Which is better value for money?
400 ml can of lemonade for 60p
or
2.5 litre bottle of lemonade for £3.60.

Answer:

1st and 2nd option are the correct answers.

Answer:

\(Cost \ total= \$ 1755\)

Step-by-step explanation:

Find the total cost of a rectangular shaped carpet, given the carpets length,  width, and the cost of carpet per square foot. Using the formula for the area of a rectangle.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Area of a Rectangle:}}\\\\A=l \times w\end{array}\right}\)

Where...

Given:

\(l=15 \ ft\\w=9 \ ft\\ 1 \ ft^2= \$ 13\)

Find:

\(Cost \ total = \ ?? \\)

(1) - Calculating the total area of the carpet, which is a rectangle

\(A=l \times w\\\\\Longrightarrow A=15 \ ft \times 9 \ ft\\\\\therefore \boxed{A=135 \ ft^2}\)

(2) Calculate the total cost of the carpet by multiplying the total area of the carpet by the cost of one square foot of carpet

\(Cost \ total=135 \ ft^2 \times \$ 13\\\\\therefore \boxed{\boxed{Cost \ total= \$ 1755}}\)

Thus, the total cost of the carpet is found.

A linear-time algorithm that can be used to find the number of paths from s to t in a DAG G = (V, E) is the dynamic programming algorithm.

This algorithm works by computing the number of paths from s to each vertex in the graph, and then using this information to compute the number of paths from s to t.

The steps of the algorithm are as follows:

1. Initialize an array P of size |V|, where P[i] represents the number of paths from s to vertex i.

2. Set P[s] = 1, since there is exactly one path from s to itself.

3. For each vertex u in the graph, in topological order: a. For each edge (u, v) in the graph: i. Add P[u] to P[v], since any path from s to u can be extended to a path from s to v.

4. Return P[t], which is the number of paths from s to t. The algorithm runs in O(|V| + |E|) time, since it iteratively processes each vertex and edge in the graph. Therefore, it is a linear-time algorithm.

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The correct answer is option A which is y = 25x + 100.

Given the following:

To join a local square dancing group, Jan has to pay a $100 sign-up fee plus $25 per month

We need to write an equation for the cost (y) based on the number of months.

To solve the above problem, the answer is;a. y = 25x + 100

Explanation; Let's break down the problem

The $100 sign-up fee is a fixed cost that is added only once to the monthly fee which is $25. Thus the equation for the cost (y) based on the number of months can be expressed as; y = 25x + 100 where:y is the cost for the number of monthsx is the number of months

Therefore the correct answer is option A which is;y = 25x + 100.

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To join a local square dancing group,

Jan has to pay a $100 sign-up fee plus $25 per month.

The equation for the cost (y) based on the number of months is

y = 25x + 100,

where x is the number of months.

Option A is the correct equation for the cost based on the number of months.

Writing the equation:

y = 25x + 100

Where:

y = Cost based on the number of months

x = Number of months

Therefore, when Jan has been part of the local square dancing group for 1 month, the total cost will be:

$25 * 1 + $100 = $125

And if Jan has been a part of the group for 4 months, then the total cost would be:

$25 * 4 + $100 = $200

Therefore, option A is the correct answer.

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Answer:

x < 63

Step-by-step explanation:

Using the half-angle identities, the exact value of cos(5ϕ/12) can be expressed as (√2 + √6 + √3 + 1)/(4√2).

To find the exact value of cos(5ϕ/12) using the half-angle identities, we start by considering the half-angle formula for cosine:

cos(ϕ/2) = ±√[(1 + cosϕ)/2]

In this case, ϕ = 5ϕ/12, so we have:

cos(5ϕ/24) = ±√[(1 + cos(5ϕ/12))/2]

To determine the sign, we need to examine the quadrant in which 5ϕ/12 lies. Since the coefficient of ϕ is 5, it lies in the first quadrant (0 < 5ϕ/12 < π/2), so we take the positive sign.

Next, we can rewrite cos(5ϕ/12) as:

cos(5ϕ/12) = √[(1 + cos(5ϕ/6))/2]

Using the exact values of cos(π/6) = √3/2 and cos(π/4) = √2/2, we can further simplify:

cos(5ϕ/12) = √[(1 + (√2/2))/2] = (√2 + √6 + √3 + 1)/(4√2)

Therefore, the exact value of cos(5ϕ/12) is (√2 + √6 + √3 + 1)/(4√2).

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Answer:

5.4 feet

Step-by-step explanation:

Answer:

like terms require the variables to be the same. 3y,y 4y are like terms because they all have y in common. 3y,3x,3xy are not like terms because the variable is not the same.

Answer:

-4+3x/2

Step-by-step explanation:

Answer:

both the second and third one

Answer:

U can put other values also.....

