- A unicycle tire has a radius of 13 inches. About how far will the unicycle travel in 20 rotations?
F.1633 inches
G.10,613 inches
H.82 inches
J.520 inches
Answer:
1061.32 you made a typo on G
Step-by-step explanation:
To find the distance travelled by the tire we need the circumference of it
The formula for circumference is 2πr we know pi is roughly 3.14 and the radius is 13
we plug the numbers in and get
2* 3.14* 13
6.28*13
81.64
81.64 is the circumference, now we simply just multiply 81.64 by 13 to get 1061.32
Im guessing number G was supposed to be 1061.32 instead of 10,613
jim is going to buy donuts for his family. each donut costs $1.45. if the number of donuts jim buys is represented using the letter d, which expression represents the total cost? a 1.45d b 1.45/d c 1.45 d d 1.45 - d
By applying total cost concept, it can be concluded that the expression represents the total cost is 1.45d (option A).
Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.
It is usually used to solve a problem in various fields of study, such as chemistry, biology, economics, and so on.
One of the most familiar uses of algebra is how to calculate the total cost:
Total cost = n x p , where:
n = number of products
p = product price per piece
We know that Jim is going to buy donuts for his family:
p = $1.45
n = d
So the total cost can be calculated by multiplying 1.45 by d, which equals 1.45d.
Thus the expression represents the total cost is 1.45d (option A).
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Students may purchase Student may purchase ingredients from the camp store if they wish to make s'mores at the campfire. For every 15 students,the ingredients cost the camp store $31. 50 estimate the cost for 1 student
The estimated cost for one student to purchase the ingredients for s'mores at the camp store is $2.10.
To estimate the cost for one student, we can divide the total cost for 15 students by the number of students. Given that the ingredients cost $31.50 for 15 students, we can calculate the cost for one student as follows:
Cost for 1 student = Total cost for 15 students / Number of students
Cost for 1 student = $31.50 / 15
Cost for 1 student ≈ $2.10
Therefore, the estimated cost for one student to purchase the ingredients for s'mores at the camp store is approximately $2.10. This calculation assumes that the cost is evenly distributed among the students and that the quantity of ingredients per student remains constant.
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The drama club sold bags of candy and cookies to raise money for the spring show. Bags of candy cost $8.50, and bags of cookies cost $4.50, and sales equaled $79.00 in total. There were 6 more bags of cookies than candy sold.
Find the number of bags of candy and cookies sold by the drama club. Show your work.
The bags of candy that was sold is 6
The bags of cookies that was sold is 10.
What are the linear equations that represent the question?$8.50c + $4.50o = 79 equation 1
o - c = 6
o = 6 + c equation 2
Where:
o = bags of cookies soldc = bags of candies sold How many bags of candy and cookies were sold?Substitute for o in equation 1 using equation 2
$8.50c + $4.50(6 + c) = 79
$8.50c + 27 + 4.50c = 79
$8.50c + 4.50c = 79 - 27
$13c = 52
c = 52 / 13
c = 4
Substitute for c in equation 2
0 = 6 + 4 = 10
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The mode is the value of the observation that appears most frequently. true or false
The statement 'The mode is the value of the observation that appears most frequently.' is True.
We know that, the mode is the most frequent number.
It is the number that occurs the highest number of times.
The observation occurring the most number of times or which has highest frequency is known as the mode.
For example, in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 as it occurs most often.
There is no mode when all observed values appear the same number of times in a data set.
Therefore, the statement 'The mode is the value of the observation that appears most frequently.' is True.
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Find the midpoint of the segment with the following endpoints.
(8, -3) and (2, -10)
Answer:
(5, -13/2)
Step-by-step explanation:
I’ll give brainly
Is the following statement
possible or impossible?
A triangle has side lengths of
3, 7, and 10
Answer:
Possible
Step-by-step explanation:
The rule for triangle side lengths is that the two shortest sides must add up to the longest side so it is possible because
3+7 = 10
Two short sides = The longest side
Answer:
possible
Step-by-step explanation:
3+7= 10
Add.
(6x³ + 3x² − 2) + (x³ - 5x² − 3)
Express the answer in standard form. (Please and thank you)
Answer:
\(\\\sf7x^3 - 2x^2 - 5\)
Step-by-step explanation:
\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)
Remove parenthesis.
