questions 9, 10, 11, 12, 13, 14 on Unit 3: relations and functions Homework 1: relations, domain, range, and functions

S thus measures around 2.77 centimetres in length.

The law of sines is frequently used to find the elusive side or angle of a triangle. This law can be used if precise triangle measurement combinations are given. ASA The objective is to identify the unknown side given two angles and an included side.

The Law of Sines can be used to determine the length of side s: s/sin(mS) = q/sin(mQ).

replacing the specified values:

s/sin(10°) = 3.9/sin(74°)

s ≈ sin(10°) × 3.9 ÷ sin(74°)

s ≈ 0.684 × 3.9 ÷ 0.961

s ≈ 2.77 cm (rounded to the nearest 10th)

S thus measures around 2.77 centimetres in length.

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The only expression that does not belong to the other 3 is the one that is a  binomial.

A monomial is defined as an algebraic expression that has only one non- zero term. Examples of a monomial expression are x, 7xy²

A binomial is defined as an algebraic expression that has two non-zero terms. Examples of a binomial expression: x² + 2y

A trinomial is defined as an algebraic expression that possesses three non-zero terms. Examples of a trinomial expression: a + b + c

A polynomial is defined as an algebraic expression that has one, two or more terms.

The only expression that does not belong to the other 3 is (b - 2⁻¹) because it is the only binomial.

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Hence, in answering the stated question, we may say that As a result, we  angles have demonstrated that angle PQR equals angle PQS, assuming that angle article equals angle pqs and QS = PR.

An angle is a shape in Euclidean geometry that is comprised of two rays, known as such angle's flanks, that meet at a central location known as the angle's set of vertices. Two rays might combine to generate an angle there in plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential configuration between two rays and lines that meet a termination. The English name "angle" is derived from the Latin phrase "angulus," which means "horn." The apex is the point at where the two rays, also known also as angle's sides, converge.  

It is difficult to propose a specific solution without a diagram or a comprehensive description of the figure. But, based on the facts provided, we can apply the following argument to demonstrate that angle PQR equals angle PQS.

Assuming that angle article equals angle pqs and QS = PR.

To demonstrate: angle PQR = PQS angle.

We know that angle pqs = angle article. This signifies that the two angles are parallel.

We also understand that QS Equals PR. That is, these two line segments are congruent.

As a result, angle PQR equals angle PQS.

As a result, we have demonstrated that angle PQR equals angle PQS, assuming that angle article equals angle pqs and QS = PR.

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Answer:

Base=20m   height= 15m

Step-by-step explanation:

The area of a triangle is given by:

[tex]A=\frac{bh}{2}[/tex]

since base is 10 less than twice the height  b=2h-10

plugin in those values and knowing area is 150
[tex]150=[/tex][tex]\frac{h(2h-10)}{2}[/tex]

then solve for h

[tex]300=2h^2-10h[/tex] this is quadratic equation

[tex]h^2-5h-150=0[/tex]  
factorizing  (notice you can also use quadratic equation)

[tex](h-15)(h+10)=0[/tex]
which positive solution (height cant be negative) is h=15
then the base is b=2(15)-10=20

Answer:

The height is 15 meters and the base is 20 meters.

Step-by-step explanation:

Let's use the formula for the area of a right triangle:

A = (1/2)bh

Where A is the area, b is the base, and h is the height.

We're given that the area is 150 square meters, so we can substitute that in:

150 = (1/2)bh

Next, we're told that the base is 10 less than twice the height. In other words,

b = 2h - 10

We can substitute this expression for b into the equation for the area:

150 = (1/2)(2h - 10)h

Simplifying:

300 = (2h - 10)h

300 = 2h^2 - 10h

2h^2 - 10h - 300 = 0

Dividing both sides by 2:

h^2 - 5h - 150 = 0

Now we can solve for h using the quadratic formula:

h = (-(-5) ± sqrt((-5)^2 - 4(1)(-150))) / 2(1)

h = (5 ± sqrt(625)) / 2

h = (5 ± 25) / 2

We can ignore the negative root (which gives us a negative height), so:

h = 15

Now we can use the expression for b in terms of h to find the base:

b = 2h - 10

b = 2(15) - 10

b = 20

Therefore, the height is 15 meters and the base is 20 meters.

The answer of the question based on the players can fill their water bottles with the sports drink before the cooler is empty is 15 players.

An amount may refer to quantity of something that can be measured, such as amount of substance or amount of  the time.

The cooler can hold 5 1/2 gallons of sports drink, and Coach Walker fills 3/4 of it, which means he fills:

5 1/2 gallons * 3/4 = (5 * 2/2 + 1/2) * 3/4 = 15/4 gallons

We know that 1 gallon equals 8 pints, so we can convert the 15/4 gallons to pints:

15/4 gallons * 8 pints/gallon = 30 pints

Therefore, there are 30 pints of sports drink in the cooler. Assuming each player's water bottle can hold 2 pints of sports drink, we can find how many players can fill their bottles before the cooler is empty by dividing the total amount of sports drink by the amount used by each player:

30 pints / 2 pints/player = 15 players

Therefore, 15 players can fill their water bottles with the sports drink before the cooler is empty.

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Answer:

b i think let me know if im right

Step-by-step explanation:

Answer:

Here, given

present population = 20000

according to question,

population gets double every 34 years

i.e P = 20000 × 2

= 40000

now,

P = 40000

T = 68-34 = 34

ie, again p is double

so, P = 40000×2

= 80000

Hence, the population after 68 years from now is 80000

Answer:

11 11/12

Step-by-step explanation:

You can change these "mixed numbers" (a big whole numbers and also a fraction) to "improper fractions" (a single fraction with a bigger number on top and a smaller number on the bottom)

4 1/3 × 2 3/4

see image

13/3 × 11/4

Multiply straight across, top×top and bottom×bottom.

see image.

Change back to a mixed number by dividing.

The multiplication of 4 1/3 x 2 3/4 is 11 11/12.

The correct option is C.

A fraction that has the numerator higher than or equal to the denominator is said to be an improper fraction.

To multiply 4 1/3 and 2 3/4, we can first convert them to improper fractions:

4 1/3 = 13/3

2 3/4 = 11/4

Then we can multiply the fractions by multiplying the numerators and denominators separately:

(13/3) x (11/4) = (143/12)

Finally, we can convert the improper fraction back to a mixed number if desired:

143/12 = 11 11/12

Therefore, the answer is 11 11/12.

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The range, which is the distance between the smallest and greatest linear equation values in the data,  does not take into account the distribution of the data within that range.

In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.

Because it has a lower IQR, Fast Chicken can more consistently estimate their wait time (Interquartile Range). In this case, the IQR is the range of the middle 50% of the data, which is the distance between the first and third quartiles.

Super Fast Food, on the other hand, has a higher IQR, indicating that the data is more dispersed. This means that customers report a wider range of wait times, making it more difficult to estimate a consistent wait time. The range, which is the distance between the smallest and greatest values in the data, is not as useful for measuring consistency in this case because it does not take into account the distribution of the data within that range.

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Answer:

120km/h

Step-by-step explanation:

Distance=14km

Time       =7m

A driver was fined for speeding in 100km/h

∴ we convert time into hours

Time =(7/60)h

Average speed of the car = total distance ÷total time

                                           =14km×60/7h=120km/h which is greater than                          

                                                                                                        100km/h

Answer:

two are supplementary. the measure of one of these angles is 12 degrees less than one-third the measure of the other.what is the measure of each angle

Let's call the measures of the two angles x and y, where x is the larger angle. We know that the two angles are supplementary, which means they add up to 180 degrees:

x + y = 180

We also know that one of the angles (let's say y) is 12 degrees less than one-third the measure of the other angle (x):

y = (1/3)x - 12

Now we can substitute the second equation into the first equation to solve for x:

x + (1/3)x - 12 = 180

Multiplying both sides by 3 to get rid of the fraction, we have:

3x + x - 36 = 540

Combining like terms, we get:

4x - 36 = 540

Adding 36 to both sides, we get:

4x = 576

Dividing both sides by 4, we get:

x = 144

Now we can use the first equation to solve for y:

144 + y = 180

Subtracting 144 from both sides, we get:

y = 36

Therefore, the measures of the two angles are 144 degrees and 36 degrees.

Answers:

[tex]\text{Derivative: } \ \ \frac{dy}{dx} = \frac{-260x^{9} - 156x^{25}y}{6x^{26}+7y^6}\\\\ \text{Tangent line at (1,1) is: } \ y = -32x + 33\\\\[/tex]

==========================================================

Work Shown:

Let's determine the derivative dy/dx.

Part 1

[tex]26x^{10} + 6x^{26}y+y^7 = 33\\\\ \frac{d}{dx}(26x^{10} + 6x^{26}y+y^7) = \frac{d}{dx}(33)\\\\ \frac{d}{dx}(26x^{10}) + \frac{d}{dx}(6x^{26}y)+\frac{d}{dx}(y^7) = 0\\\\ 10*26x^{10-1} + \frac{d}{dx}(6x^{26})y+(6x^{26})*\frac{dy}{dx}+7y^6\frac{dy}{dx} = 0\\\\[/tex]

Part 2

[tex]260x^{9} + 26*6x^{26-1}y+6x^{26}*\frac{dy}{dx}+7y^6\frac{dy}{dx} = 0\\\\ 260x^{9} + 156x^{25}y+6x^{26}*\frac{dy}{dx}+7y^6\frac{dy}{dx} = 0\\\\ 260x^{9} + 156x^{25}y+(6x^{26}+7y^6)\frac{dy}{dx} = 0\\\\ (6x^{26}+7y^6)\frac{dy}{dx} = -260x^{9} - 156x^{25}y\\\\ \frac{dy}{dx} = \frac{-260x^{9} - 156x^{25}y}{6x^{26}+7y^6}\\\\[/tex]

There are many other possible ways to express the dy/dx expression.

GeoGebra and WolframAlpha are two useful tools to help verify the answer. Make sure you use the CAS mode in GeoGebra.

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

Part 3

Now that we know dy/dx, we can determine the slope of the tangent at any point (x,y) on the implicit function curve.

Plug in x = 1 and y = 1.

[tex]\frac{dy}{dx} = \frac{-260x^{9} - 156x^{25}y}{6x^{26}+7y^6}\\\\ \frac{dy}{dx} = \frac{-260(1)^{9} - 156(1)^{25}(1)}{6(1)^{26}+7(1)^6}\\\\ \frac{dy}{dx} = \frac{-260(1) - 156(1)(1)}{6(1)+7(1)}\\\\ \frac{dy}{dx} = \frac{-260 - 156}{6+7}\\\\ \frac{dy}{dx} = \frac{-416}{13}\\\\ \frac{dy}{dx} = -32\\\\[/tex]

The slope of the tangent line at (1,1) is m = -32.

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

Part 4

Apply the point-slope formula to determine the tangent line.

[tex]m = -32 = \text{ slope}\\(x_1,y_1) = (1,1) = \text{the point the tangent line goes through}[/tex]

So,

[tex]y - y_1 = m(x - x_1)\\\\y - 1 = -32(x - 1)\\\\y - 1 = -32x + 32\\\\y = -32x + 32 + 1\\\\y = -32x + 33\\\\[/tex]

Answer:

C) 69

Step-by-step explanation:

23 x 6 ÷ 2 =69feet2

ok!

The ordered pair solutions for the system of equations are (-2, 5) and (1, 2).

To determine if an ordered pair is a solution to two systems of equations, substitute the values ​​of the variables into each equation. If an ordered pair makes both equations true, it is the solution of the system. 

To find the ordered pair solutions for the system of equations, we need to solve the two equations simultaneously.

f(x) = x² + 1 ...(1)

f(x) = -x + 3 ...(2)

Setting the two equations equal to each other, we get:

x² + 1 = -x + 3

Rearranging this equation, we get:

x² + x - 2 = 0

Factoring this quadratic equation, we get:

(x + 2)(x - 1) = 0

Therefore, the solutions for x are x = -2 and x = 1.

Substituting these values of x into either equation (1) or (2), we get:

For x = -2: f(-2) = (-2)² + 1 = 5, and f(-2) = -(-2) + 3 = 5.

For x = 1: f(1) = 1² + 1 = 2, and f(1) = -1 + 3 = 2.

Therefore, the ordered pair solutions for the system of equations are (-2, 5) and (1, 2).

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Solution is in da attachment mate!! :D

Step-by-step explanation:

that is a college question ?

x = cost of a ham sandwich

y = cost of a turkey sandwich

2x + 3y = 29

3x + 2y = 31

let's multiply the first equation by 3, abd the second equating by -2, and then we add them :

6x + 9y = 87

-6x - 4y = -62

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

0 5y = 25

y = 25/5 = $5

let's use the original first equation to get x (but we could use also the second equation, it does not matter).

2x + 3×5 = 29

2x + 15 = 29

2x = 14

x = $7

each ham sandwich costs $7.

each turkey sandwich costs $5.

Answer: Let's assume the two original numbers to be x and y.

If one of them is increased by 50%, then the new value will be 1.5x, and if the other one is decreased by 50%, the new value will be 0.5y.

The product of the two new numbers will be:

1.5x * 0.5y = 0.75xy

So, the new product is 0.75 times the original product. This means the product of the two numbers has decreased by 25%.

To summarize:

If one number is increased by 50% and the other number is decreased by 50%, the product of the two numbers will decrease by 25%.

The new product is 0.75 times the original product.

Brainiest is appreciated (:

Answer:

  0.3176523

Step-by-step explanation:

You want the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70%.

The desired probability is the product of the probability of 5 success and 2 failures, multiplied by the number of ways that result might occur.

  P(x=5) = 7C5·(0.7^5)(1 -0.7)^2 = 0.3176523

The probability of exactly 5 successes is 0.3176523.

__

Additional comment

Any of a number of probability calculators can tell you this probability. Spreadsheets have appropriate functions built in as well.

[tex]\blue{\huge {\mathrm{PROBABILITY}}}[/tex]

[tex]\\[/tex]

[tex]{===========================================}[/tex]

[tex]{\underline{\huge \mathbb{Q}{\large \mathrm {UESTION : }}}}[/tex]

[tex]{===========================================}[/tex]

[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]

[tex]{===========================================}[/tex]

[tex] {\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}} [/tex]

We can use the binomial probability formula to find the probability of exactly 5 successes in 7 trials:

[tex]\sf P(5\: successes\: in\: 7\: trials) = (7\: choose\: 5) (0.7)^5 (0.3)^2[/tex]

where:

Plugging in these values, we get:

[tex]\begin{aligned}\sf P(5\: successes\: in\: 7\: trials)& =\sf 21 (0.7)^5 (0.3)^2\\& =\bold{ 0.3176523}\end{aligned}[/tex]

Therefore, the probability of exactly 5 successes in 7 trials of a binomial experiment in which the probability of success is 70% is 0.3176523.

[tex]{===========================================}[/tex]

[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\tt 04/01/2023[/tex]

Hence, in response to the provided question, we can say that As a result,  exponents [tex]/sqrt(196y^8)[/tex] simplifies to [tex]14y^4[/tex].

Exponentiation, sometimes known as "raising b to the nth power," is a substitution cipher that includes two numbers: a base quantity, b, and an argument, meaning power, n. Exponents represent the number of times a value has been increased by itself. As an example, 2-3 (represented as 23) represents: 2 x 2 x 2 = 8. 2 + 3 = 6 does not equal 23. Remember that an integer multiplied by one equals itself. Exponents are a method for expressing large numbers as powers. The amount that represents however many times a statistic has already been amplified by itself is called the exponent. As an example, multiplying 6 by 4 yields 6 x 6 x 6.

Using exponent principles and the square root of perfect squares, we may simplify sqrt(196y8) as follows:

[tex]\sqrt(196y8) = \sqrt((142*(y4)2) [since 196 = 142 and (y4)2 = y8]\\\sqrt(142) * \sqrt((y4)2) [using the \sqrt(ab) = \sqrt(a) * \sqrt(b) rule]\\= 14y^4[/tex]

As a result, [tex]/sqrt(196y^8)[/tex] simplifies to [tex]14y^4[/tex].

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Answer:

$14500

Step-by-step explanation:

$10 per unit means 1 unit is equivalent to 10 dollars.

∴Unit multiplier = [tex]\frac{10 dollars}{unit}[/tex]

$5 per unit means 1 unit is equivalent to 5 dollars

∴Unit multiplier = [tex]\frac{5 dollars}{unit}[/tex]

Remaining units = 1000 - 100 = 900 units

The unit multipliers are arranged in such a way that the "units” in the numerator and denominator will cancel each other out leaving us with “dollars” in the numerator. Our answer should be expressed in dollars
since the question requires us to calculate the bill

Bill of the House = Charge of first 100 units + Charge of remaining units

                            = (1000 units)([tex]\frac{10dollars}{unit}[/tex]) + [(900)units][[tex]\frac{5dollars}{unit}[/tex]]

                            = $10000 + $4500

                            = $14500

The equation of the hyperbola with the given foci and vertices is (x - 3)² - (y - 1)² = 64

Hyperbola is a type of conic section, which is a curve formed by the intersection of a cone with a plane. It is similar to a circle, but with two separate halves that are mirror images of each other. These two halves are called branches, and the point where they intersect is the vertex. The hyperbola is characterized by its two foci, which are points that lie on the inside of the structure.

The equation of a hyperbola with foci (h, k) and (h, l) and vertices (m, n) and (p, n) is given by:
((x - h)² / (m - h)²) - ((y - n)² / (k - n)²) = 1
In this case, h = 3, k = 11, l = -9, m = 11, and n = 1. Plugging these values into the equation, we get:
((x - 3)² / (11 - 3)²) - ((y - 1)² / (11 - 1)²) = 1
Simplifying, we get:
(x - 3)² - (y - 1)² = 8²
Therefore, the equation of the hyperbola with the given foci and vertices is: (x - 3)² - (y - 1)² = 64.

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The value of the functions are;

f(3) = - 3

g(5) = -77

A function can be defined as an equation or expression hat shows the relationship between two variables.

These variables are termed;

From the information given, we have that;

f(x) = -5x + 2

g(x) = -3x²- 2

To determine the function, f(3), and g(5), we have to substitute the value of x as 3 in the function f(x) and the value of x as 5 in the function g(x).

We have;

f(3) = -5(3) + 2

expand the bracket

f(3) = - 13

For the second function;

g(5) =  - 3(5)² -2

g(5) = -77

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To find the equation of the drone's path, we can first find the coordinates of the center of the circle that the drone is flying around. We can do this by finding the midpoint between the two points the drone passes over:

Midpoint in the x-direction: (220 ft - 180 ft)/2 = 20 ft to the right of the origin.

Midpoint in the y-direction: (230 ft - 180 ft)/2 = 25 ft above the origin.

Therefore, the center of the circle is located at (20, 25) ft.

The radius of the circle can be found by calculating the distance between the center of the circle and either of the two points the drone passes over:

Radius: sqrt((20-(-180))^2 + (25-180)^2) = sqrt(40000 + 15625) = 205 ft (rounded to the nearest whole number)

So the equation for the drone's path is:

(x - 20)^2 + (y - 25)^2 = 205^2

To find how far north of Megan's position the drone is when it passes due north, we can substitute x = 0 into the equation:

(0 - 20)^2 + (y - 25)^2 = 205^2

400 + (y - 25)^2 = 42025

(y - 25)^2 = 41625

y - 25 = +/-sqrt(41625)

y = 25 +/- 204.06

So the drone is either 229.06 ft north or 22.94 ft south of Megan's position when it passes due north. Rounded to three decimal places, the answer is 229.06 ft north.

Answer:

2^7 or 128

Step-by-step explanation:

When we multiply two powers with the same base, we add their exponents. In this case, the base is 2 and the exponents are 3 and 4.

So, 2^3 • 2^4 can be simplified as:

2^3 • 2^4 = 2^(3+4) = 2^7

Therefore, 2^3 • 2^4 is equal to 128.

Answer:128

Step-by-step explanation:

i assume that by ^ you meant power,

2^3=2*2*2=8

2^4=2*2*2*2=16

8*16=128

Answer:

No solutions

Step-by-step explanation:

i have a feeling it's "no solutions". looking at the equations, the only thing that's different is the y intercepts (one being +1 and the other +7). that tells me they are parallel, so they'll never touch each other

A triangle is a geometrical shape that is formed by three straight lines connecting three non-collinear points. The three points are called the vertices of the triangle, and the lines connecting them are called sides or edges.

To prove that triangle QRS is similar to triangle TUV, we need to show that their corresponding angles are equal and their corresponding sides are proportional.

Let's start by identifying the corresponding angles:

Now, let's look at the corresponding sides:

To prove that the triangles are similar, we need to show that the ratios of the corresponding sides are equal:

QS/TV = RS/UV (given)

QS/TV = 3/3 (since QR=3TU)

QS/TV = 1

RS/UV = 3/3 (since QR=3TU)

RS/UV = 1

Since the ratios of the corresponding sides are equal, the triangles are similar. Therefore, we can conclude that triangle QRS ~ triangle TUV.

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Answer:

Step-by-step explanation:

To find the cost per hour of bike use at Cheng's Bike Rentals, we need to divide the total cost of renting the bike by the number of hours it was rented for.

If it costs $22 to rent a bike for 4 hours, then the cost per hour is:

$22 / 4 hours = $5.50/hour

Therefore, it costs $5.50 per hour of bike use at Cheng's Bike Rentals.

The correct answer is "The extreme value theorem applies, and f(x) has both a minimum and a maximum."

What is the extreme value theorem?

The extreme value theorem states that if a function is continuous on a closed interval, then it must have both a maximum and a minimum value on that interval. To determine whether the extreme value theorem applies to the graph of f(x), we need to check if the function is continuous on a closed interval and whether it has a highest and lowest point within that interval.

Looking at the graph of f(x), we can see that the function is continuous on the closed interval [-3, 3] since it has no breaks or jumps. Additionally, the graph has the highest point at (1, 2) and the lowest point at (-3,-2). Therefore, we can conclude that the extreme value theorem applies and that f(x) has both a minimum and a maximum value on the interval [-3, 3].

Therefore, the correct answer is (a) "The extreme value theorem applies, and f(x) has both a minimum and a maximum."

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Number line  that represents the solution to |x − 21| < 3 is C.

Tο sοlve the inequality |x - 21| < 3, we need tο find all the values οf x that are less than 3 units away frοm 21 οn the number line.

Starting frοm 21, we can cοunt 3 units tο the left and 3 units tο the right tο find the interval οf values that satisfy the inequality:

| x - 21 | < 3 can be written as -3 < x - 21 < 3

Adding 21 tο all parts οf the inequality gives:

18 < x < 24

Therefοre, the sοlutiοn tο the inequality is the interval οf values between 18 and 24, excluding the endpοints.

Lοοking at the answer chοices, we can see that οptiοn C represents this interval οf values:

A:

B:

C: |----|----|----|----|----|----|

18 19 20 21 22 23 24

D:

Therefore, the correct answer is C.

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Answer:

So g would be 15.