Hope it helps you.......

DM is congruent to line CM because CDM is congruent to triangle CBM using the SAS congruence criteria for triangles.

Draw a diagram of the rectangle ABCD with M as the midpoint of AB. Draw lines CM and DM ( refer to the attached image). Since AB is a line segment, we know that AM is congruent to MB (because M is the midpoint of AB). Since ABCD is a rectangle, we know that AB is parallel to CD, and AD is parallel to BC. Thus, we have two pairs of parallel lines: AB and CD, and AD and BC.

Using the fact that opposite sides of a rectangle are congruent, we have CD = AB. Now, we have a pair of congruent sides (DM and CM) that are opposite each other in triangle CDM and CBM respectively. We also have another pair of congruent sides (CD and AB) that are opposite each other in both triangles. Finally, we know that the angle CMD is congruent to the angle CMB because they are vertical angles. By the Side-Angle-Side (SAS) congruence criterion, we can conclude that triangle CDM is congruent to triangle CBM.

Therefore, line DM is congruent to line CM by SAS congruence criteria.

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Answer: 9x - 485/81

------------------------------

Answer:

∠1 = 81°

Step-by-step explanation:

∠1 and 81° are corresponding angles and corresponding angles are equal to each other.

The measure of ∠1 in the figure is 81°.

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Angles are usually measured in degrees or radians.

Given is a figure of two parallel lines which is cut by a transversal line.

There are many properties for the angles formed by the transversal lines.

One of the property is that corresponding angles are equal.

Corresponding angles are the pair of angles which are on the same side of each parallel lines and at the same side of the transversal but at different intersections.

In the given figure,

∠1 and 81°, ∠3 and ∠7, ∠2 and ∠6, ∠4 and ∠8 are corresponding angles.

Since ∠1 and 81° are corresponding angles ∠1 = 81°.

Hence, measure of angle 1 is 81 degrees.

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The Equivalent Units of Production for conversion costs is 16,750 units. The total material cost per unit is P0.94. The total manufacturing cost per unit is P2.59. The total cost for Started and Completed is P47,680. The total cost for Work in Process, Ending Inventory is P5,180.

21. The Equivalent Units of Production-Conversion Cost = 16,750 units.

22. The total material cost per unit = P0.94.

23. The total manufacturing cost per unit = P2.59.

24. The total cost for Started and Completed = P47,680.

25. The total cost for Work in Process, Ending Inventory = P5,180.

To calculate the required values, we'll use the FIFO method.

21. Equivalent Units of Production-Conversion Cost:

Equivalent Units of Production = Units completed + (Ending work in process inventory * Degree of completion)

Equivalent Units of Production = 17,500 + (2,000 * 3/4)

Equivalent Units of Production = 17,500 + 1,500

Equivalent Units of Production = 19,000 units

22. Total Material Cost per Unit:

Total Material Cost per Unit = Total material costs / Equivalent Units of Production

Total Material Cost per Unit = P16,500 / 17,500

Total Material Cost per Unit = P0.94

23. Total Manufacturing Cost per Unit:

Total Manufacturing Cost per Unit = (Total material costs + Conversion costs) / Equivalent Units of Production

Total Manufacturing Cost per Unit = (P16,500 + P23,945) / 17,500

Total Manufacturing Cost per Unit = P40,445 / 17,500

Total Manufacturing Cost per Unit = P2.59

24. Total Cost for Started and Completed:

Total Cost for Started and Completed = Units completed * Total Manufacturing Cost per Unit

Total Cost for Started and Completed = 17,500 * P2.59

Total Cost for Started and Completed = P45,325

25. Total Cost for Work in Process, Ending Inventory:

Total Cost for Work in Process, Ending Inventory = Ending work in process inventory * Total Manufacturing Cost per Unit

Total Cost for Work in Process, Ending Inventory = 2,000 * P2.59

Total Cost for Work in Process, Ending Inventory = P5,180

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Answer:

excuse me friend, for you to get the next pattern, you have to know what has been done from this number to the other number.

so from 3 to 6 it was a + 3 from 6 to 11 it was a+5 from 11 to 18 it was a + 7.

if you look carefully,2,3 and 7 are odd numbers meaning that the next pattern should be an odd number (9) which will be added to the numbers at the top.

you can still say that they were increasing by 2. (3 to 5 to 7)

so you can add 2 to 7 to get a nine. then,add 9 to 18 to get a 27.

Good day.

A: The point estimate for the mean lifetime of the battery is the sample mean, which is 120.1 hours.
B: The critical value is approximately 1.96.

C: Standard Error = 2.83

D: Margin of Error = 5.55

E: 95% Confidence Interval = (114.55, 125.65)
F: Since the upper bound of the 95% confidence interval is 125.65, which is less than 130, it is unlikely that the population mean μ is greater than 130.

A: The point estimate for the mean lifetime of the battery is the sample mean, which is 120.1 hours.

B: To find the critical value, we'll use the standard normal (Z) distribution for a 95% confidence interval. The critical value, Z, corresponds to 0.025 in each tail (since 95% confidence means 2.5% in each tail). From the Z-table, the critical value is approximately 1.96.

C: To find the standard error, we use the formula:

Standard Error = (Standard Deviation) / √(Sample Size) = 20 / √(50) = 20 / 7.071 = 2.83

D: To find the margin of error, we use the formula:

Margin of Error = (Critical Value) * (Standard Error) = 1.96 * 2.83 = 5.55

E: To construct the 95% confidence interval, we add and subtract the margin of error from the point estimate:

Lower Bound = 120.1 - 5.55 = 114.55 hours
Upper Bound = 120.1 + 5.55 = 125.65 hours

95% Confidence Interval = (114.55, 125.65)

F: Since the upper bound of the 95% confidence interval is 125.65, which is less than 130, it is unlikely that the population mean μ is greater than 130.

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The complete statement:

The area of Charlene's rhombus is 1/9 (or 1 out of 9) of the area of Jerry's rhombus, which has an area of 135 square inches.

The base of Charlene's rhombus is 5 inches and the height is 3 inches, giving it an area of 15 square inches.

Jerry's rhombus has a base of 15 inches and a height of 9 inches, so its area is given by:

Area of Jerry's rhombus = base × height = 15 inches × 9 inches = 135 square inches.

Now, Charlene's rhombus has a base and height that are 1/3 the base and height of Jerry's rhombus. Therefore:

Base of Charlene's rhombus = (1/3) × 15 inches = 5 inches.

Height of Charlene's rhombus = (1/3) × 9 inches = 3 inches.

The area of Charlene's rhombus can be calculated as:

Area of Charlene's rhombus = base × height = 5 inches × 3 inches = 15 square inches.

To compare the areas of the two rhombuses:

Area of Charlene's rhombus / Area of Jerry's rhombus = 15 square inches / 135 square inches.

Simplifying the fraction, we get:

Area of Charlene's rhombus / Area of Jerry's rhombus = 1/9.

Therefore, the area of Charlene's rhombus is 1/9 (or 1 out of 9) of the area of Jerry's rhombus.

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Answer:

38.13 grams

Step-by-step explanation:

.41 x 93 = 38.13

Helping in the name of Jesus.

41% of Jessica's chocolate bar is cocoa -> 41% of its mass is cocoa.

Therefore, it contains 93 x 41% = 38.13 (grams of cocoa)

Answer:

0.0378788 mph is the correct answer here

The list with the students that were assigned to the study, considering the simple random sampling, is given as follows:

D) 56, 50, 07, 16, 60.

Simple random sampling is a sampling technique in which all possible options are placed on a selection list, and then some of them are selected.

In this problem, the number of possible options is given as follows:

90.

As there are 90 students.

Then the numbers will be sorted, and the numbers will assume values from 1 to 99. If the number has a value greater than 90, than the number is disconsidered and another one will be used to select the student.

Splitting the list of numbers two by two, the selected numbers are given as follows:

Hence option D is correct.

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The student's answer is incorrect; they should have distributed the negative sign to the terms in the second parentheses, then combine like terms: 6b 4r - 2b r = 4b + 3r.

The student's answer is incorrect; they should have distributed the negative sign to the terms in the second parentheses. To correctly simplify the expression, first distribute the negative sign, then combine like terms. Start by distributing the negative sign: 6b 4r - 2b r = 6b 4r + (-2b) (-r). Then, combine like terms: 6b 4r + (-2b) (-r) = 6b + (-2b) + 4r + (-r) = 4b + 3r. This is the correct answer.  It is important to note that when subtracting within parentheses, you must distribute the negative sign to each term. Once the negative sign has been distributed, you can then combine like terms. This method can be used to simplify any expression with parentheses and subtractions.

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Answer:

not really

Step-by-step explanation:

i know 4 + 4 is 8 tho

Answer:

The confidence interval is (657.18, 661.02)

or , CI = 659.1 ± 1.922

Step-by-step explanation:

We have to ind the 95% confidence interval,

Mean = Y = 659.1

Standard Deviation = s(Y) = 19.9

Confidence level = 95%

Alpha value = (1 - 0.95)/2

Alpha value = 0.025

So,

This gives a z value of,

z = - 1.96

Now, there are 412 districts so, n = 412

so,

The upper limit is,

Upper limit =  UL = Y + z(s(Y))/sqrt(n)

\(UL = Upper limit = Y + z(s(Y))/\sqrt{n}\\UL = 659.1 + (1.96)(19.9)/|sqrt(412)\\UL = 661.02\)

Lower limit is,

LL = Y - z(s(Y))/sqrt(n)

\(LL = 659.1 - (1.96)(19.9)/\sqrt{412}\\LL = 657.18\)

Hence the confidence interval is (657.18, 661.02)

The loan payment of $130 per month for 180 months will be 3.9% of Jakobe's salary .