6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3
Rearrange:
6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3
Combine like terms to get:
7x^3 - 2x^2 - 5----------------------------------------
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Hope this helps! :)
Answer:
7x³ - 2x² - 5
Step-by-step explanation:
(6x³ + 3x² - 2) + (x³ - 5x² - 3)
Remove the round brackets.
= 6x³ + 3x² - 2 + x³ - 5x² - 3
Put like terms together.
= 6x³ + x³ + 3x² - 5x² - 2 - 3
Do the operations.
= 7x³ - 2x² - 5
____________
hope this helps!
Please help. Pls. I will give you brainliest. You dont have to write 200 words Just choose a topic and write some sentences- I will do the rest ~~~Ty
Answer:
I had to screenshot from my computer because it said (you have an inappropriate word or link in your answer)
we do things called culture monday at our school where we write about a problem and then do a discussion on it in the classroom
this was mine so nooooo plagiarism or anything.
please mark brainliest......
Answer:
World War II started on September 1st, 1939, a decade after America’s stock market crash and downfall of the economy, which was in 1929, when Germany, led by a man born in Austria called Adolf Hitler, invaded Poland. France and England immediately declared war on Germany and Germany’s allies.
Germany had two allies, Japan and Italy, Italy mostly provided food and supplies, while Japan provided manpower, along with Germany. Germany, Japan, and Italy were called the Axis powers, and England, Russia (Then called the Soviet Union), and America (When America joined the war), along with many other countries, such as China and France (Except for the four years which Germany occupied France, 1940--1944), were called the Allied powers.
Germany invaded and occupied Austria, Belgium, France, Norway, Luxembourg, Greece, Czechoslovakia, Greece, Denmark, Holland, Hungary, the Netherlands, and many other countries with the help of Italy and Japan.
The United States wanted to be neutral through World War II like the Irish and Swiss, but the Axis Powers did not let this happen. Instead, Japan bombed Pearl Harbor and utterly destroyed and sunk many ships, so the United States had no choice but to join the war and the Allied forces.
The United States both lost and won many battles, and Germany was losing battles against the Soviet Union and England. Germany lost many battles in the Soviet Union, which was fought in harsh and bitter cold, and also lost the Battle of Britain fought in the skies over England between Britain’s Royal Air Force (RAF) and Germany’s Luftwaffe.
Many people died as a result of the Battle of Britain by bombs and flying shrapnel. In order to try to get their country back to normal, Great Britain started to ration food, drafted men over eighteen to go to the war front, made shelters all over England, in cities, towns, even in the country, in case of an air raid. The Battle of Britain was mostly fought in the skies of London, but enemy planes heading towards London to fight might drop a bomb to wipe away towns, cities, or a part of country off the map.
Germany soon retreated from Great Britain and thought that England would surrender with the rest when Germany conquered and ruled the world, which was Germany’s goal, but England, after some recovery, fought Germany as hard as ever, angered by the people and planes lost because of the Battle of Britain.
In the middle of this, President Franklin Delano Roosevelt died because of a mixture of bad health, too much stress, and his polio. Americans grieved for President Roosevelt, and elected a new president, President Harry Truman.
With forces fighting with both the Soviet Union and England, and later fighting on D-Day, Germany could not last for long, even with its two allies. But the number of allies Germany had soon reduced to one, for Italy joined the Allied powers, betraying the Axis Powers. Germany desperately tried to fight back the forces of the Allied powers, but soon surrendered days after Adolf Hitler’s death, on May 8th, 1945.
Even when its ally Germany had surrendered and Italy had gone over to the Allies, Japan still fought, even though there was very little chance they would win. This was a bad idea, an idea which would change history. The Allied powers turned their full attention on defeating Japan, which was a bad thing, since Japan could only take over a few islands in the Pacific belonging to the United States and could not defeat any others in the beginning when the Allied powers’ attention was divided. As a result, many, at least hundreds, died, deaths that were not even necessary. The United States dropped two atomic bombs from one of America’s bomber planes on Japan’s two major cities, Hiroshima and Nagasaki days apart, so Japan surrendered, unable to lose any more people then it had already.
The two atomic bombs were built in the midst of fighting and stress of World War II in Manhattan, New York by a group of people who specialized in physics, math, and chemistry. The atomic bomb’s code name was: The Manhattan Project. The Manhattan Project, when done and ready, after dropped from an American bomber plane, killed over a hundred thousand Japanese in the two major cities Hiroshima and Nagasaki, most of them regular Japanese civilians going about their daily life.
World War II was a very important war and time period that changed the world. It changed the human race. The atomic bomb, invented in World War II, soon led other countries, such as England, France, the Soviet Union (Later known as Russia), and China to build it too, which gave these countries a huge advantage in war. America’s stock market bounced back. President Harry Truman became popular for ending World War II.
Step-by-step explanation:
Sorry I'm late
803 words
Brainliest, Please!A random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important. The interval that is 95% certain to contain the proportion of all 18-24 year olds who believe that their health is extremely important is
Between 48% and 54% believe that their health is extremely important.
According to the statement
Given that a random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important.
Here
Sample size n =1001
sample proportion p = 0.51
By these values we calculate the Standard error of proportion.
So, Standard error of proportion = 0.0158.
Since sample size is sufficiently large we can take Z critical value for confidence interval
Z critical value for 95% = 1.96
Margin of error = ±1.96*std error
= ±0.0310
confidence interval = 0.51 ±0.0310
= (0.48, 0.54)
So, Between 48% and 54% believe that their health is extremely important.
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The cat population in catonsville has been recorded since 2010. The population. p. can be represented by the equation p = 1600(2)t where is time in years since the begging of 2010. What was that cat population 2007
A. 4000
B. 200
C. 800
D. 100
The cat population in Catonsville in 2007 was 200. The answer is option B.
What is population?Population refers to the total number of people, animals, or objects in a particular group or area. It is the entire group or collection of individuals, things, or events that we are interested in studying or describing.
According to question:We can use the given equation to find the cat population at any given time in years since the beginning of 2010. However, to find the population in 2007, we need to make a conversion from years since the beginning of 2010 to years since the beginning of 2007.
From the beginning of 2007 to the beginning of 2010, there are 3 years, so if we subtract 3 from the number of years since the beginning of 2010, we will get the number of years since the beginning of 2007. Therefore, we need to substitute t = -3 into the given equation and solve for p:
\(p = 1600(2)^t\\p = 1600(2)^(-3)\\p = 1600(1/8)\\p = 200\)
Therefore, the cat population in Catonsville in 2007 was 200. The answer is option B.
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Joseph traveled from Boston to Framingham at 50 mph and then back to Boston at 40 mph, What was Joseph average speed on the round trip? (its not 45mph just to let you know)
Answer:
44.44 mph
Step-by-step explanation:
Since we are given 50 from the start, and 40 at the end, we will add 50 and 40.
50 + 40 = 90
Then, Divide the result by 2.
90 ÷ 2 = 45
Here is the tricky part: we are not done!
Don't be mistaken by the question. Some people may think the answer is 45mph because that is what it is rounded up, however, the question did not ask for the answer rounded up.
This is a round trip, so reduce this to the nearest value in both tenths and units. Hence, it would be 44.44.
I need help with calculating the volume of this shape
The volume of the oblique rectangular prism is 216 m³.
How to calculate the volume of an oblique rectangular prism?
The volume of an oblique rectangular prism is given by the formula:
V = l * w * h
Where l and w are the length and width of the base respectively, and h is the perpendicular distance between the bases
In this case, l = 7.5 m and w = 4.5 m
Using trig. ratio:
tan 65 = h/3
h = 3 * tan 65
h = 6.4 m
Thus,
V = 7.5 * 4.5 * 6.4
V = 216 m³
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please please please help!
AD = ___ units
The Guiness Book of World Records holder for Fastest Rapper is a guy
from Seattle named NoClue. He can rap 70 syllables in just 5 seconds. (He
actually did 723 in 51.27 seconds). What is his speed in syllables per
second?
Answer:
Write a ratio.
70 : 5
x : 1
To solve for x, cross multiply.
70 : 5x
Divide both sides by 5.
14 = x
So, NoClue can rap 14 syllables per second.
:)
Chan Resources incurred $280,000 of research and development costs to develop a product for which a patent was granted on January 2, 2014. Costs associated with obtaining the patent totaled $97,000. On March 31, 2020, Chan paid $180,000 for legal fees in a successful defense of the patent. The total amount capitalized for the patent through March 31, 2020 should be
The total develop a product amount capitalized for the patent through March 31, 2020, is $557,000.
To the total amount capitalized for the patent through March 31, 2020, the research and development costs, the costs associated with obtaining the patent, and the legal fees for defending the patent.
The research and development costs incurred by Chan Resources to develop the product amount to $280,000. These costs are eligible for capitalization.
The costs associated with obtaining the patent total $97,000. These costs are also eligible for capitalization.
The legal fees paid for the successful Defense of the patent amount to $180,000. These fees are considered direct costs of maintaining and defending the patent and are also eligible for capitalization.
To calculate the total amount capitalized for the patent through March 31, 2020,
Research and development costs: $280,000
Costs associated with obtaining the patent: $97,000
Legal fees for defense: $180,000
Total amount capitalized for the patent through March 31, 2020:
$280,000 + $97,000 + $180,000 = $557,000
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Find the quotient of the quantity 32 times ten raised to the negative twenty second power end quantity divided by the quantity 8 times ten raised to the negative twenty second power end quantity.. write the final answer in scientific notation. 4 x 10−44 4 x 1044 4 x 1022 4 x 100
The final answer in scientific notation is 4 × 10⁰.
Firstly writing both dividend and divisor in scientific notation.
Dividend = 32 × 10⁻²²
Divisor = 8 × 10⁻²²
Now performing division to find the quotient.
Quotient = Dividend ÷ Divisor
Quotient = 32 × 10⁻²² ÷ 8 × 10⁻²²
As per the known rule of exponents, aˣ ÷ aⁿ = aˣ⁻ⁿ
Quotient = (32 ÷ 8) × 10⁻²² ⁻ ⁽⁻²²⁾
Dividing the base numbers
Quotient = 4 × 10⁻²²⁺²²
Performing subtraction on exponents
Quotient = 4 × 10⁰
Also, as per the known fact, a⁰ = 1. So, the final answer is 4 and in scientific notation the final answer is 4 × 10⁰.
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In at least 100 words independently write your response to the statement, "Anyone can do well in math."
Answer:
I believe that this is true. Anyone can do well in math, not everyone. The main difference being that if EVERYone could, that means every one person in the world, no matter the circumstance, so by saying ANYone, it's saying that however many people in the world want to do it, can do it, if they try and put in the work. Math is not biased against any one person, nor is it favored for any one person. Any person who studies, or learns it can do well in math. Someone who has never learned anything about math will not do well at all. So, yes, ANYone can do well, but not EVERYone.
Not 100 words, but should do trick if you just add in some extra words between phrases, and substitute some words with one or two synonyms.
please help !
A local paintball facility charges $30 to play plus $0.25 per paintball pellet used. Elijah plans on playing paintball and has $60 to spend at the facility. Which equation can be used to determine p, the number of paintball pellets he can use if he spends exactly $60?
A. 30 + 0.25p = 60
B. 30 + 0.25 = 60p
C. 30p + 0.25 = 60
D. 30 − 0.25p = 60
Step-by-step explanation:
Hello! I believe the answer is A. 30+0.25p=60.
Elijah has to pay a facility charge which is 30$. So we can go ahead and write that down! He has 60$ to spend, but he has to pay $0.25 per paintball. So we write that as 30+0.25p=60!! If you have any questions comment doen below!
Answer:i think it A to
Step-by-step explanation: it is the only one correct
Kayla was on holiday in Turkey for 90 days.
She was in Istanbul for 4/9 of her holiday.
She was in Izmir for 1/3 of her holiday.
She was in Ankara for 3/5of the rest of her holiday.
How many days did Kayla spend in Ankara?
Kayla was in Ankara for 12 days during her holiday.
Total number of holidays = 90 days.
Holidays in Istanbul = 4 / 9
So, by using the Fractions and multiplication, we get that:
Holidays in Istanbul = 90 × 4 / 9 = 40 days
Holidays in Izmir = 1 / 3 × 90 = 30 days.
Remaining holidays = 90 - 40 - 30 = 20
Holidays in Ankara = 3 / 5 × 20 = 12 days.
Therefore, Kayla was in Ankara for 12 days during her holiday.
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Using the Factor Theorem, which of the polynomial functions has the zeros 4, \(\sqrt7\), and \(-\sqrt{7\\}\)?
f (x) = x3 – 4x2 + 7x + 28
f (x) = x3 – 4x2 – 7x + 28
f (x) = x3 + 4x2 – 7x + 28
f (x) = x3 + 4x2 – 7x – 28
Answer:
B
Step-by-step explanation:
According to the Factor Theorem, if (x - a) is a factor (where a is a zero) of the polynomial P(x), then P(a) must equal zero.
Our zeros are 4, √7, and - √7. Hence, when evaluating P(4), P(√7), and P(-√7), all must evaluate to zero.
Testing each choice, we can see that only choice B is true. That is:
\(\displaystyle \displaystyle \begin{aligned} f(4)&= (4)^3 - 4(4)^2 - 7(4) + 28 \\ &= (64) - (64) - (28) + 28 \\ &= 0 \stackrel{\checkmark}{=}0 \\f(\sqrt{7}) &= (\sqrt{7})^3 - 4(\sqrt{7})^2 - 7(\sqrt{7}) + 28 \\ &= (7\sqrt{7}) - (28) - (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0\\ f(-\sqrt{7}) &= (-\sqrt{7})^3 - 4(-\sqrt{7})^2 - 7(-\sqrt{7}) + 28 \\ &= (-7\sqrt{7}) - (28) + (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0 \end{aligned}\)
In conclusion, our answer is B.
Please show how to solve step by step with instructions and what formulas in Excel to use. Thank you.
Powder Puffs sells pom-poms to schools internationally. It has an offer from a private
buyer and the owners would like to know the value of each share of common equity so
they don't undervalue their shares. The cost of capital for this firm is 6.65% and there are
60,797 common shares outstanding. The firm does not have any preferred equity, however, it
has outstanding debt with a market value of $3,833,340. Use the DCF valuation model based
on the expected FCFs shown below; year 1 represents one year from today and so on. The
company expects to grow at a 2.2% rate after Year 5. Rounding to the nearest penny, what is the
value of each share of common stock?
The value of each share of common stock, rounded to the nearest penny, is approximately $66.61 according to the given information and values in the question.
step by step:
To calculate the value of each share of common stock using the Discounted Cash Flow (DCF) valuation model, we need to discount the expected future cash flows to their present value and subtract the market value of the outstanding debt. The formula for calculating the value of each share of common stock is:
Value per Share = (Present Value of Future Cash Flows - Debt) / Number of Common Shares
To calculate the present value of future cash flows, we discount each cash flow using the cost of capital.
Let's calculate the present value of future cash flows and the value per share of common stock:
Year 1: FCF = $250,000
Year 2: FCF = $300,000
Year 3: FCF = $350,000
Year 4: FCF = $400,000
Year 5: FCF = $450,000
\(Year 6 onwards: FCF = $450,000 * 1.022^(Year - 5)\)
Cost of Capital = 6.65%
Outstanding Debt = $3,833,340
Number of Common Shares = 60,797
First, let's calculate the present value of future cash flows:
\(PV = FCF / (1 + r)^n\)
where:
PV = Present Value
FCF = Future Cash Flow
r = Cost of Capital
n = Number of years
\(Year 1:PV1 = $250,000 / (1 + 0.0665)^1 ≈ $234,837.45Year 2:PV2 = $300,000 / (1 + 0.0665)^2 ≈ $268,084.17Year 3:PV3 = $350,000 / (1 + 0.0665)^3 ≈ $301,706.42Year 4:PV4 = $400,000 / (1 + 0.0665)^4 ≈ $335,693.63Year 5:PV5 = $450,000 / (1 + 0.0665)^5 ≈ $369,035.06Year 6 onwards:PV6 = $450,000 * 1.022^(Year - 5) / (1 + 0.0665)^Year\)
Now, let's calculate the total present value of future cash flows:
\(Total PV = PV1 + PV2 + PV3 + PV4 + PV5 + ∑(PV6)\)
∑(PV6) represents the sum of present values for Year 6 onwards, up to infinity. Since we have a constant growth rate of 2.2%, we can use the perpetuity formula to calculate this sum:
\(∑(PV6) = PV6 / (r - g)\)
where:
r = Cost of Capital
g = Growth rate
\(∑(PV6) = PV6 / (0.0665 - 0.022) = PV6 / 0.0445Now, let's calculate PV6 and ∑(PV6):PV6 = $450,000 * 1.022^1 / (1 + 0.0665)^6 ≈ $303,212.65∑(PV6) = $303,212.65 / 0.0445 ≈ $6,820,510.11\)
Next, let's calculate the total present value:
\(Total PV = PV1 + PV2 + PV3 + PV4 + PV5 + ∑(PV6)Total PV = $234,837.45 + $268,084.17 + $301,706.42 + $335,693.63 + $369,035.06 + $6,820,510.11Total PV ≈ $8,329,866.84\)
Finally, let's calculate the value per share of common stock:
Value per Share = (Total PV - Debt) / Number of Common Shares
Value per Share = ($8,329,866.84 - $3,833,340) / 60,797
Value per Share ≈ $66.61
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How do you find the hypotenuse of a 45-45-90 triangle if you know the length of the legs?
