The length of the arc of the circle with a radius of 2 ft and the angle made at the centre equal to [tex]\dfrac{5\pi}{3}[/tex] is 10.5ft.
What is the length of the arc of a circle?The length of the arc of a circle is equal to the product of the circumference of the circle and the ratio of the angle made by the arc of the circle to 2π. It is given by the formula,
[tex]\text{Length of the arc}= 2\pi r\times \dfrac{\theta}{2\pi}[/tex]
It is given that the radius of the circle is equal to 2 ft while the angle made by the arc at the centre of the circle is equal to [tex]\dfrac{5\pi}{3}[/tex]. And we know the formula for the length of the arc, therefore, the length of the arc,
[tex]\text{Length of the arc}= 2\pi r\times \dfrac{\theta}{2\pi}[/tex]
[tex]= 2\pi \times 2 \times \dfrac{\frac{5\pi}{3}}{2\pi}\\\\= 10.471 \approx 10.5\rm\ ft[/tex]
Hence, the length of the arc of the circle with a radius of 2 ft and the angle made at the centre equal to [tex]\dfrac{5\pi}{3}[/tex] is 10.5ft.
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Answer:
C or 10.5 ft
Step-by-step explanation:
6
Rewrite the expression 2(2x + 1) using the Distributive Property.
Answer:
4x + 2
Step-by-step explanation:
2 times 2x is 4x plus 2 times 1 is 2
Which rule can be used to describe the x-coordinates in the translation below?. on a coordinate plane, triangle a b c is shifted 6 units up. x 0 x 6 x – 6 x 2
The rule that can be used to describe the x-coordinates in the translation is (x+6).
What is a translation?A translation is a sort of transformation that moves each point in a figure in the same direction by the same amount of distance.
We know that the coordinate is moving up, therefore, the coordinate of x will be increasing by 6 units.
Hence, the rule that can be used to describe the x-coordinates in the translation is (x+6).
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Answer:
x + 6
Step-by-step explanation:
Each problem below gives the endpoints of a segment. Find the coordinates of the midpoint of the segment.
a. (-3,11) and (5,6)
b. (-4,-1) and (8,9)
Answer: A
Step-by-step explanation:
Can anyone help me pls asap???
Answer:
Lin is taller than 150 centimeters but shorter than 160 centimeters. She could be ... (just put any number that is in between 150 and 160, like 155
Step-by-step explanation:
Answer:
lin is taller than 150
But shorter than 160
She could be 154 centimeters tall
The sign > means greater than.
The sign < means less than.
So, if h > 150, h is greater than 150
And, if h < 160, h is less than 160
h represents Lin
So, lin is taller than 150
But shorter than 160
She could be anywhere in between 150 and 160
So, she could be
151, 152, 153, 154, 155, 156, 157, 158, or 159
Just choose one of those.
What is 1 3/8 equals to
Answer:
1.375 in decimal form
Step-by-step explanation:
11. What is the value of x in the figure shown? (15x) 15 °
Answer:
x = 11
Step-by-step explanation:
15x + 15x + 15 + 15 = 360 (sum of all sides equal to 360)
30x + 30 = 360
30x = 360 - 30
30x = 330
30x/30 = 330/30
x = 11
Find the perimeter of the triangle as a simplified polynomial if the sides are 3x + 2, 5x - 5, and 8x + 7
Answer: 16x+4
Step-by-step explanation:
perimeter = side + side + side
So in this case:
Perimeter= 3x+2+5x-5+8x+7= 3x+8x+5x+2+7-5 = 11x+5x+9-5 = 16x+4
Why is math literacy important?
Answer:
Math literacy (also known as numeracy) means having the ability to problem-solve, reason, and analyze information.
Step-by-step explanation:
Given Set and Set. Calculate the mean and mean absolute deviation for both sets. Then, answer the following questions. How many data points in Set are closer than one mean absolute deviation from the mean of Set ? How many data points in Set are further than two mean absolute deviations from the mean of Set ? Find the difference between the two means. How does this difference relate to the mean absolute deviation of each set? For example, is it the same as the mean absolute deviation, twice as much, half as much, etc?.
The difference between the mean of the two sets is 1, which is half the Mean absolute deviation.
What is mean absolute deviation?The mean absolute deviation is the average distance between the data points and the mean of the data set.
A.) For the data set M, {0, 1, 3, 4, 7}, the mean and the mean absolute deviation can be written as,
[tex]\text{Mean of M}, (\mu_M) = \dfrac{0+1+3+4+7}{5} = 3[/tex]
The mean absolute deviation of the set M,
[tex]MAD = \dfrac{1}{n}\sum_{i=0}^{n}|x_i-m(x)|[/tex]
[tex]MAD = \dfrac{1}{5}\sum_{i=0}^{5}|x_i-m(x)|\\\\MAD_M= \dfrac{10}{5} = 2[/tex]
Now, since the MAD of the set M is 2, therefore, the data points in Set M that are closer than one mean absolute deviation from the mean are 3 because the range of the one mean absolute deviation from the mean,
Mean±MAD
= 3±2
= 3+2, 3-2
= 5, 1
Thus, the numbers coming between 1 to 5 are the data points that are closer than one mean absolute deviation which is 3{1, 3, 4}.
B.) For the data set N, {1, 2, 3, 4, 5, 9}, the mean and the mean absolute deviation can be written as,
[tex]\text{Mean of N}, (\mu_N) = \dfrac{1+2+3+4+5+9}{6} = 4[/tex]
The mean absolute deviation of the set N,
[tex]MAD = \dfrac{1}{n}\sum_{i=0}^{n}|x_i-m(x)|[/tex]
[tex]MAD = \dfrac{1}{6}\sum_{i=0}^{6}|x_i-m(x)|\\\\MAD_m= \dfrac{12}{6} = 2[/tex]
Now, since the MAD of the set N is 2, therefore, the data points in Set N that are further than two mean absolute deviations from the mean of Set are 3 because the range of the one mean absolute deviation from the mean,
Mean±2MAD
= 4±2(2)
= 4+4, 4-0
= 8, 0
Thus, the number not coming between 8 to 0 are the data points that are further than two mean absolute deviations from the mean of Set N which are 1{9}.
C.) The difference between the mean of the two sets is 1, which is half the Mean absolute deviation.
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Which of the following scatterplots would have a trend line with a positive slope?
(7xy-8yz+3x)-(4x-8yz)
Answer:
7xy-8yz+3x-4x+8yz
7xy-8yz+8yz+3x-4x
7xy-x
Step-by-step explanation:
(9w^2+7w-2)+(8w^2-8w-7)-(-5w^2+5w+4)
Step-by-step explanation:
Our expression;
[tex](9w^2+7w-2)+(8w^2-8w-7)-(-5w^2+5w+4)[/tex]
Also represented as after using the distributive property;
[tex]9w^2+7w-2+8w^2-8w-7+5w^2-5w-4[/tex]
Simplify;
[tex]9w^2+7w-2+8w^2-8w-7+5w^2-5w-4[/tex]
[tex]22w^2+7w-2-8w-7-5w-4[/tex]
[tex]22w^2-6w-2-7-4[/tex]
[tex]22w^2-6w-13[/tex]
Answer:
22w² - 6w - 13
Step-by-step explanation:
Given expression: (9w² + 7w - 2) + (8w² - 8w - 7) - (-5w² + 5w + 4)
Step-1: Open the parenthesis
⇒ (9w² + 7w - 2) + (8w² - 8w - 7) - (-5w² + 5w + 4)⇒ 9w² + 7w - 2 + 8w² - 8w - 7 + 5w² - 5w - 4Step-2: Combine like terms
⇒ 9w² + 7w - 2 + 8w² - 8w - 7 + 5w² - 5w - 4⇒ w²(9 + 8 + 5) + w(7 - 8 - 5) + (-2 - 7 - 4)Step-3: Simplify the expression
⇒ w²(9 + 8 + 5) + w(7 - 8 - 5) + (-2 - 7 - 4)⇒ w²(22) + w(-6) + (-13)⇒ 22w² - 6w - 13Therefore, the simplified expression is 22w² - 6w - 13.
the squar of any rational number is non negative
[tex]\mathbb{FINAL\:ANSWER:}[/tex]
[tex]\huge\boxed{\sf{True}}[/tex]
[tex]\mathbb{SOLUTION\:WITH\:STEPS:}[/tex]
Hi! Hope you are having a nice day!
Yes, the square of a rational number is always positive.
We know that a negative times a negative equals a positive only.
Well, a negative squared also equals a positive.
For example, (-4)² is equal to 16.
Because
(-4)×(-4)=16
A negative times a negative is a positiveHope you could understand everything.
#CarryOnLearning
What type of graph would you use for a set of categorical data with 25 people surveyed?bar graphline graphpictographstem-and-leaf plot
The type of graph I would use for a set of categorical data with 25 people surveyed is bar graph.
Which types of graphs are good for categorical data?The type of graph or chart that is good for showing categorical data are:
Frequency tables Pie chartsBar chartsNote that bar graph is one of the the most appropriate graphical form of displays for any categorical variables.
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Kaitlyn solved the equation for x using the following calculations. Negative 5. 4 x = 12. 2. Minus 5. 4. X = 6. 8. What error, if any, did she make? She should have added 5. 4 to each side. She should have added the inverse of 5. 4 to each side. She made a computational error when she subtracted 5. 4 from 12. 2. She should have added 12. 2 to each side.
The value of x is 17.6. She should have added 5.4 on both sides to get the correct value of x. Then the correct option is A.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
Kaitlyn solved the equation for x using the following calculations.
[tex]\rm -5.4 + x =12.2[/tex]
and she did the calculation will be
[tex]\rm -5.4x = 6.8[/tex]
The mistake she did in this equation is the plus sign is removed between the -5.4 and x. And she subtracted 5.4 from 12.2.
The correct solution of the equation is to add both sides 5.4. Then we have
[tex]\begin{aligned} \rm -5.4 + x+5.4 &=12.2+5.4\\\\\rm x &= 17.6\end{aligned}[/tex]
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Ava's math certificate is 18 centimeters tall and 26 centimeters wide. Ava wants to put the certificate in a fancy frame that costs $1.53 per centimeter. How much will it cost to frame Ava's math certificate?
Help help help help help help help help
Answer:
Roughly 10%
Step-by-step explanation:
We just need to reduce this fraction: 13/119
It is in the lowest terms already, so now we need to make this fraction a percent.
13/119 = 10.12
10.12 ≈ 10%
This is a linear equation what is the answer
6a - 2b = 8 + b
Answer:
Slope = 2
a-intercept = 8/6 = 4/3 = 1.33333
b-intercept = 8/-3 = -2.66667
Step-by-step explanation:
Pls, choose me as brainliest!
Answer:
Slope = 2
a-intercept = 8/6 = 4/3 = 1.3...
b-intercept = 8/-3 = -2.6...
Step-by-step explanation:
your welcome
4. Akeego is making a ribbon shirt. She has 60 cm of ribbon that she will cut into 5 pieces with 2 different lengths: 2 pieces have the same length and the remaining 3 pieces also have equal lengths.
a) Generate some data for this relation showing the possible lengths of the pieces.
b) Graph the data.
c) Write an equation for the relation in general form.
d) i) Can each of 2 pieces be 18 cm long and each of 3 pieces be 3 cm long?
ii) Can each of 2 pieces be 3 cm long and each of 3 pieces be 18 cm long?
Use the graph and the equation to justify your answers.
Answer:
1m
Step-by-step explanation:
because there is some thing to tell I am a kid and my age is 13 and how should I answer your question.
Can you help please I really need it
Answer:
65cm
Step-by-step explanation:
100cm= 1 metre
?=2.5m
=2.5*100=250cm
250-(60+35+90)=65cm
remaining length=65cm
6. select all the values for d that make the equation 9 = 18 / d true
Answer: 2
Step-by-step explanation:
Maki paid a $14 basic fee plus $25 a day to rent a car. Evaluate the expression 14 + 5 X 25 to find out how much it cost her to rent the car for 5 days
Answer:
25(5)+14=139
$139
Step-by-step explanation:
The Thompson family was moving and hired Town Movers to move them for a fee of $30 plus $15 per hour. City Movers called and offered a fee of $72 plus $8 an hour, which they thought might be a better deal. The family made a graph of the two offers. When would City Movers be the better deal?
If the Thompsons need the movers for more than 6 hours, City movers would be the better deal. Therefore, option D is the correct answer.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Given that, the Thompson family was moving and hired Town Movers to move them for a fee of $30 plus $15 per hour.
Let the number of hours be x.
Now, 30+15x
Movers called and offered a fee of $72 plus $8 an hour, which they thought might be a better deal
72+8x
From the graph, both the movers have same charge at 6th hour and City movers charge is decreasing then compare to Town Movers.
Therefore, option D is the correct answer.
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Classify the expression: 5x 3x2 − 7x3 2. Linear expression Quadratic expression Cubic expression Quartic expression.
The given expression 5x+3x²-7x³+2 is a cubic expression.
What is a cubic expression?A cubic expression is a three-dimensional algebraic equation of the form ax³ + bx² + cx + d = 0, where the coefficients are a, b, and c, and the constant is d.
In order to classify the given expression as 5x+3x²-7x³+2, we need to rearrange the given expression,
[tex]5x+3x^2-7x^3+2\\\\=-7x^3+3x^2+5x+2[/tex]
Since the highest power that is in the expression is 3, therefore, the given expression is a cubic expression.
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if a town with a population of 500 doubles in size ever 9 years, what will the population be 36 years from now?
The population of the town in 36 years would be 8000.
What would be the population of the town in 36 years?The formula that can be used to determine the town's population is:
FV = P (1 + r)^n
Where:
FV = Future value P = Present value R = rate of growth = 100%N = number of years = 36/9 = 4500 x 2^4 = 8000
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3.2. A sporting goods store sells soccer balls for a regular price of $40 each. If a team buys 20 or more
soccer balls, the store offers a discount of 15% off the price of each soccer ball.
How much more will it cost a team to buy 20 soccer balls than to buy 15 soccer balls?
A. $80
B. $100
C. $170
D. $200
Answer:
A. $80
Step-by-step explanation:
First, let's find the cost of 15 soccer balls.
[tex]15*40[/tex] $600Next, cost of 20 soccer balls.
20 x 40 = 80015 x 800 = 1200012000/100 = 120800 - 120 = 680Lastly, the difference between 20 and 15 soccer balls:
680 - 600 = $80PLEASE HELP I WILL GIVE 20
Answer:
80°
Step-by-step explanation:
since 4x+5x=180, it means that x is 20.
to find SVW, you multiply 4 by 20 which is 80°
find the distance between A (2,-3)B(-4,5)
distance between point A and B is = 10
PLEASE HELP
I put a photo
The table shows the approximate height of an object x seconds after the object was dropped. the function h(x) = –16x2 100 models the data in the table. a 2-column table with 5 rows. the first column is labeled time (seconds) with entries 0, 0.5, 1, 1.5, 2. the second column is labeled height (feet) with entries 100, 96, 84, 65, 37. for which value of x would this model make the least sense to use? –2.75 0.25 1.75 2.25
The value of x for which this model will make the least sense to use is at x=-2.75 seconds.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function that is given to us is h(x) = –16x²+100 where x is the time in seconds.
Now, use the function to know the height of the object, therefore, the height of the object can be written as,
Time, t₁=0
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(0)=0+100\\\\h_1=100[/tex]
Thus, the height of the object when the time is 0 seconds is 100.
Time, t₂=0.5
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(0.5)=-4+100\\\\h_2=96[/tex]
Thus, the height of the object when the time is 0.5 seconds is 96.
Time, t₃=1
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(1)=-16+100\\\\h_1=84[/tex]
Thus, the height of the object when the time is 1 second is 84.
Time, t₄=1.5
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(1.5)=-36+100\\\\h_4=64[/tex]
Thus, the height of the object when the time is 1.5 seconds is 64.
Time, t₅=2
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(2)=0+100\\\\h_5=36[/tex]
Thus, the height of the object when the time is 2 seconds is 36.
Now as we can see that the error in the height of the object can be a maximum of 1, therefore, for different values of x, the change in height will be,
Time, t₆= -2.75
Now, the height can be written as,
[tex]h(x) = -16x^2+100\\\\h(-2.75)=-121+100\\\\h_6= -21[/tex]
Thus, the height of the object when the time is -2.75 seconds is -21.
Hence, the value of x for which this model will make the least sense to use is at x=-2.75 seconds.
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Answer:
-2.75
Step-by-step explanation:
A