a circle has a radius 6 in in a central age of 60 what is the measure of the arc length is associated with this angle a 2pie b pie c 6pie d 3 pie
Answers
Formula for arc length when the angle is in degrees:
[tex]\text{Arc length = }\frac{\theta}{360}\times2\pi r[/tex]r = radius = 6 in
θ= 60 degrees
[tex]\begin{gathered} \text{Arc length = }\frac{60}{360}\times2\times\pi\times6 \\ \text{arc length = }2\pi\text{ in ches (option A)} \end{gathered}[/tex]Related Questions
A U-Haul moving truck covered a total distance of 6223 kilometers averaging a speed of 47 km/h in slow moving traffic and 87 km/h in fast moving traffic. The journey took 89 hours. How many hours did the U-Haul moving truck spend in slow moving traffic?
Answers
10. Seth is analyzing his basketball statistics. The following table shows a probability model for the results of his next two free throws. Outcome Miss both free throws. Is this a valid probability model? True) Yes, this is a valid probability model.False) No, this is not a valid probability model.
Answers
Please, give me some minutes to take over your question
_________________________________
I'm working on it
__________________________
a probability model has some features
Events (This part is ok, the probabilities are between 0 - 1 )
1) p1 = 0.2
2) p2 = 0.5
3) p3 = 0.1
____________________
The sample space is not 1 because p1+p2+p3 = 0.8
______________________________________
Answer
FALSE. No, this is not a valid probability model
Amber solved the equation −2=10−3(2+6).
Match the property with each of Amber's steps for solving the equation.
Answers
The property use to solve the equation is as follows:
Distributive propertyCombine like termsAdditive property of equalityDivision property of equalityHow to solve equations?The equation can be solved as follows:
−2a = 10 − 3(2a + 6)
Using distributive property,
−2a = 10 − 3(2a + 6)
- 2a = 10 - 6a - 18
According to distributive law, multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.
Combine like terms
- 2a = 10 - 6a - 18
- 2a = -6a - 8
Using additive property of equality, we will add 6a to both sides of the equation.
The additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.
- 2a = -6a - 8
- 2a + 6a = -6a + 6a - 8
4a = - 8
using division property of equality, we will divide both sides of the equation by 4.
The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.
4a = - 8
4a / 4 = -8 / 4
a = - 2
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Evaluate the expression when y=30 and z=6 .y + z^2/y - 4z
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The answer is 11.
A bag of chips costs $2.42. Your total grocery bill, b, is a function of the number of bags of chips, n, you purchase. Write an equation to represent this function,
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Answer:
[tex]b(n)=2.42n[/tex]Explanation:
We are told that the grocery bill b is a function of n (the number of bags of chips). This means that the grocery bill can be represented as b(n).
Furthermore, we know that each bag of chips costs 2.42, meaning n bags of chips will cost 2.42n - which is the grocery bill b(n); therefore,
[tex]b(n)=2.42n[/tex]which is the equation the gives the grocery bill (as a function of n, the number of chips bags bought).
A 70-meter vertical tower is braced with a cable secured at the top of the tower and tied 30 meters from the base. What angle does the cable form with the ground? round measure of the angle to the nearest degree
Answers
Given: The statement in the question
To Determine: The angle the cable form with the ground
Solution
The statement can be represented using the diagram below
Using trigonometry ratio
[tex]\begin{gathered} tan\theta=\frac{70m}{30m} \\ tan\theta=2.333 \\ \theta=tan^{-1}(2.333) \\ \theta=66.8^0 \\ \theta\approx67^0 \end{gathered}[/tex]Hence, the angle the cable makes with the ground approximately to the nearest degree is 67⁰
What statement is true? 3/7 is greater than 0.516 3/7 is less than 0.516 3/7 equal 0.516
Answers
ANSWER
3/7 is less than 0.516
EXPLANATION
Wwe want to compare the two numbers 3/7 and 0.516.
Let us convert 3/7 to decimal so we can compare properly:
3/7 = 0.429
As we can see:
0.429 is less than 0.516
So, 3/7 is less than 0.516
Match each of the following expressions to its meaning in the context of this situation.Question is in picture
Answers
Step 1
Given;
[tex]\begin{gathered} Pizza\text{ store charges 6\% sales tax and \$5 on delivery} \\ Functions\text{ that represent the situation are;} \\ f(a)=1.06a \\ g(b)=b+5 \end{gathered}[/tex]Step 2
Match each of the following expressions to its meaning in the context of this situation.
