At math Olympiads, participants get 8 points for each correct answer and lose 5 points for each incorrect answer. Lucia got 38 points and she did not skip any of 8 problems. How many problems did Lucie solve incorrectly?

The travelled distance functions for the particle is the integral equation [tex]\Delta s = \int\limits^{t = 3}_{t = 0} {|t^{3} - 3 \cdot x^{2} + 2\cdot x|} \, dt[/tex]. (Correct choice: C)

In this problem we find the case of a particle whose velocity is defined by cubic function v(t) = t³ - 3 · t² + 2 · t and we are asked to find its travelled distance, that is the distance traveled by the particle along its path. Since travelled distance is a scalar, then we must apply the following definition:

[tex]\Delta s = \int\limits^{t = b}_{t = a} {|v(t)|} \, dt[/tex]

Where:

Therefore, the travelled distance function is shown below:

[tex]\Delta s = \int\limits^{t = 3}_{t = 0} {|t^{3} - 3 \cdot x^{2} + 2\cdot x|} \, dt[/tex]

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The dimensions of the sides of the triangular flower bed are 27ft, 54ft and 52ft.

A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.

Given the data in the question;

Let the shortest side b x.

Since a triangle has three side, the perimeter of the triangle will be;

Perimeter = side 1 + side 2 + side 3

Plug in the values and solve for x

133 = x + 2x + x +25

133 = 4x + 25

133 - 25 = 4x

108 = 4x

4x = 108

x = 108/4

x = 27

Therefore, the dimensions of the flower bed are;

Shortest side = x = 27ft

Second side = 2x = 2( 27) = 54 ft.

Third side = x + 25 = 27 + 25 = 52 ft

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a) The 99% confidence interval for the proportion of all adults in the United States who would have chosen the minimum wage statement is given as follows: (0.3926, 0.4474).

The interpretation is that we are 99% sure that the true population proportion is in this interval.

b) The condition has to be satisfied as the confidence interval is constructed considering an assumption of normality, and by the Central Limit Theorem, at least 10 successes and 10 failures are needed for the sampling distribution of sample proportions to be normal.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The sample size and the estimate are given as follows:

[tex]n = 2150, \pi = 0.42[/tex]

Hence the lower bound of the interval is given as follows:

[tex]0.42 - 2.575\sqrt{\frac{0.42(0.58)}{2150}} = 0.3926[/tex]

The upper bound of the interval is given as follows:

[tex]0.42 + 2.575\sqrt{\frac{0.42(0.58)}{2150}} = 0.4474[/tex]

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Given a set A={1,2,3,4,5,6,7}, a relation induced by the partition of set A is

(1,2,3) -> {1,2,3}, (4,5) -> {4,5}, (6,7)-> {6,7}

Generally, A set comprises elements or members that may be mathematical objects of any sort, including numbers, signs, points in space, lines, other geometric forms, variables, or even other sets. A set is a mathematical formula for a collection of various things.

A relation induced by a partition of a set is a relation that defines a way of grouping elements in the set into subsets, called "blocks" or "cells". In this case, the set

A={1,2,3,4,5,6,7}

can be partitioned into at least 3 subsets. For example, one possible partition is

A={1,2,3}, {4,5}, {6,7}.

The relation induced by this partition is a relation that assigns to each element in one of the 3 subsets, i.e.

(1,2,3) -> {1,2,3}, (4,5) -> {4,5}, (6,7)-> {6,7}

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Using the given information, the measure of angle AEB is 62

From the question, we are to determine the measure of angle AEB

From the given information, we have that

Angle A = 86°

Angle C = 110°

Angle D = 40°

First, we will calculate the measure of angle B

A + B + C + D = 360°

86 + B + 110 + 40 = 360 (Sum of angles in a quadrilateral)

B + 236 = 360

B = 360 - 236

B = 124

∴ Angle ABC = 124

Then,

Angle ABC is bisected

Therefore,

Angle AEB = 1/2 × 124

Angle AEB = 62

Hence, angle AEB is 62

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The value of q in the equation 3x-4=x+q when x=2 is 0.

We can find the value of q in the equation 3x-4=x+q by solving for q:

First, we can substitute the given value of x (x=2) into the equation:

3(2)-4=2+q

Simplifying:

6-4=2+q

2=2+q

Now we can subtract 2 from both sides of the equation:

q = 0

So, the value of q in the equation 3x-4=x+q when x=2 is 0.

Answer: q = 0

Step-by-step explanation:

3x - 4 = x + q

2x - 4 = q

Substitute x = 2 in the equation,

2 x 2 - 4 = q

q = 0

Therefore, the correct answer is 0.

Answer: The formula for the mathematical function that takes as input an RGB color vector ⟨r,g,b⟩ and yields as output the RGB color vector that is the unique shade of gray whose total amount of light (r+g+b) is equal to that of the input is:

(r+g+b)/3, (r+g+b)/3, (r+g+b)/3

Step-by-step explanation: RGB color space is a way to represent colors digitally, where each color is represented by a combination of red, green, and blue values ranging from 0 to 255. To obtain a unique shade of gray whose total amount of light (r+g+b) is equal to that of the input color, we have to set all three color channels to the average value of the red, green and blue values.

To calculate this average value we use the formula: (r+g+b)/3

So the output of the function is ⟨(r+g+b)/3, (r+g+b)/3, (r+g+b)/3⟩ which is the unique shade of gray whose total amount of light is equal to that of the input color.

Note: This is one way to convert color to gray, other methods exist like using luminosity or other weights to RGB channels.

Answer:

1.6 g/cm³

Step-by-step explanation:

230g = 0.23 kg

0.23 kg x 8 = 1.84 kg

So, the weight of chutney in the 8 jars is 5.68kg - 1.84kg = 3.84kg or 3840g.

So, 1 jar weight is 3840g/8 or 480g of chutney.

Density = 480/300 or 1.6 g/cm³

Answer:

2.36

Step-by-step explanation:

5.68 kg into grams = 5680 and 300*8 is 2400

5680/2400 is 2.36

[tex] \sf {x}^{2} + 5x - 14 \\ \sf {x}^{2} - 2x + 7x - 14 \\ \sf x(x - 2) + 7(x - 2) \\ \sf \: (x - 2)(x + 7) = 0 \\ \sf \: x = 2 \: and \: x = - 7[/tex]

Answer:

To solve this problem, we will use the following steps:

Step 1: Let's assume that the number of quarters is x, and the number of dimes is y

Step 2: We know that the number of dimes is three more than four times the number of quarters, so we can write the equation: y = 4x + 3

Step 3: We also know that Chi has $13.30 in dimes and quarters. Since dimes are worth $0.10 and quarters are worth $0.25, we can write the equation: 0.25x + 0.10y = 13.30

Step 4: Now we have two equations with two unknowns, we can substitute one equation into another to find the value of x and y.

y = 4x + 3

0.25x + 0.10(4x + 3) = 13.30

0.25x + 0.40x + 0.30 = 13.30

0.65x = 13

x = 20

Step 5: We can substitute the value of x in one of the equation, to find the value of y

y = 4(20) + 3

y = 83

Final Answer: Chi has 20 quarters and 83 dimes.

Note: We can check our solution by multiplying the number of quarters by $0.25 and the number of dimes by $0.10 to check if the total money is $13.30 which is true.

If Just before Henderson Laboratories opened for business. The totals that would appear in the firm’s fundamental accounting equation is $96,875

Using this formula

Assets = Liabilities + Owner’s Equity

Total Owners Equity = Assets - Liabilities

Where:

Assets:

Assets = Laboratory Equipment + Laboratory supplies+ Cash

Assets=$75,000 + $6,200 + $39,900

Asset= $121,100

Liabilities:

Liabilities= Loan Payable+ Accounts Payable

Liabilities = $14,500 + $9,725

Liabilities= $24,225

Let plug in the formula

Total Owners Equity = Assets - Liabilities

Total Owners Equity =$121,100 - $24,225

Total Owners Equity= $96,875

Therefore the totals that would appear in the firm’s fundamental accounting equation is $96,875.

