Question 5
Tell whether the lines are parallel, perpendicular, or neither
Line 1: (4, -3) and (-8, 1)
Line 2: (5, 11) and (8, 20)

Answer:

-7

Step-by-step explanation:

2-3(3)=-7

The equation that shows the relationship between the angles in the triangle is m∠1 + m∠2 + m∠3 = 180.

The equation that shows the relationship between the angles in the triangle is determined as follows;

The sum of angles in a triangle is equal to 180 degrees.

So based on this information, the equation that shows the relationship between the angles in the triangle is formulated as;

angle 1 + angle 2 + angle 3 = 180

We can re-write the equation as follows;

m∠1 + m∠2 + m∠3 = 180

Thus, the equation that shows the relationship between the angles in the triangle is the sum of angle 1 plus angle 2 plus angle 3.

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A.  To ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.

b. We find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.

n > 2401

a) Using the Chebyshev inequality, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02.

The Chebyshev inequality states that for any random variable X with mean μ and standard deviation σ, the probability of X deviating from the mean by k standard deviations is at least 1 - 1/k^2.

In this case, we want the relative frequency estimate to deviate from 0.20 by less than 0.02, which means we want the difference to be within 0.02 standard deviations of the mean. Since the relative frequency estimate is a sample proportion, its standard deviation can be approximated by sqrt(p(1-p)/n), where p is the true proportion (0.20) and n is the sample size.

We can set up the inequality as follows:

1 - 1/k^2 ≥ 0.95

Solving for k:

1/k^2 ≤ 0.05

k^2 ≥ 1/0.05

k^2 ≥ 20

Taking the square root of both sides:

k ≥ sqrt(20)

k ≥ 4.47

To ensure that the difference between the relative frequency estimate and 0.20 is within 0.02, we need k standard deviations to be less than 0.02. So, we have:

k * sqrt(p(1-p)/n) < 0.02

4.47 * sqrt(0.20(1-0.20)/n) < 0.02

Simplifying:

sqrt(0.20(1-0.20)/n) < 0.02/4.47

sqrt(0.16/n) < 0.00448

0.4/sqrt(n) < 0.00448

sqrt(n) > 0.4/0.00448

sqrt(n) > 89.29

n > 89.29^2

n > 7975.84

Therefore, to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.

b) Using the central limit theorem, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the sample mean differs from 0.20 by less than 0.02.

According to the central limit theorem, the sample mean follows a normal distribution with mean μ and standard deviation σ/sqrt(n), where σ is the population standard deviation (unknown in this case), and n is the sample size.

To ensure that the difference between the sample mean and 0.20 is within 0.02, we can set up the following inequality:

z * (σ/sqrt(n)) < 0.02

Since the population standard deviation σ is unknown, we can use a conservative estimate by assuming the worst-case scenario, which is p(1-p) = 0.25. Therefore, σ = sqrt(0.25) = 0.5.

Using the standard normal distribution table, we find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.

1.96 * (0.5/sqrt(n)) < 0.02

0.98/sqrt(n) < 0.02

sqrt(n) > 0.98/0.02

sqrt(n) > 49

n > 49^2

n > 2401

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The area of the largest circle that can be cut out of the square piece of wood is approximately 31.8 square feet.

The diameter of the largest circle that can be cut out of the square piece of

wood will be equal to the diagonal of the square, which is found using the

Pythagorean theorem.

The diagonal of the square is

√(4.5² + 4.5²) = √(40.5) ≈ 6.36 feet.

The radius of the circle will be half of the diameter,

so r ≈ 6.36/2 = 3.18 feet.

The area of the circle is

A = πr² ≈ π(3.18)² ≈ 31.8 square feet.

Therefore, the area of the largest circle that can be cut out of the square

piece of wood is approximately 31.8 square feet.

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Answer:

The answer depends on how much each cake costs.

Step-by-step explanation:

For example, divide (price of one cake) by $675. Thats how many cakes she made.

The required solution in scientific notation is 2 × 10¹ .

Scientific notation can be used to indicate values that are either too large or too little to be conveniently written in decimal form (typically would result in a long string of digits).

The given expression is (6.4 × 10³) ÷ (3.2 × 10²)

Simplifying we get :

(6.4 × 10³) ÷ (3.2 × 10²) = 20

This can be written in the scientific notation as : 2 × 10¹

Therefore the required solution is 2 × 10¹

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Answer: Therefore, the plastic for the prototypes will cost $1,452,150.

