A baker used 12 cups of batter to make muffins. It took
cup of batter to make one muffin. How many muffins
did the baker make?

Answer:

156 jackfruits

Step-by-step explanation:

Let there are 6x jackfruit in baseket P, 2x in basket Q and 5x in basket R.

The total number of jackfruit  in basket P is 48 more than the number of  jackfruit in basket Q. ATQ,

6x = 48 + 2x

Solving for x.

6x - 2x = 48

4x = 48

x = 12

Jackfruits in basket P = 6x = 6(12) = 72

Jackfruits in basket Q = 2x = 2(12) = 24

Jackfruits in basket R = 5x = 5(12) = 60

Total no of jackfruits = 72 + 24 + 60

= 156

So, there are 156 jackfruits in the three baskets.

Answer:

its C

Step-by-step explanation:

Answer:

a = 1/42, b = 1/7, c = 1/3 and d = 1/2

Step-by-step explanation:

a = bcd (1)

a + b = cd (2)

a + b + c = d (3)

a + b + c + d = 1  (4)​

Substituting equation (3) into equation (4), we have

a + b + c = d (3)

a + b + c + d = 1  (4)​

(a + b + c) + d = 1  (4)​

d + d = 1  (5)

2d = 1

dividing through by 2, we have

d = 1/2

Taking equation (2) and equation (3), we have

a + b = cd (2)

a + b + c = d (3)

substituting equation (2) into equation (3), we have

a + b = cd (2)

(a + b) + c = d (3)

cd + c = d

Factorizing, we have

c(d + 1) = d

dividing through by d + 1, we have

c = d/(d + 1)

substituting d = 1/2 into the equation, we have

c = d/(d + 1)

c = 1/2 ÷ (1/2 + 1)

c = 1/2 ÷ 3/2

c = 1/2 × 2/3

c = 1/3

Taking equations (1) and (2), we have

a = bcd (1)

a + b = cd (2)

Substituting equation (1) into (2), we have

a = bcd (1)

a + b = cd (2)

bcd + b = cd (2)

Factorizing, we have

b(cd + 1) = cd

dividing through by (cd + 1), we have

b = cd/(cd + 1)

substituting the values of c and d into the equation,, we have

b = cd/(cd + 1)

b = 1/3 × 1/2/(1/3 × 1/2 + 1)

b = 1/6/(1/6 + 1)

b = 1/6 ÷ 7/6

b = 1/6 × 6/7

b = 1/7

Since a = bcd, substituting the values of b,c and d into the equation, we have

a = bcd

a = 1/7 × 1/3 × 1/2

a = 1/42

So, a = 1/42, b = 1/7, c = 1/3 and d = 1/2

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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The mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

To find the mean score for all ninth graders in the city, we need more information than just three scores. Without additional data, we cannot accurately determine the mean score for all ninth graders in the city.

However, we can calculate the mean of the given scores to verify that it is not 79.7 as claimed by the PR manager:

Mean = (77 + 91 + 71) / 3 = 79.7/3 = 79.7 ÷ 3 ≈ 79.7/3 ≈ 26.6

So the mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.

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The critical path is the longest path in a network diagram, which determines the shortest time needed to complete a project. It also represents the sequence of tasks that cannot be delayed without affecting the completion time of the project.

In this context, the critical path between A and L can be found by assigning labels to each vertex and then identifying the longest path. To do this, the following steps can be followed:

- Assign an initial label of zero to vertex A.
- Determine the earliest start time (EST) for each vertex by adding the duration of the previous activity to its earliest start time. This can be represented by the formula EST = max(EFT of predecessors).
- Assign the EST to each vertex.
- Determine the earliest finish time (EFT) for each vertex by adding its duration to its EST. This can be represented by the formula EFT = EST + duration.
- Assign the EFT to each vertex.
- Determine the latest finish time (LFT) for each vertex by subtracting its duration from the LFT of its successor. This can be represented by the formula LFT = min(LST of successors) - duration.
- Assign the LFT to each vertex.
- Determine the latest start time (LST) for each vertex by subtracting its duration from its LFT. This can be represented by the formula LST = LFT - duration.
- Assign the LST to each vertex.
- Calculate the slack time for each vertex by subtracting its EST from its LST. This can be represented by the formula Slack = LST - EST.
- Identify the critical path by selecting the longest path from A to L, which has zero slack time.

