A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 70 pounds. The truck is transporting 50 large boxes and 60 small boxes. If the truck is carrying a total of 3800 pounds in boxes, how much does each type of box weigh?

The statement that best assesses the linearity of the relationship between age and vertical jump, given that the scatterplot appears to be approximately linear, is:

Although it is given that the scatterplot is reasonably linear, because the residual plot has no obvious pattern, it is appropriate to use the line of best fit to predict vertical jump based on age.

The second option is correct.

What is a  residual plot ?

A  residual plot is described as a graphical technique that attempts to show the relationship between a given independent variable and the response variable given that other independent variables are also in the model.

If the residual plot has no obvious pattern, it suggests that the relationship between the variables is linear and that the line of best fit is appropriate for predicting the vertical jump based on age.

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Answer:

thx to the comments

Step-by-step explanation:

41 clients can be checked out in an hour on a lane with a checker and a bagger. Only 25 people can be checked out per hour at a checker-only line.

a. The Good'n'Fresh Grocery Store's total production and average labor productivity are 92 customers per hour and 23.5 customers per hour per worker, respectively.

b. Two lanes with a checker and a bagger, and one lane with a checker only, are the ideal configurations for reassigning the workers to duties.

a. The total output of the Good’n’Fresh Grocery Store is:

Total output = 2 lanes x 46 customers/lane/hour + 2 lanes x 25 customers/lane/hour

             = 92 customers/hour

The average labor productivity is:

Average productivity = Total output / Total number of workers

                    = 92 customers/hour / 4 workers

                    = 23 customers/hour/worker

                    ≈ 23.0 customers/hour/worker                    

Therefore, the total output is 92 customers per hour, and the average labor productivity is 23.0 customers per hour, per worker.

b. With three lanes, the best way to reallocate the workers to tasks is to have:

Two lanes with a checker and a bagger, and one lane with a checker only.

This way, each lane will have one checker and one bagger, which is the most efficient way to operate a lane. The total output will be:

Total output = 3 lanes x 46 customers/lane/hour

            = 138 customers/hour

The average labour productivity is:

Average productivity = Total output / Total number of workers

                    = 138 customers/hour / 4 workers

                    = 34.5 customers/hour/worker

                    ≈ 34.5 customers/hour/worker                    

Therefore, the total output is 138 customers per hour, and the average labour productivity is 34.5 customers per hour, per worker.

c. With four lanes, the best way to reallocate the workers to tasks is to have:

Two lanes with a checker and a bagger, and two lanes with a checker only.

This way, each lane will have either one checker and one bagger or one checker only, which is the most efficient way to operate a lane. The total output will be:

Total output = 4 lanes x 46 customers/lane/hour

            = 184 customers/hour

The average labour productivity is:

Average productivity = Total output / Total number of workers

                    = 184 customers/hour / 4 workers

                    = 46 customers/hour/worker

                    ≈ 46.0 customers/hour/worker                    

Therefore, the total output is 184 customers per hour, and the average labour productivity is 46.0 customers per hour, per worker.

d. With five lanes, the best way to reallocate the workers to tasks is to have:

Two lanes with a checker and a bagger, and three lanes with a checker only.

This way, each lane will have either one checker and one bagger or one checker only, which is the most efficient way to operate a lane. The total output will be:

Total output = 5 lanes x 46 customers/lane/hour

            = 230 customers/hour

The average labour productivity is:

Average productivity = Total output / Total number of workers

                    = 230 customers/hour / 4 workers

                    = 57.5 customers/hour/worker

                    ≈ 57.5 customers/hour/worker                    

Therefore, the total output is 230 customers per hour, and the average labour productivity is 57.5 customers per hour, per worker.

e. Yes, we observe diminishing returns to capital in this example because adding more lanes does not increase output proportionally. Adding a third lane increases output by 46 customers/hour, adding a fourth lane increases output by 46 customers/hour, and adding a fifth lane increases output by 46 customers/hour. Therefore, the marginal output of adding each additional lane is decreasing. The correct multiple-choice answer is:

Certainly, adding a fifth lane won't boost productivity.

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The answer of the given question based on the  number best describes a typical rating in the contest the answer is 7.9.

The median is  measure of central tendency in statistics that represents  middle value of  dataset. It is  value that separates  highest 50% of  values from the lowest 50%.

To find  median of a dataset, you first need to sort  data in ascending or descending order.

