Please help!
1.) You are the crew chief of the Algebra 2 formula racing team. Your current task is to
determine fuel consumption of both cars. Car A travel x² + 3x miles and Car B travels 2x + 8 miles. Based upon tire wear (x), the cars will use x² + 4x gallons of fuel.
a.) What is the mileage
(miles/gallons) for each car?
Car A:
Car B:
b.) What is the total mileage for both cars in simplified form? (3 points)
Total:
2.)Solve for x: (5 points)
3r+3=−x+6
Answers
The mileage of Car A, Car B, and the average of is (x+3)/(x+4), 2/x and [tex]\frac{x^{2} +5x +8 }{x^{2} +4x}[/tex]
It is given that the distance traveled by the car A = x² + 3x
And the distance traveled by car B = 2x + 8
The mileage is given by mile/gallon.
So, the mileage of Car A = distance traveled by car A/gallons of fuel used.
Then,
Mileage of Car A = [tex]\frac{x^{2} +3x }{x^{2} +4x} =\frac{x(x +3)}{x(x+4)} = \frac{x+3}{x+4}[/tex] miles /gallons
Similarly, the mileage of Car B = distance traveled by car B/gallons of fuel used.
Then,
Mileage of Car B = [tex]\frac{2x+8}{x^{2} +4x} = \frac{2(x+4)}{x(x+4)} =\frac{2}{x}[/tex] miles/gallons
Now, the total mileage of A and B is the average of car A and car B,
Mileage of Car A + Mileage of Car B = [tex]\frac{x^{2} +3x }{x^{2} +4x} + \frac{2x+8}{x^{2} +4x} = \frac{x^{2} +5x +8 }{x^{2} +4x}[/tex]
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Related Questions
(10,-3),(5,-4)i need help finding the midpoint
Answers
The given points are (10, -3) and (5, -4).
The midpoint formula is
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})_{}[/tex]Where,
[tex]\begin{gathered} x_1=10 \\ x_2=5 \\ y_1=-3 \\ y_2=-4 \end{gathered}[/tex]Replacing these coordinates, we have
[tex]\begin{gathered} M=(\frac{10+5}{2},\frac{-3-4}{2}) \\ M=(\frac{15}{2},-\frac{7}{2}) \end{gathered}[/tex]Therefore, the midpoint is M(15/2, -7/2).If the rate of inflation is 2.5% per year, the future price P(T) in dollars of a certain item can be modeled by the following exponential function, where T is the number of years from today
Answers
Solution:
The future price p(t), in dollars, can be modelled by the exponential function;
[tex]p(t)=800(1.025)^t[/tex](a) The current price is;
[tex]\begin{gathered} t=0; \\ \\ p(0)=800(1.025)^0 \\ \\ p(0)=800(1) \\ \\ p(0)=800 \end{gathered}[/tex]ANSWER: $800
(b) The price 8 years from today;
[tex]\begin{gathered} t=8 \\ \\ p(8)=800(1.025)^8 \\ \\ p(8)=800(1.2184) \\ \\ p(8)=974.72 \\ \\ p(8)\approx975 \end{gathered}[/tex]ANSWER: $975
The population of Boom town is 775,000 and is increasing at a rate of 6.75% each year. How many years will it take to reach a population of 1,395,000?
Answers
To study population growth, we use the following formula
[tex]P=P_0\cdot e^{rt}[/tex]Where,
[tex]\begin{gathered} P=1,395,000 \\ P_0=775,000 \\ r=0.0675 \end{gathered}[/tex]Let's replace the values above, and solve for t.
[tex]\begin{gathered} 1,395,000=775,000\cdot e^{0.0675t} \\ e^{0.0675t}=\frac{1,395,000}{775,000} \\ e^{0.0675t}=1.8 \\ \ln (e^{0.0675t})=\ln (1.8) \\ 0.0675t=\ln (1.8) \\ t=\frac{\ln (1.8)}{0.0675} \\ t\approx8.7 \end{gathered}[/tex]Hence, it would take 8.7 years to reach a population of 1,395,000.How to solve question 21? Area of the shaded region
Answers
The shaded region covers an area of 86.
Given that,
In the picture,
We have to find the area of the shaded region of question 21.
We know that,
The Area of the square is side square.
The area of the circle is πr².
The radius of the circle is 10.
We know that,
The circle's diameter is the same as a square's side length.
The diameter=10+10 =20
The side is 20
The area of the square
= 20² = 400
The area of the circle = π (10)²=π×100=314
Subtract the area of the square and area of the circle.
400-314
86
Therefore, The shaded region covers an area of 86.
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Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4)-1 and 3 + 2i A) (x)= x3 + 5x2 +7x + 13 B)(x) = x3 - 5x2 + 7x - 13 C)(x)= x3 - 5x2 + 7x + 13 D) f() = x3 - 5x2 + 7x + 14
Answers
Mia made a pencil box in the shape of a right rectangular prism what's the surface area of the box 20cm,6cm,7cm
Answers
1) Let's visualize it to better understand:
A right rectangular prism is made from
2 faces 6 x 7
4 faces 20 x 6
Since we have rectangles, we can write calculating the area of each rectangle.
S base = 2 (6x 7) ⇒ S base = 84 cm²
S faces = 2 (20 x 6) ⇒ S faces = 240 cm²
S faces = 2 (20 x 7) ⇒ S faces = 280 cm²
2) Then the total surface area
84+240+280=604 cm²
What is the slope for this equation y = -2.5x + 92
Answers
EXPLANATION
Given the equation y = -2.5x + 92
The slope is equal to -2.5
Linda must choose a number between 55 and 101 that is a multiple of 3,5, and 9. Write all the numbers that she could choose.
Answers
We will have the following:
*The LCM of the numbers given (3, 5 & 9) is 72. [This is the value to chosse]. We will have that 90 is also a multiple of 3, 5 & 9 [This is other value that can be chosen].
If x is multiplied by 5 and then 3 is subtracted, then the function isf(x) = 5x -3.What are the steps to find the inverse to this function?
Answers
Step:
Concept:
First, find the inverse of subtraction which is addition
x + 3
Step 2:
The multiplicative inverse is division, hence, you will divide x + 3 by 5.
Therefore, we have
[tex]\begin{gathered} y\text{ = }\frac{x\text{ + 3}}{5} \\ \end{gathered}[/tex]The inverse of the function is given below.
[tex]f^{-1}(x)\text{ = }\frac{x\text{ + 3}}{5}[/tex]Method 2
[tex]\begin{gathered} \text{If f(x) = 5x - 3} \\ \text{let y = 5x - 3} \\ \text{Make x subject of the formula} \\ \text{y + 3 = 5x} \\ x\text{ = }\frac{y\text{ + 3}}{5} \\ \text{Write the inverse of f(x) by changing y to x} \\ f^{-1}(x)\text{ = }\frac{x\text{ + 3}}{5} \end{gathered}[/tex]Answer:
Add 3, then divide by 5
Step-by-step explanation:
A randomly generated list of integers from O to 4 is being used to simulate anevent, with the number 3 representing a success. What is the estimatedprobability of a success?
Answers
We have that:
• A randomly generated list of, integers from 0 to 4 i,s being used to simulate an event.
• The number 3 represents a success.
And we need to find the estimated probability of success.
We can achieve that if we know that:
1. We have the following sample space for the experiment - we have a list of integers from 0 to 4:
[tex]\Omega=\lbrace0,1,2,3,4\rbrace[/tex]2. Then the probability of having a 3 is:
[tex]P(3)=\frac{1}{5}=0.2\Rightarrow20\%[/tex]We have one possibility of getting a 3 (one possibility) out of 5 possibilities (0, 1, 2, 3, 4).
Therefore, the estimated probability of success is 20% (option D.)
what does translation mean?
Answers
translation means moving a geometric object in the cartesian plane without rotating it.
4x + 8 = 28Describe a real-world situation the equation could represent.
Answers
In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?
The equation 4x +8=28 could be used to describe a scenario like this below:
In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?
Notice the fixed amount (8) and the variable (4x) and the total of money you have (28). So the sum above describes the amount of money for that club.
With that equation you can find that:
4x +8=28
4x+8 -8 =28-8
4x=20
x=5
5 cans of soda.
