A farmer produces both beans and corn on her farm. If she must give up 16 bushels of corn to be able to get 6 bushels of beans, then her opportunity cost of 1 bushel of beans is ______________.

Step-by-step explanation:

t=2+5×j

j=5

t=2+5×5

t=27

Tom has 2 more than 5 times what Jane has, so you would multiply the amount Jane has by 5, then add 2 to that:

Tom  = 5(5) +2

Tom = 25 +2

Tom = 27 CD's.

Answer:

The difference in per-mile costs for the two companies is $0.12

Step-by-step explanation:

Gabi sets up the equation [tex]0.22m+7.20=0.1m+8.40[/tex] to find out after how many miles, m, the companies will charge the same amount.

The first company charges [tex]c_1=0.22m+7.20[/tex] for m miles driven.

The second company charges [tex]c_2=0.1m+8.40[/tex] for m miles driven.

In both these functions, numbers 7.20 and 8,40 represent the initial fee the companies charge.

Numbers 0.22 and 0.1 represent per-mile costs.

Thus, the difference in per-mile costs is [tex]0.22-0.1=0.12[/tex]

Another way to solve this problem is to find the cost per mile driven for each company:

1. Cost per-mile 1st company

[tex]c_1(0)=0.22\cdot 0+7.20=7.20\\ \\c_1(1)=0.22\cdot 1+7.20=7.42\\ \\c_1(1)-c_1(0)-7.42-7.20=0.22[/tex]

2. Cost per-mile 2nd company

[tex]c_2(0)=0.1\cdot 0+8.40=8.40\\ \\c_2(1)=0.1\cdot 1+8.40=8.50\\ \\c_2(1)-c_2(0)=8.50-8.40=0.1[/tex]

3. Difference:

[tex]0.22-0.1=0.12[/tex]

Answer:

29 homework problems

Addition Property was used

Step-by-step explanation:

15+5=20+9=29

Addition

By using the associative property of addition, we calculate that Brooke has 29 problems for homework. This total is found by adding 15 math problems, 5 social studies problems, and 9 science problems together.

To calculate how many problems Brooke has for homework, we need to add together the numbers of math, social studies, and science problems. This operation is typically done using the property of addition. The property of addition we've applied here is known as the Associative Property of Addition. This property states that the way numbers are grouped does not change their sum.

So, if Brooke has 15 math problems, 5 social studies problems, and 9 science problems, we calculate the total as follows: 15 (math) + 5 (social studies) + 9 (science) equals 29 problems. So, Brooke has 29 problems to do for her homework.

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Answer:

Rachel's score is 2.3333 standard deviations above the mean

Step-by-step explanation:

GRE scores are normally distributed

Let be G the random variable ''Gre scores''

G  ~ N (mean,standard deviation)

G ~ N (600,30)

Rachel scored 670 on the analytic portion of the GRE.

670 - 600 will be the score above the mean

670 - 600 = 70

To find this in terms of standard deviation we divide by the standard deviation

70/standard deviation = 70/30 = 7/3 = 2.33333333 standard deviations

Rachel's GRE score is approximately 2.33 standard deviations above the mean. The calculation is made by subtracting the mean from the observed score and dividing this by the standard deviation.

The subject of this question pertains to the mathematical concept of Z-scores, used in statistics to measure how many standard deviations an element is from the mean. In the case of Rachel's GRE score, we can calculate the number of standard deviations her score is above the mean using the formula z = (X - μ) / σ where:

By substituting these values into the formula, we get:

z = (670 - 600) / 30 = 70 / 30 = 2.33

This means that Rachel's score is approximately 2.33 standard deviations above the mean.

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Answer:

sorry  can you write it down and take a pic of it

please that is the only way i can answer it

Step-by-step explanation:

Answer:

  b. f(x) = x³ +3x² -6x -18

Step-by-step explanation:

You want the cubic function with zeros ±√6 and -3.

