i need help please
2. Majority Rules [15 points] Consider the ternary logical connective # where #PQR takes on the value that the majority of P, Q and R take on. That is #PQR is true if at least two of P,

The equation that represents the number of pages Ben can read per minute is p = (3/4)m.

The two quantities are said to be in a directly proportionate relation when the connection between them is such that if we increase one, the other will also increase, and if we reduce one, the other quantity will also drop.

If x and y are in direct proportion then

=>  x ∝ y

=>  x = ky  [ where k is constant ]

Here we have,

Ben reads 6 pages in 8 minutes

9 pages can be read in 12 minutes

30 pages can be read in 40 minutes

And the number of minutes = m

Number of pages = p

If observe the given data,

When the number of pages increases, the number of minutes are also increasing, So here we can conclude that the number of minutes is directly proportional to the number of pages

=> p ∝ m

=> p = km --- (1)  

[ where k is constant ]  

From the given data,

At p = 6 pages, m = 8 minutes

=> 6 = k(8)

=> k = 6/8 = 3/4

From (1)

=> p = (3/4)m

Therefore,

The equation that represents the number of pages Ben can read per minute is p = (3/4)m

Learn more about Direct Proportion at  

https://brainly.com/question/28730073

#SPJ1

Answer:

Step-by-step explanation:

\((3x+15)\\\\3x+15\\\\\mathrm{Rewrite\:}15\mathrm{\:as\:}3\times\:5\\\\=3x+3\times\:5\\\\\mathrm{Factor\:out\:common\:term\:}3\\\\=3\left(x+5\right)\)

There would be about 12 pieces of fruit in the bag.

The length of IKE is 2x - 12.

A condition on a variable that is true for just one value of the variable is called an equation.

Since KITE is a kite, we know that KT = IT and KE = IE. Let's call the length of these diagonals d. Then we have:

KT + TI = d

KE + EI = d

Substituting in the given values, we get:

x + 6 + 2x = d

2x + IE = d

Solving for d in the first equation, we get:

3x + 6 = d

Substituting this into the second equation, we get:

2x + IE = 3x + 6

Solving for IE, we get:

IE = x + 6

Therefore, IKE is equal to:

IKE = IT - IE

IKE = (d - KT) - (x + 6)

IKE = (3x + 6 - x - 6) - (x + 6)

IKE = 2x - 12

So, the length of IKE is 2x - 12.

Learn more about equation on:

https://brainly.com/question/27893282

#SPJ4

The probability of no earthquakes occurring in one year is approximately 0.000911881965. The probability that exactly three out of the next eight years will have no earthquakes , we can apply the binomial distribution.

The probability of no earthquakes occurring in one year in the given region of California, which follows a Poisson process with a rate of seven earthquakes per year, can be calculated using the Poisson distribution formula. The Poisson distribution describes the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence. In this case, the average rate is seven earthquakes per year. To calculate the probability of zero earthquakes in one year, we can use the formula:

P(X = 0) = e^(-λ) * (λ^0) / 0!

where λ is the average rate of occurrence. Substituting λ = 7 into the formula, we get:

\(P(X = 0) = e^{(-7)} (7^0) / 0!\)

The exponential term \(e^{(-7)\)evaluates to approximately 0.000911881965, and 0! is equal to 1. Therefore, the probability of no earthquakes occurring in one year is approximately 0.000911881965.

To find the probability that exactly three out of the next eight years will have no earthquakes, we can apply the binomial distribution. The binomial distribution describes the probability of a certain number of successes (no earthquakes) in a fixed number of independent trials (eight years) with a constant probability of success (the probability of no earthquakes in one year). In this case, the probability of no earthquakes in one year is the value we calculated earlier: approximately 0.000911881965. The formula for the binomial distribution is:

\(P(X = k) = C(n, k) p^k (1 - p)^{(n - k)\)

where P(X = k) is the probability of exactly k successes, C(n, k) is the number of combinations of n trials taken k at a time, p is the probability of success, and n is the total number of trials. Substituting k = 3, n = 8, and p = 0.000911881965 into the formula, we can calculate the probability.

Learn more about probability here: https://brainly.com/question/31828911

#SPJ11

Answer: hmmm can we see the answer choices because I think I. Ight know the answer

Step-by-step explanation:

Answer:

17= Prime number

54= Composite

77=Composite

23=Prime

Hello there!

Prime numbers have 2 factors and composite numbers have 3 or more factors.

17 is prime because it has only 2 factors: 1 and itself.

54 is composite because it has more than 3 factors.

77 is composite because it has more than 3 factors.

23 is prime because it has only 2 factors.

Hope this helps you!

~Just a joyful teen

\(SilentNature\)

Answer:

5.76

Step-by-step explanation:

Multiply them together.

Based on the transformation of the given parent function f(x), the function g(x) is: C. g(x) = ∛(x) + 2

In Mathematics, the translation of a geometric figure to the right is a type of transformation which simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure up is a type of transformation that simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

Translating the parent function f(x) = ∛(x) two (2) units up, would produce an image of function f(x):

g(x) = f(x) + 2

g(x) = ∛(x) + 2

In this context, we can reasonably infer and logically deduce that the parent function f(x) was shifted 2 units up to produce function g(x).

Read more on translation here: brainly.com/question/20720324

#SPJ1

The function f(x) = 2(x-4x^2 + 3) represents a parabola. The constants in the function, specifically 2, -4, and 3, define different characteristics of the parabola.

1. The constant 2:

This constant represents the vertical stretch or compression of the parabola. If the constant is greater than 1, the parabola will be stretched vertically. If it is between 0 and 1, the parabola will be compressed vertically.

In this case, the constant 2 indicates that the parabola is stretched vertically by a factor of 2 compared to the standard parabola.

2. The constant -4:

This constant determines the shape of the parabola. A positive constant would make the parabola open upwards, while a negative constant would make it open downwards. In this case, the negative constant -4 indicates that the parabola opens downwards.

3. The constant 3:

This constant determines the vertical shift of the parabola. It indicates how much the parabola is shifted up or down from its standard position. In this case, the constant 3 suggests that the parabola is shifted upwards by 3 units.

By considering these constants, we can understand how they individually affect the parabola's stretch or compression, its orientation (upwards or downwards), and its vertical shift.

To know more about parabola visit:

https://brainly.com/question/21685473

#SPJ11

Answer:

Step-by-step explanation:

\(\frac{\sqrt{x}+1 }{x-\sqrt{x}+1 }=\frac{\sqrt{x}+1}{(x+1)-\sqrt{x}}\\\\=\frac{(\sqrt{x}+1)([x+1]+\sqrt{x})}{([x+1]-\sqrt{x})+([x+1)+\sqrt{x}])}\\\\=\frac{\sqrt{x}*x+\sqrt{x}*1+\sqrt{x}*\sqrt{x}+1*x+1*1+1*\sqrt{x}}{(x+1)^{2}-(\sqrt{x})^{2}}\\\\\\=\frac{x\sqrt{x}+\sqrt{x}+x+1+x+\sqrt{x}}{x^{2}+2x+1-x}\\\\=\frac{x\sqrt{x}+2\sqrt{x}+2x+1}{x^{2}+x+1}\\\\\)

The points on the tangent plane are (1/10, 1/20, 3/20) and (-1/10, -1/20, -3/20) if the tangent plane to this ellipsoid is parallel to the normal plane.

The given ellipsoid equation points are :

\(x^{2} + 5y^{2} + z^{2} = 18\)

\(3z - (2x + 5y)=0\)

To find the points on the ellipsoid surface x^{2} + 5y^{2} + z^{2} = 18 which is the tangent plane to this ellipsoid is parallel to the plane 3z - (2x + 5y)=0,  we must to calculate the gradient of the surface and set it comparable to the normal vector of the plane.

The gradient of the surface is calculated by the product of square numbers by its coefficients.

Gradient surface = 2x + 10y + 2z =18

normal vector = (-2, -5, -3)

Considering that the tangent plane is parallel to the plane

2x + 10y + 2z = k(-2, -5, -3)

Therefore we can get the equations,

2x = -2k = -1 x

10y = -5k = (1/2)x

2z = -3k = 3/2 x

Now, these equations are substituted in the Gradient surface equation,

2(-1x)+ 10(1/2x) + (3/2x) =18

3/2x = 18- 3 = 15

3/2x = 15

x = 1/10

similarly, we can calculate the y and z values

y = (1/2) * (1/10) = 1/20

z = (3/2) * (1/10) = 3/20

Therefore we can conclude that the points on the tangent plane are (1/10, 1/20, 3/20) and (-1/10, -1/20, -3/20).

