what is pi and why do we need it
Answer:
See below
Step-by-step explanation:
π, pronounced as pi is the ratio between 2πr which is circumference to 2r which is diameter.
In word, π is circumference/diameter which has exact value of 3.14159... and it is also an irrational number too.
π is often used to be defined as 3, 3.14 or 22/7 [Keep in mind, these numbers are only approximation.] in some fields. In trigonometry, π is mostly used to refer as π radians or π rad which is equivalent to 180°.
Why do we need it? Because it’s useful in a field that requires rotation. If you notice, figure with circular base will always have π with it, the volume is an example.
In calculus, you need π to do solid of revolution method which is:
\(\displaystyle \large{V =\pi \int\limits^a_b {[f(x)]^2} \ dx }\\\\\displaystyle \large{V = \pi \int\limits^a_b {[g(y)]^2} \ dy}\)
In trigonometry, you need it for measurement/angle.
So anything that’s related to revolution, rotation or related to circle must require π at least.
In general life, you do not use it but this is mostly applied in engineering field and anything related to science that involves with circle or revolve.
Let me know if you have any questions!
a student says that the sum of two repeating decimals must be a repeating decimal. how should you respond?
it is not a universal rule that the sum of two repeating decimals will always be a repeating decimal. There are instances where their sum can result in a terminating decimal or an integer, as demonstrated in the examples above.
It is not always true that the sum of two repeating decimals must be a repeating decimal.
There are cases where their sum can result in a terminating decimal or even an integer.
Let me provide you with a step-by-step explanation:
Firstly, understand what a repeating decimal is. A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point, such as 0.333... or 0.272727...
Now, let's consider two repeating decimals as examples: 0.333... and 0.666...
Add these two repeating decimals together:
0.333...
+ 0.666...
---------
= 0.999...
Observe that the result, 0.999..., is also a repeating decimal. In fact, it is mathematically equal to the integer 1. This demonstrates that the sum of two repeating decimals can be an integer.
Let's consider another example: 0.333... and 0.467467...
Add these two repeating decimals together:
0.333...
+ 0.467467...
------------
= 0.800467...
In this case, the sum of the two repeating decimals is a mixed decimal with a terminating part (0.800) and a repeating part (467).
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How many solutions exist in the given expression?
x+1/2y=1
20x+10y = 6
O infinite number of solutions exist
O no solution exists
O one unique solution exists
The given system of equations, x + (1/2)y = 1 and 20x + 10y = 6, has no solution. The equations represent parallel lines that do not intersect, indicating that there are no common points of intersection.
To determine the number of solutions in the given system of equations, we can analyze the coefficients of the variables. The first equation can be simplified as 2x + y = 2, while the second equation can be simplified as 20x + 10y = 6. By comparing the coefficients, we can see that the second equation is obtained by multiplying the first equation by 10. This indicates that the two equations represent the same line and are dependent.
When two equations represent the same line, they intersect at infinitely many points, which means there are an infinite number of solutions. However, in this case, the two equations have different right-hand side constants (1 and 6), indicating that the lines are parallel and will never intersect. Therefore, there are no common points of intersection and no solution exists.
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Write down the gradient and y intercept of each of these lines y=2x
Answer:
\(gradient = 2 \\ y - intercept = 0\)
The gradient of this line is 2 and the y-intercept is (0, 0)
Direction: Match the exponential notation in Column A to its
equivalent in column B.
Column A
Column B
1.3.
2.54
3.82
• B. 243
C. 512
4.94
. D. 625
5.2.
E. 1.024
Answer:
446565688987888888 ti ifyx
You are working with the following selection of a spreadsheet: a b 1 customer address 2 sally stewart 9912 school st. North wales, pa 19454 3 lorenzo price 8621 glendale dr. Burlington, ma 01803 4 stella moss 372 w. Addison street brandon, fl 33510 5 paul casey 9069 e. Brickyard road chattanooga, tn 37421 in order to extract the five-digit postal code from brandon, fl, what is the correct function?
The correct function that gives the right syntax for the given data analysis is; =RIGHT(B3,5)
How to Interpret Data Cleaning Analysis?Data cleaning is defined as the process of fixing or removing data that are incorrect, incorrectly formatted, duplicate, corrupted, or even incomplete data that exists within a dataset.
Now, when we combine multiple data sources, what it means is that there could be many opportunities for the data to be duplicated or mislabeled.
Now, from the question, we can see the given data of the spreadsheet with customer names and address and as such, we can easily say that the correct syntax is =RIGHT(B3,5). This is because the RIGHT Function usually returns a set number of characters from the right side of a text string.
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Which expression is equivalent to 7h^2-252k^2?
A. 7(h-6k)^2
B. 7(h-18k)^2
C. 7(h-6k)(h+6k)
D. None of these
Answer:
c
Step-by-step explanation:
252 = 7 *36
36 = 6 *6 = 6²
a² -b² = (a + b)(a - b)
7h² - 252k² = 7(h² - 36k²)
= 7(h² - [6k]² )
= 7(h +6k)(h - 6k)
Answer:
cccccccccccccccc
Step-by-step explanation:
y = X + 3 can someone please tell me I beg of youuu
Based on the given equation y = X + 3, the solution is X = y - 3.
How do we solve the equation?First, we use the property of equality, which allows us to perform the same operation on both sides of the equation to solve for X.
Here we subtract 3 from both sides of the equation as follows:
Y-3 = X + 3-3
Then we simplify the right-hand side:
Y-3 = X
So X = Y - 3
Therefore the equation y = X + 3 is X = Y - 3.
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The licensed practitioner has ordered gemcitabine 400 mg/m^2 IV for a patient whose BSA is 0.47 m^2. You have on hand a 200 mg vial of gemcitabine for injection that contains 38 mg per mL. How much medication should this patient receive?
Answer:
4.95 mL
Step-by-step explanation:
Since we have 400 mg/m² of gemcitabine for a patient whose BSA is 0.47 m², the mass of drug required for the patient is thus m = 400 mg/m² × 0.47 m² = 188 mg.
Also, since 200 mg vial of gemcitabine for injection that contains 38 mg per mL, so the concentration of gemcitabine is 38 mg/mL.
Since concentration = mass/volume, and
volume = mass/concentration,
the volume of gemcitabine injection required is
V = mass of gemcitabine/concentration of gemcitabine in injection
V = 188 mg/38 mg/mL
V = 4.95 mL
The Center for Disease Control and Prevention reports that 25% of bay boys 6-8 months old in the United States weigh more than 20 pounds. A sample of 16 babies is studied.
Okay, it seems like you want to analyze a sample of 16 babies based on their weight.
The information you provided states that the Center for Disease Control and Prevention reports that 25% of baby boys aged 6-8 months in the United States weigh more than 20 pounds.
However, you haven't mentioned the specific question or analysis you want to perform on the sample. Could you please clarify what you would like to know or do with the given information?
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Solve by ELIMINATION
-3x - y = -11 x - 4y = -18
Steph makes 90 % 90%90, percent of the free throws she attempts. She is going to shoot 3 33 free throws. Assume that the results of free throws are independent from each other. Let X XX represent the number of free throws she makes. Find the probability that Steph makes exactly 1 11 of the 3 33 free throws. You may round your answer to the nearest hundredth. P ( X = 1 ) =
Using the binomial distribution, it is found that there is a 0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.
For each free throw, there are only two possible outcomes, either he makes it, or he misses it. The results of free throws are independent from each other, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
He makes 90% of the free throws, hence \(p = 0.9\).He is going to shoot 3 free throws, hence \(n = 3\).The probability that he makes exactly 1 is P(X = 1), hence:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 1) = C_{3,1}.(0.9)^{1}.(0.1)^{2} = 0.027\)
0.027 = 2.7% probability that he makes exactly 1 of the 3 free throws.
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Answer:
0.03
Step-by-step explanation:
I just did it on Khan
how do i solve this .75x4 – 8 = -12
2 1/2t = 11
what is t
There are 2 gyms. One, Buff Billy's, has a joining cost
of $80 and charges $25 a month. The other,
Shredded Eddie's, has no joining cost but charges
$35 a month. At what month are both gyms the same
total cost?
In linear equation, the intersection at coordinate (9, 315).
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Gym one:
f(x) =80 x + 25
Gym two:
g(x) = 35x (+ 0 [since there was no joining fee])
The first month is easy.
Gym one's cost is just the joining fee plus the one month of membership fee. Or...
105 = 80(1) + 25
Gym two's cost is just that first month's membership fee. Or...
35 = 35(1) + 0
then second month
[f(x) = 185 = 80(2)+25
g(x) = 70 = 35(2)],
then a tenth month [
f(x) = 825 = 80(10) + 25;
g(x) = 350 = 35(10)]
and that gym one's cost exceeded the cost of gym two,
back one month and found the answer.
By month nine, both gyms had equalized at $315.
the intersection at coordinate (9, 315).
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the lowest temperature is usually around 3^\circ c3 ∘ c3, degrees, c, and the highest temperature is around 18^\circ c18 ∘ c18, degrees, c. the temperature is typically halfway between the daily high and daily low at both 10\text{ a.m.}10 a.m.10, start text, space, a, point, m, point, end text and 10\text{ p.m.}10 p.m.10, start text, space, p, point, m, point, end text, and the highest temperatures are in the afternoon.
The lowest temperature is usually around 3 degrees Celsius (3°C), and the highest temperature is around 18 degrees Celsius (18°C).
The temperature is typically halfway between the daily high and daily low at both 10 a.m. and 10 p.m. Additionally, the highest temperatures are usually in the afternoon.
During the morning, the sun starts to warm up the atmosphere, causing the temperature to rise from its lowest point. By 10 a.m., the temperature has increased but is not yet at its peak.
Similarly, during the evening, the sun starts to set, resulting in a gradual decrease in temperature from its highest point. By 10 p.m., the temperature has dropped but is not yet at its lowest point
The temperature at 10 a.m. and 10 p.m. is typically halfway between the daily high and daily low because it represents the transition period between the warmest and coolest parts of the day.
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for each multiplication sentence, Write two related division sentences.
1. 1/6 x 1/3 = 1/18
2. 2 2/5 x 4 1/2 = 10 4/5
3. 5 5/8 x 1 1/5 x 1 1/5 = 6 3/4
100 POINTS IF YOU CAN SOLVE
solve using quadratic formula and include steps
2x^2 + 6x - 3 = 0
Answer:
x = (-3+√15)/2 or, x = (-3-√15)/2
Step-by-step explanation:
2x²+6x-3=0
Standard quadratic formula,
ax²+bx+c = 0
where,
x =(-b±\(\sqrt{b^{2}-4ac }\))/2a ...............................(i)
Here,
a = 2
b = 6
c = -3
Putting the values in equation(i), we get,
x = (-6±\(\sqrt{6^{2} -4.2.(-3)}\))/2.2
=(-6 ± √60)/4
=(-6 ± 2√15)/4
= (-3 ± √15)/2
Therefore, x = (-3+√15)/2 or x = (-3-√15)/2 :)
The volume of a spherical balloon is 3054 cm^3. Find the surface area of the balloon to the nearest whole number.
15. Davis wants to pour 5 gallons of punch into
gallon jugs How many jugs will he need?
81
(А)
2
NI
(В)
BE
2
© 10
D 15
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Davis wants to pour 5 gallons of punch into ½ gallon jugs How many jugs will he need?
A. 2½
B. 5½
C. 10
D. 15
Answer:
Number of jugs = 10
Davis will need 10 jugs to pour 5 gallons of punch into ½ gallon jugs.
Step-by-step explanation:
David has 5 gallons of punch that he wants to pour into jugs.
The capacity of 1 jug is ½ gallon.
The required number of jugs may be found as
Number of jugs = gallons of punch/capacity of jug
For the given case, we have
Gallons of punch = 5
capacity of jug (in gallons) = ½ = 0.5
So, the required number of jugs is,
Number of jugs = 5/½
Number of jugs = 5/0.5
Number of jugs = 10
Therefore, Davis will need 10 jugs to pour 5 gallons of punch into ½ gallon jugs.
2. List one proportion that is correct and one that is incorrect for AABC and ARST.
<A ? <B 61° <C 90° <R 29° <T 90° <S ?
Correct proportion for AABC: <A <B <C
Incorrect proportion for ARST: <R <T <S
To determine a correct proportion for AABC and an incorrect proportion for ARST, we need to analyze the given information.
1. AABC:
From the given information, we know that <C is a right angle (90°) and <B is 61°. Since the sum of angles in a triangle is always 180°, we can find <A by subtracting the known angles from 180°.
<A = 180° - <C - <B
<A = 180° - 90° - 61°
<A = 29°
Therefore, the correct proportion for AABC is:
<A <B <C
29° <B 61° <C
2. ARST:
The given information states that <R is 29° and <T is a right angle (90°). To find <S, we subtract the known angles from 180° (since it's a triangle).
<S = 180° - <R - <T
<S = 180° - 29° - 90°
<S = 61°
Therefore, the incorrect proportion for ARST is:
<R <T <S
29° <T 61° <S
In conclusion, the correct proportion for AABC is <A <B <C (29° <B 61° <C), while the incorrect proportion for ARST is <R <T <S (29° <T 61° <S).