A sample was done, collecting the data below. Calculate the standard deviation, to one decimalplace.х24726573
Answers
We have the following data
[tex]24,7,26,5,13[/tex]The standard deviation is given by
[tex]\sigma=\sqrt[]{\frac{\sum(x_i-\mu)^2}{N}}[/tex]Where μ is the mean and N is the number of data points
Let us first find the mean of the data.
[tex]\mu=\frac{\text{sum}}{number\text{ of data points}}=\frac{24+7+26+5+13}{5}=\frac{75}{5}=15[/tex]Finally, the standard deviation is
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(24-15)^2+(7-15)^2+(26-15)^2+(5-15)^2+(13-15)^2}{5}} \\ \sigma=\sqrt[]{\frac{(9)^2+(-8)^2+(11)^2+(-10)^2+(-2)^2}{5}} \\ \sigma=\sqrt[]{\frac{81^{}+64^{}+110^{}+100^{}+4^{}}{5}} \\ \sigma=\sqrt[]{\frac{359}{5}} \\ \sigma=\sqrt[]{71.8} \\ \sigma=8.5 \end{gathered}[/tex]Therefore, the standard deviation of the data set is 8.5
I need help with fractions and word problem can you help me
Answers
Grace wants to bring a small wedge of cheese for the next 12 days, but there are three small rounds of cheddar cheese in Grace's refrigerator, That is to say, that Grace needs to buy cheese to fulfill this purpose, the small wedge of cheese that Grace needs are:
[tex]12-3=9[/tex]but we must represent this infraction, for this, we will take the 12 small wedges of cheese as a unit, which is formed by having the 12 portions.
That is, out of 12/12 portions, we only have 3/12, To do this we do subtraction and see how many we need in fractional form.
[tex]\begin{gathered} \frac{12}{12}=1 \\ \frac{12}{12}-\frac{3}{12}=\frac{9}{12} \end{gathered}[/tex]In conclusion, Grace need 9 portions i.e. 9/12
Now, that we know this fraction, this is a correct answer, however, we can simplify this fraction.
[tex]\frac{9}{12}=\frac{3}{4}[/tex]In conclusion, Grace needs 3/4 small wedge of cheese.
Note: the answer can be 9/12, but also its simplified form which corresponds to the same, this simplified form is 3/4.
points a,b, and are b lies between a and c. if ac=48,ab =2x+2and bc =3x+6, what is bc?
Answers
Given that A, B, and C are collinear and B lies between A and C, then:
AB + BC = AC
Replacing with data:
(2x + 2) + (3x + 6) = 48
(2x + 3x) + (2 + 6) = 48
5x + 8 = 48
5x = 48 - 8
5x = 40
x = 40/5
x = 8
Then,
BC = 3x + 6
BC = 3(8) + 6
BC = 24 + 6
BC = 30
For the interval expressed in the number line, write it using set-builder notation and interval notation.
Answers
Answer:
Writing the number line in set builder notation we have;
[tex]\mleft\lbrace x\mright|x>0\}[/tex]Writing in interval notation.
[tex]x=(0,\infty)[/tex]Explanation:
Given the number line in the attached image.
x starts on 0, with a non shaded circle and pointed to the right/positive direction.
So;
[tex]x>0[/tex]Writing the number line in set builder notation we have;
[tex]\mleft\lbrace x\mright|x>0\}[/tex]Writing in interval notation.
[tex]x=(0,\infty)[/tex]Since the upper boundary of x is not stated then we will represent it with infinity in the interval notation.
[tex]\begin{gathered} (\text{ }\rightarrow\text{ greater than} \\ \lbrack\text{ }\rightarrow\text{ greater than or equal to } \\ so,\text{ } \\ 09.A piece of wood is cut into 3 pieces. The lengths are 8'15, 634 and953/8".If 1/4" is used up for each saw cut (kerf), what is the length of the original board?HINT: 2 kerfs are made in cutting the board. Reduce fraction to simplest terms.
Answers
The Solution.
First, we shall convert the given lengths to inches.
[tex]undefined[/tex]I have 3 more questions but it didn’t fir here
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Probability = number of required outcome/number of the possible outcome
(a) To determine the theoretical probability for mary
[tex]\begin{gathered} \text{ Probability of spinner landing on grey = }\frac{\text{ number of grey}}{Total\text{ colour}} \\ \text{Probability of spinner landing on grey = }\frac{593}{1000} \\ \text{Probability of spinner landing on grey = 0.}593 \end{gathered}[/tex](b) To determine the experimental probabiity for mary's result
[tex]\begin{gathered} \text{Experimental probabil}ity\text{ = }\frac{\text{ number of grey}}{Total\text{ number}} \\ \text{Experimental probabil}ity\text{ = }\frac{3}{5\text{ }} \\ \text{Experimental probabil}ity=\text{ 0}.600 \end{gathered}[/tex](c) Assuming the spinner is fair, with a large number of spins there might be a difference between the experimental and theoretical probability but the difference will be small.
u ptsBirths are approximately Uniformly distributed between the 52 weeks of the year. They can be saidto follow a Uniform distribution from 1 to 53 (a spread of 52 weeks). Round answers to 4 decimalplaces when possible.a. The mean of this distribution isb. The standard deviation isC. The probability that a person will be born at the exact moment that week 18 begins isP(x = 18) =d. The probability that a person will be born between weeks 10 and 43 isP(10 < x < 43) =e. The probability that a person will be born after week 35 isP(x > 35)f. P(x > 18 x < 32) =g. Find the 47th percentile.h. Find the minimum for the upper quarter.
Answers
Step 1
A) The mean distribution
[tex]\frac{1+53}{2}=\frac{54}{2}=27.0000[/tex]Step 2
B) The standard deviation
[tex]\begin{gathered} SD=\sqrt[]{\frac{1}{12}\times(b-a)^2} \\ SD=\sqrt[]{\frac{1}{12}(53-1)^2} \\ SD=\text{ }15.0111 \end{gathered}[/tex]Step 3
C)
[tex]P(x=18)=0[/tex]Step 4
D)
[tex]\begin{gathered} P(10Step 5E)
[tex]P(x>35)=\text{ }\frac{53-35}{52}=\frac{18}{52}=0.3462[/tex]Step 6
F)
[tex]P(x>18|x<32)=\text{ }\frac{32-18}{32-1}=\frac{14}{31}=0.4516[/tex]Step 7
G)
[tex]\begin{gathered} \text{The 47th percentile}=1\text{ + }\frac{47}{100}(53-1)_{} \\ =1+0.47(52)=25.44_{}00 \end{gathered}[/tex]Step 8
[tex]\begin{gathered} \text{The minimum for the upper percentile = 1+((}\frac{3}{4})(53^{}-1) \\ =1+0.75(52) \\ =1+\text{ 39=40}.0000 \end{gathered}[/tex]Determine if the triangles, △YPQ and △NPD, are similar. if so, Identify criterion.
Answers
Answer:
Yes, they are similar.
Criterion: AA Similarity
Explanation:
Looking at triangles YPQ and NPD, we can see that angles NPD and YPQ are vertically opposite angles and are congruent since vertically opposite angles are always congruent;
[tex]\angle YPQ\cong\angle NPD\text{ (vertically opposite angles)}[/tex]We can also observe that angles N and Y are congruent since they are alternate angles;
[tex]\angle N\cong\angle Y\text{ (alternate angles)}[/tex]From the AA similarity rule, we know that two triangles are said to be similar if two angles in one triangle are equal to two triangles in the other triangle.
Therefore, from the AA rule, we can say that triangles YPQ and NPD are similar.
I am having a hard time finding the apt for this question pls help me?
Answers
The APR, that is Annual Percentage Rate, is calculated using the formula below;
[tex]undefined[/tex]A standard pair of six sided dice is rolled what is the probability of rolling a sum greater than or equal to 11
Answers
The diagram below shows all the possible outcomes from rolling a pair of six sided dice.
The first row and first columns represents the numbers on each die. The numbers in the other rows and columns are outcomes for each roll. Thus, the total number of outcomes is the total number of pairs in the other rows and columns.
Total number of outcomes = 36
Number of outcomes with sum greater than or equal to 11 are the circled pairs. They are 3
Thus, the probability of rolling a sum greater than or equal to 11 is
3/36 = 1/12
A tourist at scenic Point Loma, California uses a telescope to track a boat approaching the shore. If the boat moves at a rate of5 meters per second, and the lens of the telescope is 30 meters above water level, how fast is the angle of depression of thetelescope (0) changing when the boat is 200 meters from shore? Round any intermediate calculations to no less than sixdecimal places, and round your final answer to four decimal places.
Answers
Lest first we hte sine theorem to relate the given measures:
[tex]\frac{\sin (\theta)}{30}=\frac{\sin(90^{\circ})}{\sqrt[]{x^2+30^2}}[/tex]x represents the distance from the boat to the shore.
[tex]\frac{\sin (\theta)}{30}=\frac{1}{\sqrt[]{x^2+30^2}}[/tex][tex]\frac{\sin(\theta)}{1}=\frac{30}{\sqrt[]{x^2+30^2}}[/tex][tex]\sin (\theta)=\frac{30}{\sqrt[]{x^2+30^2}}[/tex][tex]\theta=\sin ^{-1}(\frac{30}{\sqrt[]{x^2+30^2}})[/tex]Then we must calculate the derivative in order to know the rate of change at a certain point.
[tex]\frac{d}{dx}(\sin ^{-1}(\frac{30}{\sqrt[]{x^2+30^2}}))=-\frac{30x}{\sqrt[]{\frac{x^2}{x^2+900}}\cdot(x^2+900)^{\frac{3}{2}}}[/tex]To find how fast is the angle of depression of the telescope is changing when the boat is 200 meters from shore, replace by 200 on the derivative:
[tex]-\frac{30\cdot200}{\sqrt[]{\frac{200^2}{200^2^{}+900}}\cdot(200^2+900)^{\frac{3}{2}}}=-0.0007\text{ rad/s}[/tex]Find anequation for the perpendicular bisector of the line segment whose endpointsare (5,-4) and (-9, -8).
Answers
First, we need to find the slope of the line:
Let:
(5, -4) = (x1,y1)
(-9, -8) = (x2,y2)
m = (y2-y1)/(x2-x1) = (-8-(-4))/(-9-5) = -4/-14 = 2/7
Also, we need to find the midpoint:
let:
MP = (xp,yp)
xp= (x1+x2)/2 = (5-9)/2 = -2
yp = (y1+y2)/2 = (-4-8)/2 = -6
MP = (-2, -6)
Now, the slope for the perpendicular bisector is -m = -7/2
y = -mx + b
Using the midpoint
-6 = -7/2(-2) + b
-6 = 7 + b
Solving for b:
b = -13
Therefore, the equation for the perpendicular bisector is:
y = -7x/2 - 13
Write the point-slope form of the equation of the line through the points (-1, -1) and (2, 4)
Answers
The point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1) - 1.
The point-slope form is simply writing an equation of a line so that the slope or steepness and x-intercept i.e. where the line crosses the vertical x-axis are immediately apparent.
The slope-intercept equation is y - y1 = m(x - x1), where x and y are two variables, and m is the slope.
Slope m = (y2-y1) / (x2-x1)
Let,
(x1, y1) = (-1, -1)
(x2, y2) = (2, 4)
Slope (m) = ((4) - (-1)) / ((2) - (-1))
= 5/3
y - y1 = m(x - x1) => (y - (-1)) = 5/3(x - (-1))
=> y+1 = 5/3(x + 1)
=>y = 5/3(x+1)-1
Therefore, the point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1)-1.
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Given two vectors,find y so that a and b are orthogonal,
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In they are orthogonal the their scarlar product will be zero.
So
[tex]a\cdot b=0[/tex][tex]\begin{gathered} (9,-7,-7)\cdot(6,y,-4)=0 \\ 54-7y+28=0 \\ -7y=-82 \\ y=11.714 \end{gathered}[/tex]Hence, [tex]y=11.714[/tex] when the [tex]a[/tex] and [tex]b[/tex] are orthogonal.
What is the vectors?
Vectors in math is a geometric entity that has both magnitude and direction. Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point.
Various operations can be applied to vectors such as addition, subtraction, and multiplication.
Here given that,
[tex]a=(9,-7,-7)\\b=(6,y,-4)[/tex]
If they are orthogonal the their scarlar product will be zero.
So,
[tex](9,-7,-7).(6,y,-4)=0\\54-7y+28=0\\-7y=-82\\As,\\a.b=0\\y=\frac{82}{7}\\y=11.714[/tex]
Hence, [tex]y=11.714[/tex] when the [tex]a[/tex] and [tex]b[/tex] are orthogonal.
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Aubrey paints 4 square feet of her house each minute. How many square feet does she paint in 20 seconds? Round to the nearest tenth.
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We were told that Aubrey paints 4 square feet of her house each minute.
Recall that 1 minute = 60 seconds.
The statement can be written as
Aubrey paints 4 square feet of her house each 60 seconds
If x represents the number of square feets that she paints in 20 seconds, it means that
4 = 60
x = 20
By cross multiplying, it becomes
60 * x = 4 * 20
60x = 80
x = 80/60
x = 1.333
Rounding to the nearest tenth, it becomes 1.3 square feet
She paints 1.3 square feet in 20 seconds
the density of aluminum is 2700 kg/m3. what is the mass of a solid cube of aluminum with side lengths of 0.5 meters?
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SOLUTION
Density is calculated as
[tex]\begin{gathered} Density=\frac{mass}{volume} \\ \end{gathered}[/tex]The side lengths of the aluminium cube has been given as 0.5 m
The volume becomes
[tex]\begin{gathered} volume=length\times length\times length \\ V=L\times L\times L \\ V=0.5\times0.5\times0.5=0.125m^3 \end{gathered}[/tex]so the volume is 0.125 cubic-meters.
The mass becomes
[tex]\begin{gathered} Density=\frac{mass}{volume} \\ mass=density\times volume \\ mass=2700\times0.125 \\ =337.5 \end{gathered}[/tex]Hence the answer is 337.5 kg
Solve: 9x 2+ 2x = –3 using the quadratic formula. step by step please to understand better
Answers
Explanation: To solve the following equation
[tex]9x^2+2x=-3[/tex]We can use the following quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Step 1: Let's compare our equation with a generic quadratic equation as follows
As we can see above, first we move -3 from the second term to the first term and when we do that we change its sign to +3. Now we know that a = +9, b = +2 and c = +3.
Step 2: Now all we need to do is to substitute the values of a, b and c into our quadratic formula and solve it to find the roots as follows
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-2\pm\sqrt[]{2^2-4\cdot9\cdot3}}{2\cdot9} \\ x=\frac{-2\pm\sqrt[]{4^{}-108}}{18} \\ x=\frac{-2\pm\sqrt[]{-104}}{18} \\ x=\frac{-2\pm\sqrt[]{-104}}{18} \end{gathered}[/tex]Final answer: As we can see above inside the square root there is a negative number -104 which means this quadratic equation has no real solutions.
4. Tickets for a carnival cost $6 for adults and $4 for children. The school has abudget of $120 for a field trip to the carnival. An equation representing thebudget for the trip is 120 = 6x + 4y. Here is a graph of this equation:
Answers
Given:
The equation is 6x + 4y = 120.
Explanation:
The points that lies on the line satifies the equation. So point (0,30) lies on the number which 0 adults and 30 children could go to school. So "if no adult chaperons were needed, 30 students could go to school is true.
For ten students and 15 adults point is (15,10). The point (15,10) does not lie on number line and not satifies the equation so second statement is false.
The cost of tickets for 4 adults is,
[tex]4\cdot6=24[/tex]and cost of tickets for six students is,
[tex]6\cdot4=24[/tex]Both costs are equal, means for six fewer students 4 additional adults can go to the zoo. Thus third statement is correct.
The cost of tickets for two children is,
[tex]4\cdot2=8[/tex]The cost of tickets for 3 adults is,
[tex]6\cdot3=18[/tex]Since cost of tickets for 3 adults is more than cost of tickets for two children which means two children can not go to the zoo for 3 fewer adults in the trip. Thus fourth statement is wrong.
For 16 adults and 6 students point is (16,6). The point (16,6) lies on the number line, which point (16,6) satifies the equation. So fifth statement is correct.