In 2 and 3 wrote each number in standard form 4x100+7x10+6x1+6x(1/10)+3x(1/100)+7x(1/1000) four and sixty eight thousandths

y = 3x, represents the number of strawberries (y) in terms of the number of apples (x). 52 = x + y, represents the total number of fruit used.  Therefore, Tay used 13 apples and 39 strawberries in total.

Let's solve the equations to find the number of apples (x) and strawberries (y) Tay used.

From the first equation, y = 3x, we can substitute this expression for y in the second equation:

52 = x + 3x

Combining like terms, we have:

52 = 4x

Dividing both sides of the equation by 4:

13 = x

Now, substituting this value of x back into the first equation:

y = 3(13)

y = 39

Therefore, Tay used 13 apples and 39 strawberries in total.

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Adriana applies the same arrangement of books on the new bookshelf, which is based on the classification of books.

She put the novels, short stories, and poetry books on the top shelf, history and biography books on the second shelf, textbooks and reference materials on the third shelf, and cookbooks and magazines on the bottom shelf. Adriana has already organized her books based on the genre or category before she buys a new bookshelf. The same classification will be applied to the new bookshelf that will be added to accommodate more books. It is an easy and convenient way of arranging and finding books

Adriana has an efficient way of arranging her books on her bookshelves based on genre or category. She applies the same arrangement of books on the new bookshelf that she bought to accommodate more books. It is a convenient and efficient way of organizing books that can help anyone easily find the book they need.

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The expression 14 × 23 represents the total number of cups of dirt needed for 14 pots of flowers. By multiplying the number of pots (14) by the amount of dirt needed per pot (23), we find that a total of 322 cups of dirt are required to fill all 14 pots.

To calculate the total number of cups of dirt needed for 14 pots of flowers, we can use the expression 14 × 23.

Let's break down the problem and explain the steps involved.

Given information:

Each pot of flowers requires 23 cups of dirt.

We want to find the total number of cups of dirt needed for 14 pots.

To solve this, we can multiply the number of pots (14) by the number of cups of dirt required for each pot (23).

Expression: 14 × 23

When we multiply 14 by 23, we perform the following calculation:

14 × 3 = 42 (multiplying the units digit)

14 × 20 = 280 (multiplying the tens digit)

Summing the results: 280 + 42 = 322

Therefore, the total number of cups of dirt needed for 14 pots is 322 cups.

Let's analyze this further.

When we say that 1 pot of flowers requires 23 cups of dirt, it means that each individual pot needs a specific amount of dirt to be properly filled. Multiplying this amount by the number of pots (14) gives us the cumulative requirement for all the pots.

Using the expression 14 × 23, we are essentially multiplying the number of pots (14) by the amount of dirt needed per pot (23). This expression allows us to find the total quantity of dirt required to fill all 14 pots.

The multiplication process involves multiplying the units digit (4) of 14 by 3, which gives us 12. The result has a carry-over of 1, which we then multiply by the tens digit (2) of 14, resulting in 20. Finally, we add these two products (12 and 20) to obtain the final result of 322.

In conclusion, the expression 14 × 23 represents the total number of cups of dirt needed for 14 pots of flowers. By multiplying the number of pots (14) by the amount of dirt needed per pot (23), we find that a total of 322 cups of dirt are required to fill all 14 pots.

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Answer:60118.93636

Step-by-step explanation: Based on the given conditions, formulate:: 49236.45 x (10.5%+1)² Evaluate the equation/expression:: 60118.93636

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 240000\\ P=\textit{original amount deposited}\\ r=rate\to 4.6\%\to \frac{4.6}{100}\dotfill &0.046\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}[/tex]

[tex]240000 = P\left(1+\frac{0.046}{12}\right)^{12\cdot 20} \implies 240000=P\left( \cfrac{6023}{6000} \right)^{240} \\\\\\ \cfrac{240000}{ ~~ \left( \frac{6023}{6000} \right)^{240} ~~ }=P\implies 95810\approx P[/tex]

The expression involves finding the square root of a combination of numbers and expressions, including the square root of 5. It requires simplification and order of operations to obtain the result.