By following these steps, the critical path between A and L in the diagram can be determined. It is important to note that the labels assigned to each vertex represent the earliest start time (EST), earliest finish time (EFT), latest start time (LST), latest finish time (LFT), and slack time for each vertex.

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Answer:

Two solutions: -0.12 and 1.75.

Step-by-step explanation:

The quadratic formula is:

\(\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}\). Assuming that the x² term is a, the x term is b, and the constant is c, we can plug the values into the equation.

\(\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {8^2 - 4\cdot-4.9\cdot1} }}{{2\cdot-4.9}}} \end{array}\)

\(\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {64 + 19.6} }}{{-9.8}}} \end{array}\)

\(\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {83.6} }}{{-9.8}}} \end{array}\)

\(\begin{array}{*{20}c}{\frac{{ - 8 \pm \sqrt {9.14} }}{{-9.8}}} \end{array}\)

\(\frac{-8 + 9.14}{-9.8} = -0.12\)

\(\frac{-8-9.14}{-9.8} =1.75\)

Hope this helped!

The two ports can the ferry travel the distance of 7/18 in one hour.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

We have been given that a ferry traveled 1/6 of the distance between 2 ports 3/7 hour.

Since the ferry travels at a constant rate.

We have to determine the distance between the two ports can the ferry travel in one hour.

So, the average speed = (1/6) / (3/7) = (1/6) × (7/3) = 7/18

So the distance between the two ports can the ferry travel in one hour.

⇒ distance = time × average speed = 1 × 7/18 = 7/18

Thus, the two ports can the ferry to travel the distance of 7/18 in one hour.

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Answer: 64

Step-by-step explanation:

(47 + 39) - 22

= 86 - 22

= 64

System of equations 2y-x=10 and 2x-4y=-20 have infinitely many solutions.

Two or more expressions with an Equal sign is called as Equation.

The given equations are 2y-x=10...(1)

and 2x-4y=-20...(2)

From equation 1, 2y-10=x

Now plug in x value in equation 2

2(2y-10)-4y=-20

4y-20-4y=-20

0=0

So the system of equation has infinitely many solutions.

Hence, system of equations 2y-x=10 and 2x-4y=-20 have infinitely many solutions.

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To write the equation in standard form for the circle passing through (–2, 4) centered at the origin, we need to find the radius and the center of the circle.

Since the circle passes through (–2, 4), we can use the distance formula to find the radius, which is the distance from the origin to (–2, 4).

The distance formula is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, x1 = 0, y1 = 0, x2 = –2, and y2 = 4. So, the radius is:

radius = sqrt((-2 - 0)^2 + (4 - 0)^2) = sqrt(20) = 2sqrt(5)

The center of the circle is the origin, since the circle is centered at the origin. Therefore, the equation of the circle in standard form is:

x^2 + y^2 = (2sqrt(5))^2 = 20

So, the equation of the circle passing through (–2, 4) centered at the origin is x^2 + y^2 = 20.

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Answer:

Step-by-step explanation:

Q1

Q2

Q3

Q4

Answer: 50%

Step-by-step explanation:

For an even # to result, the fraction would be 3/6 or 1/2 which would become 0.5 or 50%.

(a) The probability of rolling a 3 is 1/6.

(b) The probability of rolling a 10 is 0 since a standard six-sided die only has numbers from 1 to 6.

(c) The probability of rolling an even number is 3/6 or 1/2. This is because there are three even numbers (2, 4, and 6) out of the six possible outcomes.

(a) The probability of rolling a 3 on a six-sided die is 1/6. There are 6 possible outcomes when rolling a die, and only 1 of those outcomes is a 3.

(b) The probability of rolling a 10 on a six-sided die is 0. There are no possible outcomes when rolling a die that will result in a 10.

(c) The probability of rolling an even number on a six-sided die is 1/2. There are 3 possible outcomes when rolling a die that will result in an even number: 2, 4, and 6.

Here are the answers in mathematical notation:

(a) P(3) = 1/6

(b) P(10) = 0

(c) P(even) = 1/2

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Let the event that a tree has disease be D and the event that tree is being damaged by insects be I.

Therefore,

Recall that:

The required probability is given by:

Hence, the required probability is 20%=0.2

The equation of the line in point-slope form is y + 3 = (1/2)(x - 6), and in slope-intercept form is y = (1/2)x - 6.

To write the equation of a line in point-slope form and slope-intercept form given a point (6, -3) and a slope of 1/2:

1. Point-Slope Form:

The point-slope form of a linear equation is given by: \(y - y_1 = m(x - x_1)\), where (\(x_1, y_1\)) is a point on the line and m is the slope.