The median rating is 7.9, which means that half of the contestants scored above 7.9 and half scored below. This suggests that 7.9 is a representative value of the ratings overall.

Additionally, the interquartile range (IQR) is a measure of the spread of the middle 50% of the ratings, and it is given as 0.8. This means that the ratings between the 25th and 75th percentile fall within a range of 0.8, which suggests that the ratings are fairly tightly clustered around the median of 7.9.

Therefore, the number that best describes a typical rating in the contest is 7.9.

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Answer:

Step-by-step explanation:

a) Without fertilizer with weights less than 50 grams:

Let X be the weight of radishes produced without fertilizer. Then, X ~ N(40, 10^2).

We need to find P(X < 50).

Using the standard normal distribution, we have:

Z = (X - 40)/10

P(X < 50) = P(Z < (50-40)/10) = P(Z < 1) = 0.8413 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown without fertilizer with weights less than 50 grams is 0.8413.

b) Without fertilizer with weights between 20 and 60 g:

We need to find P(20 < X < 60).

Using the standard normal distribution, we have:

Z1 = (20 - 40)/10 = -2

Z2 = (60 - 40)/10 = 2

P(20 < X < 60) = P(-2 < Z < 2) = 0.9544 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown without fertilizer with weights between 20 and 60 grams is 0.9544.

c) Without fertilizer with weights greater than 60 g:

We need to find P(X > 60).

Using the standard normal distribution, we have:

Z = (60 - 40)/10 = 2

P(X > 60) = P(Z > 2) = 0.0228 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown without fertilizer with weights greater than 60 grams is 0.0228.

d) With fertilizer with weights less than 60 grams:

Let Y be the weight of radishes produced with fertilizer. Then, Y ~ N(140, 40^2).

We need to find P(Y < 60).

Using the standard normal distribution, we have:

Z = (60 - 140)/40 = -2

P(Y < 60) = P(Z < -2) = 0.0228 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown with fertilizer with weights less than 60 grams is 0.0228.

e) With fertilizer with weights between 20 and 60 g:

We need to find P(20 < Y < 60).

Using the standard normal distribution, we have:

Z1 = (20 - 140)/40 = -3

Z2 = (60 - 140)/40 = -2

P(20 < Y < 60) = P(-3 < Z < -2) = 0.0668 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown with fertilizer with weights between 20 and 60 grams is 0.0668.

f) With fertilizer with weights greater than 60 g:

We need to find P(Y > 60).

Using the standard normal distribution, we have:

Z = (60 - 140)/40 = -2

P(Y > 60) = P(Z > -2) = 0.9772 (using a standard normal table or calculator)

Therefore, the proportion of radishes grown with fertilizer with weights greater than 60 grams is 0.9772.

The closest mark on the tape measure to 3.16228 inches in eighths of an inch is the mark for 25 eighths of an inch.

To find the closest mark on the tape measure to 3.16228 inches, we need to convert 3.16228 inches to sixteenths of an inch, which is the unit used on the tape measure.

We can start by multiplying 3.16228 by 16 to convert it to sixteenths of an inch:

3.16228 * 16 = 50.59648

Next, we can round 50.59648 to the nearest whole number, which is 51. This means that the closest mark on the tape measure to 3.16228 inches is the mark for 51 sixteenths of an inch.

Note that we can also convert 3.16228 inches to eighths of an inch by multiplying by 8, which gives us:

3.16228 * 8 = 25.29824

Rounding 25.29824 to the nearest whole number gives us 25. This means that the closest mark on the tape measure to 3.16228 inches in eighths of an inch is the mark for 25 eighths of an inch.

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Answer:

Step-by-step explanation:

To find the slope of the line represented by the equation 5x-4y=3(x+3), we can rearrange the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

5x - 4y = 3(x + 3)

5x - 4y = 3x + 9

5x - 3x = 4y + 9

2x = 4y + 9

y = (2/4)x - 9/4

So, the slope of the line is 2/4, which can be simplified to 1/2.

To find the y-intercept, we can set x = 0 in the equation:

y = (1/2)(0) - 9/4

y = -9/4

Therefore, the y-intercept is -9/4.

To find the x-intercept, we can set y = 0 in the equation:

0 = (1/2)x - 9/4

9/4 = (1/2)x

x = (9/4) / (1/2)

x = 9/2

Therefore, the x-intercept is 9/2.

Answer:

Slope: -1/2 Y-Intercept: -9/4

Step-by-step explanation:

5x - 4y = 3x + 9

Subtract 3x from both sides

2x - 4y = 9

Divide both sides by -4

y = (-1/2)x + (-9/4)

The correct option is C. Point B as only the line BC touching the circle at point B is tangent to the circle.

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

We can observe that the line BC touches the circle at point B and the radius of the circle will be perpendicular to the line BC

Therefore, since the radius of the circle is perpendicular to the line BC at point B, then it is tangent to the circle

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The solution to  4^x = 5^x +^2 is

x = -2log 5/( log 5 - log 4)

Option C is correct.

We will rewrite the equation as:

4^x = 5^x * 5^2

applying  the logarithm function to both sides of the equation.

log(4^x) = log(5^x * 5^2)

simplifying the right side of the equation, using the properties of logarithms,

log(4^x) = log(5^x) + log(5^2)

log(4^x) = xlog(4) = x2log(2)

log(5^x) + log(5^2) = xlog(5) + log(25)

Substituting these results back into the original equation, we have:

x2log(2) = x*log(5) + log(25)

x*(2*log(2) - log(5)) = log(25)

Divide  both sides by (2*log(2) - log(5)), we get:

x = x = -2log 5/( log 5 - log 4)

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The magnitude of CD is 5 miles and its direction is approximately 53.13°.

option D.

To find the magnitude and direction of CD, we first need to calculate the distance between points C and D, which will give us the magnitude of the vector CD.

The distance formula between two points (x1, y1) and (x2, y2) is:

d = √((x2 - x1)² + (y2 - y1)²)

Plugging in the values for points C and D, we get:

d = √((0 - (-4))² + (1 - 4)²)

= √(16 + 9)

= √(25)

= 5 miles

To find the direction of CD, we can use the arctan function to find the angle that CD makes with the x-axis.

tan(θ) = (y2 - y1) / (x2 - x1)

Plugging in the values for points C and D, we get:

tan(θ) = (1 - 4) / (0 - (-4))

= -3/4

Taking the arctan of both sides, we get:

θ = arctan(-3/4)

≈ -36.87°

However, since CD points in the negative x-direction, we need to add 90 degrees to get the correct direction.

θ = arctan(-3/4) + 90°

≈ 53.13°

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The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.

Spread and distribution of data are statistical concepts that describe how a set of data is spread out or distributed.

Distribution refers to how the data is distributed or arranged. It is typically described in terms of its shape, center, and spread. Common types of distributions include normal distribution, skewed distribution, and uniform distribution. The distribution can be visualized using various graphs such as histograms, box plots, and scatter plots.

Based on the histogram description, the best answer is:

The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.

The histogram shows that the frequency of calls is highest for the 1 to 25 interval, with decreasing frequency for each subsequent interval. The fact that the shaded bars stop at relatively low frequencies for each interval suggests that there are very few patients who call the doctor frequently, skewing the data towards the lower values. The histogram also shows a wide range of values, or spread, with the highest interval going up to 100, but the low frequencies in each interval suggest that the data is not normally distributed.

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Answer:its b

Step-by-step explanation:

A polynomial equation for the area of one side of the zinc washer is given by A = pi*(r+1)² - pi*r².

Polynomial is a mathematical expression containing one or more terms, each of which is composed of a constant coefficient and one or more variables raised to a power. It can be used to represent a variety of functions, such as linear, quadratic, and cubic functions.

This equation is derived from the area formula for a circle, which states that the area of a circle is equal to pi multiplied by the square of the radius. In this case, the inner radius of the zinc washer is r and the outer radius is r + 1, so the area of one side of the zinc washer is equal to the area of a circle with a radius of r + 1 minus the area of a circle with a radius of r. This can be expressed mathematically as pi*(r+1)² - pi*r², which is a polynomial equation for the area of one side of the zinc washer.

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The value of the numer is negative seven ( -7 ).

Given the statement in the question; the quotient of a number and negative eight is seven-eighths.

Let's translate the given statement into an algebraic equation to solve for the unknown number.

"The quotient of a number and negative eight" means that we are dividing the number by -8.

We can represent this using the division symbol " / ":

Let the number be represented by x.

x / (-8)

"Is" means "equals" " = "

"Seven-eighths" can be written as a fraction:

7/8

Nowm putting it all together, we get:

x / (-8) = 7/8

To solve for x, we can multiply both sides by -8:

x = (-8) × (7/8)

Simplifying the right side, we get:

x  = -7

Therefore, the value of x is -7.

