A 30° central angle in a circle is equivalent to π6 radians. Drag a tile to each box to correctly complete the sentence.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The length of the arc intercepted by this central angle is Response area times the length of the Response area.
Answers
The length of the arc intercepted by the angle is \(\frac{\pi}{6}\) times the length of the radius
Calculating length of an arcFrom the question, we are to determine the length of the arc intercepted by the angle
The length of an arc can be calculated by using the formula,
\(l =\frac{\theta}{360 ^\circ} \times 2\pi r\)
Where \(l\) is the length of the arc
\(\theta\) is the central angle
and r is the radius
From the given information,
θ = 30°
∴ \(l =\frac{30 ^\circ}{360 ^\circ} \times 2\pi r\)
\(l = \frac{1}{12}\times 2 \pi r\)
\(l = \frac{2 \pi}{12}\times r\)
\(l = \frac{ \pi}{6}\times r\)
Hence, the length of the arc intercepted by the angle is \(\frac{\pi}{6}\) times the length of the radius
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Related Questions
I need help with this ASAP
Answers
Answer:
x=5
Step-by-step explanation
Move all terms containing x to the left side of the equation.
4x-8=12
Move all terms not containing x to the right side of the equation.
4x=20
Divide each term by 4 and simplify.
x=5
What is the area of the shape ?
Answers
Answer:
The Picture is of a trapezium
Area of Trapezium= 1/2h(L1+L2)
=1/2×7(11+3)
=49
Hence the area of the shape is 49
ASAP!!! NEED AN ANSWER
In this budget scenario, use 15 per hour as the current wage for 40 hour work weeks. Hint: There are 52 weeks in a year, and 12 months in a year.
1. What is the gross yearly income?
2. What is the gross monthly income using this pay rate?
Answers
1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year
Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year
Gross Yearly Income = $31,200
2)Gross Monthly Income = Gross Yearly Income / Months in a Year
Gross Monthly Income = $31,200 / 12 months
Gross Monthly Income ≈ $2,600
find the slope
a line that passes between (-5, 8) and (2,4)
Answers
Answer:
Step-by-step explanation:
formula : m=(y2-y1)/(x2-x1)
(4 - 8) / (2 - - 5)
-4 / 7
m = -4 / 7 = -0.57143
OMG I NEED HELP!!!!!
Answers
Answer:
5
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
When you scale down you divide. it showed that 9 = 3. to go from 9 to 3 you divide by 3. So you have to do the same thing for the other number. So, 18 divided by 3, which is 6.
When you scale up you multiply. it showed that 18 = 36. To get from 18 to 36 you multiply by 2. So, you do the same thing to the other number, 9 times 2, which is 18.
Which expression is equivalent to the expression quantity negative 6 over 5 times t plus 3 over 16 end quantity minus expression quantity negative 7 over 10 times t plus 9 over 8 end quantity?
13 over 10 times t plus 12 over 16
1 over 10 times t plus 6 over 16
negative 5 over 10 times t plus 21 over 16
negative 5 over 10 times t minus 15 over 16
Answers
The equivalent of the expression [-(6/5)t + 3/16] - [-(7/10) + 9/8] will be - (5/10)t - 15/16. Then the correct option is D.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ [-(6/5)t + 3/16] - [-(7/10) + 9/8]
Simplify the equation, then we have
⇒ [-(6/5)t + 3/16] - [-(7/10) + 9/8]
⇒ -(6/5)t + (7/10)t + 3/16 - 9/8
⇒ -(5/10)t - 15/16
The equivalent of the expression [-(6/5)t + 3/16] - [-(7/10) + 9/8] will be - (5/10)t - 15/16. Then the correct option is D.
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Suppose Blue Cab Company charges $2.85 a ride up to 0.1 miles and $0.30 for each additional tenth of a mile. If the mean distance a passenger wants to go is 5.3 miles with a standard deviation of 1.4 miles, what is the standard deviation of the fare passengers pay
Answers
Answer:
$4.20
Step-by-step explanation:
Calculation for the standard deviation of the fare passengers pay of Blue Cab Company:
T = Total amount of the cab fare
Formula for Standard deviation of T will be:
T = σa+bX= bσX.
