Part A: Describe in words how you can find the rate of change of a bushel of corn in the current year, and find the value. (5 points) Part B: How many dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year? Show your work. (5 points) Number of Bushels
Price of Corn (dollars)
2
10
4
20
6
30
8
40

Answer:

[tex]\huge\boxed{\sf 10s + 93}[/tex]

Step-by-step explanation:

= 10 (s + 9) + 3

= 10s + 90 + 3

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

10(s + 9) +3

10s + 90 + 3

10s + 90 +3

10s + 93

Solution 10s + 93

Answer:

x=-153

Step-by-step explanation

3/4(1/6x) + 3/4(16) = 3/7(35/8)-3/7(21)

1/8x+12=15/8-9

8(1/8x+12=15/8-9)

1x+96=15-72

1x+96=-57

x=-153

In linear equation, the store will get $468.72 from the sale of the couch.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                           Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

a.

Commission can be referred to as the reward given by the company on goods for the employee to sell products in order to make more sales and more money.

Commission is calculated as follows:

Total commission = Total Sales * Commission Percentage

Given

Total Sales = $495

Commission Percentage = 5½%

Substitute in, the above values

Total Commission = $496 * 5½%

Total Commission = $496 * 5.5%

Total Commission = $496 * 0.055

Total Commission = $27.28

Hence, the total commission is calculated as $27.28

b. The amount remitted to the store is calculated as

Amount = Total Sales - Total Commission

Where Total Sales = $496

Total Commission = $27.28

Amount = $496 - $27.28

Amount = $468.72

Hence, the store will get $468.72 from the sale of the couch.

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The complete question is -

Lin is shopping for a couch with her dad and heard him ask the salesperson “how much is your commission?” The salesperson says that her commission is 5½% of the selling price.

A.How much commission will the salesperson earn by selling a couch for $495?

B.How much money will the store get from the sale of the couch?

Answer:

a. The total commission is $27.28

b. The store will get $468.72 from the sale of the couch

The average speed of whole trip was 6.7 mile per hour.

Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.

Given that, the total distance =6+6=12 miles and total time

=58+49= 107 minutes

So, number of hours = 107/60

= 1.8 hours

Now, the average speed = 12/1.8

= 6.7 mile per hour

Therefore, the average speed is 6.7 mile per hour.

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Answer: mass of silver is 75g

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula of volume is length x width x height.

Answer:

40 to 60 is the answer of this question

Answer: 37 degrees

Hope this helps :)

Step-by-step explanation:

(The box in the corner tells you this is a right angle)

A right angle is 90 degrees

90 - 53 = 37

Answer:

37 degrees

Step-by-step explanation:

Angle a is equivalent to 37 degrees because the picture signifies a right angle; all right angles are equal to 90 degrees. The equation to solve this would be: 53+x=90, you would solve this by subtracting 90-53=x; x=37

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The expected time (also known as the expected value or the mean) Is approximately 12.5 days.

The expected time for an activity is the average time it is likely to take, taking into account its optimistic, most likely, and pessimistic estimates. The three-point estimate formula is used to calculate the expected time by weighting the most likely estimate four times as much as the optimistic and pessimistic estimates. In this case, the optimistic time is 15 days, the most likely time is 18 days, and the pessimistic time is 27 days. By plugging these values into the formula, the expected time is calculated to be 12.5 days. This means that, on average, the activity is likely to take 12.5 days to complete.

The expected time (also known as the expected value or the mean) can be calculated using the three-point estimate formula, which is:

Expected time = (Optimistic time + 4 * Most likely time + Pessimistic time) / 6

Plugging in the values, we get:

Expected time = (15 + 4 * 18 + 27) / 6 = (75) / 6 = 12.5

So the expected time for this activity is 12.5 days.

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Answer:

The population of the city in 2020 was 89,500 to the nearest 100 people.

Step-by-step explanation:

The original population in 2010 is 100%.  

If the population is increased by 7.7% from 2010 to 2015, the total percentage in 2015 is 107.7% of the population in 2010.

Convert this to a decimal and multiply by the original population of 87,000 to find the population of the city in 2015.

[tex]\begin{aligned}\implies \sf 107.7\%\;of\;87000&=\sf 1.077 \times 87000\\&=\sf 93699\end{aligned}[/tex]

Therefore, the population of the city in 2015 was 93,699.

The population in 2015 is 100%.  

If the population is decreased by 4.5% from 2015 to 2020, the total percentage in 2020 is 95.5% of the population in 2015.

Convert this to a decimal and multiply by the population in 2015 to find the population of the city in 2020.

[tex]\begin{aligned}\implies \sf 95.5\%\;of\;93699&=\sf 0.955 \times 93699\\&=\sf89482.545 \end{aligned}[/tex]

Therefore, the population of the city in 2020 was 89,500 to the nearest 100 people.