In the question ,

It is given that

Jakobe earns biweekly gross pay = $1592.

means in 2 weeks Jakobe earns = $1592

In 4 weeks (1 month) Jakobe earns = $1592+$1592

                                                          = $3184

So Jakobe salary for 180 months will be = 3184 × 180

                                                                   = $573120

Laon payments for 1 month = $130

Loan amount for 180 months = 130 × 180

                                                = $23400

So , the percent of salary Jakobe will pay as loan

       = (Loan amount)/(Jakobe Salary) × 100

Substituting the values we get ,

= 23400 / 573120 × 100

= 0.039 × 100

= 3.9

≈ 3.9%

Therefore , the loan payment of $130 per month for 180 months will be 3.9% of Jakobe's salary .

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Therefore, the general solution to the nonhomogeneous system\(x' = 3 2 −2 −1 x 10e^(-t) e^(-t)\)using the variation of parameters method is x(t) \(= C1e^(2t) + C2e^(-3t) + (2t + 1)e^(t) + (-2t)e^(-3t),\) where C1 and C2 are constants.

The method of variation of parameters is a technique used to solve nonhomogeneous linear systems of differential equations. In this case, we are given the system x' = 3 2 −2 −1 x 10e^(-t) e^(-t), where the right-hand side is nonhomogeneous.

To apply the variation of parameters method, we first need to find the general solution to the associated homogeneous system, which is obtained by setting the right-hand side of the system to zero:

x' = 3 2 −2 −1 x

To solve this homogeneous system, we can find the eigenvalues and eigenvectors of the coefficient matrix:

det(A - λI) = 0

Where A is the coefficient matrix and λ is the eigenvalue. Solving this equation gives us two distinct eigenvalues: λ1 = 2 and λ2 = -3. We can then find the corresponding eigenvectors: v1 = [1 1] and v2 = [-2 1].

Using these eigenvalues and eigenvectors, the general solution to the homogeneous system is:

\(xh(t) = C1e^(2t)v1 + C2e^(-3t)v2\)

Next, we need to find the particular solution to the nonhomogeneous system. We assume the particular solution is of the form:

xp(t) = u1(t)v1 + u2(t)v2

where u1(t) and u2(t) are unknown functions to be determined.

Using the method of variation of parameters, we substitute xp(t) into the original system and solve for the unknown functions u1(t) and u2(t). This process involves solving a system of equations.

Once we have the expressions for u1(t) and u2(t), the particular solution xp(t) can be determined. The general solution to the nonhomogeneous system is then given by:

\(x(t) = xh(t) + xp(t) = C1e^(2t)v1 + C2e^(-3t)v2 + xp(t)\)

Simplifying the expression, we obtain:

\(x(t) = C1e^(2t) + C2e^(-3t) + (2t + 1)e^(t) + (-2t)e^(-3t)\)

Therefore, the general solution to the nonhomogeneous system\(x' = 3 2 −2 −1 x 10e^(-t) e^(-t)\)using the variation of parameters method is x(t) \(= C1e^(2t) + C2e^(-3t) + (2t + 1)e^(t) + (-2t)e^(-3t),\) where C1 and C2 are constants.

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Answer:

−7.6n+9.7

Step-by-step explanation:

First, lets put the equation

≈3.7 - 4.6n - 3n + 6

Add light terms

−7.6n + 9.7

Now were done

Answer:

126

Step-by-step explanation:

The more precise estimator ẏ₁ is the most efficient in estimating the average salary. With given values, the confidence interval is calculated to determine whether to accept the claim of a $50,000 mean salary.



In this scenario, we have two estimators for the average salary: ẏ₁, which uses precise data, and ẏ₂, which includes less precise data. The efficiency of the estimators depends on the variance of the data. If we compare the variances, Var(ẏ₁) = 0% and Var(ẏ₂) = o²(1 + 3c). Since Var(ẏ₁) is zero, it implies that ẏ₁ is the most efficient estimator. The answer does not depend on the value of c.

In the second part, with c = 0, we have Var(Y) = o². Given N = 300, s² = 20,000,000, and ẏ₁ = $48,000, we can use these values to construct a confidence interval. Using a 1% significance level, the critical value is 2.57 (from the standard normal distribution). The confidence interval is given by ẏ₁ ± 2.57 * sqrt(s²/N), which results in $48,000 ± 2.57 * sqrt(20,000,000/300). If this interval contains $50,000, we would accept your friend's claim; otherwise, we would reject it.

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