Given 4 dou of corn and 12 dou of sesame, the total cost is 72 coins. Given 10 dou of sesame and 5 dou of corn, the total cost is 75 coins. Tell: what is the cost of 1 dou of corn and 1 dou of sesame?

A propane tank with a volume of 43.7 ft³ can produce 107,639 BTUs of heat energy when burned.

Propane is a commonly used fuel for heating and cooking. It has a heat energy content of 2,470 BTUs per cubic foot (ft³). To calculate how much energy a propane tank with a volume of 43.7 ft³ can produce, we need to use a simple formula:

Energy = Volume x Energy Content

Plugging in the values we have:

Energy = 43.7 ft³ x 2,470 BTU/ft³

Energy = 107,639 BTUs

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Chad drinks  389.28  fluid ounces of water in 6 days.

A unit of weight equal to ¹/₁₂ troy pound see Weights and Measures Table. : a unit of weight equal to ¹/₁₆ avoirdupois pound. : a small amount. an ounce of sense.

An ounce (oz) is a unit of weight that is equal to one-sixteenth of a pound. Items that weigh approximately one ounce include a slice of bread and a pencil. A fluid ounce is a unit of liquid volume that is equal to one-eighth of a cup. A medicine cup has a volume of approximately one fluid ounce.

given that,

chad drinks 64.88 fluid ounces of water per day,

so in 6 days

he will drink = 6 x water drink per day

= 6 x 64.88

= 389.28

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We can use proportions to solve this problem. If 2 inches represent 75 miles, then we can set up a proportion:

2 inches / 75 miles = x inches / 11 miles

To solve for x, we can cross-multiply:

2 inches * 11 miles = 75 miles * x inches

22 inches = 75 miles * x inches

Divide both sides by 75 miles:

22 inches / 75 miles = x inches

Simplify:

0.2933 inches = x inches

Therefore, 11 miles on the map would be represented by approximately 0.2933 inches.

Step-by-step explanation:

7 + x = 2x, so x = 7

When we look across each row of the table the pattern we observe is that the multiplication of the table leads to 12.

The quantity of space a three-dimensional item occupies is measured by its volume. Usually, it is expressed in cubic units like cubic metres or cubic feet. If an object has irregular or curved shapes, the volume can be determined by using its measurements, such as length, breadth, and height, or by employing more difficult mathematical calculations. In several disciplines, such as physics, engineering, and architecture, volume is a crucial notion.

From the table we see that the arrangement of the 12 cubes is made in different length and width, such that the multiplication of the three is 12.

Here we have,

Long    wide       tall

2            3             2

2             6            1

3             1             4

3             2            2

3             4            1

4              1            3

6              2            1

Hence, when we look across each row of the table the pattern we observe is that the multiplication of the table leads to 12.

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The complete question is:

Answer:

17.2 hours, or 17 hours and 12 minutes

Step-by-step explanation:

If she reads 50 pages per hour, then 860/50 = 17.2

The opportunity of drawing a chocolate from the bag is 0.4, therefore, the answer is A. 0.4.

Steven has a bag of 20 pieces of candy, out of which 8 are chocolates. If he draws one piece of sweet at random, the opportunity of it being a chocolate may be calculated through dividing the wide variety of chocolates in the bag with the aid of the full quantity of chocolates inside the bag. In this situation, there are 8 chocolates out of 20 total candies.

The formulation to calculate the opportunity is:

P(chocolate) = number of candies / total range of candies

Substituting the given values, we get:

P(chocolate) = 8 / 20

Simplifying this fraction, we get:

P(chocolate) = 0.4

Consequently, the opportunity of drawing a chocolate from the bag is 0.4  

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Answer:

The answer for z=137°

Step-by-step explanation:

y=43°

x=z

x+z+y+43=360(angles at a point)

Note:x=z

x+x+43+43=360

2x=86=360

2x=360-86

2x=274

divide both sides by 2

x=137°

Remember x=z

therefore

z=137°

The top of the ladder is dropping at a rate of -5/24 ft/s (approximately -0.208 ft/s) when the base is 5 feet from the wall.To answer your question, we'll use the Pythagorean theorem for the right triangle formed by the ladder, wall, and ground.