Step-by-step explanation:

The volume of the cube can be calculated as:

Volume of the cube = (side length)^3 = (14 mm)^3 = 2,744 mm^3

The volume of the hole can be calculated as:

Volume of the hole = (1/4) x π x (diameter)^2 x thickness = (1/4) x π x (12 mm)^2 x 14 mm = 5,049 mm^3

The volume of plastic used to create one prototype can be calculated as:

Volume of plastic = Volume of cube - Volume of hole = 2,744 mm^3 - 5,049 mm^3 = -2,305 mm^3

Note that the result is negative because the hole takes up more space than the cube.

However, we can still use the absolute value of this result to calculate the cost of the plastic:

Cost of plastic per prototype = |Volume of plastic| x Cost per cubic millimeter = 2,305 mm^3 x $0.07/mm^3 = $161.35/prototype

To find the cost of the plastic for 9,000 prototypes, we can multiply the cost per prototype by the number of prototypes:

Cost of plastic for 9,000 prototypes = 9,000 x $161.35/prototype = $1,452,150

The plastic for the prototypes will cost $1,452,150.

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We need to find the general solution of the above PDE. Let's solve the above PDE by the method of characteristic. Let us first solve the PDE by using the method of characteristics.

The method of characteristics is a well-known method that provides a solution to the first-order partial differential equations. To use this method, we first need to find the characteristic curves of the given PDE. Thus, the characteristic curves are given by $x = t + c_1$.

Now, we need to eliminate $t$ from the above equations in order to obtain the general solution. By eliminating $t$, we get the general solution as:$$u(x,y) = f(2x - 3y) + 3(x - 2y)$$ where $f$ is an arbitrary function of one variable. Hence, the general solution of the PDE $u_{xx} - 2u_{xy} - 3u_{yy} = 0$ is given by the above equation. Thus, the main answer to the given question is $u(x,y) = f(2x - 3y) + 3(x - 2y)$. In order to find the general solution of the PDE $u_{xx} - 2u_{xy} - 3u_{yy} = 0$, we first used the method of characteristics. The method of characteristics is a well-known method that provides a solution to the first-order partial differential equations.

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Answer: y=17 x=10

Step-by-step explanation:

so they have equal measures and they’re a linear pair (make a line) and a line is 180° so that would means you can set both equal to 90°

9y-63=90 and 9x=90

so for the first one you subtract 63 from 90 then divide by 9 to get 17

the next one you just divide by 9 to get 10 therefor y=17 and x=9

Answer:

A. x= 13/12, y = -3/4

Explanation:

Given the system of equations:

First, the two linear functions are graphed using a calculator:

The solution to the system of equations is the point where the two lines intersect.

From the graph, the point where the two lines intersect is:

Thus, the solution to the system is:

Option A is correct.

Answer:

Step-by-step explanation:

65.246

The correct answer is Yes, past age 85 years of age, for every 100 men, there are 200 women.

Given,

In the question:

Your grandmother is 87 years old and she has remarked to you that nearly all of her friends are women. She told you that it is rare to see a man older than age 85. She is correct because, after age 85, for every 100 men, there are __________.

Now, According to the question:

Your grandmother is 87 years old and she told you that all of her friends are women. There is no single man in her circle of friends. She also told that it is rare to see a man over the age of 85. It is because of the fact that women are more in number than man above the age of 85 and this ratio is like 100 men per 200 women, which means the chances of getting a male friend is almost half after the age of 85. So women are more in number than men.

Hence, The correct answer is Yes, past age 85 years of age, for every 100 men, there are 200 women.

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x' evaluated at the point (-1,1) is -1/2. x' = -1/2 at the point (-1,1). Differentiating both sides of the equation with respect to t.

To find x' for x(t) defined implicitly by the equation x + tx + t - 3 = 0, we can use implicit differentiation.

Differentiating both sides of the equation with respect to t, we have:

1 + x' + t(dx/dt) + dx/dt = 0.

Simplifying this expression, we get:

1 + 2(dx/dt) + (t+1)(dx/dt) = 0.

Now, we can solve for dx/dt (which represents x'):

dx/dt = -(1)/(2+t+1) = -1/(t+3).

To evaluate x' at the point (-1,1), we substitute t = -1 into the expression for dx/dt:

dx/dt = -1/(-1+3) = -1/2.

Therefore, x' evaluated at the point (-1,1) is -1/2.

Therefore, x' = -1/2 at the point (-1,1).

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Answer:

Precalculus Examples

Popular Problems Precalculus Find the Center and Radius x^2+y^2=121

x^2+y^2=121

This is the form of a circle. Use this form to determine the center and radius of the circle.

