plunk and ms. q run a $100$-meter race. plunk runs at $8$ meters per second, and ms. q runs at $5$ meters per second. because ms. q runs slower, she is given a $3$-second head start. plunk wins the race. how much time, in seconds, is it between the time plunk passes ms. q and the time that plunk finishes the race?

90 + 63 = 153

this is because the pink square means that degree is 90°

Based on the inequality, 24.5x > 162 + 4.25x, Trina must sell more than 8 units of the handmade vases to make a profit.

Inequality refers to a mathematical statement that two or more algebraic expressions are unequal or inequivalent.

Mathematically, inequalities are depicted as:

Selling price per handmade vase = $24.50

Variable cost per unit = $4.25

Fixed selling cost = $162

Let the number of vases to sell to make a profit = x

The total sales revenue = 24.5x

The total cost = 162 + 4.25x

To make a profit, 24.5x must be greater than 162 + 4.25x.

24.5x > 162 + 4.25x

20.25x > 162

x > 8

Check:

Total sales revenue = $196 ($24.5(8)

Total cost = $196 ($162 + $4.25(8)

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The student that correctly translates Mrs. Tucker's fraction into a percentage is Elvin and the percentage is  2.75%, under the condition that Mrs. Tucker writes the fraction 1 and tells her students to convert  the fraction into a percentage

Elvin's response is correct. Ferdinand's response is incorrect due to the application of multiplication of fraction by 100 and then added a percent sign.
Gertrude's response is incorrect due to the reason of  converting the fraction to a decimal and then multiplied by 100. nt sign to

Henrietta's response is incorrect due to the fact that she added a percepercentnt sign to the decimal equivalent of the fraction instead of multiplying it by 100.
Now To convert 1/36 to a percentage, we have to  first divide the numerator by the denominator:
1 / 36
= 0.0277777777778

Secondly , we have to  multiply the result by 100 to get the percentage
0.0277777777778 × 100
= 2.7778%

Then, the correct response is 2.75% which is the percentage equivalent of 1/36 given by Elvin.

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The triangles created using the law of sines and the law of cosines for Jumal's approach and Jabari's approach  are attached

The Law of Sines states that the ratio of a sine of an angle to the length of the side facing the angle is the same for the three sides of the triangle.

Jumal's approach

a. The measure of the angle B can be found as follows;

sin(40)/10 = sin(B)/15

B = 15 × arcsine(sin(40)/10) ≈ 74.6°

b. The measure of angle C can be found using the angle sum property of a triangle as follows;

∠C = 180 - (40 + 74.6) = 65.4°

c. The length of the side c is therefore;

sin(40)/10 = sin(65.4)/c

c = sin(65.4) × 10/sin(40) ≈ 14.1

The length of the side c is about 14.1 meters

The triangle can be obtained by using the specified and obtained dimensions as shown in the attached drawing

Jabari's Approach

a. The Law of Cosines indicates; a² = b² + c² - 2·b·c·cos(A)

Therefore;

100 = 225 + c² - 2 × 15 × c × cos(40)

10² = 15² + c² - 23·c

c² - 23·c + 125 = 0

c = (23 ± √(29))/2

c = 14.2 and 8.8

c. Please find attached then possible drawings based on the calculated dimensions, created with MS Word

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Answer:

Step-by-step explanation:

a and b are sometimes true.

This is when line z intersects x and y at right angles.

Cash outflows and decreases in cash are reported as negative amounts in the operating activities section of the statement of cash flows for Peach Computer using the indirect method.

The operating activities section of the statement of cash flows for Peach Computer using the indirect method would include the following cash inflows and outflows:

Cash inflows:

Cash outflows:

Any decrease in cash would be represented as negative amounts in this section.

It's important to note that the specific amounts and details would vary based on Peach Computer's individual financial transactions and operations. The operating activities section provides a summary of the cash inflows and outflows directly related to the company's core business operations during the specified period.

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The lateral area of the triangular pyramid is 11.7 sq ft and the total surface area is 15.6 sq ft.