To compute the expression: square root of 9 minus 4 times the square root of 5, divided by 2 minus the square root of 5, we need to follow the order of operations (PEMDAS/BODMAS). Let's break down the calculation step by step:

First, we simplify the expression inside the square root: 9 - 4 times the square root of 5 becomes 9 - 4√5.

Next, we divide this expression by 2 minus the square root of 5: (9 - 4√5) / (2 - √5).

To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is 2 + √5.

Expanding the expression: [(9 - 4√5) / (2 - √5)] * [(2 + √5) / (2 + √5)].

Simplifying the numerator and denominator: (18 + 9√5 - 8√5 - 20) / (4 - 5).

Combining like terms: (-2 - √5) / (-1).

Finally, simplifying the expression gives us the result: 2 + √5.

In conclusion, the square root of 9 - 4 times the square root of 5 divided by 2 minus the square root of 5 simplifies to 2 + √5.

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Let's consider a regular hexagon with a side length of 4 units. To find the area of this polygon, we can divide it into six equilateral triangles.

The formula to calculate the area of an equilateral triangle is:

Area = (side length^2 * sqrt(3)) / 4

In this case, the side length is 4 units. Substituting the values into the formula, we get:

[tex]Area = (4^2 * sqrt(3)) / 4\\\\\\\\ea = (16 * sqrt(3)) \\\\\\ 4Area = 4 * sqrt(3)[/tex]

Approximating the value of sqrt(3) to 1.732, we have:

Area ≈ 4 * 1.732

Area ≈ 6.928 square units

Therefore, the approximate area of the regular hexagon is 6.928 square units.

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Given the cost of 6 cans of dog food is $3.90Rate = Cost/ No. of cans of dog food

Rate = 3.9/6= 0.65$ per can of dog food

Hence, the rate is $0.65 per can of dog food and the unit of measure is dollars per can of dog food.

Proportional relationship can be written as;

Cost of dog food ∝ No. of cans of dog food

We know, for a proportional relationship; Cost of dog food = k × No. of cans of dog food

Where k is the constant of proportionality.

By substituting the given values in the above equation;

3.9 = k × 6

k = 3.9/6

k = 0.65

Given the cost of 6 cans of dog food is $3.90, we can calculate the rate by dividing the cost by the number of cans of dog food. Therefore, the rate of the dog food cans is $0.65 per can. The units of measure are dollars per can of dog food.We can also represent the proportional relationship between the cost and the number of cans of dog food using the formula; Cost of dog food ∝ No. of cans of dog food.

In this formula, the constant of proportionality is represented as k. We can find the value of k by substituting the given values in the equation and solving for k. Hence, the required equation that represents the proportional relationship is Cost of dog food = 0.65 × No. of cans of dog food.

We found that the rate of the dog food cans is $0.65 per can. We also found that the proportional relationship between the cost and the number of cans of dog food can be represented using the equation

Cost of dog food = 0.65 × No. of cans of dog food, where the constant of proportionality is 0.65.

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It's worth noting that New Orleans is a vibrant and culturally rich city known for its unique history, music, and cuisine.

New Orleans is a city in the state of Louisiana, located in the southeastern United States. What sets New Orleans apart from many other cities is its geographical situation below sea level.

The city is situated in a basin, with the Mississippi River flowing through it and the surrounding area consisting of marshlands and swamps.

Due to its unique geography, New Orleans faces challenges related to water management. The city is prone to flooding, especially during heavy rainfalls or hurricanes. To mitigate the risk of flooding, a system of levees, pumps, and canals has been implemented.

When we say that Zula's aunt Mikki's home is located at an elevation of 7 feet below sea level, it means that the ground level of her home is 7 feet lower than the average sea level. This implies that the land where the home is built is situated below the level of the nearby bodies of water, such as the Mississippi River or the Gulf of Mexico.

