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The equation of line P passing through the points of intersection is y = -1/2x + 2.

To find the coordinates of the points of intersection between curve C and line L, we need to solve the system of equations formed by their respective equations.

The equations are:

C: y = 2x^2 - 6x + 5 ...(1)

L: 2y + x = 4 ...(2)

We can solve this system by substituting the value of y from equation (1) into equation (2):

2(2x^2 - 6x + 5) + x = 4

4x^2 - 12x + 10 + x = 4

4x^2 - 11x + 6 = 0

To solve this quadratic equation, we can factorize it:

(4x - 3)(x - 2) = 0

Setting each factor to zero, we get:

4x - 3 = 0 --> x = 3/4

x - 2 = 0 --> x = 2

Now, substitute these x-values back into equation (1) to find the corresponding y-values:

For x = 3/4:

y = 2(3/4)^2 - 6(3/4) + 5

y = 9/8 - 18/4 + 5

y = 9/8 - 9/2 + 5

y = 9/8 - 36/8 + 40/8

y = 13/8

For x = 2:

y = 2(2)^2 - 6(2) + 5

y = 8 - 12 + 5

y = 1

Therefore, the coordinates of the points of intersection between C and L are (3/4, 13/8) and (2, 1).

Now, we need to find the equation of line P passing through the points of intersection.

We have two points on line P: (3/4, 13/8) and (2, 1).

First, let's find the slope of line P using the formula:

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

m = (1 - 13/8) / (2 - 3/4)

m = (-5/8) / (5/4)

m = -1/2

Now, we have the slope of line P, -1/2. We can use one of the points, let's say (3/4, 13/8), and the slope to find the equation of line P using the point-slope form:

y - y1 = m(x - x1)

Substituting the values:

y - 13/8 = -1/2(x - 3/4)

Simplifying:

y - 13/8 = -1/2x + 3/8

y = -1/2x + 3/8 + 13/8

y = -1/2x + 16/8

y = -1/2x + 2

Therefore, the equation of line P passing through the points of intersection is y = -1/2x + 2.

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Answer:

Step-by-step explanation:how many grams of active dry yeast must be used for bread recipe

The required selling price of each water bottle is $554.06 such that Michelle's robotics club will achieve 25% increase in the purchase price.

Given that number of water bottles purchased is 75 and cost price (C,P) of the 75 water bottles is $443.25. The increase %  on the purchase price is profit % = 25%.

To calculate the selling price when cost price and profit % is given by following steps:

Step 1 - Calculate the 25% of the cost price which gives profit.

Step 2 - Calculate SP, Selling price = Cost price + profit.

That implies, Profit = 25% of C.P.

Profit = 25/100 × 443.25.

Therefore, Profit = $110.81.

That implies, Selling price(S.P) = Cost price + profit.

S.P = 443.25 + 110.81.

Thus, S.P = $554.06.

Hence, the required selling price of each water bottle is $554.06 such that Michelle's robotics club will achieve 25% increase in the purchase price.

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The given set is defined as the cartesian product of two sets X and Y.

In the given set,

We have to explain the meaning of {(x,y) : Ψ(x,y)}

Since we know,

The Cartesian product AxB of two sets A and B is the set of all feasible ordered pairs with A as the first element and B as the second element

Then,

 AxB ={ (p,q): p ∈ A and q ∈ B}

The typical Cartesian coordinates of the plane,

Where A is the set of points on the x -axis, B is the collection of points on the y -axis, and AxB is the xy -plane, are one example.

And we also know that,

A function of two variables is a function in the sense that each input has precisely one output.

The inputs are ordered pairs of letters (x,y). Real numbers (each output is a single real number) are the outputs.

A function's domain is the set of all possible inputs (ordered pairs), but its range is the set of all possible outputs (real numbers).

The function is expressed as z = f(x,y)

Hence,

The set {(x,y) : Ψ(x,y)} is defined as the set of cartesian product of X and Y in which the cartesian product is defined by the function  Ψ(x,y), which is a function of two variables.

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Answer:

  2.5%

Step-by-step explanation:

You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.

The z-score of 335 is ...

  Z = (X -µ)/σ

  Z = (335 -555)/110 = -220/110 = -2

The empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.

  P(X < 335) = 5%/2 = 2.5%

The percentage of people taking the test who score below 335 is 2.5%.

