The radius of a circle is 6 centimeters. What is the area of a sector bounded by a 150 degree arc?Give the exact answer in simplest form._____ square centimeters
Answers
Concept
[tex]\text{Area of a sector = }\frac{\theta}{360}\text{ }\times\text{ }\pi r^2[/tex][tex]\begin{gathered} \theta\text{ is the angle subtend at the center} \\ r\text{ is the radius} \end{gathered}[/tex]Step 1: List the given data
[tex]\begin{gathered} \theta=150^o \\ r\text{ = 6cm} \\ \pi\text{ = }\frac{22}{7} \end{gathered}[/tex]Step 2: Substitute the values to find the area of the sector.
[tex]\begin{gathered} \text{Area of the sector = }\frac{150}{360}\text{ }\pi\text{ }\times6^2 \\ =\text{ }\frac{150\text{ }\pi\text{x 36}}{360\text{ }} \\ =15cm^2 \end{gathered}[/tex]Ok
Related Questions
The number of people in thousands who own a cell phone is a function of the time in years starting in 1990 where p(t) = 20(1.075)^tGrowth or Decay?What is the initial amount of people who own cell phones?Determine the growth/decay rate.
Answers
Solution
[tex]\begin{gathered} 1)\text{ Answer, This is GROWTH } \\ 2)\text{ The initial amount of people wo own a cell phone is },\text{ means when t = 0} \\ P(t)=20(1.075)^t \\ p(t)\text{ = }20(1.075)^0 \\ p(t)\text{ = 20 }\times\text{ 1} \\ p(t)\text{ = 20} \end{gathered}[/tex][tex]\begin{gathered} 3)\text{ To }\det er\min e\text{ the growth/decay rate, we have} \\ p(t)=20(1.075)^t \\ p(t)=20(1+0.75)^t \\ \text{Answer, growth rate is: 0.75 =0.75\%} \\ \end{gathered}[/tex]Maleri Designs sells cartons of cloth face masks ($18) and cartons of hand-sanitizer ($9) on eBay. One of their
customers, Mod World, purchased 21 cartons for $297. How many of cartons of each did Mod World purchase?
Check your answer. Hint: Let F= Face masks.
Answers
Answer:
F=12 C=9
Step-by-step explanation:
$18 12 times is $216 $9 9 times is $81 $216+81=$297
Suppose you pay only the interest on a loan. Will the loan ever be paid off? Why or why not? I have no idea if this is correct
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No. if only the interest is paid, the principal never decreases
19. Which repon(s) represent students that enjoy wimming and tennis?TennisSwimmingAFHikingA BBDC. (BAND D)D. IA AND C)
Answers
To determine the regions that represent the students that enjoy swimming and tennis, we need to determine the intersection between the Swimming group and the Tennis group. This intersection is represented by the groups B and D. The correct answer is C.
18. ALGEBRA Angles Q and R are supplementary. If m angle Q = 4x + 9 and m angle R = 8x + 3, what is the measure of each angle?
Answers
Find the length of the minor axis of the ellipse described by the equation:x squared over 12 plus y squared over 13 equals 1
Answers
This equation of the ellipse can be modeled by
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]The major axis is the y-axis and minor axis is the x-axis.
So, the length of the minor axis of this ellipse is "2a".
First, let's find "a",
[tex]\begin{gathered} a^2=12 \\ a=\sqrt[]{12} \end{gathered}[/tex]The length of the minor axis is >>>
[tex]\begin{gathered} 2a \\ =2(\sqrt[]{12}) \\ =2\sqrt[]{12} \end{gathered}[/tex]Answer[tex]2\sqrt[]{12}[/tex]Can someone solve this equation using the quadratic formula and simplifying in radical form if needed
Answers
For a quadratic equation of the form:
[tex]av^2+bv+c=0[/tex]The quadratic formula is:
[tex]v_{1,2}=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]In this case, we have the eqaution:
[tex]11v^2+8v=4[/tex]First, let's rest 4 on both sides to get 0 in the right hand side:
[tex]11v^2+8v-4=0[/tex]Then we can use the quadratic formula:
[tex]v_{1,2}=\frac{-8\pm\sqrt[]{8^2-4\cdot11\cdot(-4)}}{2\cdot11}[/tex]And solve:
[tex]\begin{gathered} v_{1,2}=\frac{-8\pm\sqrt[]{64^{}+176}}{22} \\ v_{1,2}=\frac{-8\pm\sqrt[]{240}}{22} \\ v_{1,2}=\frac{-8\pm\sqrt[]{16}\sqrt[]{15}}{22} \\ v_{1,2}=\frac{-8\pm4\sqrt[]{15}}{22} \\ v_{1,2}=\frac{-4\pm2\sqrt[]{15}}{11} \end{gathered}[/tex]Then the two solutions are:
[tex]\begin{gathered} v_1=\frac{-4-2\sqrt[]{15}}{11} \\ v_2=\frac{-4+2\sqrt[]{15}}{11} \end{gathered}[/tex]A+(b+c)=(a+b)+c what property is this? The options are as follows
Identity property of multiplication
Associative property of multiplication
Identity prop. Of addition
Multiplicative inverse prop.
Additive inverse prop.
Commutative prop of addition
Commutative prop of multiplication
Transitive property
Properties
Answers
Given:
The properties and their notations are given.
To match:
Explanation:
31. It is given that,
[tex]a+0=a[/tex]Since zero is the additive identity.
So, the property is an identity property of addition.
32. It is given that,
[tex]a+b=b+a[/tex]Here, the property is the commutative property of addition.
33. It is given that,
[tex]a\cdot(b\cdot c)=(a\cdot b)\cdot c[/tex]Here, the property is an Associative property of multiplication.
34. It is given that,
[tex]a+(-a)=0[/tex]Since -a is the additive inverse of a.
So, the property is the Inverse property of addition.
35. It is given that,
[tex]a\cdot1=a[/tex]Since 1 is the multiplicative identity.
So, the property is an identity property of multiplication.
36. It is given that,
[tex]a\cdot(b+c)=ab+ac[/tex]Here, the property is a distributive property of addition.
37. It is given that,
[tex]a\cdot b=b\cdot a[/tex]Here, the property is a commutative property of multiplication.
38. It is given that,
[tex]a\cdot\frac{1}{a}=1[/tex]Here, the property is an inverse property of multiplication.
39. It is given that,
[tex]a+(b+c)=(a+b)+c[/tex]Here, the property is an Associative property of addition.
Final answer:
31. E
32. A
33. D
34. AC
35. AB
36.
Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute. For how many minutes has the water been draining when Tank B contains 75 liters of water?
Answers
We get that the function that models this situation is
[tex]L=80-2.5m[/tex]where L is the liters the tank contains and m is the minutes that has passed. So we get:
[tex]75=80-2.5m\rightarrow m=\frac{-80+75}{-2.5}=2[/tex]so the tank has been drained for 2 minutes
Luisa bought 4.4 kilograms of apples. How
many ounces of apples did she buy? Use the
conversion rates 1 kilogram = 2.20 pounds
and 1 pound = 16 ounces. Round to the
nearest ounce.
Answers
Answer:
155
Step-by-step explanation:
4.4(2.2)=9.68
9.68(16)=154.88
Orlandis earned 2.5% interest on a bank balance of $80. What is the amount of interest earned?
Answers
Given
Bank balance = $80
Interest rate = 2.5%
Amount of interest earned = 2.5% of $80
Amount of interest earned = 2.5/100 of $80
Amount of interest earned = (2.5*80)/100
Amount of interest earned = 200/100
Amount of interest earned = $2.0
hence the amount of interest rate is $2.0
In anatomy, a student learned that the average resting heart rate is between 60 and 100 beats per minute. The student decided to record the heart rate of people over five minutes while waiting in line at the pharmacy. The dot plot shows the results.
Dot plot with 1 dot at 62, 3 dots at 68, 1 dot at 69, 2 dots at 70, 3 dots at 72, 2 dots at 75, 1 dot at 76, 2 dots at 78, 3 dots at 80, and 2 dots at 89
Which statement below best describes the shape of the distribution?
The data is roughly symmetrical distributed, with most values clustered from 68 to 80 beats per minute. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is not symmetrically distributed, with most values clustered from 68 to 80 beats per minute. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
The data is skewed left, with fewer values on the left end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
Answers
The correct option regarding the data-set represented by the dot plot is represented as follows:
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
Dot plotA dot plot shows the number of times that each observation appears in the data-set.
Hence, the complete data-set in this problem is given as follows:
62, 68, 68, 68, 69, 70, 70, 72, 72, 72, 75, 75, 76, 78, 78, 80, 80, 80, 89, 89.
The mean of a data-set is the sum of the observations divided by the number of observations, hence it is given by:
Mean = (62 + 3 x 68 + 69 + 2 x 70 + 3 x 72 + 2 x 75 + 76 + 2 x 78 + 3 x 80 + 2 x 89)/20 = 74.55.
The median is the middle value of the data-set. The data-set has 20 elements, hence the median is the mean of the 10th and the 11th element, given as follows:
Median = (72 + 75)/2 = 73.55.
The mean is greater than the median, hence the data is right skewed and the correct option is given as follows:
The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.
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Answer: A/The data is roughly symmetrical distributed, with most values clustered from 68 to 80 beats per minute.
Step-by-step explanation: Just got it right on the test
Due to increased mailing costs, the new rate will cost publishers $50 million; this is 12.5% more than they
paid the previous year. How much did it cost publishers last year? Round to the nearest hundreds.
Answers
The amount it will cost the publishers last year is 44.4 million
How to calculate the amount it will cost the publishers?The first step is to write out the parameters
The cost of mailing increased for the last one year
Due to this increase, it will cost the publishers $50 million for this current year
The increase is at the rate of 12.5%
The amount it will cost the publishers last year can be calculated as follows
= 12.5/100
= 0.125 + 1
= 1.125
The next step is to calculate last year cost
last year cost= 50/1.125
= 44.4 million
Hence the publishers spent 44.4 million last year
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in a classroom challenge,students had to create a triangular pyramid using various items. Each group then use your measurements to remind the volume . which group found the volume of triangle pyramid with a base area of 16 square in?
Answers
Volume of a triangular pyramid = 1/3 × base area × height
We have been given base area as 16 square in
Volume of a triangular pyramid = 1/3 × 16 × height
We need to check the options for the expression whose result will give a base area of 16 square in.
From the options:
(8×3)/2 = 12
(11×4)/2 = 22
(16 ×18)/2 = 144
(8 × 4)/2 = 16
1/3 and the height is common to all options. The expression in bracket represent the base area.
Hence, the group that found the volume of triangle pyramid with a base area of 16 square in is
[tex]\frac{1}{3}(\frac{8 ×4}{2})\times q\text{ (option D)}[/tex]Help please!
I can’t find the probability of a pretty girl telling me the answer to what 2x2 is
May I ask you, pretty girl, what is it?
Answers
Answer: depends how often you meet someone
Step-by-step explanation: You can multiply 2 times 2 and if you know the answer to that multiply that times the number of times u meet someone and divide by 2.
Find the probability of selecting a 10 or diamond when a card is drawn from a standard deck of cards.
Answers
The probability of selecting a 10 or Diamond when a card is drawn from a standard deck of cards is: 17/52
The question asks us to find the probability of picking a 10 or diamond from a deck of cards.
A standard deck of cards contains 52 cards in total.
The deck contains 4 "10s"
And the deck also contains 13 diamond cards.
Thus, we can find the probability of drawing a "10" as:
[tex]P(10)=\frac{n\text{umber of 10s}}{total\text{ number of cards in deck}}=\frac{4}{52}[/tex]Similarly, we can find the probability of drawing a diamond as:
[tex]P(\text{diamond)}=\frac{n\text{umber of diamonds}}{total\text{ number of cards in deck}}=\frac{13}{52}[/tex]Now that we have the individual probabilities, we can find the probability of drawing a 10 or a diamond using the OR probability:
[tex]\begin{gathered} P(A\text{ OR B)= P(A) + P(B)} \\ \text{where, A and B are independent events} \end{gathered}[/tex]Therefore, we can solve the question. This is done below:
[tex]\begin{gathered} \text{Probability of selecting a 10 or a diamond P(10 OR Diamond)=} \\ P(10)+P(\text{Diamond)} \\ \\ \text{But P(10)=}\frac{4}{52} \\ P(\text{Diamond)}=\frac{13}{52} \\ \\ \therefore P(10\text{ OR Diamond)=}\frac{4}{52}+\frac{13}{52}=\frac{17}{52} \end{gathered}[/tex]Thus, the probability of selecting a 10 or Diamond when a card is drawn from a standard deck of cards is: 17/52
Equation: y =
Write an equation of the line that passes through the given point and is parallel to the given I
(-4, 2); y = 1/4x + 1
Answers
The equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3
The equation of the line parallel to the line is
y = 1/4 x +1
The slope intercept form is
y = mx + b
Where m is the slope of the line and b is the y intercept
By comparing the given equation and slope intercept form of the line
The slope of the line is m = 1/4
Then the point slope form is
[tex](y-y_1)= m(x-x_1)[/tex]
The line is passing through the point (-4,2)
Substitute the values in the equation
(y-2) = 1/4(x-(-4))
y-2 = 1/4(x+4)
y-2 = (1/4)x+1
y = (1/4)x+3
Hence, the equation of the line that passes through the point (-4,2) and the parallel to the line y = 1/4x + 1 is y = (1/4)x+3
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Hi Please help me with math
Answers
Answer:12
Step-by-step explanation:
help meeeeeee pleaseee !!!!
Answers
The equation of the line that passes through point (8,-1) and perpendicular to 8y = x - 16 is f(x) = -8x + 63.
What is the equation of line that passes through the given points and is perpendicular to the given line?Given the data in the question;
Equation of line: 8y = x - 16Point: (8,-1)First we determine the slope of the initial line using the slope intercept-form. y = mx + b
8y = x - 16
y = (1/8)x - 2
Compared with the slope intercept form,
Slope m = 1/8
Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.
Hence, slope of the perpendicular line is;
Slope m = -1/1/8 = -8
To find the equation of the perpendicular line, we use the point slope formula.
y - y₁ = m( x - x₁ )
Plug in the slope m ( -8) and point (8,-1).
y - (-1) = (-8)( x - 8 )
y+1 = -8x + 64
y = -8x + 64 - 1
y = -8x + 63
Therefore, the equation of the perpendicular line is y = 8x + 63
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Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?
Answers
The number of students who chose not to take French their freshman year is 147.
According to the question,
We have the following information:
72% of students chose to study French their freshman year.
Now, 72% of students is equal to 378.
Let's take the number of students to be x.
So, we have:
72x/100 = 378
72x = 378*100
x = (378*100)/72
x = 525
Now, we have to find the number of students who chose not to take French their freshman year:
(100%-72%)
28%
Now, we have to find the 28% of total number of students:
(28*525)/100
14700/100
147
Hence, the number of students who chose not to take French their freshman year is 147.
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The table shows the linear relationship between the balance of a student's savings account and the number of weeks he has been saving Savings Account Week 0 1 13 Balance (dollars) 123 Based on the table, what was the rate of change of the balance of the student savings account in dollars and cents per week?
Answers
7 dollars per week
Explanation:Rate of change = change in balance (dollars)/change in weeks
for (0, 32) and (1, 39)
Rate of change = (39 - 32)/(1 - 0)
Rate of change = 7/1 = 7
For (1, 39) and (3, 53)
Rate of change = (53 - 39)/(3 - 1)
Rate of change = 14/2
Rate of change = 7
Since the rate of change is constant from calculation, then the rate of change of the balance of the student savings account in dollars and cents per week is 7 dollars per week
Sean and Darryl are racing on a track. Sean runs 6 miles per hour and gets a 0.25 mile head start. Darryl runs 0.7 mile per hour faster than Sean. If Darryl and Sean run the same distance, how many hours, x, do they run? 6x + 0.25 = 0.7x 0 6x - 0.25 = 3.7x 0 6x +0.25 = 6.7x D 6x + 0.25 = 4.7x
Answers
The relation between speed, distance and time is express as :
[tex]\text{ Sp}eed\text{ =}\frac{Dis\tan ce}{Time}[/tex]Sean and Darryl are racing on a track.
Sean runs 6 miles per hour and gets a 0.25 mile head start.
Speed of Sean = 6
x is the time taken by Sean
So, Distance = speed x Time
Distance travel by sean = 6x
Since, Sean gets a 0.25 mile head start.
So, total distance travel = 6x + 0.25
Darryl runs 0.7 mile per hour faster than Sean,
Speed of darryl = 0.7 + Speed of sean
Speed of daryl = 0.7 + 6
Speed of darryl = 6.7 miles per hour
x is the time taken by Darryl
So, Distance = Speed x Time
Distance = 6.7x
Distance travel by Darryl = 6.7x
Since distance travel by darryl and sean is equal so,
6x + 0.25 = 6.7x
Answer : C) 6x + 0.25 = 6.7x
A-) who won the race? a1)By how many yards of difference? B-) How many yards behind the starting line does Yolanda have to leave for the race to end in a draw?
Answers
EXPLANATION
Let's see the facts:
Race = 100-yard
Toko--> 10 yards < Yolanda
Second part:
Yolanda --> 10 yards behind the starting line
If each geil ran at the same speed as the first race, the appropiate relationship is as follows:
Yolanda's speed = 100 yards/race
Yoko's speed = 90 yards/race
Distance= ratex time
For the second race, Yolanda ran 110 yards at the same speed --> So it will take 110/100 = 1.1 times to finish the race.
Yoko runs 100 yards at the same speed so it will take her 100/90= 1.11111... times to finish the run.
As 1.11 is less time than 1.1111, Yolanda will win the race.
b) In order to finish in a tie, the times must be the same.
Let x be the head start given to Yoko so that they tie.
time = distance / rate
[tex]\frac{100+x}{100}=\frac{100}{90}[/tex]Multiplying both sides by 100:
[tex]100+x=100\cdot\frac{100}{90}[/tex]Subtracting -100 to both sides:
[tex]x=100\cdot\frac{100}{90}-100[/tex]Simplifying:
[tex]x=111.11111\ldots-100=11.111\ldots[/tex]So, if Yoko has 11.111... head start, they should tie on the next race.
Find the value of X in the length of VR
Answers
Since V is between R and T, then:
[tex]RT=VR+VT\text{.}[/tex]Substituting VR=3x, VT=5x+9, RT=33, and solving for x we get:
[tex]\begin{gathered} 33=3x+5x+9, \\ 33=8x+9, \\ 33-9=8x, \\ 8x=24, \\ x=3. \end{gathered}[/tex]Substituting x=3 in VR we get:
[tex]\text{VR}=3\cdot3=9.[/tex]Answer:
The value of x is 3.
The length of VR is 9.
Instructions for a chemical procedure state to mix salt, baking soda, and water in a 22 : 14 : 5 ratio by mass. How many grams of baking soda would be required to make a mixture that contains 55 grams of salt?
Answers
35 grams of baking soda will be required for the mixture
The ratio of mix salt to baking soda to water = 22:14:5
Let x be the total quantity of the mixture
A mixture is a substance composed of two or more unrelated chemical components. A physical blending of two or more substances that maintains their own identities takes the form of solutions, suspensions, or colloids.
Now the sum of the ratio is 22+14+5 = 41
So, 55 grams of salt = 22/41x
Solving for x we get:
x = 55*41/22
x = 102.5 grams
The total quantity of the mixture is 102.5 grams
Quantity of baking soda required = 14/41 of 102.5
= 14/41*102.5
= 35 grams
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7. Write the slope-intercept form of the equation of the line through the given point with the given slope. Write answer as y=mx+b. through: (-1, 1), slope = -6 Vour answer
Answers
Answer:
y = -6x - 5
Explanation:
The equation of a line with slope m that passes through the point (x1, y1) can be calculated using the following equation:
[tex]y-y_1=m(x-x_1)[/tex]So, replacing (x1, y1) by (-1, 1) and m by -6, we get:
[tex]\begin{gathered} y-1=-6(x-(-1)) \\ y-1=-6(x+1) \end{gathered}[/tex]Now, to write the answer as y = mx + b, we need to solve the equation for y, so we get:
[tex]\begin{gathered} y-1=-6(x)-6(1) \\ y-1=-6x-6 \\ y-1+1=-6x-6+1 \\ y=-6x-5 \end{gathered}[/tex]Therefore, the answer is y = -6x - 5
If 35% of your candies was 42 candies, how many candies do you have?
Answers
Answer:
120 candles
Step-by-step explanation:
42/35 = x/100 and solve for x
x = 120
Answer:
120
Step-by-step explanation:
35%/100=42/x
LOTS OF POINTS!!!!! The table of values represents a linear function g(x), where x is the number of weeks that have passed and g(x) is the balance in the bank account. Find the slope of the function.
A.
-500
B.
-1/100
C.
-100
D.
-1/500
Answers
Answer: easy it's A -500
The slope of the function (x) is -500!! :D
10. Given: BD || CE25= 26Prove: AC = AE(a) BD ICE(b) AC AE(c) 25* LC; 26 = LE(d) 25 = 26(e) LC= LE6DE
Answers
The image contains a figure in which angles and sides are named, some data is given, and the proof is to be provided.
Every proof starts with the given data.
Thus, from the options, we select those containing the information provided:
a) BD is parallel to CE
d) Angle 5 is congruent to angle 6
Now we can see the segments AB and AD have one tick mark. This means they are congruent or have the same measure.
AB is congruent to AD
The triangle ABD, having two equal sides, is isosceles. Every isosceles triangle has two congruent angles, in this case, angles 5 and 6.
Thus, the next step in the proof is:
c) Angle 5 is congruent to C and angle 6 is congruent to E
Because of the transitive property of congruence, it follows:
e) Angles C and D are congruent
Being two angles in a triangle congruent, it follows the triangle is isosceles, thus:
b) AC and AE are congruent
This is the final step of the proof
Question: Between what two conSecutive integers does v145 fall?{ } { }
Answers
We can find the answer to this question by using the known exact square roots of the following numbers:
[tex]\begin{gathered} \sqrt[]{144}=12 \\ \sqrt[]{169}=13 \end{gathered}[/tex]And as you can see, the number 145 is between 144 and 169.
Thus, its square root, must be between the integer values of 12 and 13.