The GFC of 16 and 24 is ___.
Numerical answers expected!

Answer:

x = \(\frac{22}{5}\)

Step-by-step explanation:

Given

\(\frac{7+x}{3}\) = 2x - 5 ( multiply both sides by 3 to clear the fraction )

7 + x = 3(2x - 5) ← distribute

7 + x = 6x - 15 ( subtract x from both sides )

7 = 5x - 15 ( add 15 to both sides )

22 = 5x ( divide both sides by 5 )

\(\frac{22}{5}\) = x ( x = 4.4 )

The final itinerary will depend on your preferences, the specific national parks you plan to visit, and the distances between them.

Let's clarify the itinerary for the 15-day tour visiting 5 national parks.

You have a 15-day tour, and you plan to visit 5 national parks. Each park will have a stay of two days.

When you multiply the number of parks (5) by the number of days spent in each park (2), you get a total of 10 days allocated for staying in those 5 parks.

However, there seems to be a discrepancy in the calculation because allocating 10 days for park stays leaves only 5 days remaining, not 15.

To resolve this issue and ensure a 15-day tour, we need to reevaluate the itinerary. Let's assume you want to spend two days at each park, which gives you a total of 10 days for park stays.

To fill the remaining 5 days, you have a few options:

1. Travel Days: You can allocate a day for travel between each park, which would require an additional 4 days. This accounts for the transportation time and allows you to enjoy the journey between the parks.

2. Additional Park Visits: If there are other nearby national parks or attractions in the area, you can extend your tour to include visits to these places. This would allow you to explore more diverse locations and make the most of your 15-day tour.

3. Rest and Relaxation: Alternatively, you might choose to use the extra days for relaxation or leisure activities. You can spend some time enjoying the amenities and attractions available near the parks, such as hiking trails, wildlife observation, or local cultural experiences.

Ultimately, the final itinerary will depend on your preferences, the specific national parks you plan to visit, and the distances between them. Make sure to consider travel times, desired activities, and any additional locations you wish to explore when creating your 15-day tour.

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The correct answer is (a) standard deviation. The measure of central tendency that is NOT included among the given options is the standard deviation (a).

Measures of central tendency are statistical measures that represent the central or average value of a dataset. They provide insight into the typical or central value around which the data tends to cluster. The three commonly used measures of central tendency are the mean, median, and mode.

a. Standard deviation is not a measure of central tendency. It is a measure of dispersion or variability in a dataset. It quantifies how spread out the data points are from the mean. Standard deviation provides information about the spread or scatter of the data rather than representing a central value.

b. Median is a measure of central tendency that represents the middle value in a dataset when the data points are arranged in ascending or descending order. It divides the data into two equal halves.

c. Mean is a measure of central tendency that represents the arithmetic average of a dataset. It is calculated by summing all the data points and dividing by the total number of observations.

d. Mode is a measure of central tendency that represents the most frequently occurring value or values in a dataset. It identifies the value(s) that appear(s) with the highest frequency.

Therefore, the standard deviation (a) is the measure of central tendency that is NOT included among the given options.

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Step-by-step explanation:

The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.

On average, if the null hypothesis is false, the expected value for the F-ratio is much greater than 1.00.

The F-ratio is a statistic used in analysis of variance (ANOVA) tests to compare the variances between groups. In the context of hypothesis testing, the F-ratio measures the ratio of the variability between groups to the variability within groups. When the null hypothesis is false, it means that there is a significant difference between the groups being compared.

If the null hypothesis is false, it implies that there are systematic differences between the groups, resulting in larger variation between groups compared to within groups. This leads to a higher F-ratio value. The F-ratio is calculated as the ratio of the mean square between groups to the mean square within groups. As the differences between groups become more pronounced, the F-ratio increases, indicating a greater likelihood of rejecting the null hypothesis.

Therefore, if the null hypothesis is false, the expected value for the F-ratio is much greater than 1.00, indicating significant variability between groups.

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The distribution of the types of houses in the town is as follows:
- 25% of houses are Cape houses
- 35% of houses are Garrison houses
- 40% of houses are Split houses.