The length of the hypotenuse of a 45-45-90 triangle is √2x units.
To find the hypotenuse of a 45-45-90 triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).
Let's denote the length of each leg of the triangle as "x". Since the triangle is isosceles, both legs are of equal length. Therefore, we can write:
Leg 1 = Leg 2 = x
To find the length of the hypotenuse (which we'll call "h"), we can use the Pythagorean theorem as follows:
x² + x² = h²
Simplifying this equation, we get:
2x² = h²
To solve for h, we need to take the square root of both sides of the equation:
√(2x²) = √(h²)
√2 * x = h
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Let g(t)=t^4 ct^2 dg(t)=t 4 ct 2 d, where c and d are real constants. what can we say about the critical points of g?
Answer: The critical points of g(t) occur at t = ±sqrt(-d/2) if d < 0. If d ≥ 0, then dg(t)/dt is always greater than or equal to zero, so g(t) has no critical points.
Step-by-step explanation:
To find the critical points of g(t), we need to find the values of t where the derivative dg(t)/dt is equal to zero or does not exist.
Using the given information, we have:
dg(t)/dt = 4ct^3 + 2dct
Setting this equal to zero, we get:
4ct^3 + 2dct = 0
Dividing both sides by 2ct, we get:
2t^2 + d = 0
Solving for t, we get:
t = ±sqrt(-d/2)
Therefore, the critical points of g(t) occur at t = ±sqrt(-d/2) if d < 0. If d ≥ 0, then dg(t)/dt is always greater than or equal to zero, so g(t) has no critical points.
Note that we also need to assume that c is nonzero, since if c = 0, then dg(t)/dt = 0 for all values of t and g(t) is not differentiable.
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i’ll give brainliest help
Answer:
This will be letter j). 1,767.1 in 3
Step-by-step explanation:this is the closest estimate to the cubic inch plz brainliest
An academic senate has 15 members. It will form a special committee of 5 members. In how many different ways
can you form this committee?
There are 3,003 different ways to form the committee.
To calculate the number of different ways to form the committee, we can use the concept of combinations. The number of combinations of n objects taken r at a time is given by the formula:
C(n, r) = n! / (r!(n-r)!)
In this case, we have 15 members in the academic senate and we want to form a committee of 5 members. Plugging the values into the formula, we have:
C(15, 5) = 15! / (5!(15-5)!)
= 15! / (5! * 10!)
= (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)
= 3,003
Therefore, there are 3,003 different ways to form the committee of 5 members from the 15 members of the academic senate.
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The peak current passing through an inductor is 2. 0 aa. part a what is the peak current if the peak emf e0e0 is doubled?
Answer:
22
I remember this question in school
Let f = (–2, 4), (–1, 2), (0, 0), (1, –2), (2, –5). Let g = (–3, 3), (–1, 1), (0, –3), (1, –4), (3, –6). Determine:
a) f + g
b) g - f
c) f + f
d) g - g
The operations results are:
a) f + g = (–5, 7), (–2, 3), (0, –3), (2, –6), (5, –11)
b) g - f = (–1, –1), (0, –1), (0, –3), (0, –2), (1, –1)
c) f + f = (–4, 8), (–2, 4), (0, 0), (2, –4), (4, –10)
d) g - g = (0, 0), (0, 0), (0, 0), (0, 0), (0, 0)
To perform the operations on the given sets of points, we will add or subtract the corresponding coordinates of each point.
a) f + g:
To find f + g, we add the coordinates of each point:
f + g = (–2 + –3, 4 + 3), (–1 + –1, 2 + 1), (0 + 0, 0 + –3), (1 + 1, –2 + –4), (2 + 3, –5 + –6)
= (–5, 7), (–2, 3), (0, –3), (2, –6), (5, –11)
b) g - f:
To find g - f, we subtract the coordinates of each point:
g - f = (–3 - –2, 3 - 4), (–1 - –1, 1 - 2), (0 - 0, –3 - 0), (1 - 1, –4 - –2), (3 - 2, –6 - –5)
= (–1, –1), (0, –1), (0, –3), (0, –2), (1, –1)
c) f + f:
To find f + f, we add the coordinates of each point within f:
f + f = (–2 + –2, 4 + 4), (–1 + –1, 2 + 2), (0 + 0, 0 + 0), (1 + 1, –2 + –2), (2 + 2, –5 + –5)
= (–4, 8), (–2, 4), (0, 0), (2, –4), (4, –10)
d) g - g:
To find g - g, we subtract the coordinates of each point within g:
g - g = (–3 - –3, 3 - 3), (–1 - –1, 1 - 1), (0 - 0, –3 - –3), (1 - 1, –4 - –4), (3 - 3, –6 - –6)
= (0, 0), (0, 0), (0, 0), (0, 0), (0, 0)
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Gonzalez Manufacturing borrowed $21000. Part of the money was borrowed at 10%, part at 12%, and part at 14%. The total amount borrowed at 10% and 12%
was twice the amount borrowed at 14%. Find the amount borrowed at each rate if the annual interest was $2580
How much money was borrowed at 10%?
How much money was borrowed at 12%?
How much money was borrowed at 14%?
Answer:
10% — $550012% — $700014% — $8500Step-by-step explanation:
You want to know the amount borrowed at 10%, 12%, and 14% if the total borrowed was $21000, the total interest was $2580, and the total of amounts borrowed at 10% and 14% was double the amount borrowed at 12%.
EquationsThe relations give rise to three equations. If we let x, y, z represent the respective amounts borrowed at 10%, 12%, and 14%, we have ...
x + y + z = 21000 . . . . . . total borrowed
0.10x +0.12y +0.14z = 2580 . . . . . . total interest
x + y = 2z . . . . . . . . . . . relationship between amounts
Writing the last equation as ...
x -2y +z = 0
we can formulate the problem as a matrix equation and use a solver to find the solution. We have done that in the attachment. It tells us the amounts borrowed are ...
10% — $550012% — $700014% — $8500__
Additional comment
Recognizing that the amount at 12% is 1/3 of the total, we can use that fact to rewrite the other two equations. The interest on the $7000 at 12% is $840, so we have ...
x + y = 140000.10x +0.14y = 1740These two equations have the solution shown above. (It is usually convenient to solve them by substituting for x in the second equation.)
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Find the area of rectangle ABCD.
Round to the nearest hundredth if necessary.
Show work.
The area of the rectangle ABCD is 26 square units
Finding the area of rectangle ABCD.From the question, we have the following parameters that can be used in our computation:
The rectangle
The side lengths of the rectangles are calcualated as
Length 1 = √(3² + 2²) = √13
Length 2 = √(6² + 4²) = √52
The area of rectangle ABCD is then calculated as
Area = Length 1 * Length 2
substitute the known values in the above equation, so, we have the following representation
Area = √13 * √52
Evaluate
Area = 26
Hence, the area of the rectangle ABCD is 26 square units
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Answer:
26 square units
Step-by-step explanation:
You want the area of the rectangle with vertices A(4, 1), B(0, 7), C(3, 9) and D(7, 3).
Pick's theoremThe area of a polygon whose vertices are grid points can be found using the formula ...
A = i + b/2 -1
where i is the number of grid points inside the polygon, and b is the number of grid points on the boundary.
ApplicationIn addition to the given vertices, the points (2, 4) and (5, 6) lie on the boundary, for a total of 6 boundary points.
Counting the points on the graph that lie completely within the boundary of the rectangle, we see there are 24.
The area is ...
A = 24 +6/2 -1 = 26 . . . . square units
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