Select the law that shows that the two propositions are logically equivalent. -((w V p) ^(-91q1w)) -(w V p) v-(-91qAw) a. DeMorgan's law b. Distributive lawc. Associative law d. Complement law

Answers

Answer 1

The rule demonstrating the logical equality of the two claims. -((w V p) ^(-91q1w)) DeMorgan's law has the form -(w V p) v-(-91qAw).

What is meant by DeMorgan's law?By using their opposites, De Morgan's Laws explain how mathematical assertions and concepts are connected. The intersection and union of sets are connected by complements according to De Morgan's Laws in set theory. The De Morgan's Laws are rules of propositional logic that use negation to connect conjunctions and disjunctions of propositions.The complement of the intersection of the complements of two sets A and B is equal to the complement of the union of two sets A and B, according to De Morgan's first law. According to De Morgan's Law, "(P and Q)" and "not (not P or not Q)" are logically equal. If they are logically similar, then it should follow that "(P and Q)" implies "not (not P or not Q)," and "not (not P or not Q)" implies "(P and Q)".

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Related Questions

A car travels 19 mph slower in a bad rain storm than in sunny weather. The car travels the same distance in 2 hr in sunny weather as it does in 3 hr in rainy weather.

Find the speed of the car in sunny weather.

Answers

It is in good conditions, the automobile travels at 57 mph.

Explain about the distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

A scalar quantity known as distance measures "how much ground an object has traversed" while moving. The term "how far out of place an object is" is referred to by the vector quantity displacement, which is the object's overall change in position.

Simply draw a vector from your initial position to your destination and solve for the length of this line to determine displacement. In the case of a circular 5K path, where your beginning and ending positions are identical, your displacement is 0. Displacement in physics is denoted by s.

"A automobile moves 20 mph more slowly in heavy rain than in bright sunshine."

x - 19 = y

where "x" stands for speed in good weather and "y" stands for speed in bad weather.

"The same distance is covered by the car in two hours in the sun as it is in three hours in the rain."

2x = 3y

where "x" stands for speed in good weather and "y" stands for speed in bad weather.

The speed of the car in good weather, or "x," is what we are looking for. In the second equation, substitute the first equation's value for the variable "y."

x - 19 = y

2x = 3y

2x = 3 (x - 19)

Distribute:

2x = 3x - 57

3x off on both sides equals:

-x = -57

Give both sides a -1:

x = 57

It is in good conditions, the automobile travels at 57 mph.

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To solve the system of equations below, Zach isolated x2 in the first equation and then substituted it into the second equation. What was the resulting equation?

Answers

Since Zach isolated x^2 in the first equation and then substituted it into the second equation, the resulting equation is equal to: C. 25 - y^2/16 - y^2/9 = 1.

What is an equation?

In Mathematics, an equation is sometimes referred to as an expression and it can be defined as a mathematical expression which shows that two (2) or more quantities are equal.

From the information provided above, we have the following system of equations;

x^2 + y^2 = 25 ....... equation 1.

x^2/16 - y^2/9 = 1   ....... equation 2.

By making x^2 the subject of formula in equation 1, we have the following:

x^2 = 25 - y^2     ....... equation 3.

By substituting equation 3 into equation 2, we have the following:

25 - y^2/16 - y^2/9 = 1

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When you take samples from a population and compute a proportion from each one, you can consider the distribution of those proportions. This is called the sampling distribution for the population proportion.The Central Limit Theorem tells us that the sampling distribution for the population proportion is a) skewed left b) skewed right c) approximately normal d) uniform with the a) true population standard deviation b) true population proportion c) true population mean as its a)standard deviation b) mean c) proportion .

Answers

The sampling distribution is approximately normal.

What is the standard deviation?

Standard Deviation is calculated by first squaring the differences between the observations and the mean and then taking the square root of the sum of the squares of the differences divided by the number of observations - 1.

The Central Limit Theorem tells us that the sampling distribution for the population proportion is approximately normal.

The mean of the sampling distribution is equal to the true population proportion and the standard deviation of the sampling distribution is equal to the true population proportion times (1 - true population proportion) divided by the sample size.

So, the sampling distribution is approximately normal, with the true population proportion as its mean and the true population proportion times (1 - true population proportion) divided by the sample size as its standard deviation.

Hence, the sampling distribution is approximately normal.

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Ten less than twice a number is equal to at least 52. What are all the possible values of the number? Write an inequality so that X term comes first.

Answers

The inequality equation which represents Ten less than twice a number is equal to at least 52 is 10 - 2x ≥ 52 and x ≤ -21

How to write and solve inequality?

Let

The unknown number = x

Ten less than twice a number is equal to at least 52;

10 - 2x ≥ 52

Subtract 10 from both sides

- 2x ≥ 52 - 10

- 2x ≥ 42

divide both sides by - 2

x ≤ 42/-2

x ≤ -21

Hence, x ≤ -21 is the solution to the inequality 10 - 2x ≥ 52 if x comes first.

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A 14-foot ladder is leaning against a building. The ladder makes a 50° angle with the ground as shown in the diagram.
14 ft,
50ft
Which expression can be used to find the height, h, in feet that the ladder reaches on the building?

Answers

The height that the ladder reaches on the building is 10.7 feet

What is an equation?

An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

A 14-foot ladder is leaning against a building. The ladder makes a 50° angle with the ground. Let h represent the height of the building. Using trigonometric ratio:

sin(50) = h/14

h = 14 * sin(50)

h = 10.7 feet

The height is 10.7 feet

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one gallon of paint covers 400 squars feet. what is the least amount of paint needed to paint the walls of s room in the shape of a rectangular prism with a length of 20 feet, a width of 18 feet. and a height of 12 feet?

Answers

The minimum amount of paint needed to paint the walls of the room would be 2,2 gallon.

How to calculate the amount of paint we need?

To calculate the amount of paint we need to paint the walls of the room we must calculate the area of each of the walls, in this case it would be 4 rectangles with the following dimensions:

(12ft x 18ft)*2(20ft x 12ft)*2

According to the above, the area of the walls would be:

12*18=216cm²20*12=240cm²

216cm² * 2 = 432cm² 240cm² * 2 = 880cm²

880cm² + 432cm² = 1312cm²

Based on the above, it can be inferred that 2.2 gallons of paint are needed to paint all the walls.

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use the graphs to determine the intervals on which the functions are increasing, decreasing, or constant

Answers

For the first graph, the function is increasing when the graph is sloping upwards, which is the case between the points (-1,1) and (1,3). For the second graph, the function is increasing when the graph is sloping upwards, which is the case between the points (0,2) and (2,4).

For the first graph, the function is increasing from interval (-1,1) and decreasing from interval (1,3).

For the second graph, the function is increasing from interval (0,2) and decreasing from interval (2,4).

For the first graph, the function is increasing when the graph is sloping upwards, which is the case between the points (-1,1) and (1,3). This indicates that the function is increasing on the interval (-1,1). Similarly, the function is decreasing when the graph is sloping downwards, which is the case between the points (1,3) and (3,1). This indicates that the function is decreasing on the interval (1,3).

For the second graph, the function is increasing when the graph is sloping upwards, which is the case between the points (0,2) and (2,4). This indicates that the function is increasing on the interval (0,2). Similarly, the function is decreasing when the graph is sloping downwards, which is the case between the points (2,4) and (4,2). This indicates that the function is decreasing on the interval (2,4).

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at a point feet from the base of a church, the angles of elevation to the bottom of the steeple and the top of the steeple are and , respectively. find the height of the steeple.

Answers

the height from B to c is 54.95 feet and B to D is 35.01 feet and the height of the steeple is 19.94 feet.

at a point 50 feet from the base of a church, the angle of elevation to the bottom of the steeple and top of steeple are 35 and 47 40' respectively.

We need to find out the height of steeple.

observe the right-angle triangle corresponding to the given problem,

let find the height from the point B to the point D.

the angle of elevation =35

we know about the trigonometric representation of the function tan is.

[tex]tan\theta=\frac{opposite}{adjacent}[/tex]

observing the right-angle triangle ABD as we know

angle =35, adjacent =50 and the opposite leg is x,

[tex]tan35=\frac{35}{50} \\\\x=50tan35\\\\x=35.01 feet[/tex]

now let's find the height from B to C.

angle 2=47°40'

[tex]\theta2=47+\frac{40}{60} \\\\\theta=47.7\\\\now, tan47.7=\frac{y}{50} \\\\y=54.95 feet\\[/tex]

therefore the height of steeple is 54.95-35.01=19.94 feet.

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59+1/6r when r= -1/2

Answers

The value of the expression 59 + (1/6)r at r = - 1/2 will be 707/12.

What is the value of the expression?

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 59 + (1/6)r

The value of the expression at r = - 1/2 will be given as,

⇒ 59 + (1/6)(-1/2)

⇒ 59 - 1 / 12

⇒ (708 - 1) / 12

⇒ 707 / 12

The value of the expression 59 + (1/6)r at r = - 1/2 will be 707/12.

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Find the least common denominator of 1/2x-6 and 2x/7x-21.

Answers

The least common denominator or LCD of the given fractions  1/2x-6 and 2x/7x-21 is (2x-6)(7x-21)

What is a fraction?

A fraction can simply be defined in mathematics as the part of a whole variable or number.

Some types of fractions in mathematics are;

Proper fractionsImproper fractionsMixed fractionsComplex fractionsSimple fractions

What is the least common denominator?

The least common denominator of a fraction is seen as the lowest or smallest number in all the common multiples of the denominator given.

Given the information, the fractions are;

1/2x-6 and 2x/7x-21

It is crucial to identify that the denominator of the two fractions are;

(2x-6)(7x-21)

They are in form of algebraic expressions, thus, the  least common denominator is the product of the expression.

Hence, the lowest common denominator is (2x-6)(7x-21)

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Cameron determined that an ordered pair made a true statement when substituted into one of the equations but not in the other equation. Is her ordered pair a solution to the system of equations? If not, explain.

Answers

The ordered pair is not solution to the system of equations.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Cameron determined that an ordered pair made a true statement when substituted into one of the equations but not in the other equation.

As, we know we enter the values of the variables into each equation to see if an ordered pair is a solution to the system of two equation. The system has a solution if the ordered pair proves both of the equations.

So, the ordered pair is not solution..

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Among recent graduates of mathematics departments, half intend to teach high school. A random sample of size 2 is to be selected from the population of recent graduates. a. If mathematics departments had only four recent graduates total, what is the chance that the sample will consist of two graduates who intend to teach high school? b. If mathematics departments had 10 million recent graduates, what is the chance that the sample will consist of two graduates who intend to teach high school? c. Are the selections technically independent in part a? Are they technically independent in part b? In which part can you assume independence anyway? Why?

Answers

In part a, since the population mean  is small, selections are independent and can be assumed to be so. In part b, the population size is too large for selections to be independent, so independence can not be assumed.

a. If mathematics departments had only four recent graduates total, the chance that the sample will consist of two graduates who intend to teach high school is

0.5 * 0.5

= 0.25.

b. If mathematics departments had 10 million recent graduates, the chance that the sample will consist of two graduates who intend to teach high school is

0.5 * 0.5

= 0.25.

c. The selections are technically independent in part a, since the population size is small enough that the selection of one person will not affect the probability of selecting the other person. The selections are not technically independent in part b, since the population size is so large that selecting one person affects the probability of selecting the other person. In part a, you can assume independence since the population size is small enough that it is reasonable to assume that the selections are independent. In part b, you cannot assume independence since the population size is too large to make this assumption.

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a company makes rugs. their smallest rug is a 2 ft-by-3 ft rectangle. their largest rug is a similar rectangle. if one side of their largest rug is 18 ft, what are the possible dimensions of their largest rug? there are two possible sets dimensions. list the two sets below. the smallest dimension is listed first.

Answers

Answer:

The company's largest rug dimensions are either 18 ft by 27 ft Or 12 ft by 18 ft.

Step-by-step explanation:

Given:

Dimension of the smaller rug are 2 ft by 3 ft.

Also One side of the largest rug is 18 ft.

We need to find the possible dimension of largest rug.

Also Given:

Both the smaller rug and larger rugs are similar.

Now By Similar rectangles property which states that;

"When 2 rectangles are similar then their lengths are in proportion."

In this case there are 2 possibilities.

either the largest rug's 18 ft side is similar to the 2 ft side or the 3 ft side

Now let us consider the other side be 'x'.

Now when he largest rug's 18 ft side is similar to the 2 ft side we get;

Now when he largest rug's 18 ft side is similar to the 3 ft side we get;

Hence the company's largest rug dimensions are either 18 ft by 27 ft OR 12 ft by 18 ft.

We know 15 x 3 = 45.
So, which of the following statements are also true?
Choose all answers that apply
D) 3 is a multiple of 45
C) 15 is a factor of 45
E) All of the Above
B) 45 is a multiple of 15
A) 45 is a factor of 15

Answers

Answer:

B, C

Step-by-step explanation:

A) No, factors of 15 = 1, 3, 5, 15... so 45 is not a factor of 15

B) yes, 45 is the third multiple of 15 ( 15×3=45)

C) yes, factor of 45 is the number that divides 45 without leaving any remainders (45÷15=3), therefore 15 is a factor of 45

D) No, multiples must be bigger in value than the actual number because( a multiple of 45) means, the number we get when we multiply 45 by an integer... Here we can't multiply an integer by 45 and get the answer 3

12. Hydrology A reservoir has a capacity of 9000 cu ft. How long will it take
to fill the reservoir at the rate of 250 gallons per minute?

Answers

It will take approximately 270.28 minutes, or 4 hours and 30.28 minutes, to fill the reservoir at a rate of 250 gallons per minute.

How to calculate the time it takes to fill a reservoir?

we can use the formula:

time = volume ÷ flow rate

where volume is the capacity of the reservoir in cubic feet and flow rate is the rate at which the reservoir is filled in cubic feet per minute.

Since the capacity of the reservoir is given in cubic feet and the flow rate is given in gallons per minute, we need to convert the flow rate to cubic feet per minute. One gallon is equal to 0.133681 cubic feet, so:

250 gallons/minute x 0.133681 cubic feet/gallon = 33.342 cubic feet/minute

So the flow rate in cubic feet per minute is 33.342. Now we can calculate the time it takes to fill the reservoir:

time = 9000 cubic feet ÷ 33.342 cubic feet/minute = 270.28 minutes

So it will take approximately 270.28 minutes, or 4 hours and 30.28 minutes, to fill the reservoir at a rate of 250 gallons per minute.

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Obtain an estimate for the computation shown below by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head.
0.87 x 310

Answers

The estimation of the numbers given as 0.87 × 310 will give 270.

Howw to calculate the estimation?

You must approximate (eliminate or round off) the decimals to obtain whole numbers before you can use the whole numbers to find the product of two decimals using estimation.

A figure is discovered through estimation.

A value, amount, or size that rounds off to the nearest whole number is said to be approximating.

The estimation of the numbers given as 0.87 × 310 will give:

= 0.9 × 300

= 270.

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Set up the integral to find the area of the region inside the circle
(x−1)^2+y^2=1
and outside the circle x^2+y^2=1. [Hint: First sketch the region of integration. Next convert the equations to polar coordinates. Use these equations to solve for their intersection points, this will give you the bounds to set up the integral.]

Answers

The area of the region inside the circle (x−1)^2+y^2=1 and outside the circle x^2+y^2=1  is 4.

The area of the region inside the circle (x−1)^2+y^2=1 and outside the circle x^2+y^2=1 can be calculated using polar coordinates.

The equation of the inner circle in polar coordinates is r_1^2=1+2cosθ and the equation of the outer circle in polar coordinates is r_2^2=1.

The intersection points of the two circles can be found at θ=±π/3.

The area of the region can be calculated using the integral:

Area=∫_π/3^-π/3 (1+2cosθ)dθ=(2+4sinθ)|_π/3^-π/3=(2+4sin(-π/3))-(2+4sin(π/3))=4.

Therefore, the area of the region is 4.

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Which figure is a quadrilateral?

Answers

Answer:

The rectangle (option 2)

Step-by-step explanation:

A quadrilateral is any enclosed polygon with four sides. Only the rectangle (option 2) is a quadrilateral.

The other options are not quadrilaterals because they don't have four sides (options 1 and 3) or are not enclosed (option 4). Hope this helps!

2 What is the derivative of the function f(x) = 3x² + 2√x - 4x at x=1?​

Answers

Answer:

The derivative of the function f(x) = 3x² + 2√x - 4x at x=1 is

[tex]\boxed{f'(1) = 3}[/tex]

Step-by-step explanation:

We have f(x) = 3x² + 2√x - 4x

[tex]f'(x) = \dfrac{d}{dx}\left(3x^2+2\sqrt{x}-4x\right)\\\\=\dfrac{d}{dx}\left(3x^2\right)+\dfrac{d}{dx}\left(2\sqrt{x}\right)-\dfrac{d}{dx}\left(4x\right)\\\\[/tex]

[tex]\dfrac{d}{dx}\left(3x^2\right) = 6x\\\\[/tex]

[tex]\dfrac{d}{dx}\left(2\sqrt{x}\right) = 2\dfrac{d}{dx}\left(\sqrt{x}\right)\\\\=2\dfrac{d}{dx}\left(x^{\frac{1}{2}}\right)\\\\= =2\cdot \dfrac{1}{2}x^{\frac{1}{2}-1}\\\\\\=\dfrac{1}{\sqrt{x}}\\\\[/tex]

[tex]\dfrac{d}{dx}\left(4x\right)=4[/tex]

Therefore

[tex]f'(x) = 6x+\dfrac{1}{\sqrt{x}}-4\\\\f'(1) = 6(1) + \dfrac{1}{\sqrt{1}} - 4\\\\f'(x) = 6 + 1 - 4\\\\f'(x) = 3\\\\[/tex]

4x5x8+1x58-3+41-27x4?

Answers

Answer:37,396

Step-by-step explanation:

Solve:
7x+5(x-1)=-5+12x
please show work!

Answers

The solution for the given equation; 7x+5(x-1)=-5+12x as required to be determined is; Infinitely many solutions.

What is the solution for the given equation; 7x+5(x-1)=-5+12x?

It follows from the task content that the solution for the given equation; 7x+5(x-1)=-5+12x is to be determined.

Since the given equation is; 7x + 5 (x-1) = -5 + 12x

Hence, by the distributive property; we have that;

7x + 5x - 5 = -5 + 12x

12x - 5 = 12x - 5

On this note, since both sides of the equation are same, it follows that the equation has infinitely many solutions.

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Is 8.608 a rational number

Answers

Answer: Yes

Step-by-step explanation:

Answer:

[tex] \sf \textbf{8.608} \: is \: a \: rational \: number[/tex]

Step-by-step explanation:

Rational Numbers: Any number that can be written as a ratio (or fraction) of two integers is a rational number.

Which of these do not include direction? Distance, Force, Acceleration or Velocity?

Answers

Scalar quantities of these do not include direction distance, Force, Acceleration, or Velocity.

scalar, a physical quantity whose sole description is its magnitude. Scalars include, but are not limited to, time, energy, mass, volume, density, and speed.

A scalar quantity is one that doesn't depend on movement in any direction. Vector quantities can have a magnitude and a direction. Scalar quantities have just a magnitude.

All of the option values are scalar, with the exception of impulse. A force can be an impulse. Similar to force, it has both magnitude and direction.

Additional examples of scalar quantities are mass, velocity, distance traveled, time passed, energy, density, volume, temperature, work, etc.

Since speed has a simple magnitude and no discernible direction, it is a scalar number.

A scalar quantity is something like distance. Any quantity that has both a direction and a magnitude is a vector.

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If 12 workers clean up a certain stretch of the Jukskei river in 4 days, how long would it have taken to clean up this stretch if only 8 workers had been available? ​

Answers

Answer:

6 days

Step-by-step explanation:

12 workers will clean up in 4 days

how many days would it take 8 workers?

let the number of days be x

x=(12×4)/8

x= 6 days

Drag each item to the container that best describes it.

Answers

Answer:

Rate : 1 page for every 4 students.  

Unit Rate: 500 pages per ream.40 pages for every blooket.15 pages for evry blooket

Neighter: 25 pages

Step-by-step explanation:

I hope this helps :)

The diffrence between unit rate and rate is the unit rate refers to those rates in which the numerator is 1. Rate would be like there is 1 person per car. Unit rate would mean There are 3 cars for each person.

Out of 300 people sampled, 60 preferred Candidate A. Based on this, estimate what proportion of the voting population ( p ) prefers Candidate A. Use a 95% confidence level, and give your answers as decimals, to three places.
___ < p < ___

Answers

At 95% confidence level, the proportion will be between .0.19912815 and 0.200086, when you have a mean of 0.2 and a standard error of 0.00053.

How do you calculate population proportion?

P′ is equal to x / n, where x is the total number of successes and n is the sample size. As a point estimate for the genuine population proportion, the variable p′ represents the sample proportion.

FPC = (N-n)/(N-1), where Z/2 is the critical value of the Normal distribution at /2, p is the sample proportion, n is the sample size, and N is the size of the population (for example, at a confidence level of 95%, is 0.05 and the critical value is 1.96).

A portion of a population that possesses a certain characteristic, given as a percentage, fraction, or decimal of the entire population. The population percentage for a finite population is equal to the population's size divided by the proportion of its members who possess a given attribute.

Given data :

p = 60 / 300 = 0.2

q = 1 - p = 0.8

mean proportion = p = .2

standard error = sqrt(p * (1-p / 300) = sqrt(0.2 * 0.8/ 300) =0.00053333333

critical z-score at 95% confidence level is plus or minus 1.645.

use the z-score formula to find the critical raw score.

for the low side, z = (x - m) / s becomes:

-1.645 = (x - 0.2) / 0.00053

solve for x to get:

x = -1.645 * 0.00053 + 0.2 = 0.19912815

for the high side, z = (x - m) / s becomes:

1.645 = (x - 0.2) / 0.00053

solve for x to get:

x = 1.645 * 0.00053 + 0.2 = 0.200086125

At 95% confidence level, your proportion will be between .0.19912815 and 0.200086, when you have a mean of 0.2 and a standard error of 0.00053.

Here's what it looks like on a z-score normal distribution calculator output.

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in 1973, braley and nelson studied the effect of price increases on school lunch participation in the city of pittsburgh. the revenue function for the program was given by: r ( q )

Answers

The new revenue can be calculated as R = q*p = 2,000*4 = $8,000.

R(q) is the revenue function for the school lunch program, which is given by the equation q*p, where q is the quantity and p is the price. According to Braley and Nelson's study, the city of Pittsburgh had an increase in price of school lunches. The revenue can be calculated by multiplying the quantity (q) of school lunches with the new price (p) after the increase. Therefore, the new revenue (R) can be calculated by R = q*p. As an example, if the quantity of school lunches is 2,000 and the price is increased to $4, then the new revenue can be calculated as R = q*p = 2,000*4 = $8,000.

R(q) is the revenue function for the school lunch program, which is given by the equation q*p, where q is the quantity and p is the price. According to Braley and Nelson's study, the city of Pittsburgh had an increase in price of school lunches. The revenue can be calculated by multiplying the quantity (q) of school lunches with the new price (p) after the increase. Therefore, the new revenue (R) can be calculated by R = q*p. As an example, if the quantity of school lunches is 2,000 and the price is increased to $4, then the new revenue can be calculated as R = q*p = 2,000*4 = $8,000.

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a = bh; h
solve
pls show work

Answers

The solution for h according to the given equation a = bh as required is; h = a / b.

What is the solution for the equation for variable, h?

It follows from the task content that the solution for the given equation for variable, h be determined.

On this note, since the given equation is;

a = bh

To solve for variable, h; divide both sides of the equation by b so that we have;

h = a / b.

Ultimately, the required solution for variable, h is; h = a / b.

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I need help with math

Answers

The measure of r is 24°

Vertically Opposite Angles:

The opposing angles created by the junction of two lines are known as vertically opposite angles or vertical angles. A pair of angles that are vertically opposed to one another is always equal.

Additionally, the vertical angle and its adjacent angle add up to 180° which is said to be a supplementary angle.

Here we have

3 straight lines are met at a point  

Let's name each name as l, m, and n as the given figure

From the line l  

=> ∠LOM + ∠MON + 122° = 180°  [ Pairs of Linear angles ]

=>  34° + ∠MON + 122° = 180°  

=> ∠MON = 180° - 122°- 34°

=>  ∠MON = 24°  

Here

∠MON and r are two vertically opposite angles

As we know vertically opposite angles are equal

=> r = 24°    

Therefore,

The measure of r is 24°

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Help with this equation

Answers

The measure of ∠ADB is equivalent to 90°.

What is geometry?

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

Given is a geometrical image as shown.

We can write -

∠ADC = ∠ADB + ∠BDC

(- 3c + 120°) + (- 10 c + 145°) = 135°

- 3c + 120° - 10c + 145° = 135°

- 13c + 265° = 135°

265° - 135° = 13c

13c = 130

c = 10

Now -

∠ADB = (- 3c + 120) = 90°

∠ADB = 90°

Therefore, the measure of ∠ADB is equivalent to 90°.

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