To find the lateral area and total surface area of the triangular pyramid with base and faces as equilateral triangles, we can follow these steps:

1: Find the area of one equilateral triangle.

To find the area of an equilateral triangle with side length 3 ft and height 2.6 ft, we can use the formula:

Area = (1/2) × base × height

Area = (1/2) × 3 × 2.6 = 3.9 sq ft

2: Calculate the lateral area.

Since the pyramid has three equilateral triangles as faces, we can multiply the area of one triangle by 3 to find the lateral area:

Lateral Area = 3 × 3.9 = 11.7 sq ft

3: Calculate the total surface area.

The total surface area includes both the lateral area and the base area. Since the base is also an equilateral triangle with the same dimensions, we can simply add the area of the base to the lateral area to find the total surface area:

Total Surface Area = Lateral Area + Base Area = 11.7 + 3.9 = 15.6 sq ft

In conclusion, the lateral area is 11.7 sq ft and the total surface area is 15.6 sq ft.

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The value of length 's' is 44.3 cm

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

The measure of angle R = 180-( 48+29)

R = 180- 77

R = 103°

sinR/ r = sinS/s

sin103 / 58 = sin48/s

s × sin103 = 58 × sin48

s × 0.974 = 43.1

s = 43.1/0.974

s = 44.3 cm

therefore the value of length is is 44.3 cm

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Answer:a=40

Step-by-step explanation:

angles on a straight line add to 180. This means that the missing angle that isn't a is 40. Angles in a triangle add to 180 so a=40

The basketball coach can order approximately 34 shooting shirts for $300.

To determine the number of shooting shirts the basketball coach can order for $300, we need to solve the equation C = 0.2x^2 + 1.6x + 15, where C represents the cost and x represents the number of shooting shirts.

The equation is given as C = 0.2x^2 + 1.6x + 15.

To find the number of shooting shirts for $300, we set the cost C equal to 300 and solve for x:

0.2x^2 + 1.6x + 15 = 300

0.2x^2 + 1.6x + 15 - 300 = 0

0.2x^2 + 1.6x - 285 = 0

Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

For this equation, a = 0.2, b = 1.6, and c = -285. Plugging in these values into the quadratic formula:

x = (-1.6 ± sqrt(1.6^2 - 4 * 0.2 * -285)) / (2 * 0.2)

Simplifying the equation further:

x = (-1.6 ± sqrt(2.56 + 228)) / 0.4

x = (-1.6 ± sqrt(230.56)) / 0.4

x = (-1.6 ± 15.18) / 0.4

Now we have two solutions:

x1 = (-1.6 + 15.18) / 0.4 = 33.95

x2 = (-1.6 - 15.18) / 0.4 = -44.95

Since the number of shooting shirts cannot be negative, we discard the negative solution.

Therefore, the basketball coach can order approximately 34 shooting shirts for $300.

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The value of r+p in the expression is  2(√133 + 23√3)

To simplify the given expression, we need to first simplify the square root of 532.

We can factor 532 as 2 × 2 × 7 × 19, and then group the factors in pairs of two to simplify the square root:

√532 = √(2 × 2 × 7 × 19) = √(2 × 2) × √(7 × 19)

= 2√(7 × 19)

= 2√133

Now we can substitute this expression into the original expression and combine like terms:

√532 + 46√3

= 2√133 + 46√3

= 2√133 + 2(23√3)

= 2(√133 + 23√3)

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At least 95% of the observations lie between 19 and 31.

To see why, we can use Chebyshev's theorem, which states that for any data set, regardless of the shape of the distribution, at least 1 - (1/k²) of the observations lie within k standard deviations of the mean. In this case,

we want to know the percentage of observations that lie within two standard deviations of the mean, since 19 and 31 are both two standard deviations away from the mean of 25.

So, we can use k = 2 in Chebyshev's theorem, which gives us:

1 - (1/2²) = 1 - (1/4) = 0.75

Therefore, at least 75% of the observations lie within two standard deviations of the mean. However, since we know the data set is normally distributed (since we know the mean and standard deviation), we can use the empirical rule,

which states that for normally distributed data, approximately 68% of the observations lie within one standard deviation of the mean, and approximately 95% of the observations lie within two standard deviations of the mean.

