Answers
Answer:
Remember that the area of a square of sidelength L is:
A = L^2
And the area of a circle of diameter D is:
A = pi*(D/2)^2
If we inscribe a square in a circle, we will get four segments, like the ones shaded in the image below:
Notice that the diameter of the circle will be equal to the diagonal of the square.
And the diagonal of a square of side length L is:
d = √(2)*L
knowing that the side length of our square is 6 inches, the diameter of the circle will be:
D = √2*6in
Now, the total area of the four shaded parts will be equal to the difference between the area of the circle and the area of the square.
The area of the circle is:
A = pi*(√2*6in/2)^2 = (pi/2)*36in^2
The area of the square is:
A' = (6in)^2 = 36in^2
The difference is:
A - A' = (pi/2)*36in^2 - 36in^2 = (pi/2 - 1)*36in^2
And there are 4 of these segments, then the area of every single one is one-fourth of that:
a = (1/4)*(pi/2 - 1)*36in^2 = (pi/2 - 1)*9 in^2
The area of each segment is:
a = (pi/2 - 1)*9 in^2
if we replace pi by 3.14, the exact area will be:
a = (3.14/2 - 1)*9in^2 = 5.13 in^2
Related Questions
in a survey of 100 people, 60 like farming and 65 like civil service. find the number of people who likes farming as well as civil service. also find out how many people like only civil war
Answers
Let
A=set of people like farmingB=set of people like civil service A[tex]\cup[/tex] B =Total peopleA[tex]\cap[/tex]B=People like bothWe know
[tex]\boxed{\sf n(A\cup B)=n(A)+n(B)-n(A\cap B)}[/tex]
[tex]\\ \sf\longmapsto n(A\cap B)=n(A)+n(B)-n(A\cup B)[/tex]
[tex]\\ \sf\longmapsto n(A\cap B)=60+65-100[/tex]
[tex]\\ \sf\longmapsto n(A\cap B)=125-100[/tex]
[tex]\\ \sf\longmapsto n(A\cap B)=25[/tex]
For a beverage, Lisa mixes cups of lemonade to cups of ice tea in a ratio of 2:5. Which of the following best describes the amount of lemonade to iced tea
Answers
Answer:
lemonade is 4:10 to ice or .4:1
Step-by-step explanation:
Assuming lemonade is 2 and tea is 5, you can use a table or multiply both reciprocals by 2 so 2x2 and 2x5 = 4:10. then if you want to see how much is in just once cup of tea divide by ten to each for the product of .4:1
Answer: For every 2 cups of lemonade, there are 5 cups of iced tea.
if the ratio is 2:5 then for every 2 cups of lemonade there are 5 cups of tea.
it is just another way of saying the ratio
15) The sum of one-fourth, one-ninth and one- third of a number is 25. Find the number.
Answers
Answer:
Step-by-step explanation:
(1/4 + 1/9 + 1/3)x = 25.
x = 36
Answer:
Let the number be x
(1/4 + 1/9 + 1/3) * x = 25
25/36 * x = 25
25x = 25*36
x = 25*36/25
x = 36
Step-by-step explanation:
Felix is now six times as old as Debbie. In twelve years time Felix will be two times as old as Debbie. How old are they
Answers
Step-by-step explanation:
let debbie be x years
let felix be 6x years
in 12 years felix will be 2x older than debbie
do the calc
show the work please and thank you
Answers
Answer:
Option a, 13
if you solve it, you get 13 as the answer
³√(5x-1)=4
or, 5x-1=64
or, 5x=65
or, x=13
1. Calculate the slope of a line going trough A (-4,3) and B (0,6)
2. Calculate the slope of a line with a run of 3 and a rise of 9
3. Calculate the equation if two points are (1,6) and (5,0)
Answers
Write a function rule for table
Is it a, b, c or d?
Answers
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (2, 5 ) ← 2 ordered pairs from the table
m = [tex]\frac{5-4}{2-1}[/tex] = [tex]\frac{1}{1}[/tex] = 1
The line crosses the y- axis at (0, 3 ) → c = 3
y = x + 3 ← equation of line → A
what is the point-slope equation of a line with slope-4 that contains the point (-2 7)\
Answers
Answer:
y - 7 = -4 (x + 2)
Step-by-step explanation:
y - 7 = -4 (x + 2)
Pleeeeeeeeaaaaaaaaaaaasse help 71 points!!!!!!!!!
Answers
Answer:
54
Step-by-step explanation:
The perimeter is the sum of the outside
P = 8+4+5+10+( 4+10) +(8+5)
P = 54
If mn, solve for x.
(3x + 9) (x + 21)
Answers
2
3x. + 63x + 9x + 189
Step-by-step explanation:
Use distributive law, in other words multiply the first bracket terms by the second bracket terms
mountains poem in nepali for class 7
Answers
Step-by-step explanation:
म नजन्मिदै विधवा भएकी हिमाल
खै! किन हो मेरा यी हेर्ने नयनले उनलाइ
अझै पनि दिन र रातमा
सेतै लुगा पहिरिएकी देख्छ
अचम्म लाग्छ मलाइ पहिरिएकी सेतो लुगा माथि
मुनालले पाइला टेके पनि विष्ठा गरे पनि कहिल्यै
मैलो हुदैन सेतो लुगाको वास्तविक रङ
उत्तिकै सेतो देख्छु म
निर्जीव वस्तु भएनी हिमाललाइ
सजीव मनुस्यको जस्तै चोटको कल्पना गरेको छु मैले
किनकी चोटै चोटले ग्रसित भएकी उनी आजभोली
अपाङ्गको सिकार बनिसकेकी छिन
उनलाइ अन्धो भन्छु म किनकी उनी आँखा देख्दैनन
आँखा नदेखे पनि अरु कसैलाइ सुम्सुम्याउन समेत सक्दैनन
तर पनि कस्तुरी, डाफे,मुनाल,घोरल,चितुवा आदि जनावरहरुको
सहारा दिने आश्रय स्थल भएर उभिएकी छिन, के कम छिन र?
जमिन भित्र उनको खुट्टा गाडिएर होला
खुट्टाको दृश्य मैले अझै पनि देख्न पाएको छैन
कस्तो होला है! हिमालको खुट्टा ? सोचिरहन्छु म
सायद खुट्टा नै छैन र पो कहिल्यै पनि हिड्डुल गर्न सक्दैनन कि?
जब कुनै समयमा चुचुरोमा हावा बहन थाल्यो
एकदिन सेतो कपाल धरतीमा हाम फालेर
नदिहरु बढ्न थाले तर उहीँ बहेको हावाले
हिमालको श्रवण गर्ने कानको जाली
नै फुटाइदिएछ त्यही भएर म भन्छु
हिमाललाइ बहिरो पनि हुनुहुन्छ तपाईं
सधै टोलाएर बसेकी देख्छु म
रोजगारी भन्ने कुरा त उहीँ हो हिमाललाइ
बिहानीपख देखि सन्ध्या काल सम्म
प्रकृतिले बसिबसी ऐना टल्काउने
पदभार ग्रहण गराइदिएको छ जब घाम
झुल्किन्छ उनी अस्ताउन्जेल सम्म ऐना टल्काइरहन्छिन्
त्यसैले म भन्छु हिमाललाइ बिधवा भएर के भो त
खान लाउनको लागि रोजगारी मिलेकै छ क्यारे !
Sequence Problem Below
Answers
Answer:
[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\dddddd \displaystyle \Large \boldsymbol{} t_1=\boxed{5} \\\\d=\boxed{-4} \\\\t_n=\boxed{9-4n}[/tex]
Step-by-step explanation:
[tex]\displaystyle\large \boldsymbol{Rule: t_n=S_{n}-S_{n-1}} \\\\\\S_n=7n-2n^2 \ \ \ \ then \\\\\Longrightarrow S_{n-1}=7(n-1)-2(n-1)^2 =7n-7-2n^2+4n-2 \\\\then \\\\\\S_{n}-S_{n-1}=7n\!\!\!\!\!\!\diagup-2n^2\!\!\!\!\!\!\diagup-7n\!\!\!\!\!\!\diagup+7+2n^2\!\!\!\!\!\!\diagup-4n+2=9-4n \\\\t_n=9-4n => t_1=5\\\\d=t_2-t_{1}=1-5=-4[/tex]
marked price of an item is 4000, what will be it's selling price having 20% discount and 10% vat.
Answers
Answer:
I HOPE IT WILL HELP
EXPLANATION IS IN THE PHOTO .
Multiplying the original value by the discounted percent, the percent taxed but add one to it.
(4,000)(.80)(1+10/100)= 3,520
4000 is the original value
.80 is the value of the item with 20% off
1.1 gives value after tax, adding the one allows you to see the value of the item after tax.
PLEASE HELP!!
BRAINLYEST TOO 1st
Answers
9514 1404 393
Answer:
A, C
Step-by-step explanation:
Any table with no repeated x-values is a relation that is a function.
whats the area in square inches
Answers
Answer:
Area of triangle =1/2b×h
1/2×10×8.7
=44 square inches
Answer:
44
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
where b is the base and h is the height
A = 1/2 (10) (8.7)
A= 43.5
Rounding to the nearest whole number
A = 44
The half life of a substance is 30 days. If there are 4.5 grams to start with, how much will be left after 23 days? Round to the nearest tenth of a gram. Be sure to label your answer.
Answers
65.4Step-by-step explanation:KHAN
Important formula:
[tex]N_t = N_0 (1/2)^\frac{t}{t_{1/2}}[/tex]
Here, you are trying to find Nt and you have N0 = 4.5g, t = 23 days, t1/2 = 30 days. Plug the values in and you should get 2.7g left after 23 days.
How to find interquartilte range
Answers
============================================================
Explanation:
Each x represents a data point location.
So, for example, having an x over 60 means 60 is part of the set.
The set of values we're working with is
{59,60,61,63,63,64,66,68,70,71,71,73}
The repeated values are due to the fact we have a stack of two 'x' markers, and they occur at 63 and 71.
To find the IQR (interquartile range), we'll first need to find the median of this set. That's the middle most value.
Count out the number of values to find that there are n = 12 values.
The list splits into two halves that are n/2 = 12/2 = 6 items each
Between slots 6 and 7 is where the median is located.
The value in slot 6 is 64 and the value in slot 7 is 66. Average those two items to get (64+66)/2 = 65
The median is 65
---------------------------------
Next, we'll form two groups L and U such that
L = set of items lower than the median
U = set of items larger than the median
Because n is even, we simply just break the original set into two equal groups (6 items each)
L = {59,60,61,63,63,64}
U = {66,68,70,71,71,73}
The values of Q1 and Q3 represent the medians of L and U in that order.
The median of set L is (61+63)/2 = 62, so Q1 = 62
The median of set U is (70+71)/2 = 70.5, which is Q3
-----------------------------------
To summarize everything so far, we have found
Q1 = 62Q3 = 70.5Subtract those items to get the IQR
IQR = Q3 - Q1
IQR = 70.5 - 62
IQR = 8.5 which points us to choice C as the final answer.
What are the solutions to the system of equations?
{y=2x²−6x+3
{y=x−2
Answers
Answer:
x = 1, y = −1
x = 5/2, y = 1/2
Step-by-step explanation:
From the question given above, the following data were obtained:
y = 2x² − 6x + 3 ........ (1)
y = x − 2 ...... (2)
We can obtain the solutions to the equation as follow:
y = 2x² − 6x + 3 ........ (1)
y = x − 2 ...... (2)
Substitute the value of y in equation 2 into equation 1
y = 2x² − 6x + 3
y = x − 2
2x² − 6x + 3 = x − 2
Rearrange
2x² − 6x − x + 3 + 2 = 0
2x² − 7x + 5 = 0
Solve by factorization
Obtain the product of 2x² and 5. The result is 10x².
Find two factors of 10x² such that their sum will result to −7x.
The factors are −2x and −5x.
Replace −7x in the equation above with −2x and −5x as shown below:
2x² − 2x − 5x + 5 = 0
2x(x − 1) − 5(x − 1) = 0
(x − 1)(2x − 5) = 0
x − 1 = 0 or 2x − 5 = 0
x = 1 or 2x = 5
x = 1 or x = 5/2
Substitute the value of x into equation 2 to obtain y
y = x − 2
x = 1
y = 1 − 2
y = −1
x = 5/2
y = x − 2
y = 5/2 − 2
y = (5 − 4)/2
y = 1/2
SUMMARY:
x = 1, y = −1
x = 5/2, y = 1/2
square root of 800 to the nearest thousandth
Answers
Answer:
28.284
Step-by-step explanation:
(solving rate problems). Michelle can
complete a
landscaping job in 6
days and Danielle
can complete the
same job in 4 days.
Working together, in
how many days
could they complete
the job
Answers
They could complete the job together in 2.4 days
The known parameters are;
The number of days it would take Michelle to complete the landscaping job = 6 days
The number of days it would take Danielle to complete the landscaping job = 4 days
The unknown parameter;
The number of days can the job be completed if they work together
The process of finding the solution;
The rate at which Michelle works = 1/6 of the landscaping work per day
The rate at which Danielle works = 1/4 of the landscaping work per day
Method;
Find their combined work rate, from which the time would take them to complete the job together can be found
Let, C, represent their combined work rate
Therefore, we have;
C = (1/6 + 1/4) = 5/12 of the landscaping (work) job/(per) day
The number of days they could complete the, 1, job = 1 job(work)/(5/12 (work)job/day) = 12/5 days = 2.4 days
∴ The number of days they could complete the job together = 2.4 days.
Learn more about unit rate here;
https://brainly.com/question/19605901
solve for θ.
sin(74) = cos(θ)
1. 6°
2. 74°
3. 36°
4. 16°
Answers
Sin74 = Cos16
cause 16 + 74 = 90
Whenever the sum of two angles is equal with 90, the Sin of one is equal with the Cos of the other like :
Sin(30) = Cos(60)
and also
Tan(30) = Cot(60)
Answer:
16
Step-by-step explanation:
sin(74) = cos(x)
sin(x)=cos(90-x)
sin (74) = cos(90-74)
sin 74 = cos( 16)
Find the missing term and the missing coefficient.
(6a −_)5a =_a2 − 35a
Answers
Answer:
[tex](6a-7)5a=30a^2-35a[/tex]
Step-by-step explanation:
Message if you want a detailed explanation.
A rectangular field is to be fenced off, and then divided in two by a fence running parallel to one of the sides. If 996 meters of fencing can be used, find the dimensions of the field that will maximize the total area, and then find the maximum area. List the smaller dimension first.
Answers
Solution :
Maximize, S = xy
subject to 2x + 2y = 996
So,
2x + 2y = 996
2(x + y) = 996
x + y = 498
y = 498 - x
Therefore,
S = x (498 - x)
S = 498x - [tex]x^2[/tex]
S = [tex]-x^2 + 498x[/tex]
[tex]$S = -(x^2-498x + 249^2) + 300^2$[/tex]
[tex]$S= -(x-249)^2 + 249^2$[/tex]
S = x (498 - x)
S = 498x - [tex]x^2[/tex]
[tex]$\frac{dS}{dx}= 498 - 2x$[/tex]
[tex]$\frac{dS}{dx}= 0$[/tex]
498 - 2x = 0
2x = 498
x = 249
∴ y = 498 - x
y = 498 - 249
= 249
Answer:
A = 249 x 249 = 62001 square meter.
Side is L = 249 m
Step-by-step explanation:
Total length of the fence is 996 m.
Let the length is L and the width is W.
Perimeter = 2 (L + W)
996 = 2 (L + W)
498 = L + W
L = 498 - W ...... (1)
Let the area is
A = L W
A = (498 - W) W
A = 498 W - W^2
Differentiate with respect to W.
dA/dW = 498 - 2 W
Put it equal to zero.
498 - 2 W = 0
W = 249 m
Now, L = 498 - 249 = 249 m
Differentiate with respect to W again
[tex]\frac{d^2A}{dW^2} = - 2[/tex]
As it is negative so the area is maximum.
The maximum area is
A = 249 x 249 = 62001 square meter.
Side is L = 249 m
I don’t know if this is enough but please help me
Answers
Answer:
1 A
2c
3B
4f
do not use the last one f(X)=x
Step-by-step explanation:
The equation k(x+1)^2/3+(y+2)^2/4=1 represent circle if
Answers
Answer:
Can you Specify the Question?
Find y when = 22, if y varies directly as x,
and y = 39 when x = 7.
Answers
Answer:
let,
x=ky
y=39 when x=7 so,
7=39k
or, k=7/39
now, when x=22
22=7y/39
or, y=39×22/7
or, y=858/7
or, y=122.57 (rounded to the nearest hundredth)
Find the value of x in Circle O.
Answers
Answer:
x=8
Step-by-step explanation:
x^2+15^2=17^2, x=sqrt(64)=8
What is the slope of the function? Then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?
Answers
Complete question is;
Alejandra correctly wrote the equation y – 3 = (1/5) (x – 10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?
Answer:
y – 3 = 2(x – 10)
Step-by-step explanation:
Since the original line is;
y – 3 = (1/5) (x – 10)
This means the slope is 1/5 and the x and y coordinates are (10, 3) respectively.
Now, if she changes the slope to 2 and it still passed through the same point, then it means it's x and y points are still (10, 3). Thus, the equation will now be;
y – 3 = 2(x – 10)
In trying to determine whether air pollution causes reduction in children's lung health a researcher proposes to see if the lung volume of 10-year-old boys who live in high ozone pollution is significantly less than the lung volume of all 10-year-old boys. The mean volume for all 10-year-old boys is 2.05 liters. A random sample of 26 10-year-old boys who live in a community with high levels of ozone pollution is found to have a mean volume of 1.98 liters, with a sample standard deviation of 0.3 liters. Test the researcher's claim that the mean lung volume of 10 -year-old boys who live in a community with high levels of ozone pollution is less than 2.05 at the 5% significance level.
Answers
Answer:
The test statistic will be "-2.33". A further explanation is provided below.
Step-by-step explanation:
According to the question,
[tex]H_0: \mu = 2.05[/tex]
[tex]H_0: \mu < 2.05[/tex]
Given:
[tex]\bar x = 1.98[/tex]
[tex]s = 0.3[/tex]
[tex]n = 100[/tex]
The test statistics will be:
⇒ [tex]t_0 = \frac{\bar x - \mu_0}{\frac{s}{\sqrt{n} } }[/tex]
[tex]=\frac{1.98-2.05}{\frac{0.3}{\sqrt{100} } }[/tex]
[tex]=-2.33[/tex]
and the P-value will be:
= [tex]0.011< \alpha[/tex]
If (3+√5)(4-√5)=a+b√5, where a and b are integers, then what is the value of a + b?
Answers
So, if a and b are integers, a=2 and b=3