Each zero p gives rise to a factor (x-p). This means the factored form of f(x) will be ...

  f(x) = (x -√6)(x +√6)(x -(-3))

Expanding this product gives ...

  f(x) = (x² -6)(x +3)

  f(x) = x³ +3x² -6x -18 . . . . . . . matches choice B

Answer:

a) ∀x∃y ¬∀zT(x, y, z)

∀x∃y ∃z ¬T(x, y, z)

b) ∀x¬[∃y (P(x, y) ∨ Q(x, y))]

∀x∀y ¬ [P(x, y) ∨ Q(x, y)]

∀x∀y [¬P(x, y) ^ ¬Q(x, y)]

c) ∀x ¬∃y (P(x, y) ^ ∃zR(x, y, z))

∀x ∀y ¬(P(x, y) ^ ∃zR(x, y, z))

∀x ∀y (¬P(x, y) v ¬∃zR(x, y, z))

∀x ∀y (¬P(x, y) v ∀z¬R(x, y, z))

d) ∀x¬∃y (P(x, y) → Q(x, y))

∀x∀y ¬(P(x, y) → Q(x, y))

∀x∀y (¬P(x, y) ^ Q(x, y))

Answer:

a) ∃x∀y∃z~T(x, y, z)

b) ∃x∀y~P(x, y) ∧ ∃x∀y~Q(x, y)

c) ∃x∀y(~P(x, y) ∨ ∀z~R(x, y, z))

d) ∃x∀y(P(x, y) → ~Q(x, y))

Step-by-step explanation:

The negation of a is written as ~a.

Note the following properties that are going to be applied in the problems here :

~(P → Q) = P → ~Q

De Morgan's Laws

~(P ∨ Q) = ~P ∧ ~Q

~(P ∧ Q) = ~P ∨ ~Q

~∃xP = ∀xP

~∀xP = ∃xP

So back to the original problem.

a) ∀x∃y∀zT(x, y, z)

We have the negation as

~[∀x∃y∀zT(x, y, z)]

= ∃x~∃y∀zT(x, y, z)

= ∃x∀y∀~zT(x, y, z)

= ∃x∀y∃z~T(x, y, z)

b) ∀x∃yP(x, y) ∨ ∀x∃yQ(x, y)

Negation is:

~[∀x∃yP(x, y) ∨ ∀x∃yQ(x, y)]

= ~∀x∃yP(x, y) ∧ ~∀x∃yQ(x, y)

= ∃x~∃yP(x, y) ∧ ∃x~∃yQ(x, y)

= ∃x∀y~P(x, y) ∧ ∃x∀y~Q(x, y)

c) ∀x∃y(P(x, y) ∧ ∃zR(x, y, z))

Negation is:

~[∀x∃y(P(x, y) ∧ ∃zR(x, y, z))]

= ~∀x∃y(P(x, y) ∧ ∃zR(x, y, z))

= ∃x~∃y(P(x, y) ∧ ∃zR(x, y, z))

= ∃x∀y~(P(x, y) ∧ ∃zR(x, y, z))

= ∃x∀y(~P(x, y) ∨ ~∃zR(x, y, z))

= ∃x∀y(~P(x, y) ∨ ∀z~R(x, y, z))

d) ∀x∃y(P(x, y) → Q(x, y))

Negation is:

~[∀x∃y(P(x, y) → Q(x, y))]

= ~∀x∃y(P(x, y) → Q(x, y))

= ∃x~∃y(P(x, y) → Q(x, y))

= ∃x∀y~(P(x, y) → Q(x, y))

= ∃x∀y(P(x, y) → ~Q(x, y))

Answer: y= -1/2x + 3/4

Step-by-step explanation: For a line in the for of y=mx + b, the slope is m and y intercept is b.

Answer:

y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 6x + 12y = 9 into this form

Subtract 6x from both sides

12y = - 6x + 9 ( divide all terms by 12 )

y = - [tex]\frac{6}{12}[/tex] x + [tex]\frac{9}{12}[/tex], that is

y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{3}{4}[/tex]

Answer: The value of cross price elasticity is 1.6.

Step-by-step explanation:

Since we have given that

Percent change in price = 10%

Percent change in quantity = 16%

So, we need to find the cross price elasticity between the two movie club memberships.

As we know the formula for cross price elasticity :

[tex]\dfrac{\%\text{change in demand}}{\%\text{change in price}}\\\\=\dfrac{16}{10}\\\\=1.6[/tex]

Hence, the value of cross price elasticity is 1.6.