Let x be the distance from the base of the ladder to the wall, and y be the distance from the top of the ladder to the ground. The ladder's length (13 ft) is the hypotenuse of the triangle.
According to the Pythagorean theorem:
x² + y² = 13²
When the base is 5 feet from the wall:
5² + y² = 13²
y² = 144
y = 12 ft
Now, we'll differentiate the equation with respect to time (t):
2x(dx/dt) + 2y(dy/dt) = 0
Given that the base is being pulled away at 0.5 ft/s (dx/dt = 0.5 ft/s), we can find the rate at which the top of the ladder is dropping (dy/dt) when x = 5 ft and y = 12 ft:
2(5)(0.5) + 2(12)(dy/dt) = 0
5 + 24(dy/dt) = 0
dy/dt = -5/24

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The top of the ladder is dropping at a rate of [tex]5/\sqrt(119)[/tex]feet per second.

Let's begin by drawing a diagram of the situation:

           |\

           | \

           |  \   <-- ladder

           |   \

           |    \

           |     \

           |         \

           |______\

              wall

A right triangle formed by the ladder, the wall, and the ground.

Let's call the distance from the foot of the ladder to the wall "x" and the height of the ladder "y".

The ladder is 13 feet long and that the foot of the ladder is being pulled away from the wall at a rate of 0.5 feet per second.

The height of the ladder is changing when the foot of the ladder is 5 feet from the wall.

Using the Pythagorean theorem,

the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation

[tex]{\displaystyle a^{2}+b^{2}=c^{2}.}[/tex]

The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.

The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.

The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.

[tex]x^2 + y^2 = 13^2[/tex]

Differentiating both sides with respect to time t, we get:

[tex]2x dx/dt + 2y dy/dt = 0[/tex]

We want to find. [tex]dy/dt[/tex] when [tex]x = 5[/tex], so, we need to substitute. [tex]x = 5[/tex] and [tex]dx/dt = 0.5[/tex] into the equation above:

[tex]2(5)(0.5) + 2y dy/dt = 0[/tex]

[tex]y dy/dt = -5[/tex]

[tex]dy/dt = -5/y[/tex]

Pythagorean theorem to solve for y when. [tex]x = 5[/tex]:

[tex]5^2 + y^2 = 13^2[/tex]

[tex]y^2 = 144 - 25[/tex]

[tex]y^2 = 119[/tex]

[tex]y = \sqrt(119)[/tex]

The foot of the ladder is 5 feet from the wall, the height of the ladder is:

[tex]y = \sqrt(119) feet[/tex]

And the rate of change of the height of the ladder is:

[tex]dy/dt = -5/y = -5/\sqrt(119) feet per second[/tex]

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The probability that a randomly selected student will be taller than 63 inches tall is 0.9332, to the nearest thousandth.

a) 80 hours after 11:00 on a 12-hour clock would be 7:00.

b) 40 hours before 12:00 on a 12-hour clock would be 4:00.

c) 100 hours after 6:00 on a 12-hour clock would be 10:00.

a, To find this, we need to divide 80 by 12 (the number of hours on the clock), which gives us a quotient of 6 and a remainder of 8. We then add the remainder to the starting time of 11:00, giving us 7:00.

b, To find this, we need to subtract 40 from 12 (the number of hours on the clock), which gives us 8. We then subtract 8 from the starting time of 12:00, giving us 4:00.

c, To find this, we need to divide 100 by 12 (the number of hours on the clock), which gives us a quotient of 8 and a remainder of 4. We then add the quotient (which represents a full cycle of 12 hours) to the starting time of 6:00, giving us 6+8=14:00, which is equivalent to 2:00 on a 12-hour clock. Finally, we add the remainder of 4 to 2:00, giving us 10:00.

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Identifying  the first term and common difference and writing a recursive rule:

a. an = an-1 - 5, n > 1

b.  an = an-1 + 12, n > 1

a) The first term is 1 and the common difference is -5. To write a recursive rule for this sequence, we can use the formula:

an = an-1 + d

where an is the nth term of the sequence, an-1 is the (n-1)th term, and d is the common difference.

Using this formula, we get the recursive rule:

a1 = 1

an = an-1 - 5, n > 1

b) The first term is 11 and the common difference is 12. To write a recursive rule for this sequence, we can use the same formula as above:

an = an-1 + d

Using this formula, we get the recursive rule:

a1 = 11

an = an-1 + 12, n > 1

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The given statement about developing quantitative and measurable usability tests is true.

