Assignment Questions: PROBLEM 5: (30 Marks) Agri-Pro is a company that sells agricultural products to farmers in a number of provinces. One service that it provides to customers is custom feed mixing, for which a farmer can order a specific amount of livestock feed and specify the amount of corn, grain, and minerals that the feed should contain. This is an important service because the proper feed for various farm animals changes regularly depending upon the weather, and pasture conditions, for example. Agri-Pro stocks bulk amounts of four types of feeds that it can mix to meet a given customer's specifications. The following table summarizes the four feeds; their composition of corn, grain, and minerals; and the cost per kilogram for each feed type: Percent of Nutrient Nutrient Feed 1 Feed 2 Feed 3 Feed 4 Corn 10% 15% 20% 20% Grain 20% 30% 25% 25% Minerals 20% 20% 20% 30% Cost per kilogram $0.15 $0.20 $0.18 $0.25 Agri-Pro has just received an order from a local chicken farmer for 8,000 kilograms of feed. The farmer wants the feed to contain at least 10% corn; at least 25% grain; and at least 20% minerals. a) Develop the model in Excel. (10 marks) b) Solve the problem of finding the least-cost feed mix. Give the quantities of the individual feeds included and the total daily cost. (4 marks) c) In what nutritional elements will you have a surplus? In what quantities? (4 marks) d) Create a Sensitivity Report and answer the following questions: (i) Suppose we forced Feed 3 to be in the solution, what would happen to the objective function's value? (4 marks) (i) What are the max and min values of the objective function coefficients for Feed 1 and Feed 2 for which the current optimal solution is valid? (4 marks) (ii) What do the shadow prices for the grain and minerals constraints mean? What are the maximum and minimum values for the corn and grain constraints for which the current constraint value does not change? (4 marks) Hint: When you define your decision variables use thousands of kilograms as the units.

The ratio of investment is 3:4:5, which means the total ratio is 3+4+5 = 12.

Let the common ratio be x, then the amount invested by each entrepreneur is:

3x + 4x + 5x = 12x

According to the problem, 12x = $875,000

So, x = $875,000/12 = $72,916.67

Therefore, the second largest share is 4x = 4*$72,916.67 = $291,666.68

Rounding off to the nearest 100th, the second largest share is $291,666.67.

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The probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is approximately 0.1736 or 17.36%. The probability that the ballot measure might pass in Region B can be calculated using a confidence interval approach.

The confidence interval for the population proportion of voters who support the ballot measure in Region B:

CI = p ± z × SE

where p is the sample proportion, z is the critical value for the desired confidence level (e.g., z=1.96 for 95% confidence), and SE is the standard error of the sample proportion.

the standard error of the sample proportion:

SE = [tex]sqrt [p ×\frac{(1-p)}{n} ][/tex]  = [tex]sqrt[0.51 ×\frac{(1-0.51)}{400} ][/tex] = 0.025

where p is the sample proportion and n is the sample size.

the confidence interval using a 95% confidence level:

CI = 0.51 ± 1.96  0.025 = (0.46, 0.56)

Therefore, we can be 95% confident that the true population proportion of voters who support the ballot measure in Region B falls within the range of 0.46 to 0.56. Since the lower bound of the confidence interval is above 0.50, there is a possibility that the ballot measure might pass in Region B. However, the exact probability would depend on the actual population proportion and the sample size.

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55% of the pins were purple if Omar ordered a set of purple and red pins. He received 60 pins in all. 33 of the pins were purple.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants. An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

To find the percentage of purple pins, we need to divide the number of purple pins by the total number of pins and multiply by 100.

Number of purple pins = 33

Total number of pins = 60

Percentage of purple pins = (Number of purple pins / Total number of pins) x 100

= (33 / 60) x 100

= 55%

Therefore, 55% of the pins were purple.

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Multiply/divide both sides by the same non-zero constant (option C).

Both equations can be considered equivalent (yes).

To solve the equation, we can start by simplifying equation A by opening the brackets:

3(x + 2) = 18

3x + 6 = 18

We can then solve for x by dividing both sides of the equation by a non-zero constant (3):

3x + 6 = 18

3x = 18 - 6

3x = 12

x = 4

From this solution, we can simplify equation A to obtain equation B:

x + 2 = 6

x = 6 - 2

x = 4

Hence, equation B can be obtained from equation A.