To convert the rate to dollars per mile from dollars per tenth of a mile, it will be:
b= 3
Hence,
Standard deviation of T is :
3.00(1.4) = $4.20.
What can be done to the graph of y=2x2+3 to obtain the graph of y=−2x2+3?
Answers
Answer:
Reflect over the x-axis.
Step-by-step explanation:
Assuming you meant 2x^2+3, putting a negative sign in front of the x value flips the graph over the x-axis.
Which problem can be solved by performing this multiplication?
3/4×8/9
Responses
Evan practiced piano this week for 3/4 hour. Last week he practice for8/9 hour. How much longer did Evan practice last week than this week?
Jada rode her bike 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike. How far did Sarah ride her bike?
Amelie drove 3/4 mile. She then drove another 8/9 mile. How many miles did she drive in all?
Three out of 4 containers hold lemonade. Each container holds 8/9 quart of lemonade. How much lemonade do the containers all hold?
Answers
The multiplication 3/4×8/9 can be used to address the problem in response (B). which is the correct answer that would be an option (B).
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
As per option (B),
Jada rode her bike for 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike.
Sarah rides her bike = Sarah rode (8/9) of the (3/4) that Jada rode.
Sarah rides her bike = 3/4 × 8/9
Therefore, this problem can be solved by performing the above multiplication.
Hence, the correct answer would be an option (B).
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Combine like terms.
9 + 12t – 6t
Question 3 options:
9 – 12t
21
21t
9 + 6t
Answers
The expression can be simplified to obtain as 9 + 6t.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given algebraic expression is 9 + 12t – 6t.
It can be simplified as follows,
9 + 12t – 6t
Here 9 is a constant.
And, the terms 12t and 6t have the same variable t.
Which implies they are like terms.
Since the like terms in an expression can be added to subtracted, the given expression can be simplified as below,
9 + 12t – 6t
⇒ 9 + 6t
Hence, the simplification of the given expression results as 9 + 6t.
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A holiday store is having a sale on bows and rolls of wrapping paper. One sign in the store states, “Buy 1 bow and 1 roll of wrapping paper for only $6.00.” A second sign in the store states, “5 bows and 1 roll of wrapping paper will only cost $10.00.”
In dollars and cents, the cost of a single roll of wrapping paper costs $
.
Answers
Answer:
3.00
Step-by-step explanation:
One bow and and 1 roll of wrapping paper cost 6.00$
so the roll by itself would cost 6.00$
Given f(x)= 10-2x, find f(7).
-4
3
7
56
Answers
Answer:
f/97)=10-2(7)=10-14=-4
Answer:
-4 !!!
Step-by-step explanation:
ACME insurance company estimates that the probability of the owners' of a house a
worth between $120,000 to $170,000 making a claim for $5000 is 0.09, and that
the probability of the house and contents being totally destroyed is 0.0040. Should
that tragedy happen, the company will have to pay $150,000. The company charges
$1300 for the insurance policy.
What is the expected value of this policy to the insurance company?
Round your answer to two decimal places.
Answers
Answer: -$250.00
Step-by-step explanation:
\([(5000)(0.09)+150000(0.0040)]-1300 =-\$250\)
The expected value of the policy to the insurance company is -$ 250
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the value of probability owners of hours of worth between $120,000 to $170,000 making a claim of $ 5000 = 0.09
Let the value of probability of the house and contents being totally destroyed = 0.0040
Now , the tragedy happens and the company pays = $ 150,000
The amount the insurance company charges = $ 1300
So , the equation will be
The expected value of this policy to the insurance company =
( probability owners of hours of worth between $120,000 to $170,000 making a claim of $ 5000 x $ 5000 ) + ( the amount company pays x 0.0040) - amount the insurance company charges
So , the equation will be
The expected value of this policy to the insurance company =
( ( 0.09 x 5000 ) + ( 150000 x 0.0040 ) - 1300 )
The expected value of this policy to the insurance company =
( ( $ 450 + $ 600 - $ 1300 )
The expected value of this policy to the insurance company = - $ 250
Hence , The expected value of policy to the insurance company is -$ 250
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Graph the linear equation.
Y = x/3 - 4
Need help!!!!
Answers
Answer:
slope -1/3 y-intercept (0,4)
Step-by-step explanation:
Answer:
See attached image for the graph
Step-by-step explanation:
Start by finding at least two points on the plane that satisfy the equation, and join them with a line.
Pick good values for "x" that will make the evaluation easy (for example the number "0" and also multiples of "3":
when x = 0 then y = 0/3 - 4 = -4 then the point is (0, -4)
when x = 3 then y = 3/3 -4 = 1 - 4 = -3 then this new point is (3, -3)
when x = 6 then y = 6/3 - 4 = 2 - 4 = -2 then a third point is (6, -2)
We plot these points on the plane, and join them with a line, s shown in the attached image.
128x^2-162
How do you factor this
Answers
If any doubt leave a comment
Dividing fractions word problems, please help I need it........
Answers
Answer:
25
Step-by-step explanation:
l x w = h
25 x 7.2 = 180
Sketch the graph of the equation Y=2x^2-10x+9
Answers
Solution:
The equation is given below as
\(y=2x^2-10x+9\)Step 1:
We will figure out the y-intercept by putting x=0
\(\begin{gathered} y=2x^{2}-10x+9 \\ y=2(0)^2-10(0)+9 \\ y=9 \\ (0,9) \end{gathered}\)Step 2:
Calculate the vertex of the graph using the formula below
\(\begin{gathered} y=2x^2-10x+9 \\ x=-\frac{b}{2a},b=-10,a=2,c=9 \\ x=\frac{-(-10)}{2(2)}=\frac{10}{4}=\frac{5}{2} \\ \\ y=2(\frac{5}{2})^2-10(\frac{5}{2})+9 \\ y=2(\frac{25}{4})-25+9 \\ y=\frac{25}{2}-16 \\ y\frac{=25-32}{2} \\ y=-\frac{7}{2} \end{gathered}\)Hence,
The vertex of the equation is
\((\frac{5}{2},-\frac{7}{2})\)Using a graphing calculator, we will have the graph be
The owner of a deli recorded the number of customers who ordered each of four sandwiches available if the deli has 50 customers the first hour it is open predict how many customers will order turkey sandwiches
Answers
The first hour there will be 18 costumers that will order Turkey sandwiches
Probability
First, we want to find the probability of having a costumer who choose Turkey sandwich.
In order to find it, we calculate the ratio of turkey sandwiches over the total number of orders.
Turkey sandwiches: 180
Total number of orders: 160 + 100 + 180 + 60 = 500
Ratio = turkey / total
Ratio = 180 / 500 = 0.36
Then, the probability of having a costumer who choose Turkey sanwich is
P(T) = 0.36 = 36%
Secondly, in order to find the 36% of 50, we just multiply 0.36 by 50:
Hence , the first hour there will be 18 costumers that will order Turkey sandwiches
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has a perimeter of 52 feet. Let W be the width, L be the length, and P be
the perimeter, all with units in feet.
a. Given two sets of four rectangles, find one rectangle in each set that could have a
perimeter of 52 feet.
b. Which of the symbols W, L, and P are variables?
c. Which of the symbols W, L, and P are constants?
Answers
A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.
The symbols W and L are variables.
The symbol P is a constant.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);
P = 2(L + W)
Where:
P represent the perimeter of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;
P = 2(L + W)
52 = 2(12 + 14)
52 = 2(26)
52 feet = 52 feet.
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The total angle of a kite is............
Answers
Since a kite is a quadrilateral, it has the value of 360 total degrees.
Determine if true:
3+2-1x4=15
Answers
Answer:
False
Step-by-step explanation:
3+2=5
3+2=55-1=4
3+2=55-1=44x4=16
3+2=55-1=44x4=16Hence, the equation is true.
Which of the following relations be a function? Select all that apply.
Answers
B
C
E
Explanation:
The x- axis cannot repeat numbers
f(x)= -8x
Find the value of x so that
f(x) = 40
Answers
Answer:
x=-5
Step-by-step explanation:
f(x)=-8x
f(x)=40
substitute f(x) with 40 in the first equation
40=-8x
s=-5 (slove)
Which of the following materials will conduct electricity well?
A.Cotton
B. Metal
C.Rubber
D.Wood
Answers
Answer:
metal
Step-by-step explanation:
Answer:
metal
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIEST IVE BEEN ASKING FOREVER :(((((
Answers
Answer:
__C) 0.36
Step-by-step explanation:
4÷11= 0.36363636363636
so it's 0.36 with a line over it indicating a repeating decimal
a builder has built 1/6 of the floors of a new skyscraper. If the builder has built 13 floors, how many floors will the skyscraper have when it is finished? Write and solve an equation to find the answer.
Answers
Answer: 78 floors total
Step-by-step explanation:
if 13=1/6
6 x 13=78
Answer:
13*6=78
Step-by-step explanation:
If one part of something is equal to 13, then 6 parts are equal to 13*6. Let us denote that "something" by x, and we get
\(x = 6 \times \frac{1}{6} x = 6 \times 13\)
Which is obviously an identity
I WILL GIVE BRAINLIEST ANSWER CORRECTLY
Identify the segment bisector of $\overline{XY}$ .
A line segment, X Y with its midpoint M is shown. A line, n passes through segment X Y at point M. The length of X M is labeled 5 x plus 8. The length of M Y is labeled 9 x plus 12. There is a tick mark on segment X M and on segment M Y.
$\overline{XM}$
line segment cap x cap m
$X$
cap x
line $n$
line n
$\overline{YM}$
line segment cap y cap m
Question 2
The length of $\overline{XY}$ is
.
Answers
Answer:
the segment bisector should be the line n
the length of XY= 6
Step-by-step explanation:
since segment, XY is bisected, we know that each side is equal to the other
so in order to find the length of the segment, you need to set each side equal to the other
5x+8=9x+12
8=4x+12
-4=4x
x=-1
then, you plug -1 into both functions
5(-1)+8=3
9(-1)+12=3
then simply add these two numbers together to get 3+3=6
Find the distance
d(P1.P₂) between
the given points P1
and P2.
P1 = (0,0)
P2 = (6,5)
Simplify your answer, use radicals as needed.
Answers
The distance between the two points P1 and P2 is d = √61.
What is the distance?Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage. Length is measured in distance. For instance, the length of a road is its distance. The most popular units of measurement for distance in the metric system are millimeters, centimeters, meters, and kilometers.So, the distance between points P1 and P2:
Where, P1 = (0,0) and P2 = (6,5).The distance formula: d = √(x₂-x₁)²+(y₂-y₁)²Now, substitute the values in the formula as follows:
d = √(x₂-x₁)²+(y₂-y₁)²d = √(6-0)²+(5-0)²d = √36+25d = √61Therefore, the distance between the two points P1 and P2 is d = √61.
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Rachel had 7/8 of a spool of yarn. She used 3/4 of her yarn for a project. What fraction of the spool was used for the project?
Answers
if I did the math correctly the answer should be 6/8
A rectangular vegetable garden will have a width that is 3 feet less than the length, and an area of 54 square feet. If x
represents the length, then the length can be found by solving the equation:
x(x-3) = 54
What is the length, x, of the garden?
The length is
feet.
The solution is?
Answers
To determine the length of the rectangular flower garden, we need to derive equations from the given measurements and relations. The given measurements are the area, and the relation of the width and the length. From these, we generate the equation needed. We do as follows:
Area = Length x Width
where length = x ft
width = x - 3 ft
area = 54 ft^2
54 ft^2 = x ft (x -3) ft
54 ft^2 = x^2 - 3x ft^2
Solving for the value of x, we will have two values which are
x = -6 ft ( NOTE: this value can't be the answer since we cannot have a negative value for the length)
x = 9 ft = length