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Answer:

Let's denote the length, width, and

height of the cuboid as "l", "w", and

"h, respectively. Then, we have:

lw= 24 (Area of one face)

Ih 32 (Area of another face)

wh 48 (Area of the third face)

To solve for the dimensions of the

cuboid, we can use a system of

equations. We can start by solving

for one of the variables in terms of

the other two. For example, from the

first equation, we have:

W 24/

Substituting this into the second

equation, we get:

Ih 32

I(24/)h = 32

24h 32

h 32/24

h 4/3

Next, we can substitute the values of

h and w into the third equation to

solve for:

wh = 48

I(24/)(4/3) = 48

I2 72

= sqrt(72)

I= 6sqrt(2)

Finally, we can use the values of I

and w to solve for the remaining

dimension:

lw 24

(6sqrt(2))(24/(6sqrt(2))) = 24

W = 4sqrt(2)

Therefore, the lengths of the sides of

the cuboid are:

Length () = 6v2 cm

Width (w) = 4/2 cm

Height (h) = 4/3 cm

Answer: y=-9x+6

Step-by-step explanation: The common form of a line is the Slope-Intercept form which is y=Mx+B. M represents the slope of the line, B represents the y-intercept, and x and y represent a point on the xy plane such as (1,2). The y-intercept is the point at which x = 0. The slope of a line is given by the equation (y2-y1)/(x2-x1) where (y1,x1) and (y2,x2) are points on a coordinate plane.

In this problem, we are already given M or the slope which is -9. We are also given the y-intercept but it's not as clear. f(x)=y represents a general function where you input an x-coordinate x into f(x) and the function produces a y-coordinate y. If we had a function f(x)=2x+1 and we input 3 as x we replace all the x's with 3 which gives us f(x)=2(3)+1=7. f(3)=7 which can be written as (3,7) being a point on the function. Lines in the coordinate plane represent linear functions because they have a constant slope due to no exponents.

Here, we are told f(0)=6 which can be rewritten as (0,6) being a point on the linear function. I said earlier that the y-intercept is when x=0 and this point has x=0. y=6 when x=0 so 6 is our y-intercept. Now we plug into the slope-intercept form y=mx+b giving us y=-9x+6 which is our answer.

Hope this helps! For practice, find the linear function that has the two points (1,2) and (3,6) on it.

Answer: SEND ME THE PIC

Step-by-step explanation:

Answer:

approximately 1.5 times but round up to 2  

Answer

if you were to roll a dice 9 times you would have the chance to roll 6, 1.5 times.

1/6 and 0.5/3

Step-by-step explanation:

for every number on a dice there is a chance that you'll get that number 1.5 times

Answer:

Length of Bridge A = 4821

Length of Bridge B = 4635

Step-by-step explanation:

Let's call the length of Bridge A "x" which is measured in feet. According to the problem, the length of Bridge B is "186 feet shorter than Bridge A." This can be written as the following:

Length of Bridge B = x - 186

The problem also tells us that the "combined length of the two bridges is 9456 feet," which we can write as:

Length of Bridge A + Length of Bridge B = 9456

Now we can substitute the expression we found for the length of Bridge B into this equation. This can be shown as the following:

x + (x - 186) = 9456

Simplifying this equation, we can combine the two x terms and get the following:

2x - 186 = 9456

Now, we can solve for x

2x - 186 + 186 = 9456 + 186

2x = 9642

x = 4821

So the length of Bridge A is 4821 feet. To find the length of Bridge B, we can use the expression we found earlier:

Length of Bridge B = x - 186 = 4821 - 186 = 4635

Therefore, the length of Bridge A is 4821 feet, and the length of Bridge B is 4635 feet.

The answer of the given question based on the inequality is option B) all real numbers.

A real numbers are  set of numbers that include all rational and irrational numbers, which can be expressed as decimal expansions that go on forever without repeating. The set of real numbers is denoted by symbol ℝ and includes numbers such as 1, 2, 3, -4, -5/6, π, √2, and e.

B.) all real numbers

A statement "0 is greater than or equal to 0" is always true, regardless of  value of  variable or any other conditions. This is because any number is always equal to the itself, and 0 is no exception. Therefore, solution to this inequality is all the real numbers.

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Having a contract with provider B and not having cell phone are independent events.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

If two events are independent, the multiplication of the probabilities of each event is equals to the probability of both events happening.

