if the point (-2, 5) is 7 units below the point P(x,y) and 8 units to the left of it, then what are the coordinates of the point P(x,y)?​

The statement "The probability of the union of two dependent events is P(A) + P(B | A)." is False.

The correct formula for the probability of the union of two events A and B is:

P(A or B) = P(A) + P(B) - P(A and B)

This formula holds whether or not the events are dependent.

The term P(B | A) represents the conditional probability of B given that A has occurred, and it is used in the formula for the probability of the intersection of two events:

P(A and B) = P(A) x P(B | A)

So, to compute P(A or B), we need to take into account the probability of the intersection of A and B, which is subtracted from the sum of the individual probabilities P(A) and P(B).

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The table of solutions for the given equation (y = -2x²) include the following:

x                    y_

-2                  -8

-1                   -2

0                   -0

1                    -2

2                   -8

Also, a graph of the solution of this equation (y = -2x²) has been plotted in the image attached below.

In order to determine the valid and true solutions to the given quadratic equation, we would have to substitute the values of contained in the table into the quadratic equations as follows;

At x = -2, the value of point y is as follows:

y = -2x²

y = -2(-2)²

y = -2 × 4

y = -8

At x = -1, the value of point y is as follows:

y = -2x²

y = -2(-1)²

y = -2 × 1

y = -2

At x = 0, the value of point y is as follows:

y = -2x²

y = -2(0)²

y = -2 × 0

y = 0

At x = 1, the value of point y is as follows:

y = -2x²

y = -2(1)²

y = -2 × 1

y = -2

At x = 2, the value of point y is as follows:

y = -2x²

y = -2(2)²

y = -2 × 4

y = -8

In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.

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Answer:

i think its $0.20

Step-by-step explanation:

 12                 1

------      =   ---------

 2.49          0.20

1 egg = $0.20

Answer: the answer is C

Answer:

please the question is not clear

To find the local maximum and minimum values as well as saddle points of the function f(x, y) = 2y cos(x), where 0 ≤ x ≤ 2π, and answers are Local maximum value(s): DNE, Local minimum value(s): (π/2, 0), Saddle point(s) (x, y, f): (3π/2, 0, 0)

First, we find the partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = -2y sin(x)

∂f/∂y = 2cos(x)

To find the critical points, we set both partial derivatives equal to zero and solve the system of equations:

-2y sin(x) = 0

2cos(x) = 0

From the first equation, we have two possibilities:

1) y = 0

2) sin(x) = 0, which implies x = 0 or x = π

For y = 0, the second equation gives us cos(x) = 0, which implies x = π/2 or x = 3π/2.

So, the critical points are (0, 0), (π/2, 0), and (3π/2, 0).

Next, we analyze the second partial derivatives:

∂²f/∂x² = -2y cos(x)

∂²f/∂y² = 0

∂²f/∂x∂y = 2sin(x)

Now, we need to evaluate the second partial derivatives at each critical point:

For (0, 0):

∂²f/∂x² = -2(0)cos(0) = 0

∂²f/∂y² = 0

∂²f/∂x∂y = 2sin(0) = 0

For (π/2, 0):

∂²f/∂x² = -2(0)cos(π/2) = 0

∂²f/∂y² = 0

∂²f/∂x∂y = 2sin(π/2) = 2

For (3π/2, 0):

∂²f/∂x² = -2(0)cos(3π/2) = 0

∂²f/∂y² = 0

∂²f/∂x∂y = 2sin(3π/2) = -2

Now, let's analyze the nature of these critical points:

For (0, 0):

Since the second partial derivatives are both zero, the second derivative test is inconclusive.

For (π/2, 0):

The second derivative ∂²f/∂x∂y = 2 is positive, indicating a local minimum.

For (3π/2, 0):

The second derivative ∂²f/∂x∂y = -2 is negative, indicating a saddle point.