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Answer:

1.5 is the correct answer

Answer:

Step-by-step explanation:

If the dimensions of a figure are multiplied by 1/3, then the area of the new figure will be 1/9 of the original area.

Therefore, if the area of the original figure is 207 m², then the area of the new figure will be 23 m² (207 m² * 1/9).

I hope this helps!

Answer:

23 m^2

Step-by-step explanation:

As all of the dimensions have been multiplied by a constant, the two figures are similar to one another.

The ratio between the areas of two similar figures is given by the ratio of similarity (= the ratio between two similar sides between the two figures) squared.

In our case, the ratio of similarity is 1/3.
Therefore, the ratio between the two areas is (1/3)^2 = 1/9.

[tex]207 \times \frac19 = 23 \left[\text{m}^2\right][/tex]

The Euclid math contest is the annual contest held by the University of Waterloo. The students from grade-11 to grade-12 can participate in the Euclid math contest.

Euclid contest is a Mathematics contest for senior-level high school students. This contest was participated by nearly 22000 students worldwide every year. This contest allows the students to demonstrate their knowledge of secondary school mathematics. This competition was held by the University of Waterloo.

The senior-grade students will participate in this contest and it takes 2 and a half hours to complete the contest. It has 10 questions and the total mark for the contest is 100. The University of Waterloo values the results from the Euclid math contest when it comes to admission and scholarship offers.

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If the position of 5 m below sea level is expressed as -5, then the number that expresses the position of 7 m above sea level would be + 7.

In this particular instance, with the position residing 7 m above sea level, we articulate it as +7. This notation elegantly captures the notion of elevation, affirming the distance above the familiar sea level benchmark.

In the realm of vertical measurements, sea level occupies a crucial position as the reference point, embodying the zero mark on the vertical scale. It is from this fundamental reference point that we navigate the vast spectrum of altitudes.

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[tex]\cfrac{x}{4}-\cfrac{x+10}{2}=3\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{x}{4}-\cfrac{x+10}{2} \right)=4(3)}\implies x-(2x+20)=12 \\\\\\ x-2x-20=12-x-20=12\implies -20=12+x\implies \boxed{-32=x} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{2x+1}{5}-\cfrac{x-3}{7}=-2\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{2x+1}{5}-\cfrac{x-3}{7} \right)}=35(-2) \\\\\\ 14x+7-(5x-15)=-70\implies 14x+7-5x+15=-70 \\\\\\ 9x+22=-70\implies 9x=-92\implies \boxed{x=-\cfrac{92}{9}}[/tex]

The value of the function f(-1) is 1/3. Option D

A function can be defined as a law, an expression or rule that is used to show the relationship between two variables.

These variables are listed as;

From the information given, we have the function written as;

f(x) = 3ˣ

To determine the function f(-1), we need to substitute the value of the variable x as -1 in the function f(x)

Substitute the values, we have;

f(-1) = 3⁻¹

Take the inverse of the value, we get;

f(-1) = 1/3

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The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)

Thus, option (D) is correct.

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The probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.

To find the probability that a single randomly selected value is between 189.7 and 213, we can use the standard normal distribution.

Step 1: Calculate the z-scores for the given values using the formula:

  z = (x - μ) / σ

  For 189.7:

  z1 = (189.7 - 189.7) / 96.7 = 0

  For 213:

  z2 = (213 - 189.7) / 96.7 ≈ 0.2417

Step 2: Utilize a standard typical conveyance table or number cruncher to find the probabilities comparing to the z-scores.

  P(189.7 < X < 213) = P(0 < Z < 0.2417) ≈ 0.0939

Therefore, the probability that a single randomly selected value is between 189.7 and 213 is approximately 0.0939.

To find the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213, we use the central limit theorem. Under specific circumstances, the testing dispersion of the example mean methodologies a typical conveyance

Step 1: Calculate the standard error of the mean (σ_m) using the formula:

  σ_m = σ / sqrt(n)

  σ_m = 96.7 / sqrt(62) ≈ 12.2878

Step 2: Convert the given qualities to z-scores utilizing the equation:

  z = (x - μ) / σ_m

  For 189.7:

  z1 = (189.7 - 189.7) / 12.2878 = 0

  For 213:

  z2 = (213 - 189.7) / 12.2878 ≈ 1.8967

Step 3: Utilize a standard typical conveyance table or mini-computer to find the probabilities relating to the z-scores.

  P(189.7 < M < 213) = P(0 < Z < 1.8967) ≈ 0.9702

Therefore, the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.

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Answer:

664

Step-by-step explanation:

6x17

6x17

10x6

10x6

10x17

10x17

add them all up and u get 664

The circumference of a circle = pi x diameter

Circumference = 3.14 x 32 = 100.48 meters (rounded to two decimal places)

The farmer needs to build a fence around the edge of the field, which has a circumference of 100.48 meters. So the total length of fence needed is 100.48 meters.

Each meter of fence cost £15.95, therefore the cost of building the entire fence can be calculated as:

Total Cost = Length of fence x Cost per meter of fence Total Cost = 100.48 x £15.95 Total Cost = £1601.08

Therefore, it would cost the farmer a total of £1601.08 to build a fence around the edge of the circular field.

Answer:

$1603.47

Step-by-step explanation:

The largest possible number of people attending the match is 31,249, and the smallest possible number is 31,100.

To determine the largest and smallest possible number of people attending the football match, given that the figure is stated as 31,200 with 3 significant figures, we need to consider the range of values that can be represented within that significant figures constraint.

For a number to be stated with 3 significant figures, the last significant figure is uncertain and can be either rounded up or down.

To find the largest and smallest possible numbers, we'll consider the cases where the last significant figure is rounded up and rounded down.

Rounding up:

If we round up the last significant figure, the possible range of values is from 31,150 to 31,249.

So the largest possible number of people attending the match would be 31,249.

Rounding down:

If we round down the last significant figure, the possible range of values is from 31,100 to 31,199.

So the smallest possible number of people attending the match would be 31,100.

Therefore, the largest possible number of people attending the match is 31,249, and the smallest possible number is 31,100.

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[tex]3a-2b=13\\4a+b=21|\cdot2\\\\3a-2b=13\\\underline{8a+2b=42}\\11a=55\\a=5\\\\3\cdot5-2b=13\\2b=2\\b=1[/tex]

Answer:

a = 5, b = 1

Step-by-step explanation:

We need to realize that in a parallelogram, opposite sides are congruent. Therfore, the length of NO and MP must be the same if we assume that Quadrilateral MNOP is a parallelogram.

Length of NO = 21

Length of MP = 4a + b

Therfore, we can get this equation: 4a + b = 21

We can do the same with the other 2 sides to get: 3a - 2b = 13

As you can see, this is a systems of equations! Lets solve it!

To find the values of "a" and "b" in the given system of equations:

Equation 1: 4a + b = 21

Equation 2: 3a - 2b = 13

We can solve this system of equations using either the substitution method or the elimination method. Let's use the elimination method:

Multiply Equation 1 by 2:

2(4a + b) = 2(21)

8a + 2b = 42

Now, we can add Equation 2 and the modified Equation 1 to eliminate the "b" term:

(3a - 2b) + (8a + 2b) = 13 + 42

3a + 8a - 2b + 2b = 55

11a = 55

Divide both sides of the equation by 11:

a = 55 / 11

a = 5

Substitute the value of "a" into Equation 1 to find "b":

4(5) + b = 21

20 + b = 21

b = 21 - 20

b = 1

Therefore, the solution to the system of equations is a = 5 and b = 1.

