Dylan, eli and fabian share some sweets.
the amount of sweets dylan gets to the amount of sweets eli gets is in the ratio 7:3
the amount dylan gets to the amount fabian gets is in the ratio 4:5
given fabian gets 21 more sweets than dylan.
work out how many sweets eli gets.

System developers can initiate a formal project as early as the preliminary investigation stage, or later on, as analysis, design, and implementation activities occur. True.

System developers can initiate a formal project as early as the preliminary investigation stage or at any point in the analysis, design, and implementation activities.

The decision to initiate a formal project depends on various factors, including the scope of the project, the availability of resources, the complexity of the system, and the stakeholders' needs and requirements. A formal project may involve a team of developers, analysts, and other experts who work collaboratively to design and implement a system that meets the stakeholders' requirements and objectives.

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True. System developers can initiate a formal project as early as the preliminary investigation stage or later on as

analysis, design, and implementation activities occur.

The initiation stage is when the need for a new system is identified, and preliminary investigations are conducted to

determine the feasibility of the project.

If the project is deemed feasible, the formal project can be initiated at this stage.

However, if the project is initiated later on, the analysis, design, and implementation activities will have already begun.

System developers can initiate a formal project as early as the preliminary investigation stage or later on as

analysis, design, and implementation activities occur. therefore, the given statement is true.

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the exact formula for X(n) is given by the sum of i from 1 to 4n + 1. The closed-form formula for X(n) is (4n + 1)(4n + 2)/2, expressed as a polynomial function. The asymptotic value of X(n) is approximately 4n^2, representing the growth rate as n approaches infinity.

(i) The exact formula for X(n) can be determined by analyzing the procedure PrintXs(n) and counting the number of times the letter "X" is printed. In this case, the outer loop runs for 4n + 1 iterations, and for each iteration, the inner loop runs i times. Thus, the total number of "X" letters printed is given by the sum of i from 1 to 4n + 1.

(ii) To express X(n) as a closed-form polynomial function, we can simplify the sum mentioned above. By using the formula for the sum of an arithmetic series, the closed-form formula for X(n) can be written as X(n) = (4n + 1)(4n + 2)/2.

(iii) The asymptotic value of X(n) can be expressed using the e-notation, which represents an estimate of the growth rate. In this case, as n approaches infinity, the dominant term in the expression (4n + 1)(4n + 2)/2 is 4n^2. Therefore, we can express the asymptotic value of X(n) as X(n) ~ 4n^2.

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The equation is a linear combination of three angles that add up to 180°, he might consider using systems of linear equations or other algebraic methods to solve for the variables.

given that za + 2d + g = 180°, some observations that could potentially be useful to Jason include:

Identifying any relationships or constraints between the variables za, d, and g that might help him simplify or solve the equation. For example, if he knows that za and g are complementary angles (i.e., they add up to 90°), he could substitute 90 - za for g in the equation to get a new expression in terms of za and d.

Using additional information about the angles or the situation to derive new equations or constraints that could help him solve for one or more variables. For example, if he knows that za and d are equal (i.e., za = d), he could substitute za for d in the equation to get a new expression in terms of za and g.

Identifying any patterns or structures in the equation that might suggest a particular approach or technique for solving it. For example, if he notices that the equation is a linear combination of three angles that add up to 180°, he might consider using systems of linear equations or other algebraic methods to solve for the variables.

Ultimately, the most effective observations for completing the proof will depend on the specific details of the problem and the approach that Jason is taking.

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The complete question:Jason knows that za + 2d + g = 180°. Which of the following observations, if true, would allow him to prove a statement or theorem related to the angles za, d, and g?

Step-by-step explanation:

(3x-2/x)^10

(r+1)th term = 10Cr (3x)^10-r (-2/x)^r

= 10Cr (3)^10-r (-2)^r (x)^10-2r

Let 10-2r = 12

- 2r = 2

r= - 1

The coefficient of x^12

= 10C-1 (3)^11 (-2)^-1

= 10C11 (3)^12 (-1/2)

= (1/11) (3)^12 (-1/2)

= - 1/22 × (3)^12

Answer:

It is false

Step-by-step explanation:

Answer: See explanation

Step-by-step explanation:

Point slope formula = y - y₁ = m (x - x₁)

y - 4 = 7 (x + 2)

y - 4 = 7x + 14

Add 4 to both sides

y = 7x + 18

↑This is also the slope intercept form (y = mx + b)

Hope this helped!

Answer:

x=-11

Step-by-step explanation:

-2(x+3)+5x: 3x-6

-2(x+3): -2x-6

=-2x-6+5x

-2x-6+5x: 3x-6

3x-6=-39

Add 6 to both sides

3x-6+6=-39+6

Simplify

3x=-33

x=-11

Answer:

angle 1 and 8 - neither

Step-by-step explanation:

angle 2 and 4 - vertical pair

where r u from btw ?