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The complete question is:

Just before Henderson Laboratories opened for business, Eugene Henderson, the owner, had the following assets and liabilities. Cash $ 39,900 Laboratory equipment 75,000 Laboratory supplies 6,200 Loan payable 14,500 Accounts payable 9,725. Determine the totals that would appear in the firm’s fundamental accounting equation (Assets = Liabilities + Owner’s Equity).

Answer:

7x2−4x/5

Step-by-step explanation:

7x2−4x over 5

A quadratic equation, or second-order polynomial equation with a single variable, has the form ax^2 + bx + c = 0. The solution to the given equation is v = 7, -5 and 3

The form ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given the quadratic expression below:

(v-7)(v+5)(v-3)=0

Required

The solution to the system of equation

Equate each expression to zero calculate the value of 'v' as shown:

v - 7 = 0

v = 0 + 7

v = 7

Also, v + 5 = 0

v = 0 - 5

v = -5

Similarly, v - 3 = 0

v = 0 + 3

v = 3

Hence the solution to the given equation is v = 7, -5 and 3

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Please find attached herewith the solution of your question.

Answer: 2.8 m

Hope it helps.

If you have any query, feel free to ask.

The area of a outdoor carpet is 42 square feet.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

In the given figure, the outdoor carpet consist two triangles and one rectangle.

Here, rectangle measures length=11 ft and width = 3 ft, small triangle has base= 2 ft and height =3 ft and large triangle has base= 4ft and height =3 ft.

So, area of rectangle is 11×3 = 33 square ft

Area of small triangle = 1/2 ×Base×Height

= 0.5×2×3

= 3 square feet

Area of large triangle = 1/2 × 4×3

= 6 square feet

Total area = 33+3+6

= 42 square feet

Therefore, the area of a outdoor carpet is 42 square feet.

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The expression √5x × √30x is simplified using the product rule to give 12.25x

Square root of a number can be defined as the inverse operation of the square of a number.

It is the number obtained by finding a number that when squared would give the original number.

Square root is represented using the symbol '√ '. The symbol is called a radical.

Also, the number under the symbol is called the radicand.

To multiply two square roots, we have to multiply the radicands and leave the radical sign.

From the information given, we have;

√5x × √30x

Multiply the radicands and retain the square root symbol, we have;

√150x²

Find the square root

12.25x

Hence, the value is 12.25x

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Using the above equation 1/i is equal to 2/(9-5j^2+3k)

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given; 2i+5j^2-3k=9

2i+5j^2-3k=9

2i=9-5j^2+3k

i=(9-5j^2+3k)/2

1/i=2/(9-5j^2+3k)

Therefore, the value of 1/i according to the given equation will be

2/(9-5j^2+3k)

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The cost of labor per hour is $125.

The equation that can be used to solve for the cost of labor per hour is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

The form of the linear equation is:

Total cost = cost of the parts + (cost per hour x total hours worked)

$585.25 = $54 + (4.25 x d)

$585.25 = $54 + 4.25d

In order to determine the value of x, take the following steps:

Combine similar terms:

$585.25 - $54 = 4.25d

Add similar terms

$531.25 = 4.25d

Divide both sides of the equation by 4.24

d = 531.25 / 4.25

d = 125

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The given angle 2.59 radian into degree is 148.40°.

What is radian and degree?

While a radian is another unit of measurement that is used to measure angles, a degree is a unit of measurement that is used to measure circles, spheres, and angles. The radian, or one pi radian, is only half the diameter of a circle, which has 360 degrees, or its entire area.

Given:

The angle in radian is 2.59.

We have to convert this angle into degree.

Since, the formula to convert angle θ from radian to degree is,

Radian = [tex]\frac{180}{\pi }[/tex] degree

= 2.59 x (180/π)

= 148.40°

Hence, the given angle 2.59 radian into degree is 148.40°.