Part 2: Equivalent equations are algebraic equations that have the same solutions.

To determine if both equations are equivalent, we can solve them to their simplest form:

Equation A:

3(x + 2) = 18

3x + 6 = 18

3x = 18 - 6

3x = 12

x = 4

Equation B:

x + 2 = 6

x = 6 - 2

x = 4

Since both equations have the same solution, we can conclude that they are equivalent.

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1. The probability of finding 1 toy in the 24 packages is 0. This is because the company offers a toy in every 5 cereal packages, so if the father buys 24 packages, he is guaranteed to find at least 4 toys (24/5 = 4.8, rounded down to 4). Therefore, the probability of finding only 1 toy is 0.

2. The probability of finding no toy at all is also 0, for the same reason as above. The father is guaranteed to find at least 4 toys in the 24 packages he bought.

3. The mean number of toys in the 24 packages is 4.8, which is the result of 24/5. The standard deviation can be calculated using the formula sqrt(np(1-p)), where n is the number of packages, p is the probability of finding a toy in each package, and 1-p is the probability of not finding a toy. In this case, n=24, p=1/5, and 1-p=4/5. Plugging these values into the formula gives us:

Standard deviation = sqrt(24*(1/5)*(4/5)) = 1.732

So the mean number of toys in the 24 packages is 4.8, and the standard deviation is 1.732.

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The equation of the line satisfying the given conditions. It passes through (1,6); parallel to the line y = 9x - 4 is y = 9x - 3.

To find an equation of the line that satisfies the given conditions, we need to use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

Since the line we are looking for is parallel to the line y = 9x - 4, it will have the same slope, which is 9. Therefore, the equation of the line we are looking for will be y = 9x + b.

Now, we need to find the value of b. We can do this by plugging in the given point (1,6) into the equation and solving for b:

6 = 9(1) + b
6 = 9 + b
b = -3

So the equation of the line that satisfies the given conditions is y = 9x - 3.

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The pair of integers to be used to rewrite the middle term when factoring 6t^(2)+5t-4 by grouping is (5t - 4) and (6t^2 + 5t). By factoring by grouping, we can factor the middle term out of the polynomial and then factor the remaining terms separately.

First, the middle term is factored out of the equation. This is done by multiplying the first and last terms together, which in this case is (6t^2)(-4). This results in the equation 6t^2 + 5t - 4 being rewritten as 6t^2 + (5t - 4)(-4).

Next, the remaining terms are factored separately. The first term, 6t^2, is a perfect square and can be factored as (3t)(2t). The second term, (5t - 4)(-4), can be factored by taking out a common factor from each term. In this case, the common factor is (-4). This results in the equation being rewritten as (3t)(2t) + (-4)(5t - 4).

The final step is to group the terms together and factor out the greatest common factor. In this equation, the greatest common factor is (3t)(-4). Thus, the equation 6t^2 + 5t - 4 can be rewritten as (3t)(-4)(2t + 5).

In conclusion, the pair of integers used to rewrite the middle term when factoring 6t^2 + 5t - 4 by grouping is (5t - 4) and (6t^2 + 5t).

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According to the information, it can be predicted that the number of missed shots after six weeks of practice is zero (0).

To calculate the number of lost shots after six weeks of practice, we must take into account the function that relates the weeks of practice with lost shots. In this case we must replace the value of X that corresponds to the weeks of practice and we will obtain as a result the amount of lost shots as shown below:

According to this function, we can infer that after six weeks of practice there will be 0 missed shots.

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Answer:

please give brainliest

Step-by-step explanation:

P(x)=(x+5)(x−4)(x−5)

is the lowest order of all polynomials with given zeroes.

Therefore, it is not possible to determine how much Jim was charged for each shirt, each pair of slacks, and each sports coat with the given information.

