The vertices of a figure are given. Rotate the fig
of the image.
A(2,-2), B(4, -1), C(4, -3), D(2,-4)
90° counterclockwise about the origin
Whats the coordinates

Answer:

For B, 40% of the cars were trucks.

Step-by-step explanation:

If 2/5 of the cars are trucks, and you can convert 2/5 to 20 out of 50, and then 40 out of 100, making it 40%

The function f(x) = 8x^3 represents a cubic polynomial with a constant coefficient of 8. It follows the pattern of multiplying 8 by the cube of the input value, and its behavior remains consistent for both positive and negative values of x. The graph of the function is a cubic curve that passes through the origin and extends infinitely in both directions.

The function f(x) = 8x^3 represents a cubic polynomial with a constant coefficient of 8. This means that for any value of x, the function will output a value that is 8 times the cube of x. The first paragraph provides a brief summary of the given function, while the second paragraph explains the concept of a cubic polynomial and how the function behaves for different values of x.

The function f(x) = 8x^3 represents a cubic polynomial. A polynomial is an algebraic expression that consists of variables and coefficients combined using addition, subtraction, multiplication, and exponentiation. In this case, the variable is x, and its exponent is 3. The coefficient of the term is 8, indicating that for every x value, the function will output a value that is 8 times the cube of x.

To understand how the function behaves for different values of x, we can substitute various values into the equation. For example, if we substitute x = 1, we get f(1) = 8(1^3) = 8. Similarly, if we substitute x = 2, we get f(2) = 8(2^3) = 64. This demonstrates that the function follows the pattern of multiplying 8 by the cube of the input value.

Since the exponent is odd (3), the function will exhibit similar behavior for both positive and negative values of x. For negative values, the function will still produce an output that is 8 times the cube of x. For instance, if we substitute x = -1, we get f(-1) = 8((-1)^3) = -8, indicating that the function also handles negative inputs.

The graph of the function f(x) = 8x^3 will be a cubic curve that passes through the origin (0, 0) and extends to the positive and negative infinity. It will exhibit a steep slope for large values of x, whether positive or negative, due to the exponentiation of x to the power of 3. As x approaches infinity or negative infinity, the function will also tend to positive or negative infinity, respectively.

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Answer:

-5/8

Step-by-step explanation:

Convert standard form to slope-intercept form to find the slope.

5x + 8y = 50

8y = -5x + 50

y = -5/8x + 50/8

Slope: -5/8

Answer:

-5/8x

Step-by-step explanation:

First you need to find the slope of the given line.

Do this by converting it to slope intercept form (y=mx+b)

Divide the whole equation by 8 to isolate the y variable.

After dividing by 8 you should now have 5/8x + y = 6.25

Now you need to subtract y and 6.25 to isolate y

5/8x - 6.25 = -y

Now you have to divide the whole equation by negative 1 to make y positive. You end up with: y = -5/8 + 6.25

We know that the slopes of parallel lines are equal. Therefore the answer is -5/8x

The probability that x is less than 5 = 0.45

Discrete probability distribution:

It is a type of probability distribution that displays all the possible values of a discrete random variable accompanying the affiliated probabilities. We can also say that a discrete probability distribution provides the chance of occurrence of every possible value of a discrete random variable.

Discrete probability distribution:

x          = -10      0       10        20

P(X=x) = 0.35  0.10   0.15     0.40

The probability that x is less than 5:

P(X<5) = 1 - P (X = 10) - P(X= 20)

1 - 0.15 - 0.40 = 0.45

The probability that x is less than 5 is = 0.45

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The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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The complementary function for the differential equation is ye(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\). The particular solution for the differential equation is \(Yp(x) = -7e^(^6^x^)\). The general solution for the differential equation is y(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\) -\(7e^(^6^x^)\).

To find the complementary function for the given differential equation, we assume a solution of the form \(ye(x) = e^(^r^x^)\), where r is a constant to be determined. Plugging this into the differential equation, we get:

\(r^2e^(^r^x^) + 6e^(^r^x^) = 0\)

Factoring out \(e^(^r^x^)\), we obtain:

\(e^(^r^x^)(r^2 + 6) = 0\)

For a nontrivial solution, the term in the parentheses must equal zero:

\(r^2 + 6 = 0\)

Solving this quadratic equation gives us r = ±√(-6) = ±i√6. Hence, the complementary function is of the form:

ye(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\)

Next, we need to find the particular solution Yp(x) for the differential equation. The particular solution is assumed to have a similar form to the forcing term \(-294x^2^e^(^6^x^).\)

Since this term is a polynomial multiplied by an exponential function, we assume a particular solution of the form:

\(Yp(x) = (A + Bx + Cx^2)e^(^6^x^)\)

Differentiating this expression twice and substituting it into the differential equation, we find:

12C + 12C + 6(A + Bx + Cx^2) = \(-294x^2^e^(^6^x^)\)

Simplifying and equating coefficients of like terms, we get:

12C = 0 (from the constant term)

12C + 6A = 0 (from the linear term)

6A + 6B = 0 (from the quadratic term)

Solving this system of equations, we find A = -7, B = 0, and C = 0. Therefore, the particular solution is:

\(Yp(x) = -7e^(^6^x^)\)

Finally, the general solution for the differential equation is given by the sum of the complementary function and the particular solution:

y(x) = ye(x) + Yp(x)

y(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\) - \(7e^(^6^x^)\)

This is the general solution to the given differential equation.

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Both equalities hold true for any value of a > 0, as the probability of a continuous random variable taking any specific value is always 0.

Given that the random variable x is uniformly distributed over the interval [-a,a], the probability density function (PDF) of x is given by:

f(x) = 1/(2a), for -a ≤ x ≤ a
f(x) = 0, otherwise

To determine the parameter a, we need to use the given equalities:

a. P(-1 < x < 1) = 0.4

The probability of x lying between -1 and 1 is given by:

P(-1 < x < 1) = ∫(-1)^1 f(x) dx
             = ∫(-1)^1 1/(2a) dx
             = [x/(2a)]|(-1)^1
             = 1/(2a) + 1/(2a)
             = 1/a

Therefore, we have:

1/a = 0.4
a = 1/0.4
a = 2.5

So, for the equality P(-1 < x < 1) = 0.4 to hold, the parameter a should be 2.5.

b. P(|x| < 1) = 0.5

The probability of |x| lying between 0 and 1 is given by:

P(|x| < 1) = ∫(-1)^1 f(x) dx
          = ∫(-1)^0 f(x) dx + ∫0^1 f(x) dx
          = [x/(2a)]|(-1)^0 + [x/(2a)]|0^1
          = 1/(2a) + 1/(2a)
          = 1/a

Therefore, we have:

1/a = 0.5
a = 1/0.5
a = 2

So, for the equality P(|x| < 1) = 0.5 to hold, the parameter a should be 2.

c. P(x > 2) = 0

The probability of x being greater than 2 is given by:

P(x > 2) = ∫2^a f(x) dx
        = ∫2^a 1/(2a) dx
        = [x/(2a)]|2^a
        = (a-2)/(2a)

For the equality P(x > 2) = 0 to hold, we need:

(a-2)/(2a) = 0
a - 2 = 0
a = 2

So, for the equality P(x > 2) = 0 to hold, the parameter a should be 2.

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The Solution:

Given the system of inequalities below:

Graphing the inequalities, we have:

To choose the type of boundary line for the inequalities.

Enter two points on the boundary line.

For the inequality x>4:

For the second inequality, two points on the boundary line are:

The region to be shaded is region B as shown in my graph above (though I do not know how A and B are labeled in the given graph)

Answer:

9 Miles to be specific 8.95

Step-by-step explanation:

3 miles = 4.83 km

4.83 km = 4830 m

60 seconds X 45 =2700 Seconds

4830 divided by 2700 = 1.78 m/s

you want to know the distance so its speed X time

135 minutes X 60 seconds = 8100 secs

1.78 m/s X 8100 =14418 meters

14418 = 14.418 km

14.418 km = 9 miles

P.S. There is a shorter version but i think this is simpler for me and I use metric units.

