Work out the area of this circle. Give your answer in terms of pi and state its units.
Answers
9514 1404 393
Answer:
36π mm²
Step-by-step explanation:
You know that (ab)² = a²b². This tells you that ...
πr² = π(6 mm)² = π(6² mm²) = 36π mm²
The units of area are square millimeters (mm²).
_____
Additional comment
For a variety of reasons, I find it is often helpful to keep units of measure with the associated number. It serves as a check on the arithmetic, among other things. If the units don't make sense, chances are good that the math doesn't make any sense.
It should be fairly obvious that if linear dimensions are in millimeters, then the corresponding area dimensions will be square millimeters. (Volume will be cubic millimeters.)
In the math, the units can be treated in the same way as any other variable. This tells you, for example, that you can only add (or subtract) measures with the same units (like terms). Division can be used to cancel same units, or to get from volume to area, for example (mm³/mm = mm²).
Related Questions
Can someone help me
Answers
Answer:
sorry sorry sorry
Step-by-step explanation:
I don't know
Suppose that the distribution of IQ's of North Catalina State University's students can be approximated by a normal model with mean 130 and standard deviation 8 points. Also suppose that the distribution of IQ's of Chapel Mountain University's students can be approximated by a normal model with mean 120 and standard deviation 10 points.
Required:
What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?
Answers
Answer:
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
North Catalina:
Population has mean 130 and standard deviation 8 points. Sample of 3. This means that:
[tex]\mu_{N} = 130, s_{N} = \frac{8}{\sqrt{3}} = 4.6188[/tex]
Chapel Mountain:
Population has mean 120 and standard deviation 10 points. Sample of 3. This means that:
[tex]\mu_{C} = 120, s_{C} = \frac{10}{\sqrt{3}} = 5.7735[/tex]
What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?
We want that: [tex]N - C > 5[/tex]
Distribution N - C:
The mean is:
[tex]\mu = \mu_N - \mu_C = 130 - 120 = 10[/tex]
The standard deviation is:
[tex]s = \sqrt{s_N^2+s_C^2} = \sqrt{4.6188^2+5.7735^2} = 7.3937[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5 - 10}{7.3937}[/tex]
[tex]Z = -0.68[/tex]
[tex]Z = -0.68[/tex] has a pvalue of 0.2483
1 - 0.2483 = 0.7517
0.7517 = 75.17% probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students
Ella ran 6 times around her school building. Then she ran 4 miles home.
Her phone told her that she ran 7 miles total.
Select an equation that represents this situation
A. 6+4x=7 B. 6x+4=7 C. 6 (x+4) =7
Determine the value of x.
Answers
Answer:
B.6x+4=7
Step-by-step explanation:
x represents how many miles is around her school building which she did 6 times, 4 miles is for the amount she ran home and 7 miles is the combination of the 6 times the miles around her school, 6x and the miles she ran home 4
making the equation 6x+4=7
6(.5)+4=7
3+4=7
Helping to give out points!! Whoever solves the math riddle correctly with a brief explanation will get brainliest and a thanks (the other answers will just get a thanks).
Riddle: I have a big family. I am 16 years old. My sister Reina is 22 years old. The twins are 14 years old. Susana is 10 years old and my brother Robert is 7 years old. If the total number of our ages added together is 100, how old is Albert?
Answers
Answer:
Robbert is 7
Step-by-step explanation:
because you already said it
(extra text for character minimum)
Four teams will receive prize money based on their ticket sales. The total prize amount to be apportioned is $63. Determine the standard divisor based on the ticket sales. The ticket sales are: Applejacks: 66 tickets sold Broncos: 769 tickets sold Colts: 652 tickets sold Deers: 556 tickets sold Calculate the standard divisor to two decimal places.
Answers
Answer:
32.43
Step-by-step explanation:
To get the standard divisor
We sum up the tickets sold
Applejack's = 66 tickets
Broncos = 769 tickets
Colts = 652 tickets
Deers = 556 tickets
The total prize amount = $63
Total tickets = 66 + 769 + 652 + 556 = 2043
Standard divisor = 2043/63
= 32.43
The standard divisor to two decimal places is 32.43
Find the greatest common factor of 28 and 35
Answers
Answer:
7
Step-by-step explanation:
Factors for 28: 1, 2, 4, 7, 14, and 28
Factors for 35: 1, 5, 7, and 35
is 29.6 = 29.600 true or false???
Answers
Answer:
true
Step-by-step explanation:
this is the decimal helps shorten up 29.600
just simplify the two numbers
Whichever answer is correct will get brainliest!
Find the value of x. Round to the nearest tenth. 35 12. х x = [?] Enter
Answers
Answer:
Round to the nearest tenth. 35 12. х x = [?] Enter
Step-by-step explanation:
Please help due soon.
Answers
Please help me on this answer I am 1 week behind
Answers
Please help me! I need help finding this slope.
Answers
Answer:
4/-9
Step-by-step explanation:
divide 4 questions
Answers
Answer:
huh
Step-by-step explanation:
Can someone please help me with these 2 problems
Answers
Answer:
uhururfjfhfufjfjfjfjfjfif
Answer:
I believe the first one is 250
the second one I haven't got a clue
A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open
box. If the volume of the box is 1050 in3, what were the original dimensions of the piece of metal?
What is the original width? in
What is the original length in
Answers
breadth= X
L= x+30
after you cut a square with 6in from the corners, the length becomes x+30-6 =x+24 and breadth becomes x-6.
The eqn for volume of box is Length x Breadth x height
it's given that LxBxH = 1050
here height is 6, because u are folding the edge where it's been cut off and that side becomes the height.
rewrite with the given information we get
(x+24)*(x-6)*6 = 1050
divide both sides with 6
(x+25)*(x-6) = 175
distribute the brackets we get,
x^2 -18x -144 =175
x^2 -18x-319 = 0
solve for x using quadratic formula.
we get x= 29, -11
since length cannot be negative x= 29
B= 29, L=59.
Find the next number in the pattern.
4, 6, 11, 19, 30, ______
Answers
Answer: 44
Step-by-step explanation:
Use the Distributive Property to
REWRITE 2/3(x - 9)
Answers
Answer:
2/3x-6
Step-by-step explanation:
Helpp with math!!!!!!!!
Answers
I think the area is 63. Sorry if it is incorrect.
Given the geometric sequence tn with t1=96 and r=−1/4, find t4.
Give your answer as a fraction, if necessary. Do not include "t4=" in your answer. For example, if you found t4=9, you would enter 9.
Answers
Answer:
3/2
Step-by-step explanation:
Given
[tex]t_1 = 96[/tex]
[tex]r = \frac{1}{4}[/tex]
Required
Find t4
The nth term of a geometric sequence is calculated as:
[tex]t_n = t_1 * r^{n-1[/tex]
So:
[tex]t_4 = t_1 * r^{4-1[/tex]
[tex]t_4 = t_1 * r^3[/tex]
This gives:
[tex]t_4 = 96 * \frac{1}{4}^3[/tex]
[tex]t_4 = 96 * \frac{1}{64}[/tex]
Express as a single fraction
[tex]t_4 = \frac{96}{64}[/tex]
[tex]t_4 = \frac{3}{2}[/tex]
Hence, the 4th term is 3/2
There are 20 pieces of fruit in a basket and 12 of them are oranges. What percentage of the pieces of fruit in the basket are oranges? Show your work in the box and circle your answer
Answers
Answer:60 percent
Step-by-step explanation: You have fraction the two numbers which will be 12/20 them you times it by 100 which equals 60 oranges.
Which of the equations below could be the equation of this parabola?
(0,0)
Vertex
A. y = 1/4x²
B. x = 1/4y²
C. y = -1/4x²
D. x= -1/4y²
Answers
Answer:
B. x = 1/4y²
Step-by-step explanation:
The equation of a parabola is x = 1/4y². Therefore, option B is the correct answer.
What is the parabola?A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
From the graph,
x-intercept(s): (0,0)
y-intercept(s): (0,0)
Vertex is (0, 0)
Directrix, x=-1
Here, the axis of symmetry is y=0
So, the equation is x = 1/4y²
Therefore, option B is the correct answer.
To learn more about the parabola visit:
https://brainly.com/question/21685473.
#SPJ7
How many solutions does the equation 6a − 3a − 6 = −2 + 3 have?
Two
None
One
Infinitely many
Answers
Answer: There is only one solution
6a - 3a - 6 = -2 + 3
3a - 6 = 1
3a = 7
What percent 39 is 26
Answers
Answer: 66.67
Step-by-step explanation:
a shark is located 45 feet directly below a swimmer on the surface of the water. the angle of depression from a boat nearby to the shark is 64 degrees. how far is the swimmer from the boat
Answers
Using the slope concept, it is found that the swimmer is 21.95 feet from the boat.
What is a slope?The slope is given by the vertical change divided by the horizontal change.It's also the tangent of the angle of depression.In this problem:
A shark is located 45 feet directly below a swimmer on the surface of the water, hence the vertical change is 45.The distance d is the horizontal change, which we want to find.The angle is of 64º.Hence:
[tex]\tan{64^{\circ}} = \frac{45}{d}[/tex]
[tex]d = \frac{45}{\tan{64^{\circ}}}[/tex]
[tex]d = 21.95[/tex]
The swimmer is 21.95 feet from the boat.
You can learn more about the slope concept at https://brainly.com/question/26342863
Please help me with my hw thank you so much
Answers
Answer: d
Step-by-step explanation:
The Hiking Club is taking another trip. The hike leader's watch shows that they gained 296 feet in altitude from their starting position.
Their altitude is now 285 feet, but there is no record of their starting altitude.
Write and solve an equation to represent this situation and find their starting altitude.
Answers
Step-by-step explanation:
Equation for this situation will be
A = Ag - 11
A = actual altitude
Ag = altitude gained.
At starting point, altitude gained is zero, therefore;
A = 0 - 11
A = -11ft
Answer:
Step-by-step explanation:
The required equation is x+295=285 , where x= starting altitude( in feet).
The starting altitude is -11 feet.
Let x be the starting altitude( in feet) .
Given: The Hiking Club is taking another trip. The hike leader's watch shows that they gained 296 feet in altitude from their starting position.
Then, the altitude is now = x+ 296
Since their altitude is now 285 feet.
So the required equation is x+296=285
Subtract 296 from both sides, we get
x= -11
Bryce grew
33 inches each year for the past 4 years. How many inches total has Bryce grown in the
past 4 years ?
Answers
Answer:
132 inches
Step-by-step explanation:
33 x 4 = 132 inches
This Question: 1 pt
17 of 29
Emma has $160 cash to spend at a music store. How much can she spend on items if there is a 7% sales tax?
Emma can spend on items.
(Round to the nearest cent as needed.)
Answers
Answer:
i would say $148.80
Step-by-step explanation:
tax would amount to 11.20 so when you subyract that from the total then the rest is what she can spend.
What is the slope of a line perpendicular to the line whose equation is x+3y=-12
Answers
Answer: 3
Step-by-step explanation:
Find slope of that line which is -1/3x-4
then flip its sign and the equation to get 3
kaylee Bryant purchased taz software that regularly sells for 74.95 but is on sale for 59.95
Answers
Answer:
well that is 15$$ off
Step-by-step explanation:
Which equation describes the line with the slope 2/3 that passes through the given point on the graph?
Answers
Answer: y=2/3x-2
Step-by-step explanation:
Slope intercept form is: y=mx+b
m=slope
b= y-intercept
slope is 2/3