What is the domain and range for the following function and its inverse?
f(x) = x2 + 3

f(x)
domain:
f–1(x)
domain:

Answers

Answer 1

Answer:

Step-by-step explanation:

The domain of that function is all real numbers.  The x values will drop into negative infinity and will grow to positive infinity.

The range is found from the vertex form of a parabola, which is

[tex]y=(x-h)^2+k[/tex]

where h indicates side to side movement of the vertex and k indicates up or down.  Our function has a +3 at the end of it and is positive (so it opens upwards), so the range is y ≥ 3.

To find the inverse of that function, switch the x and y coordinates and solve for the new y.  Let f(x) be y, then switch the x and y:

[tex]x=y^2+3[/tex]

Now solve for the new y:

y = ±[tex]\sqrt{x-3}[/tex]

To find the domain of a radical, set the radicand greater than or equal to 0 and solve for x (this is because the radicand cannot be a negative number or we are dealing with imaginary numbers and that's not what you want.  BTW, a radicand is the term under the radical sign).  

x - 3 ≥ 0  so   x ≥ 3.  The domain of the inverse is all real numbers greater than or equal to 3.

This is a sideways parabola (the inverse is), and it opens to the right starting at the x value of 3.  It will grow into positive values of y to infinity and will drop into negative values of y into negative infinity.

Just a little trick here to remember, and it ALWAYS holds true:  the domain of a function is the range of its inverse, and the range of a function is the domain of its inverse.  Look to our solution for your problem here and you'll see that it is true.


Related Questions

A hotel in Las Vegas, Nevada, is the largest pyramid in the United States. Prior to the construction of the building, the architects designed a scale model. The height of the scale model is 9 inches less than its length and its base is a square. If the volume of the model is 6300 cubic inches, write an equation describing the situation.

Answers

Answer:

The equation that describe the situation is

[tex]b^{3}-9b^{2}-18,900=0[/tex]

Step-by-step explanation:

we know that

The volume of a square pyramid is equal to

[tex]V=\frac{1}{3}b^{2} h[/tex]

where

b is the length side of the square

h is the height of the pyramid

we have

[tex]V=6,300\ in^{3}[/tex]

[tex]h=(b-9)\ in[/tex]

substitute the values and solve for b

[tex]6,300=\frac{1}{3}b^{2} (b-9)\\ \\18,900=[b^{3}-9b^{2}]\\ \\b^{3}-9b^{2}-18,900=0[/tex]

Using a graphing calculator

[tex]b=30\ in[/tex]

[tex]h=(30-9)=21\ in[/tex]

Answer:

A is correct on edge 2022

Step-by-step explanation:

Drag the tiles to the boxes to form correct pairs. Match each mixed number to its equivalent decimal number.


20 4/5 , 20 1/5 , 20.75 . 20.875 , 20.8 , 20 3/4 , 20 7/8 , 20.2 .

Answers

Answer:

20 3/4 is to 20.75

20 1/5 is to 20.2

20 7/8 is to 20.875

and 20 4/5 is to 20.8

The matching of each mixed number to its equivalent decimal number is given below -

What is the matching of each mixed number to its equivalent decimal number ?

The mixed number is represented as a b/c where a, b, c are three positive non zero integers .

Mathematically -

a b/c = {(a*c) + b}/ c

Thus, the matching of each mixed number to its equivalent decimal number is -

20 3/4 is to 20.7520 1/5 is to 20.220 7/8 is to 20.87520 4/5 is to 20.8

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100 POINTS AND BRAINLIEST

please answer #4 and #5

Answers

4. His percentage is 79% so making each shot is 79%

Multiply the percent for each shot for each shot:

Making two shots = 0.79 x 0.79 = 0.624 = 62.4% Round the answer to 62% if needed.

5. They have 4 different flavors and 6 different toppings.

a. Picking vanilla is 1 out of 4 = 1/4 and picking chocolate chips is 1 out of 6 = 1/6.

The probability of picking both is 1/4 x 1/6 = 1/24

b.  There are a total of 10 different things to pick.

Picking chocolate ice cream is 1 out of 10 = 1/10, picking marshmallow topping is 1 out of 10 = 1/10

Picking one or the other would be 2 out of 10 = 2/10 which reduces to 1/5

Answer:

4. 79%

5. 1/24 and 1/5 for part a and b

Please please help me out

Answers

12x18.2/2=109.2 is the area of the big triangle and also the same area could be found 20 x h=109.2 so

h= 109.2/20=5.46 m

50 points, Based on the table, write a function rule that represents the relationship between x and y.

Answers

Answer:

  y = (1/2)|x -8| -3

Step-by-step explanation:

The first five points fall on a straight line with a slope of ...

  ∆y/∆x = -0.5/1 = -0.5

The last point is not on that line.

So, several options are available:

write a piecewise function with f(10) having a special definition: y={1-x/2, x≠10; -2, x=10}write a piecewise function with any definition for x > 5 such that f(10) = -2: y={1-x/2, x≤6; -2, x>6}use a function, such as absolute value, that changes slope in a way that makes f(10) = -2. Such a function is shown in the first attached graphsimply list the points. Such a list is a "function rule". (x, y) ∈ {(1, 0.5), (2, 0), (3, -0.5), (4, -1), (5, -1.5), (10, -2)}.

HELP PLEASE I WILL GIVE 99 POINTS IM DESPERATE!
Ivan bought a box of macadamia nuts to bring home from his trip.What volume of nuts could the container hold?

Answers

18 x 15 x 3 is 810. The volume is 810. (Also you cant give 99 points but I’ll take a brainlist answer?)

Answer:

[tex]810\text{ cm}^3[/tex].

Step-by-step explanation:

We have been given an image of a container. We are asked to find the volume of nuts could the container hold.

We can see that our given container is in form of cuboid, so we will use volume of cuboid formula to solve our given problem.

[tex]\text{Volume of cuboid}=\text{Length*Width*Breadth}[/tex]

Upon substituting our given values in above formula, we will get:

[tex]\text{Volume of container}=18\text{ cm}\times 15\text{ cm}\times 3\text{ cm}[/tex]

[tex]\text{Volume of container}=810\text{ cm}^3[/tex]

Therefore, the container can hold 810 cubic cm of macadamia nuts.

victor jogged 8 3/7 kilometers on Monday and 7 4/6 kilometers o Tuesday. what is the difference between these two distances?

Answers

Answer:

16/21 km

Step-by-step explanation:

The LCD here is 42.  Thus, 8  3/7 km = 8  18/42 and 7  4/6 km = 7  28/42 km.

The difference in the two distances is

 8  18/42  km

- 7   28/42 km

---------------------

or:

 7  60/42 km         Here I have borrowed 42/42 from that 8.

- 7  28/42 km

---------------------

     32/42 km,   or 16/21 km

Kim and her two brothers each use one and a half cups of milk for breakfast. How many fluid ounces of milk do they use in four days

Answers

Answer: 48 fl oz ( fluid ounces )

Explanation:

1 c = 8 fl oz

1 1/2 c = 12 fl oz

12 fl oz of milk × 4 Days =

48 fl oz in four days

how many revolutions does each tire make while traveling 500 feet? Include the calculations and provide appropriate units (sorry that the picture isn’t great)

Answers

Answer:

tire A=39 revolutions

tire B=38 revolutions

tire C= 37 revolutions

Step-by-step explanation:

The question is on circumference

Tire A diameter = 15 +4.60+4.60=24.20 inches

Tire B diameter= 16+4.43+4.43=24.86 inches

Tire C diameter=17+4.33+4.33=25.66 inches

Finding the circumference/single revolution

Tire A = 2×3.14×24.20=151.98 inches

Tire B= 2×3.14×24.86=156.12 inches

Tire C=2×3.14×25.66=161.15 inches

Number of revolutions made

Track length=500 feet.............change feet to inches

500×12=6000inches

Revolutions for tire A= 6000/151.98 =39.47⇒39 revolutions

Revolutions for tire B=6000/156.12 =38.43⇒38 revolutions

Revolutions for tire C= 6000/161.15 =37.23⇒37 revolutions

Please please help me

Answers

The area of a parallelogram is given by

[tex]A=bh[/tex]

Now, if we consider the 9.9 inches side as the base, then the height is the one labeled with 5.5 inches.

If instead we choose the 11 inches side as the base, the height is h.

So, we can express the area in this two equivalent ways:

[tex]A = 9.9\cdot 5.5 = 11\cdot h[/tex]

Solving for h, we have

[tex]h = \dfrac{9.9\cdot 5.5}{11} = 4.95[/tex]

Please please help me out

Answers

Answer:

[tex]\frac{15}{17}[/tex]

Step-by-step explanation:

Using the Pythagorean identity

sin²x + cos²x = 1, then

sin²x = 1 - cos²x

sinx = [tex]\sqrt{1-cos^2x}[/tex]

Hence

sinΘ = [tex]\sqrt{1-(8/17)^2}[/tex]

        = [tex]\sqrt{1-\frac{64}{289} }[/tex]

        = [tex]\sqrt{\frac{225}{289} }[/tex] = [tex]\frac{15}{17}[/tex]

Please help me out with this

Answers

Value of x is 140

Tangent are present that means those angles are of 90° and 90° + 90° = 180°

One angle is already given 40°

By angle sum property of Quadrilateral

We can get its value

Love from India❤

please please help! A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec^2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10. What is the velocity of the car when t = 6? You must show your work and include units in your answer.

Answers

Answer:

  42 ft/s

Step-by-step explanation:

The change in velocity is given by the area under the curve from t=0 to t=6. The average acceleration over that period is (10+4)/2 = 7 ft/s^2, so the change in velocity is ...

  (7 ft/s^2)(6 s) = 42 ft/s

The velocity of the car at t=6 is 42 ft/s.

The velocity of the car at t=6 is 42 ft/s.

The change in velocity is given by the area under the curve from t=0 to t=6. The average acceleration over that period is [tex](10+4)/2 = 7 ft/s^2[/tex], so the change in velocity is ...

[tex](7 ft/s^2)(6 s) = 42 ft/s[/tex]

The velocity of the car at t=6 is 42 ft/s.

Find the probability an observation is on a Thursday when the temperature is between 90 and 99. Find the probability an observation is on a Monday when the temperature is less than 90. Find the probability an observation is on a Friday when the temperature is greater than 89. Find the probability that the temperature is between 90 and 99, it will be a Thursday. Find the probability that if the temperature is between 110 and 120 and it will be a Sunday.

Answers

Answer:

Out of the 6 observations when the temperature is between 90 and 99, 2 are on Thursday.

2/6 = 33%

Out of the 4 observations when the temperature is less than 90, 1 was on Monday.

1/4 = 25%

Out of the 26 observations when the temperature is greater than 89, 4 were on Friday.

4/26 = 15%

Out of the 6 observations when the temperature is between 90 and 99, 2 are on Thursday.

2/6 = 33%  

Out of the 1 observation when the temperature is between 110 and 120, none were on Sunday.

0%

Final answer:

To calculate probabilities of certain observations concerning different variables, we need relevant data pertaining to those variables. Without this data, it's challenging to calculate precise probabilities. In such cases, we use the closest available data or make educated assumptions.

Explanation:

To find the probability of different observations, we need specific data that relates to those situations. For example, to find the probability that an observation is on a Thursday when the temperature is between 90 and 99, we would need historic data that captures temperature observations on Thursdays. Similarly, other probabilities also need specific data. For instance, to know the probability of an observation being on a Monday with temperature less than 90, or a Friday where the temperature is greater than 89, we would need historic temperature measurements for these specific days. However, since the provided information doesn't include specific data needed to calculate the probabilities asked in the question, we can't provide precise probabilities. Probability in statistics is generally calculated based on relevant data that is representative of the situation of interest. In situations where it is necessary to estimate the probability without access to specific data, we might use available data that is as closely matching as possible, or might make educated assumptions.

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The Eiffel Tower is 984 feet. A model of the tower is 24 inches tall. What is the ratio of the height of the model to the height of the actual Eiffel Tower?

Answers

Answer:

The ratio is [tex]\frac{1}{492}[/tex]

Step-by-step explanation:

Remember that

1 ft=12 in

The Eiffel Tower is 984 feet

Convert to inches

984 ft=984*12=11,808 in

Find the ratio of the height of the model to the height of the actual Eiffel Tower

The height of the model is 24 in

The height of the actual Eiffel Tower is 11,808 in

the ratio is equal to

[tex]\frac{24}{11,808}=\frac{1}{492}[/tex]

That means----> The height of the actual Eiffel Tower is 492 times greater than the height of the model

Final answer:

To find the ratio of the height of the model to the actual Eiffel Tower, convert the model's height to feet (24 inches = 2 feet) and then divide by the tower's height (2 feet / 984 feet) to get the simplified ratio of 1:492.

Explanation:

To calculate the ratio of the height of the model Eiffel Tower to the actual Eiffel Tower, we need to ensure both measurements are in the same unit. Since the actual Eiffel Tower's height is given in feet and the model's height is in inches, we will convert one of these measurements so they can be directly compared.

First, we convert the model's height from inches to feet. We know that 1 foot equals 12 inches, so:

24 inches × (1 foot / 12 inches) = 2 feet.

Now we have the model's height in feet, and we can form the ratio:

Height of model / Height of actual Eiffel Tower = 2 feet / 984 feet.

By simplifying this fraction, we get:

1 / 492.

So, the ratio of the height of the model to the height of the actual Eiffel Tower is 1:492.

The exam had 60 questions. Phelix got 85 •/• (percent) correct. How many questions did he answer correctly?

Answers

felix got 51 questions correct

Zeituni's standard deduction on her federal income tax return is $5700. If she paid $4670 in state taxes and $1180 in mortgage interest last year, should she use her standard deduction?


A. Yes, because it's less than the deduction she would get from itemizing.

B. No, because it's less than the deduction she would get from itemizing.

C. No, because it's more than the deduction she would get from itemizing.

D. Yes, because it's more than the deduction she would get from itemizing.

Answers

No, she should not use her standard deduction because it is less than the deduction she will get from itemizing OPTION B is correct answer.

What is Standard deduction ?

Standard deduction is that amount of someone's income, for which tax is not to be paid, thus reducing the tax bill amount. The amount of the standard deduction is based on one's filing status, age, disability, dependency etc.

Zeituni's standard deduction on her federal income tax return is $5700.

she paid $4670 in state taxes and $1180 in mortgage interest last year, totaling to = $4670+ $1180

                 = $5850

So, no, she should not use her standard deduction because it is less than the deduction she will get from itemizing.

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Final answer:

Zeituni should itemize her deductions, as the total of her state taxes and mortgage interest ($5850) is more than her standard deduction ($5700). So the correct answer is B.

Explanation:

To decide whether Zeituni should use her standard deduction or itemize her deductions, we should add up her state taxes and mortgage interest. The total of her state taxes ($4670) and mortgage interest ($1180) comes to $5850. Comparing this with her standard deduction of $5700, we can see that $5850 is more than $5700. Thus, the better option would be for Zeituni to itemize her deductions.

So the answer is B. No, because it's less than the deduction she would get from itemizing.

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The largest prime number is a factor of 42 is multiplied by the smallest prime number tht is a factor of 28

Answers

Answer:

14

Step-by-step explanation:

largest prime number which is a factor of 42=7

smallest prime number which is a factor of 28=2

7x2=14

Answer:

14

Step-by-step explanation:

largest prime number which is a factor of 42=7

smallest prime number which is a factor of 28=2

7x2=14

Sondra wants to put a fence in a triangular area of her backyard as shown in the illustration. The fence will enclose a right triangle, with two of the sides measuring 8 yards and 15 yards long. How long will the third side of the triangle be?

(the question did not contain an illustration)

Answers

17 yards. The fence that enclose Sondra's backyard is a right triangle whose sides measuring 8 yards, 15 yards and 17 yards  respectively.

The key to solve this problem is using the Pythagorean Theorem that dictates; In every right triangle the square of the hypotenuse is equal to the sum of the squares of the legs and the equation hypotenuse²=leg1²+leg2².

For this problem we know the measuring of two side, which mean that we can apply Pythagorean Theorem equation as follow:

Let's say that one of the side is a = 8yards, and the other side is b = 15yards. So, we want to know how long the third side c long.

Applying the Pythagorean Theorem:

[tex]c^{2} =a^{2}+b^{2}  \\c=\sqrt{a^{2}+b^{2}}[/tex]

Substituting the values of the sides a and b:

[tex]c=\sqrt{(8yards)^{2}+(15yards)^{2}}\\c=\sqrt{64yards^{2}+225yards^{2}}\\c=\sqrt{289yards^{2}}\\c=17yards[/tex]

Answer:

17 yds

Step-by-step explanation:

Lacking further info about this situation, I will assume that 8 yards and 15 yards represent the two legs of this right triangle, and not the hypotenuse.  If that's the case, then the hypotenuse is found by applying the Pythagorean Theorem:

(8 yd)² + (15 yd)² = hyp², or

64 yd² + 225 yd² = 289 yd²

Taking the square root of this result yields 17 yds.

The third side will be 17 yds long.

The graph of a linear function has a slope of 1/4 and passes through the point (1,3). What is the y-intercept of the function?

A. b=1/4
B. b=11/4
C. b= -1/4
D. b=4

Answers

Answer:

B

Step-by-step explanation:

In slope intercept form, y = mx + b, the m is the slope, the b is the y intercept, and x and y can be subbed in from the point you are given of (1, 3).  We are told the slope, so everything we have fills in like this:

[tex]3=\frac{1}{4}(1)+b[/tex]

Now we just need to solve for b:

[tex]3-\frac{1}{4}=b[/tex] and

[tex]\frac{12}{4}-\frac{1}{4}=b[/tex] so

[tex]b=\frac{11}{4}[/tex]

The diameter of the base of the cone measures 8 units.
The height measures 6 units.
What is the volume of the cone?
A)240 cubic units
B)321 cubic units
C)48X cubic units
D)647 cubic units

Answers

Answer:   [tex]32\pi[/tex] cubic units.

Step-by-step explanation:

You can use this formula for calculate the volume of a cone:

[tex]V_{cone}=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

You know that the diameter of the base of the cone measures 8 units, then, the radius can be found by dividing the diameter by 2:

[tex]r=\frac{8units}{2}\\\\r=4units[/tex]

Since you already know that height and  the radius, you can substitute them into the formula. Then, the volume of this cone is:

[tex]V_{cone}=\frac{1}{3}\pi (4units)^2(6units)[/tex]

[tex]V_{cone}=32\pi \ units^3[/tex]

Answer:

b. 32

Step-by-step explanation:

e2020 says so

Can someone help me out

Answers

Answer:

88?

Step-by-step explanation:

Since XPY is a lot smaller and 23 degrees, 88 degrees makes the most sense.

Find a unit vector in the same direction as the given vector: v = −14.5i + 2.5 j.

Answers

ANSWER

[tex]- \frac{29}{866} \sqrt{866} i + \frac{5}{866} \sqrt{866} j[/tex]

EXPLANATION

The given vector is v = −14.5i + 2.5 j.

The magnitude of this vector is

[tex] |v| = \sqrt{ {( - 14.5)}^{2} + {2.5}^{2} } [/tex]

[tex]v| = \sqrt{ {( - 14.5)}^{2} + {2.5}^{2} } [/tex]

[tex]v| = \sqrt{ 216.5} = \frac{ \sqrt{866} }{2} [/tex]

The unit vector in the direction of this vector is

[tex] = \frac{v}{ |v| } [/tex]

[tex] = - \frac{14.5}{ \frac{ \sqrt{866} }{2} } i + \frac{2.5}{ \frac{ \sqrt{866} }{2} } j[/tex]

[tex] = - \frac{29}{866} \sqrt{866} i + \frac{5}{866} \sqrt{866} j[/tex]

Please help me out please

Answers

Answer:

11.7

Step-by-step explanation:

a^2+b^2=c^2

10^2+6^2=c^2

100+36=c^2

add 100+36=136

square root of 136 = 11.6619037897

= 11.7

On the main floor of a theatre the number of seats per row increases at a constant rate. Jack counts 31 seats in row 3 and 37 seats in row 6. How many seats are there in row 20

Answers

Answer: 65 seats in row 20

Step-by-step explanation: 3 = 31, 6 = 37 the difference is 3 rows but 6 seats so its going up 2 every row therefor you need 14 rows after row 6 so 14 * 2 + 37 = 65 seats

By finding a linear equation, we will see that on the row 20 there are 65 seats.

How many seats are in row 20?

Here we have a linear relationship, that can be written as:

y = a*x + b

Where a is the slope and b the y-intecept.

We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, we have points of the form (row, seats), and the two points that we have are:

(3, 31) and (6, 37)

So the slope is:

[tex]a = \frac{37 - 31}{6 - 3} = 2[/tex]

So the equation is:

y = 2*x + b

To find the value of b, we replace one of the points in the equation. If we use the first one, we have x = 3 and y = 31, so:

31 = 2*3 + b

31 = 6 + b

31 - 6 = 25 = b

The equation is:

y = 2x + 25

The number of seats in row 20 is what we get if we replace x by 20, then:

y = 2*20 + 25 = 65

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From the ten books that you've recently bought but not read, you plan to take four with you on vacation. How many different sets of four books can you take

Answers

Answer:

Step-by-step explanation:

2 sets of books

The heights of a group of trees is normally distributed with a mean of 14.3 feet. If the z score for a 20-foot y’all tree is 1.9, what is the standard deviation?

Answers

Answer:

The standard deviation of the heights of the group of trees is 3 feet

Step-by-step explanation:

For a normal distribution, the z-score corresponding to a particular observed value is calculated as;

z-score = (observed value - mean) / (standard deviation)

The mean is given as 14.3

The z-score is 1.9

The observed value is 20 (the given height)

We can make the standard deviation to be the subject of the formula in the above equation;

standard deviation = (observed value - mean) / ( z-score)

We then substitute the given values into this equation;

standard deviation = [tex]\frac{20-14.3}{1.9}=3[/tex]

What are the angle measures of triangle VUW?


A) m∠V = 30°, m∠U = 60°, m∠W = 90°


B) m∠V = 90°, m∠U = 60°, m∠W = 30°


C) m∠V = 30°, m∠U = 90°, m∠W = 60°


D) m∠V = 60°, m∠U = 90°, m∠W = 30°

Answers

Answer:

its option D

Step-by-step explanation:

The angle measures of triangle VUW is D) m∠V = 60°, m∠U = 90°, m∠W = 30°

What are the 3 angles of a triangle?

All three angles in any triangle always upload as many as 180 degrees. So in case you best have of the angles with you, just upload them together, after which subtract the sum from 180. EX: A Triangle has three angles A, B, and C.

What is the angle measure formula?

The method for finding the sum of the measure of the indoor angles is (n - 2) * 180. To discover the degree of 1 indoors perspective, we take that method and divide via the range of aspects n: (n - 2) * a hundred and eighty / n.

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7. John's seafood restaurant is trying to estimate its profits. John has found that on average, each meal served costs the restaurant $14.56 and takes in $17.12. John has also found that on average, each beverage served costs the restaurant $1.20 and takes in $5.40. If c customers order a meal, and half of those customers order a beverage, which of the following functions models the restaurant's total profit?
f(c) =17.12c -14.56c + 5.40(.5c) - 1.20(.5c)
f(c) = 17.12c - 14.56c + 5.4c - 1.20c
f(c)=14.56c - 17.12c + 1.20c - 5.40c14.56c - 17.12c + 12(.5c) - 5.40(.5c)

Answers

Answer:

f(c) =17.12c -14.56c + 5.40(.5c) - 1.20(.5c)

Step-by-step explanation:

Profit is the difference between revenue (17.12c +5.40(.5c)) and cost(14.56c+1.20(0.5c)). That difference is expressed by the function shown above.

Answer:

f(c) =17.12c -14.56c + 5.40(.5c) - 1.20(.5c)

Step-by-step explanation:

Let's build the f(c) function by steps.

There are c customers.

John has found that on average, each meal served costs the restaurant $14.56 and takes in $17.12.

So, the costs for the restaurant are negative, and what takes positive.

f(c) =17.12c -14.56c

Now the final part

John has also found that on average, each beverage served costs the restaurant $1.20 and takes in $5.40.

Half of these customers order a beverage, and this is why we multiply by 0.5.

So

f(c) =17.12c -14.56c + 5.40(.5c) - 1.20(.5c)

Select the statement that is NOT equivalent to-- "It is not true that England and Africa are both countries."

a. If England is a country, then Africa is not a country.

b. England is not a country and Africa is not a country.

c. England is not a country or Africa is not a country.

d. If Africa is a country, then England is not a country

Answers

The original statement is true only if:

England is a country and Africa isn'tAfrica is a country and England isn'tNeither of them are countries

Options a and d are equivalent:

[tex]P\implies Q \iff \lnot Q \implies \not P[/tex]

and they both are true in the same cases as above.

Option c is also fine, because it is false only if both England and Africa are both countries, just like the original statement.

Option b, instead, is true only if neither of the two options are countries, so it doesn't cover the cases where only one of the two is a country.

Answer:

Both are cities smh ‍♂️

Step-by-step explanation:

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