Therfore, the answer is B, which is what you got as well! Good job!

~~~Harsha~~~

KM, JK, PK, and MJ are shown on the diagram.

Then the correct options are B, C, D, and F.

Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

A line segment in mathematics has two different points on it that define its boundaries.

All the line segments will be

JK, JM, KM, MP, PK, and KL

The triangle KPM.

And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.

Then the correct options are B, C, D, and F.

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Answer: rental is $415, and the standard deviation is $5.

Step-by-step explanation:

If about 99.7 percent of the monthly rentals fall between 400 and 430, it implies that this range encompasses three standard deviations from the mean.

To calculate the mean, we can find the midpoint of the given range:

Mean = (400 + 430) / 2 = 415

Since the range of three standard deviations covers about 99.7 percent of the data in a normal distribution, we can use this information to estimate the standard deviation (σ).

Standard deviation (σ) = (430 - 415) / 3 = 15 / 3 = 5

Therefore, based on the given information, the mean monthly rental is $415, and the standard deviation is $5.

Answer:

[tex]u+v=4.1\langle\cos160^\circ,\sin160^\circ\rangle[/tex]

Step-by-step explanation:

When adding two vectors, we add their horizontal components, and then their vertical components:

[tex]u=2\langle\cos325^\circ,\sin325^\circ\rangle=\langle2\cos325^\circ,2\sin325^\circ\rangle\\v=6\langle\cos155^\circ,\sin155^\circ\rangle=\langle6\cos155^\circ,6\sin155^\circ\rangle\\\\u+v=\langle2\cos325^\circ+6\cos155^\circ,2\sin325^\circ+6\sin155^\circ\rangle\\u+v\approx\langle-3.8,1.39\rangle[/tex]

We are not done however as we need to now calculate the magnitude and the direction of the resultant vector:

Magnitude:

[tex]||u+v||=\sqrt{(-3.8)^2+1.39^2}\approx4.1[/tex]

Direction:

[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{1.39}{-3.8}\biggr)\approx-20^\circ=180-20^\circ=160^\circ[/tex]

Therefore, the resultant vector is about [tex]4.1\langle\cos160^\circ,\sin160^\circ\rangle[/tex]

The equation for the regression line from the data is y = -0.98x + 56.8

Given data ,

To find the equation of the regression line, we will use the method of least squares. The regression line is represented by the equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

We need to calculate the values of m and b. Let's begin by finding the mean values of x and y:

Mean of x (x₁) = (6 + 13 + 14 + 10 + 13) / 5 = 12.2

Mean of y (y₁) = (25 + 44 + 46 + 52 + 57) / 5 = 44.8

Next, we calculate the deviations from the mean for both x and y:

Deviation from the mean of x (Δx) = x - x₁

Deviation from the mean of y (Δy) = y - y₁

Now, we calculate the sum of the products of the deviations from the mean:

Σ(Δx * Δy) = (6 - 12.2) * (25 - 44.8) + (13 - 12.2) * (44 - 44.8) + (14 - 12.2) * (46 - 44.8) + (10 - 12.2) * (52 - 44.8) + (13 - 12.2) * (57 - 44.8)

Σ(Δx * Δy) ≈ -51.6

Next, we calculate the sum of the squared deviations from the mean of x:

Σ(Δx²) = (6 - 12.2)² + (13 - 12.2)² + (14 - 12.2)² + (10 - 12.2)² + (13 - 12.2)²

Σ(Δx²) ≈ 52.8

Now, we can calculate the slope (m) using the formula:

m = Σ(Δx * Δy) / Σ(Δx²)

m ≈ -51.6 / 52.8 ≈ -0.98

Finally, we can calculate the y-intercept (b) using the formula:

b = y₁ - m * x₁

b ≈ 44.8 - (-0.98) * 12.2 ≈ 56.8

Hence , the equation of the regression line for the given data is:

y = -0.98x + 56.8

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To find the probability that 15 or more instructors choose the book with the better format and illustrations, we can use the binomial distribution formula.

Let's denote the event of an instructor choosing the book with the better format and illustrations as "success" (S), and the event of an instructor choosing the other book as "failure" (F). The probability of success is p = 0.5, and the probability of failure is q = 1 - p = 0.5.

We want to find the probability of 15 or more successes in a sample of 25 instructors. We can calculate this probability by summing the probabilities of exactly 15, 16, 17, ..., 25 successes.

P(X ≥ 15) = P(X = 15) + P(X = 16) + ... + P(X = 25)

Using the binomial distribution formula, the probability of exactly k successes in a sample of n trials is:

P(X = k) = C(n, k) * p^k * q^(n-k)