Answer:87.5%

Step-by-step explanation:

Given

Henry received \(\frac{7}{8}\) of the votes in the election

i.e. 7 parts of votes are in favor of Henry out of 8

In terms of percentage, it is  given by

\(\Rightarrow \dfrac{7}{8}\times 100=87.5\%\)

Answer:

The ratio of the areas would be the ratio of the side lengths squared.

Say the ratio of the side lengths is 1:2, the ratio of the areas would be 1:4. If the ratio of the sides were 2:3, the ratio of the areas would be 4:9.

Hope this helps

The work required is 1,200 ft-lb (foot-pounds).

To calculate this, we will first calculate the total weight of the rope and bucket. The rope weighs 100 lb and the bucket weighs 50 lb, so the total weight is 150 lb.

Then, we will calculate the work needed to lift the rope and bucket 12 ft. Work is equal to force multiplied by distance, so the work required is equal to 150 lb multiplied by 12 ft, which is 1,800 ft-lb.

Since we have to lift the rope and bucket up 12 ft, we have to do 1,800 ft-lb of work. However, since the rope is already 20 ft, we have to do only 1,200 ft-lb of work, since the rope has already been lifted 20 ft.

Therefore, the total work needed to lift the rope and bucket up 12 ft is 1,200 ft-lb.

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a) The size of each payment = $8718.4

b) The the total amount paid for the purchase = $204620.8

c) The total interest paid over the life of the loan = $104620.8

In this question we have been given that a man buys a house for $175,000. He makes a $75,000 down payment and amortizes the rest of the debt with semiannual payment sover the next 10 years. The interest rate on the debt is 12%, compounded semiannually.

We need to find the size of each payment, the total amount paid for the purchase and the total interest paid over the life of the loan.

From given data we get 175,000 - 75,000 = $100,000 amount to finance.

We know that the formula for semiannual payment of a loan,

C = PV/[1 - (1 + r)^-t / r]

Here, PV = $100,000

t = 20 (10 years times 2 payment per year)

r = 0.06 (12% annual. so, we divide by 2 to get semiannual)

So, C = 100,000/[1 - (1 + 0.06)^-20 / 0.06]

C =  100,000/[0.6882 / 0.06]

C = 100,000/11.47

C = $8718.4

The total interest paid will be the cuota times the time of the loan:

Total interest paid:

8718.4 x 12 = 104620.8

And the total amount paid over the life of the loan = 104620.8 + 100,000

                                                                                    = $204620.8

The interest will be the difference between the total amount paid and the principal of the loan

Therefore, Interest paid = $8718.4

total payment   = $204620.8

principal = $100,000

Interest expense = $104620.8

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Answer:

1/n3

Step-by-step explanation:

its the third one

g(0) is equal to -9, and h⁻¹(x) is equal to (x + 13)/2. The given function g is defined by a set of ordered pairs, where each input (x) corresponds to a unique output (g(x))

Let's break down the explanation further. The given function g is defined by a set of ordered pairs, where each input (x) corresponds to a unique output (g(x)). In this case, we have g = {(-9, 4), (-3, 2), (0, -9), (6, 0)}. To find g(0), we look for the input value 0 in the set g. From the given set, we see that when x = 0, g(x) = -9. Therefore, g(0) is equal to -9.

Next, h(x) is a separate function defined algebraically as 2x - 13. To find the inverse of h, denoted as h⁻¹(x), we need to swap the roles of x and h(x) and solve for x. So we have x = 2h(x) - 13. Let's rearrange this equation to isolate h(x): h(x) = (x + 13)/2. Therefore, h⁻¹(x) is equal to (x + 13)/2.

In conclusion, g(0) is -9, and h⁻¹(x) is (x + 13)/2.

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Answer:

x = -25.

Step-by-step explanation:

If f(x) = 2x + 1, and g(x) = -5x + 2, then f(g(x)) = 2(-5x + 2) + 1 = -10x + 4 + 1 = -10x + 5.

f(g(x)) = -10x + 5, and x = 3.

-10 * 3 + 5

= -30 + 5

= -25.

Hope this helps!

Answer:

The study, The Nature of Americans National Report, found that more than half of adults reported spending five hours or less in nature each week, and being satisfied with this small amount of time spent outdoors.

Step-by-step explanation:

The margin of error in the report is 2.39.

The margin of error is a statistic that describes how much random sampling error there is in survey data.

Given that, the upper interval is 24.96 and the lower interval is 20.18.

The margin of error is half of the difference between the upper and the lower interval.

Therefore, the margin of error is:

Margin of error = (24.96 - 20.18)/2

                        = 4.78/2

                        = 2.39

Hence, the margin of error in the report is 2.39.

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The surface area of a regular pyramid can be calculated using the formula: Surface Area = base area + lateral area. To find the base area, we need to determine the shape of the base.

In the given case, the base shape is not specified, so we cannot determine the surface area without additional information. To calculate the surface area of a regular pyramid, we need to consider the base area and the lateral area.

The base area depends on the shape of the base, which is not provided in the given information. Without knowing the shape of the base, we cannot calculate the base area. The lateral area depends on the slant height and perimeter of the base, which are also not provided.

Therefore, without further information, we cannot determine the surface area of the given regular pyramid.

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The farmer wants a rectangular area enclosed and only needs a fence on three sides then the dimensions for the maximum area, the length will be 150 meters and the width will be 75 meters.

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the data in the question,

Let the width of the rectangle is x.

For both sides, it will be 2x.

So, the length will be,

(300 - 2x)

For maximum area,

A(x) = 300x - 2x²

A'(x) = 300 - 4x

Critical point A'(x) = 0

300 - 4x = 0

4x = 300

x = 75

So, the width of the rectangle is 75 meters and,

length  = (300 - 2x)

length = 300 -150

length = 150 meters.

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Answer:

-18/7

Step-by-step explanation:

When subtracting a negative, the sign becomes positive, so now the equation would be -3 2/7 + 5/7.

By turning -3 2/7 into an improper fraction, you would get -23/7 + 5/7.

-23 +5 = -18 so -18 would be the numerator over the denominator (7) equals -18/7

The engineer measuring the western rod with a sample size of 20 is expected to have a more precise (narrower) confidence interval compared to the engineer measuring the eastern rod with a sample size of 25.

The engineer who measures the length of the western rod 20 times and calculates the average is expected to have a more precise (narrower) confidence interval compared to the engineer who measures the length of the eastern rod 25 times.

In statistical terms, the precision of a confidence interval is influenced by the sample size. The larger the sample size, the more precise the estimate tends to be. In this case, the engineer measuring the western rod has a sample size of 20, while the engineer measuring the eastern rod has a sample size of 25. Since the sample size of the western rod is smaller, it is expected to have a narrower confidence interval and therefore a more precise estimate of the true length of the rod.

A larger sample size provides more information and reduces the variability in the estimates. It allows for a more accurate estimation of the population parameter. Therefore, the engineer with a larger sample size is likely to have a more precise interval.

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Circumference of circle is 2πr

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter. A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14). How do you calculate a circle's circumference? The circle's radius is necessary to calculate the circumference: To calculate the diameter, multiply the radius by two. Divide the outcome by, or an estimate of 3.14. You have now successfully determined the circle's circumference.

Given,

Radius - r

Circumference of circle:

2πr

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a) At least 95% of the boxes contain 390 or more working devices if k = 390.

This can be determined using the cumulative distribution function (CDF) of a binomial distribution. The CDF gives the probability that a random variable is less than or equal to a certain value.

In this case, the random variable is the number of working devices in a box and the value is 390. The CDF can be calculated using a binomial calculator or approximated using a normal distribution with the same mean and variance.

The result is the probability that at least 390 devices work in a box, which is approximately 95%.

b) The largest k such that at least 95% of the boxes meet the warranty is 396.

To determine this value, we need to find the largest k such that the CDF of the binomial distribution is greater than or equal to 0.95. This can be done by solving for k in the equation CDF(k) = 0.95, or by using a binomial calculator to find the k that gives a probability closest to 0.95.

The result is k = 396, which means that if 396 or more devices per box work, at least 95% of the boxes will meet the warranty.

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The probability that the number selected is the square of a natural number will be  \(\frac{1}{5}\).

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.

Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

P is the probability

F(E) is the favorable event

T(E)is the total event

The probability is found as;

\(\rm P = \frac{F(E)}{T(E)} \\\\ \rm P = \frac{4}{20)} \\\\ \rm P = \frac{1}{5}\)

Hence the probability that the number selected is the square of a natural number will be  \(\frac{1}{5}\).

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Answer:

Option D is the correct answer

Step-by-step explanation:

D. \(\frac{1}{5}\)

When an aabbccddeeff individual is crossed with an individual with the genotype aabbccddeeff, the probability that their offspring will have the genotype aabbccddeeff would be 1/64.

The genotype of an organism refers to the complete set of genetic material. An offspring's genotype is the result of the combination of genes from their parents.  In order to obtain the overall probability, individual probabilities for each locus will be multiplied. The Parent cross would be AABbccDdEeFF x AaBBCCDdEeff and offspring would be AaBbCcddEEFf.

Multiplying all the probability:

½ * ½ * 1 * ¼ * ¼ * 1 = 1/64

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The radius of the circle with a central angle of 261 degrees that intercepts an arc with a length of 5 miles is approximately 2.184 miles.

To find the radius of a circle with a central angle of 261 degrees that intercepts an arc with a length of 5 miles, we can use the formula relating the central angle, arc length, and radius of a circle.

The formula is given as: Arc Length = (Central Angle / 360 degrees) * (2π * Radius)

In this case, we are given the central angle (261 degrees) and the arc length (5 miles), and we need to solve for the radius.

Rearranging the formula, we have: Radius = (Arc Length / (Central Angle / 360 degrees)) * (1 / 2π)

Substituting the given values into the formula, we get: Radius = (5 miles / (261 degrees / 360 degrees)) * (1 / 2π)

Simplifying further, we have: Radius = (5 miles / 0.725) * (1 / 2π)

Finally, evaluating the expression, we find the radius of the circle to be approximately 2.184 miles.

Therefore, the radius of the circle with a central angle of 261 degrees that intercepts an arc with a length of 5 miles is approximately 2.184 miles.

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Answer:

The rule used to reflect Δ ABC to its image is Reflect over y = x ⇒ B

Step-by-step explanation:

From the given figure

∵ The coordinates of point A are (-4.5, 6)

∵ The coordinates of point A' are (6, -4.5)

→ The coordinates are switched ⇒ 3rd rule

∴ Point A is reflected over the line y = x

∴ Δ ABC is reflected over the line y = x

∴ The rule used to reflect Δ ABC to its image is Reflect over y = x

Note: Point B' on the graph should be C' and point C' should be B' (correct it)

Answer:

y = 1/2x - 4.

Step-by-step explanation:

The slope of the line shown is

= (4-1) / (4 - (-2))

= 3/6

= 1/2.

Therefore, the slope of the required line has slope of 1/2 also as it is parallel to the given line.

Using the point-slope form of a line y - y1 = m(x - x1):-

y - (-3) = 1/2(x - 2)

y + 3 = 1/2x - 1

y = 1/2x - 4   (answer).

The final Table will look like this:x1x2s1s2s3RHS 1 0 0 7/6 -11/6 29/6 0 1/2 0 -1/6 2/3 29/6 0 0 -1/2 1/6 5/3

Linear Programming (LP) is a method of optimising an objective function subject to a set of constraints using linear equations.

In this problem, we are required to maximise z=3x1+5x2 subject to three constraints.

We will use the Simplex Method to solve this problem.

Here are the steps to solve this problem using the Simplex Method :

Step 1: Convert the inequalities into equalities by adding slack variables. The standard form of the problem will look like this:

max z = 3x1 + 5x2subject tox1 + 0x2 + s1 = 42x1 + 0x2 + s2 = 123x1 + 2x2 + s3 = 18 where s1, s2, and s3 are the slack variables.

Step 2: Write the initial tableau and compute the relative profits of each variable. The relative profit is the ratio of the objective function coefficient to the coefficient of the variable in the row of the pivot column. The pivot column is the one with the most negative relative profit.x1x2s1s2s3RHS 1 0 1 0 0 42 0 0 1 0 12 3 5 0 0 0 0

Step 3: Select the pivot element. The pivot element is the smallest positive number in the RHS column. In this case, it is 12. The pivot row is the one with the smallest non-negative ratio of the RHS to the coefficient of the pivot element. In this case, it is row 3, since 18/2 is smaller than 42/1 or 12/0. The pivot element is 2. We divide row 3 by 2 to make the pivot element 1.3x1 + 2x2 + s3 = 18/2 = 9/2x1 x2 s1 s2 s3 RHS 1 0 1/2 0 -1/4 9/4 0 0 1/2 1 0 21/2 0 0 -3/2 0 1 -1/2 0 15/2

Step 4: Perform row operations to make the other elements in the pivot column zero. We subtract 2 times row 1 from row 3 to make the s1 element zero.3x1 + 2x2 + s3 = 9/2-2x1 + 0x2 - s1 = -2x2 = 3/2 - (1/2)s3x1 x2 s1 s2 s3 RHS 1 0 1/2 0 -1/4 9/4 -2 0 -1/2 1 1/2 3 0 0 3/2 1 0 1/2 0 -3/2

Step 5: Repeat steps 3 and 4 until there are no more negative elements in the RHS column or the objective function cannot be further maximized. In this case, the solution is z=29 at (x1, x2) = (3, 3/2).

The final table will look like this:x1x2s1s2s3RHS 1 0 0 7/6 -11/6 29/6 0 1/2 0 -1/6 2/3 29/6 0 0 -1/2 1/6 5/3

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