To know more about normal vectors

brainly.com/question/29050578

#SPJ4

The Height of the Building is 28.87 m .

in the question ,

it is given that

distance between P and Q \(=\) 20 m

From P the angle of elevation is 28°

and from Q the angle of elevation is 40°

From the figure

In triangle BAQ

tan40° = BA/AQ

tan40° = h/x

h = x * tan40°

In triangle BAP

tan28° = BA/AP

tan28° = h/(x+20)

h = (x+20) * tan28°

Equating both the h , we get

x * tan40° = (x+20) * tan28°

x* tan40° = x*tan28° + 20* tan28°

x*(tan40° - tan28°) = 20* tan28°

x*(0.840 - 0.531) = 20*(0.531)

x*(0.309) = 10.62

x = 10.62/0.309

x = 34.368

Substitute h = 34.368 in h = x * tan40°

we get ,

h = (34.368)*(0.840)

h = 28.8699

h = 28.87

Therefore , The Height of the Building is 28.87 m .

Learn more about Trigonometry  here

https://brainly.com/question/23948529

#SPJ1

Answer: The waiting time will be 32 minutes when 240 people in line.

Step-by-step explanation:

Let us assume that the waiting time is directly proportional to the number of people in the queue.

Equation of direct proportion between variables x and y :  \(\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}\)

Put \(x_1=20,\ y_1=150,\ y_2=150\)  to find  \(x_2\).

\(\dfrac{20}{150}=\dfrac{x_2}{240}\\\\\Rightarrow\ x_2=\dfrac{20}{150}\times240\\\\\Rightarrow\ x_2=32\)

Hence, the waiting time will be 32 minutes when 240 people in line.

Answer:

32 minutes

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

For 150 people, waiting time = 20 minutes

So, for 1 minute waiting time, number of people = 150 ÷ 20

= 7.5 people per minute

So, for 240 people, waiting time = 240 ÷ 7.5

= 32 minutes.

So, the waiting time when 240 people are in line is 32 minutes.

Answer:

y = -5x + 12

Step-by-step explanation:

y - 2 = -5(x - 2)

Slope-intercept form is y - mx + b.

First, distribute the -5 across the parentheses.

y - 2 = -5x + 10

Add 2 to both sides.

y = -5x + 10 + 2

y = -5x + 12

This is your equation in slope-intercept form.

Hope this helps!

1) Rewrite the given differential equation: The given differential equation is y dx - 6(x + y^8) dy = 0. We can rewrite it as: y dx = 6(x + y^8) dy

2. Separate variables:
Now, separate the variables x and y:
(y/6) dx = (x + y^8) dy

3. Integrate both sides:
Integrate both sides of the equation with respect to their corresponding variables:

∫(y/6) dx = ∫(x + y^8) dy

(1/12)xy = (1/2)xy + (1/9)y^9 + C

4. Solve for x(y):
To find the general solution in form x(y), rearrange the equation: x(y) = 3y^8 + Cy^6

5. Find the largest interval:
To find the largest interval over which the general solution is defined, consider the domain of y.

The general solution is defined for all y except y = 0 (since this would result in a division by zero). Therefore, the largest interval is: (-∞, 0) ∪ (0, ∞)

6. Determine transient terms:
Since the general solution does not contain any terms that tend to zero as y approaches infinity, there are no transient terms. So the answer is: NONE

To know more about term click here

brainly.com/question/19774850

#SPJ11

Amount of gift wrap to cover the entire box = total surface area of rectangular box = 1,048 in.².

The total surface area of a rectangular box is the area of all the faces of the box = 2(wl + hl + hw).

Therefore, to find the material that will cover the whole rectangular box, Demarcus should find its total surface area, given the following dimensions:

Plug in the values into TSA = 2(wl + hl + hw):

Total surface area of rectangular box = 2(8×20 + 13×20 + 13×8) = 1,048 in.²

Learn more about total surface area of rectangular box on:

https://brainly.com/question/24448247

The algebraic expression for the payment of the plan with y dollar surge is A = x/2 + y.