Use cases can help with developing quantitative and measurable usability tests. Use cases are scenarios that describe how a user might interact with a system or product in a specific situation.

By developing use cases, researchers can identify specific tasks that users may need to perform and design usability tests to measure how well users can perform those tasks.

This can help make the usability tests more objective and measurable, as researchers can use metrics such as completion rates, task time, and errors to assess the usability of the system or product.

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The probability that the sample contains exactly two defective parts is 0.0058.

We may utilize the binomial probability formula to resolve this issue:

P(X = k) is equal to (n pick k) * p * k * (1-p) (n-k)

where n is the sample size, k denotes the number of successes, p denotes the likelihood that a success will occur, and (n pick k) denotes the binomial coefficient, which indicates the number of possible ways to select item k from n.

Here, n = 5, k = 2, and p = 0.025 (due to the fact that 2.5% of the pieces are flawed).

P(X = 2) therefore equals (5 pick 2)*0.025*2*(1 - 0.025)*3

We calculate P(X = 2) = 0.0058 using a calculator.

As a result, there is a 0.0058 percent chance that the sample has exactly two defective components.

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The mood of the syllogism is AEA-2 (All F are C, No R are F, therefore No R are C). The figure is 1, as both premises share the middle term C.

The Venn diagram would have three circles: one for F (fossil fuels), one for R (renewable forms of energy), and one for C (combustible gases). The F circle would be fully contained within the C circle, indicating that all fossil fuels are combustible gases. The R circle would be completely outside of the F circle, indicating that no renewable forms of energy are fossil fuels. The area where the C and F circles overlap would be shaded, indicating that some combustible gases are fossil fuels. However, the R circle would not overlap with the C circle, indicating that no combustible gases are renewable forms of energy. Overall, the diagram visually represents the syllogism and its conclusion that some combustible gases are not renewable forms of energy.

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Using the substitution method we know that the value of y in the given situation is 2 respectively.

The substitution method is typically used in mathematics to solve an equation system.

In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

A false statement is produced if the variables x = 3 and y = 2 are substituted into the first equation: 2(2) = 3 + 9.

Try changing the first equation as x = 2y 8 to solve this system.

Next, change x in the second equation to 2y 8, and then solve for y.

The right response is x = 2, y = 3.

So, get the value of y as follows:

3x - 9y =8 ...(1)

-2x + 2y= 8 ...(2)

Now, take equation (1):

3x - 9y =8

3x = 8 + 9y

x = (8 + 9y)/3

Now, substitute x = (8 + 9y)/3 in equation (2):

-2x + 2y= 8

-2[(8 + 9y)/3] + 2y= 8
-2[(8 + 9y)] + 2y= 8*3
-16 + 18y + 2y = 24

20y = 24 + 16

20y = 40

y = 40/20

y = 2

Therefore, using the substitution method we know that the value of y in the given situation is 2 respectively.

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Answer:1

1. is 2/7

2. is .5

3 is 1.94 repeating and

4 is 7/11

Step-by-step explanation:

x=47°

The degree of a triangle is equal to 180°.

Since a triange=180°, you would subtract 180 by 102+31 because the other two angles are 102° and 31°.

180-102-31=47°

Therefore the answer would be x=47°

Answer:

[tex]\begin{array}{|c|c|c|c|c|c|} \cline{1-6} & \text{Music} & \text{Gov} & \text{Theater} & \text{Sports} & \text{Total}\\\cline{1-6}\text{7th grade} & 42 & 12 & 20 & 58 & 132\\\cline{1-6}\text{8th grade} & 38 & 9 & 45 & 30 & 122\\\cline{1-6}\text{Total} & 80 & 21 & 65 & 88 & 254\\\cline{1-6}\end{array}[/tex]

"Gov" refers to "Student  Government".

==================================================

Explanation:

The rows are labeled "7th grade", "8th grade" and "Total".

The columns are labeled "Music", "Student  Government", "Theater", "Sports", and "Total".

I'll abbreviate "Student  Government" to "Gov" so that the table doesn't get too wide.

There are 254 students total. This value goes in the bottom right corner of the table. This is the grand total.

