suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. use the 6 8-9 5-99.7 rule to find the percentage of buyers who paid:

Answer:

\(\frac{dy}{dx}\) = - 10x - 3

Step-by-step explanation:

differentiate using the power rule

\(\frac{d}{dx}\) (a\(x^{n}\) ) = na\(x^{n-1}\) and \(\frac{d}{dx}\) (constant ) = 0

then

y = - 5x² - 3x + 6

\(\frac{dy}{dx}\) = 2(- 5)\(x^{2-1}\) + 1(- 3)\(x^{1-1}\) + 0

   = - 10x - 3\(x^{0}\) + 0

   = - 10x - 3

The truth table for (p ∧ q) ∨ ( ∼ p ∧ ∼ q) a tautology, a contradiction is as follows:

p  q   |   p ∧ q    | ∼ p ∧ ∼ q  |  (p ∧ q) ∨ ( ∼ p ∧ ∼ q)
---|---|---|---
T | T | F |  T
T | F | T |  T
F | T | T |  T
F | F | T |  T

Therefore, (~p ∨ q) ∨ (p ∧ ~q) is a tautology.

5. The truth table for ∼ (p ∨ q) is as follows:

p  q   |  p ∨ q    | ∼ (p ∨ q)  |  ∼ p ∧ ∼ q
---|---|---|---
T | T | F |  F
T | F | F |  F
F | T | F |  F
F | F | F |  T

Therefore, ∼ (p ∨ q) is logically equivalent to ∼ p ∧ ∼ q. This law is called the De Morgan's Law.

6a. The truth table for p → q is as follows:

p  q   |  p → q  |  ∼ p ∨ q
---|---|---
T | T | T
T | F | F
F | T | T
F | F | T

Therefore, p → q and ∼ p ∨ q are logically equivalent.

6b. The truth table for ∼ (p → q) is as follows:

p  q   |  p → q  |  ∼ (p → q)  |  p ∧ ∼ q
---|---|---|---
T | T | F | F
T | F | T | F
F | T | T | F
F | F | T | T

Therefore, ∼ (p → q) and p ∧ ∼ q are not logically equivalent.

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As asked by the question, the value of K for a given equation of a line is equal to the slope of the line.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

The value of K for a given line is equal to the slope of the line. Since lines are generally expressed in the form of y = mx +b , where m is the slope of the line and b is the y-intercept of the line. Here , the value of K will be equal to the slope m of the line.

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Answer: The equation of a line can be written in the slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of a line that passes through the point (3, 2) and cuts off equal intercepts on the x and y axes, we can use the following steps:

First, we need to find the slope of the line using the point (3, 2) and the fact that the line cuts off equal intercepts on the x and y axes. Since the line cuts off equal intercepts on the x and y axes, it means that it is a line of symmetry, which means that the slope of the line is zero.

Now we can use the point-slope form of a linear equation which is y-y1 = m(x-x1) and substitute the point (3,2) and the slope (0)

The equation of the line will be y = b where b is the y-intercept.

So the equation of the line which passes through the point (3, 2) and cuts off equal intercepts on the axes is y = 2

The line is a horizontal line passing through the point (3,2) and it cuts the x-axis at y = 2.

Step-by-step explanation:

Answer: b infinite number of solutions (blue and purple)

Step-by-step explanation:

There will be multiple solution for both inequality.

Inequality refers to the phenomenon of unequal and/or unjust distribution of resources and opportunities among members of a given society. The term inequality may mean different things to different people and in different contexts.

According to the question

y<3/2x-2      ---------- (1)    

y<3/2x -8    -----------(2)

to take out points we have to take (1) as  y= 3/2x-2

x y

-4 -8

-2 -5

0 -2

2 1

4 4

6 7

same for (2) we take  y=3/2x -8

x  y

-2 -11

0 -8

2 -5

4 -2

6 1

Then we plot our graph which is shown in sheet attached

According to the graph we can see that they both are parallel to each other now we will shade left hand side of line as per the inequality

when we shade we will observe that points left side of equation (2) are common in both  .