To solve this problem, we can use a system of linear equations. Let x be the cost of each shirt, y be the cost of each pair of slacks, and z be the cost of each sports coat. Then we can write the following equations based on the information given in the problem:

3x + 2y = 18.45 (equation 1)

7x + 2y + z = 35.40 (equation 2)

4x + 2z = 23.94 (equation 3)

Now we can use the elimination method to solve for the variables. First, we can subtract equation 1 from equation 2 to eliminate the y variable:

4x + z = 16.95 (equation 4)

Next, we can multiply equation 1 by -2 and add it to equation 3 to eliminate the y variable:

-6x - 4y + 4x + 2z = -36.9 + 23.94

-2x + 2z = -12.96 (equation 5)

Now we can subtract equation 4 from equation 5 to eliminate the x variable:

2z - z = -12.96 - 16.95

z = -29.91

This value for z does not make sense, so there must be a mistake in the calculations or the original problem. Therefore, it is not possible to determine how much Jim was charged for each shirt, each pair of slacks, and each sports coat with the given information.

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Answer: not my answer but an answer from ai, scan through, see if right, its all explained out for you

To evaluate g(f(5)), we first need to find the value of f(5) by substituting x = 5 into the definition of f(x):

f(x) = x^2 - 6x + 14

f(5) = 5^2 - 6(5) + 14

f(5) = 25 - 30 + 14

f(5) = 9

Now that we know that f(5) = 9, we can evaluate g(f(5)) by substituting 9 into the definition of g(x):

g(x) = x + 14

g(f(5)) = g(9)

g(f(5)) = 9 + 14

g(f(5)) = 23

Therefore, the value of g(f(5)) is 23.

Answer:

Your answer is 4

Step-by-step explanation:

[tex]a^2+b^2=c^2[/tex]

c = 2sqrt(5)

b = 2

a = length

[tex]a^2 = c^2 -b^2\\\\a =\sqrt{c^2-b^2} \\\\a=\sqrt{(2\sqrt{5} )^2-2^2}\\\\a=\sqrt{(2*2*5)-4}\\\\a=\sqrt{20-4}\\\\a=\sqrt{16}\\\\a=4[/tex]

The value of the given algebraic expression is 7. The solution has been obtained by using arithmetic operations.

A mathematical expression called an algebraic expression can have variables or integers in it. It cannot be solved because it lacks an equals sign. A sequence of algebraic expressions are separated by an equals sign and are part of an algebraic equation, which can be solved.

We are given an algebraic expression as (f + g)/j.

The values of f = 6, g = 8, h = 12 and j = 2.

On substituting these in the expression, we get

⇒(6 + 8)/2

⇒14/2

⇒7

Hence, the value of the given algebraic expression is 7.

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Question: Evaluate the algebraic expression (f + g)/j when f = 6, g = 8, h = 12 and j = 2.

Answer:

132.7cm²

Step-by-step explanation:

area of circle =  πr²

6.5² * π

=132.7cm²

The probability of rolling the dies and getting greater than 4 will be [tex]\dfrac{2}{6}[/tex].

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Given that the 6-sided die is rolled, the probability of getting a number greater than 4 will be calculated as,

Sample space = {1, 2, 3, 4, 5, 6} = 6

Favourable outcomes = {5,6} = 2

[tex]\rm Probability = \dfrac{Favourable \ events}{Sample\ space}[/tex]

[tex]\rm Probability = \dfrac{2}{6}[/tex]

Therefore, the probability will be [tex]\dfrac{2}{6}[/tex].

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Check the picture below.

[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-3\\ k=1\\ a=2\\ b=1 \end{cases}\implies \cfrac{(x- (-3))^2}{ 2^2}+\cfrac{(y-1)^2}{ 1^2}=1\implies \cfrac{(x+3)^2}{ 4}+\cfrac{(y-1)^2}{ 1}=1[/tex]

Answer: To find the equation of the ellipse, we need to use the standard form equation of an ellipse:

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

where (h,k) is the center of the ellipse, a is the distance from the center to the vertices (the major axis), and b is the distance from the center to the co-vertices (the minor axis).

First, let's find the center of the ellipse. The center of the ellipse is the midpoint of the line segment joining the vertices (-5,1) and (-1,1). Using the midpoint formula, we get:

$(h,k) = \left(\frac{-5+(-1)}{2}, 1\right) = (-3,1)$

Now, we need to find the values of a and b. Since the distance between the vertices is 2a, we have:

$2a = |-5-(-1)| = 4$

So, $a = 2$.