According to the given data, there are 22,000 houses in the town and they are classified into three types: Cape, Garrison, and Split. The frequency of Cape houses is 5,500, the frequency of Garrison houses is 8,800, and the frequency of Split houses is 7,700.

To find the percentage of each house type, we need to use the formula:

Percentage = (Frequency / Total number of houses) x 100

For Cape houses, the percentage is (5,500 / 22,000) x 100 = 25%
For Garrison houses, the percentage is (8,800 / 22,000) x 100 = 35%
For Split houses, the percentage is (7,700 / 22,000) x 100 = 40%

Therefore, the distribution of the types of houses in the town is as follows:
- 25% of houses are Cape houses
- 35% of houses are Garrison houses
- 40% of houses are Split houses.

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Answer:

See below ~

Step-by-step explanation:

Part 1 - Acceleration when t = 3

Part 2 - Deceleration when t = 12

Part 3 - Total Distance Covered

    2. From t = 4 to t = 8

    3. From t = 8 to t = 15

Total distance = 66 + 88 + 77 = 231 m

Part 4 - Average Speed

    2. Avg. Speed (t = 4 to t = 8)

    3. Avg. Speed (t = 8 to t = 15)

Average Speed = 16.5 + 22 + 11 / 3

Answer:

(5,-6)

Step-by-step explanation:

The solution to the system is the coordinate where the two lines intersect/cross

The lines intersect at (5,-6)

Therefore (5,-6) is the solution

The constant a should be chosen in such a way that cov(θˆ1, θˆ2) is minimized to reduce the variance of θˆ3.

In statistics, the variance of a linear combination of random variables can be affected by the covariance between those variables. In this case, we have θˆ1 and θˆ2, which are not independent but are related by their covariance, cov(θˆ1, θˆ2).

To minimize the variance of θˆ3, we need to minimize the covariance term cov(θˆ1, θˆ2). The covariance measures the extent to which θˆ1 and θˆ2 vary together, and it can be positive, negative, or zero.

To minimize cov(θˆ1, θˆ2), we should choose the constant a in a way that reduces the dependence or relationship between θˆ1 and θˆ2. This can be achieved by selecting a value of a that makes the covariance as close to zero as possible. By doing so, the contribution of the covariance term to the variance of θˆ3 will be minimized.

Therefore, the constant a should be chosen to minimize the covariance between θˆ1 and θˆ2, thus reducing the variance of θˆ3.

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Answer:

13

Step-by-step explanation:

3(-2)^2-2(-1)

3(4)+2

12+1

13

A) Where the calibration of the graph represents a unit each, the approximate coordinates of the points  of intersection of the two graphs is (4.5, 3)

This means that after after a given number of days, the area covered by both types of mold were the same.

b) given the function, the number days it takes for the mold to cover 1000 square millimeters is 46 days.

A) this is observed by exploring the graph.

b) Let A(d) = 1000
⇒ 1000 = 100 x \(e^{0.05d}\)

If we divide both sides by 100 to simplify, we will get

\(e^{0.05d}\) = 10

To solve for d we need to compute the natural log of both sides, so we get

ln \(e^{0.05d}\) = ln (10)

Recall that ln (eˣ) = x so

ln \(e^{0.05d}\) = ln (10)

⇒ 0.05d = ln (10)

Divide both sides by 0.05

d = ln10/0.05

d = 2.30258509299/0.05

d = 46.0517018599

d ≈ 46 days.

thus,

it will take about 46 days for the mold to cover 1000 millimeters.

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Answer:

The fraction is 3/10 = .3

Answer:

$5 × 2 × (26 + 25) = $5 × 2 × 51 = $5 × 102

= $510

B is the correct answer.

Answer:

The speed of the boat in still water is 33 km/h

Step-by-step explanation:

Let us denote the speed of the boat in still water as x km/h.

Thus;

Since the speed of the stream is 3 km/h, then while going downstream, the total speed on the boat would be; (x + 3) km/h

Formula for distance = speed x time

Since we are told that the time taken to cover the distance downstream is 5 hours, then;

Distance covered in 5 hours = 5(x + 3) km

Therefore, distance between A and B is 5(x + 3) km

However, while going upstream the boat will work against the water current.

Therefore, its speed upstream will be (x − 3) km/h.

we are told that the time taken to cover the distance downstream is 6 hours, then;

Distance covered in 6 hours = 6(x − 3) km

Therefore, distance between A and B is 6(x - 3) km

The true distance between A and B has to be the same.

So,

5(x + 3) = 6(x - 3)

This gives;

5x + 15 = 6x - 18

15 + 18 = 6x - 5x

x = 33

Therefore, the speed of the boat in still water is 33 km/h

Answer:

Solutions below.

Step-by-step explanation:

This Question involves the concept of Function Substitution.

Function Substitution - As the name suggests, it is about substituting an input value (normally x) to find the value of y , or f(x) which is the range of the value.

Example: f(x) = 98x , f(2) = 98(2) = 196

We are given the following function:

\(p(t) = - 16 {t}^{2} + 1638\)

a) This part is asking us to find the height of the object when t = 2, which is the same as finding the value of P(2).

P(2) =

\( - 16 {(2)}^{2} + 1638 \\ = - 64 + 1638 \\ = 1574\)

Therefore at t = 2 seconds, the object is 1,574m above the river.

b) This part is asking us to find the height of the object when t = 6, which is the same as finding the value of P(6).

P(6) =

\( - 16 {(6)}^{2} + 1638 \\ = - 16(36) + 1638 \\ = - 576 + 1638 \\ = 1062\)

Therefore at t = 6 seconds, the object is 1,062m above the river.

The area of the given symmetrical figure will be 30 cm².

The area of a rectangle is given by -

A{R} = L x B

or

A{R} = Length x Breadth

Given is a symmetrical figure shown in the image.

We will divide the figure in 5 parts. Of these five parts, four are rectangles and one is square.

So, the total area of the figure will be -

A{T} = A{R1} + A{R2} + A{R3} + A{R4} + A{S}

A{T} = (5 x 2) + (3 x 2) + (2 x 3) + (2 x 2) + (2 x 2)

A{T} = 10 + 6 + 6 + 4 + 4

A{T} = 30 cm²

Therefore, the total area of the figure given will be 30 cm².

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Thus, the magnitude of value of |a+b| is Sqrt (9), which simplifies to just 3.

To find the magnitude of the sum of two vectors, we need to add the two vectors together and then take the square root of the sum of their squares.

So, let's first add the two vectors together:

a+b = (3i+4j-4k) + (-2i-6j+2k)
    = i - 2j - 2k

Now, we can find the magnitude of this vector by squaring each of its components, summing them, and then taking the square root:

|a+b| = sqrt((1^2) + (-2^2) + (-2^2))
     = sqrt(1 + 4 + 4)
     = sqrt(9)
     = 3

Therefore, the value of |a+b| is Sqrt (9), which simplifies to just 3.

In summary, the magnitude of the sum of two vectors can be found by adding the vectors together, squaring each of their components, summing them, and then taking the square root.

For the given vectors a=3i+4j-4k and b=-2i-6j+2k, their sum is i - 2j - 2k, and the magnitude of this vector is 3.

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The probability that the first three flips come up heads or the last three flips come up tails is 1/4. Hence the answer is 1/4.

The probability of obtaining heads or tails on each single fair coin flip is 1/2. Because the coin flips are independent, the chance of obtaining a certain sequence of heads and tails is the product of the probabilities of each flip.

We want to know what the probability is that the first three flips will be heads, the last three flips will be tails, or both. This can occur in two ways:

Heads for the first three flips: (1/2) x (1/2) x (1/2)

P(H) = 1/8

The final three flips are all tails: (1/2) x (1/2) x (1/2)

P(T) = 1/8

Because these two occurrences are mutually exclusive, we may combine their probabilities to get the total:

P(H) + P(T) = 1/8 + 1/8 = 1/4

So the probability that the first three flips come up heads or the last three flips come up tails (or both) is 1/4.

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Answer:

My causins name is David but we also call him davy

Answer:

3(x + 6)/18

= x + 6 /6

Step-by-step explanation:

hope this helps you

The following examples are shown below:

In this problem we have to present five types of real numbers, which are defined and shown below:

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Answer:

Use the formula of Range Large-Small Data

I think it will help you.