Hence, there will be multiple solution .

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Answer:

-3

Step-by-step explanation:

4 x -3= -12 (a positive times a negative = a negative number)

-12 x-3 = 36 (a neg times a neg = positive num)/ the negs cancl eachother out

36 x -3 = -108 etc.

Answer: 15.876kg

Step-by-step explanation:

Answer:

Check below:

Step-by-step explanation:

To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:

Step 1: Grouping

Group the terms in pairs so that you can factor out a common factor from each pair.

3x² + 6x + 4x + 8

(3x² + 6x) + (4x + 8)

Step 2: Factoring out the common factors

Factor out the common factors from each pair separately.

3x(x + 2) + 4(x + 2)

Step 3: Factoring out the common factor from the resulting expression

Notice that we have a common factor, (x + 2), in both terms.

(x + 2)(3x + 4)

Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).

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Answer:

Step-by-step explanation:

DE = EF

DF = DE + DF

     = DE + DE

DF = 2DE

2DE = DF

DE = (1/2)DF

The equation of line is y = 20x and the number of months is x > 4

Given data ,

Let's represent the number of months as "x" and the amount of money in Rose's savings account after n months as S(x).

Since Rose deposits $20 every month, the amount of money in her savings account after n months can be expressed as:

S(x) = y = 20x

To determine when Rose will have more than $80 in her savings account, we can set up the following inequality:

y > 80

Substituting the expression for S(n):

20x > 80

Divide by 20 on both sides , we get

x > 4

Hence , the inequality that represents when Rose will have more than $80 in her savings account is: x > 4

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The radius of the Sphere is ∛9/4 meter.

A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space.

The formula of the volume of the sphere is given below :

Volume of Sphere 'V' = (4/3)πr³

We have given the volume of the sphere which is 3π m³,

So, (4/3)πr³ =  3π

r³ = 9/4

r =  ∛9/4

Therefore, the radius of the sphere will be ∛9/4 meter.

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Answer:

9.102

Step-by-step explanation:

Assuming this means multiply to each other

1.11 x 8.2 = 9.102

Answer:

a. y = -3

b. x = -3

c. z = - 1

d. y = -7

Step-by-step explanation:

a. 5y - 3 = - 18

5y = -18 +3

5y = -15

y = -15/5

y = - 3

b. -3x - 9 = 0

-3x = 9

x = 9/-3

x = -3

c. 4 + 3(z-8)= -23

4 + 3z-24 = -23

3z - 20 = -23

3z = -23 + 20

3z = -3

z = -3/3

z = - 1

d. 1 - 2(y-4) = 5

1 - 2y + 8 = 5

9 - 2y = 5

-2y = 14

y = 14/-2

y = -7

Answer:

- 22

Step-by-step explanation:

3(-4) - 5(2)

-12 - 10

- 22

Answer:

-22

Step-by-step explanation:

3(-4) = -12

5(2) =  10

-12-10 =-22

Answer:

Only the point (-4, 22)  is ON THE GRAPH of the equation. Please also check the attached graph.

Step-by-step explanation:

Given the equation

\(y=-4x+6\)

Let us substitute all the given points to check which points satisfy the equation.

Substitute (-4, -10) in the equation

\(y=-4x+6\)

\(-10=-4(-4)+6\)

\(-10=16+6\)

\(-10=22\)

As the R.H.S ≠ L.H.S, hence (-4, -10) does not satisfy the equation.

Hence, (-4, -10) is NOT ON THE GRAPH of the equation

Substitute (-4, 22) in the equation

\(y=-4x+6\)

\(22 = -4(-4)+6\)

\(22 = 16+6\)

\(22 = 22\)

As the R.H.S = L.H.S, hence (-4, 22) satisfies the equation.

Hence, (-4, 22)  is ON THE GRAPH of the equation. Please also check the attached graph.