The elevation of land is typically measured in relation to mean sea level (MSL), which is an average level determined by tidal observations over a specific period. In this case, the elevation of 7 feet below sea level indicates that the ground level of Mikki's home is 7 feet lower than the average level of the nearby sea or ocean.

To protect against flooding, the city of New Orleans relies on an extensive network of levees, which are large embankments or walls built along the edges of water bodies. These levees act as barriers to prevent water from overflowing and flooding the city. In addition to levees, a complex system of pumps and canals helps to control water levels and drain excess water during heavy rainfall.

Living below sea level can present unique challenges and considerations for the residents of New Orleans. It requires careful water management, reliance on flood protection systems, and preparedness for potential weather events.

However, it's worth noting that New Orleans is a vibrant and culturally rich city known for its unique history, music, and cuisine.

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Zula spent part of her summer visiting relatives in Louisiana. She visited her aunt Mikki, whose home is located in New Orleans at an elevation of 7 feet below sea level?

Bouquet T contains 13 flowers, which matches the number of daisies in each bouquet. Therefore, the statement "Each bouquet contains 13 daisies" is true.

According to the information given, Bouquet S contains 30 flowers. However, the number of daisies in Bouquet S is not specified. On the other hand, Bouquet T is explicitly stated to contain 13 flowers. It is also mentioned that each bouquet contains 13 daisies. Since the number of flowers in Bouquet T matches the number of daisies in each bouquet, it can be inferred that Bouquet T consists entirely of daisies. Bouquet S, on the other hand, could have a different number of daisies, as the information does not specify the composition of the flowers within it. Therefore, the statement "Each bouquet contains 13 daisies" is true, with Bouquet T serving as an example of a bouquet that matches this description.

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These equations provide different ways to calculate the value of 'd' based on the values of 'T,' 'a,' 'b,' and 'c.'

It seems like you have provided four equations involving the variable "d." I will break down each equation and explain them separately:

d = (T - a - b - c) / 2

This equation states that "d" is equal to the difference between "T," "a," "b," and "c," divided by 2.

d = T/2 - a - b - c

This equation expresses that "d" is equal to half of "T" minus the sum of "a," "b," and "c."

d = (T + a + b + c) / 2

This equation states that "d" is equal to the sum of "T," "a," "b," and "c," divided by 2.

d = 2(T - a - b - c)

This equation indicates that "d" is equal to twice the difference between "T," "a," "b," and "c."

These equations provide different ways to calculate the value of "d" based on the given variables "T," "a," "b," and "c." Each equation can be used depending on the context and requirements of the problem at hand.

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134880 divided by 240 using the long division method is 562.

In order to divide 134880 by 240 using the long division method, follow the given steps below:

Step 1: Set up the division with dividend inside the bracket and divisor outside it.

Step 2: Determine how many times the divisor goes into the first digit(s) of the dividend. Here, 240 goes into 1348 five times. Write 5 above the first digit of the dividend, to the right of the bracket.

Step 3: Multiply the divisor by the quotient. 5 x 240 = 1200. Write this product beneath the first digits of the dividend.

Step 4: Subtract the product obtained in step 3 from the first digits of the dividend. Write the result under the line. 1348 - 1200 = 148.

Step 5: Bring down the next digit of the dividend (in this case, 8) next to the remainder. Now, you have 1488.

Step 6: Determine how many times the divisor goes into the first digit(s) of the new dividend, i.e., 1488. Here, 240 goes into 1488 six times. Write 6 above the second digit of the dividend, to the right of the previous quotient digit (5).

Step 7: Multiply the divisor by the new quotient. 6 x 240 = 1440. Write this product beneath the first two digits of the dividend.

Step 8: Subtract the product obtained in step 7 from the first two digits of the dividend. Write the result under the line. 1488 - 1440 = 48.

Step 9: Bring down the next digit of the dividend (in this case, 0) next to the remainder. Now, you have 480.

Step 10: Determine how many times the divisor goes into the first digit(s) of the new dividend, i.e., 480. Here, 240 goes into 480 two times. Write 2 above the third digit of the dividend, to the right of the previous quotient digit (6).

Step 11: Multiply the divisor by the new quotient. 2 x 240 = 480. Write this product beneath the first three digits of the dividend.

Step 12: Subtract the product obtained in step 11 from the first three digits of the dividend. Write the result under the line. 480 - 480 = 0.

Therefore, 134880 divided by 240 using the long division method is 562.

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The 16 pints of milk is equal to 8 quarts.

To determine the number of quarts that 16 pints of milk is equal to, we need to understand the conversion between pints and quarts.

In the United States customary system of measurement, there are 2 pints in 1 quart. This means that 1 quart is equivalent to 2 pints.

Given that Corey bought 16 pints of milk, we can calculate the number of quarts by dividing the number of pints by the conversion factor:

16 pints / 2 pints/quart = 8 quarts

So, Corey's purchase of 16 pints of milk is equal to 8 quarts.

To understand why this conversion works, consider that both pints and quarts are units of volume. A pint is a smaller unit, and a quart is a larger unit. Since there are 2 pints in 1 quart, if we have 16 pints and we want to express it in quarts, we divide the number of pints by 2 to get the equivalent number of quarts. This conversion allows us to compare and measure volumes in different units.

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In a seventh grade class of 28 students there are 16 girls and 12 boys if one student chosen to win a prize. The probability of a girl being chosen from the seventh-grade class is 4/7.

To determine the probability of a girl being chosen from a seventh-grade class, we need to consider the number of girls and the total number of students in the class.

In this scenario, there are 28 students in total, comprising 16 girls and 12 boys.

To calculate the likelihood of an event, divide the count of desired outcomes by the total count of possible outcomes.

In this case, the favorable outcome is a girl being chosen, and the possible outcomes are any student being chosen from the class.

Hence, the probability of a girl being chosen can be calculated as follows:

The probability of an event is determined by the ratio of favorable outcomes to the total number of possible outcomes.

The number of favorable outcomes is equal to the number of girls, which is 16.

The total number of possible outcomes is equal to the total number of students, which is 28.

Hence, the probability of selecting a girl is:

Probability = 16 / 28

Simplifying the fraction:

Probability = 4 / 7

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The sum of a number, its cube root and its square is 759. So the number that satisfies the given condition is approximately 54.

Explanation: Let's assume the number is represented by "x". According to the problem, the sum of the number, its cube root (x^(1/3)), and its square (x^2) is equal to 759. Mathematically, this can be expressed as x + x^(1/3) + x^2 = 759. To find the value of "x", we can use numerical methods or approximation techniques. By solving this equation, it is found that x is approximately equal to 54. Substituting this value into the equation, we have 54 + (54)^(1/3) + (54)^2 ≈ 54 + 3.76 + 2916 ≈ 759. Therefore, the number that satisfies the given condition is approximately 54.

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Given that the standard error of the sampling proportion is 0.05. We have to find the sample size.Suppose that 25% of all new cars sold last year had at least 1 manufacturer recall.

We know that at least 25% of new cars had at least one manufacturer recall. This means that the probability that a new car sold last year had a recall was greater than 0.25. We are given that more than 250 new cars were sold last year.Therefore, the sample size can be found as follows:N = p(1 - p) / SE² wherep is the proportion of cars that had at least one manufacturer recall, which is 25% or 0.25.SE is the standard error of the sampling proportion, which is 0.05.N = (0.25)(1 - 0.25) / (0.05)²N = (0.25)(0.75) / (0.0025)N = 0.1875 / 0.0025N = 75Hence, the sample size is 75, which is option (C).

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If Shawna's sister drinks a gallon of water after each of the four races she runs, she would consume a total of four gallons of water.

Given that Shawna's sister drinks a gallon of water after running each race, we can multiply the amount of water consumed per race (1 gallon) by the number of races (4) to determine the total amount of water consumed.

1 gallon of water per race x 4 races = 4 gallons of water

Therefore, Shawna's sister would drink a total of four gallons of water after running the four races. Each race contributes 1 gallon to the total, resulting in a cumulative consumption of four gallons.

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The empirical formula for the given amounts of N and H is NH3.

To determine the empirical formula, we need to find the ratio of the number of atoms of each element present in the given masses.

First, we convert the given masses of N and H to moles using their molar masses. The molar mass of N is approximately 14 g/mol, and the molar mass of H is approximately 1 g/mol.

For N: 1.645 g N / 14 g/mol ≈ 0.1175 mol N

For H: 0.355 g H / 1 g/mol ≈ 0.355 mol H

Next, we divide the moles of each element by the smallest number of moles to get the simplest whole-number ratio. In this case, the smallest number of moles is 0.1175 mol N.

N: 0.1175 mol N / 0.1175 mol N = 1

H: 0.355 mol H / 0.1175 mol N ≈ 3

The ratio of N to H is approximately 1:3, leading to the empirical formula NH3, which represents one nitrogen atom bonded to three hydrogen atoms.

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The perimeter of the square ABCD, can be found to be 14.14 cm and the area would be 12.52 cm².

If the side of the larger square is 5 cm, then the diagonal of the smaller square ABCD is 5 cm because the diagonal connects two midpoints on adjacent sides of the larger square.

The sides of the smaller square can be found by applying the Pythagorean theorem, which in this case is a 45-45-90 right triangle theorem.

Given that in a 45-45-90 triangle, the sides are in the ratio of 1:1:√2, the sides of the smaller square (a) can be calculated as follows:

a = 5 / √2

= 5 x √2/2

=  3.54 cm

The perimeter of the square is:

= 4 x 3. 54

= 14. 14 cm

The area is:

= 3. 54 x 3. 54

= 12. 53 cm²

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The probability that both the male and female students selected are smokers is 0.024.

Let's calculate the probability of selecting a male smoker first. Out of the total number of male students, 72 are smokers and 528 are non-smokers. So the probability of selecting a male smoker is:

P(male smoker) = Number of male smokers / Total number of male students

= 72 / (72 + 528)

= 72 / 600

= 0.12

Next, let's calculate the probability of selecting a female smoker. Out of the total number of female students, 118 are smokers and 472 are non-smokers. So the probability of selecting a female smoker is:

P(female smoker) = Number of female smokers / Total number of female students

= 118 / (118 + 472)

= 118 / 590

= 0.2

To find the probability that both are smokers, we multiply the probabilities of each event:

P(both are smokers) = P(male smoker) * P(female smoker)

= 0.12 * 0.2

= 0.024

Therefore, the probability that both the male and female students selected are smokers is 0.024.

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The value of 2b - 4a can be determined by rearranging the given equation 4a - 2b = 10. By isolating 2b on one side of the equation and factoring out the common factor of 2, we can find the value of the expression.

Given the equation 4a - 2b = 10, we can rearrange it to solve for 2b - 4a. Let's isolate 2b by adding 4a to both sides of the equation:

4a - 2b + 4a = 10 + 4a.

Simplifying, we get:

8a - 2b = 10 + 4a.

Next, let's move the 4a term to the left side of the equation by subtracting 4a from both sides:

8a - 4a - 2b = 10 + 4a - 4a.

This yields:

4a - 2b = 10.

Notice that the left side of the equation is exactly the same as the expression we want to find, 2b - 4a. Therefore, we can conclude that 2b - 4a is equal to 10.

In summary, given the equation 4a - 2b = 10, we rearranged it to find the value of 2b - 4a. By isolating 2b - 4a on one side, we determined that it is equal to 10.

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The ratio of the volumes of the two similar pyramids with edges of ratio 5:7 is 125:343.

The volumes of two similar pyramids can be found using the ratio of their corresponding edge length.

Let's assume that the ratio of the edge length of the two similar pyramids is 5:7. This means that the base edge of the larger pyramid is 7x, and the base edge of the smaller pyramid is 5x.

The ratio of their corresponding volumes is equal to the cube of the ratio of their edges. This means that the volume of the larger pyramid is [tex](7x)^3[/tex] and the volume of the smaller pyramid is (5x)^3.

So, the ratio of their volumes is:

The Volume ratio is: [tex](7x)^3 / (5x)^3 = (343/125) \times x^3 = 2.744 \times x^3[/tex]

This means that the larger pyramid has a volume 2.744 times larger than the smaller pyramid.

In general, for two similar pyramids with corresponding edges of ratio a:b, the ratio of their volumes is ([tex]a^3 : b^3[/tex]).

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The value we know is lesser for 7th grade than 8th grade is the median of the data set.Oliver wants to compare the number of hours 7th graders and 8th graders play video games per week.

He makes a box-and-whisker plot for each data set.

The value we know is lesser for 7th grade than 8th grade is the median.

A box and whisker plot is a graph that demonstrates the distribution of a dataset.

It uses quartiles and boundaries to divide a set of data into four equal parts.

A box and whisker plot may also display information on the skewness and symmetry of data.

To compare data using a box-and-whisker plot:

1. Create a box-and-whisker plot for each dataset.

2. Compare the median and quartiles of each dataset.

3. Analyze the distribution of each dataset.

4. Look for any outliers or unusual data points.

5. Draw conclusions based on the data.

Oliver wants to compare the number of hours 7th graders and 8th graders play video games per week.

He makes a box-and-whisker plot for each data set.

From the given box-and-whisker plots, the value we know is lesser for 7th grade than 8th grade is the median of the data set.

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The most commonly created anthropomorphic images, such as a colorful face on a totem pole depicting an animal with fangs, are made by Native Tribes in British Columbia.

Totem poles are monumental sculptures carved from large trees and are an integral part of the indigenous cultures in the Pacific Northwest of North America. They serve various purposes, including storytelling, genealogy, social status, and spiritual beliefs. The anthropomorphic figures found on totem poles often represent mythical creatures, ancestral spirits, or animal beings from native folklore.

British Columbia is home to many indigenous communities that have been carving totem poles for centuries. These tribes have a deep connection to their ancestral lands and traditions, and their artwork reflects their cultural identity and spiritual beliefs. The intricate designs, vibrant colors, and symbolic representations on totem poles are a testament to the rich artistic heritage of these tribes.

While other regions, such as Alaska and the Pacific Northwest of the United States, also have indigenous communities that create totem poles, the most commonly associated and well-known place for this art form is British Columbia in Canada. It is important to recognize and respect the cultural diversity and artistic expressions of indigenous peoples across different regions, as they contribute to the rich tapestry of human heritage.

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The gas mileage of a 2019 vehicle must be higher than approximately 35 miles per gallon (mpg) to fall in the top 15% of all vehicles.

To explain further, if we consider the gas mileage of all 2019 vehicles, we can arrange them in ascending order. The top 15% would represent the highest gas mileage values. By finding the value at which 15% of the vehicles have a lower gas mileage, we can determine that it is around 35 mpg. Any vehicle with a gas mileage higher than this would fall in the top 15% in terms of fuel efficiency.

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OD. (g - f) (a) = 50 + 4 + 108(52). The expression (g • f)(a) represents the composition of two functions g and f evaluated at the input a. The given information states that (g • f)(a) /(+) = 10g(5x).

To find the correct expression, we need to substitute the expression for (g • f)(a) into the equation. From the given choices, only option OD satisfies this condition.

In option OD, (g - f)(a) = 50 + 4 + 108(52). This expression matches the given equation (g • f)(a) /(+) = 10g(5x).

Therefore, the correct answer is OD. (g - f) (a) = 50 + 4 + 108(52).

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The trend line equation, y = -0.14x + 12.5, can be used to predict the year when the record for the 100-meter dash was 11.8 seconds at Meander High School.

In the trend line equation y = -0.14x + 12.5, "y" represents the record time in seconds, and "x" represents the number of years since the year 2000. To predict the year when the record was 11.8 seconds, we can substitute this value for "y" in the equation and solve for "x."

11.8 = -0.14x + 12.5

Rearranging the equation, we get:

-0.14x = 11.8 - 12.5

-0.14x = -0.7

Dividing both sides by -0.14, we find:

x = -0.7 / -0.14

x = 5

The value of "x" represents the number of years since the year 2000. Therefore, to determine the year, we add "x" to the year 2000:

2000 + 5 = 2005

According to the trend line equation, the record for the 100-meter dash was predicted to be 11.8 seconds in the year 2005 at Meander High School.

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The seven in the number 7x0.001 is equivalent to 7 thousandths.

The given number is 7x0.001. This can be solved by multiplying 7 and 0.001, which is equal to 0.007. It is represented as 7 thousandths. In decimal form, the value of each place value is determined by the number of digits after the decimal point.

In the given number, 0.001 has 3 digits after the decimal point, so each place is one thousandth (0.001). Therefore, when we multiply it by 7, we get the answer in terms of thousandths, which is 7 thousandths. Hence, the answer is the seven in the number 7x0.001 is equivalent to 7 thousandths.

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The internal volume of Columbus is approximately 34.7 cubic meters. To find the internal volume of Columbus, we need to subtract 34.7 cubic meters from the total volume. Let's denote the total volume as V.

Therefore, the internal volume can be calculated as V - 34.7.

The question states that the internal volume of Columbus, which refers to the space where the astronauts live and work, is 34.7 cubic meters less than the total volume. This indicates that the internal volume is obtained by subtracting 34.7 cubic meters from the total volume.

By denoting the total volume as V, we can express the internal volume as V - 34.7. This represents the subtraction of the given amount from the total volume to obtain the specific volume occupied by the astronauts within Columbus. Hence, by subtracting 34.7 cubic meters from the total volume, we can determine the internal volume of Columbus, which is approximately 34.7 cubic meters.

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In AVWX,

w = 6 cm, ZX=126° and ZV=51º.

Find the length of v, to the nearest 10th of a centimeter.

Solution:

The given diagram is as follows:

[tex]\triangle AVX[/tex] is not a right-angled triangle.

So, we have to use sine rule here.

sine rule: [tex]\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}[/tex]

Consider [tex]\triangle AVX[/tex]

Therefore, [tex]\frac{AV}{\sin \angle XAV} = \frac{AX}{\sin \angle AVX}[/tex]

Given, w = 6 cm

Also, [tex]\angle AVX = 180 - \angle XAV = 180 - 126 = 54[/tex][tex]\sin 54 = \frac{AX}{\sin \angle AVX} \\\

Rightarrow AX = \frac{w \cdot \sin 54}{\sin (126 + 54)} = \frac{6 \cdot \sin 54}{\sin 180}[/tex][tex]\

Rightarrow AX = \frac{6 \cdot \sin 54}{0.1987} = 29.37 \approx 29.4[/tex]

Now, consider [tex]\triangle ZVX[/tex]

Clearly, [tex]\angle ZVX = 180 - (\angle ZVX + \angle VXZ) = 180 - (51 + 126) = 3[/tex][tex]\sin 3 = \frac{v}{AX}[/tex][tex]\

Rightarrow

[tex][tex]\triangle AVX[/tex] is not a right-angled triangle.

\\ [tex]\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}[/tex]\\

[tex]\triangle AVX[/tex]\\\

frac{AV}{\sin \angle XAV} = \frac{AX}{\sin \angle AVX}[/tex]\\

[tex]\angle AVX = 180 - \angle XAV = 180 - 126 = 54[/tex][tex]\sin 54 = \frac{AX}{\sin \angle AVX} \\

AX = \frac{w \cdot \sin 54}{\sin (126 + 54)} = \frac{6 \cdot \sin 54}{\sin 180}[/tex][tex]\\\

AX = \frac{6 \cdot \sin 54}{0.1987} = 29.37 \approx 29.4[/tex]\\\\

[/tex][/tex]

Hence, the length of v is approximately 1.5 cm. Thus, the length of v, to the nearest 10th of a centimeter, is 1.5 cm (approx).

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