Answer:

y = -1½x + 3 11⁄14

Step-by-step explanation:

First convert from Standard Form to Slope-Intercept Form:

2x - 3y = 4

-2x - 2x

____________

-3y = -2x + 4

___ _______

-3 -3

y = ⅔x - 1⅓ >> Slope-Intercept Form

↑

slope

Now, Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE Rate of Changes [Slopes], so since the slope is ⅔, the opposite multiplicative inverse of that would be -1½, or -3⁄2. Anyway, do the following:

4 = -1½[-⅐] + b

3⁄14

-3⁄14 - 3⁄14

_______________

3 11⁄14 = b

y = -1½x + 3 11⁄14 >> New equation

I am joyous to assist you anytime.

Answer:

Step-by-step explanation:

So a few things to know before hand.  Slope ntercept form is y = mx + b where m is the slope, and in this form that will always make b the y intercept.

A perpendicular slope is pretty easy to find.  Of course, perpendicular means it intersects that first line at a 90 degree angle.  So the x and y axis themselves are perpendicular.  Anyway, if you know the slope of the line, a perpendicular slope is -1/m where m is the slope.  S taking the simplest example, in the graph of just x, the slope is 1, so the perpendicular slope is -1/1 or just -1.

The last thing is to know how to write the equation of a linear function when you know a point and its slope.  if you have the slope m and a point on the graph (a,c) you can use the point slope form which is this.  y - c = m(x - a) where you solve for y.  x an y stay as variables here.

Now knowing all that we can start.  First we want to put the original graph into slope intercept form, which is pretty easy.  Just manipulate the equation.

2x - 3y = 4

2x -4 = 3y

y = (2x - 4)/3

y = 2/3 x - 4/3

so m = 2/3 and b = -4/3

Now, we have the slope of this line and want the slope of a perpendicular line.  Like I mentioned before the slope is -1/m so in this case that's -1/(2/3) = -3/2  Let me know if you don't get how that was gotten.

Now that we kno the perpendicular slope, we can make a perpendicular line.  How do we make a line when we know the slope and a point?  Keep in mind the point is (-1/7, 4)

y - c = m(x-a)

y - 4 = -3/2(x + 1/7)

y - 4 = -3/2 x - 3/14

y = -3/2 x + 53/14

If it weren't in slope intercept form you'd have to put it in that, but I took care of it in the process, so here's the answer.  Let me know if there's anything you don't understand.  

Answer:

Lee has more pizza

Lee has 2.24 in^2 more than John

Step-by-step explanation:

step 1

Find the area of each slice of pizza

[tex]A=\frac{1}{8}\pi r^{2}[/tex]

we have

[tex]r=16/2=8\ in[/tex] ----> the radius is half the diameter

substitute

[tex]A=\frac{1}{8}\pi 8^{2}[/tex]

[tex]A=8\pi\ in^{2}[/tex]

step 2

Find the area of John's part (area of shaded triangle)

The measure of the central angle of each slice of pizza is equal to

[tex]360\°/8=45\°[/tex]

so

the height of triangle is equal to the base

Let

x ---->the base of the shaded triangle

[tex]cos(45\°)=\frac{x}{r}[/tex]

[tex]cos(45\°)=\frac{x}{8}[/tex]

Remember that

[tex]cos(45\°)=\frac{\sqrt{2}}{2}[/tex]

substitute

[tex]\frac{\sqrt{2}}{2}=\frac{x}{8}[/tex]

solve for x

[tex]x=4\sqrt{2}\ in[/tex]

Find the area of shaded triangle

[tex]A=(1/2)(4\sqrt{2})(4\sqrt{2})=16\ in^2[/tex]

step 3

Find the area of Lee's part

The area of Lee's part is equal to the area of two slices of pizza minus the area of two triangles

so

[tex]2(8\pi)-2(16)=(16\pi-32)\ in^2[/tex]

assume

[tex]\pi =3.14[/tex]

[tex](16(3.14)-32)=18.24\ in^2[/tex]

so

Lee's part is greater than John part's

Find the difference

[tex]18.24-16=2.24\ in^2[/tex]

therefore

Lee has more pizza

Lee has 2.24 in^2 more than John

Without exact dimensions of Lee's cut, we can't calculate the precise difference in area after he cuts off an edge, but John likely has more pizza since his slice is unmodified.