(x−h)^2+(y−k)^2=r^2

Match the values in this circle to those of the standard form. The variable r represents the radius of the circle, h represents the x-offset from the origin, and k represents the y-offset from origin.

r=11

h=0

k=0

The center of the circle is found at (h,k).

Center: (0,0)

These values represent the important values for graphing and analyzing a circle.

Center: (0,0)

Radius: 11

Step-by-step explanation:

Hope it is helpful......

Answer:

9:17

Step-by-step explanation:

Answer: 9:17 am

Step-by-step explanation: I added all the minutes together and got 77 minutes. Then I simplified the 77 minutes into an hour and 17 minutes. Then I added the 1hour and 17minutes to 8:00 am.

Answer: -135

Step-by-step explanation:

90 + 45 = 135

90 - 135 = -45

I hope this helps

Answer:

3

Step-by-step explanation:

7.2 ÷ 2.4 = 3

Answer:

C

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

2(x + 8) = x + 20

2x + 16 = x + 20

-x           -x

x + 16 = 20

   -16     -16

x = 4

Answer:

x=4

Step-by-step explanation:

2x  + 16 = x + 20

-x           -x

1x + 16 = 20

   - 16 = -16

1x = 4

1      1 = 4    (x=4)

Answer:

3(x+5)

Step-by-step explanation:

x= 2

2(2) + 5 = 9

Hope this helps!

The slope of U is negative, which indicates that it is sloping downwards to the right, while the slope of V is positive, which indicates that it is sloping upwards to the right.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

||U|| = 4

||V|| = 4

Slope U = -1

Slope V = 1

To determine whether U and V are equivalent, we need to check if they have the same magnitude and direction.

Since ||U|| = ||V|| = 4, they have the same magnitude. However, since Slope U = -1 and Slope V = 1, they do not have the same direction.

Therefore, we can conclude that U and V have the same magnitude but not the same direction, so they are not equivalent.

The magnitude of each vector is 4, and the slope of U is -1 while the slope of V is 1. The slope of a vector is given by the ratio of its vertical component to its horizontal component, so we can find the horizontal and vertical components of U and V as follows:

For vector U:

Horizontal component = ||U||cos(θ) = 4cos(-45°) = 2.83

Vertical component = ||U||sin(θ) = 4sin(-45°) = -2.83

Slope U = Vertical component / Horizontal component = -1

For vector V:

Horizontal component = ||V||cos(θ) = 4cos(45°) = 2.83

Vertical component = ||V||sin(θ) = 4sin(45°) = 2.83

Slope V = Vertical component / Horizontal component = 1

Interpreting the results, we can say that U and V have the same length, but they point in opposite directions (180 degrees apart).

Therefore, The slope of U is negative, which indicates that it is sloping downwards to the right, while the slope of V is positive, which indicates that it is sloping upwards to the right.

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The length of the shortest highway that can be built between the two towns is approximately 73.38 km.

(a) Let's assume that 'd' is the shortest length of the highway that can be built between the two towns. Using the Pythagorean theorem, we can determine the value of 'd':

d² = (41.7)² + (60.3)²

d² = 1743.69 + 3636.09

d² = 5379.78

d = √5379.78

Therefore, the length of the shortest highway that can be built between the two towns is approximately 73.38 km.

(b) To find the angle that the highway makes with respect to due west, we can use the tangent function:

Tanθ = Opposite side / Adjacent side = 41.7 / 60.3

Tanθ ≈ 0.692

Using inverse tangent, we can find the angle θ:

θ ≈ tan⁻¹(0.692)

θ ≈ 34.15°

Therefore, the angle between the highway and due west is approximately 34.15°.

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The two triangles are congruent, as the Pythagorean Theorem ensures that the hypotenuse of the two triangles will be equal.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

If two triangles have congruent side lengths, the hypotenuse for the two triangles will also be the same, hence the Pythagorean Theorem ensures the congruence of the two triangles.

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Answer:

A person standing on a moving walkway travels 60 feet in 20 seconds. What equation represents this relationship? How many feet will person travel 10 seconds?

Step-by-step explanation:

HELP ME

3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.

The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.

Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8

= -13.8% / x Thus, we have: x

= -13.8% / 3.8

= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage

= 13.8 / 3.8

= 3.63% The percentage decrease in sales is 3.63%.

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Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

Answer:

24.

Step-by-step explanation:

The pattern is clearly going up by twos.

So continuing the pattern,

1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

1 2  3   4 5   6   7   8   9   10  11    12   13