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Stacy's mom is backing treats for Stacy's birthday she has 9 eggs to use for this purpose a batch of cookies use one egg and brownies use 2 eggs list three possible combinations of cookies and brownies Stacy's mom could make for the party?
Answer:
There you go!!
Step-by-step explanation:
mark me brainliest!!
\(\large\underline{\underline{\maltese{\orange{\pmb{\sf{\: Explanation :-}}}}}}\)
There can be two combinations by which stacy mom make snacks
More brownies and less cookiesMore cookies nd less brownies\(9 \div 2 = 4 \\ \sf remainder = 1\)
So, 4 batch of brownies and 1 cookie
and,\(9 - 7 = 5\)
7 batch of cookies and one batch of brownies
Some more possibilities can be there, such as
2 batch of brownies and 5 batch of cookies.3 batch of brownies and 3 batch of cookies.your quidditch league has 5 teams. you will play a tournament next week in which every team will play every other team once. each team can play at most one match each day, but there is plenty of time in the day for multiple matches. what is the fewest number of days over which the tournament can take place?
The fewest number of days over which the tournament can take place is 5 days.
How to calculate the number of days?As each team plays with other team Once and we have total 5 teams so number of matches will be (4+3+2+1)
Counted as team 1 plays with all other teams = 4 matches
Team 2 plays with team 3,4,5 =3 matches
Team 3 play with team 4,5=2 match
And the last match is between team 4 and team5
Total match = 10 and can be played two matches per day:
Number of days = 10/2
= 5 days.
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First to answer gets brainliest!
Answer:
it is the first one
Step-by-step explanation:
Jake has a can that contains 80% orange
juice and the rest water. The can has 1 liter
of water.
Write an equation using one variable that
can be used to find the total number of
liters of orange juice and water in the can.
How many liters of orange juice are
present in the can?
Answer:
equation 0.8C+1=C
4 liters of orange juice
Step-by-step explanation:
C for can
0.8 as 80%
1 for liters of water
0.8C+1=C
subtract 0.8C
1=0.2C
if 1 liter=20% of a can then 80% is 4 liters
Hope this helps! Plz award Brainliest : )
prove it =
(cosA /cotA = sinA )
Answer:
LHS=
b/h ÷b/p
b/h × p/b
p/h =Sin A
RHS proved
Step-by-step explanation:
Sin= p/h
cos= b/h
cot= b/p
in the second step we did reciprocal formula where ÷ sign will turn into × sign and b/h will turn into p/h. now we can do cancel b and b
now the answer is p/h
Help I’m struggling please respond fast I have 5 m
Answer:
whats your question
Step-by-step explanation:
what value of n make this equation true 12(n+6)=96
Answer:
2
Step-by-step explanation:
(6+2)x 12 =96
Answer:
2
Step-by-step explanation:
12(2+6)=96
12×8=96
I need 20 characters so yeah. Have a great day.
josue earned $56.25 fixing a coding issue with a popular website.it took him a total of 4.5 hours to fix the issue.The equation 4.5x=56.25 can be used to find Josue hourly rate.What is Josue hourly rate?
You are planning a trip to Disney World in Florida. You estimate for week at Disney World, you will need $1,600.00 (This includes Airfare, room and board, daily expenses, and travel). You save for 5 months and your monthly gross salary is $1,675.00. Given that Social Security is 6.2% of your biweekly income, Medicare is 1.45% of your biweekly income, your monthly expenses are $975.23, and you pay State and Federal taxes in the amount of $35.00 and $75.51 respectively biweekly, how much will you have saved up and will you have saved enough to visit Disney World in December? Round all your answers to the nearest cent. a. $1,508.25; no c. $1,753.05; yes b. $1,523.43; no d. $1,788.06; yes
Answer:
c. $1,753.05; yes
Step-by-step explanation:
All calculations below are done on a monthly basis.
Gross salary in 1 month: $1675
Deduct 6.2% from gross salary:
0.062 * $1675 = $103.85
$1675 - $103.85 = $1571.15
Deduct 1.45% from gross salary:
0.0145 * 1675 = $24.29
$1571.15 - $24.29 = $1546.86
Deduct $975.23:
$1546.86 - $975.23 = $571.63
The expenses of $35 and $75.51 are biweekly. Since we are calculating per month, we multiply each of the expenses by 2.
Deduct 2($35) and 2($75.51):
$571.63 - $70 - $151.02 = $350.61
The amount saved per month is $350.61.
In 5 months, the amount saved is 5 * $350.61 = $1753.05
$1753.05 is greater than $1,600.
Answer: c. $1,753.05; yes