The student's question involves comparing areas of pizza slices after one has been modified by cutting off an edge. To answer who has more pizza and by how much, we need to calculate the area of the pizza slices. The original pizza is 16 inches in diameter, and when divided into 8 equal slices, each slice is a sector of a circle with a central angle of 45 degrees. If Lee cuts off an edge and John takes an unmodified triangular slice, John would likely have more pizza because Lee's slice has been reduced in size. However, without knowing the exact dimensions of the removed edge, we can't calculate the precise difference in area.

]

Answer:

Part a) 9*5+2

Part b) 7*6+4

Part c) Lena is correct

Part d) see the explanation

Step-by-step explanation:

The complete question in the attached figure

Part a) Write a numerical expression to represent Lena’s way of counting

To represent Lena’s way of counting, multiply the number of stacks by the number of pennies in each stack plus the number of pennies left over

Let

x -----> the number of stacks

y ----> the number of pennies in each stack

z ----> the number of pennies left over

so

[tex]xy+z[/tex]

we have

x=9 stacks

y=5 pennies

z=2 pennies

substitute

[tex]9*5+2[/tex]

Part b) Write a numerical expression to represent her mother's way

To represent her mother’s way of counting, multiply the number of stacks by the number of pennies in each stack plus the number of pennies left over

Let

x -----> the number of stacks

y ----> the number of pennies in each stack

z ----> the number of pennies left over

so

[tex]xy+z[/tex]

we have

x=7 stacks

y=6 pennies

z=4 pennies

substitute

[tex]7*6+4[/tex]

Part c) Lena thinks her mother must have been working with fewer pennies than she was.  Is Lena correct? 

we have that

Lena’s expression

[tex]9*5+2[/tex]

Simplify

[tex]9*5+2=47[/tex]

Her mother’s expression

[tex]7*6+4[/tex]

Simplify

[tex]7*6+4=46[/tex]

therefore

Lena’s expression is more.

Lena is correct

Part d) Use a  < ,  > , or  =  symbol to show how the two expressions compare

[tex]9*5+2 > 7*6+4[/tex]

[tex]47 > 46[/tex]

The number 47 is greater than the number 46

therefore

The symbol is  " >"

Answer:

First blank: 1/4

Second blank: 2/3

Step-by-step explanation:

[tex](x+\frac{1}{4})^2=\frac{4}{9}[/tex]

Applying the square root of both sides gives:

[tex](x+\frac{1}{4})=\pm \sqrt{\frac{4}{9}}[/tex]

[tex]x+\frac{1}{4}=\pm \frac{\sqrt{4}}{\sqrt{9}}[/tex]

[tex]x+\frac{1}{4}=\pm \frac{2}{3}[/tex]

The blanks are 1/4 and 2/3.

When we take the square root on both sides of the equation, then the whole square term becomes its square root, but the constant term on the other side has a ± sign as the square root of n can be -√n as well as √n, because the square of a negative number is also a positive number.

So the given equation is (x+1/4)² = 4/9

Taking square root on both sides we get

(x+1/4) = ±2/3 using the square root property of equality.

Hence the blanks are 1/4 and 2/3 of the given question.

Learn more about the property of equality here

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Answer:

grams of gold=8x10^12 g

Step-by-step explanation:

first we calculate the volume of the ocean this is achieved by multiplying the area by the depth

A=3.63x10^8  km^2=3.63x10^14   m^2

V=AxL

V=3.63x10^14 x 3800=1.3797x10^18m^3=1.3797x10^21L

then we multiply the volume in liters by the concentration of gold in the ocean per liter

grams of gold=1.3797x10^21   x    5.8x10^-9=8x10^12 g

Answer:

8.00 *10¹² g

Step-by-step explanation:

We must calculate the grams of gold in the ocean.

We are given the concentration of dissolved gold as grams per Liter.

So we need to first calculate the Liters of the ocean, that is, the volume.

We can calculate the volume of the ocean assuming a prism shape as:

Volume = Area x Depth

We should first convert the area from km² to m² so that the units are consistent:

[tex]3.63 *10^{8}  km^{2} * (\frac{1000 m}{1 km} )^{2} = 3.63 *10^{14}  m^{2}[/tex]

So the volume:

Volume = 3.63 x10¹⁴ m² * 3800 m = 1.38 x10¹⁸ m³

Since we have the concentration given in Liters, lets convert the volume to Liters, knowing that 1 L = 1000 m³:

[tex]1.38 *10^{18} m^{3} *\frac{1000 L}{1 m^{3} } = 1.38 *10^{21} L[/tex]

Knowing that the concentration of gold is 5.8 *10⁻⁹ grams per Liter, we can multiply this value by the Liters of the ocean to calculate the grams of gold:

5.8 *10⁻⁹ g/L  x 1.38 *10²¹ L = 8.00 *10¹² g

There are 8.00 *10¹² grams of gold in the ocean

Explanation:

The term containing the variable, e^-t has a range from 0 to infinity, as all exponential terms do.

For t → -∞, e^-t → ∞ and the value of the rational expression becomes 5/∞ ≈ 0. That is, there is a horizontal asymptote at f(t)=0 for large negative values of t.

For t → ∞, e^-t → 0 and the value of the rational expression becomes approximately 5/2. That is, there is a horizontal asymptote at f(t) = 5/2 for large positive values of t.

Essentially, the curve is "S" shaped, with a smooth transition between 0 and 5/2 for values of t that make 3e^-t have values within an order of magnitude of the other term in the denominator, 2.

At t=0, 3e^-t = 1 and the denominator is 2+3=5. That is, f(0) = 5/5 = 1. Of course, the curve will cross the line f(t) = 5/4 (halfway between the asymptotes) when 3e^-t = 2, or t=ln(3/2)≈0.405. The curve is symmetrical about that point.

You can sketch the graph by finding values of t that give you points on the transition. Typically, you would choose t such that 3e^-t will be some fraction or multiple of 2, say 1/10, 1/3, 1/2, 1, 2, 3, 10 times 2.

___

f(t) is called a "logistic function." It models a situation where growth rate is proportional both to population size and the difference between population size and carrying capacity. In public health terms, it models the spread of disease when that is proportional to the number of people exposed and to the number not yet exposed.

Answer:

The sampling technique used here is Cluster Sampling.

Step-by-step explanation:

Since here Population is divided into different parts called grid and whole elements of some selected grid is taken as sample. So, Cluster Sampling is used here.

Further the different types of sampling we have are:

Simple Random Sampling is the sampling where samples are chosen randomly, where each unit has an equal chance of being selected in a sample.

If the population is divided into a different group called cluster and all elements of clusters are selected as a sample then it is Cluster Sampling.

In Convenience sampling, observers collect the sample as his\her convenience.

In Systematic Sampling sample is chosen by some criteria like he\she is taken every 10th unit as a sample from the population.

In Stratified Sampling population is divided into several groups such that within the group it is homogeneous and between the group it is heterogeneous. And now a selection of each stratum and unit has an equal chance of selection.

Answer:

31

Step-by-step explanation:

Answer:

[tex]-\frac34 -\frac14 i[/tex]

Step-by-step explanation:

Let's start with distributing: [tex]\frac1{4i}-\frac{3i}{4i}[/tex] Simplify i with i in the second term, and rearrange.[tex]-\frac34 +\frac1{4i}[/tex]. Since i in the denominator looks ugly, let's multiply top and bottom by i. [tex]-\frac34 +\frac i{4i^2} = -\frac34 +\frac i{4(-1)} =-\frac34 -\frac14 i[/tex]. The middle passage is based on the fact that, by definition, [tex]i^2=-1[/tex]

Answer:

  see below for the stretched graph; see the second attachment for the functions

Step-by-step explanation:

The transformation ...

  g(x) = f(x/a)

represents a horizontal stretch of f(x) by a factor of "a". You want a stretch by a factor of 4, so you can use a=4:

  g(x) = f(x/4)

_____

Horizontal stretch by a factor of 4 means all the points on the graph of g(x) are 4 times as far from they y-axis as they are on the graph of f(x). That is, x must be 4 times as large to give the same y-value.

The graphs of f(x) and g(x) are shown in the second attachment, along with their equations.

Answer:

10C5=252

6C5=6

6C5/10C5= 1/42

Answer:

  $64,720

Step-by-step explanation:

The straightforward way to figure this is ...

  total pay = straight commission + annual bonus

  = 1.5% × 2,555,500 + 2.5% ×(2,555,500 -1,500,000)

However, this expression can be simplified a little bit to ...

  2,555,500 × (1.5% +2.5%)  -2.5% × 1,500,000

  = 4% × 2,555,000 -2.5% × 1,500,000

  = 102,220 -37,500

  total pay = $64,720

Answer:

d) Operating expenses - Cost of goods sold = Gross profit

Step-by-step explanation:

first of all when you say gross in accounting it means the totality so gross profit would never be a subtraction.

And finally operating expenses usually go with a negative sign {-} because it means costs or something goes opposite to the revenue of the firm.

Answer:

d) Operating expenses - Cost of goods sold = Gross profit

Step-by-step explanation:

The formula of Net income is

Sales revenue

- cost of goods sold

= Gross profit

-  Operating expenses

= Net income

So,  we are going to analyze each option

a) Sales revenue - cost of goods sold - Operating expenses = Net income  CORRECT

b) Gross profit - Operating expenses = Net income  CORRECT

c) Net income + Operating expenses = Gross profit  CORRECT

d) Operating expenses - Cost of goods sold = Gross profit INCORRECT

Final answer:

To calculate the volume of a cylinder with a radius of (x+4) cm and height of 5 cm, substitute the values into the formula V = πr²h, resulting in V = 5π(x² + 8x + 16), which gives the volume in standard form.

Explanation:

The question is about finding the volume of a cylinder with a given radius of (x+4) cm and a height of 5 cm. The formula to calculate the volume of a cylinder is V = πr²h, where 'V' is the volume, 'r' is the radius, and 'h' is the height of the cylinder.

To find the volume with the given dimensions, we substitute 'r' with (x + 4) and 'h' with 5. This results in:

V = π(x + 4)² × 5 = π(x² + 8x + 16) × 5

Simplifying this expression gives us:

V = 5π(x² + 8x + 16)

This is the volume of the cylinder in standard form, expressed as a function of x. Therefore, the volume depends on the value of x, and this expression allows us to calculate it for any given 'x'.

Answer:

10.5

Step-by-step explanation:

got it on the test

The length of line segment AC in triangle ABC is 12.3 meters, derived using the sine function and the given angle and side.

To find the length of Line segment AC in the given right angle triangle ABC, we can use the trigonometry functions. Since we are given the length of side CB and the measure of angle BAC, we can apply the sine function. The sin of an angle in a right angle triangle is the length of the opposite side (which in this case is the length of AC we're trying to find) divided by the length of the hypotenuse (which in this case is length CB = 15 m).

So, sin(55 degrees) = Length of AC / 15 m. Solving this equation for Length of AC produces: Length of AC = 15 m * sin(55 Degrees). Plugging in the value of sin(55 degrees) approximately as 0.819 gives a Length of AC approximately equal to 12.3 m. "So the length of the line segment AC is 12.3 m".

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Answer: we can use the folowing polynomial.

P(x) = [tex]\frac{y1 (x - x2)(x -x3)}{(x1 - x2)(x1-x3)}[/tex] + [tex]\frac{y2 (x - x1)(x -x3)}{(x2 - x1)(x1-x3)}[/tex] + [tex]\frac{y3 (x - x2)(x -x1)}{(x3 - x2)(x3-x1)}[/tex]

you can see that P(x1) = y1

                          P(x2) = y2

                          P(x3) = y3

this is a Lagrange polynomial.

Answer:

a) ∃xP (x)

P(-5) v P(-3) v P(-1) v P(1) v P(3) v P(5)

(at least one of them is true)

b) ∀xP (x)

P(-5) ^ P(-3) ^ P(-1) ^ P(1) ^ P(3) ^ P(5)

(all of them are true)

c) ∀x((x ≠ 1) → P (x))

P(-5) ^ P(-3) ^ P(-1) ^ P(3) ^ P(5)

d) ∃x((x ≥ 0) ∧ P (x))

P(1) v P(3) v P(5)

e) ∃x(¬P (x)) ∧ ∀x((x < 0) → P (x))

[¬P(-5) v ¬P(-3) v ¬P(-1) v ¬P(1) v ¬P(3) v ¬P(5)] ^ [P(-5) ^ P(-3) ^ P(-1)]

[¬P(1) v ¬P(3) v ¬P(5)] ^ [P(-5) ^ P(-3) ^ P(-1)]

Here are the given statements expressed without quantifiers: a) P(-5) OR P(-3) OR P(-1) OR P(1) OR P(3) OR P(5), b) P(-5) AND P(-3) AND P(-1) AND P(1) AND P(3) AND P(5), c) P(-5) AND P(-3) AND P(-1) AND P(3) AND P(5), d) (1 ≥ 0 AND P(1)) OR (3 ≥ 0 AND P(3)) OR (5 ≥ 0 AND P(5)), and e) ((¬P(-5) OR ¬P(-3) OR ¬P(-1) OR ¬P(1) OR ¬P(3) OR ¬P(5)) AND (P(-5) AND P(-3) AND P(-1))).

To express your statements without quantifiers, we would consider using disjunctions (OR), conjunctions (AND) and negations (NOT). Here are your statements expressed accordingly:

a) ∃xP (x) becomes P(-5) OR P(-3) OR P(-1) OR P(1) OR P(3) OR P(5).

b) ∀xP (x) becomes P(-5) AND P(-3) AND P(-1) AND P(1) AND P(3) AND P(5).

c) ∀x((x ≠ 1) → P (x)) becomes P(-5) AND P(-3) AND P(-1) AND P(3) AND P(5).

d) ∃x((x ≥ 0) ∧ P (x)) becomes (1 ≥ 0 AND P(1)) OR (3 ≥ 0 AND P(3)) OR (5 ≥ 0 AND P(5)).

e) ∃x(¬P (x)) ∧ ∀x((x < 0) → P (x)) becomes ((¬P(-5) OR ¬P(-3) OR ¬P(-1) OR ¬P(1) OR ¬P(3) OR ¬P(5)) AND (P(-5) AND P(-3) AND P(-1))).

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Answer:

57120

Step-by-step explanation:

Total number of people in a committee = 17

We need to select a president, a vice-president, a secretary, and a treasurer from the committee .

We need to find the number of ways in which these four positions can be filled .

Also, assume that a committee member can hold at most one of these offices.

For post of president , we can choose from 17 people

For post of vice - president , we are left with 16 choices only as one person has already been selected for post of president .

For post of a secretary  , we are left with 15 choices only as two persons have already been selected for post of president and vice - president .

For post of a treasurer  , we are left with 14 choices only as three persons have already been selected for post of president , vice - president and treasurer .

So, number of ways in which these four positions can be filled  = [tex]17\times 16\times 15\times 14 = 57120[/tex]

To determine the number of ways to fill four distinct positions from 17 people where each person can only hold one position, we calculate the permutations, resulting in 17 x 16 x 15 x 14 = 40,320 different ways.

The question pertains to a combinatorial mathematics problem, specifically involving permutations. Given a committee consisting of 17 people, we need to determine in how many different ways four distinct positions (president, vice-president, secretary, and treasurer) can be filled. To solve this, we assume that no person can hold more than one office.

To choose the president, there are 17 possible candidates. Once the president is chosen, there are 16 remaining candidates for the vice-president. Similarly, there are 15 candidates for the secretary position after the president and vice-president have been chosen, and finally, 14 candidates for the treasurer. The number of permutations is the product of these choices, which is calculated as 17 x 16 x 15 x 14.

The calculation yields 40,320 different ways to fill the four positions. This calculation is an example of using factorial notation in permutations where the general formula is n!/(n-r)!, with n representing the total number to choose from, and r is the number to be chosen.

Answer:

Let's replace the h(x) function in g(x) and then use 74 as a result on the axis y. The correct answer is 4 .