The circumference of the circle is [tex]C =\dfrac{20\pi}{4+\pi}[/tex] when A is a minimum.
What is circumference?The circumference of the circle is the length of the curve traced out from the fixed point which is equidistant from the locus of the curve.
Let the side of the square be s
and the radius of the circle be r
The perimeter of the square is = 4s
The circumference of the circle is =2πr
Given that the length of the wire is 20 cm.
According to the problem,
4s + 2πr =20
⇒2s+πr =10
[tex]s=\dfrac{10-\pi r}{2}[/tex]
The area of the circle is = πr²
The area of the square is = s²
A represents the total area of the square and circle.
A=πr²+s²
Putting the value of s
[tex]A =\pi r^2 +(\dfrac{10-\pi r}{2})^2[/tex]
[tex]A =\pi r^2 +(\dfrac{10}{2})^2-2\times \dfrac{10}{2}\times \dfrac{\pi r}{2}+(\dfrac{\pi r}{2})^2[/tex]
[tex]A = { \pi r^2}(\dfrac{4+\pi}{4})-5\pi r+25[/tex]
For maximum or minimum [tex]\dfrac{dA}{dr}=0[/tex]
Differentiating with respect to r
[tex]\dfrac{dA}{dr}=\dfrac{2\pi r(4+\pi )}{4}-5 \pi[/tex]
Again differentiating with respect to r
[tex]\dfrac{d^2A}{dr^2}=\dfrac{2\pi (4+\pi )}{4}[/tex] > 0
For maximum or minimum
[tex]\dfrac{dA}{dr}=0[/tex]
[tex]\dfrac{2\pi r(4+\pi )}{4}-5 \pi=0[/tex]
[tex]r = \dfrac{10\pi}{\pi (4+\pi)}[/tex]
[tex]r=\dfrac{10}{4+\pi}[/tex]
Therefore the circumference of the circle is
C = 2 π r
[tex]C = \dfrac{20 \pi }{4+\pi }[/tex]
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Carlos wrote the number 52,700,000 in scientific notation. Which number did he write?
Answer:
5.27 × 10⁷ is the scientific notation for 52,700,000.
Wayne uses 4 inches of ribbon for each bow he makes. How many bows can he make with 3 yards of ribbon?
Answer:
27
Step-by-step explanation:
1 yard is 3 feet, so 3 yards is 9 feet.
9 feet is 108 inches, so Wayne has 108 inches of ribbon to work with.
Divide 108 by 4, because Wayne needs 4 inches of ribbon to make 1 bow, and we get 27.
Hopefully, this helps with whatever you need to do!
An airplane is flying at an altitude of 36,000 feet when it begins it's descent for landing. Twelve minutes into its descent, it's at 29,400 feet. Find the rate of change in altitude.
36000 divided by 29,400 get the answer then divide by 12
Find the area of the semicircle. Round your answer to the nearest hundredth.
Solve this question:
[tex]5 \times \frac{5}{10} \times 10 = [/tex]
Thanks :)
Answer:
25
Step-by-step explanation:
Answer:
25
Step by step explanation:
Hey
( marking right as brainliest and 5.0 star! ) Seaira measures and records the lengths, in feet, of 9 lizards. The line plot below shows the information she records, based on the line plot what is the difference between the lengths in feet, of the longest lizards and the shortest lizards?
Answer:
5/8
Step-by-step explanation:
The longest lizard there is, is 3/4 feet. The shortest lizard is 1/8. The equation to solve this is 3/4 - 1/8. The answer to this is 5/8. I hope this helps :)
QUESTION 21 ✓ Round 5 1/3 to the nearest whole number?
Answer:
5
Step-by-step explanation:
1/3 is only 0.33 and 0.33 isnt higher than 0.50, so you cant round anything. 5 is the answer.
Answer: Justice.
Step-by-step explanation:The Answers Justice.
Maths problem in simultaneous equations
Answer:
Question 6: The cost of a chocolate bar is $1.20 and the cost of a box of gum is $0.75
Question 7: There were 7 students
Step-by-step explanation:
Question 6:We will be using system of equations which a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations intersect.
Our Variables:
- chocolate bar which will be represent as b in the equation
- box of gum which will be represent as g in the equation
Forming the equations:
Sally -
bought 2 chocolate bars (b)
bought 1 box of gum (g)
to a total of $3.15
so 2b + 1g = $3.15
Evans -
bought 1 chocolate bars (b)
bought 2 box of gum (1)
to a total of $2.70
so 1b + 2g = $2.70
Solving using substation:
2b + 1g = $3.15 we want to isolate b to input into the other equation
1b + 2g = $2.70
2b + 1g = $3.15 subtract 1g from both sides, divided both sides by 2
2b / 2 + 1g - 1g = $3.15 - 1g / 2
b = $3.15 - 1g / 2
Now substation b into the second equation
1b + 2g = $2.70 becomes 1($3.15 - 1g / 2) + 2g = $2.70
simplify,
$3.15 + 3g / 2 = $2.70 isolate g
$3.15 + 3g / 2 x 2 = $2.70 x 2 multiply both sides by 2
$3.15 + 3g = $5.40 subtract $3.15, divided by 3 from both sides
$3.15 - $3.15 + 3g / 3 = $5.40 - $3.15 / 3
g = $5.40 - $3.15 / 3
g = $2.25 / 3
g = $0.75
Now plug in g to get b into any equation:
If Sally equation is used
2b + 1g = $3.15
2b + 1(0.75) = $3.15 → 2b + 0.75 = $3.15
2b + 0.75 - 0.75 = $3.15 - 0.75
2b = $2.40 → 2b / 2 = $2.40 / 2
b = $1.20
If Evans equation is used
1b + 2g = $2.70
1b + 2(0.75) = $2.70 → 1b + 1.50 = $2.70
1b + 1.50 - 1.50 = $2.70 - 1.50
1b / 1 = $1.20 / 1
b = $1.20
Question 7:
Our Variables:
- adult which will be represent as A in the equation
- student which will be represent as S in the equation
Forming the equations:
- sample size: group of 30
- Adult cost $5 (A)
- Student cost $2 (S)
- Five members are free
to a total cost is $104
so A + S = 30 - 5
this is how many of each variable from the total group and we subtract 5 as 5 members were free
so 5A + 2S = $104
Solving using substation:
A + S = 25 we want to isolate a to input into the other equation
5A + 2S = $104
a = 18
s =7
can anyone help me find the area pls ty
Any suggestions on which choice is the best?
Just please help me!!!!!
Answer:
n= 5/3 or 1.67
Step-by-step explanation:
9n^2 -9 =16
9n^2 = 16 + 9
9n^2 = 25
n^2 =25/9
n^2 =25/9
[tex]\sqrt{n^2} = \sqrt{\frac{25}{9} }[/tex]
n= 5/3 or 1.67
[tex]~~~~~~9n^2 -9 = 16\\\\\implies 9(n^2 -1) = 16\\\\\implies n^2 -1 = \dfrac{16}9\\\\\implies n^2 = \dfrac{16}{9}+1\\\\\implies n^2 = \dfrac{25}{9}\\\\\implies n=\pm\sqrt{\dfrac{25}{9}}\\\\\implies n= \pm\dfrac 53\\\\\implies n = \pm1.67[/tex]
Listing broker Bob gets a 6 .5% commission on a $280,000 sale . He pays 3% to the selling broker and splits his share evenly with the listing agent . How much does the listing agent receive?
Answer:
4900 to listing agent
Step-by-step explanation:
SO Bob gets 6.5 -3 = 3.5 % and then splits it ==>1.75% to Bob and to listing agent
1.75% = .0175
.0175 * 280000 = 4900
This pattern follows the rule add 2. What is another feature of this pattern?
An image of a pattern. Term one has one dot, term two has three dots, term three has five dots, term four has seven dots.
Group of answer choices
The terms appear even, odd, even, odd.
All the
Answer:
Option D, All of the terms are odd
Step-by-step explanation:
According to the image description provided:
Term one starts with one dot. One is an odd number.
If you add two to an odd number, the sum would be another odd number. This is what's happening with the pattern.
For example:
[tex]3+2=5[/tex]
Three is an odd number. If you add two to it, you would get five, which is another odd number.
Term two has 3 dots, term three has 5 dots, term four has 7 dots.
So, all terms should be odd.
Option D should be the correct answer.
A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 29ft long and 18ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required? Use the value 3.14 for, and do not round your answer. Be sure to include the correct unit in your answer
Answer:
The area of the garden is
797
f
t
2
.
Explanation:
First, let's find the area of the rectangle.
We know that the area of a rectangle is the length times width, or
20
⋅
32
in this example:
20
⋅
32
=
640
So the area of the rectangle is
640
f
t
2
.
You may not know the area of a semicircle, but that's fine
−
we know the area of a circle, or
π
r
2
.
Since the area of a semicircle is half the area of a circle, we just do the area of the circle divided by
2
:
So the area of a semicircle is
π
r
2
2
.
The question asks for
π
to just be
3.14
, so instead the equation is
A
=
3.14
r
2
2
The picture gives the diameter of the circle.
To find the radius, or
r
, we divide the diameter by
2
:
20
2
=
10
Now we can solve for the area of the semicircle:
3.14
(
10
)
2
2
3.14
(
100
)
2
314
2
157
f
t
2
Now that we now the areas of the rectangle and semicircle, we can add them up to find the area of the rose garden:
640
+
157
=
797
f
t
2
Carol's last credit card statement said that she had an account balance of -$118. Which of the following account balances represents a debt greater than Carol's?
A: -157
B: $157
C: $79
D: -$79
Answer: A. -$157
Step-by-step explanation:
This is would be much more in debt for his credit card statement, it would take him longer to pay off.
Suppose the McCall family wants to rent a truck for a day. They have a choice of two truck rental companies. After how many miles are the cost at the two companies equal?
if explanation is given with steps I will give brainliest
Company A: $20 per day plus $ .70 per mile
Company B: $45 per day plus $ .25 per mile
Answer:
the trip is 10 miles long
Step-by-step explanation:
im sorry i dont know the steps
Lucas has 2 chocolate bars more than Caidon. Together they have 30 chocolate bars. How
many chocolate bars does Lucas have? (hint: use only one variable)
Help me
Answer:
Lucas has 16 chocolate bars
Step-by-step explanation:
Let x = number of chocolate bars Lucas has
⇒ x - 2 = number of chocolate bars Caidon has
If they have 30 chocolate bars altogether then:
⇒ x + x - 2 = 30
⇒ 2x - 2 = 30
⇒ 2x = 32
⇒ x = 16
Therefore, Lucas has 16 chocolate bars (and Caidon has 14 chocolate bars).
if each polygon has 12 sides and each side length was 20 cm what is the area
Answer: approximately 4478.46096908264 square cm.
==========================================================
Explanation:
I'm assuming this is a regular 12-sided polygon
The area formula for regular polygons is
[tex]A = 0.25n*s^2*\cot(180/n)[/tex]
where in this case we have n = 12 sides and each side is of length s = 20
So,
[tex]A = 0.25n*s^2*\cot(180/n)\\\\A = 0.25*12*(20)^2*\cot(180/12)\\\\A = 0.25*12*(20)^2*\cot(15)\\\\A = 0.25*12*(20)^2*\frac{1}{\tan(15)}\\\\A \approx 4478.46096908264\\\\[/tex]
The area of this regular polygon is approximately 4478.46096908264 square cm.
Make sure your calculator is in degree mode when computing that value of cot(15) or 1/tan(15).
Jason earns $4,024 dollars in 20 days. He does not go to work for 7 days. Calculate his mean daily earnings
Answer:
309.54
Step-by-step explanation:
he makes about $309.54 in one day
Eight meters is equal to how many centimeters
Answer:
800 Cm
Step-by-step explanation:
bro typa question is that its common sense that 100 cm = 1 meter
As of 2007, the number of works of art displayed at the Louvre in Paris,
France, is around 35,000. This has an order of magnitude of 4.
A. True
B. False
Cathleen Brooks obtained an 18 month loan of $3,200. The interest rate is 15% Her monthly payment is $199.68. The balance of the loan after 6 payments
is $2,341.45.
a. What is the interest for the first payment?
b. What is the interest for the seventh payment?
a. The interest for the first payment is $40.
b. The interest for the seventh payment is $29.27.
What is interest?In financial accounting and management, interest refers to the finance charge for obtaining or giving a loan or credit.
The interest payment or revenue is based on the interest rate applied to the principal or loan balance.
Data and Calculations:Loan = $3,200
Monthly payment = $199.68
Interest rate = 15%
Loan balance after 6 payments = $2,341.45
Interest for the first payment = $40 ($3,200 x 15% x 1/12)
Interest for the seventh payment = $29.27 ($2,341.45 x 15% x 1/12)
Thus, while the interest for the first payment is $40, the interest for the seventh payment is $29.27.
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Find the probability of the event.
A class has seven students. What is the probability that exactly four of the students were
born on a weekday (Monday through Friday)? (round to the nearest thousandths when
needed)
Ben wants to try a new honey-glazed salmon recipe. He starts with 1
2
3
cups of honey. He uses
1
5
of it to make the glaze. How much honey does Ben have left?
What you have to do is 1. Work for it yourslef. 2. use ur brain.
Area is measured in square units. This means that if we divide the shape into squares that are equal in size and count them up, the area is the total number of squares. Square units are always one unit of length long and one unit of length wide. In the song, the unit of length we use is feet. So each square unit is one foot long and one foot wide, or one square foot. Since there are 72 of these units in total, we say the area is 72 square feet. Square units can use other units of length, like inches or miles. Make sure you know what unit of length you’re using.
Jason is finding the area of a rectangle that is 7 inches long and 4 inches wide. Jason says the area of the rectangle is 28 inches. Is Jason correct or incorrect?
A: Jason is correct because 7 x 4 = 28.
B: Jason is incorrect because the area is 28 square inches.
C: Jason is incorrect because 7 + 4 = 11.
D: Jason is incorrect because the area is 28 square feet.
Answer:
B
Step-by-step explanation:
Area is always squared; area of a rectangle is length x width so 7*4= 24in^2
If this answer helped you I would greatly appreciate brainliest :D.
Which of the following is the sum of 1/2 and -2/3
-1/6
hope it helps...!!!
The angle of elevation to a nearby tree from a point on the ground is measured to be 74^{\circ} ∘ . How tall is the tree if the point on the ground is 54 feet from the tree? Round your answer to the nearest tenth of a foot if necessary.
The height of the tree whose angle of elevation is [tex]74^{0}[/tex] and 54 feet tall is 188 foot.
Height of the tree= 188 foot (rounding off nearest tenth)
What is angle of elevation?The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".
We know by trigonometric ratios,
[tex]tan \; \theta = \frac{P}{B}[/tex]
[tex]tan \; 74^0 \;[/tex] = [tex]\frac{P}{54}[/tex]
3.48 = [tex]\frac{P}{54}[/tex]
P= 3.48 x 54
= 187.92 feet
≈ 188 foot (rounding off nearest tenth)
The height of the tree whose angle of elevation is and 54 feet tall is 188 foot.
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Answer: 188.3 feet tall*
Step-by-step explanation:
Divide. 8,375 ÷ 45 number and remainder
Answer: 186 with a remainder of 5.
Method One:
See attached for my work, I used long divison.
Method Two:
We will use a calculator to find the value, then multiply the value (without the decimals) by the divisor. Lastly, we will subtract. This makes more sense with the work:
8,375 ÷ 45 = 186.11111111
186 * 45 = 8,370
8,375 - 8,370 = 5
Question 9
2 pts
(CO 3) The probability of someone ordering the daily special is
52%. If the restaurant expected 105 people for lunch, how
many would you expect to order the daily special?
O 100
O 52
O 51
O 55
If the restaurant expected 105 people for lunch, using the given probability, the number of those who would order the daily special is D. 55.
What is the probability?Probability is the likelihood or chance that an expected outcome will occur amid many possible results.
Probability gives a fractional value of the whole when it is not 100% certain (when the possibility is 1)or 100% uncertain (when the chance is zero).
Like ratios and proportions, probabilities are depicted using fractions, decimals, or percentages.
The probability of ordering the daily special = 52%
The expected number of lunchers = 105
The number of those expected to order the daily special = 55 (105 x 52%)
Thus, if 105 are expected to attend the lunch, the probable number that will order is Option D.
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2 Latoya has 60 CDs in her collection.
• 40 are Pop
. 12 are Country
• 6 are Rock
• 2 are Jazz
.
If she randomly selects a CD from her collection, what is the probability that she will NOT select a Country CD?
60 cds - 12 country = 48 cds are not country.
probability of picking one that is not country = total of non country/ total cds
probability = 48/60 which reduces to 4/5
answer: 4/5