Substitute (1, -10) in the equation

\(y=-4x+6\)

\(-10=-4(1)+6\)

\(-10=-4+6\)

\(-10=2\)

As the R.H.S ≠ L.H.S, hence (1, -10) does not satisfy the equation.

Hence, (1, -10) is NOT ON THE GRAPH of the equation

Substitute (1, -2) in the equation

\(y=-4x+6\)

-2 = -4(1)+6

-2 = -4 + 6

-2 = 2

As the R.H.S ≠ L.H.S, hence (1, -2) does not satisfy the equation.

Hence, (1, -2) is NOT ON THE GRAPH of the equation

Therefore, from the above analysis, we conclude that only the point (-4, 22)  is ON THE GRAPH of the equation. Please also check the attached graph.

Answer:what

Step-by-step explanation:what does this mean

Answer:

5

Step-by-step explanation:

p=4 b=3 h=?

h²=p²+b²

=4²+3²

=16+9

h²=25

h=5

Answer:

\(y = \sqrt{x+25} + 5\)

Step-by-step explanation:

Swap x and y

x = y² – 10y

Add 25 to each side to complete the square

x + 25 = y² – 10y + 25

Factor

x + 25 = (y – 5)²

Take the square root of each side

\(\sqrt{x+25}\) = y – 5

Add 5 to both sides

\(\sqrt{x+25}\) + 5 = y

If the point A= (4,5), then the possible points on the x-axis which are 13 units from point A are (16,0) and (-8,0).

To find all possible points on the x-axis, follow these steps:

So, the possible points on the x-axis that are 13 units away from point A(4,5) are (16, 0) and (-8, 0).

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Answer:

Below

Step-by-step explanation:

4 [x-3] + 2    = y    is not discontinuous anywhere

However    4 / [x-3]  + 2   DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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Answer:

\(y-9 = \frac{15}{7} (x-8)\)

Step-by-step explanation:

Point-slope form is represented by \(y-y_1 = m (x-x_1)\). To write an equation with it, we need the slope of the line and a point the line crosses through. We already have at least one point the line crosses through, so let's figure out the slope.

To find the slope, use the slope formula \(\frac{y_2-y_1}{x_2-x_1}\). \(x_1\) and \(y_1\) represent the x and y values of one point the line crosses, and \(x_2\) and \(y_2\) represent the x and y values of another point the line crosses. So, using the x and y values of (1, -6) and (8, 9), substitute them into the formula and solve:

\(\frac{(9)-(-6)}{(8)-(1)} \\= \frac{9+6}{8-1} \\= \frac{15}{7}\)

Thus, the slope is \(\frac{15}{7}\).

2) Now, using the point-slope form of  \(y-y_1 = m (x-x_1)\),  substitute \(m\), \(x_1\), and \(y_1\) for real values in order to write an equation in point-slope form. The \(m\) represents the slope, so substitute \(\frac{15}{7}\) in its place. The \(x_1\) and \(y_1\) represent the x and y values of one point on the line. So, choose any one of the points given - either one is fine - and substitute its x and y values for \(x_1\) and \(y_1\). (I chose (8,9)). This gives the following equation and answer:

\(y-9 = \frac{15}{7} (x-8)\)

\( \huge{ \rm{Answer:}}\)

Hypothesis: It is winter

Conclusion: it is February

HOPE THIS HELPS^^

sorry i don't know. this answer.

Answer:

Step-by-step explanation:

Answer:

Angle F = 140°

Step-by-step explanation:

Add up all the angles and set it equal to 720°

x-20+x-40+x-60+130+120+110=

720

Add the x's together. And the numbers together.

3x - 120 + 360 =720

3x + 240 = 720

Subtract 240.

3x = 480

Divide by 3.

x = 160

Now find Angle F.

F = 160 - 20

F = 140°

Answer:

3/4

Step-by-step explanation:

3 states that are in the southwest region border Mexico which means that your fraction is 3/4 and 3/4 cannot be simplified anymore because it is in it's simplest form.