The standard error of the sample proportion of patients with high BMD is approximately 0.0834.

The standard error of the sample proportion of patients with high bone mineral density (BMD) can be calculated using the formula:

SE = sqrt((p * (1 - p)) / n)

In this case, the sample size (n) is 30, and the proportion of patients with high BMD in the population (p) is 147/622.

In summary, the standard error of the sample proportion of patients with high BMD can be found by calculating the square root of the product of the proportion and its complement divided by the sample size.

To explain the answer, let's plug in the values into the formula:

p = 147/622 ≈ 0.2363

n = 30

SE = sqrt((0.2363 * (1 - 0.2363)) / 30) ≈ 0.0834

Therefore, the standard error of the sample proportion of patients with high BMD is approximately 0.0834.

The standard error represents the variability or uncertainty in the sample proportion compared to the true proportion in the population. A smaller standard error indicates less variability and provides more confidence in the estimate of the population proportion.

In this case, a standard error of 0.0834 suggests that the sample proportion of patients with high BMD may vary by about 8.34% from the true proportion in the population.

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Answer:

(x + 12)(x - 3)

Step-by-step explanation:

\( {x}^{2} + 9x = 36 \\ {x}^{2} + 9x - 36 = 0 \\ {x}^{2} + 12x - 3x - 36 = 0 \\ x(x + 12) - 3(x + 12) = 0 \\ (x + 12)(x - 3) = 0\)

The correct option of the given statement "The present value of $5,325 to be received in one period at a rate of 6.5%" is d. 5,000.

it can be found using the formula:

PV = FV/(1 + r),

where

PV is the present value,

FV is the future value,

and r is the interest rate expressed as a decimal.

Here, FV = $5,325 and r = 0.065 (6.5% expressed as a decimal).

Substituting these values into the formula gives:

PV = $5,325/(1 + 0.065)PV

    = $5,325/1.065PV

     ≈ $5,000

Therefore, the present value of $5,325 to be received in one period if the rate is 6.5% is approximately $5,000.

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Answer:

3/26

Step-by-step explanation:

6 of the 52 cards are red

Answer:

The = sign

Step-by-step explanation:

\(\frac{7}{8} -\frac{9}{12} =\frac{1}{8}\)

1/8 = 1/8

Answer: =

Step-by-step explanation:

\(\frac{7}{8}-\frac{9}{12} ?\frac{1}{8}\)

We need to find a common denominator for the two

which will be 24

But we need to multiply the numerators as well to change them.

\(\frac{7}{8}(\frac{3}{3})-\frac{9}{12} (\frac{2}{2} )?\frac{1}{8}\\\frac{21}{24}-\frac{18}{24}? \frac{1}{8}\\\frac{3}{24} ?\frac{1}{8}\\Simplify\\\frac{1}{8} =\frac{1}{8}\)

The given system of equations, Ax = b, can be solved using the Gauss-Jordan method. The augmented matrix for the system is formed, and row operations are performed to transform the matrix into reduced row-echelon form. The solution for the variables can then be obtained from the reduced matrix.

To solve the system of equations, we can start by forming the augmented matrix [A | b] using the coefficients and the constant values:

[2 2 1 | 9] [2 -1 3 | 6] [1 -1 2 | 5]. Next, we perform row operations to transform the matrix into reduced row-echelon form. The goal is to obtain a matrix where each leading coefficient is 1, and all other entries in the same column are zero. We can begin by performing row operations to eliminate the coefficients below the leading coefficient in the first column. By subtracting the first row from the second row and subtracting the first row from the third row, we get: [2 2 1 | 9] [0 -3 2 | -3] [0 -3 1 | -4]. Next, we perform row operations to eliminate the coefficients below the leading coefficient in the second column. By subtracting the second row from the third row, we obtain: [2 2 1 | 9] [0 -3 2 | -3] [0 0 -1 | -1]. Now, we can proceed with backward substitution to obtain the solution. From the last row, we have -x₃ = -1, so x₃ = 1. Substituting this value into the second row, we have -3x₂ + 2(1) = -3, which gives x₂ = 1. Finally, substituting the values of x₂ = 1 and x₃ = 1 into the first row, we have 2x₁ + 2(1) + 1 = 9, which gives x₁ = 2. Therefore, the solution to the system of equations is x₁ = 2, x₂ = 1, and x₃ = 1.