Therefore, the results are as follows:

Local maximum value(s): DNE

Local minimum value(s): (π/2, 0)

Saddle point(s) (x, y, f): (3π/2, 0, 0)

If you have three-dimensional graphing software, I recommend plotting the graph of the function f(x, y) = 2y cos(x) within the domain 0 ≤ x ≤ 2π to visualize the function and its important aspects, including the local minimum and saddle point.

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Answer:

you can get .2 of a pint

Step-by-step explanation:

3 pints is $15 which means that one pint is 5. that one pint of ice cream has 5 dollars worth and since you only want for one dollar, it would be .2 because it's split into 5 parts.

Answer:

9)  1/48

11)  1/24

13)  5/16

14)  1/8

Step-by-step explanation:

9) P(A and 5) = 1/8 × 1/6

11) P(J and LT 3) = 1/8 x 2/6

13) P (consonant and odd) = 5/8 x 1/2

14) P ('M' or 'T' and GT 3) = [(1/8+1/8) × 1/2]  = 2/8 x 1/2

By applying the binomial distribution formula, it can be concluded that the probability that more than 6 will say yes is 0.423 (option B).

Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

C(n,r) = n! / (r! (n-r)!) where

n = number of samples

r = number of selected samples

The binomial distribution formula is used to find the probability of the specific outcome in a discrete distribution.

P(X) = C(n,r) * \(p^{r}\) * \(q^{n-r}\) where:

C = combination value

p = probability of success on a single trial

q = probability of failure on a single trial

n = 22

p = 28% = 0.28

q = 1 - 0.28 = 0.72

The probability that r adults will say yes is given by the binomial distribution:

P(X=r) = C(n,r) * \(p^{r}\) * \(q^{n-r}\)

= C(22,r) * \(0.28^{r}\) * \(0.72^{22-r}\)

P(X≤6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)

Now we calculate for each probability:

P(X=0) = C(22,0) * 0.28⁰ * 0.98²² = 0.000726633

P(X=1) = C(22,1) * 0.28¹ * 0.98²¹ = 0.00621676

P(X=2) = C(22,2) * 0.28² * 0.98²⁰ = 0.025385

P(X=3) = C(22,3) * 0.28³ * 0.98¹⁹ = 0.0658131

P(X=4) = C(22,4) * 0.28⁴ * 0.98¹⁸ = 0.121571

P(X=5) = C(22,5) * 0.28⁵ * 0.98¹⁷ = 0.1702

P(X=6) = C(22,6) * 0.28⁶ * 0.98¹⁶ = 0.187535

If we sum up the results, we get P(X≤6) = 0.577447493

P(X>6) = 1 - P(X≤6)

           = 1 - 0.577447493

           = 0.422552507

           ≈ 0.423

Thus the probability that more than 6 will say yes is 0.423.

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Answer:

Since both equations are satisfied, the point (-3,5) is the solution of the system

Step-by-step explanation:

System of Equations

If a system of equations of two variables has a single solution (x,y), then both equations must be satisfied for x and y.

We are given the system:

6 x + 5 y = 7

x + 4y = 17

Betty found the solution (-3,5). Substituting in both equations:

6*(-3) + 5 * 5 = -18 + 25 = 7

-3 + 4*20 = 17

Since both equations are satisfied, the point (-3,5) is the solution of the system

Answer:

D. (–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.

Step-by-step explanation:

The given equations are:

and

Betty correctly determined that the ordered pair  is a solution by substituting it into both equations.

Betty's work will look like this;

First Equation:

This statement is True.

Second equation;

This is also TRUE

Hence the correct answer is

D. (–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.

Answer:

−28hw+9w+3

Step-by-step explanation:

5w(1-8h) = 5w-40wh

+12wh = -28hw

-28hw+5w+5w = -28hw+10w

-w = -28hw+9w

+3 = -28hw+9w+3

The cosine function with amplitude 2 and period 6π is given by:

y = 2cos(x/3).

The standard cosine function is given by:

y = Acos(Bx).

In which:

For a cosine function with amplitude 2 and period 6π, we have that A = 2 and B = 1/3, hence:

y = 2cos(x/3).