Substituting the values into the equation:

y - (-3) = 1/2(x - 6)

y + 3 = 1/2(x - 6)

2. Slope-Intercept Form:

The slope-intercept form of a linear equation is given by: y = mx + b, where m is the slope and b is the y-intercept.

Using the given slope (1/2) and the point (6, -3), we can solve for the y-intercept (b).

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

-3 = 3 + b

b = -6

The equation in slope-intercept form is:

y = 1/2x - 6

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The solution set to the given inequality is

(-∞, -4) U (2,∞)

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

5(x – 2)(x + 4) > 0

First we solve for x, we replace the inequality sign by = sign

5(x – 2)(x + 4) = 0

Divide both sides by 5

(x – 2)(x + 4) = 0

Now we set each factor =0  and solve for x

x-2 =0 , so x= 2

x+4 =0, so x= -4

Now we use number line and make three intervals

First interval -infinity to -4

second interval -4 to 2

third interval 2 to infinity

Now we check each interval with our inequality

First interval -infinity to -4, pick a number in this interval and check with our inequality. lets pick -5

5(-5 – 2)(-5 + 4) > 0

35>0 is true

second interval -4 to 2, pick a number in this interval and check with our inequality. lets pick 0

5(0– 2)(0 + 4) > 0

-40>0 is false

Third interval 2 to infinity, pick a number in this interval and check with our inequality. lets pick 3

5(3 – 2)(3 + 4) > 0

35>0 is true

solution set are the intervals that make the inequalities true

(-∞, -4) U (2,∞)

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Question:

What is the solution set to the inequality 5(x – 2)(x + 4) > 0?

Step-by-step explanation:

A o option

-(-45)

hope it helps

Answer:

(x+3) and (5x-2)

Step-by-step explanation:

first get everything onto one side

5x^2+13x-6=0

then multiply 5 by 6 to get 30 and 15 times 2 is thirty and 15-2=13

5x^2+15x-2x-6=0

then split in half and factor both sides

5x^2+15x factored is 5x(x+3)

-2x-6 factored is -2(x+3)

so the answer is (x+3) and (5x-2)

Answer: The initial amount in the account is $650.​

Step-by-step explanation:

The formula for compound interest is:

Future value = P * (1 + i)^t

Where,

P = Initial amount

i is the interest rate

t is the time period

The equation in the question takes the same format which means that the $600 is the initial amount in the account. It will then be compounded by the interest rate in the brackets over the amount of years the cash will be in that savings account.

Danika walks 50 blocks in one week.

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer. The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to make repetitive adding of the same number easier. It is used for combining groups of identical size.

As per the data given,

We have,

Danika lives at 5 blocks from her school.

As Danika walks 5 blocks to and from school, making her round trip

So, total distance covered by Danika will be: 5 blocks + 5 blocks = 10 blocks.

As Danika walks to and from school 5 days a week,

Hence, she walks 10 blocks * 5 days = 50 blocks in one week.

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Answer:

The 15th term is 103

Step-by-step explanation:

Arithmetic Sequence

An arithmetic sequence is a list of numbers with a definite pattern by which each term is found by adding or subtracting a fixed quantity to the previous term. If n is the number of the term, then:

\(a_n=a_{n-1}+d\)

Where d is called the common difference. If we know the first term, the nth term is calculated by:

\(a_n=a_1+(n-1)*d\)

The question asks us to find the term n=15 of an arithmetic sequence with a common difference d=7 and first term a1=5.

Applying the formula above:

\(a_{15}=5+(15-1)*7\)

\(a_{15}=5+14*7\)

\(a_{15}=5+98=103\)

The 15th term is 103

Answer:

419

Step-by-step explanation:

Answer:

B. 1/2, and D. 5/10.

Step-by-step explanation:

All the equivalent fractions are:

1/2, 2/4, 4/8, 8/16, 5/10, 10/20, 6/12, and 3/6.

The height of the triangular face is 15 yards.

To find the height of the triangular face, we will use the formula for the volume of a triangular prism:
Volume = (1/2) * Base * Height * Length.

We are given the following values:
- Volume (V) = 720 cubic yards
- Length (L) = 8 yards
- Base (B) = 12 yards
We need to find the height of the triangular face (H).