The concept of algebraic expressions is the use of letters or alphabets to represent numerical values without stating their exact meanings. The fundamentals of algebra taught us how to express an unknown value using letters like x, y, and z. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Given that the annual premium plan is x dollars.

The payment is made semi-annually this is represented as follows:

x/2

There is a surplus charge of y, this is written as:

A = x/2 + y

Hence, the algebraic expression for the payment is A = x/2 + y.

Learn more about word problems here:

https://brainly.com/question/29027588

#SPJ1

Answer:

2.4 × 101

Step-by-step explanation:

that is 24 in scientific notation

Answer:

24 * 10^1

Step-by-step explanation:

Hope this helps. :)

Answer:

1) 85

2) 95

3) 75

4) 90

5) 120

6) 110

7) 65

8) 130

Answer:

0.74

Step-by-step explanation:

0.7439 = 0.74

π/16 is the area enclosed by the curve r= sin(4θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)

where a and b is the boundary at which r=0

so after equation r=0

sin(4θ) =0

=> sin(4θ) =0

=> 4θ = 0,π

=> θ = 0, π/4

so a=0 , b= π/4

now  

  A =  \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)   ------(i)

so   \(r^2\) = (sin(4θ))^2

=>   \(sin^2\)( 4θ )

ans we know that

cos(2α) = 1 -  \(2sin^2\)2 α

so     \(sin^2\)= (1- cos(8θ) )/2

putting the value of r in the equation (i) we get :-

A = \(\int\limits^b_a {\frac{1}{4} *(1-cos8\theta) } \, d\theta\)

=> 1/4*  \(\int\limits^b_a {(1-cos8\theta) } \, d\theta\)

here a=0 and b=π/4

after putting the value and solving the integral

A = π/16

so A is the area enclosed by r=sin(4θ) is π/16

To know more about polar curve click on below link:

brainly.com/question/1094340#

#SPJ4

Answer:

Step-by-step explanation:

( 2x - 8 )° = ( x + 28 )° ⇒ x = 36

m∠1 = m∠4 = 180° - ( 36 + 28 )° = 116 °

m∠2 = 123° - 64° = 59 °

m∠3 = 123 °

The product of 4 and the sum of a number and 12 is at most 18 can be written as

4(x+12)<=18

or

x+12<=4.5

or

x<=-7.5

Therefore, the value of x can be at most -7.5.

Answer:

Width = 3.75 feet

Length = 9.75 feet

Step-by-step explanation:

Given:

Length of fencing = 27 feet

Find:

Dimensions of the garden

Computation:

Assume

Width = x

So,

Length = x + 6

2(L+B) = Perimeter

2(x + x + 6) = 27

2(2x + 6) = 27

4x + 12 = 27

4x = 15

x = 3.75

Width = 3.75 feet

Length = 3.75 + 6 = 9.75 feet

The bicycle manufacturer is studying the reliability of its models and analyzing the probability of defects. They found the probability of a brake defect is 4 percent and the probability of both brake and chain defects is 1 percent.

Given that the probability of a defect with brakes or chain is 6 percent, we can find the probability of a chain defect using the formula: P(A and B) = P(A|B) * P(B), where P(A and B) is the probability of both events A and B occurring, P(A|B) is the probability of event A occurring given that event B has occurred, and P(B) is the probability of event B occurring.

In this case, we want to find the probability of a chain defect given that there is a defect with either the brakes or the chain. Let's use the events: A = brake defect, B = chain defect, From the problem statement, we know that: P(A) = 0.04 (probability of a brake defect), P(A and B) = 0.01 (probability of both a brake defect and a chain defect)
P(A or B) = 0.06 (probability of a defect with the brakes or the chain).

To find P(B|A or B), we can use the formula: P(B|A or B) = P(A and B) / P(A or B) = 0.01 / 0.06, = 1/6, = 0.1667, So the probability of a chain defect given that there is a defect with either the brakes or the chain is 16.67%, or approximately 2/12 or 1/6.

Therefore, the correct answer is option 2: 2%, Solving for the probability of a chain defect, we get: P(chain defect) = 0.06 - 0.04 + 0.01 = 0.03, So, the probability of a chain defect is 3 percent.

To know more about probability click here

brainly.com/question/15124899

#SPJ11

Answer:

Store=$190 for 10 movies a month

Online=$15 for 10 movies a month

Step-by-step explanation:

times price by number of movies