[tex]undefined[/tex]Please help with this question
Answers
The sum of the expression will be given as 26. Thus, option B is correct.
An expression may be defined as the collection of numbers and variables related to one another by arithmetic operations. A number x is said to be a perfect square of a certain number y if the number y is multiplied to itself again. The square root of the number y will be equal to x. For example, 25 is the perfect square of 5 and 9 is the perfect square of 3. Square root of a number may be defined as the number to the power of half. The square root of √121 = 11 as 121 is perfect square of 11 and square root of √225 = 15 as 225 is perfect square of 15.
Now, √121 + √225 =?
As, √121 = 11 and √225 = 15
=> 11 + 15 = 26 which is the required answer.
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Graph a line that is perpendicular to the given line. Determine the slope of the given line and the one you graphed in simplest form
Answers
Let's first identify at least two points that pass through the given line.
Let's use the following points:
Point A: x1, y1 = 0, -7
Point B: x2, y2 = 6, 2
a.) Let's determine the slope of the original line:
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{2\text{ - (-7)}}{6\text{ - 0}}\text{ = }\frac{2\text{ + 7}}{6}[/tex][tex]\text{ m = }\frac{9}{6}\text{ = }\frac{\frac{9}{3}}{\frac{6}{3}}\text{ = }\frac{3}{2}[/tex]Therefore, the slope of the given line is 3/2.
b.) Let's determine the slope of the line perpendicular to the given line:
[tex]\text{ m}_{\perp}\text{ = -}\frac{1}{\text{ m}}\text{ }[/tex][tex]\text{ = -}\frac{1}{\frac{3}{2}}\text{ = -1 x }\frac{2}{3}[/tex][tex]\text{ m}_{\perp}\text{ = -}\frac{2}{3}[/tex]Therefore, the slope of the line perpendicular to the given line is -2/3.
c.) Let's plot the graph of the perpendicular line.
Let's first determine the equation of the given line.
m = 3/2
x,y = 0, -7
y = mx + b
-7 = (3/2)(0) + b
-7 = b
y = mx + b
y = 3/2x - 7
Let's determine the equation of the perpendicular line.
m = -2/3
x,y = 0, -7 ; let's use this as the point of intersection.
y = mx + b
-7 = -2/3(0) + b
-7 = b
y = mx + b
y = -2/3x - 7
Let's now plot the graph.
Select all of the segments that must be 9 centimeters long.
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Given:
KM=12 cm.
KO=1+KL
[tex]KL=\frac{1}{3}LM[/tex]Since KM=12 cm, we can write
[tex]\begin{gathered} KM=KL+LM \\ KM=\frac{1}{3}LM+LM \\ 12\text{ =}\frac{4}{3}LM \\ LM=\frac{12\times3}{4} \\ LM=9 \end{gathered}[/tex]Therefore, KL can be calculated as,
[tex]\begin{gathered} KL=\frac{1}{3}LM \\ =\frac{1}{3}\times9 \\ =3 \end{gathered}[/tex]Now, KO can be calculated as,
[tex]\begin{gathered} KO=1+KL \\ =1+3 \\ =4 \end{gathered}[/tex]Now, using geometric property,
[tex]KM\times KL=KN\times KO[/tex]Putting the values in the above equation, KN can be calculated as,
[tex]\begin{gathered} 12\times3=KN\times4 \\ KN=\frac{12\times3}{4} \\ KN=9 \end{gathered}[/tex]Now, ON can be calculated as,
[tex]\begin{gathered} ON=KN-KO \\ =9-4 \\ =5 \end{gathered}[/tex]Since LM=9 is a chord longer than MN in the given circle, the length of MN is less than 9.
Therefore, the segments with length 9 are LM and KN.
How can I divide these5/614/3
Answers
Let's divide 5/6, we just place each part as an extended division
When the dividend is less than the divisor, we have a decimal point
15. Higher Order Thinking Jane bought three sheets
of poster board and a pack of markers. Denise
bought two packs of construction paper and a
tube of glue. Who spent more? How much more?
16. If Jane buys two more sheets of poster board, how
much does she spend all together?
