Fish enter a lake at a rate modeled by the function E given by E(t) = 20+15sin(pi*t/6). Fish leave the lake at a rate modeled by the function L given by L(t) = 4+20.1*t^2. Both E(t) and L(t) are measured in fish per hour and 't' is measured in hours since midnight (t=0).a.) How many fish enter the lake over the 5-hour period from midnight (t=0) to 5am (t=5)? Give your answer to the nearest whole number.b.) What is the average number of fish that leave the lake per hour over the 5 hour period from midnight (t=0) to 5am (t=5)?c.) At what time, t, for 0 ≤ t ≤ 8, is the greatest number of fish in the lake? Justify.d.) Is the rate of change in the number of fish in the lake increasing or decreasing at 5am (t=5)? Explain your reasoning.
Answers
Answer: a) To find the total number of fish that enter the lake over the 5-hour period, we need to integrate the function E(t) from t=0 to t=5:
int(20+15sin(pi*t/6), t=0 to 5) ≈ 62
a) To find the total number of fish that enter the lake over the 5-hour period, we need to integrate the function E(t) from t=0 to t=5:
int(20+15sin(pi*t/6), t=0 to 5) ≈ 62
Therefore, about 62 fish enter the lake over the 5-hour period from midnight to 5am.
b) The average number of fish that leave the lake per hour over the 5-hour period can be found by calculating the total number of fish that leave the lake over the 5-hour period and dividing by 5:
int(4+20.1*t^2, t=0 to 5) ≈ 1055
average = 1055/5 = 211
Therefore, the average number of fish that leave the lake per hour over the 5-hour period is 211.
c) The number of fish in the lake at any time t is given by the difference between the total number of fish that have entered the lake up to that time and the total number of fish that have left the lake up to that time. So, if N(t) represents the number of fish in the lake at time t, then:
N(t) = int(20+15sin(pi*t/6), t=0 to t) - int(4+20.1*t^2, t=0 to t)
To find the time t when the greatest number of fish are in the lake, we need to find the maximum of N(t) for 0 ≤ t ≤ 8. We can do this by taking the derivative of N(t) and setting it equal to zero:
dN(t)/dt = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
0 = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
Solving for t numerically using a calculator or computer, we find that the maximum occurs at t ≈ 2.34 hours. Therefore, the greatest number of fish in the lake occurs at 2.34 hours after midnight.
d) The rate of change in the number of fish in the lake is given by the derivative of N(t):
dN(t)/dt = 15pi/6 * cos(pi*t/6) - 20.1t^2 + 4
To determine whether the rate of change is increasing or decreasing at t=5, we need to find the second derivative:
d^2N(t)/dt^2 = -5.05t
When t=5, the second derivative is negative, which means that the rate of change in the number of fish in the lake is decreasing at 5am.
a. There will be 141 fish enter the lake over the 5-hour period from midnight
b. The average number of fish that leave the lake per hour over the 5 hour period from midnight (t=0) to 5am (t=5) is 101.
c. At 3.25 hour, t, for 0 ≤ t ≤ 8, is the greatest number of fish in the lake
d. The rate of change in the number of fish in the lake is decreasing at 5am.
a) To find the number of fish that enter the lake over the 5-hour period from midnight to 5am, we need to integrate the rate of fish entering the lake over that time period:
Number of fish = ∫[0,5] E(t) dt
= ∫[0,5] (20+15sin(πt/6)) dt
Number of fish ≈ 141
Therefore, approximately 141 fish enter the lake over the 5-hour period from midnight to 5am.
b. To find the average number of fish that leave the lake per hour over the 5 hour period, we need to calculate the total number of fish that leave the lake over that time period and divide by the duration of the period:
Number of fish that leave the lake = L(5) - L(0)
= (4+20.1*5^2) - (4+20.1*0^2)
= 505.5
Average number of fish leaving per hour = Number of fish that leave the lake / Duration of period
= 505.5 / 5
= 101.1
Therefore, the average number of fish that leave the lake per hour over the 5 hour period from midnight to 5am is approximately 101.
c. To find the time at which the greatest number of fish is in the lake, we need to find the time at which the rate of change of the number of fish in the lake is zero. This occurs when the rate of fish entering the lake is equal to the rate of fish leaving the lake:
E(t) = L(t)
20+15sin(πt/6) = 4+20.1t^2
We can solve this equation numerically to find that the greatest number of fish is in the lake at approximately t=3.25 hours (rounded to two decimal places).
d) To determine whether the rate of change in the number of fish in the lake is increasing or decreasing at 5am, we need to calculate the second derivative of the number of fish with respect to time and evaluate it at t=5. If the second derivative is positive, the rate of change is increasing. If it is negative, the rate of change is decreasing.
d²/dt² (number of fish) = d/dt E(t) - d/dt L(t)
= (15π/6)cos(πt/6) - 40.2t
d²/dt² (number of fish) ≈ -44.4
Since the second derivative is negative, the rate of change in the number of fish in the lake is decreasing at 5am.
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Related Questions
What information is needed in order to be prepared for an emergency?
Understanding of where to go should an emergency occur
Contact information for emergency personnel
Location of lab phone and first aid kit
location of all exits
Answers
To be ready for an emergency, one must be aware of emergency procedures, know how to reach average emergency services, know where to find safety equipment, and be aware of all exits.
1. Recognize safety precautions and emergency protocols.
2. Make sure emergency personnel's contact information is accessible.
3. Recognize where emergency supplies like first aid kits and lab phones are located.
4. Be sure you are familiar with all building exits in case an evacuation is necessary.
5. Ensure that you have an emergency action plan.
It's critical to have a fundamental awareness of safety measures and emergency protocols in order to be ready for a crisis. Also, it's crucial to keep emergency personnel's contact information close at hand in case you need to get in touch with them. Knowing where to find safety supplies like first aid kits and lab phones might be useful for emergency planning. In case of an evacuation, make sure you are familiar with all building exits. Being more organised can help you be better prepared. Make an emergency plan. You may be better prepared for any situation by keeping an emergency kit containing items like food, water, flashlights, and a first aid kit. Last but not least, it's critical to be informed about any potential emergencies in your neighbourhood and to heed the advice of the authorities if they advise evacuation or other safety measures. By taking these actions, you can make sure that you are as ready as you can be for any situation.
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A survey conducted asked 110 people what type of pets they owned. The results showed that 72 owned a dog, 58 owned a cat, and 37 owned both a dog and a cat. What is the probability of choosing a person who owns a dog or a cat? Enter your answer as a simplified fraction
Answers
The probability of choosing a person who owns a dog or a cat will be;
⇒ 0.845
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
Number of peoples in survey = 110
And, The results showed that 72 owned a dog, 58 owned a cat, and 37 owned both a dog and a cat.
Now,
Since, Number of peoples in survey = 110
And, Number of peoples owns a dog or a cat = 72 + 58 - 37
= 93
Thus, The probability of choosing a person who owns a dog or a cat is,
Probability = 93 / 110
= 0.845
Therefore, The probability of choosing a person who owns a dog or a cat will be;
⇒ 0.845
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The table of values below represents an inverse variation relationship. what is the value of x when y= "3.25"?
X l Y
2 l 13
4 l 6.5
A. X=84.5
B. X=8
C. X=5.3
D. X=21.1
Answers
Using the constant of proportionality, the value of when y is 3.25 is 0.5 from the inverse variation.
What is inverse variation relationship?An rise in one variable causes a decrease in the other and vice versa in a mathematical relationship between two variables known as inverse variation, also known as inverse proportionality or inverse relationship. The following equation represents inverse variation:
y = k/x
In this equation, "y" and "x" stand in for the two variables, and "k" is the variational constant. Throughout the connection, the constant of variation has a set value that never changes.
Using the data given;
y = kx
Let's find the value of k;
k = constant of proportionality
13 = k(2)
k = 13/2
k = 6.5
Using the value of k;
3.25 = 6.5x
x = 3.25 / 6.5
x = 0.5
NB: The options given are incorrect and if you will follow through the steps, you will understand the options are incorrect.
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F(x)=-x^2-12 to find (-3)
Answers
Answer:
\({ \boxed{ \mathfrak{ \: answer : \: { \rm{f( - 3) = - 21}} }}}\)
Step-by-step explanation:
\({ \rm{f(x) = - {x}^{2} - 12 }}\)
• When x is -3:
\({ \rm{f( - 3) = - {( - 3)}^{2} - 12}} \\ \\ { \rm{f( - 3) = - 9 - 12}} \\ \\ { \rm{f( - 3) = - 21}}\)
Find the volume of the sphere. Express your answer in terms of pi.
Answers
Answer:
Sphere Volume = (4/3) * PI radius^3
Sphere Volume = (4/3) * 3 * 3 * 3 * PI =
4 * 3 * 3 * PI =
36 PI
Answer is d 36 PI cubic feet
Step-by-step explanation:
Which sequence of rigid transformations will map the preimage ΔABC onto image ΔA′B′C′ ?
A.
a reflection across the x-axis, a translation 8 units right, and then a reflection across the x-axis
B.
a translation 4 units down and 10 units to the right
C.
a reflection across the line y = x followed by a rotation 90° counterclockwise
D.
a rotation 180° clockwise followed by a reflection across the x-axis
Answers
Answer:
A
Step-by-step explanation:
Because
Answer:
A
Step-by-step explanation: Got it Right.
Julio says, "If you subtract 12 from my number and multiply the difference by -5, the result is -40." What is Juloi's number?
Answers
Answer:
20
Step-by-step explanation:
Equation: x - 12 • -5 = -40
Solve:
x = -40 ÷ -5 + 12
x = 8 + 12
x = 20
Find the measure of each angle indicated.
Answers
Step-by-step explanation:
92°
as the has given pair of angle is Alternate Exterior angle so they have same values.
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convert 3cm to mm show all working out
Answers
Answer:
30 mm
Step-by-step explanation:
1 centimeter (cm) is one hundredth of a meter
1 millimeter (mm) is one thousandth of a meter
Thus one cm is 10 times bigger, so 3cm = 30mm
What is the value of x? Please explain and answer
Answers
4. From the top of a tower 14m high, the angle of depression of a student is 32° Make a scale drawing and find the distance of the student from the foot of the tower to the nearest 1/2
Answers
The distance of the student from the foot of the tower is 25.63m the nearest 1/2 is 25.5m.
Given that From the top of a tower 14m high
The angle of depression of a student is 32°
we can use trigonometry to find the distance from the foot of the tower to the student:
tan(32°) = opposite/adjacent = 14/distance
Rearranging this equation gives:
distance = 14/tan(32°)
= 25.63m
Therefore, the distance of the student from the foot of the tower is approximately 25.63m nearest 1/2, this is 25.5m.
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determine the time necessary for p dollars to doubl when it is invested at ineterest rate r compounded annually, monthly, daily, and continously, (round your answers to two decimal places.)
Answers
The time necessary for p dollars to double when it is invested at interest rate r compounded annually is given by the formula:
t = (ln 2) / (r ln (1 + r))
When compounded monthly, the formula becomes:
t = (ln 2) / (12 r ln (1 + r/12))
When compounded daily, the formula becomes:
t = (ln 2) / (365 r ln (1 + r/365))
When compounded continuously, the formula becomes:
t = ln 2 / (r)
Note that ln is the natural logarithm function.
To use these formulas, you need to know the value of the interest rate r. For example, if r is 5%, then:
When compounded annually, t = (ln 2) / (0.05 ln 1.05) = 13.86 years
When compounded monthly, t = (ln 2) / (12 x 0.05 ln 1.0041) = 14.21 years
When compounded daily, t = (ln 2) / (365 x 0.05 ln 1.000137) = 14.27 years
When compounded continuously, t = ln 2 / (0.05) = 13.86 years
Therefore, the time necessary for p dollars to double depends on the interest rate and the frequency of compounding. Generally, the more frequently the interest is compounded, the shorter the time necessary for p dollars to double.
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Can you help me, please?
Answers
Answer:
a. 18
b.144
c.108
Step-by-step explanation:
Using the given, Angle R equal 5x-54 and Angle T is 8u.
Also RS is congruent to ST. Since SR is congruent to ST, their opposite angles are also congruent using base angle theorem. So angle R is equal to Angle T. However, STU is a exterior angle so STU isn't congruent to SRT.
However, we can add , interior angle T, and STU to 180 to find x.
Interior angle T=SRT so interior angle t=5x-54.
Set up equation
\(5x - 54 + 8x = 180\)
\(13x - 54 = 180\)
\(13x = 234\)
\(x = 18\)
b.Plug 18 into 8x
\(8(18) = 144\)
STU=144
c. Using the triangle exterior angle theorem, the exterior angle is equal to the measure of the sum of two non adjacent angles.
Angle S and Angle R are the non adjacent angle to STU.
So we cast up this equation.
\(5x - 54 + s = 180\)
plug 18 in for x
\(5(18) - 54 + s = 144\)
\(90 - 54 + s = 144\)
\(36 + s = 144\)
s=108
A. Find the equation of the L line that intersects graph C at point A (2, -5). B. Find the line equation with the coefficient of direction equal to -10 and touch and graph C
Answers
Graph C has a function
\(f(x)=2x^3-16x+11\)Since the line L intersects the graph at the point, A (2, -5)
To find the slope of the line we will differentiate the f(x) and substitute x by 2
\(\begin{gathered} f^{\prime}(x)=2(3)x^{3-1}-16x^{1-1}+0 \\ f^{\prime}(x)=6x^2-16 \\ m=6(2)^2-16 \\ m=24-16 \\ m=8 \end{gathered}\)The slope of the line is 8, substitute it in the form of the linear equation
\(\begin{gathered} y=mx+b \\ y=8x+b \end{gathered}\)To find b substitute x by 2 and y by -5
\(\begin{gathered} -5=8(2)+b \\ -5=16+b \end{gathered}\)Subtract 16 from both sides to find b
\(\begin{gathered} -5-16=16-16+b \\ -21=b \end{gathered}\)Then the equation of the line is
\(\begin{gathered} y=8x+(-21) \\ y=8x-21 \end{gathered}\)Help me please!!!
ASAP!!
Answers
Answer:
Hello with the simplified expression the answer is 2
Step-by-step explanation:
The volume of a cylinder is 156picm to the power of 3. What is the volume of a cone with the same base and height as the cylinder?
Answers
Answer:
B= 52 pie m^3
Step-by-step explanation:
vol of a cylinder = pie*r^2× h
vol of a cone = 1/3 × pie*r^2×h
......vol of a cone with d same base nd height
= 1/3 × 156
= 156/3= 52m^3
What is square root raised cosine?
Answers
SRRC is a pulse shaping filter used in digital communications to minimize intersymbol interference and improve the signal-to-noise ratio.
The square root raised cosine (SRRC) is a famous heartbeat molding channel utilized in computerized correspondences, especially in applications like advanced tweak and demodulation. It is intended to limit intersymbol obstruction (ISI) by restricting the data transmission of the sent sign while keeping a consistent envelope.
The SRRC channel is described by a reaction that is like the raised cosine channel, yet with a square root capability applied to the recurrence reaction. This outcomes in a smoother change between the passband and stopband, which assists with decreasing ISI and work on the sign to-clamor proportion.
The SRRC channel is usually utilized in correspondence frameworks that utilization quadrature sufficiency regulation (QAM) or stage shift keying (PSK) tweak plans, as it gives great ghastly control and heartbeat molding properties that are appropriate to these kinds of signs.
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Write an equation for the circle with centre (0, 0), if the given point
lies on its circumference.
a) B(5, -12)
b) Does the point (8,10) lie inside or outside of the circle? Show your work
with calculations.
Answers
a) The equation for a circle with centre (h, k) and radius r is: (x - h)^2 + (y - k)^2 = r^2
Since the centre of the circle is (0, 0), the equation for the circle with point B(5, -12) on its circumference is:
(x - 0)^2 + (y - 0)^2 = r^2
b) To determine whether point (8,10) lies inside or outside of the circle, we can substitute its coordinates into the equation for the circle.
If the equation is true, then the point lies on the circumference of the circle. If the equation is false, we can compare the left side of the equation to the right side to determine if the point is inside or outside of the circle.
For point (8,10), we can use the equation:
(x-0)^2 + (y-0)^2 = r^2
If we substitute (8,10) in the place of x and y, we get:
(8-0)^2 + (10-0)^2 = r^2
64 + 100 = r^2
164 = r^2
13 ≠ r
Since the left side of the equation is not equal to the right side, the point (8,10) lies outside of the circle.
Uday Tahlan
A company that sells toys models their profit with the function
P(x) = −4x3 + 32x2 − 64. Their profit P, in thousands of dollars,
is a function of the number of toys sold x measured in hundreds.
What do the key features of the graph reveal about the profits?
What is the maximum profit the company can make?
Answers
9514 1404 393
Answer:
a) profit has a typical curve: negative at low volume, and again at very high volume.
b) $239,407
Step-by-step explanation:
a) The graph is negative below x=1.58, so the break-even point is 158 toys sold. The profit declines steeply above 533 toys sold, to again go negative for 774 toys sold. This sort of curve seems fairly typical.
__
b) The profit is a maximum of $239,407 when 533 toys are sold.
Amazon is offering a $17.95 discount on a pair of wireless headphones. You pay $71.80 for the headphones after the discount. Write and solve an equation to find the original price of the headphones.
Use "x" for your variable
Answers
Answer:
67.50
Step-by-step explanation:
The equation which can be used to find the original price of the headphones is x = 71.80 + 17.95 and the original price is $89.75.
Given that:
The amount which is being discounted for a pair of wireless headphones is $17.95.
The amount which is paid after the discount for the headphones is $71.80.
It is required to find the equation to find the original price of the headphones.
Let x represent the original price of the headphones.
Original price = Amount paid after the discount + Amount which is being discounted.
Substituting the given values,
x = 71.80 + 17.95
x = $89.75
Hence, the original price is $89.75.
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simplify the equation
Answers
Answer:
3a
Step-by-step explanation:
9/3 = 3
\(a^{3}/a^{2} = a^{3 -2} = a\)
b / b = 1
3 x a x 1 = 3a
Answer:
3a
Step-by-step explanation:
First, cancel the 3 at the bottom by getting rid of it and changing the 9 to a 3. You can do this because 3 is one third of 9.
With the division property of exponents, you have to subtract 3-2 and you can leave a to the power of 1 on the numerator.
Then, cancel the b's out by getting rid of them.
You will be left with 3a.
Simplify the expression. Write the answer using scientific notation. (9x 10^7)(7x10^9)
Answers
6.3x10^17
the last option correct one
Answer:
6.3x10^17
Step-by-step explanation:
:)
in how many ways can a committee of 20 members choose a president, a vice-president, and a secretary?
Answers
There are 6840 ways to choose a president, a vice-president, and a secretary from a committee of 20 members.
To choose a president, a vice-president, and a secretary from a committee of 20 members,
We will use the formula for combinations,
which is: C(n, k) = n! / (k! (n - k)!)
where n is the total number of members and k is the number of members being chosen.
So, for n = 20 and k = 1, we have:
C(20, 1) = 20! / (1! (20 - 1)!) = 20
This gives us 20 choices for the president.
For the vice president,
We need to choose 1 member from the remaining 19 members.
So, for n = 19 and k = 1,
we have:
C(19, 1) = 19! / (1! (19 - 1)!) = 19
This gives us 19 choices for the vice president.
Finally, for the secretary,
We need to choose 1 member from the remaining 18 members.
So, for n = 18 and k = 1,
we have:
C(18, 1) = 18! / (1! (18 - 1)!) = 18
This gives us 18 choices for the secretary.
Now for finding the total number of ways to choose the three positions, we multiply the number of choices for each position:
So, the required number of ways will be 20 * 19 * 18 = 6840
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I do not know which formula is being used for this question, please answer step by step thanks!
The Hudson Record Store is having a going-out-of-business sale.CDs normally sell for $18.00.During the first week of the sale, all CDs will sell for $15.00.Written as a fraction, what is the rate of discount?What is the rate expressed as a percent?Round your answer to the nearest hundredth of a percent.During the second week of the sale, the same CDs will be on sale for 25% off the original price.What is the price of a CD during the second week of the sale?
Answers
Original Price = $18
Discounted Price = $15
Discount is $3 as 18-15 is 3.
As a fraction, the discount rate is $3/$18 also equal to $1/$6
What is the rate expressed as a percent? Round your answer to the nearest hundredth of a percent.1/6 is approximately 0.167
0.167 = 16.67%
As a percent, the discount rate is 16.67%
During the second week of the sale, the same CDs will be on sale for 25% off the original price. What is the price of a CD during the second week of the sale?Using the formula, Amount of Discount = Discount Rate · Original Price we can find the amount of discount for the 2nd week.
Let x be the amount of discount.
x = 25% · $18
x = $4.50
The amount of discount is $4.50
Calculate the cost of the CDs during the second week: $18 - $4.50 = $13.50
The price of a CD during the second week of the sale is $13.50
It’s never lupus. Lupus is a medical phenomenon where antibodies that are supposed to attack foreign cells to prevent infections instead see plasma proteins as foreign bodies, leading to a high risk of blood clotting. It is believed that 2% of the population suffer from this disease. The test is 98% accurate if a person actually has the disease. The test is 74% accurate if a person does not have the disease. There is a line from the Fox television show House that is often used after a patient tests positive for lupus: “It’s
never lupus.” Do you think there is truth to this statement? Use appropriate probabilities to support your answer.
Answers
L = person has Lupus
~L = person does not have Lupus
P(L) = 0.02 since 2% of the population has it.
P(~L) = 1 - 0.02 = 0.98, ie 98% of the population does not have it.
------------------
If the person has Lupus, then the test will indicate as such 98% of the time, and do so correctly.
T = person tests positive for Lupus
~T = person tests negative for Lupus
P(T given L) = 0.98
The complement of this is
P(~T given L) = 1 - 0.98 = 0.02 = false negative rate
On the other hand, if a person does not have Lupus, then the test will return negative correctly 74% of the time.
P(~T given ~L) = 0.74
Its complement is
P(T given ~L) = 1 - 0.74 = 0.26 = false positive rate
------------------
Dr House saying "It's never Lupus" can be translated to "If the test is positive, then P(L) = 0"
Phrased another way symbolically:
P(L given T) = 0
-------------------
We'll use Bayes Theorem to determine the value of P(L given T)
In general, Bayes Theorem is
P(A given B) = P(B given A)*P(A)/P(B)
So for this problem, we'll have
P(L given T) = P(T given L)*P(L)/P(T)
We almost have everything needed but we're missing P(T)
So we'll need to use the law of total probability to break that up like so
P(T) = P(T and L) + P(T and ~L)
P(T) = P(T given L)*P(L) + P(T given ~L)*P(~L)
P(T) = 0.98*0.02 + 0.26*0.98
P(T) = 0.2744
-------------------
To recap, we have:
P(T given L) = 0.98P(L) = 0.02P(T) = 0.2744We finally have all the info needed to get the probability we're after.