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The Maclaurin series of the given function f(x) = 1/5 + x can be found by using the formula for the Maclaurin series of a function, which is given by:

f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

where f'(0), f''(0), f'''(0), etc. denote the derivatives of the function evaluated at x=0. Since f(x) is a polynomial function of degree 1, we only need the first two terms of the Maclaurin series, which are:

f(0) = 1/5, and

f'(x) = 1

evaluated at x=0, so f'(0) = 1. Therefore, the Maclaurin series of f(x) is:

f(x) = 1/5 + x

= f(0) + f'(0)x

= 1/5 + x

This is the final answer, written in summation notation. The Maclaurin series of f(x) is simply the function itself, since it is a polynomial of degree 1.

To understand why this is the case, consider the formula for the Maclaurin series and the derivatives of f(x):

f(x) = 1/5 + x

f'(x) = 1

f''(x) = 0

f'''(x) = 0

...

Notice that all of the derivatives of f(x) after the first one are equal to zero. This means that all of the higher-order terms in the Maclaurin series formula are zero, so we only need the first two terms to get the full series. This is why the Maclaurin series of f(x) is just the function itself.

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Answer:

T=50.99

Step-by-step explanation:

Given:

I=3,875.78

P=1,900

R=4% I.e 4/100 , 0.04

T=?

I=PRT

3,875.79=($1,900)(0.04)t

3,875.79=76t

3,875.79/76= t

T=50.99

Based on the ratings system and the summarize() and mean() functions, the code chunk to add is summarize(mean(Rating)) and the mean rating is 3.185933.

To find the mean rating, the complete code should be trimmed_flavors_df %>% summarize(mean(Rating)).

This code would allow you to see the mean rating of your data by combining the summarize() and mean() functions such that you can display summary statistics.

Because of the "mean()" function, the statistic that will be displayed is the mean rating which in this case would be 3.185933.

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The skydiver deploys the parachute 20 seconds after jumping from the airplane.

The elevation is a term used to describe the vertical distance above or below a reference point or surface, usually the Earth's surface. In the context of a plane, elevation refers to the height of the plane above or below the ground or sea level.

The elevation is typically measured in feet or meters above sea level. The altitude of a plane is closely related to its elevation, but it specifically refers to the height of the plane above a standard reference level, such as sea level or a specific airport elevation.

The elevation of a plane can have significant effects on its performance and safety. High elevations can reduce the density of the air, which in turn can affect the plane's lift, thrust, and maneuverability. This can be particularly challenging for aircraft taking off or landing at high-altitude airports.

Pilots use a variety of instruments to measure the elevation and altitude of a plane, including radar altimeters, barometric altimeters, and GPS systems. These instruments can provide accurate and real-time information about the plane's position and height above the ground or sea level, helping the pilot to navigate and operate the plane safely.

In summary, elevation refers to the vertical distance above or below a reference point or surface, such as the Earth's surface. In the context of a plane, elevation refers to the height of the plane above or below the ground or sea level. Understanding and monitoring the elevation and altitude of a plane is crucial for safe and efficient flight operations.

We need to find the time when the elevation y is equal to 3600 feet. So, we can set y = 3600 and solve for x.

\(-16x^2\) + 10,000 = 3600

Subtracting 3600 from both sides:

\(-16x^2\) + 6400 = 0

Dividing both sides by -16:

\(x^2\)- 400 = 0

Adding 400 to both sides:

\(x^2\) = 400

Taking the square root of both sides:

x = ±20

Since the skydiver is not going to deploy the parachute before jumping from the airplane, the time must be a positive value. Therefore, x = 20 seconds.

