Question 6
What is the 10th term in this arithmatic sequence if u is 0.2?
0.2, 1.55, 2.9, 4.25, 5.6 ....

To make 5 cups of fruit punch, you would need 3 cups of pineapple juice and 2 cups of apple juice. To determine the quantities of pineapple juice and apple juice needed to make 5 cups of fruit punch.

We can use the given ratio of 3 cups of pineapple juice to 2 cups of apple juice.

1: Add the ratio values together to find the total number of parts. In this case, 3 + 2 = 5.

2: Determine the ratio of pineapple juice to the total parts. Divide the total number of cups of pineapple juice (3) by the total number of parts (5). 3/5 = 0.6.

3: Determine the ratio of apple juice to the total parts. Divide the total number of cups of apple juice (2) by the total number of parts (5). 2/5 = 0.4.

4: Multiply the ratios by the desired total cups of fruit punch (5). 0.6 * 5 = 3 cups of pineapple juice. 0.4 * 5 = 2 cups of apple juice.

Therefore, to make 5 cups of fruit punch, you would need 3 cups of pineapple juice and 2 cups of apple juice.

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By applying the Kuhn-Tucker theorem, the maximum value of xy is: 18/25

The constraints are:-4x² - 2xy - 4y²x + 2y ≤ 22x - y ≤ -1

Let us solve this problem by applying the Kuhn-Tucker theorem.

Let us first write down the Lagrangian function:

L = xy + λ₁(-4x² - 2xy - 4y²x + 2y - 2) + λ₂(2x - y + 1)

Then, we find the first order conditions for a maximum:

Lx = y - 8λ₁x - 2λ₁y + 2λ₂ = 0

Ly = x - 8λ₁y - 2λ₁x = 0

Lλ₁ = -4x² - 2xy - 4y²x + 2y - 2 = 0

Lλ₂ = 2x - y + 1 = 0

The complementary slackness conditions are:

λ₁(-4x² - 2xy - 4y²x + 2y - 2) = 0

λ₂(2x - y + 1) = 0

Now, we solve for the above equations one by one:

From equation (3), we can write 2x - y + 1 = 0, which implies:y = 2x + 1

Substitute this in equation (1), we get:

8λ₁x + 2λ₁(2x + 1) - 2λ₂ - x = 0

Simplifying, we get:

10λ₁x + 2λ₁ - 2λ₂ = 0 ... (4)

From equation (2), we can write x = 8λ₁y + 2λ₁x

Substitute this in equation (1), we get:

8λ₁(8λ₁y + 2λ₁x)y + 2λ₁y - 2λ₂ - 8λ₁y - 2λ₁x = 0

Simplifying, we get:

-64λ₁²y² + (16λ₁² - 10λ₁)y - 2λ₂ = 0 ... (5)

Solving equations (4) and (5) for λ₁ and λ₂, we get:

λ₁ = 1/20 and λ₂ = 9/100

Then, substituting these values in the first order conditions, we get:

x = 2/5 and y = 9/5

Therefore, the maximum value of xy is:

2/5 x 9/5 = 18/25

Hence, the required answer is 18/25.

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Answer: 1.

3.

The exponential function representing the spread of Ben's social media post is given by-

f(x)=2(3)^x

4.

4.

The green line represents the social media post of Amber, the orange line represents the social media post of Ben while the purple line represent the social media post of Carter.

5.

6.

7.

Amber's function- f(x)=3(4)^x

For day 3, x = 3. The number of shares Amber's post would have received on day 3 is given by- f(3)=3(4)^x

And for day 10, x = 10. The number of shares Amber's post would have received on day 10 is given by-

f(10)=3(4)^10=3(1,048,576)=3,145,728

Ben's function- f(x)=2(3)^x

For day 3, x = 3. The number of shares Ben's post would have received on day 3 is given by- f(3)=2(3)^3=2(27)=54

And for day 10, x = 10. The number of shares Ben's post would have received on day 10 is given by- f(10)=2(3)^10=2(59,049)=118,098

The black line represents the new function while the green line represents the old function.

The graph of the new function representing Amber's photo share after she mailed copies of her photo to the 45 residents of her grandmother's assisted living facility is the same as the graph of the old function, but the graph of the new function is translated (shifted) up by 45 units.

Based on the result, Amber's post traveled faster.

In an exponential function, the base (growth factor) determines how fast the function grows. The greater the growth factor, the faster the growth of the function.

So, since Amber's growth factor is 4, which is greater than Ben's 3 and Carter's 2, Ambers post traveled faster.

I would want my post to spread faster, so I would prefer a post with fewer friends initially but more shares. Based on the explanations given in question 6 above. The greater the growth factor (in this case: the number of shares), the faster the spread of the function (the faster the spread of the post).

Carter's function- f(x)=10(2)^x

For day 3, x = 3. The number of shares Carter's post would have received on day 3 is given by- f(3)=2(3)^3=2(27)=54

And for day 10, x = 10. The number of shares Carter's post would have received on day 10 is given by- f(10)=2(3)^10=2(59,049)=118,098

2.

The exponential function representing the spread of Carter's social media post is given by-

f(x)=10(2)^x

Step-by-step explanation:

In the four levels of measurement : nominal,  interval, ordinal, ratio: "ordinal," is most appropriate for the given for positions of the persons standing in a line

Four degrees of measuring exist:

Thus, in the four levels of measurement : nominal,  interval, ordinal, ratio: "ordinal," is most appropriate.

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The complete question is-

determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for positions of persons in a line (extra?)

The numerical value of variable x must be known in order to calculate the partial effect on dummy variable d in a regression model with an interaction variable = b0 + b1x + b2d + b3xd. The assertion is accurate. given statement is true.

In order to determine the partial effect on the dummy variable d in a

regression model with an interaction term, the numeric variable x value

needs to be known.

This is because the coefficient for the interaction term  b3 represents the

change in the slope of the relationship between the  numeric variable x

and the dependent variable y, when the dummy variable  d is equal to 1.

Thus, in order to determine the partial effect of the dummy  variable d on

the dependent variable y, we need to know the value of the  numeric

variable x at which we want to evaluate this effect.

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Yes, according to the Central Limit Theorem, when the sample size is large enough (typically n ≥ 30), the sampling distribution of the sample mean tends to follow a normal distribution, regardless of the shape of the population distribution.

In this case, since the sample sizes are n = 33 and n = 66, which are both larger than 30, we can conclude that the sampling distribution of the sample mean will be approximately normally distributed.

To clarify, the Central Limit Theorem states that as the sample size increases, the distribution of sample means becomes increasingly close to a normal distribution, even if the population distribution is not normally distributed. This is a fundamental concept in statistics that allows us to make inferences about population parameters based on sample statistics.

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The formula you have given (SS₁ + SS₂) / (n₁+ n₂) is actually the formula for the unweighted average of the variances, which is not appropriate when the sample sizes and variances are different between the two samples.

The formula for pooled variance is:

pooled variance = (SS₁+ SS₂) / (df₁ + df₂)

where SS₁ and SS₂ are the sum of squares for the two samples, df₁ and df₂ are the corresponding degrees of freedom, and the pooled variance is the weighted average of the variances of the two samples, where the weights are proportional to their degrees of freedom.

Note that the denominator is df₁ + df₂ not n₁+ n₂. The degrees of freedom take into account the sample sizes as well as the number of parameters estimated in

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The intersection points of the equations represents; C: The time when the height of the ball and the bird are the same.

We are given;

The height of the baseball over time:

h = -16t² + 65t

The height of the bird over time:

h = 8t + 20

The intersection point will be the value of t when; 8t + 20 = -16t² + 65

Rearranging gives;

16t² + 8t - 45 = 0

Using online quadratic equation calculator gives us;

t = -1.94 s or t = 1.44 s

Now, since both equations measure height vs time, it means that the points of intersection tell us the time when the height of the ball and the bird are the same.