----------

We have 80 students in music. This value goes at the bottom of the "music" column since we're in a "total" row. Basically it's the total of all the music students regardless of grade.

Of those 80 students in music, 42 are in seventh grade. Write 42 in the first row of this column and 38 just underneath it (because 80-42 = 38). The two values 42 and 38 should add to the 80 mentioned.

----------

There are 21 students in student government. This value goes at the bottom of the "student government" column.

9 of these students are in eighth grade, so the remaining 21-9 = 12 must be in seventh grade.

----------

There are 65 students in theater. This value goes at the bottom of the "theater" column.

There are 20 such students in 7th grade and 45 in 8th grade (because 65-20 = 45).

----------

There are 88 students in sports.

30 are in 8th grade, so 88-30 = 58 must be in 7th.

----------

At this point, you should have these values along the bottom row:

80, 21, 65, 88, 254

The first four values (80, 21, 65, 88) should add to the grand total 254.

Along each row, add up the values to get the row total.

7th grade: 42 + 12 + 20 + 58 = 132

8th grade:  38 + 9 + 45 + 30 = 122

There are 132 seventh graders and 122 eighth graders.

Those subtotals add to 132+122 = 254 total students, which helps confirm we did things correctly.

Answer:

x = 8, y = 3

Step-by-step explanation:

Assuming the figure is a parallelogram, opposite sides on a parallelogram are equal.

This means that 3x-2 = 2x+6 and 3y-5 = y+1.

To solve these equations:

3x-2 = 2x+6 (collect like terms)

3x-2x = 6+2

x = 8

3y-5 = y+1 (collect like terms)

3y-y = 1+5

2y = 6 (divide both sides by 2)

y = 3

∴ x = 8, y = 3

The probability of the weekend being dry for the school picnic is approximately 23.4%.

First, let's define some terms:

1. Probability: The likelihood of a specific event happening
2. Picnic: The school event that is scheduled for a two-day weekend in May
3. Rainy: Refers to days with rain

Now, let's calculate the probability that the weekend will be dry:

There are 16 rainy days in May, and May has 31 days. So, there are (31 - 16) = 15 dry days in May.

Each weekend has two days. Since May has 31 days, there are (31 / 7) = approximately 4.43 weeks in May. To account for the remaining days, we round down to 4 weeks and add the remaining 2 days as another weekend, resulting in 5 weekends.

Now, we'll determine the probability of having a dry day on any given day in May:

Dry day probability = (number of dry days) / (total days in May) = 15 / 31 ≈ 0.484

Since we want the probability of having two consecutive dry days (the whole weekend), we'll multiply the probabilities of each day being dry:

Weekend probability of being dry = (dry day probability) * (dry day probability) ≈ 0.484 * 0.484 ≈ 0.234

So, the probability of the weekend being dry for the school picnic is approximately 23.4%.

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So the transformation is: (x, y) → (x + -8, y - 4) which is equivalent to option B.

In mathematics, a transformation is a process that manipulates the position, size, or shape of a geometric object. Transformations can include translations, rotations, reflections, and dilations. They are used to study geometric properties and relationships and are often used in fields such as geometry, algebra, and computer graphics. Transformations are important in understanding symmetry and congruence, as well as in solving problems involving geometric figures.

Here,

We can see that the transformation takes each point of the form (x, y) in ABC to a corresponding point of the form (x', y') in A'B'C'. To find the correct transformation, we need to determine how the coordinates of the points in ABC are related to the coordinates of the corresponding points in A'B'C'. One way to do this is to use the fact that the transformation should preserve the relative distances and angles between the points. Another way is to use the known coordinates of three corresponding points to determine the transformation directly.

In this case, we can see that the transformation maps (-3,-2) to (5,2), (-1,-4) to (7,0), and (-6,-5) to (2,-1). We can use these points to find the transformation:

(x, y) → (x', y')

To map (-3,-2) to (5,2), we need to add 8 to the x-coordinate and add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-1,-4) to (7,0), we again add 8 to the x-coordinate, but this time we only add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-6,-5) to (2,-1), we subtract 4 from the x-coordinate and subtract 4 from the y-coordinate:

x' = x - 4

y' = y - 4

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The exponential function for the new participants is f(x) = 3 * 4^x

Let's start with the initial number of participants who sent selfies on Day 0.

