We know that the angle terminates in the fourth quadrant and that the tangent of it is -3/4.
Angles that are on the fourth quadrant have a negative sine and a positive cosine.
We can start with the cot():
[tex]\cot\theta=\frac{1}{\tan\theta}=\frac{1}{-\frac{3}{4}}=-\frac{4}{3}[/tex]We can relate the cosine with the tangent as:
[tex]\begin{gathered} \tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{\sqrt{1-\cos^2\theta}}{\cos\theta} \\ -\frac{3}{4}=\frac{\sqrt{1-\cos^2\theta}}{\cos\theta} \\ -\frac{3}{4}\cos\theta=\sqrt{1-\cos^2\theta} \\ (-\frac{3}{4}\cos\theta)^2=1-\cos^2\theta \\ \frac{9}{16}\cos^2\theta=1-\cos^2\theta \\ (\frac{9}{16}+1)\cos^2\theta=1 \\ \frac{9+16}{16}\cos^2\theta=1 \\ \frac{25}{16}\cos^2\theta=1 \\ \cos^2\theta=\frac{16}{25} \\ \cos\theta=\sqrt{\frac{16}{25}} \\ \cos\theta=\frac{4}{5} \end{gathered}[/tex]We can now calculate the sine of the angle as:
[tex]\begin{gathered} \sin\theta=\tan\theta\cdot\cos\theta \\ \sin\theta=-\frac{3}{4}\cdot\frac{4}{5}=-\frac{3}{5} \end{gathered}[/tex]We can now calculate the sec() and csc() as:
[tex]\begin{gathered} \sec\theta=\frac{1}{\cos\theta}=\frac{5}{4} \\ \\ \csc\theta=\frac{1}{\sin\theta}=-\frac{5}{3} \end{gathered}[/tex]Answer:
sin() = -3/5
cos() = 4/5
cot() = -4/3
sec() = 5/4
csc() = -5/3
Write an equation of the line passing through the points (3,2) and (-2,- 18).
To answer this question, we can use the two-point form of the line equation:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot(x-x_1)[/tex]Then, we have the points:
(3, 2) --->x1 = 3, y1 = 2
(-2, -18)---> x2 =-2, y2 = -18
Then, we have:
[tex]y-2=\frac{-18-2}{-2-3}\cdot(x-3)\Rightarrow y-2=\frac{-20}{-5}\cdot(x-3)\Rightarrow y-2=4(x-3)[/tex]The question in the slope-intercept form is:
[tex]y=4x-10[/tex]Translate Pre Image coordinates using the rule (x + 18) and (y - 12).
We need to translate the points under the rule (x+18) and (y-12).
The points are given by the x-coordinate and y-coordinate following the form (x,y).
Now, let us use this rule for each point:
A.(-6,15)
Under the translation rule (-6+18,15-12) = (12,3)
So, A'=(12,3)
For B(-8,7)
Under the translation rule (-8+18,7-12)= (10,-5).
Then, B'=(10,-5)
For C(-11,12)
Under the translation rule (-11+18,12-12)=(7,0).
Then, C'(7.0)
g(n)=-2n-2
h (n)=4n-2
Find (goh) (-3)
Answer:
[tex](g \circ h)(-3)[/tex] = 26
Step-by-step explanation:
We are told that:
• [tex]g(n) = -2n - 2[/tex]
• [tex]h(n) = 4n - 2[/tex]
In order to calculate the value of [tex](g \circ h)(-3)[/tex], we need to first define [tex](g \circ h)[/tex].
[tex](g \circ h)[/tex] means that the input for the function [tex]g(n)[/tex] is the function [tex]h(n)[/tex]. Therefore, we have to replace the [tex]n[/tex] in the definition of [tex]g(n)[/tex] with the definition of [tex]h(n)[/tex]:
[tex](g \circ h)[/tex] = [tex]-2(4n - 2) - 2[/tex]
= [tex]-8n + 4 - 2[/tex]
= [tex]-8n + 2[/tex]
Now that we know the definition of [tex](g \circ h)[/tex], we can find the value of [tex](g \circ h)(-3)[/tex] by substituting -3 into the definition:
[tex](g \circ h)(-3)[/tex] = [tex]-8(-3) + 2[/tex]
= [tex]24 + 2[/tex]
= [tex]26[/tex]
Need help with part C. I have the first integral but cannot seem to get the second.
Answer:6_7
Step-by-step explanation:
14 socks in a drawer . Four of them are navy blue and 10 white What’s the probability that the second sock is navy blue if the first one was white
The Solution:
Given:
We are required to find the probability that the second sock is navy blue if the first one was a white sock.
Step 1:
The probability of the first sock being a white is:
[tex]P(first\text{ }W)=\frac{Number\text{ of white}}{Total\text{ number of socks}}=\frac{10}{14}=\frac{5}{7}[/tex]Step 2:
The probability of the second sock being a Navy blue is:
Note:
One sock has been taken out without replacement. So, the total number of socks is now 13.
[tex]P(second\text{ Navy Blue\rparen}=\frac{Number\text{ of navy blue socks}}{Current\text{ Total number of socks}}=\frac{4}{13}[/tex]Thus, the probability of the first being White and the second being Navy Blue is:
[tex]P(W\text{ NB})=P(W)\times P(NB)=\frac{5}{7}\times\frac{4}{13}=\frac{20}{91}=0.2198\approx0.22[/tex]Therefore, the correct answer is 20/91 or 0.22
Solve for xx and graph the solution on the number line below
-2 > -5+ x
Answer:
x< 3 this is for inequality and interval (inf,3)
What is the slope of the line represented by 4x-2y=10?
ANSWER:
2
STEP-BY-STEP EXPLANATION:
We have the following equation of line:
[tex]4x-2y=10[/tex]The equation of the line in its slope and intercept form is like this:
[tex]\begin{gathered} y=mx+b \\ \text{where, m is the slope and b is the y-intercept} \end{gathered}[/tex]Therefore, we must solve for y to know the value of the slope (m), like this:
[tex]\begin{gathered} 4x-2y=10 \\ 2y=4x-10 \\ y=\frac{4x-10}{2} \\ y=\frac{4x}{2}-\frac{10}{2} \\ y=2x-5 \\ \text{therefore,} \\ m=2 \end{gathered}[/tex]The slope is 2
Question 3 Below are hvo parallel lines with a third line intersecting them. Find the value of x
In this case, we are given the value of one angle and told to find the value of angle x. To do so, we will try to relate them based on the position they have in the diagram.
Notice that the two parallel lines split the space into two. One space is in between the lines, and the other space is outside the lines. We can see that both angles are located outside of the parallel lines.
Now, see that the third line splits the space into two. One space is on the left of the third line, and the other one is on the right of the third line. From the diagram, we can tell that each angle is on an opposite side of the third line.
This two relations between these angles (being outside the parallel lines and on opposite sides of third line) gives them the name of alternate outer angles. This angles have the property that they have the same measure.
So, we have the following
[tex]x=56[/tex]so the measure of x, in degrees, is 56°.
graph the polygon and it’s image after a dilation centered C with scale factor k
We plot and join the given ordered pairs.
Graphing the image of the polygon after the dilationThe formula of dilation when it is not centred at the origin is:
[tex]\begin{gathered} (x,y)\rightarrow(k(x-a)+a,k(y-b)+b) \\ \text{ Where} \\ k\text{ is the scale factor} \\ (a,b)\text{ is the center of the dilation} \end{gathered}[/tex]Then, we can find the coordinates of the image:
[tex]\begin{gathered} k=\frac{2}{3} \\ (a,b)=C(-2,4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(\frac{2}{3}(7-(-2))-2,\frac{2}{3}(1-4)+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(\frac{2}{3}(7+2)-2,\frac{2}{3}(-3)+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(\frac{2}{3}(9)-2,\frac{2}{3}(-3)+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(6-2,-2+4) \\ T(7,1)\operatorname{\rightarrow}T^{\prime}(4,2) \end{gathered}[/tex][tex]\begin{gathered} k=\frac{2}{3} \\ (a,b)=C(-2,4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(\frac{2}{3}(4-(-2))-2,\frac{2}{3}(4-4)+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(\frac{2}{3}(4+2)-2,\frac{2}{3}(4-4)+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(\frac{2}{3}(6)-2,\frac{2}{3}(0)+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(4-2,0+4) \\ U(4,4)\operatorname{\rightarrow}U^{\prime}(2,4) \end{gathered}[/tex][tex]\begin{gathered} k=\frac{2}{3} \\ (a,b)=C(-2,4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(\frac{2}{3}(1-(-2))-2,\frac{2}{3}(13-4)+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(\frac{2}{3}(1+2)-2,\frac{2}{3}(13-4)+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(\frac{2}{3}(3)-2,\frac{2}{3}(9)+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(2-2,6+4) \\ V(1,13)\operatorname{\rightarrow}V^{\prime}(0,10) \end{gathered}[/tex][tex][/tex]10. Trapezoid PQRS is dilated about point P by a scale factor of 3 to form trapezoid P'Q'R'S'.-QTRPIsWhich statement is NOT true?The measure of angle P'is 3 times the measure of angle P.The perimeter of PQRS is one-third the perimeter of P'O'RS.The length of PQ'is 3 times the length of PO.QR and Q'R' are parallel.
Given:
Trapezoid PQRS is dilated about point P by a scale factor of 3 to form trapezoid P'Q'R'S'.
Required:
We need to find the dilation of Trapezoid PQRS by scale factor 3.
Explanation:
Recall that dilation is a type of transformation that enlarges or reduces a figure (called the preimage) to create a new figure.
Dilations preserve angle measure, betweenness of points and collinearity.
Let P be the perimeter of PQRS.
The dilation P'O'R'S' is enlarged by scale factor 3.
The perimeter of the P'O'R'S' is 3 times the perimeter of PQRS.
[tex]The\text{ perimeter of P'Q'R'S' =3p}[/tex][tex]\frac{1}{3}(The\text{ perimeter of P'Q'R'S' \rparen=p}[/tex]The perimeter of PQRS is one-third of the perimeter of P'O'RS is true.
The length of PQ' is 3 times the length of PQ is true since the scale factor is 3.
QR and Q'R' are parallel is true.
The measure of angle P' is 3 times the measure of angle P is not true.
Dilations preserve angle measure.
Final answer:
There are 18 girls and 24 boys who want to play a game. They created the greatest number of teams possible.
How many boys will be on each team if each gender is split equally among the teams?
Answer:
your a bot
Step-by-step explanation:
A 240 horsepower automobile engine delivers only 210 horsepower to the driving wheels of the car. What is the efficiency of the transmission and drive mechanism
The efficiency of the transmission and drive mechanism is 87.5%
Given,
The power of the automobile engine = 240 horsepower
The power that the automobile engine delivers to the driving wheels of the car = 210 horsepower
We have to find the efficiency of the transmission and drive mechanism:
Efficiency of the transmission and drive mechanism = (power that delivers / power of engine) × 100
= (210 / 240) × 100 = 2100 / 24 = 700/8 = 87.5%
That is the efficiency of the transmission and drive mechanism is 87.5%
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Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 34 liters per minute. There are 400 liters in the pond to start.
Let W represent the total amount of water in the pond (in liters), and let T represent the total number of minutes that water has been added. Write an equation relating W to T. Then use this equation to find the total amount of water after 18 minutes.
Equation:
Total amount of water after 18 minutes:
Total amount of water after 18 minutes is 1365 Liters.
Given that
1) Owners of a recreation area are filling a small pond with water.
2) They are adding water at a rate of 35 liters per minute.
3) There are 700 liters in the pond to start.
4) Let W represent the total amount of water in the pond (in liters),
5) let T represent the total number of minutes that water has been added.
Now we have originally 700 litres i.e. when time =0 W =300
Next is rate of change of water per minutes = Positive 35
Thus the linear relationship between w and T has slope as 35 and y intercept as 300
Hence equation is
y = m x + c
W = 35T + 700
When T=19 minutes
W = 35(19) + 700
W = 1365 litres
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The equation relating W to T is W = 400 + 34T and total amount of water after 18 minutes is 1012 liters.
Equation will be formed by adding the amount of water already present with product of rate of water adding and amount of time in minutes. Representing this as equation -
W = 400 + 34T
Keep the value of T in the equation to find the total amount of water after 18 minutes.
W = 400 + 34×18
Performing multiplication on Right Hand Side of the equation
W = 400 + 612
Performing addition on Right Hand Side of the equation
W = 1012 liters
Therefore, the equation is W = 400 + 34T and amount of water is 1012 liters.
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A submarine is sitting still along the surface of the ocean as a part of a drill it does at a constant speed to a certain number of feet below the surface of the ocean
The intervals in which the submarine is diving with a constant velocity is the intervals in which the graph is linear.
Velocity and positionThe velocity is given by the change in the position divided by the change in time, as follows:
Velocity = change position/change time.
It means that the velocity is the derivative of the position. Hence, if the velocity is constant, the position is represented by a linear graph, as the derivative of a line is a constant.
Hence, the submarine has a constant speed when the graph is linear, either constant, increasing or decreasing.
This problem is incomplete, hence I cannot give the exact intervals, as I can't see the graph, however you need to just check the graph and verify where it has linear behavior.
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The table shows the speeds s (in feet per second) of sound in water at various
temperatures t (in degrees Fahrenheit). Write a function that models the data. Use
the model to approximate the speed of sound when the water temperature is 100°F.
Temperature (°F), t: 32 50 90 120 180 212
Speed (ft/sec), s: 4603 4748 4960 5049 5095 5062
A function which models the data in the given table is y = 3848.2x^0.054. Also, an approximate speed of sound when the water temperature is 100°F is equal to 4935 ft/sec.
What is a line of best fit?A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.
In this scenario, the temperature of water would be plotted on the x-axis of the scatter plot while the speed of sound would be plotted on the y-axis of the scatter plot.
By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that a function for the line of best fit is given by:
y = 3848.2x^0.054
Next, we would determine the speed of sound when the water temperature is 100°F as follows:
y = 3848.2x^0.054
y = 3848.2 × (100)^0.054
y = 3848.2 × 1.2823
y = 4934.55 ≈ 4935 ft/sec.
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In the xy-plane, line l is parallel to the line with equation 4x-y=1. If line l contains the point (0,2), which of the following is an equation of line l? A) 4x-y = -2 B) 4x-y = 2C) 4x+y= -2 D) 4x+y =2
The equation for the second line is:
[tex]4x\text{ - y = 1}[/tex][tex]\text{The general equation of a line is y = mx + c}[/tex]Where m = slope and c = Intercept
Let us rewrite the given equation in that form :
[tex]\text{ y = 4x - 1}[/tex]Comparing y = 4x - 1 with y = mx + c:
m = 4 and c = -1
Since line I is parallel to the given line, it means their slopes are equal. Therefore, the slope for line I is also m = 4
Line I contains the Point:
[tex](x_1,y_{1)\text{ = }}(0,\text{ 2)}[/tex]The equation of a line can also be written in the form:
[tex]y-y_1=m(x-x_{1\text{ }})[/tex][tex]y\text{ - 2 = 4 (x - 0)}[/tex][tex]y\text{ - 2 = 4x}[/tex]By rearranging the above equation:
[tex]4x\text{ - y = -2}[/tex]The above is the equation for line I
A group of 45 people attended a ball game. There were twice as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group. A. system15 adults, 30 children B. system30 adults; 22 children C. system22 adults; 30 children D. system30 adults, 15 children
Answer:
A
Step-by-step explanation:
45/2
A coastline is lost to erosion at a constant rate. The graph shows the amount of coastline lost overtime . How many years will it take to lose 48 feet of the coastline
48 years falls between 40 to 50 on the graph
If you trace from a point close to 50 on the y -axis to meet the slope line
the point of intersection between the trace and the slope line, trace it down to x-axis
The value falls in between 6years and 9 years
A company has recently been hiring new employees. Today the company has 26% more employees than it did a year ago. If there are currently 44,100 employees, how many employees did the company have a year ago?
the current amount of employees today represents an increase of 26% from the previous year, this can be written as:
[tex]\begin{gathered} 1+26\% \\ 1+0.26 \\ 1.26 \end{gathered}[/tex]then,
[tex]44100=1.26x[/tex]where x is the number of employees the previous year, then, solve for x
[tex]\begin{gathered} x=\frac{44100}{1.26} \\ x=35000 \end{gathered}[/tex]Answer:
there were 35000 employees one year ago.
y= -2/3x - 2 2x + y = 2 Find the solution of the systems of linear equation by graphing
x = 3, y = -4
Explanations:The given system of linear equations is:
[tex]\begin{gathered} y\text{ = }\frac{-2}{3}x\text{ - 2}\ldots\ldots\ldots\ldots.(1) \\ 2x\text{ + y = 2}\ldots\ldots\ldots\ldots\text{.}\mathrm{}(2) \end{gathered}[/tex]The graph representing the equations is plotted below:
[tex]\begin{gathered} \text{The red line represents y = }\frac{-2}{3}x\text{ -2} \\ \text{The blue line represents 2x + y = 2} \end{gathered}[/tex]The point where both lines intersect is the solution to the system of equations.
The lines intersect at the point (3, -4), therefore, (3, -4) is the solution to the system of equations
Let M be the event that a randomly chosen person has a master's degree. Let B be the event that a randomly chosen person was a business major. Place the correct event in each response box below to show:
Given that the person has a master's degree, the probability that a randomly chosen person was a business major.
The probability that the person has a business major is going to be represented by: p(B | M)
What is probability?This is the concept that is used in statistical and mathematical analysis to refer to the likelihood and the chances of something happening. That is the likelihood of an event occurring.
We have to define M as the event that the person that has been chosen randomly has a masters degree.
We have to define B as the event that the person that has being chosen randomly has a business major.
Given that the person has a master's degree, the probability that a randomly chosen person was a business major is given as p(B|M)
This would be the conditional probability that is written in the form of
p(B|M) = P(B and M) / P(M)
Where probability P(M) is the probability of having a masters degree, while the prbability P(B) is the probability of having a business degree.
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Sammy's teacher gives partial credit on quizzes if students show all of their work. Sammy earned the following points on his last quiz. Arrange the questions in order from least points earned to the greatest points earned.Questions- points1. 2 1/22. 1 2/53. 1 3/44. 2 2/35. 3 1/4
First, express all the mixed numbers as decimals:
2 1/2 = (2x2+1)/2 = 5/2 = 2.5
1 2/5 = (5x1+2)/5 = 7/5 = 1.4
1 3/4 = (1x4+3)/4 = 7/4 = 1.75
2 2/3 = (2x3+2)/3 = 8/3 = 2.67
3 1/4 = (3x4+1)/4 = 13/4 = 3.25
Now, we have
1. 2.5
2. 1.4
3. 1.75
4. 2.67
5. 3.25
From least to greatest.
2. 1.4
3. 1.75
1. 2.5
4. 2.67
5. 3.25
i dont really get what it means by pattern can u help me understand
Well the principals patterns are that the equations are quadratic equations, and the graphs are parables and that the equations and the graphs are related.
Terrell opened a savings account 10 years ago. The account earns 9% interest, compounded annually. If the current balance is $300.00, how much did he deposit initially? Round your answer to the nearest cent.
1) Gathering the data
Time: 10 yrs ago
Interest rate (r) : 9% (0.09)
Future Value: 300
Initial Deposit:?
2) Since the current balance is given, let's call it Future Value because the amount that made that $300 is what we need to find out. Let's go find the Future Value since it's been 10 yrs ago. Plugging into the formula we have:
[tex]\begin{gathered} F=P(1+r/n)^{nt} \\ 300=P(1+\frac{0.09}{1})^{1\cdot10} \\ 300=P(1.09)^{10} \\ 300=2.367363675P \\ P=\frac{300}{2.367363675} \\ P=126.723 \\ P\cong126.72 \end{gathered}[/tex]Notice that, since this investment was compounded yearly, so n=1.
3) So the initial deposit, 10 years ago was approximately $126.72
please help this is for my study guide thanks! (no rounding)
Answer:
The volume of the cylinder is;
[tex]653.45\text{ }in^3[/tex]Explanation:
Given the figure in the attached image;
[tex]\begin{gathered} r=4\text{ in} \\ h=13\text{ in} \end{gathered}[/tex]Recall that the volume of a cylinder can be calculated using the formula;
[tex]V=\pi r^2h[/tex]Substituting the given values;
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi(4)^2\times13 \\ V=653.45\text{ }in^3 \end{gathered}[/tex]Therefore, the volume of the cylinder is;
[tex]653.45\text{ }in^3[/tex]The ratio of white roses to red roses in a garden is 8:7 . Check all statements that must be true based on the statement above. If none of the statements is true, check "None of the above".
A. There are exactly 8 white roses and exactly 7 red roses in the garden.
B. For every 7 white roses in the garden, there are 8 red roses.
C. Fer every 8 white roses in the garden, there are 7 red roses.
D. There are 8 white roses to every 7 roses in the garden.
E. None of the above.
The true statement is for every 8 white roses in the garden, there are 7 red roses.
What is the true statement?
Ratio is used to compare two or more numbers together. It shows the relationship that exists between two or more numbers. In this question, for every 8 white roses, there would be 7 red roses.
This ratio does not mean that there are exactly 8 white roses and 7 red roses. It means that regardless of the number of white roses and red roses, when expressed in its simplest form the ratio would be 8 : 7. For example, there can be 56 : 49 white roses and red roses.
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Rewrite the function by completing the square. g(x) = x^2 + 15x +54
g(x) = _ ( x + _ )^2 + _
What’s the correct answer answer asap for brainlist
Answer: Maybe B
Step-by-step explanation:
The cost of living last year went up 13%. fortunately, Alice Swanson got a 13% raise in her salary from last year. this year she is owning $22,570. How much did she make last year? Round to the nearest hundredth.
According to the information given in the problem, you know that Alice got got a 13% raise in her salary from last year, therefore, this year she is owning $22,570.
Let be "x" the amount of money in dollars Alice made last year.
Set up the following equation:
[tex]x+0.13x=22,570[/tex]So, to solve this equation, you must solve for the variable "x". The procedure for this is shown below:
[tex]\begin{gathered} 1.13x=22,570 \\ x=\frac{22,570}{1.13} \\ x=19,973.451 \end{gathered}[/tex]Rounded to the nearest hundredth:
- Look at the digit in the hundreths place. In this case it is 5.
- Look at the digitt to the right of the digit 5 (In this case is the digit 1, which is located in the thousandths place).
- Since the number in the thousandths place is less than 5, you must round down and just remove all the digits located after the digit 5.
Then:
[tex]x\approx19,973.45[/tex]She made about $19,973.45 last year.
PLEASEEE HELP I"LL GIVE LOTS OF POINTSS
and don't scam me
Answer:
The difference in the depths is equal to 5ft
Step-by-step explanation:
A) snapper (-10 ft) : (b) redfish (-3ft): (c) clam (0 ft) : (d) Hermit Crab (2 ft)
B The comparison of the depth of hermit crab and redfish,
D = hermit crab - redfish = 2 - (-3) = 5 ft
In order would be 1 snapper) 2 red fish) 3 clam)4 hermit
Answer:
a) Flounder, Bluefish, Clam, Hermit Crab
b) The bluefish is deeper than the hermit crab.