Hence, the skydiver deploys the parachute 20 seconds after jumping from the airplane.

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The assumption that Q can be written as a countable union of open subsets is false, and we conclude that Q cannot be written as Q = nn=1 Un where ( un : n N ) is a sequence of open subsets in R.

According to the Baire Category Theorem, a complete metric space cannot be written as a countable union of nowhere dense sets. The set Q of rational numbers is a dense subset of the complete metric space R, and therefore it cannot be written as a countable union of nowhere dense sets.

To prove this, assume that Q = nn=1 Un, where each Un is an open subset of R. Since Q is dense in R, each Un must also be dense in R. However, this contradicts the Baire Category Theorem, which states that a complete metric space cannot be written as a countable union of nowhere dense sets. Therefore, the assumption that Q can be written as a countable union of open subsets is false, and we conclude that Q cannot be written as Q = nn=1 Un where ( un : n N ) is a sequence of open subsets in R.

In summary, the set Q of rational numbers cannot be written as a countable union of open subsets in R due to the Baire Category Theorem and the fact that Q is a dense subset of the complete metric space R.

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Answer:

The answer is C

Step-by-step explanation:

Khan Academy

Answer:

C

Step-by-step explanation:

Is the relation a function:

To determine if the relation is a function, we need to check if there is exactly one output for each input.

Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).

This means that there are two outputs for the same input, so the relation is not a function.

Therefore, the correct answer is: "No, because for each input there is not exactly one output."

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Reflexive property of congruence states that ∠a ≅ ∠A, ab ≅ AB.

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

The reflexive property of congruence shows that any geometric figure is congruent to itself. A line segment has the same length, an angle has the same angle measure, and a geometric figure has the same shape and size as itself. The figures can be thought of as being reflection of itself.

If the relation defined on a set is congruence and if the relation defioned on a set of numbers is equality, then it is called the reflexive property of equality. This property is generally used in proofd such as proving two triangles are congruent and in proofd of parallel lines. If two triangles share a common side or a common angle, then we can use the reflexive property of congruence to prove the two triangles are congruent.

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The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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The simplified difference quotient for the function f(x) = 5/x^2 is h^2/(5x^2h).

The difference quotient is a mathematical expression that represents the average rate of change of a function over a small interval. It is commonly used to calculate the derivative of a function. In this case, the given function is f(x) = 5/x^2.

To find the difference quotient, we substitute (x+h) in place of x in the function and subtract the original function value. Simplifying the expression gives us (5/(x+h)^2 - 5/x^2) / h. Further simplification leads to (5x^2 - 5(x+h)^2) / (x^2(x+h)^2) / h. By expanding and simplifying, we get h^2 / (5x^2h).

Therefore, the simplified difference quotient for the given function f(x) = 5/x^2 is h^2/(5x^2h).

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Answer:

It depends on how many dimes are in the piggy bank. It could be any answer that didn't have a 5 in the tenths place. For example, it couldn't be a number like $1.05 because any whole number multiplied by 10 would end in a 0

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Answer:

\(y=\frac{2}{-0.5} x\)

Step-by-step explanation:

Since we know that the line starts at (0,0), it goes up by 2 and goes 0.5 to the left. I hope this was helpful & if it is correct.

From the calculations;

The equations of motion are used in kinematics to obtain the various variables that has to do with motion.

In this case;

distance covered = 30 ft

initial velocity = 40 ft/second

Final velocity = 0 m/s at the maximum height

Hence;

v^2 = u^2 - 2gh

since v = 0

u^2 = 2gh

h = u^2/2g

h = (40)^2/2(9.8)

h = 82 feet

highest point above the ground = 82 feet + 30 feet = 112 feet

Now;

v = u - gt

since v = 0

u = gt

t = u/g

t = 40/9.8

t = 4 seconds

Time taken to hit the ground = 2(4 seconds) = 8 seconds

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