We know that Aliyah, Kim, and Reese each sent selfies to 4 friends, so there are 3 x 4 = 12 participants on Day 1.

On Day 2, each of these 12 participants will send selfies to 4 friends, so we will have 12 x 4 = 48 new participants.

We can see that the number of new participants each day is increasing exponentially. In fact, the number of new participants each day is multiplied by 4, since each participant sends selfies to 4 friends.

Therefore, we can write an exponential function of the form:

f(x)=a * 4^x

Where x is the number of days since the challenge started, and $a$ is the initial number of participants who sent selfies on Day 0.

We know that a = 12 from our earlier calculations.

So, we have

f(x) = 3 * 4^x

Hence, the function is f(x) = 3 * 4^x

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Answer: x=23±√609/10

Step-by-step explanation:

The incorrect expressions are given as follows:

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents.

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents.

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The best center is the mean because there are no outliers

To determine the best center, we need to examing the ages of the player withing the range of age.

The ages of the players are: 11, 10, 11, 11, 8, 11, 12, 11, 9, 10, 11, 12

In the above list of age, we can seee that there are no outliers are

When there are no outliers in a dataset, the best center to use is the mean

Hence, the best center is the mean

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The probability of getting a straight in a five-card poker hand is 0.0019, which is calculated by dividing the total number of possible straights by the total number of possible five-card hands.

To calculate the probability of getting a straight in a five-card poker hand, we need to first understand the concept of a straight. A straight is a combination of five cards that are in consecutive ranks, such as 6-7-8-9-10 or 10-J-Q-K-A.

The total number of possible five-card hands is given by the mathematical formula 52 choose 5, which is equal to 2,598,960. To calculate the number of possible straights, we need to consider the number of ways that we can choose five consecutive ranks out of the thirteen ranks available in a standard deck of cards. There are 10 ways to do this, since we can start with each of the 10 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10) and have one unique straight for each.

However, there are different ways to arrange the cards in a straight. For example, the straight 10-J-Q-K-A can be arranged in five different ways (10-J-Q-K-A, A-10-J-Q-K, K-A-10-J-Q, Q-K-A-10-J, J-Q-K-A-10). Therefore, the total number of possible straights is 10 * 5 = 50.

To calculate the probability of getting a straight, we divide the number of possible straights by the total number of possible five-card hands. Thus, the probability of getting a straight in a five-card poker hand is 50/2,598,960, or approximately 0.0019. Therefore, the chances of getting a straight are relatively low, but not impossible.

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The total number of ways to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores is 137.

To determine the number of ways to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores, we can use a combination of counting techniques.

First, we can consider the total number of ways to buy 10 pieces of fruit without any restrictions. This can be represented by the number of solutions to the equation:

x1 + x2 + x3 + x4 = 10

where x1 represents the number of bananas, x2 represents the number of apples, x3 represents the number of pears, and x4 represents the number of strawberries. Using the stars and bars method, we can find that there are C(13,3) = 286 ways to do this.

Next, we need to subtract the number of ways to buy 10 pieces of fruit where we buy 3 or more pieces with inedible cores.

We can do this by considering the number of ways to buy 3, 4, or 5 apples and pears, and then finding the number of ways to distribute the remaining pieces of fruit. Using the same method as before, we can find that there are C(12,2) + C(11,2) + C(10,2) = 221 ways to do this.

Finally, we can subtract the number of ways to buy 10 pieces of fruit where we buy 3 or more pieces with inedible cores twice, since we double-counted these cases in the previous step. Using the inclusion-exclusion principle, we can find that there are 2 * C(9,2) = 72 ways to do this.

Therefore, the total number of ways to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores is 286 - 221 + 72 = 137.

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The 80% confidence interval is 1501 to 1599 square feet, indicating with 80% confidence that the true population mean of square feet per house falls within this range based on the sample data.

Based on the given information, we can calculate the 80% confidence interval for the true population mean of the number of square feet per house using the sample mean of 1550 square feet and the population standard deviation of 154 square feet. The interval is 1501 to 1599 square feet. This means that if we were to repeat the sampling process and construct confidence intervals in the same way for an infinite number of times, approximately 80% of these intervals would contain the true population mean. Therefore, we can estimate with 80% confidence that the true population mean falls within the range of 1501 to 1599 square feet.

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