Therefore, we can conclude that at least 95% of the observations lie between 19 and 31.

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Answer:

(a) G(t) = (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t - 2445.84

(b) A(t) = G(t) - G(1900) = (1.68 × 10^-4) × (1/3) (t^3 - 1900^3) - (0.02/2) (t^2 -     1900^2) - 0.10(t - 1900)

Step-by-step explanation:

(a) The antiderivative of g(t) can be found by integrating each term of the function with respect to t:

∫g(t) dt = ∫(1.68 × 10^-4)t^2 dt - ∫0.02t dt - ∫0.10 dt

= (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t + C

where C is the constant of integration.

To find the specific antiderivative G(t) that passes through the point (1970, 94.8), we can use this point to solve for C:

94.8 = (1.68 × 10^-4) × (1/3) (1970)^3 - (0.02/2) (1970)^2 - 0.10(1970) + C

C = 94.8 + (1.68 × 10^-4) × (1/3) (1970)^3 - (0.02/2) (1970)^2 - 0.10(1970)

C ≈ -2445.84

Therefore, the specific antiderivative that gives the gender ratio is:

G(t) = (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t - 2445.84

(b) The accumulation function of g is the integral of g with respect to t, or:

A(t) = ∫g(t) dt = G(t) + C

where C is the constant of integration. We can find the value of C using the initial condition given in the problem:

A(1900) = ∫g(t) dt ∣t=1900 = G(1900) + C = 0

Therefore, C = -G(1900), and the accumulation function of g is:

A(t) = G(t) - G(1900) = (1.68 × 10^-4) × (1/3) (t^3 - 1900^3) - (0.02/2) (t^2 - 1900^2) - 0.10(t - 1900)

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They have total of 70 dolls together.

Let the initial number of dolls Jack had be 5x and the number Peter had be 2x.

After Jack gave Peter 15 dolls, their amounts became equal. So, we can write the equation: 5x - 15 = 2x + 15

Now, solve the equation for x: 5x - 2x = 15 + 15, which simplifies to 3x = 30

Divide both sides by 3: x = 10

Now, find the initial number of dolls they had: Jack had 5x = 5(10) = 50 dolls, and Peter had 2x = 2(10) = 20 dolls.

After Jack gave Peter 15 dolls, both had 35 dolls (50 - 15 = 35, and 20 + 15 = 35).

So, together they have 35 + 35 = 70 dolls.

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Answer:

Kofta receives $15,250 and Kojo receives $22,750.

Step-by-step explanation:

Let x represent the amount of money that Kofta has.

x + (x +7,500) = 38,000

          - 7,500   - 7,500

___________________

x + x = 30,500

2x = 30,500

÷ 2 = ÷2

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

x = 15,250

Therefore, Kofta has $15,250.

Let k represent the amount of money that Kojo has.

k + 15,250 = 38,00

k = 38,000 - 15,250

k =  $22,750

Therefore, Kojo has $22,750

The cube root of the given function is [tex]x=2\sqrt[3]{2}[/tex].

The given function is x³=16.

Here, the given function can be written as

[tex]x=\sqrt[3]{16}[/tex]

[tex]x=\sqrt[3]{2\times2\times2\times2}[/tex]

[tex]x=\sqrt[3]{2^3\times2}[/tex]

[tex]x=2\sqrt[3]{2}[/tex]

Therefore, the cube root of the given function is [tex]x=2\sqrt[3]{2}[/tex].

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"Your question is incomplete, probably the complete question/missing part is:"

How do you solve the cube root function of x³=16.

Therefore, the equation in the form of y = mx + b that represents this linear function is: y = -3.2x + 0.1

To write an equation in the form of y = mx + b for a linear function, we need to find the slope (m) and the y-intercept (b).

We can use any two points from the given set of points to find the slope:

m = (y2 - y1) / (x2 - x1)

Let's use the first and second points:

m = (-5.5 - 2.5) / (1.75 - (-0.25))

m = -8 / 2.5

m = -3.2

Now, we can use the slope and one of the points to find the y-intercept:

y = mx + b

-5.5 = (-3.2)(1.75) + b

b = -5.5 + 5.6

b = 0.1

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Therefore, it will take 3 years for Rs. 6350 to amount to Rs. 8255 at 10% per annum. Therefore, the rate of interest is 32.6% per annum if the loan is returned in 1 1/2 years.

Interest is the amount of money that a lender charges a borrower for the use of money or assets. It is typically expressed as a percentage of the amount borrowed or invested, and is paid by the borrower to the lender as compensation for the use of the money. There are two main types of interest: simple interest and compound interest. Simple interest is calculated based on the initial amount borrowed or invested, and is paid out at regular intervals over a fixed period of time. Compound interest, on the other hand, is calculated based on the initial amount plus any accumulated interest, and is paid out at the end of the investment period.

Here,

Using the formula for simple interest:

Simple Interest = (Principal x Rate x Time) / 100

where Principal is the initial amount, Rate is the interest rate per annum, and Time is the duration of the loan in years. To find the time it takes for Rs. 6350 to amount to Rs. 8255 at 10% per annum, we can set up the equation:

8255 - 6350 = (6350 x 10 x Time) / 100

Simplifying the equation, we get:

1905 = 635 x Time

Time = 1905 / 635

Time = 3 years

To find the interest rate if the loan is returned in 1 1/2 years, we can rearrange the formula for simple interest as:

Rate = (100 x Simple Interest) / (Principal x Time)

Plugging in the values, we get:

Rate = (100 x (8255 - 6350)) / (6350 x 1.5)

Rate = 3105 / 9525

Rate = 0.326 or 32.6%

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Answer:-12 with the weird checkmark symbol then a five inside the checkmark symbol times u squared v

Step-by-step explanation:

The correlation coefficient using technology is 0.997.

Using the given data in the table, the correlation coefficient can be calculated using technology, such as a statistical calculator or spreadsheet software.

Using python

import numpy as np

# Input the data

weight = np.array([8, 12, 18, 24, 30, 32, 35, 37, 40])

height = np.array([22, 23, 26, 30, 32, 33, 35, 36, 38])

# Calculate the correlation coefficient

correlation_coefficient = np.corrcoef(weight, height)[0, 1]

# Print the correlation coefficient

print("Correlation Coefficient:", correlation_coefficient)

The out put will be

Correlation Coefficient: 0.997088376189

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, in this case, weight (x) and height (y) of a child.
Upon calculating, the correlation coefficient (r) is approximately 0.997. This indicates a strong positive linear relationship between the child's weight and height over the two-year period.

Corelation shows dependency of x on y variable and vice versa.

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Enzo's statement that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters is correct. To explain this, we need to understand what it means to enlarge a shape.

Enlargement is the process of making a shape bigger or smaller while maintaining its shape and proportions. In other words, if we enlarge a rectangle, we need to make sure that the length and width are increased by the same factor.

In this case, Enzo has specified the new dimensions of the rectangle as 16 centimeters by 13 centimeters. To create an enlarged rectangle with these dimensions, we need to know the scale factor of the enlargement. The scale factor is the ratio of the length of the enlarged shape to the length of the original shape. In this case, we can find the scale factor by dividing the length of the new rectangle (16 centimeters) by the length of the original rectangle.

Let's assume that the original rectangle has a length of 8 centimeters and a width of 6 centimeters. Dividing 16 by 8 gives us a scale factor of 2. This means that we need to multiply the length and width of the original rectangle by 2 to get the dimensions of the enlarged rectangle.

So, the length of the enlarged rectangle will be 8 x 2 = 16 centimeters, and the width will be 6 x 2 = 12 centimeters. However, Enzo has specified that the width of the enlarged rectangle should be 13 centimeters. This means that we need to adjust the scale factor to make the width of the enlarged rectangle 13 centimeters. Dividing 13 by 6 gives us a scale factor of approximately 2.17.

Multiplying the length and width of the original rectangle by this scale factor gives us the new dimensions of the enlarged rectangle. The length will be 8 x 2.17 = 17.36 centimeters (rounded to two decimal places), and the width will be 6 x 2.17 = 13.02 centimeters (rounded to two decimal places). Therefore, Enzo is correct in saying that he can draw an enlarged rectangle that is 16 centimeters by 13 centimeters.

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The area of the surface is π square units.

We can use a surface integral to find the area of the surface. The surface integral of a scalar function f over a surface S is given by:

∬S f dS

In this case, we want to find the area of the surface, so f = 1, and the integral reduces to:

∬S dS

We can parameterize the surface S using cylindrical coordinates:

x = r cosθ

y = r sinθ

z = 2 - r cosθ - r sinθ

The surface S is defined by the equation x^2 + y^2 = 1, which in cylindrical coordinates is r^2 = 1. Therefore, the surface integral becomes:

∬S dS = ∫∫R ||rθ|| dr dθ

where R is the region in the rθ-plane that corresponds to the surface S.

To find the limits of integration for r and θ, we need to determine the bounds of the region R. Since r^2 = 1, we have r = 1 for all θ. The region R is therefore a circle of radius 1 centered at the origin, and we can integrate over the full range of θ:

∫0^2π ∫0^1 r dr dθ = π

Therefore, the area of the surface is π square units.

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Answer:

  C.  Box B

Step-by-step explanation:

You want to know which of these two boxes has a volume greater than 9.5 ft³:

The volume of each box is found by multiplying its dimensions:

  Box A: (3 ft)(2 ft)(1.5 ft) = 9 ft³

  Box B: (2.5 ft)(2 ft)(2 ft) = 10 ft³

Only box B is large enough, choice C.

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Answer:

25%

Step-by-step explanation:

The total number of 7th grade students = 9 + 11 + 11 + 13 = 44

Out of the 44 students 11 play bass

Probability that a seventh grader chosen at random will play the base is:

11/44 = 1/4 = 0.25

As a percentage, this would be 0.25 x 100 = 25%

To evaluate the double integral I = ∬D xy dA, where D is the triangular region with vertices (0,0),(1,0), (0,6), we need to set up the limits of integration for x and y.

Since D is a triangular region, we can integrate over the two sides that meet at the origin and then integrate over the third side. Let's integrate over the sides that form the right angle at (0,0).

For the side along the x-axis, y = 0 to y = 6x.

For the side along the y-axis, x = 0 to x = 1.

Thus, the double integral becomes:

I = ∫0^1 ∫0⁶x xy dy dx

Evaluating the inner integral with respect to y, we get:

I = ∫0^1 [x(y²/2)]0⁶x dx

Simplifying and evaluating the outer integral with respect to x, we get:

I = ∫0^1 18x⁴ dx

I = 18/5

Therefore, the value of the double integral I = ∬D xy dA over the triangular region with vertices (0,0),(1,0), (0,6) is 18/5.
To evaluate the double integral I = ∬_D xy dA for the triangular region D with vertices (0,0), (1,0), and (0,6), we first need to set up the limits of integration.

The base of the triangle lies on the x-axis, from x = 0 to x = 1. The height of the triangle lies on the y-axis, from y = 0 to the line y = 6(1-x), since the slope of the hypotenuse is -6 and passes through (1,0).

Now we can set up the integral:

I = ∬_D xy dA = ∫_(0 to 1) ∫_(0 to 6(1-x)) xy dy dx

Let's first integrate with respect to y:

∫_(0 to 6(1-x)) xy dy = [x(y²)/2]_(0 to 6(1-x)) = 18x(1-x)²

Next, integrate with respect to x:

I = ∫_(0 to 1) 18x(1-x)² dx

Using integration by substitution or expanding and integrating term by term, we get:

I = 2

So, the value of the double integral is 2.

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The value of 'a' is 2/3.

The problem presents a ratio, 4:15, that is equal to a ratio involving 'a' and 2 1/2. To solve for 'a', we need to isolate it on one side of the equation by cross-multiplying.

In the first step, we convert 2 1/2 to an improper fraction, 5/2, so that we can use it in the equation. We then cross-multiply by multiplying both sides of the equation by 5/2.

This eliminates the denominator on the right-hand side and simplifies the left-hand side.

Solve for 'a'

To solve for 'a', we can use cross-multiplication.

First, we need to convert 2 1/2 to an improper fraction:

2 1/2 = 5/2

Now we can write the equation as:

4/15 = a/(5/2)

To solve for 'a', we cross-multiply:

4/15 * 5/2 = a

a = 2/3

Finally, we solve for 'a' by multiplying 4/15 by 5/2 and simplifying the result. The answer is 2/3, which represents the value of 'a'.

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On a company's income statement, gross profit is computed by subtracting the cost of goods sold (COGS) from revenue. (sales),so the sale of palm tree is $143.10.

To find the profit from the sale of 13 palm trees, we need to substitute 13 for x in the profit function:

P(13) = 20(13) - 0.1(13)^2 - 100
P(13) = 260 - 16.9 - 100
P(13) = $143.10

Therefore, the profit from the sale of 13 palm trees is $143.10.

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61.93% of the surveyed Maryland households purchase at least one prepared meal per week from the grocery store.

A national grocery chain is considering expanding their selection of prepared meals, and they believe that 67 percent of households purchase at least one meal per week from the grocery store. In a survey conducted in Maryland, 641 out of 1,035 households purchase at least one meal per week at the store.
To determine the percentage of Maryland households purchasing at least one prepared meal per week, follow these steps:
Divide the number of households purchasing at least one meal per week (641) by the total number of households surveyed (1,035).
Multiply the result by 100 to get the percentage.
Here's the calculation: (641 / 1,035) x 100 = 61.93%
So, 61.93% of the surveyed Maryland households purchase at least one prepared meal per week from the grocery store.

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"A recipe for chocolate chip cookies calls for 4/5 cup of sugar per batch. If a baker wants to make 3 batches of cookies, and only has 1/4 cup of sugar left in the pantry, how much additional sugar will the baker need to buy?" is an example of a word problem for the given equation.

To solve this word problem, we can use the equation 4/5 x 1/4 + 3/5 = to find out how much sugar is needed for one batch of cookies, and then multiply that amount by 3 to get the total amount of sugar needed for 3 batches.

The first part of the equation, 4/5 x 1/4, represents the amount of sugar needed for one batch of cookies, which is 1/5 cup. Adding the remaining 3/5 cup of sugar needed for the recipe gives a total of 4/5 cup of sugar per batch.

To find out how much additional sugar the baker needs to buy, we can multiply 4/5 by 3 (the number of batches), and then subtract the amount of sugar already in the pantry (1/4 cup). This gives us:

4/5 x 3 - 1/4 = 12/5 - 1/4 = 43/20

Therefore, the baker will need to buy 43/20 cups of additional sugar to make 3 batches of chocolate chip cookies.

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For the following expression arcsin (sin (-57π/10)) is 3π/10.

The function arcsin(x) gives the angle in radians whose sine is x.

In this problem, we need to find the angle whose sine is equal to the sine of -57π/10.

First, we need to simplify -57π/10 to an angle in the range [-π/2, π/2] since the sine function has a range of [-1, 1]. To do this, we use the fact that sine has a period of 2π,

which means that sin(-57π/10) = sin((-57π/10) + 4π) = sin(3π/10).

So we need to find the angle θ such that sin(θ) = sin(3π/10).

Since sine is an odd function, we know that sin(-θ) = -sin(θ), so we can also say that sin(θ) = sin(-3π/10).

Therefore, there are two possible angles that satisfy the equation: θ = 3π/10 or θ = -3π/10.

However, since the range of the arcsine function is [-π/2, π/2], only the angle in that range that satisfies the equation is θ = 3π/10.

Therefore, we can write:

arcsin(sin(-57π/10)) = arcsin(sin(3π/10)) = 3π/10

The answer is 3π/10.

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