Answer: To happen before

Step-by-step explanation:

The major plate motion rates range from less than 10 mm/y to more than 100 mm/y. The fastest plate is the Pacific Plate, followed by the Australian and Nazca Plates. The North American Plate is one of the slowest, with average rates ranging from around 1 cm/y in the south to nearly 4 cm/y in the north.

Plates move as rigid bodies, it may appear surprising that the North American Plate can move at different rates in different locations. Plates move in a rotational fashion, as explained. For example, the North American Plate rotates counter-clockwise, while the Eurasian Plate rotates clockwise.

There are three types of plate boundaries: divergent, convergent, and transform (moving side by side). Before we discuss processes at plate boundaries, it is critical to note that there are no gaps between plates.

The plates are made up of crust and the lithospheric part of the mantle, and despite moving in different directions all the time, there is never a significant amount of space between them.

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According to the given data, Ryan walked 12 small dogs.

Let x be the number of small dogs that Ryan walked.

The number of large dogs that Ryan walked would then be y = 4 - x.

Using the information given, we can set up the following equation:

x * 2 + (4 - x) * 5 = 40

Expanding and solving for x, we get:

2x + 4 - 5x = 40

-3x = 36

x = 12

So, Ryan walked 12 small dogs.

In this problem, we used a system of equations to solve for the unknown variable, x, which represents the number of small dogs that Ryan walked. By substituting this value back into the equation for the number of large dogs, we were able to confirm that Ryan walked 4 - x = 4 - 12 = 4 large dogs.

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Los intervalos numéricos para la recta numérica en el punto x=2, con 2>x<7, son: (2,7) e (2,∞).

Esto significa que los valores de x pueden oscilar entre 2 y 7, o bien entre 2 y el infinito.

Por ejemplo, el intervalo numérico (2,7) incluiría todos los números entre 2 y 7, incluyendo 2 y 7, pero excluyendo los números menores que 2 y mayores que 7. El intervalo numérico (2, ∞) significa que todos los números mayores que 2 están incluidos, mientras que los números menores que 2 no están incluidos.

Versión en inglés:

The numerical intervals for the number line at the point x=2, with 2>x<7, are: (2,7) and (2,∞).

This means that the values of x can range from 2 to 7, or from 2 to infinity.

For example, the numerical interval (2,7) would include all numbers between 2 and 7, including 2 and 7, but excluding numbers less than 2 and greater than 7. The numerical interval (2, ∞) means that all numbers greater than 2 are included, while numbers less than 2 are not included.

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Answer:

60

good luck!

Considering all the given information, the probability of a widget being less than or equal to 56 is approximately 0.1587

The formula for converting a value to a standard score, also known as a z-score, is:

z = (x - μ) / σ

Where x is the value of interest, μ is the mean, and σ is the standard deviation.

To find the probability of a widget being less than or equal to 56, we first find the corresponding z-score:

z = (56 - 65) / 9 = -1

We can then use the cumulative distribution function (CDF) of the standard normal distribution to find the probability of a z-score being less than or equal to -1:

P(z ≤ -1) = 0.1587

So the probability of a widget being less than or equal to 56 is approximately 0.1587, or 15.87%.

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Step-by-step explanation:

It is translated up 6 units, with the y value is vertical (up and down). The y value is 5, (x, y). Because it only moves up you would keep the x value, -3, and add 6 to the y value. So 5+6=11

The new coordinates are now (-3,5)

Hope this helps :)

Answer:

0.7619047619≈0.76

Step-by-step explanation:

The skier's displacement from his starting point is 127.179 m and makes an angle of 33.78°.

The law of cosines, commonly referred to as the cosine rule or the cosine formula, in trigonometry essentially connects the length of the triangle to the cosines of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.

Given A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º

base distance = 100 m

We will utilize the cosine rule to determine the magnitude of displacement because the triangle formed by the starting point, where he begins to ascend, and the ending point does not have a 90-degree angle. Cosine law requires a triangle with two sides and an angle between them, both of which are present.

a² = b² + c² - 2.b.ccos(α)

here a is the length of the third side,

b = base = 100m

c = 35 m

and α = 180 - 35 = 135°

so a² = b² + c² - 2.b.ccos(α)

a² = 100² + 35² - 2(100)(35)cos(135)

a² = 10000 + 1225 + 4949.74

a² = 16174.74

a = 127.179 m

and the angle between sides 100m and 127.179 m is given by

cosβ = (a² + c² - b²)/2a.c

cosβ = (127.179² + 35² - 100²)/2(127.179)(35)

cosβ = 0.831

β = cos⁻¹(0.831)

β = 33.78°

Hence displacement from the starting point is 127.179 m and forms an angle of 33.78°.