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Answer:

25 median. 29 mean.

Step-by-step explanation:

7, 16, 18, 25, 43, 47, 47

25 is the middle number when ordered by value, so 25 is the median

7 + 47 + 43 + 47 + 25 + 16 + 18 = 203

203 / 7 (amount of numbers in the set) = 29

29 mean

Pie graphs can be used to display percentages of an entire group and depict percentages at a certain moment. Customers contacted via the web = x(let) then.as a result, customers contacted online (chart = x = 100), 25 customers were reached by social media, or x/4

Pie charts can be used to show percentages for the whole group or for a specific time period.

In contrast to bar and line graphs, pie charts do not show changes over time.

The following pages provide descriptions of the various pie chart elements.

Since the slices of a pie chart represent different parts of the whole, their sum must always equal 100%.

Number of customers overall = 250 clients were contacted via email for every 500 customers contacted via phone, or 50% of phone contacts.

=(50÷100)×250

=125

Customers reached via social media

= total customers + 250 + 125 + x+1 = 500 x+1

=125 × 5

T=125

x=100.

Customers contacted via the web = x(let) then.

as a result, customers contacted online (chart = x = 100)

25 customers were reached by social media, or x/4

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The value each segment length in right triangle ABC are AD = 6 units, BC = 4 units, AB = 4√3 units and BD = 2√3 units

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

Since AC = 8 and CD = 2.

Thus, AD = AC - CD = 8 - 2 = 6 units

sin 30° = BC/AC

0.5 = BC/8

BC = 0.5 × 8

BC = 4 units

AB = √(8²-4²)   (Pythagoras theorem)

AB = 4√3 units

BD = √(4²-2²)   (Pythagoras theorem)

BD = 2√3 units

Therefore, drag the value of each segment length in the box accordingly

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Answer:

Step-by-step explanation:

2424242424242424hhj

Answer:

Step-by-step explanation:

The problem can be solved by using the information provided to set up a system of equations and then solving for the unknown variable, which in this case is the fixed charge.

Let x be the fixed charge.

We know that the total cost of the 11-mile trip is the fixed charge plus the charge for the distance covered, so we can write the equation:

x + 11y = 88 (1)

We also know that the total cost of the 16-mile trip is the fixed charge plus the charge for the distance covered, so we can write the equation:

x + 16y = 108 (2)

Where y is the cost per mile

We can solve for y by subtracting equation (1) from equation (2), so:

16y - 11y = 108 - 88

5y = 20

y = 4

Now we know that cost per mile is 4$, we can substitute it in equation (1)

x + 11(4) = 88

x = 24

Now we know the fixed charge is 24$ and cost per mile is 4$, we can calculate the fare for 6 miles

24 + 6(4) = $48

Therefore, Linus would have to pay $48 to travel 6 miles.

The point at which the perpendicular bisectors of a triangle's sides come together is known as the circumcenter of that triangle. The line's equation is x=-2.5.

The circumcenter is, in other words, the point at which the bisector of a triangle's sides coincides. P serves to indicate it (X, Y).

This intersection represents the point on the triangle's perimeter. Distance d = (a - ax)2 + (b - bx)2 is the geometry formula for distance. "d" represents the separation between a vertex and the circumference, where x = 1, 2, 3.

The junction of the perpendicular bisectors of each side of the triangle, or the lines that are perpendicular to each side's midpoint, is where the triangle's circumcenter can be located.

To determine it, we locate the intersection of the circumcenter and the first name of the triangle, which is the point at which each line intersects the other

(-4,0) B=(-4,-4) C=(-1,-4) (-1,-4) (-4, -2),

y=-2 is the perpendicular line to AB's midpoint.

The intersection of the line at (-2.5,-2) and (-5/2,-2)

where BC's midpoint is located.

The line's equation is x=-2.5.

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Answer: I'm guessing this is addition.

Shipping 1 large box would be $51. Shipping 2 large boxes would be $54 dollars.

Step-by-step explanation: I don't know if you wanted addition or multiplication but the answer I gave is addition