Let's plug in the given values into the formula and solve for H:
720 = (1/2) * 12 * H * 8
First, simplify the equation:
720 = 6 * H * 8
720 = 48 * H
Now, divide both sides by 48 to find the value of H:
H = 720 / 48
H = 15 yards.

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Answer:

1/4

Step-by-step explanation:

You cannot subtract (or add) a fraction with different denominators so first, you need to find a common denominator. You can do this by finding the least common multiple (LCM).

Here the denominators are 2 and 4 so the LCM is 4.

After you find the LCM you need to multiply the denominator by a number that equals the LCM. Then multiply the numerator by that same number.

So convert both 1/2 and 1/4

1/4 x 1/1 = 1/4

1/2 x 2/2 = 2/4

Now we can just subtract the numerator from each other.

2/4 - 1/4 = 1/4

We cannot simplify the difference any more so keep it the same.

The values for numbers #21 through #26 are as follows:

#21: 2.33% or 0.0233. #22: $56.4842. #23: 1.85% or 0.0185. #24: $56.4148. #25: 3.64% or 0.0364. #26: $57.4397

#21: 2.33% (arithmetic mean as a fraction: 0.0233)

#22: $56.4842 (result of the calculation)

#23: 1.85% (geometric mean as a fraction: 0.0185)

#24: $56.4148 (result of the calculation)

#25: 3.64% (continuous mean as a fraction: 0.0364)

#26: $57.4397 (result of the calculation)

To fill out numbers #21 through #26, we need to calculate the values for each term using the given information and convert the percentages to fractions.

#21: The arithmetic mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #21 = 2.33% = 0.0233.

#22: Multiply the starting price ($53.07) by the compound factor (1 + arithmetic mean)^3. Substitute the value of #21 into the calculation. Therefore, #22 = $53.07 x (1 + 0.0233)^3 = $56.4842.

#23: The geometric mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #23 = 1.85% = 0.0185.

#24: Multiply the starting price ($53.07) by the compound factor (1 + geometric mean)^3. Substitute the value of #23 into the calculation. Therefore, #24 = $53.07 x (1 + 0.0185)^3 = $56.4148.

#25: The continuous mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #25 = 3.64% = 0.0364.

#26: Multiply the starting price ($53.07) by the continuous factor e^(continuous mean x 3). Substitute the value of #25 into the calculation. Therefore, #26 = $53.07 x e^(0.0364 x 3) = $57.4397.

Hence, the values for numbers #21 through #26 are as calculated above.

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Yes, we need financial accounting theory even if we are only interested in 'doing'.

Financial accounting theory provides a conceptual framework for financial accounting. It is an important tool that helps to understand the concepts and principles that guide financial accounting practice.Even if a person is only interested in doing financial accounting, they still need to have an understanding of the theory underlying the practice to make informed decisions.

Financial accounting theory explains the underlying assumptions and concepts that govern the practice of financial accounting. It provides a framework for understanding the principles of financial accounting, which can then be applied to real-world situations.

For example, if an individual is only interested in doing financial accounting for a small business, they still need to have an understanding of the accounting principles and concepts that guide the practice.

This knowledge will enable them to make informed decisions when recording financial transactions and preparing financial statements. Without an understanding of financial accounting theory, the person may make errors or misinterpretations that could lead to incorrect financial statements.

Financial accounting theory is essential even if one is only interested in 'doing' financial accounting. It provides the underlying principles and concepts that guide the practice of financial accounting, enabling individuals to make informed decisions when recording financial transactions and preparing financial statements.

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The volume of filled water in half of a right circular cylinder glass is 113.04 cm³.

A right cylinder is a cylinder with two congruent parallel circular bases, and each line segment that is part of a side or curved surface is perpendicular to the bases. The volume of a right cylinder is the number of unit cubes that fit inside it. The unit of volume is "cube". Expressed in m³, cm³, km³, etc., depending on the unit specified. Let's see how to find the formula for the volume of a right cylinder.

V = base area × height = πr²× h = πr²h

where, π is special constant, π = 3.14 or 22/7

We have, a glass in form of right circular cylinder

Base radius of cylinder, R = 3 cm

Height of cylinder, h = 8 cm

cylinder is half of full water i.e volume of water is half of volume of right circular cylinder.

Let us assume "V" be volume of right circular cylinder. We have to calculate the volume of water. For this, V = π R²h/2

=> V = π(3)²×(8)/2

=> V = 72π/2 = 36× 3.14

=> V = 113.04 cm³

Hence, required volume is 113.04 cm³.

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