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The values of x for the different diagrams are given below.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

There are four diagrams.

Diagram 1:

By the alternate exterior angles,

8x + 19 = 139

8x = 120

x = 15

Diagram 2:

By the corresponding angles,

17x - 45 = 108

17x = 153

x = 9

Diagram 3:

By the alternate interior angles,

7x -1 = 13x - 43

6x = 42

x = 7

Diagram 4:

By the consecutive interior angles,

8x + 19 = 139

8x = 120

x = 15

Hence, the solutions for all the values are given above.

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Answer: To solve the inequality, we start by isolating the variable n:

-6(n-1) < 3

-6n + 6 < 3

-6n < -3

n > 1/2

And for the other inequality:

2(n+1) > 0

2n + 2 > 0

2n > -2

n > -1

Now, we can plot these solutions on a number line:

[-----1/2-----][-------------n > 1/2----------------]

[-----n > -1-----][-------------]

So, the solution set for the inequality is n > -1 and n > 1/2, which means that n belongs to the interval (1/2, +∞).

Step-by-step explanation:

Answer:

7 packs of floorboards

Step-by-step explanation:

total area of floor= (4.5×2)+(2×3)

= 9+6

= 15m2

15÷2.25= 6.6666666

~7 packs (rounded up to the nearest whole no.)

Answer: The original price of the bracelet before tax can be found using the following formula:

original price = (total price) / (1 + sales tax rate as decimal)

In this case, the total price is 0.72 dollars, and the sales tax rate as a decimal is 0.06. Plugging these values into the formula, we get:

original price = 0.72 / (1 + 0.06)

original price = 0.72 / 1.06

Step-by-step explanation:

A direct variation equation that shows the relationship between x and y is,

y = 8x.

A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.

Given:

In a direct variation, y=16 when x=2.

The proportional relationship between x and y:

y ∝ x.

y = kx, where k is constant.

When x = 2,

16/2 = k

k = 8.

Therefore, the relationship is y = 8x.

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The slope of the linear function in this problem is given as follows:

m = -4.

The slope of a linear function represents the rate of change of the linear function, hence it is calculated as the change in y divided by the change in x, taking two points.

From the graph of the function, when x increases from 0 to 3, y decays from 5 to -7, hence the slope is calculated as follows:

m =(-7 -5)/3

m = -4.

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Answer:

I only

Step-by-step explanation:

any point and its coordinates is an ordered pair of (x, y).

in other words, we get the x value used for the function and the resulting y value.

if the equation is true for such a pair, then the point is on the line. if it is false, then not.

y = (-5/4)x + 5

(4, 0)

0 = (-5/4)×4 + 5 = -5 + 5 = 0

true.

(0, 5)

5 = (-5/4)×0 + 5 = 0 + 5 = 5

true.

y + 5 = (-5/4)(x - 4)

(4, 0)

0 + 5 = (-5/4)(4 - 4)

5 = (-5/4)×0 = 0

false.

so, II is not containing (4, 0).

therefore, only I is contains both points.

At 0.0175% of the carbon-14 is released each year, rounded to the nearest hundredth.

The amount of carbon-14 released each year can be represented as the rate of change of the amount of carbon-14 in the body of an organism with respect to time.

Where

To find the percent of the carbon-14 that is released each year, we can divide the rate of change by the initial amount of carbon-14 and multiply by 100 to express it as a percentage:

⇒percent released/year =[tex]=100*\frac{ d(y)}{dt}[/tex]/a

[tex]=\frac{-100*y}{a* tau}[/tex] = [tex]-100 * (0.5)^(t / tau) / tau[/tex]

At t = tau, the percent released/year will be[tex]-100 * (0.5)^\frac{(1) }{tau}[/tex],

which is approximately -0.0175 per year.

So,

Therefore, each year approximately 0.0175 percent of the carbon-14 is released, rounded to the nearest hundredth.

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Answer:

It's because the graph of arithmetic sequence forms a set of discrete points lying on a straight line.

Answer: We can use the formula for exponential growth to find the value of the quantity after 23 years:

Q(t) = 8500 * 2^(t/9)

Where Q(t) is the value of the quantity after t years, and t/9 is the number of doublings that have occurred.

Substituting t = 23 into the formula:

Q(23) = 8500 * 2^(23/9) = 8500 * 2^2.56 = 8500 * 12.90 = 109350

So, after 23 years, the quantity has a value of approximately 109,350, rounded to the nearest hundredth.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

a)  DIRECT variation    y = k  x

                                    10 = k (4)

                                      10/4 = k = 2.5

                y = 2.5 x

b)    y = 2.5 x

       y = 2.5 (10) = 25