The probabilities for this problem are given from the table as follows:

The multiplication of the probabilities of each event is:

0.5 x 0.14 = 0.07 -> independent events = Provider B and no cell phone: 0.07.

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The transformation that it could have been is either a rotation or a reflection, over one of the vertices of the figure.

The possible transformations on a figure are listed as follows:

Either a reflection or a rotation can happen over one of the vertices of the graph, which will keep it's coordinates constant, and thus the transformation in the context of this problem is either one of these two.

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Answer:

Their average velocity during their trip was 59.19 miles per hour.

Step-by-step explanation:

To calculate the average velocity of the family's trip, we divide the total distance traveled by the time it took to travel that distance:

Average velocity = total distance ÷ time

In this case, the total distance traveled is 509 miles and the time it took to travel that distance is 8.6 hours. So, we can plug these values into the formula:

Average velocity = 509 miles ÷ 8.6 hours

Simplifying this equation, we get:

Average velocity = 59.19 miles per hour (rounded to two decimal places)

Therefore, the family's average velocity during their trip was 59.19 miles per hour.

Answer:

24% of $400,000 = 0.24 x $400,000 = $96,000

The amount he financed is:

$400,000 - $96,000 = $304,000

To calculate the total amount Roberto will pay for the house, we need to add up the principal (the amount he borrowed), the interest, and any fees or charges. We can use the formula for the monthly payment of a mortgage to find the total amount:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

where M is the monthly payment, P is the principal, i is the monthly interest rate (6.2% divided by 12), and n is the total number of payments (30 years times 12 months per year).

Plugging in the values, we get:

$1861.91 = $304,000 [ 0.00516667(1 + 0.00516667)^360 ] / [ (1 + 0.00516667)^360 - 1]

Solving for P, we get:

P = $304,000

So the total amount Roberto will pay for the house is:

$96,000 (down payment) + $1861.91 x 360 (monthly payments for 30 years) = $96,000 + $670,287.60 = $766,287.60

Therefore, Roberto will pay a total of $766,287.60 for the $400,000 house.

The correct solution to the expression 3 + 5^2 is C. 28.

Mathematically, an expression is a combination of variables with numbers, values, or constants.

Mathematical or algebraic expressions use the mathematical operands like addition (+), subtraction (-), division (÷), multiplication (×), exponents (^), etc.

An algebraic expression does not go with the equal symbol (=), unlike an equation.

3 + 5^2

= 3 + 5 x 5

= 3 + 25

= 28

Thus, an evaluation of the algebraic expression 3 + 5^2 gives the solution as Option C.

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Answer:

To calculate Jerry's total price, we need to know the cost of each Michelin tire from Sears. Let's assume that each tire costs $100.

The total cost of the 4 Michelin tires is:

4 tires x $100/tire = $400

Next, we need to calculate the amount of tax that Jerry will need to pay on his purchase. The tax rate is 8%, so we can calculate the amount of tax as:

$400 x 0.08 = $32

Finally, we can calculate Jerry's total cost by adding the cost of the tires to the tax:

$400 + $32 = $432

Therefore, Jerry's total price for 4 Michelin tires from Sears, including tax, is $432

Using Cauchy-Euler equation, the solution of the second-order homogeneous differential equation  is y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x

The given LODE is a second-order homogeneous differential equation with constant coefficients. The characteristic equation is given by:

9r^2 - 6r + 2 = 0

Using the quadratic formula, we find the roots to be:

r = (1/3) ± i/sqrt(3)

Thus, the general solution to the differential equation is:

y(x) = c1 * x^(1/3) * cos((1/3)*arccos(sqrt(3)*r)) + c2 * x^(1/3) * sin((1/3)*arccos(sqrt(3)*r))

To find the first solution, we can choose either the cosine or sine term. Let's choose the cosine term for simplicity:

y1(x) = x^(1/3) * cos((1/3)*arccos(sqrt(3)*r))

To find the second solution, we can use the method of reduction of order. Assume that the second solution has the form:

y2(x) = v(x) * y1(x)

Substituting this into the differential equation, we obtain:

9x^2(v''(x)*y1(x) + 2v'(x)*y1'(x) + v(x)*y1''(x)) - 6x(v'(x)*y1(x) + v(x)*y1'(x)) + 2v(x)*y1(x) = 0

Simplifying this equation by dividing by x^2*y1(x), we get:

9v''(x) + (18/r)x*v'(x) + ((2/r^2) - 1)v(x) = 0

where r = sqrt(3)

This is a Cauchy-Euler equation, which can be solved by assuming a solution of the form:

v(x) = x^m

Substituting this into the equation, we obtain:

9m(m-1) + (18/r)m + ((2/r^2) - 1) = 0

Simplifying this equation, we get:

9m^2 + 6m + 1 = 0

Using the quadratic formula, we find the roots to be:

m = (-1/3) or (-1/3)

Thus, the second solution is given by:

y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * ln(x)

To determine the first four leading terms in the second solution, we can use the Taylor series expansion of the natural logarithm:

ln(x) = (x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...

Substituting this into the second solution, we obtain:

y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * [(x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...]

Simplifying this expression, we get:

y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * (x-1) - c4 * x^(1/6) * (1/2)(x-1)^2 + c4 * x^(1/3) * (1/3)(x-1)^3 - ...

Thus, the first four leading terms in the second solution are:

y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x

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Answer:

length = 0.89π yd

area = 14.22π yd^2

Step-by-step explanation:

Given r = 4, θ = 40

Length of an arc = 2πr(θ/360º)

l = 2π(4)(40/360) = π(320/360) = π(8/9) = 0.89π

Given r = 4, θ = 360 - 40 = 320

Area of a sector of circle = πr^2(θ/360º)

A = π(4^2)(320/360) = π(16)(8/9) = 14.22π

The answer of the given question based on finding the values of a and b are 12 and 9, respectively.

A triangle is  geometric shape that consists of the three straight sides and three angles. Triangles are one of  basic shapes in geometry and often used in the various mathematical applications.

Since  triangles are similar, their corresponding sides are in the proportion. That is:

AB/DE = BC/EF = AC/DF

We can use this proportion to find the values of a and b.

From the diagram, we can see that:

AB = 12 + a

BC = 9 + b

AC = 15

DE = 8

EF = 6

Using the proportion, we get:

AB/DE = BC/EF

(12 + a)/8 = (9 + b)/6

Cross-multiplying, we get:

6(12 + a) = 8(9 + b)

72 + 6a = 72 + 8b

6a = 8b

a/b = 4/3

Similarly, using the other part of the proportion, we get:

AC/DF = 15/DF = (AB + BC)/(DE + EF) = (12 + a + 9 + b)/(8 + 6)

15DF = 21 + a + b

Substituting the value of a/b = 4/3, we get:

15DF = 21 + (4/3)b + b

15DF = 21 + (7/3)b

45DF = 63 + 7b

45DF = 7(b + 9)

Dividing both sides by 7, we get:

DF = (b + 9)

Substituting this value in the previous equation, we get:

45(b + 9) = 63 + 7b

45b + 405 = 63 + 7b

38b = 342

b = 9

Substituting the value of b in the equation a/b = 4/3, we get:

a/9 = 4/3

a = 12

Therefore, the values of a and b are 12 and 9, respectively.

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The expressiοn that tells the weight οf the flοur left in the bag is 2 - 0.25

A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expression or mathematical expression. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression.

Here, we have

Given: From a 2-pound bag of flour, Marcella took 1/4 pound to bake bread.

We have to find the expression that tells the weight of the flour left in the bag.

Marcella took 1/4 pound to bake bread = 0.25

If Marcella took 0.25 pounds from a 2-pound flour bag then she left with 1.75 pounds.

Hence,  the expression that tells the weight of the flour left in the bag is 2 - 0.25

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Mark has 23 marbles and Don has 48 marbles.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

Mark and Don, are selling their marbles at a garage sale. Don has more marbles than Mark and his number of marbles is equal to "2 more than 2 times the number of marbles Mark has."

Let x be the number of marbles that Mark has. Then, we can represent the number of marbles that Don has as 2x + 2.

Since the total number of marbles is 71, we can set up the equation:

x + (2x + 2) = 71

Simplifying the left side of the equation, we get:

3x + 2 = 71

Subtracting 2 from both sides, we get:

3x = 69

Dividing both sides by 3, we get:

x = 23

So Mark has 23 marbles. To find out how many marbles Don has, we can substitute x = 23 into the expression we derived earlier:

2x + 2 = 2(23) + 2 = 48

Therefore, Don has 48 marbles.

In total, they have 23 + 48 = 71 marbles, as given in the problem statement.

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