $187.80 − $30.44

= $157.36

Therefore, the balance of the loan after the 35th payment is:

192.80 − 157.36 = $35.44.

The balance of the loan after the 35th payment is $35.44.

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The radioactive material currently has 70 mg that decays at 3.5% per year. The material must be safely stored until it reaches its half-life, at which time it can be disposed.

To find out how long it will take the material to decay to half its original amount, you can use the half-life formula, which is:t1/2 = (ln 2) / kw here t1/2 is the half-life, ln is the natural logarithm, and k is the decay constant. To find k, you can use the following formula: k = 0.693 / t where t is the half-life in years. Using the given percentage of decay per year, you can find the decay constant as follows: k = 0.693 / t = ln(100/96.5) / t = 0.03515 / t Therefore, the half-life is:t1/2 = (ln 2) / k = (ln 2) / (0.03515 / t) = 19.8 years So, it will take approximately 19.8 years for the material to decay to half its original amount.

The lab will have to safely store the material for twice the half-life, which is 2 × 19.8 = 39.6 years. Therefore, the lab will have to safely store the material for more than 39.6 years before it can be disposed of according to federal regulations.

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There are 45 winning tickets (e.g., 123, 234, 345, etc.) among the range of tickets from 001 to 999 i.e., the correct answer is option A: 45 winning tickets.

The charity is selling tickets with 3 digits ranging from 001 to 999, and a winning ticket is one where the first two digits add up to the third digit.

We need to determine how many winning tickets there are among the available range of tickets.

To find the number of winning tickets, we need to count the number of combinations where the first two digits add up to the third digit.

Let's consider the possible combinations for each digit:

For the first digit, we have 9 options (1 to 9) since it cannot be zero.

For the second digit, we also have 9 options (0 to 9).

For the third digit, the value is determined by the sum of the first two digits, so we have a limited number of options based on the values of the first two digits.

To count the winning tickets, we need to consider all possible combinations and determine the valid ones.

We can start with the first digit, go through all the possible combinations of the second digit, and check if the sum of the first two digits matches the third digit.

By analyzing all the combinations, we find that there are 45 winning tickets (e.g., 123, 234, 345, etc.) among the range of tickets from 001 to 999.

Therefore, the correct answer is option A: 45 winning tickets.

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The probability that they will pick neither the chocolate chip nor the walnut topping is, 0.7

Since, the total of all probabilities is 1.00, or 100%.

Now, In the Venn diagram, we have the probabilities 0.2, 0.4 and 0.1;

these sum to,

0.2+0.4+0.1

= 0.6+0.1

= 0.7.

Therefore, the probability that they will pick neither the chocolate chip nor the walnut topping is,

⇒ 1.00-0.7 = 0.3

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After 10 seconds, the snail is 14 inches away from Diana. Let's assume that Diana is at the origin (0,0) and the snail moves at a constant speed. Let's consider the snail is at point (x, y) and Diana is at the origin (0,0). The snail is moving away from Diana at a constant speed. It moves 2 inches in 4 seconds.

Then the distance traveled by the snail in 1 second is

= 2/4inches

= 0.5 inches.

So, the distance the snail travels from (0,0) in x seconds is 0.5x. After 3 seconds, the snail moves

= 0.5(3)

= 1.5 inches away from Diana, and its distance from her is 9 inches.

So, we have y = 9 + 0.5x. This is the equation for the snail's distance from Diana, y, as a function of time, x.

We can see that the equation y = 9 + 0.5x provides the snail's distance from Diana. Here, y is the distance between Diana and the snail and x is the current time. We can observe that the snail moves at a constant pace of 0.5 inches per second since the coefficient of x is equal to 0.5. The constant term in the equation is 9, which stands for the separation between Diana and the snail at the initial value of x, or 0, the starting point.

Therefore, we can infer that the distance between the snail and Diana, y, as a function of time, x, is represented by the equation y = 9 + 0.5x. The distance between Diana and the snail can be calculated at any time using this equation. The distance between Diana and the snail after 10 seconds, for instance, can be calculated using this equation.

For this,

we substitute x = 10 in the equation and get

y = 9 + 0.5(10)

= 14.

Therefore, after 10 seconds, the snail is 14 inches away from Diana.

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7,875 lbs.

Old furniture weighs = 1,123 lbs.

Combined weight of furniture and truck = 8,122 lbs.

New items = 876 lbs.

First, subtract the weight of the old furniture from the combined weight:

8,122 lbs - 1,123 lbs. = 6,999 lbs.

Then, add the weight of the new items:

6,999 lbs + 876 lbs. = 7,875 lbs.

The area of a quarter circle with a radius of 18 cm is approximately 254.34 cm² (rounded to the nearest hundredth), using the value of 3.14 for π.

To find the area of a quarter circle, we can use the formula A = (π * r²) / 4, where A represents the area and r is the radius. Plugging in the given radius of 18 cm, we can calculate the area as follows:

A = (3.14 * 18²) / 4

≈ (3.14 * 324) / 4

≈ 1017.36 / 4

≈ 254.34 cm²

Rounding the answer to the nearest hundredth, we find that the area of the quarter circle with a radius of 18 cm is approximately 254.34 cm².

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The best estimate using compatible numbers is approximately 23.33.

To find the best estimate using compatible numbers for the quotient of -137.56 divided by -6.12, we need to identify compatible numbers that are close to the given values.

Compatible numbers are numbers that are easy to work with mentally and provide a close approximation of the actual values.

Let's consider compatible numbers for -137.56 and -6.12:

For -137.56, we can use -140, which is close to -137.56.

For -6.12, we can use -6, which is close to -6.12.

Now, let's calculate the estimate:

-137.56 ÷ -6.12 ≈ -140 ÷ -6

Dividing -140 by -6, we get:

-137.56 ÷ -6.12 ≈ 23.33

Therefore, the best estimate using compatible numbers is approximately 23.33. By selecting compatible numbers close to the given values and performing the division using those numbers, we can obtain a reasonable estimate of the quotient.

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"t" is the independent variable representing the number of minutes since Willie started firing the retro-rocket, while "d" is the dependent variable representing the distance from the surface of Mars

The independent variable "t" represents the number of minutes since Willie started firing the retro-rocket. It is the variable that Willie has control over and chooses to manipulate. By changing the value of "t," Willie can observe how it affects the dependent variable "d," which is the distance from the surface of Mars. The independent variable is typically the input or the cause in a relationship or function.

On the other hand, the dependent variable "d" represents the distance from the surface of Mars. It depends on the value of "t" and is influenced by the independent variable. As Willie changes the number of minutes, the distance "d" changes accordingly. The dependent variable is usually the output or the effect in a relationship or function.

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