where C(n, k) is the binomial coefficient "n choose k," given by:

C(n, k) = n! / (k! * (n-k)!)

Applying this to our problem, we can calculate the probability as follows:

P(X ≥ 15) = P(X = 15) + P(X = 16) + ... + P(X = 25)

= Σ[ k = 15 to 25 ] ( C(25, k) * p^k * q^(25-k) )

Let's calculate this probability using the binomial distribution formula:

P(X ≥ 15) = Σ[ k = 15 to 25 ] ( C(25, k) * (0.5)^k * (0.5)^(25-k) )

Calculating this sum gives us the probability that 15 or more instructors choose the book with the better format and illustrations.

The value of x in the expression is 66/114.

Let's begin by addressing the issue in detail:

Emma runs 12 km, hence the time it takes her to complete that distance is 12/x hours.

Emma cycles 26 kilometers at a speed that is 10 kilometers per hour faster than she runs.

Her cycling pace is therefore (x + 10) km/hr. Her cycle distance is 26 kilometers, which can be calculated as 26/(x + 10) hours.

Emma's total time spent cycling and running is 22 hours and 48 minutes. By dividing 48 minutes by 60, we can translate it to hours: 48/60 = 0.8 hours.

We can now formulate an equation to express the entire amount of time spent:

12/x + 26/(x + 10) = 22.8

To get rid of the denominators and solve this equation, multiply both sides by x(x + 10).

12(x + 10) + 26x = 22.8x(x + 10)

To make the calculation easier:

12x + 120 + 26x = 22.8x² + 228x

Combining comparable phrases

38x + 120 = 22.8x² + 228x

Changing the equation's order:

22.8x² + 228x - 38x - 120 = 0

22.8x² + 190x - 120 = 0

By dividing the equation by 0.4, the coefficients are made simpler:

57x² + 475x - 300 = 0

Solving the equation by x = (-b ± √(b² - 4ac)) / (2a),

x = (-475 ± √(475² - 4 * 57 * -300)) / (2 * 57)

Simplifying further:

x = (-475 ± √(225625 + 68400)) / 114

x = (-475 ± √293025) / 114

x = (-475 ± 541) / 114

Now, we can calculate the two possible solutions:

x₁ = (-475 + 541) / 114

x₁ = 66 / 114

x₁ ≈ 0.579

x₂ = (-475 - 541) / 114

x₂ = -1016 / 114

x₂ ≈ -8.912

Take x = 66/114

Hence the value of x in the expression is 66/114.

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To determine the annual interest rate paid, we need to calculate the simple interest for one month and then convert it to an annual rate.

The formula for simple interest is:

Simple Interest = Principal × Rate × Time

In this case, the principal amount is $720, and after one month, you pay back a total of $1272. Therefore, the interest paid is:

Interest = $1272 - $720 = $552

We can now calculate the monthly interest rate:

Rate = Interest / Principal = $552 / $720 ≈ 0.7667

To convert the monthly interest rate to an annual rate, we multiply it by 12:

Annual Rate = Monthly Rate × 12 = 0.7667 × 12 ≈ 9.20

Therefore, you paid an annual interest rate of approximately 9.20%.

Answer:  $62.40

Step-by-step explanation:

Original price $80

22% of 80%

.22(80) = 17.60   >This is the discount

Sale price = Original price -  discount

Sale price = 80 - 17.60

Sale price = $62.40

Answer:

[tex]\Huge \boxed{\text{\$62.40}}[/tex]

Step-by-step explanation:

In the sale, the prices decrease by 22%. This means that the sale price is 78% of the original price.

[tex]\Large \text{Sale price = (100 - 22)\% of old price}\\\text{Sale price = 78\% of \$80}\\\text{Sale price = 0.78 $\times$ 80}\\\text{Sale price = \$62.40}[/tex]

part a.

the expected value of playing the game is  found as -$0.50.

part b.)

Jim can expect to lose money in the long run if he plays the game many times because the expected value is negative.

The expected outcomes and their corresponding values are:

If we roll a 1 =  Jim wins $1.

If we roll a 2 =Jim wins $2.

If we roll  a 3 = Jim wins $3.

If we roll  a 4 = Jim wins $4.

If we roll  a 5 or 6 =  Jim loses $6.50.

We then calculate the value:

Expected value = (Probability of rolling a 1) × (Value of rolling a 1) + (Probability of rolling a 2) × (Value of rolling a 2) + (Probability of rolling a 3) × (Value of rolling a 3) + (Probability of rolling a 4) × (Value of rolling a 4) + (Probability of rolling a 5 or 6) × (Value of rolling a 5 or 6)

Expected value = (1/6) × $1 + (1/6) × $2 + (1/6) × $3 + (1/6) × $4 + (2/6) × (-$6.50)

EV = $1/6 + $2/6 + $3/6 + $4/6 - $13/6

EV = ($1 + $2 + $3 + $4 - $13)/6

EV = -$3/6

Expected value = -$0.50

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