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Answer:

C: the time when the height of the ball and the bird are the same

Step-by-step explanation:

because i just took it on edge 2022.

Answer:

Approximately 85 m

Step-by-step explanation:

Let x represent the distance between the origination point and the target

Distance between original point and mirror 1 = 120 m

Distance between mirror 1 and mirror 2 = 90 m

The measure of angle Opposite the distance between the origination point and the target = 20 + 25 = 45°

Use Cosine rule to find x as shown below:

Use The Law of Cosines to find side a first:

\( a^2 = b^2 + c^2 - 2bc \times Cos(A) \)

Where,

a = x

b = 90 m

c = 120 m

A = 45°

Plug in the values

\( x^2 = 90^2 + 120^2 - 2(90)(120) \times Cos(45) \)

\( x^2 = 22,500 - 21,600 \times Cos(45) \)

\( x^2 = 22,500 - 15,273.5065 \)

\( x^2 = 7,226.4935 \)

Square both sides

\( x = \sqrt{7,226.4935} \)

\( x = \sqrt{7,226.4935} \)

x ≈ 85 m

Answer: AAAAAAA-85!!!!!

Step-by-step explanation:

Answer:

87 cm

Step-by-step explanation:

H = M + 51

H = 36 + 51

H = 87

The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

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Answer:

Let x = software program

Let y = video game

x < 200 ; y < 300

x + y < 425

50x ; 35y

x = 200 ; y = 225

50(200) + 35(225) = 10,000 + 7,875 = 17,875

x = 125 ; y = 300

50(125) + 35(300) = 6,250 + 10,500 = 16,750

x = 175 ; y = 250

50(175)  + 35(250) = 8,750 + 8,750 = 17,500

It is more profitable to maximize production of software program when working within the limits provided.

Step-by-step explanation:

The company should produce 175 software programs and 250 video games per week in order to maximize its profit.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Let the company can produce most p software programs and most q video games per week

So p < 200 and q < 300

Total production cannot exceed 425 items per week

So the constrain is p + q < 425

Given that company makes a profit of $50 per software program and $35 per video game

So 50p and 35q

For p = 200 and q = 225

⇒ 50(200) + 35(225) = 10,000 + 7,875 = 17,875

For p = 125 and q = 300

⇒ 50(125) + 35(300) = 6,250 + 10,500 = 16,750

For p = 175 and q = 250

⇒ 50(175)  + 35(250) = 8,750 + 8,750 = 17,500

Hence, the company should produce 175 software programs and 250 video games per week in order to maximize its profit.

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the lunch cost, including tax and tip 67.31$.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, the Patterson family went to eat lunch at a new restaurant. They spent $52.30 on their meal. The restaurant will add a 7 1/4% tax to the cost of the meal.

total cost after the tax = 52.30*(1 + 7 1/4)%

total cost after the tax = 52.30* 7.25/100 + 52.30

total cost after the tax = 3.79 + 52.30

total cost after the tax = 56.09

Since,

Mr Patterson was very happy with the food and service so he gave a 20% tip to the waitress.

Thus,

Total cost after the tip = 56.09(1 +20/100)

Total cost after the tip = 56.09 * 1.2

Total cost after the tip =  67.308

Therefore, the lunch cost, including tax and tip 67.31$.

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By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

From the given figure, KR=9 units, RL=15 units, MT=7.5 units and TL=12.5 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Consider ΔKML and ΔRTL, we get

RL/KL =15/(15+9)

= 15/24

= 5/8

TL/ML =12.5/(12.5+7.5)

= 12.5/20

= 5/8

Here, RL/KL=TL/ML

Here, ∠KLM≅∠RLT

By SAS similarity, ΔKML and ΔRTL are similar triangles

So, ∠KMT≅∠RTL

By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

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Answer:

a

Step-by-step explanation:

got it right in edmentum

The probability of selecting red balls from a bag containing both red and blue balls is equal to the number of red balls divided by the total number of balls. In this example, let's assume there are 10 red balls and 10 blue balls, so the probability of selecting a red ball would be 10/20 or 1/2, or 50%.

To explain further, the probability is the likelihood of an event occurring and is expressed as a number between 0 and 1, or a percentage between 0% and 100%. A probability of 0 means the event will never happen, while a probability of 1 means it will always happen. The probability of selecting a red ball in this example is 50%, meaning that it is equally likely to select either a red ball or a blue ball.

In other words, if the bag contained 10 red balls and 10 blue balls and you randomly selected one ball from the bag, there is a 50% chance that the ball will be red and a 50% chance that the ball will be blue.

If the number of red balls or blue balls changes, the probability of selecting a red ball would also change. For example, if the bag contained 6 red balls and 10 blue balls, the probability of selecting a red ball would be 6/16 or 3/8, or 37.5%.

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To multiply negative numbers, you need to remember the following rules:

- When you multiply two negative numbers, the result is a positive number. For example: (-3) * (-5) = 15

- When you multiply a positive number and a negative number, the result is a negative number. For example: 3 * (-5) = -15

- When you multiply two positive numbers, the result is a positive number. For example: 3 * 5 = 15


So, to multiply negative numbers, you just need to follow the rules above. Here's an example:


-3 * -5 * 2 * -4 = 15 * 2 * -4 = 30 * -4 = -120


The result is a negative number because you have an odd number of negative numbers being multiplied together. If you had an even number of negative numbers, the result would be a positive number.

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Answer: she could serve 8 people

Step-by-step explanation:

each guest wanted 1/8 so first she would have to make it into 8 equal parts then give each guest 1 slice of pie.

The probability that if Air America books 15 persons, there will be enough seats available is 0.913.

First of all, we would determine the probability that if Air America books 15 persons, there won't be enough seats available by using binomial distribution:

P(x = 15) = 0.85¹⁵

P(x = 15) = 0.087.

Based on logic, the probability that if Air America books 15 persons, there will be enough seats available is given by:

P = 1 - 0.087

P = 0.913.

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The amount of storage required to represent a simple graph with n vertices and m edges can vary depending on the chosen representation. Here's the storage requirement for each representation:

a) Adjacency lists:

In an adjacency list representation, we typically use an array of size n to store the vertices, and for each vertex, we maintain a linked list or an array to store its adjacent vertices. The space complexity of this representation is O(n + m), where n is the number of vertices and m is the number of edges.

Each vertex requires constant space, and each edge is represented by a link or entry in the adjacency list.

b) Adjacency matrix:

In an adjacency matrix representation, we use a 2D matrix of size n x n to represent the graph. Each entry (i, j) in the matrix represents whether there is an edge between vertices i and j. The space complexity of this representation is O(n^2), as we need to store n^2 entries for the complete matrix. However, if the graph is sparse (few edges compared to vertices), the space complexity can be reduced to O(n + m) by only storing the entries corresponding to the existing edges.

c) Incidence matrix:

In an incidence matrix representation, we use a 2D matrix of size n x m, where n is the number of vertices and m is the number of edges. Each entry (i, j) in the matrix represents whether vertex i is incident to edge j. The space complexity of this representation is O(n * m), as we need to store n * m entries for the matrix.

Similar to the adjacency matrix, if the graph is sparse, the space complexity can be reduced to O(n + m) by storing only the entries corresponding to the existing edges.

In summary:

a) Adjacency lists: O(n + m)

b) Adjacency matrix: O(n^2) or O(n + m) for sparse graphs

c) Incidence matrix: O(n * m) or O(n + m) for sparse graphs

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In the given right triangle ABC, with a right angle at vertex B and angles A and C measuring 45 degrees, the segment lengths are as follows:

Segment AB = Segment BC = 9 units

Segment AC = 9√2 units

Segment BD = 18 units

Segment CD = 9 units

We know that angles A and C are both 45 degrees in a right triangle ABC with the right angle at vertex B. The triangle ABC is therefore a 45-45-90 triangle.

The sides of a 45-45-90 triangle are arranged in the ratio 1:1:2. In this way, in the event that we mark the length of side Stomach muscle as x, the length of side BC will likewise be x, and the length of side AC (the hypotenuse) will be x√2.

Given that segment AD has a length of nine units in this instance, x = 9. As a result, both segments AB and BC have lengths of nine units.

We now know that segment CD has a length of nine units as well. Segment BD, the dashed segment extending from vertex B to point D, must also have a length of 9 units because segment BC has a length of 9 units. Consequently, section BD = 18 units.

To sum it up:

Segment AB consists of 9 units; segment BC of 18 units; segment AC of 92 units; and segment CD of 9 units.

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a) 2x(x - 5)First, we need to multiply 2x by x which will give us 2x² and then we multiply 2x by -5 which will give us -10x.

Finally, we add these products to get:2x(x - 5) = 2x² - 10x

Ans: 2x² - 10xb) (q² +3q) (2q- 3)

Here, we need to use the distributive property.

We can multiply q² by 2q, then q² by -3, then 3q by 2q, and then 3q by -3.

After multiplying, we can combine like terms.(q² +3q) (2q- 3)

= 2q³ - 3q² + 6q² - 9q

= 2q³ + 3q² - 9q

Ans: 2q³ + 3q² - 9qc) (3m² - 2m + 1)(5m-3)

We can use the distributive property to multiply (3m² - 2m + 1) by (5m-3).

We can multiply 3m² by 5m, then 3m² by -3, then -2m by 5m, then -2m by -3, then 1 by 5m, and finally 1 by -3.(3m² - 2m + 1)(5m-3)

= 15m³ - 9m² - 10m² + 6m + 5m - 3

= 15m³ - 19m² + 11m - 3Ans: 15m³ - 19m² + 11m - 3

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32 papers would Ashley have to remain to grade after working for 6 hours.

What is simplification?

Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Ashley is a teacher and takes home 98 papers to grade over the weekend.

She can grade at a rate of 11 papers per hour.

We have to calculate how many papers would Ashley has remaining to grade after working for 6 hours.

Based on the given conditions, formulate:: 98 - 11 × 6

Calculate the product or quotient: 98 - 66

Calculate the sum or difference: 32

Hence, 32 papers would Ashley have to remain for a grade after working for 6 hours.

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The number that is divisible by both 2 and 4 is option c. 2,836.

To determine which number is divisible by both 2 and 4, we need to identify the number that is divisible by the prime factorization of both 2 and 4.

To be divisible by 2, a number must be even, meaning it should end with 0, 2, 4, 6, or 8. Looking at the given options, we can eliminate options a. 1,022 and d. 2,918 because they end with 2 and 8 respectively.

To be divisible by 4, a number must be divisible by 2 twice. In other words, the last two digits of the number should form a multiple of 4. Examining the remaining options b. 1,974 and c. 2,836, we find that only option c. 2,836 satisfies this condition. The last two digits of 2,836, 36, form a multiple of 4 (9 times 4 is 36).

Therefore, the number 2,836 is divisible by both 2 and 4, hence the correct answer is: c.2,836

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24 hours takes all five machines to fill the same production order.

Given,

Four machines take 30 hours to fill a certain production order.

\(Rate = \frac{Work}{Time}\)

Let, Total work = 1 unit

The rate of 4 machines = \(\frac{1}{30}\)

We can let the rate of 5 machines be n and create the equation:

\(\frac{4}{\frac{1}{30} }=\frac{5}{n}\)

\(120=\frac{5}{n}\)

\(120n = 5\)

\(n=\frac{5}{120}\)

\(n=\frac{1}{24}\)

Time taken by five machines = \(\frac{1}{\frac{1}{24} }\)

Time is taken by five machines = 24 hours

Hence, 24 hours takes all five machines to fill the same production order.

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Answer:

Step-by-step explanation:

The answer is 48 feet because 4x6=24 and 24x2=48

Answer:

where is the graph

Step-by-step explanation:

Answer:

hyuh

Step-by-step explanation: