What is the area of the slice of pie that was cut, rounded to the nearest hundredth?
79.09 ft2
85.31 ft2
97.23 ft2
98.83 ft2
Answers
A = 37/360 x pi x r^2
37/360 x 3.14 x 17.5^2
A = 98.8 square feet
The approximate area of the slice was 98.8 square feet. That is one big pie!!
The area of the slice of pie that was cut, rounded to the nearest hundredth is; D: 98.83 ft²
Area of a Sector
We are given the angle of the sector of the circle as θ = 37°.
We are given;
Diameter; d = 35 ft
Thus;
Radius; r = 35/2 = 17.5 ft
Now, the formula for area of a sector of a circle is;
A = (θ/360) * πr²
Thus;
A = (37/360) * π * 17.5²
Approximating to the nearest hundredth gives;
A = 98.883 ²
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Related Questions
Suppose that on a particular computer, it takes the merge sort algorithm a total of 60 seconds to sort an array with 60,000 values. approximately how long will it take the algorithm to sort an array with 120,000 values? round to the nearest second.
Answers
If line segment ab is defined by the endpoints a(4,2) and b(8,6) , write an equation of a line that is the perpendicualr bisector line segment ab
Answers
So the slope of the perpendicular line is -1/1 = -1
This line passes through the midpoint of ab
The midpoint of ab = ( 8+4 / 2 , 2+6 / 2) = (6, 4)
Finding the equation of the perpendicular line:-
y - y1 = -1(x - x1) where x1 = 6 and y1 = 4:-
y - 6 = -1(x - 4)
y = -x + 10 is the answer
An equation of a line that is the perpendicular bisector line segment AB is y=-x+10.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, line segment AB is defined by the endpoints A(4,2) and B(8,6).
Midpoint of line AB is (x, y) =[(x₂+x₁)/2, (y₂+y₁)/2]
= [(8+4)/2, (6+2)/2]
= (6, 4)
Slope of line AB is (y₂-y₁)/(x₂-x₁)
= (6-2)/(8-4)
= 4/4
= 1
The slope of a line perpendicular to given line is m1=-1/m2
So, the slope of a line is -1
Now, substitute m=-1 and (x, y)=(6, 4) in y=mx+c, we get
4=-1(6)+c
c=10
Substitute m=-1 and c=10 in y=mx+c, we get
y=-x+10
Therefore, an equation of a line that is the perpendicular bisector line segment AB is y=-x+10.
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Which measure is of an angle that is coterminal with a 425 degree angle
A. 425 degree-(1,000n)degree, for any integer n
B.425 degree-(840n)degree, for any integer n
C. 425 degree+(960n)degree, for any integer n
D. 425 degree+(1,440n)degree, for any integer n
Answers
We know that co terminal angles are those angles which have a difference equal to a multiple of 360 degrees. For example co terminal angle of 45 degrees is 76 degrees because their difference is equal to 720 degrees, which is a multiple of 360.
We have been given an angle 425 degrees.
From the given choices, we need to check if angles being added or subtracted to 425 degrees are multiples of 360 or not.
Let us check each of the options one by one.
(A) The angle being subtracted is [tex]1000n[/tex]. Therefore, we have [tex]\frac{1000n}{360}=2.77n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(B)
The angle being subtracted is [tex]840n[/tex]. Therefore, we have [tex]\frac{840n}{360}=2.33n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(C)
The angle being added is [tex]960n[/tex]. Therefore, we have [tex]\frac{960n}{360}=2.67n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(D)
The angle being added is [tex]1440n[/tex]. Therefore, we have [tex]\frac{1440n}{360}=4n[/tex], which is an integer for all values of n. Therefore, angle given in this option is indeed a co terminate angle to 425 degrees.
Hence, correct answer is option (D).
In ∆ABC, ∠BAC= 80°, ∠ABC=60°, a = 7, b = x.
Find x. (accurate to 3 significant figures)
The value of x = .
Answers
a/sinA = b/sinB = c/sinC
Where a, b, and c are the opposite sides of angle A, B. and C respectively.
x/sin60 = 7/sin80
x =(7sin60)/sin80
= 6.062/0.9848
=6.155696691
To 3 significant figures the answer is 6.16
Way 1:
x / sine (60) = 7 / sine (80)
Rewriting we have:
x = (7 / sine (80)) * (sine (60))
x = 6.16
Way 2:
x / sine (80) = 7 / sine (60)
Rewriting we have:
x = (7 / sine (60)) * (sine (80))
x = 7.96
Answer:
x = 6.16
or
x = 7.96
Note: it depends on the location of a and b in the triangle.
How many zeros does the function f(x) = 4x^11 − 20x^7 + 2x^3 − 15x + 14 have?
I'm between 3 & 11.
Answers
Therefore, the answer is 11.
How many permutations exist of the letters a, b, c, d taken four at a time?
Answers
There are 24 permutations of the letters a, b, c, d taken four at a time, calculated using the formula 4!.
Explanation:The question revolves around finding the number of permutations of the letters a, b, c, d taken four at a time. To solve this, we need to understand that a permutation represents the arrangement of all members of a set in every possible order.
In the case of the letters a, b, c, d, we want to arrange them in all possible ways where order matters and taking all four at a time. The formula to calculate permutations is P(n, r) = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items to choose. However, since we are taking all four letters each time, we are essentially looking for 4!, which simplifies to 4*3*2*1.
Therefore, 4! equates to 24. This means there are 24 possible ways to arrange the letters a, b, c, d when taking all four at a time. It's an excellent exercise to manually write out all of these permutations to get practical experience with the concept.
The central angle of a circle is equal in measure to one radian when the corresponding arc length is equal to which of the following? A) The radius of the circle B) Any chord of the circle C) The diameter of the circle D) One-half the circumference of the circle
Answers
L = r*theta
where r is the radius and theta is the central angle in radians (this formula will not work if theta is in degrees)
If the central angle is 1 radian, then theta = 1 and
L = r*theta
L = r*1
L = r
So the arc length is the same as the radius
Answer: Choice A) The radius of the circle
In how many different ways can someone arrange 6 books on a shelf
Answers
Number of ways = 6 x 5 x 4 x 3 x 2 x 1
Number of ways = 720
------------------------------
Answer: 720 ways
------------------------------
6x5x4x3x2x1---- this equals 720.
So, there are 720!
Anyone know the answer?
Answers
The combined cost of one advance ticket and one same-day ticket to a show was $50. it is known that 17 advance tickets were sold and 48 same-day tickets were sold, for total receipts of $1842. what was the price of each kind of ticket?
Answers
17 advance + 17 same-day = $50 x 17 = $850
$1842 - $850 = $992
48 - 17 = 31 same-day
31 same-day = $992
1 same-day = $32
1 advance + 1 same-day = $50
1 advance + $32 = $50
1 advance = $50 - $32 = $18
Answer: same day ticket costs $32 and advance-day ticket costs $18.
Express each product in the simplest form. 3wx\6x * 3wx\9w
Answers
Answer: xw/6
Leo has 100 coins in his piggy bank. All coins are either nickels, or dimes, or quarters. There are as many nickels as dimes and quarters together. How much money are nickels in Leo's piggy bank worth?
Answers
Answer:
33
Step-by-step explanation:
an initial deposit of $200 is made into an account that pays 4.2% annual interest. What is a model to represent the balance in the account after x years?
Answers
A = Original amount = 200
r = interest rate = 0.042 (when converted from percent to decimal)
t = time = x
Plug them in and you get the model: y = 200(1+0.042)^x
or just simplify the parentheses to (1.042)
The model to represent the balance in an account from an initial deposit of $200 at an annual interest of 4.2% is given by the formula A = 200(1.042)^x. Here A is the amount accrued after x years.
Explanation:The subject of the given problem is related to exponential growth as it involves the growth of a principal amount in a bank account accruing annual interest. The model to represent the balance in the account after x years can be described by the formula A = P(1 + r/n)^(nt). Where, A represents the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, t is the time the money is invested for in years.
In this case, P = $200, r = 4.2/100 = 0.042 (converted percentage to decimal), n = 1 (since it is compounded annually), and t = x (number of years). Substituting these values into the formula, we obtain the model: A = 200 (1 + 0.042) ^ (1*x) simplified to, A = 200(1.042)^x. Which is used to represent the balance in the account after x years.
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Need help please ASAP!!
Answers
Good Luck C:
Conor buys 75 tokens for games at the arcade. the price to play each game is 3 tokens. if conor has already played x games, which expression is equivalent to the number of tokens that remain?
Answers
x: number of games
y: number of remaining tokens
The expression that models the problem is given by:
y = -3x + 75
Answer:
the number of tokens that remain is:
y = -3x + 75
Answer:
y = 75 - 3x
Step-by-step explanation:
Let the number of token left = y
total number of token bought = 75
Number of games played by Conor = x
It is given for playing one game, the price = 3 token
Therefore for playing x games, the price is = 3x
Therefore, the number of tokens left with Conor is given by
y = 75 - 3x
Thus, the expression that is equivalent to the number of remaining tokens is
y = 75 - 3x
Rearrange the formula to calculate the diameter of a circle.
Answers
a=1/4pid^2
4a=pid^2
4a/pi=d^2
square both sides to get d
Answer: Square root of 4a over pi equals d.
1) Start by multiplying both sides by 4 to get rid of the 4 in the denominator on the right. bringing it to the other side:
[tex]A = \frac{1}{4} \pi d^{2} \\ 4(A) = 4(\frac{1}{4} \pi d^{2} )\\ 4A = \pi d^{2} [/tex]
2) Divide both sides by π to move the π to the other side of the equation (I put the d squared on the left, but you can keep it on the right):
[tex]4A = \pi d^{2} \\ d^{2} = \frac{4A}{ \pi } [/tex]
3) Finally, take the square root of both sides to get the value of d:
[tex]d^{2} = \frac{4A}{ \pi } \\ d = \sqrt{\frac{4A}{ \pi } } [/tex]
-----
Answer: [tex]d = \sqrt{\frac{4A}{ \pi } } [/tex]
In the united states, 20 ounces of a beverage that is 25% ethanol contains __________ ounces of alcohol
Answers
10PTS!!!!!! UGRENT WILL MARK BRAINLYEST, THANK AND 5 STARS!!
Find the volume of the tank below.
could't inbed the image but it a cylindar 5m tall and has a radius of 2m
96 m3
78 m3
54 m3
63 m3
Answers
Cylinder Volume = PI * 2^2 * 5
Cylinder Volume = 62.8318530718 cubic meters
Correct answer is the last one.
The mathematics department of a college has 1414 male professors, 99 female professors, 99 male teaching assistants, and 1111 female teaching assistants. if a person is selected at random from the group, find the probability that the selected person is a professor or a male.
Answers
and 99 male assistant.
Probability is (1513+99)/(1414+99+1111+99)=1612/2723
I think the answer is Probability is (1513+99)/(1414+99+1111+99)=1612/2723
What is the least common multiple (LCM) of 8 and 10?
Answers
Answer:
LCM (8,10) = 2 × 2 × 2 × 5 = 40
Step-by-step explanation:
Least common multiple is the smallest number that is multiple of both the given numbers.
Example: LCM of 2 and 3 is 6 .
6 is a multiple of both 2 and 3 .
Given numbers are 8 and 10
First write both in factor form,
⇒ 8 = 2 × 2 × 2
⇒ 10 = 2 × 5
We find LCM by writing common terms one times and multiplying all terms together,
Here, 2 is common to both 8 and 10 so we write it once only.
Thus, LCM (8,10) = 2 × 2 × 2 × 5 = 40.
how do we find the volume ?
Answers
The volume of figure is 877.876 yd³
1. Volume of Cone
= 1/3πr²h
= 1/3 x 3.14 x 2 x 2 x 4
= 16.746
2. Volume of cylinder
= 3.14 x 2 x 2 x 8
= 100.48
3. Volume of Hemisphere
= 2/3πr³
= 7.065
4. Volume of cylinder
= 3.14 x 1.5 x 1.5 x 9
= 63.585
5. Volume of prism
= 1/2 x ( 6 x 6) x 12
= 216
6. Volume of Cuboidal prism
= l w h
= 6 x 6 x 12
= 432
7. Volume of pyramid
= 1/3 x 3 x 2
= 2
8. Volume of cuboidal prism
= 10 x 2 x 2
= 40
So, the volume of figure is
= 16.746 + 100.48 + 7.065 + 63.585 + 216 + 432 + 2 + 40
= 877.876 yd³
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How many combinations with 3 numbers 0-6?
Answers
6x7x7=294
(5.4+3)×(6−2) help plzzz
Answers
What is the interval for the number of people who are likely to want this restaurant in their city?
Answers
112,483 * 0.24 = 26,996
112,483 * 0.38 = 42,744
Answer: (26996, 42744)
A hang glider is soaring over a 100-acre area that consists of thick forest and open fields. In the diagram below, the forested area is shaded in green and the open field is the white space. Upon landing, the hang glider realizes she has dropped her keys.
What is the probability that her keys have landed within the forest?
The blacked out middle section of the pyramid is 20 acres
A 0.2
B 0.6
C 0.8
D 1.0
Answers
The probability that her keys have landed within the forest will be C. 0.8.
How to calculate probability?From the information given, the blacked out middle section of the pyramid is 20 acres. Therefore, the probability will be:
= 20/100 = 0.2
Now, the probability that her keys have landed within the forest will be:
= 1 - 0.2
= 0.8
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Can anybody help me with this question(#6)? It’s over systems word problems. ASAP!
Answers
Matt's sale can be represented by the equation
3S +14L = 203
Ming's sale can be represented by the equation
11S +11L = 220
There are a number of ways to solve a pair of equations. One is to graph them. The graph shows the costs to be ...
The cost of a small box of oranges is $7.
The cost of a large box of oranges is $13.
A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function h = −16t2 + 32t + 6. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?
Answers
We find the maximum by finding the vertex. We first find the axis of symmetry, whose equation is
x = -b/2a
x = -32/2(-16)
x = -32/-32 = 1
This gives us that it reaches the maximum in 1 second.
To find the y-coordinate, the maximum height, we substitute this into the equation:
h(1) = -16(1²)+32(1)+6
h(1) = -16+32+6 = 22
It reaches a height of 22 feet.
The ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.
To find the time at which the ball reaches its maximum height, we can first determine the vertex of the quadratic function [tex]\( h(t) = -16t^2 + 32t + 6 \),[/tex] where t represents time in seconds and h represents height in feet.
The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] is given by the formula:
[tex]\[ t_{\text{max}} = \frac{-b}{2a} \][/tex]
For the function [tex]\( h(t) = -16t^2 + 32t + 6 \)[/tex], we have a = -16 and b = 32 . Plugging these values into the formula:
[tex]\[ t_{\text{max}} = \frac{-32}{2(-16)} \]\[ t_{\text{max}} = \frac{-32}{-32} = 1 \][/tex]
So, the ball reaches its maximum height at t = 1 second.
To find the maximum height, we substitute t = 1 into the function h(t) :
[tex]\[ h(1) = -16(1)^2 + 32(1) + 6 \]\[ h(1) = -16 + 32 + 6 \]\[ h(1) = 22 \][/tex]
Therefore, the ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.
Given:
CDKM is a parallelogram,
DA
⊥
CK
, DK – CD = 7
CA = 6, AK = 15
Find: CD and DK
Answers
So we can form 2 equation and solve them simultaneously.
(AD)²=(CD)²-(AC)²
(AD)² = (CD)² - 6² ...........(i)
(AD)² = (DK)² - (AK)²
(AD)² = (DK)² - 15² ..............(ii)
But DK - CD = 7. So, DK=7+CD
Now let CD=x
From the 2 equations above,
(AD)²=x²-36 .......(i)
(AD)²=(7+x)²-225 .......(ii)
x²-36=49+14x+x²-225
14x=140
x=10
CD = 10.
DK = 7+CD
= 7+10
= 17
In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
The quadrilateral CDKM is a parallelogram. In this parallelogram, the side DA is perpendicular to the side CK.
The difference of the side DK and CD is,
[tex]DK - CD = 7\\DK=7+CD[/tex]
The length of the line segment CA and AK is 6 units and 15 units respectively.Then by the Pythagoras theorem,
[tex](AD)^2=(CD)^2-(AC)^2\\(AD)^2=(CD)^2-(6)^2[/tex] ....1
Again by using the Pythagoras theorem
[tex](AD)^2=(Dk)^2-(AK)^2\\(AD)^2=(DK)^2-(15)^2[/tex]
Put the value of (AD)², from equation 1 in the above equation as,
[tex](CD)^2-6^2=(DK)^2-(15)^2\\(CD)^2-36=(DK)^2-225[/tex]
Put the value of DK in the above equation as,
[tex](CD)^2-36=(7+CD)^2-225\\(7+CD)^2-(CD)^2=225-36\\(CD)^2+14CD+49-(CD)^2=189\\CD=10[/tex]
Hence, the value of DK is,
[tex]DK=7+10DK=17[/tex]
Hence, In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.
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HELPPPPPPPPPPPP and explain
Answers
If you want to remove the power (3/4) the rule is that you multiply every power inside the brackets by 3/4.
2 has a power of 1
2^1 is the way you think of it.
(2^1)^3/4 = 2^(3/4). It would look like this.[tex]2^\frac{3}{4} [/tex]
(a ^2 ) ^(3/4) = 2^(6/4) which would look like this [tex]a^\frac{6}{4} [/tex]
which could be written as [tex]a^\frac{3}{2} [/tex] or a^1.5
x ^ (-5) can be written as [tex]x^\frac{-15}{4} [/tex] Notice that - 5 * 3/4 = - 15/4 It could also be written as 1/x^(15/4) That would get rid of the - sign.
(y ^ 8) ^(3/4) = y^(24/4) = y^6
On your page, number the questions from a to h
e is the only one I found to be correct. I will go through the errors. Sometimes I did not list them all. There's just too many of them. The key point is that all the powers are multiplied by 1/4. You need 4 letters or numbers to take 1 letter or number outside the root sign.
a
wrong because a should be 6/4 and not 5/4. As noted, this may not be the only error.
b
is because the y should be y^1 outside the root sign and y^2 inside the root.
c
is wrong because there should be a y^2 inside the brackets.
d
is wrong 2 should be 8 raised the the 1/4 power. 8^1/4
e
correct but I sure don't like z^0 sitting there.
f
has all kinds of problems. Start with the 268 That is wrong. If you are going to bring 36 inside the root sign, it should be 36^3 which is 44656. y is wrong and so is x. For x you will have to use the -15 somewhere.
g
is wrong. The 36 is not to be altered and if it is it must be done as it was in the above question
y should be to the 6/4
h
is wrong. You lost a y somewhere.
Remark
Up until now, the questions you have asked could have been answered and it would have cleared up any of the problems you have been having. This one is quite different.
It is extremely long and it supposes that you know the multiplication rule for powers. You must have been been taught something before you tackled this monster. You need to go to a help center if you are in school or ask a tutor if you are not. It is not you that's the problem. It's the question that's the problem. It is very long and there are all sorts of tricks in it. In my opinion, it's not really a fair question without a lot of help.
The total price of an article is $7.02, including tax. If the tax rate is 8%, what is the retail price of the article?
Answers
Tax is 8% of article = 0.08x
x+0.08x=7.02
1.08x=7.02
x=7.02/1.08
x=6.5
The retail price is $6.50.
The solution is: The retail price is $6.50.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Here, we have,
given that,
The total price of an article is $7.02, including tax.
If the tax rate is 8%
Lets price of article = x
Tax is 8% of article = 0.08x
so, we get,
x+0.08x=7.02
1.08x=7.02
x=7.02/1.08
x=6.5
The retail price is $6.50.
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