Similarly, the distance between the co-vertices is 2b, we have:

$2b = |2-0| = 2$

So, $b = 1$.

Now, we have all the values we need to write the equation of the ellipse:

$\frac{(x+3)^2}{2^2}+\frac{(y-1)^2}{1^2}=1$

Simplifying this equation, we get:

$\frac{(x+3)^2}{4}+(y-1)^2=1$

So, the equation of the ellipse is:

$(x+3)^2/4 + (y-1)^2/1 = 1$

Step-by-step explanation:

In response to the supplied query, we may state that Hence, Brenda's Pythagorean theorem home is around 7.2 kilometers away from the school.

The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.

Points A, B, and C can be used to create a right triangle in this situation. The hypotenuse of the line segment between points A and C is its length, while the other two sides are the lengths of the segments connecting A and B and B and C.

We'll refer to the separation between positions A and C as "x". Next, we have:

[tex]x2 = 6 + 4, x2 = 36 + 16, x2 = 52, x = \sqrt(52) = 7.2.[/tex]

Hence, Brenda's home is around 7.2 kilometers away from the school.

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Answer:

Answer:

Step-by-step explanation:

based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest who

7 x 4 = 28

than you need to do y + 5x

than you get you answer 6

Jane can buy 20 melons for the price of 32 apples.

To find out how many melons Jane can buy for the price of 32 apples, we need to use the given ratios to find the equivalent value of melons in terms of apples.

First, we know that 6 apples are equivalent to 3 bananas. So, we can simplify this ratio to 2 apples per 1 banana.

Next, we know that 4 bananas are equivalent to 5 melons. So, we can simplify this ratio to 4/5 of a banana per 1 melon.

Now, we can use these ratios to find the equivalent value of melons in terms of apples. If 2 apples are equivalent to 1 banana, and 4/5 of a banana is equivalent to 1 melon, then we can multiply these ratios together to find the equivalent value of melons in terms of apples:

2 apples/1 banana × 4/5 banana/1 melon = 8/5 apples/1 melon

This means that 1 melon is equivalent to 8/5 apples, or 1.6 apples.

Finally, we can use this ratio to find out how many melons Jane can buy for the price of 32 apples:

32 apples × 1 melon/1.6 apples = 20 melons

Therefore, Jane can buy 20 melons for the price of 32 apples.

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Sky can run 3 miles per hour faster than her sister rose can walk. If Sky ran 12 miles in the same time it took Rose to walk 8 miles, the speed of each sister in this case is 6 miles per hour for Rose and 9 miles per hour for Sky.

To find the speed of each sister, we can use the formula distance = speed × time. We can set up a system of equations to solve for the speeds of Sky and Rose. Let s be the speed of Sky and r be the speed of Rose. Then we have:

12 = s × t (equation 1)
8 = r × t (equation 2)

We are also told that Sky can run 3 miles per hour faster than Rose, so we can write:

s = r + 3 (equation 3)

Now we can substitute equation 3 into equation 1 and solve for t:

12 = (r + 3) × t
t = 12 / (r + 3)

Next, we can substitute this value of t into equation 2 and solve for r:

8 = r × (12 / (r + 3))
8(r + 3) = 12r
8r + 24 = 12r
24 = 4r
r = 6

So the speed of Rose is 6 miles per hour. We can use equation 3 to find the speed of Sky:

s = 6 + 3
s = 9

So the speed of Sky is 9 miles per hour. Therefore, the speed of each sister in this case is 6 miles per hour for Rose and 9 miles per hour for Sky.

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The speed of each sister is as follows: Rose's speed is 6 miles per hour, and Sky's speed is 9 miles per hour.

Let's begin by defining some variables: let x be Rose's walking speed, and x + 3 be Sky's running speed. Since we know that Sky ran 12 miles and Rose walked 8 miles in the same amount of time, we can write an equation to represent this:

12 / (x + 3) = 8 / x

Cross-multiplying and simplifying gives us:

12x = 8x + 24

4x = 24

x = 6

So Rose's walking speed is 6 miles per hour, and Sky's running speed is 6 + 3 = 9 miles per hour.

Therefore, the speed of each sister is as follows: Rose's speed is 6 miles per hour, and Sky's speed is 9 miles per hour.

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Below, you will learn how to solve the problem.

(a) To find the linear relationship y = mx + b between x = year and y = profit, we first need to find the slope (m) and the y-intercept (b).

The slope (m) is the change in y (profit) divided by the change in x (year):
m = (17 - 5)/(6 - 2)

m = 12/4

m = 3

Next, we can use one of the data points (2, 5) and the slope (3) to find the y-intercept (b):
5 = 3(2) + b
b = 5 - 6

b = -1

So the linear relationship between x = year and y = profit is:

y = 3x - 1

(b) To find the company's profit at the end of 3 years, we can plug in x = 3 into the equation:
y = 3(3) - 1

y = 8

So the company's profit at the end of 3 years is $8 million.

(c) To predict the company's profit at the end of 8 years, we can plug in x = 8 into the equation:

y = 3(8) - 1 = 23

So the company's profit at the end of 8 years is predicted to be $23 million.

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All four statements are logically equivalent.

The statements (a), (b), (c), and (d) are all logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.

Let's start with statement (a): For each b∈Rm, the matrix equation Ax=b has a solution. This means that for any vector b in Rm, there exists a vector x in Rn such that Ax=b.

Now, let's look at statement (b): Each b∈Rm is a linear combination of the columns in A. This means that for any vector b in Rm, we can write b as a linear combination of the columns of A, which is equivalent to saying that Ax=b has a solution.

Statement (c) says that the columns of A span Rm. This means that the columns of A can be combined in a linear combination to produce any vector in Rm, which is equivalent to saying that Ax=b has a solution for any vector b in Rm.

Finally, statement (d) says that the reduced echelon form of A has a pivot in every row. This means that the matrix A is of full rank and that there are no free variables in the equation Ax=b. This implies that there is a unique solution for every vector b in Rm, which is equivalent to saying that Ax=b has a solution for any vector b in Rm.

Therefore, all four statements are logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.

The solution to this question is to understand that all four statements are logically equivalent because they all describe the same concept: that the matrix A has a solution for every possible vector b.

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The statement (3)/(2)>(4)/(5) is true because cross-multiplication shows that 15>8.

To determine whether a statement is true or false, we can cross-multiply the fractions and compare the products.

In this case, (3)*(5)>(2)*(4), which simplifies to 15>8. Since 15 is greater than 8, the statement is true and does not need to be rewritten.

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Answer:

2/3 of the fruits in the basket are red apples.

Step-by-step explanation:

5 apples of 6 total fruit are in a basket.

4 apples are red.

Take 4 and divide it by 6, you will get 0.67 or 2/3.

2/3 cannot be simplified.

The length of AC is 224 meters to 3 significant figures.

a² + b² = c²

where c is the hypotenuse (the side opposite the right angle) and a and b are the two legs (the sides adjacent to the right angle).

In this case, we can treat Stanley's path as a right triangle with legs AB and BC, and hypotenuse AC. Since we are given the lengths of AB and BC, we can plug those into the Pythagorean theorem and solve for AC.

AC² = AB² + BC²

AC² = (200 m)² + (160 m)

AC² = 40,000 m² + 25,600 m²

AC² = 65,600 m²

To find AC, we take the square root of both sides:

AC = [tex]\sqrt{65600}[/tex] m

AC ≈ 256

Finally, we round to 3 significant figures to get length of AC ≈ 224 meters.

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Let's say that the number of metal paperweights is "x", then the number of glass paperweights is "2x" since she has twice as many glass paperweights as metal.

We know that she has a total of 12 paperweights, so we can set up an equation:

x + 2x + 3 = 12

Simplifying the equation, we get:

3x + 3 = 12

Subtracting 3 from both sides, we get:

3x = 9

Dividing both sides by 3, we get:-

x = 3

So Teri has 3 metal paperweights, and since she has twice as many glass paperweights as metal, she has:

2x = 2(3) = 6 glass paperweights.

Therefore, Teri has 3 metal paperweights, 6 glass paperweights, and 3 wood paperweights in her collection.

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