DATA
Poster board
Markers
Tape
Glue
8.90
Craft Supplies
Construction paper
17.MP.2 Reasoning Julene has $25 to make posters. She buys
two packs of markers, one pack of construction paper, two tubes
of glue, and a roll of tape. How many sheets of poster board can
she buy with the money she has left? Explain your answer.
:
$1.29/sheet
$4.50/pack
$1.99/roll
$2.39/tube
$3.79/pack
Answers
Answer: Denise spent more than Jane.
Step-by-step explanation: Denise spent $9.97. We know now that Denise spent more than Jane. For the second part of the question how much more? We basically just subtract the two values. $9.97-$8.37 which is $1.60. There you go.
Felipe the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On
Answers
Using system of equations:
Length of each Plan A workout is: 0.5 hour
Length of each Plan B workout is: 1.25 hours
How to Solve a System of Linear Equations?The number of hours that each of the workout plans last can be represented as a system of linear equations. The explanation below shows how to solve this problem using the elimination method.
Let,
x = number of hours for each plan A workout.
y = number of hours for each plan B workout.
Create the system of equations below:
Equation for Friday would be:
3x + 2y = 4 --> equation 1
Equation for Saturday would be:
8x + 4y = 9 --> equation 2
Multiply equation 1 by 4 and equation 2 by 2:
12x + 8y = 16 --> eqn. 3
16x + 8y = 18 --> eqn. 4
Substract eqn. 4 from eqn. 3:
-4x = -2
x = 1/2 = 0.5 [0.5 hours or 1/2 an hour for Plan A]
Substitute x = 0.5 into eqn.1:
3(0.5) + 2y = 4
1.5 + 2y = 4
2y = 4 - 1.5
2y = 2.5
y = 2.5/2
y = 1.25 [1.25 hours for Plan B]
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I don't remember what an isosceles triangle is
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An isosceles triangle is a triangle which has two of its sides with the same length
Really need help on this
Answers
You can use rise/run (y/x) to find the slope of the line. If you plug in 0 for x you will find y which just so happens to be -4
What is the exact value of [tex] { \cos}^{ - 1} \frac{ \sqrt{2} }{2} [/tex]when0° < A < 360°Choices- A. 135°B. 225°C. 315°D. 45°
Answers
Assuming that the question is as follows:
[tex]\arccos (\frac{\sqrt[]{2}}{2})=\cos ^{-1}_{}(\frac{\sqrt[]{2}}{2}),0The question is asking for the function arccos (or inverse cosine) of the value, that is the angle, theta, that gives us a cosine(theta) = (sqrt(2)/2). Then, we have that this value is, in degrees, as follows:If we represented this angle as a right triangle (in fact, a right-angled isosceles triangle) with sides (legs) equal to one, then, we have that (for this case, the triangle has two angles that equal 45 degrees):
[tex]\cos (\theta)=\cos (45)=\frac{adj}{hyp}=\frac{1}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}}=\frac{\sqrt[]{2}}{\sqrt[]{2^2}}=\frac{\sqrt[]{2}}{2}\Rightarrow cos(45)=\frac{\sqrt[]{2}}{2}[/tex]We need to multiply both, the numerator and the denominator by the square root of 2 to have no irrational number in the denominator.
Therefore, the value of the inverse cosine of sqrt(2)/2 is the angle 45 (the correct answer is option D).
three dice are tossed. what is the probability of rolling 3 different numbers?
Answers
Given:Three dice are tossed.
To find: Probability of rolling 3 different numbers.
Let E be the event of getting same number on three dice.
So,the favorable cases for E will be
(1,1,1) , (2,2,2) , (3,3,3), (4,4,4), (5,5,5) , (6,6,6).
So, the number of favorable cases=6
Now,the total number of cases for E will be
[tex]6\times6\times6[/tex]Since each dice has 6 numbers so three dice will have these number of cases.
Now, the probability to have a same number on 3 dice will be
[tex]P(E)=\frac{\text{Number of favorable cases}}{\text{Number of cases}}\text{ }[/tex][tex]\begin{gathered} P(E)=\frac{6}{6\times6\times6} \\ =\frac{1}{36} \end{gathered}[/tex]Now, probability of rolling 3 different numbers is
[tex]P(nu\text{mbers are different on thr}ee\text{ dice)}=1-P(E)[/tex][tex]\begin{gathered} =1-\frac{1}{36} \\ =\frac{30}{36} \\ =\frac{15}{18} \end{gathered}[/tex]Hence, the probability of rolling three different numbers is
[tex]\frac{15}{18}[/tex]When a rate is simplified so that it has a _ , it is called a unit rate
Answers
Answer:
When a rate is simplified so that it has a denominator of 1, it is called a unit rate
Step-by-step explanation:
Hope it helps!
Alocal aquarium found that if the price of admission was $10, the attendance was about 1000 customers per week. When the price of admission was dropped to $6,attendance increased to about 2950 per week. Write a linear equation for the attendance in terms of the price,p. (A = mp+b)
Answers
Given:
$10 price = 1000 customers per week.
$6 price = 2950 customers per week.
Let's write a linear equation for the attendance in terms of the price, p.
Apply the slope-intercept form:
y = mx + b
In this case, let's use the form:
A = mp + b
Where m is the average rate of change(slope) and b is the y-intercept.
To find the slope, m, apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where:
(x1, y1) ==> (10, 1000)
(x2, y2) ==> (6, 2950)
Hence, we have:
[tex]m=\frac{2950-1000}{6-10}=\frac{1950}{-4}=-487.5[/tex]The average rate of change is -$487.5
To find the y-intercept, b, substitute either of the points for A and p, substitute -487.5 for x then evaluate.
Let's take the first point: (10, 1000)
A = mp + b
1000 = -487.5(10) + b
1000 = -4875 + b
Add 4875 to both sides:
1000 + 4875 = -4875 + 4875 + b
5875 = b
b = 5875
Therefore, the lineart equation for the attendance in terms of the price, p is:
A = -487.5p + 5875
ANSWER:
[tex]A=-487.5p+5875[/tex]The height of a windmill blade above the ground (in feet) is given by the function ff where f(k)=14sin(1.1k)+24. Match the following expressions with the appropriate quantity.expressions-sin(1.1k)-1.1-24-14sin(1.1k)-k-1.1k- 14sin(1.1k)+24quantitiesspeed of the blade (in feet per second)height of the blade above ground (in radii)speed of the blade (in radians per second)height of the horizontal diameter of the fan above the ground (in radii)height of the blade above the horizontal diameter of the fan (in feet)angle measure rotated from the 3 o'clock position (in radians)height of the blade above the horizontal diameter of the fan (in radii)height of the horizontal diameter of the fan above the ground (in feet)height of the blade above ground (in feet)number of seconds elapsed since windmill started rotating
Answers
f (k ) =14 sin ( 1.1 k) + 24
The expressions with the appropriate quantity is f ( k) = - 14sin(1.1k
9. A rectangle is inscribed in a circle.
a. Calculate the area of the circle.
b. Calculate the area of the rectangle.
c. Calculate the area of the shaded region.
Answers
Answer:
a. 227 in.
b. 120 in.
c. 107 in.
Step-by-step explanation:
a. diameter is the radius 2x. divide 17 by 2 to get the radius which is 8.5 plug it in to the formula A=π(8.5)2 to get 226.98 rounded to 227
b. formula: length x width. length is 15 width is 8. 15x8 = 120
c. subtract the area of the circle & the area of the rectangle to get 107.
R1.56P12TSIn the diagram, QT || RS, PQ = 6, QR = 1.5 and PT = 12. Find ST.STtype your answer...units
Answers
Answer:
[tex]ST=3\text{ units}[/tex]Explanation:
Let x represent the length of segment ST.
Given that the lines QT and RS are parallel, the, then the triangles QPT and RPS are similar.
So, the ratio of their sides will be equal;
[tex]\frac{QP}{PT}=\frac{RP}{PS}[/tex]Given;
[tex]\begin{gathered} QP=6 \\ PT=12 \\ RP=6+1.5=7.5 \\ PS=12+x \end{gathered}[/tex]substituting;
[tex]\begin{gathered} \frac{6}{12}=\frac{7.5}{12+x} \\ 12+x=\frac{7.5\times12}{6} \\ 12+x=15 \\ x=15-12 \\ x=3 \\ ST=3\text{ units} \end{gathered}[/tex]Therefore;
[tex]ST=3\text{ units}[/tex]what is the remainder when 1234 is divided by 34
Answers
Answer:
10
Step-by-step explanation:
1234 / 34 = 1224
1234 - 1224 = 10
The remainder = 10
A new computer cost $890 but is being discounted 15%. Find total cost (include 7% sales tax).
Answers
Answer:
$809.455
Step-by-step explanation:
How to find the new cost:
890/100*15
= 133.5
So: 890-133.5
= 756.5
next we find 7% of it (tax):
Which we will find the 7% of it and plus it in
so the new answer is: 809.455
How do I solve this?
Answers
The functions and its domain are a representation of their dependance on one another.
Functionsfunction, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). In the given question, we have two functions and we are required to find the composite of which ever form of the functions as well as the domain of the said function.
[tex]f(x) = \frac{3}{x}, g(x) = 2x + 8;\\(f.g)(x) = \frac{3}{2x + 8}[/tex]
The domain of the function is given as
[tex]domain = (-\infty , -4) U (-4, \infty)\\[/tex]
In the second composition of the function,
[tex](g.f) = \frac{6}{x} + 8\\domain = (-\infty, 0) U (0, \infty)[/tex]
The third composition of function
[tex](f.f) = x\\domain = (-\infty, \infty)[/tex]
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1. The number of identity theft cases from 2005 through 2010 can be represented by
the function f(x) = 0.058x + 2.175x + 340.2x² - 1,500x+20,000, where x
represents the number of years since 2005. Approximately when will the number of
identity theft cases reach 50,000
Answers
We need to know about quadratic equation to solve the problem. The year when the number of cases will be 50,000 is 2017.
Quadratic equation is an equation that has a maximum degree of two. Quadratic equations always have two roots, it can be solved by factorization method. In this question we have been given a function that we can simplify to get a quadratic equation. We need to find the year when the identity theft cases reach 50,000, we need to equate the equation to 50,000 and then solve the quadratic equation to get x.
f(x)=0.058x+2.175x+340.2[tex]x^{2}[/tex]-1500x+20000 =340.2[tex]x^{2}[/tex]-1497.767x+20000
50000=340.2[tex]x^{2}[/tex]-1497.767x+20000
340.2[tex]x^{2}[/tex]-1497.767-30000=0
Using Sridharacharya's method,
x=1497.767±[tex]\sqrt{2243305.99+40824000}[/tex]/680.4=1497.767±6562.56855/680.4
x=11.85 or x=-7.44
Here x cannot be negative, so the right value of x is approximately 12,
year when cases is 50000= 2005+12=2017
Therefore the year when identity theft cases reach 50000 is 2017.
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Question 2A bag of marbles contains 8 black marbles, 4 redmarbles, 3 blue marbles, and 5 white marbles. What isthe probability of not drawing a black marble?
Answers
Probability of not drawing a black marble = (Number of marbles which are not black)/ (Total number of marbles)
Probability of not drawing a black marble = 12/ 20 (Replacing)
Probability of not drawing a black marble = 3/5 (Simplifying)
The answer is 3/5
Can you help me understand how to do this please?
Answers
1/8
Explanation:The given expression is:
[tex]-\frac{1}{4}+\frac{3}{8}[/tex]Find the Least Common multiple(LCM) of the denominators
LCM of 4 and 8 = 8
After simplification, the addition expression then becomes:
[tex]\begin{gathered} \frac{-2(1)+1(3)}{8} \\ =\frac{-2+3}{8} \\ =\frac{1}{8} \end{gathered}[/tex]Help what would be the answer to this question?
Answers
Based on the division of polynomials and logical inference, the missing factor is 10x².
What is the proof for the above answer?Note that the result of:
[15x³ - 22x² + (?)] / (5x-4) = 3x²
This means that
3x² * (5x-4) = [15x³ - 22x² + (?)] .............................1
But
3x² * (5x-4) = 15x³ - 12x²
By reverse calculation, therefore,
We state:
-22x² + (?) = - 12x² [Assume for a moment that x² is eliminated]
-22 + (?) = -12
(?) = -12 +22, Hence
(?) = 10x²
Thus,
[15x³ - 22x² + 10X²) ] / (5x-4) = 3x² .........................................2
Proof:
15x³ - 22x² + 10x² ...................................................................3
= 15x³ - 12x²
Taking common factors:
15x³ - 12x² ⇒ 3(5x³-4x²)
Find one factor
3x² (5x-4) .....................................................................................4
Recall that the problem states that equation 3 / (5x-4) = 3x²
If 15x³ - 22x² + 10x² when simplified =
3x² (5x-4)
Then
15x³ - 22x² + 10x²/ (5x-4) = 3x² (5x-4)/(5x-4)
= 3x²
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