Answer:
The length of the arc is approximately [tex]\( 17.27 \)[/tex] units.
Explanation:
To find the length of the arc, we use the formula:
[tex]\[ \text{Arc Length} = \frac{\text{Central Angle}}{360^\circ} \times 2\pi r \][/tex]
where:
- Central Angle is the measure of the angle formed by the arc and the center of the circle
- [tex]\( r \)[/tex] is the radius of the circle
Given:
- Radius ([tex]\( r \)[/tex]) = 6
- Central Angle = 330º
Plugging the values into the formula:
[tex]\[ \text{Arc Length} = \frac{330^\circ}{360^\circ} \times 2\pi \times 6 \][/tex]
[tex]\[ \text{Arc Length} = \frac{330}{360} \times 2\pi \times 6 \][/tex]
[tex]\[ \text{Arc Length} = \frac{11}{12} \times 2\pi \times 6 \][/tex]
[tex]\[ \text{Arc Length} = \frac{11}{2} \pi \][/tex]
Using [tex]\( \pi \approx 3.14 \)[/tex], we can approximate the value:
[tex]\[ \text{Arc Length} \approx \frac{11}{2} \times 3.14 \][/tex]
[tex]\[ \text{Arc Length} \approx 17.27 \][/tex]
So, the length of the arc is approximately [tex]\( 17.27 \)[/tex] units.
Anthony surveys a group of students at his school about whether they play a sport...
Answer:
Yes they are independent, because P(girl) ≈ 0.42 and P(girl l plays a sport) ≈ 0.42
Step-by-step explanation:
A.P.E.X
Yes, being a girl and playing a sport are independent events as P(girl) = P(girl plays a sport) = 0.4
What is mean by Probability?The term probability refers to the likelihood of an event occurring. It is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Given that;
We have been given a table that shows the results broken down by gender.
Play sports Do not play sports Total
Boy 105 75 180
Girl 70 50 120
Total 175 125 300
Here, Formula for probability of independent events:
"If A and B are independent events then, P(A∩B) = P(A).P(B)"
And, Formula of the probability of an event A is:
⇒ P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
Now, Using the definition of probability:
⇒ P(girl) = Number of girls/ Number of students
⇒ P(girl) = 120/300
⇒ P(girl) = 0.4 .....(1)
And, we find the probability of girls that play a sport.
Using the definition of probability:
P(girl plays a sport) = Number of girls who plays a sport/ number of students who plays a sport
= 70/ 175
= 0.4 ...(2)
From (1) and (2),
P(girl) = P(girl plays a sport)
Thus, Being a girl and playing a sport are Independent events.
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The complete question is this,
Anthony surveys a group of students at his school about whether they play a
sport. This table shows the results broken down by gender.
Play a sport
Total
Do not play a
sport
105
70
175
Boys
Girls
75
50
125
Total
180
120
300
Are being a girl and playing a sport Independent events? Why or why not?
O A. Yes, they are independent, because P(girl) = 0.58 and P girl plays
a sport) = 0.6.
O B. Yes, they are independent, because (girl) = 0.42 and girl plays
a sport) - 0.42
O c. No, they are not independent, because P(girl) = 0.42 and
P(girl plays a sport) = 0.42.
D. Yes, they are independent, because (girl) = 0.58 and P(girl plays
a sport) = 0.58
If a hiker starts at sea level and increases her elevation at a rate of 1 foot per minute what will her elevation be in 20 minutes
Answer:
20 feet above sea level.
Explanation:
This can be solved by looking at the Rate of Change. It is given that for ONE minute that passes by, her elevation increases by ONE foot.
With this rate, after 20 minutes, the elevation can be shown as:
20 min × 1 foot= 20 feet.
Answer:
20ft
Step-by-step explanation:
Sea level is at 0 and the hiker hikes for 20 minutes at a rate of 1 foot. 20*1=20.
0+20=20
Someone help me with this please. It is not circumference, so I do not know what to do...
5 stars and thanks for anyone who answers, asks for details, and comments.
Choose the factored form of the quadratic expression.
6x^2+ 33x-18
(6x-3)(x+6)
(9x+1)(x-2)
(9x-1)(x+2)
(6x+3)(x-4)
a 19.7%
b 24.6%
c 80.3%
d 15%
Answer:
. How to calculate percentage of a number. Use the percentage formula: P% * X = Y
Convert the problem to an equation using the percentage formula: P% * X = Y.
P is 10%, X is 150, so the equation is 10% * 150 = Y.
Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.
Step-by-step explanation:
easy to read. Then solve the problem.
You climb a steep hill with 5 of your friends. You climb at a steady rate of 13 feet per minute. After 9
minutes, you are the second person to reach the top of the hill. How many feet did you climb?
Answer:
117 ft
Step-by-step explanation:
13 x 9 = 117
Answer:
117
Step-by-step explanation: since you climb 13 feet per minute you do 13×9 to get the answer of 117
How much would $500 invested at 6% interest compounded monthly be
worth after 4 years? Round your answer to the nearest cent.
ACO) - P(1)
There are 5 pennies, 7 nickels, and 9 dimes in an antique coin collection
two coins are to be selected at random from the collection. Find each
10. P(selecting 2 pennies), if no replacement occurs
11. P(selecting 2 pennies), if replacement occurs
12. P(selecting the same coin twice), if no replacement occurs
Answer:
10. 4.8%
11. 5.67%
12. 30.39%
Step-by-step explanation:
The total number of coins is 5 + 7 + 9 = 21 coins
The probability of selecting two pennies without replacemente is:
First penny: 5 possibilities over 21 coins: 5/21
Second penny: 4 possibility over 20 coins: 4/20
P(selecting 2 pennies) = (5/21) * (4/20) = 1/21 = 0.048 = 4.8%
With replacement, we have:
First penny: 5 possibilities over 21 coins: 5/21
Second penny: 5 possibilities over 21 coins: 5/21
P(selecting 2 pennies) = (2/21) * (2/21) = 25/441 = 0.0567 = 5.67%
The cases for selecting the same coin are:
First penny: 5 possibilities over 21 coins: 5/21
Second penny: 4 possibilities over 20 coins: 4/20
P(selecting 2 pennies) = (5/21) * (4/20) = 20/420
First nickel: 7 possibilities over 21 coins: 7/21
Second nickel: 6 possibilities over 20 coins: 6/21
P(selecting 2 nickels) = (7/21) * (6/21) = 42/441
First dime: 9 possibilities over 21 coins: 9/21
Second dime: 8 possibilities over 20 coins: 8/21
P(selecting 2 dimes) = (9/21) * (8/21) = 72/441
P(selecting the same coin twice) = P(selecting 2 pennies) + P(selecting 2 nickels) + P(selecting 2 dimes) = (20+42+72)/441 = 0.3039 = 30.39%
The probabilities for picking 2 pennies either with or without replacement from a total of 21 coins is calculated. With no replacement, the chance is approximately 4.76%, while with replacement, it is approximately 5.67%. It's impossible to choose the same coin twice without replacement.
Explanation:The total number of coins is 5 pennies + 7 nickels + 9 dimes = 21 coins. We are asked to calculate the probability of selecting 2 specific coins from these total coins.
10. P(selecting 2 pennies), if no replacement occurs:
Since no replacement is occurring, we first select one penny out of 5, then another penny out of the remaining 4. That constitutes 5/21 * 4/20 = 0.0476, or 4.76% probability of selecting two pennies without replacement.
11. P(selecting 2 pennies), if replacement occurs:
Since replacement is possible in this scenario, even after choosing a penny, we still have 5 pennies left. Hence, the probability of selecting a penny twice is (5/21) * (5/21) = 0.0567, or approximately 5.67%.
12. P(selecting the same coin twice), if no replacement occurs:
If no replacement occurs, it's impossible to choose the exact same coin twice because once a coin is chosen, it is removed from consideration. Therefore, the probability here is 0.
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When might it NOT be a good idea to use a dot plot to organize data?
Dot plots will not work well for large sets of data, because a dot would need to be plotted for each value.
What is interquartile range?In descriptive statistics, the interquartile range is a measure of statistical dispersion, which is the spread of the data.It is defined as the difference between the 75th and 25th percentiles of the data.Given is to investigate the disadvantage of using the dot plot to organize data.
Dot plots work very well for data with a small number of values.They would not work well for large sets of data, because a dot would need to be plotted for each value. Histograms or box plots are more useful for large sets of dataTherefore, Dot plots will not work well for large sets of data, because a dot would need to be plotted for each value.
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Luigi’s Pizza sells an extra‐large pizza with a 40 inch diameter. If the pie is cut into 8 equal slices,what is the area of one slice of Luigi’s pizza?
Answer:
14.1 inches squared.
Step-by-step explanation:
A = (3.141)(6)^2
A = 113.1 inches squared
Now that we know the area, we simply divide it by 8, as there are 8 EQUAL pieces, and so each piece must have an EQUAL area. This gives us:
113.1 / 8 = 14.1
Answer:
14.1
Step-by-step explanation:
What number would you add to both sides of 2 + 7x = 4 to complete the square?
2^2
7^2
7/2^2
{7/2)2
Answer:
{7/2)2
Step-by-step explanation:
A French submarine is at a depth of -200 meters, and a Russian submarine is at
a depth of -205 meters, which submarine is deeper?
A. French submarine
B. Russian submarine
The Russian submarine is deeper since -205 meters is a greater depth than -200 meters when comparing negative values.
To compare the depths of the two submarines, we need to consider the numerical value of their depths. When we look at depths, the larger the negative number, the deeper the location. In this case, a depth of -200 meters means the French submarine is closer to the surface than a depth of -205 meters.
Therefore, the Russian submarine is deeper because -205 is lower than -200 when considering depths below sea level.
Each letter of the word PROBABILITY is written on an individual card, each of which
is the same size, and all are put in a bag. A card is drawn without looking. Find
P(Letter A or Letter B)
Inclusive Event
Independent Event
O Dependent Event
Mutually Exclusive Event
Answer:
P(Letter A or Letter B)
15 BRAINLY
What is the slope, m, and y-intercept for the line that is plotted on the grid below?
On a coordinate plane, a line goes through points (0, 4) and (negative 2, 0).
Answer:
y=-2x+4
Step-by-step explanation:
we use the formula for the line and substitute what we already know, which is that the y-intercept is (0,4):
y=mx+4
then, you use the formula for slope:
Δy/Δx
(4-0)/(0-2)
4/-2
-2
you substitute the slope into the equation and the answer:
y=-2x+4
Hope this helps :)
P.S: m is the variable for the slope
During a basketball game, Stephanie made a total of 20
shots, some of them worth two points and some of them
worth three points.
If Stephanie scored 48 points in the game (and none of
them came from single point free throws), how many two
point shots did she make?
Answer:
24 two point shots
Step-by-step explanation:
48/2 =
24
A coin weighs 3/4
ounces. Trey picked up 6 of these coins.
What is the total weight of the coins he picked up?
Write your answer in simplest form.
Answer:
4 2/4
Step-by-step explanation:
3/4 + 3/4 + 3/4 + 3/4 + 3/4 + 3/4
To find the total weight of the coins Trey picked up, multiply the weight of one coin by the number of coins. The total weight is 9/2 ounces or 4.5 ounces in decimal form.
Explanation:To find the total weight of the coins Trey picked up, we need to multiply the weight of one coin by the number of coins picked up. The weight of one coin is 3/4 ounces, and Trey picked up 6 of these coins. To multiply a fraction by a whole number, we multiply the numerator (top number) of the fraction by the whole number. So, the total weight of the coins Trey picked up is (3/4) * 6 = 18/4 ounces.
Next, we simplify the fraction to its simplest form. To do this, we find the greatest common divisor (GCD) of the numerator and denominator, and divide both by the GCD. In this case, the GCD of 18 and 4 is 2. Dividing both the numerator and denominator by 2, we get 18/4 = 9/2. So, the total weight of the coins Trey picked up is 9/2 ounces or 4.5 ounces in decimal form.
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Find the volume of the cylinder in terms of x?
1- 127.16x m3
2- 74.8 m3
3- 432.34x m3
4- 63.58x m3
Select the correct answer.
What is a car loan?
© A.
a way to pay in advance for using a car for a given time period
B. a way to pay for a car that is dependent on the number of miles you drive
C
a way to borrow money from a bank or financial institution to pay for a car
Reset
Next
Answer:
The answer is C, take the quiz and you are bound to get it right.
Step-by-step explanation:
Ramesh examined the pattern in the table. Ramesh says that based on the pattern 7 to the power of -5 equals -16,807 . Which statement explains where the Ramesh is correct?
(I will mark brainliest)
D) Ramesh is not correct because as the exponents decrease, the previous value is divided by 7, so 7^-5 = 1/7/7/7/7/7 = 1/16,807.
I just took the quiz on edge
What is the surface area of the cylinder? Express the answer in terms of -
d = 8 cm
h = 18 cm
Recall the formula SA - 23+ + 2
152
cm
Answer:
Surface area is 176π cm²
Step-by-step explanation:
Data
diameter, d = 8 cmheight, h = 18 cmSurface area (SA) of the cylinder is computed as follows:
SA = π*d*h + π*d²/2
Replacing with data:
SA = π*8*18 + π*8²/2
SA = 144π + 32π
SA = 176π cm² ≈ 552.92cm²
A music fraternity is giving instrument lessons as part of a
fundraiser to help repair old instruments for local middle schools
and high schools. Each student pays $8 per lesson. If the fraternity
gives 21 lessons per week, about how much will they be able to
donate to the schools after 18 weeks?
more than $3300
less than $2300
$2800 to $3300
$2300 to $2800
Answer:
2800 to 3300 i believe
Solve:
|x +4| +8 > 2
Answer:
all real numbers
Step-by-step explanation:
|x +4| +8 > 2
Subtract 8 from each side
|x +4| +8-8 > 2-8
|x +4| >-6
Absolute values must be greater than or equal to zero
This is always true so x can be any value
Which equation best represents the data?
The data in the table represents a company's profit based
on the number of items produced
O
Profit Based on Number of Items Produced
y = -1.026x2 + 1016.402x - 162075
y = -1.036x2 + 1024.771x - 163710
y = 298.214x - 66317.667
y = 196.2x - 18710
Answer:
Well, Your best answer will be is Y = -1.026x2 + 1016.402x - 162075. Because, When x = 100
y = -1.036x^2 + 1024.771x - 163710
y = -1.036(100)² + 1024.771(100) - 163710
y = -10360 + 102477.1 – 163710
y = -71592.9
Good Luck!
[tex]_{Itsbrazts}[/tex]
The equation best represents the data is : Y = -1.026x² + 1016.402x - 162075.
What is equation?
An equation is a mathematical expression that contains an equals symbol.
As, per the given table
Y = -1.026x² + 1016.402x - 162075.
When x = 100
y = -1.036(100)² + 1024.771(100) - 163710
y = -10360 + 102477.1 – 163710
y = -71592.9
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cylinder has a height of 15 centimeters and a radius of 10 centimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
cubic centimeters
Answer: 4712.39 centimeters
Step-by-step explanation: Using the volume of a cylinder calculator, I got the answer of 4712.3889803847 centimeters, but rounded it to the nearest hundreth. Hope this helps!
The volume of the cylinder will be 4,710 cubic centimeters.
What is the volume of a right circular cylinder?Let r be the radius and h be the height of the cylinder. Then the volume of the cylinder will be given as,
V = π r²h cubic units
Given that:
Radius, r = 10 cm
Height, h = 15 cm
The volume of the cylinder is calculated as,
V = 3.14 x 10 x 10 x 15
V = 4,710 cubic cm
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Construct a tangent to the circle at point B.
PLEASE HELP!!
Answer:
this is it
Step-by-step explanation:
and yes that is greg heffley
The construction of the tangent to the circle at point P gives the
attached image having markings which are the steps in the construction.
How can the tangent to the circle be constructed?
The steps to draw a tangent to a circle are as follows;
With the straight edge, construct passing through the center of the circle P and the point B on the circle and extend the further from the point BPlace the compass at point P and draw an arc intersecting the above line on both sides of point P at points Q and RExtend the compass to make it larger than PQ, place the compass at points Q and draw an arc on one side of the line PQPlace the compass on point R and with the same radius (arc width) above and draw an arc on the same side of the circle intersecting the arc drawn aboveJoin the point of intersection of the arcs to the point B to complete the construction of the tangent to the circle
A drawing showing the completed drawing and the relevant markings in
the steps to construct a tangent to a circle created with MS Visio is
attached.
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Triangle A B C. Line A B and C B extend past the triangle to form an angle with measure 70 degrees. Angle A C B is 58 degrees. What is the measure of AngleCAB? 38° 52° 70° 128°
Answer:
CAB=52°
Step-by-step explanation:
58°+70°+x=180°
128°+x=180°
x=180°-128°
=52°
Answer:
CAB=52
Step-by-step explanation:
The opening of a garden hose is 3 centimeters wide. What is the circumference of the the opening to the nearest tenth centimeter?
a. 7.1 cm
b. 9.4 cm
c. 18.8 cm
d. 28.3 cm
Answer:
B. 9.4 cm
Step-by-step explanation:
The formula for circumference is 2(pi)r; so 2(3.14)1.5=9.42
complete the table of values for x+y=6
Please could you write it down as a table ,
The complete table of values for the equation x + y = 6
x 4 8 12
y 2 -2 4
Completing the table of values for the equation
From the question, we have the following parameters that can be used in our computation:
x + y = 6
This can be expressed as
y = 6 - x
The missing y values are at x = 4, 8 and x = 12
Substitute the known values in the above equation, so, we have the following representation
y = 6 - 4 = 2
y = 6 - 8 = -2
y = 6 - 12 = -4
So, the missing values are 2, -2 and 4
Question
Complete the table of values for x+y=6
x 4 8 12
y
Solve for X ; 9x – 4 – 6x = 2(x + 1) – 5
Answer:
x = 1
Step-by-step explanation:
Identify the infinite sequence generated by the formula an = (−1)n ⋅ 2n.
Answer:
E2020
Step-by-step explanation:
The infinite sequence can be written as -2, 4, -6, 8 ..... with common difference -2.
What is a geometric sequence?In a geometric sequence, the ratio of two consecutive terms are always equal.
The general expression for the nth term is given as aₙ = a₁ × rⁿ⁻¹ .
The sum of n terms for this sequence is given as Sₙ = (rⁿ - 1)/(r - 1).
The expression for the general term for the given sequence is as below,
aₙ = (-1)ⁿ2n
The various terms can be written for different values of n as follows,
⇒ a₁ = (-1)¹ × 2 × 1 = -2
⇒ a₂ = (-1)² × 2 × 2 = 4
⇒ a₃ = (-1)³ × 2 × 3 = -6
⇒ a₄ = (-1)⁴ × 2 × 4 = 8
The common ratio can be given as a₂/a₁ = 4/-2 = -2
Hence, the given infinite sequence can be written as -2, 4, -6, 8 ..... with common ratio -2.
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