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Answer:

8 nine tenths

Step-by-step explanation:

Step-by-step explanation:

By AAS congruence, triangles RNM and RNP are congruent. Hence 7x = 2x + 25, x = 5.

Line RM = 7x = 7(5) = 35 units.

Answer:

a

Step-by-step explanation:

(3x3) + (5x3) + 25

9 + 15 + 25

=49

\(r(-6)=-\frac{2}{3}(-6)+4=4+4=\boxed{8}\)

The value of r(x) at f(- 6) = 8.

We have the function r(x) = \(-\frac{2}{3} x + 4\)

We have to find the value of r(x) at x = - 6.

Substitute x = - 2 in the value of f(x) -

f(-2) = 5 (-2) + 3 = - 10 + 3 = - 7.

According to question, we have -

f(x) = \(-\frac{2}{3} x + 4\)

Substitute r = -6 in f(x), we have -

f(-6) = \(\frac{-2}{3} \times -6 + 4\)

f(-6) = - 2 x - 2 + 4

f(-6) = 4 + 4 = 8

Hence, the value of f(x) at f(- 6) = 8.

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Mean of country A is $29600 and median $29000. Mean of country B is $49800 and median is $29000. Country B has greater income inequality. So option B is the correct answer.

Mean of incomes in country A = (9000+ 21000+ 29000 + 39000+ 50000)/5   =  $29600

Median income of country A = (5+1)/2 th term = 3rd term = $29000

Mean to median ratio = 29600/ 26000= 1.02

Mean income of country B = ( 9000+ 21000+ 29000+ 39000+ 151000)/5 = $ 49800

Median income = (n+1)/2 th term = (5+1)/2 = 3rd term = 29000

Mean to median ratio of country B = 49800/29000 = 1.71

Since mean and median are closer to each other, standard deviation is less. The mean to median ratio is greater for country B. So country B has greater income inequality.

If the income inequality has been increasing, then the mean-median ratio will increase, due to the extreme values, mean will increase. So option B is the correct answer.

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Answer: D. < CBA

Step-by-step explanation:

The area in the first quadrant between the given circles is 2π.

The given equation of circles are:

x²+y²=16,

x²+y²=16,

x²−4x+y²=0

To evaluate the integral, we'll need to convert the equations into polar coordinates.

The first circle, x² + y² = 16.

In polar coordinates,

x = rcosθ

y = rsinθ.

Substituting these into the equation,

we get r²cos²θ + r²sin²θ = 16.

Simplifying this equation, we have r² = 16,

which simplifies further to r = 4.

The second circle, x² - 4x + y² = 0.

Converting this into polar coordinates, we have

(rcosθ)² - 4(rcosθ) + (rsinθ)² = 0.

Simplifying this equation, we get

r² - 4rcosθ = 0,

Which leads to r = 4cosθ.

To find the area in the first quadrant between these two circles,

Integrate the area element dA over the given region.

The area element in polar coordinates is given by

dA = 1/2 (r² dθ).

Now, set up the integral to evaluate the area:

\(A = \int\limits^{\frac{\pi}{2}}_0 {(\frac{1}{2} r^2)} \, d\theta\\ =\frac{1}{2} \int\limits^{\frac{\pi}{2}}_0 {4cos^2\theta} \, d\theta \\= 8 \int\limits^{\frac{\pi}{2}}_0 {cos^2\theta} \, d\theta\)

Using trigonometric identities,

We can simplify this integral further:

\(= 8 \int\limits^{\frac{\pi}{2}}_0 {(1+cos2\theta)/2} \, d\theta\)                                 [∵ cos2θ = 2cos²θ - 1]

= (1/2) [(8(π/2) + 4sin(2(π/2))) - (8(0) + 4sin(2(0)))]

= (1/2) [(4π + 0) - (0 + 0)]

= 2π

Hence,

The area in the first quadrant between the given circles is 2π.

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Answer:

Step-by-step explanation:

$350 -$275= $75 profit

Answer:

40 cm^2

Step-by-step explanation:

Area of rectangle = length * width.
Area of square = length^2

To find the area of the given shape, we must subtract the area of the square from the area of the rectangle.

Area of the given rectangle = 8 * 7 = 56 cm^2
Area of the given square = 4^2 = 16 cm^2

56 - 16 = 40 cm^2

Answer:

4.5 x 0.72

Step-by-step explanation:

I AM ASSUMING THAT YOU FORGOT TO ADD 2 AFTER 0.7 IN 4.5 x 0.7

Answer:

you need to add the graph

Answer:

no graf

Step-by-step explanation:

Answer:

See the attached worksheet

Step-by-step explanation:

The function is transformed by subtracting 3 from both the x and y values. I'm uncertain how this is expressed in a functional form.

The value of t(-u + 2v) is 5/6.

To find the value of t(-u + 2v), we can use the linearity property of linear transformations.

We know that t(u) = 1/2 and t(v) = 2/3.

Let's break down the expression t(-u + 2v):

t(-u + 2v) = t(-1u + 2v)

Since t is a linear transformation, we can distribute the transformation across the addition and scalar multiplication:

t(-u + 2v) = t(-1u) + t(2v)

Using the linearity property, we can factor out the scalars:

t(-u + 2v) = -1t(u) + 2t(v)

Now substitute the given values of t(u) and t(v):

t(-u + 2v) = -1×(1/2) + 2×(2/3)

Simplifying the expression:

t(-u + 2v) = -1/2 + 4/3

To add these fractions, we need a common denominator:

t(-u + 2v) = -3/6 + 8/6

Combining the fractions:

t(-u + 2v) = 5/6

Therefore, t(-u + 2v) equals 5/6.

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The maximum area of the rectangular plot enclosed with 600m of wire is approximately 20,000 square meters. The function y = x^5/4 passes through the origin, is symmetric about the y-axis, and is increasing for x > 0 and decreasing for x < 0.

The maximum area of the rectangular plot that can be enclosed with 600m of wire is obtained when the length of the longer side is twice the length of the shorter side. Therefore, the maximum area is obtained when the shorter side of the rectangular plot is approximately 100m and the longer side is approximately 200m. The maximum area of the rectangular plot is then approximately 20,000 square meters.

To graph the function y = x^5/4, we can analyze its properties. The function is a power function with an exponent of 5/4. It has a single real root at x = 0, which means the graph passes through the origin. The function is increasing for x > 0 and decreasing for x < 0.

The graph of the function y = x^5/4 exhibits symmetry about the y-axis. This means that if we reflect any point (x, y) on the graph across the y-axis, we obtain the point (-x, y). The graph approaches positive infinity as x approaches positive infinity and approaches negative infinity as x approaches negative infinity.

As for the intervals where the function is increasing or decreasing, it is increasing for x > 0 and decreasing for x < 0. This means that the function is increasing on the interval (0, ∞) and decreasing on the interval (-∞, 0).

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The most appropriate choice for perimeter of a shape will be given by-

UT = 19 ft

ST = 19 ft

RS = 19 ft

UR = 19 ft

What is perimeter of a shape?

Perimeter of a shape is the length of the boundary of the shape.

It is obtained by taking the sum of all the length of the boundary.

Here,

UT = (25 - x) ft

ST = (3x + 1) ft

RS = (13 + x) ft

UR = (4x - 5) ft

Perimeter = UT + ST + RS + UR

                = (25 - x + 3x + 1  + 13 + x +4x -5) ft

                = (7x + 34) ft

By the problem,

\(7x +34 =76\\7x = 76 -34\\7x = 42\\x = \frac{42}{7}\\x =6\)

UT = \(25 - 6\) = \(19\) ft

ST = \(3 \times 6 + 1\) = \(19\) ft

RS = \(13 + 6 = 19\) ft

UR = \(4\times 6 - 5\) = 19 ft

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Answer:

N=5

Step-by-step explanation:

38N = 10*4 + (4+6)15

38N = 180

N=5

Answer:

Answer:

N=5

Step-by-step explanation:

Step-by-step explanation:

38N = 10*4 + (4+6)15

38N = 190

N=5