During a flu epidemic, the total number of students on a state university campus who had contracted influenza by the xth day was given by N(r) 8000 1+199e-1 (20) (a) How many students had influenza initially? students (b) Derive an expression for the rate at which the disease was being spread and prove that the function N is increasing on the interval (0,0). Is the function increasing, decreasing, or a constant on the interval (0, [infinity])? increasing decreasing constant
Answers
(a) The initial number of students who had influenza on the state university campus was 200 students.
(b) The expression for the rate at which the disease was being spread is \(199e^{(-0.05r)\), and the function N is increasing on the interval (0,∞).
(a) To find the initial number of students who had influenza, we need to determine N(0) in the given expression N(r) = 8000(1+19\(9e^{(-0.05r))\). Plugging in r = 0, we get:
N(0) = 8000(1+1\(99e^{(-0.05(0)))\)
N(0) = 8000(1+1\(99e^0)\)
N(0) = 8000(1+199)
N(0) = 200 * 8000
N(0) = 160,000
Therefore, the initial number of students who had influenza is 200.
(b) To derive the expression for the rate at which the disease was being spread, we differentiate N(r) with respect to r:
dN/dr = 8000 * (0 + 199\(e^{(-0.05r\)) * (-0.05))
dN/dr = -8000 * 0.05 * 19\(9e^{(-0.05r\))
dN/dr = -8000 * 9.9\(5e^{(-0.05r\))
dN/dr = -7960\(0e^{(-0.05r\))
To determine if the function N is increasing or decreasing, we need to analyze the sign of dN/dr on the given intervals.
On the interval (0, ∞):
For any positive value of r, \(e^{(-0.05r\)) is also positive. Therefore, the sign of dN/dr depends on the coefficient -79600. Since -79600 is negative, dN/dr is negative. This means that the function N is decreasing on the interval (0, ∞).
Therefore, the function N is increasing on the interval (0, 0) and decreasing on the interval (0, ∞).
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Related Questions
From the simulation we learned that for a greater than alternative hypothesis, as the true mean gets farther away from the hypothesized value, the probability of a type ii error will?
Answers
As the true mean moves farther away from the hypothesized value, the probability of a Type II error decreases, leading to a higher probability of correctly detecting a true effect or difference.
As the true mean gets farther away from the hypothesized value in a hypothesis test, the probability of a Type II error (also known as a false negative) will decrease.
In a hypothesis test, the null hypothesis assumes that there is no significant difference or effect, while the alternative hypothesis suggests that there is a significant difference or effect.
A Type II error occurs when we fail to reject the null hypothesis when it is actually false. In other words, it is a failure to detect a true effect.
When the true mean is far away from the hypothesized value, the difference between the observed data and the hypothesized value becomes more pronounced.
This increases the likelihood of obtaining a test statistic that falls in the critical region (the region where we reject the null hypothesis). Consequently, the probability of correctly rejecting the null hypothesis (i.e., the probability of not making a Type II error) increases.
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13. The following series is arithmetic:
5+8+11+..+116
(a) Determine the number of terms in this series. Show how you arrived at your answer.
Answers
Answer:
Step-by-step explanation:
5+8+11+...+116x(n)=a+d(n-1) a=first term, d=common difference, n=term116=5+3(n-1)116=5+3n-3116=2+3n116-2=3n114=3nn=114/3n=38 terms S(n)=(n/2)(2a+[n-1]d)S(38)=(38/2)(10+37*3)S(38)=19(10+111)S(38)=19(121)S(38)=2299
help is highly appreciated <3
Answers
Answer:
5(5r - 6)
Step-by-step explanation:
25r - 30
we can factor out a 5 since 25 and 30 are both multiples of 5
so we get 5(5r - 6)
hope this helps!
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A 12 hour circular analogue clock shows 6 o'clock, with the hour hand pointing at 6, and the minute hand pointing at 12. Sometime between 7 and 8 o'clock the hour hand and minute hand are at 180° to each other. At how many minutes past 7 o'clock does this happen?
Answers
After 11 minutes, the angle between the hour's hand and the minute hand is 180°.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
A 12 hours roundabout simple clock shows 6 o'clock, with the hour hand pointing at 6, and the moment hand pointing at 12.
The angle between the hour hand and minute hand is 180°. Then the number of minutes is given as,
In each hour, the hour hand rotates 30°. Then in 8 hours, the hour hand rotation is calculated as,
⇒ 30° x 8
⇒ 240°
After 11 minutes the position of the hour hand is given as,
⇒ 240° + (11 / 60) x 30°
⇒ 240° + 5.5°
⇒ 245.5°
The rotation of the minute hand is given as,
⇒ (360° / 60) x 11
⇒ 66°
Then angle between the hour and the minute hand is calculated as,
Angle = 245.5° - 66°
Angle = 179.5°
Angle ≈ 180°
The number of minutes past 7 o'clock will be 11 minutes.
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If you are allocated 1 TB data to use on your phone, how many
years will it take until you run out of your quota of 1 GB/month
consumption?
Answers
If you are allocated 1 TB data to use on your phone, it will take you 83.33 years until you run out of your quota of 1 GB/month consumption.
1 Terabyte (TB) = 1,000 Gigabytes (GB
So, 1 TB = 1,000 GB
So, the total data available is 1,000 GB/month
Then, to find how many years it will take until you run out of your quota of 1 GB/month consumption, divide the total data available by the monthly consumption:
1,000 GB/month ÷ 1 GB/month = 1,000 months
To convert months to years, divide by 12:1,000 months ÷ 12 months/year ≈ 83.33 years
Therefore, it will take you 83.33 years until you run out of your quota of 1 GB/month consumption.
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What is the number of one-to-one functions f from the set {1, 2, . . . , 2n} to the set {1, 2, . . . , 2n} so that f(x)\neqx for all 1 ≤ x ≤ n and f(x) = x for some n+1 ≤ x ≤ 2n?
Answers
the number of one-to-one functions f from the set {1, 2, . . . , 2n} to the set {1, 2, . . . , 2n} so that f(x)\neqx for all 1 ≤ x ≤ n and f(x) = x for some n+1 ≤ x ≤ 2n is n(2n-1-n)(2n-2)!.
We can approach this problem using the principle of inclusion-exclusion. Let A be the set of all one-to-one functions from {1, 2, . . . , 2n} to itself, B be the set of all one-to-one functions that fix at least one element in {n+1, n+2, . . . , 2n}, and C be the set of all one-to-one functions that fix at least one element in {1, 2, . . . , n}. We want to count the number of functions in A that are not in B or C.
The total number of one-to-one functions from {1, 2, . . . , 2n} to itself is (2n)!.
To count the number of functions in B, we can choose one element from {n+1, n+2, . . . , 2n} to fix, and then permute the remaining elements in (2n-1)! ways. There are n choices for the fixed element, so the number of functions in B is n(2n-1)!.
Similarly, the number of functions in C is n(2n-1)!.
To count the number of functions in B and C, we can choose one element from {1, 2, . . . , n} and one element from {n+1, n+2, . . . , 2n}, fix them both, and permute the remaining elements in (2n-2)! ways. There are n choices for the first fixed element and n choices for the second fixed element, so the number of functions in B and C is n^2(2n-2)!.
By inclusion-exclusion, the number of functions in A that are not in B or C is:
|A - (B ∪ C)| = |A| - |B| - |C| + |B ∩ C|
= (2n)! - n(2n-1)! - n(2n-1)! + n^2(2n-2)!
= n(2n-1)! - n^2(2n-2)!
= n(2n-2)!(2n-1-n)
= n(2n-1-n)(2n-2)!
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the lateral surface area of right circular cylinder is 120 pi cm squared and the circumference is 12 cm find the height
Answers
Answer:
h=31.4 cm
Step-by-step explanation:
A=lateral surface area
c=circumference
h=height
A= c*h
solving for h we get:
h=A/c=120pi/12=10pi
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1. According to the podcast, why and how is chicken the reason American trucks dominate the truck market in the United States? Briefly explain. 2. Name two reasons a party (e.g., a politician or an industry association) may want to impose a tariff? 3. Who are they usually trying to protect? Who would be hurt by a tariff on automobiles? Explain. 4. Describe how competition encourages innovation? In your answer to this question, include a discussion on why American trucks "basically stayed the same over the years. 5. Describe ways foreign companies tried to get around American-imposed tariffs on automobiles. 6. Do you think the methods you described in your previous answer are efficient for an economy? Why or why not? 7. Lastly, how can a tariff be used as a bargaining chip? In your opinion, is that a good reason to impose tariffs - why or why not?
Answers
1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.
2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.
3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.
4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.
5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.
6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.
7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.
1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.
This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.
To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.
However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.
This led to the development of the modern pickup truck, which is now a staple of the American automobile market.
2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.
Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.
3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.
However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.
4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.
In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.
However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.
5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.
6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.
However, they may be necessary for individual companies to remain competitive in the short term.
Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.
7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.
While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.
In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.
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A blueprint for a lighthouse uses a scale of 1 in.:5 ft. The lighthouse in the blue print is 6 in. tall. How tall is the actual lighthouse?
Answers
it would be 30ft tall, because each inch = 5 ft, therefore, 6 x 5 = 30.
Answer:
30 ft
Step-by-step explanation:
5 X
— = —
1 6
5•6=30
30/1= 30
therefore the answer is 30 ft
One thing that many students think about when they register for classes at a university is how many textbooks they are going to have to buy for the class and how much the books are going to cost. To add to this, a lot of the students wonder if they are even going to use the books that they are required to buy. In fact, some students don’t buy books for their classes because they are convinced that they don’t really need them to achieve an acceptable grade.
This is exactly the line of thinking that textbook writers are afraid of—they want students to have to use their books to get good grades in their classes, and they want professors to think that students need their books so that they require them as part of their classes.
Even though textbooks have a definite value—they are available to students who use them when their professors are not—there is some debate on whether they are really needed as part of university classes.
Recently, a researcher conducted an experiment to address this question. In the experiment, the researcher compared two sections of his introductory statistics course, a course required for all liberal arts and sciences students. Students who were enrolled in the fall semester of the course were told that buying the textbook was optional, whereas students enrolled in the spring semester were told that buying the textbook was required. All 380 of the students (190 in the fall and 190 in the spring) completed the course, and they all took the final exam, which consisted of some calculations and several conceptual essay questions.
When the professor finished scoring the essays, he compared the final exam grades of both sections of the class. He found just what he thought he would—there were no differences in the scores on the exams between the section that thought the textbook was optional and the section that thought the textbook was required. The average grade for the fall semester was 84.3%, and for the spring semester it was 85.2%.
Based on this study, the researcher concluded that textbooks were not necessary or helpful for learning, since there were no differences in scores between the two sections.
No control or comparison group
No random assignment
Participant bias
Small sample size
Poor sample selection
Attrition or mortality
Experimenter bias
Confuse correlation with causality
DV is not reliable, precise or accurate
DV is not valid
DV is not objectively scored
Premature generalization of results
Answers
The study conducted by the researcher suffers from several limitations, including the absence of a control group, small sample size, participant bias, and experimenter bias. Furthermore, the sample selection is inadequate, as all the participants are students of one course in a single university.
Moreover, the study fails to account for extraneous variables that might affect the results. Therefore, that textbooks are not necessary or helpful for learning is premature and cannot be generalized to other courses or universities. T he study is flawed, and more research is needed to assess the effect of textbooks on learning.
The study conducted by the researcher suffers from several limitations. First, there is no control group, which makes it difficult to determine whether the results are due to the absence or presence of the textbook. Second, the sample size is small, which reduces the generalizability of the findings.
Third, there is participant bias, as some students might have bought the textbook even though it was optional, while others might not have bought it even though it was required. Fourth, there is experimenter bias, as the professor who scored the essays knew which section had the textbook and which did not.
Fifth, the sample selection is inadequate, as all the participants are students of one course in a single university. Moreover, the study fails to account for extraneous variables that might affect the results, such as the students' prior knowledge, motivation, and study habits.
Therefore, the textbooks are not necessary or helpful for learning is premature and cannot be generalized to other courses or universities. The study is flawed, and more research is needed to assess the effect of textbooks on learning.
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Find:11/3 ÷ 2/3
the quotient is 5 and _____
Answers
Answer:
5.5 quotient 5 and rest 1
But I would answer quotient is 5 and half
Step-by-step explanation:
11/3 ÷ 2/3 = 11/3 * 3/2 = 11/2= 5.5
So the quotient is 5 and rest is 1
Hope this helps, have a good day
Answer:
5 1/2
Step-by-step explanation:
11/3÷2/3
Applying the fractions formula for division,
=11/3×3/2
=33/6
Simplifying 33/6, the answer is
=5 1/2
I need help with this!
Answers
Answer:
Solution = Infinitely many
Step-by-step explanation:
y = -x + 1
y - 1 = -x
y = -x + 1
y = -x + 1 (Multiply by -1)
y = -x + 1
-y = x - 1
0 = 0
Since 0 = 0 is true, this is an identity solution that has an infinite set of solutions
A shirt that normally costs $19.99 is on sale for 15% off. How much would Jason pay for 3 of the shirts with an 8% sales tax?
Answers
$19.99 x 0.15 = $2.999 (rounded to $3)
So each shirt costs:
$19.99 - $3 = $16.99
To find the cost of 3 shirts, we can multiply the cost of one shirt by 3:
$16.99 x 3 = $50.97
Next, we need to add the sales tax. To do this, we first need to find 8% of the total cost (including the discount):
$50.97 x 0.08 = $4.08
Finally, we add the sales tax to the total cost:
$50.97 + $4.08 = $55.05
Therefore, Jason would pay $55.05 for 3 of the shirts with an 8% sales tax.
1. Solve for the unknown in each triangle. Round each answer to the nearest tenth.
Answers
The values of the missing sides are;
a. x = 35. 6 degrees
b. x = 15
c. x = 22. 7 ft
d. x = 31. 7 degrees
How to determine the valuesTo determine the values, we have;
a. Using the tangent identity;
tan x = 5/7
Divide the values
tan x = 0. 7143
x = 35. 6 degrees
b. Using the Pythagorean theorem
x² = 9² + 12²
find the square
x² = 225
x = 15
c. Using the sine identity
sin 29= 11/x
cross multiply the values
x = 11/0. 4848
x = 22. 7 ft
d. sin x = 3.1/5.9
sin x = 0. 5254
x = 31. 7 degrees
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Find the Values of y
Y ² = 169
Answers
Answer:
Y= 13,-13
Step-by-step explanation:
a businessman bought a personal computer for $10768,he incurred a loss of 21% on the cost price. find the selling price of the computer
Answers
The selling price of the computer was $8507.52.
We have,
If the businessman incurred a loss of 21% on the cost price, then the selling price (SP) must have been 79% of the cost price (CP), since:
SP = CP - Loss
SP = CP - 0.21 x CP
SP = 0.79 x CP
We know that the cost price was $10768, so we can substitute this value into the equation above to find the selling price:
SP = 0.79 x CP
SP = 0.79 x $10768
SP = $8507.52
Therefore,
The selling price of the computer was $8507.52.
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For problems 1 - 6, determine whether the relationships represented are A. Exponential., B. Linear., or C. Neither.
Answers
Step-by-step explanation:
a linear function is following
y = ax + b
that means the ratio of the y and x differences between the data points is constant (a).
an exponential function is in the form y = a^x. or some constant variations of it.
the base is constant (a), and the exponent of the constant is the variable (x).
1.
clearly exponential.
this is the typical graph of an exponential function.
it looks like y = 2^x, as e.g. f(4) = 2⁴ = 16, and the graph seems to be at least very close to this.
2.
exponential.
y = 3^(x - 0.5)
3¹ = 3
3² = 9
3³ = 27
3⁵ = 243
this is just y = 3^x shifted to the right by 0.5 units.
3.
linear.
the difference ratio between the data points is constant :
x is the row number (1, 2, 3, 4, 5, ...).
y is the number of seats per row (14, 16, 18, 20, 22, ...).
so,
(16-14)/(2-1) = 2/1 = 2
(18-16)/(3-2) = 2/1 = 2
...
(22-14)/(5-1) = 8/4 = 2
always constant (2).
4.
neither.
it is y = x²
when you compare 4. and 1. you see the clear difference between the 2 graphs.
5.
exponential.
remember, y = a^x.
well, here, a = 1/2. but that is still constant and doesnot change the principle.
the factor 10 stretches the graph a bit up (in fact, this 10 is the starting number of an exponential growth). but the function in its core is still exponential.
6.
linear.
when written that way, it just means that x = n, and for every increase of n by 1, y (f(n)) increases by +4.
so, the difference ratio stays constant (4/1 = 4).
A woman is rowing a boat across a 60 wide river from west to east. She can row at 2 mph in still water, but the river's current is 5 mph from north to south. To the nearest foot, how far downstream on the east bank will she land?
Answers
Answer:
S, and the other day. I have been a while. I have a great drea the most important things. The may have to pay a fee of the most popular and I will not 66 the most of the most of my life. I was a bit of the best, but the 15th. I have been a while. I am your what is happening in the next couple days 6 the most of the most of the most
Step-by-step explanation:
popular and I will not be hurt by a friend of the day, and the other side, I think I have a great drea, I think I have been a while. I have been in touch. Thanks for the next day delivery. We have a great drea the same time. I was just the right place for the use of the most of the most popular and I am a beautiful person. The comments for your email.
The woman will land on the east bank of the river at a downstream of 37.5 miles.
What is meant by relative velocity ?Relative velocity of an object in motion is defined as the velocity of the object with respect to another object.
Here,
Width of the river, W = 60 miles
Velocity of the boat in still water, Vb = 2 mph
Velocity of river, Vr = 5 mph
Relative velocity of the boat with respect to river in downstream,
Vbr = Vb + Vr
Vbr = 8 mph
Drift of the boat, d = Vr W/Vbr
d = 5 x 60/8
d = 37.5 miles downstream
Hence,
The woman will land on the east bank of the river at a downstream of 37.5 miles.
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Solve dy/dx=1/3(sin x − xy^2), y(0)=5
Answers
The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5
To solve this differential equation, we can use separation of variables.
First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:
dy/dx = 1/3(sin x − xy^2)
dy/(sin x - xy^2) = dx/3
Now we can integrate both sides:
∫dy/(sin x - xy^2) = ∫dx/3
To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:
∫dy/(sin x - xy^2) = ∫du/(sin x - u)
= -1/2∫d(cos x - u/sin x)
= -1/2 ln|sin x - xy^2| + C1
For the right side, we simply integrate with respect to x:
∫dx/3 = x/3 + C2
Putting these together, we get:
-1/2 ln|sin x - xy^2| = x/3 + C
To solve for y, we can exponentiate both sides:
|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)
|sin x - xy^2| = 1/e^(2C/3 - x/3)
Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.
Case 1: sin x - xy^2 > 0
In this case, we have:
sin x - xy^2 = 1/e^(2C/3 - x/3)
Solving for y, we get:
y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]
Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:
y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5
Squaring both sides and solving for C, we get:
C = 3/2 ln(1/25)
Putting this value of C back into the expression for y, we get:
y = √[(sin x - e^(x/2)/25)/x]
Case 2: sin x - xy^2 < 0
In this case, we have:
- sin x + xy^2 = 1/e^(2C/3 - x/3)
Solving for y, we get:
y = ±√[(e^(2C/3 - x/3) - sin x)/x]
Again, using the initial condition y(0) = 5 and solving for C, we get:
C = 3/2 ln(1/25) + 2/3 ln(5)
Putting this value of C back into the expression for y, we get:
y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]
So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:
y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5
y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5
Note that there is no solution for y when sin x - xy^2 = 0.
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1+1/4+60-x/x+10=60/x
Answers
The value of x is 30 and -80
To solve the equation:
1 + 1/4 + (60 - x)/(x + 10) = 60/x
5/4 + (60 - x)/(x + 10) = 60/x
(5(x + 10)+4(60 - x))/4(x + 10) = 60/x
(5x + 50 + 240 -4x)/(4x + 40) = 60/x
(x + 290)/(4x + 40) = 60/x
x(x + 290) = 60(4x + 40)
x² +290x = 240x + 2400
x² + 50x - 2400 = 0
x² - 30x +80x - 2400 = 0
x(x - 30) +80(x - 30)=0
(x - 30)(x+ 80) = 0
x = 30, - 80
Therefore the value of x is 30 and -80
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Given question is incomplete, the complete question is below
Solve the following equation for x:
1 + 1/4 + (60 - x)/(x + 10) = 60/x
5x10=50-100=50 hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answers
Answer:
correct
Step-by-step explanation:
Answer:
hello
Step-by-step explanation:
İ from Turkish
thanks :)
My name is Elfida
6.
5. The 7 A.M. temperature is 65°F. Each hour until 10 A.M.
the temperature rises at least 2 degrees. Which inequality
can be used to find t, the minimum temperature at 10
A.M.?
a. t +6 > 65
b. t-6 2 65
C. t-6 < 65
d. t +6 < 65
Answers
The main answer is C. The inequality t-6 < 65 can be used to find t, the minimum temperature at 10 A.M.
We know that the temperature rises at least 2 degrees each hour from 7 A.M. to 10 A.M. That means by 10 A.M., the temperature will have risen by at least 6 degrees (2 degrees per hour for 3 hours).
If we let t be the temperature at 10 A.M., then we can write an inequality that represents the minimum temperature at 10 A.M.:
t - 6 < 65
This inequality says that the temperature at 10 A.M. (t) minus the 6 degree increase must be less than the initial temperature at 7 A.M. (65°F). This makes sense, because the temperature cannot decrease from 7 A.M. to 10 A.M.
Option a, t + 6 > 65, is incorrect because adding 6 to t would mean the temperature at 10 A.M. is greater than the initial temperature at 7 A.M., which is not guaranteed.
Option b, t - 6 2 65, is incorrect because the symbol "2" is not a valid inequality symbol.
Option d, t + 6 < 65, is incorrect because adding 6 to t would mean the temperature at 10 A.M. is less than the initial temperature at 7 A.M., which is not possible.
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What is the square root of 50? Round to the hundredths place. Please help I will give Brainliest.
Answers
Answer:
7.07
Step-by-step explanation:
It is so close to seven so that is why it is not a whole number.
Answer:
7.07
Step-by-step explanation:
How many whole numbers from 0 to 55?
Answers
Answer:
56
Step-by-step explanation:
Need answers quickly need it step by step
(−5)2 −2×(−9)+6=
(−9)−(−8)+2×42=
8÷(−4)×(−6)2 +7=
10×5−(−6)2 +(−8)=
(10 ÷ (−5) − (−2)) × (−3)3=
3×10+8−42=
(−3)3 −2+8÷(−8)=
4×(−8)+6−(−2)3=
(−5)2 ×3÷5+9=
4 × (−6) ÷ 8 + 33=
Thanks
Answers
Answer:
Step-by-step explanation:
1. -10+18+6=8+6=14
2. -1+84=83
3. -2×(−6)2 +7=12×2+7=24+7=31
4. 50-(−6)2 +(−8)=50+12-8=62-8=54
5. (-2+2)× (−3)3=0× (−3)3=0
6. 30+8-42=38-42=-4
7. -9-2-1=-12
8. -32+6+6=-20
9. -10×3÷5+9=-30÷5+9=-6+9=3
10. -24÷ 8 + 33=-3+33=30
Given the functions k(x) = 2x2 − 7 and p(x) = x − 4, find (k ∘ p)(x). (k ∘ p)(x) = 2x2 − 8x + 16 (k ∘ p)(x) = 2x2 − 16x + 32 (k ∘ p)(x) = 2x2 − 16x + 25 (k ∘ p)(x) = 2x2 − 11
Answers
Answer:
(k ∘ p)(x) = 2x² - 16x + 25Step-by-step explanation:
k(x) = 2x² - 7
p(x) = x - 4
To find (k ∘ p)(x) substitute p(x) into k(x),
that's replace any x in k(x) by p(x)
We have
(k ∘ p)(x) = 2(x - 4)² - 7
Expand
(k ∘ p)(x) = 2( x² - 8x + 16) - 7
= 2x² - 16x + 32 - 7
Simplify
We have the final answer as
(k ∘ p)(x) = 2x² - 16x + 25Hope this helps you
Answer:
(k ∘ p)(x) = 2x² - 16x + 25
Step-by-step explanation:
hope this helps
Carmen is 12 years older than David. Five years ago the sum of their ages was 28. How old are they now?
Answers
Answer:
i think 38
Step-by-step explanation:
5x2 =10 + 28 =38
Answer:
David is 13
Carmen is 25
Step-by-step explanation:
5yrs ago Carmen was 20 and David was 8 8+5=13 20+5=25
1. A recipe for salad dressing calls for three parts oil for every one part vinegar. How many tablespoons of vinegar are needed to make 1/2 cup of salad dressing?
Answers
Answer: The answer is 8
Step-by-step explanation: 16 tablespoon is 1 cup now find half of 16. Half of 16 is 8. So 8 tablespoon should be equal 1/2 cup
given vector u equals open angled bracket negative 11 comma negative 5 close angled bracket and vector v equals open angled bracket 4 comma 8 close angled bracket comma what is projvu?
Answers
The required projection of u onto v is the vector (-23/20)i - (23/10)j, or approximately <-1.5, -2.13>.
To calculate the projection of vector v onto vector u (proj_vu), we can use the formula:
\(proj_{vu} =\dfrac {(v \times u)}{||u||^2} *v\)
Here, u is the vector -11i - 5j and v is the vector 4i + 8j.
Compute the dot product of u and v.
u · v = (-11)(4) + (-5)(8)
= -92
Compute the magnitude of v.
\(||v|| = \sqrt{(4^2 + 8^2)} \\= \sqrt{80}\\ = 4\sqrt{5\)
Compute \(proj_{vu}\)using the formula.
\(proj_{vu} = \dfrac{u \times v} {||v||^2} * v\\ proj_{vu} = (-92 / (80)) * (i + 2j)\\proj_{vu} = (-23/20)i - (23/10)j\)
Therefore, the projection of u onto v is the vector (-23/20)i - (23/10)j, or approximately <-1.5, -2.13>.
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The question is incomplete, the complete question is given below:
Find the projection of vector v onto vector u or what is proj_vu?
Where.
Vector u = <-11, -5>
Vector v = <4, 8>
Suppose c(x) = x3 - 24x2 + 30,000x is the cost of manufacturing x items. Find a production level that will minimize the average cost per item of making x items.
Answers
Answer:
hence the required minimum production level is 12units
Step-by-step explanation:
Given the cost function expressed as c(x) = x^3 - 24x^2 + 30,000x
The average cost function will be c(x)/x
Dividing the cost function through by x
Average cost function = c(x)/x = x³/x - 24x²/x + 30,000x/x
Average cost function = x²-24x + 30,000
A(x) = x²-24x + 30,000
If the average cost is minimized, hence dA/dx = 0
dA/dx = 2x - 24
0 = 2x - 24
-2x = -24
Divide both sides by -2
-2x/-2 = -24/-2
x = 12
For the second deriviative
d²A/dx² = 2 which is greater than zero
Hence a production level that will minimize the average cost per item of making x items is 12
The production level that will minimize the average cost per item of making x items is x = 12
How to obtain the minimum value of a function?To find the minimum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.
Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.
For this case, the function in consideration is: \(c(x) = x^3 - 24x^2 + 30000x\)
This is cost function for x items' manufacturing.
The average cost per item would be c(x) / x
This gives us a function a(x) as:
\(a(x) = c(x)/x = x^2 -24x + 30000\)
For finding the minimum of a(x), getting its first two derivatives as:
\(a'(x) = 2x - 24\\a''(x) = 2 > 0\)
Equating first rate to 0,
\(a'(x) = 2x - 24 = 0\) critical point.
Since second rate is positive, the point x = 12 is point of minima, and since only one critical point is there, it is the point on which a(x) is minimum.
Thus, the production level that will minimize the average cost per item of making x items is x = 12
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