Answer:

\(7-8x+4y=-21\)

Step-by-step explanation:

\(2x-y=7 \implies 8x-4y=28 \\ \\ \implies 7-8x+4y=7-28=-21\)

Answer:

Quota Sampling

Step-by-step explanation:

Quota Sampling is a non-probability sampling method in research, where the researcher forms subgroups of individuals who are representative of the entire population through random selection. Quota sampling is often used by researchers who want to get an accurate representation of the entire population. It saves time and money especially if accurate samples are used.

In the example given above, where the research creates subgroups of 30 pre-school children by dividing them into 10 two-year-old children, 10 three-year-old, and 10 four-year-old children, he has applied the quota sampling.  These subgroups would give a proper representation of the preschool children in local daycare centers.

A 11.544 acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3). So, correct option is C.

To solve the problem, we need to integrate the given rate of melting with respect to time over the interval [0,3] to find the total amount of ice that melts during this time.

First, we can simplify the given rate of melting by using the identity: sin³(t) = (3sin(t) - sin(3t))/4

So, M(t) = 4 - (3sin(t) - sin(3t))/4 = 16/4 - 3sin(t)/4 + sin(3t)/4 = 4 - 0.75sin(t) + 0.25sin(3t)

Integrating this expression with respect to t over the interval [0,3], we get:

\(\int\limits^3_0\) M(t) dt = \(\int\limits^3_0\) (4 - 0.75sin(t) + 0.25sin(3t)) dt

= [4t + 0.75cos(t) - (1/3)cos(3t)]|[0,3]

= (12 + 0.75cos(3) - (1/3)cos(9)) - (0 + 0.75cos(0) - (1/3)cos(0))

= 11.544

Therefore, the answer is (C) 11.544.

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The equivalent expression of the expression \(\sqrt[4]{\frac{16x^{11}y^{8} }{81x^{7}y^{6} } }\) is \(\frac{2}{3}\sqrt[x]{y}\)

What is equivalent expression?

The expression is given as-

\(\sqrt[4]{\frac{16x^{11}y^{8} }{81x^{7}y^{6} } }\)

Take the 4th root of 16 and 81

\(\frac{2}{3} \sqrt[4]{\frac{x^{11} y^{8} }{x^{7}y^{6} } }\)

Apply the law of indices

\(\frac{2}{3}\sqrt[4]{x^{11 - 7} y^{8 - 6} }\)

Evaluate the difference

\(\frac{2}{3}\sqrt[4]{x^{4}y^{2} }\)

Take the 4th root of y^2

\(\frac{2}{3}x\sqrt{y}\)

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Answer: The mean will increase and the median would not change

Step-by-step explanation:

Recorded data by Priya :

Data: 1,8,6,2,4

Mean of data = (1+8+6+2+4)/5

=21/5 = 4.2

Median of data = 1,2,4,6,8

Median = 4

Correct data: 1,18,6,2,4

Mean of data = (1+18+6+2+4)/5

=31/5 = 6.2

Median of data = 1,2,4,6,18

Median = 4

Therefore ; according to the evaluation above, the median will remain unchanged, but the mean increased from 4.20 to 6.20.

Answer:

a). y = 3/2x - 3/4    b).-2/3       c).y = -2/3x + 3

Step-by-step explanation:

a). 6x – 4y = 3

-4y = -6x + 3

y = 3/2x - 3/4

 - The slope is 3/2.

b). The slope of a perpendicular line would be the opposite: -2/3

c). y = -2/3x + b

-1 = -2/3(6) + b

-1 = -4 + b

3 = b

y = -2/3x + 3

The answer that describes the polygon RSTU is as follows:

A quadrilateral is a polygon with 4 sides. Therefore, let's use the properties to find the name of the shape  RSTU as follows:

The polygon has 4 sides therefore, it is a quadrilateral.

The quadrilateral has opposite side parallel to each other. The opposite sides are RS and TU.

A trapezoid is a quadrilateral with only one pair of opposite side parallel to each other.

Therefore, the shapes that defines the polygon are as follows:

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Answer:

f(8) = 44

Step-by-step explanation:

Simply plug in 8 for x:

f(8) = 6(8) - 4

f(8) = 48 - 4

f(8) = 44