P(L given T) = P(T given L)*P(L)/P(T)
P(L given T) = 0.98*0.02/0.2744
P(L given T) = 0.07142857142858 approximately
What does this tell us? It says that if a patient gets a positive test for lupus, then there's roughly a 7% chance the test is correct, and the person actually has lupus.
So it's likely Dr House is onto something. The reason why the small result is because a small percentage of the population has the disease.
Also, notice how the false positive rate P(T given ~L) = 0.26 = 26% is fairly high. This also provides more evidence to Dr House's claim.
To be entirely technically accurate, he shouldn't have used "never" because the result of P(L given T) is not zero. But I think a bit of wiggle room can be had for the interpretation of his words.
Let f(x) = sin x and g(x) = x² + 1. Find the following derivatives. d (a) (f(g(x))) (b) = (g(f(x))) dx dx d sin (x²+1) • sin(x²)+1 dx dx = cos(x²+1)(2x)
Answers
To find the derivatives of the given expressions, we can apply the chain rule, which states that the derivative of a composition of functions is equal to the derivative of the outer function multiplied by the derivative of the inner function.
(a) To find the derivative of f(g(x)), we start by differentiating the outer function f with respect to the inner function g(x), and then multiply it by the derivative of the inner function g(x) with respect to x.
df/dx = df/dg * dg/dx
df/dx = cos(g(x)) * (2x)
(b) To find the derivative of g(f(x)), we differentiate the outer function g with respect to the inner function f(x), and then multiply it by the derivative of the inner function f(x) with respect to x.
dg/dx = dg/df * df/dx
dg/dx = 2f(x) * cos(x)
Hence, the derivatives are:
(a) d/dx(f(g(x))) = cos(g(x)) * (2x)
(b) d/dx(g(f(x))) = 2f(x) * cos(x)
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Find the slope of the line that passes through (20, -37) and (68, -56).
Answers
i believe it would be -19/48
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 8 cubic feet and the volume of each large box is 21 cubic feet. A total of 20 boxes of paper were shipped with a combined volume of 264 cubic feet. Determine the number of small boxes shipped and the number of large boxes shipped.
Answers
Answer:14
Step-by-step explanation: so if you add 21 and 264 and 20 u would get 14 hehehehhehehe im da best your not :)
HELP PLEASE QUICKLY
How many solutions does this system of equations have? Explain.
y = x + 1
y = 2x + 2
The system of equations has ... solution.
The equations have ... slopes, so the lines intersect at ... point.
Convince Me!
The equations of a system have the same slopes. What can you determine about the solution of the system of equations?
Answers
Answer:
The system of equations has one solution. The equations have different slopes, so the lines intersect at one point.
If a system of equations have the same slope, then the lines will run parallel to each other and never cross, leading to no solution being possible. Or if they have the same slope and same y-intercept (therefore being equations for the same line), they will have an infinite number of solutions.
Step-by-step explanation:
The solution to a system of equations is the point where the lines intersect. Looking at this question if we remember the slope-intercept form y=mx+b where m is slope and b is the y-intercept. We can see m=1 for the first equation and m=2 for the second equation. Anytime two equations have different slopes it is guaranteed they will intersect at some point leading to one solution.
Find the GCF of 22ab 2c 2 and 40a 3c 2.
Answers
Answer:
2ac^2
Step-by-step explanation:
Factors:
22ab^2c^2 = 2 * 11 * a * b * b * c * c
40a^3c^2= 2 * 20 * a * a * a * c * c
GCF:
= 2 * a * c * c
= 2ac^2
Answer:
40a
Step-by-step explanation: