A group of 9 students has these numbers of children in their families:
3, 2, 4, 2, 1, 5, 1 ,3 ,7
Answers
_________________________________
Answers:Median=3
Mean=3.12
Step by step explanation:
1. Arranging the data in ascending order:
=1,1,2,2,3,3,4,5,7
N(total number of items)=9
Now,
Median= (N+1/2) th item
=(9+1/2)th item
=(10/2) th item
=5 th item.
Median= 3
------------------------------------------------------------
2. Given data: 3,2,4,2,1,5,1,3,7
Summation FX= 28
N(total number of items)=9
Now,
Mean= summation FX/N
= 28/9
=3.12
Mean =3.12
Hope it helps....Good luck on your assignment
_______________________________
Step-by-step explanation:
median (need to be arranged first):
1,1,2,2,3,3,4,5,7 (9 numbers)
median=9+1/2
=5 (5th)
=3
mean=x/n
=(1+1+2+2+3+3+4+5+7)/9
=28/9
=3.111
Related Questions
Compute Δy and dy for the given values of x and dx = Δx.
Compute Δy and dy for the given values of x and dx = Δx.
y = x2 − 6x, x = 5, Δx = 0.5
Answers
Answer:
∆y = 2.25dy = 2.0Step-by-step explanation:
You want values of ∆y and dy for y = x² -6x and x = 5, ∆x = dx = 0.5.
DyThe value of dy is found by differentiating the function.
y = x² -6x
dy = (2x -6)dx
For x=5, dx=0.5, this is ...
dy = (2·5 -6)(0.5) = (4)(0.5)
dy = 2
∆yThe value of ∆y is the function difference ...
∆y = f(x +∆x) -f(x) . . . . . . . where y = f(x) = x² -6x
∆y = (5.5² -6(5.5)) -(5² -6·5)
∆y = (30.25 -33) -(25 -30) = -2.75 +5
∆y = 2.25
__
Additional comment
On the attached graph, ∆y is the difference between function values:
∆y = -2.75 -(-5) = 2.25
and dy is the difference between the linearized function value and the function value:
dy = -3 -(-5) = 2.00
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select the correct answer for x, each answer is rounded to the nearest tenth.
Answers
Answer:
x ≈ 27.2
Step-by-step explanation:
Using the sine ratio in the right triangle
sin54° = \(\frac{opposite}{hypotenuse}\) = \(\frac{22}{x}\) ( multiply both sides by x )
x × sin54° = 22 ( divide both sides by sin54° )
x = \(\frac{22}{sin54}\) ≈ 27.2 ( to the nearest tenth )
Let pi = P{X = i} and suppose that p1 + p2 + p3 = 1. If E[X] = 2, what values of p1, p2, p3 (a) maximize and (b) minimize Var(X)?
Answers
The values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.
We can use the following formulas to find the variance of X:
Var(X) = E[X^2] - (E[X])^2
E[X] = p1 + 2p2 + 3p3
E[X^2] = p1 + 4p2 + 9p3
Substituting these expressions into the formula for the variance, we get:
Var(X) = p1 + 4p2 + 9p3 - (p1 + 2p2 + 3p3)^2
Simplifying this expression, we get:
Var(X) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\)
To maximize Var(X), we want to maximize this expression subject to the constraint p1 + p2 + p3 = 1. We can use Lagrange multipliers to find the maximum. Let:
L(p1, p2, p3, λ) = -\((p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3 + λ(1 - p1 - p2 - p3)\)
Taking partial derivatives and setting them equal to zero, we get:
-2p1 + 2p2 + 6p3 - λ = 0
4p1 - 4p2 + 4p3 - λ = 0
6p1 + 8p2 - 6p3 - λ = 0
p1 + p2 + p3 = 1
Solving these equations, we get:
p1 = 2/7, p2 = 3/7, p3 = 2/7, λ = 4/7
Therefore, the values of p1, p2, p3 that maximize Var(X) are p1 = 2/7, p2 = 3/7, and p3 = 2/7.
To minimize Var(X), we want to minimize the expression \(-(p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3\) subject to the constraint p1 + p2 + p3 = 1. We can use the same Lagrange multiplier method to find the minimum. Taking partial derivatives and setting them equal to zero, we get:
-2p1 + 2p2 + 6p3 - λ = 0
4p1 - 4p2 + 4p3 - λ = 0
6p1 + 8p2 - 6p3 - λ = 0
p1 + p2 + p3 = 1
Solving these equations, we get:
p1 = 0, p2 = 1/3, p3 = 2/3, λ = 2/3
Therefore, the values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.
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student researchers wanted to see whether a short delay between seeing a list of words and when people were asked to recall them would hinder memorization. the subjects were shown a list of words to memorize for 1 minute and were then given 1 minute to recall as many words as they could. each subject did this once with no delay between memorizing and recall and another time with a 30-second wait between memorizing and recall. they were randomly assigned the order of the two conditions. the number of words memorized under each condition can be found in the statcrunch data set memorizingwords. questions: use the appropriate simulation applet to calculate an approximate p-value. is there strong evidence that a short delay hinders the memorization process? explain.
Answers
The appropriate simulation applet to calculate an approximate p-value is 0.0077.
The strong evidence that a short delay hinders the memorization process is strong data suggests that a brief delay impairs memorization.
Delay or no delay, answer: the number of words remembered
The mean distance between words remembered with and without delay over time is null, or zero.
Alt: The mean distance in words remembered over the long term (with no delay minus with delay) is higher than 0.
Yes, the majority of the lines do skew to the right. The mean for no delay is 10.55 whereas that for with delay is 8.7.
The mean distance in words remembered is 1.85.
1)0.0077 as the p-value
2)Strong data suggests that a brief delay impairs memorization.
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Erin is volunteering at a soup kitchen. At the start of her shift, she is provided with a 16.3-
ounce jar of peanut butter. She uses it to make peanut butter sandwiches, each with 0.8
ounces of peanut butter. How much peanut butter will be left after Erin makes 20
sandwiches?
Answers
Answer:
0.3
Step-by-step explanation:
total:16.3
20*0.8=16 (amount she will use)
16.3-16=0.3
At Lara' party, 4 gallon of fruit punch are hared equally among 18 friend. How much fruit punch will each peron get?
Answers
Answer: About 0.2 gallons
Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.
Each of her friend will get 4 and a half gallons of juice.
What is division?Division is one of the four main arithmetical operations by which we find the equal distribution of something.
Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.
To find how much each of them got, we will divide total amount of punch by total number friends
Amount of juice each of them gets, = 18/4 = 4.5
Hence, Each of her friend will get 4 and a half gallons of juice.
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the side lengths of an equiangular octagon are $1$, $2$, $3$, $4$, $1$, $2$, $3$, and $4$ in clockwise order. find the octagon's area.
Answers
The side lengths of an equiangular octagon are 1, 2, 3, 4, 1, 2, 3, and 4 in clockwise order so area of octagon is 11 + 12√2 square units.
The sides of octagon are 1, 2, 3, 4, 1, 2, 3, 4 as shown in the figure,
The area of the octagon = area of the rectangle - the area of the four right isosceles triangular corners.
A = (lxb) - 1/2[√2×√2 + √8×√8]x2
A = [(3+√2+√8)(1+√2+√8)] -1/2[√2×√2 + √8×√8 + √2×√2 + √8×√8]
A = 3 + 12√2 +7
A = 11 + 12√2
Therefore, The area of the octagon is 11 + 12√2 square units.
A closed two-dimensional shape having eight sides, eight vertices, and eight internal angles is known as an octagon. An octagon is referred to as a regular octagon if all of its sides and internal angles are of equal length; otherwise, it is referred to as an irregular octagon. The next sections also discuss the various octagon types, such as convex and concave octagons.
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Select the correct answer.
What is the approximate measure of exterior angle B in the polygon?
Answers
Answer:
C
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
sum the 4 exterior angles and equate to 360
8x + 9x + 5 + 5x + 4 + 9x + 3 = 360 , that is
31x + 12 = 360 ( subtract 12 from both sides )
31x = 148 ( divide both sides by 31 )
x ≈ 11.23 ( to 2 dec. places )
then exterior angle at B is
9x + 3 = 9(11.23) + 3 ≈ 104° → C
The approximate measure of exterior angle B in the polygon is 104° option (C) is correct.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
\(\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|\)
It is given that:
A polygon is given in the picture with angle measures.
As we know,
The sum of the exterior angles of a polygon = 360°
8x + 9x + 5 + 5x + 4 + 9x + 3 = 360
31x + 12 = 360
31x = 148
x ≈ 11.23
= 9x + 3 = 9(11.23) + 3
≈ 104°
Thus, the approximate measure of exterior angle B in the polygon is 104° option (C) is correct.
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Point M (3,-2) is the midpoint of AB. If the coordinates of A are (-1, 4) then find the coordinates of point B.
Answers
Answer:
C (7, -8)
Step-by-step explanation:
¿Qué es la poblacion en estadistica?
Answers
Answer:
Que?
Step-by-step explanation:
I don't speak Español
find the indefinite integral by using the substitution x = 5 sec(). (use c for the constant of integration.) x2 − 25 x dx
Answers
The given expression is x² - 25x.
To solve for the indefinite integral using the substitution x = 5 sec(), we will use the following steps:
Find the value of dx in terms of dθ.
Substitute x = 5 sec() in the given expression.
Use the identity 1 - sec²(θ) = tan²(θ) to simplify the expression.
Evaluate the indefinite integral.
Therefore, Find the value of dx in terms of dθ.
dx/dθ = 5 sec(θ) tan(θ)dθ
Substitute x = 5 sec(θ) in the given expression.
x² - 25x = (5 sec(θ))² - 25(5 sec(θ))= 25 [sec²(θ) - 5sec(θ)]
Use the identity 1 - sec²(θ) = tan²(θ) to simplify the expression.
= 25 [1 - (1/cos²(θ))] - 125/cos(θ)= 25 [tan²(θ)] - 125/cos(θ)
.Evaluate the indefinite integral by substituting u = tan(θ) and du = sec²(θ) dθ.
∫[25 tan²(θ) - 125/cos(θ)] dθ
= ∫[25 u² du - 125/(1 - u²)] (1/u²) du
= ∫ [25 - 125/(u²(1 - u²))] du
= 25u + (125/2) ln |(u - 1)/(u + 1)| + c
Substitute u = tan(θ)
= 25 tan²(θ) + (125/2) ln |(tan(θ) - 1)/(tan(θ) + 1)| + c.
Therefore, the indefinite integral is given by 25x²/25 + (125/2) ln |(x/5 - 1)/(x/5 + 1)| + c.
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evaluate f(3) for the function f(x)= 15x^2 -x+20
Answers
Answer:
\( \huge \boxed{f(15) = 152 }\)
Step-by-step explanation:
\(f(x) = 15 {x}^{2} - x + 20\)
To find f(3) , substitute the value of x that's 3 into f(x). That is for every x in f(x) replace it with 3.
We have
\(f(15) = 15( {3})^{2} - 3 + 20 \\ \: \: = 15(9) + 17 \\ = 135 + 17 \: \\ = 152 \: \: \: \: \: \: \: \: \: \: \)
We have the final answer as
\(f(15) = 152 \)
Hope this helps you
A 60
B 30
C 1 20
D 15
fastest answer gets brainiest
Answers
Answer:
i think it would be A
Step-by-step explanation:
Answer:
B 30
Step-by-step explanation:
The answer is B :)
15x-7y=-49 standard form to slope-intercept form
Answers
Answer:
y= \frac{15}{7}x + 7
not sure if that will work so
y = 15x/7x + 7
Step-by-step explanation:
Classify this triangle.
Answers
First, we'll take a look at the angle measures.
An obtuse triangle has one angle that is greater than 90 degrees.
An acute triangle has three angles that are less than 90 degrees.
A right triangle has one angle that is 90 degrees.
In the case of the given triangle, it has one angle that is greater than 90 degrees, so it must be an obtuse triangle.
Next, we'll look at the side lengths. One way to tell the side lengths without solving them is by looking at the angle measures. The shortest side is opposite the smallest angle, and the longest side is opposite the largest angle. If two angles are the same, then there would be two sides that are the same.
A scalene triangle has three sides that are all different lengths.
An iscosceles triangle has two sides that are the same length.
An equilateral triangle has three sides that are all the same length.
In the case of the given triangle, all of the angle measures are different, so all of the sides must be different, so it must be a scalene triangle.
Answer: Obtuse, Scalene
(Option C / third option)
Hope this helps!
4x -2y = 2
2x +2y = 16
Answers
Answer:
x = 3
y = 5
Step-by-step explanation:
we can add these equations together
4x - 2y +2x + 2y = 18
6x = 18
x = 3
to find y
6 + 2y = 16
2y = 10
y = 5
When I was 4 years old my sister was half of my age.Now I am 100 years. How old is my sister?
Answers
Answer:
when you 4, your sister is 2 years old
now that you 100, your sister should be 50 years old
half equal x/2 x indicates 100
If n is an odd integer, which equation can be used to find three consecutive odd integers whose sum is 15?
Answers
Answer:
n+(n+2)+(n+4)=15
Step-by-step explanation:
Let n= the smallest odd integer
n+(n+2)+(n+4)=15
n=3
A rectangle's length and width are in a ratio of 7:1. The area is 112 square yards. What are the length and width?
Answers
Answer:
ouygghjkjhhhggfdddthjj
it is given that
H=(x:x
Answers
Answer:
is rational number.......
in 10 years,Kamdyn will be 3 times as old as she is now.Which equation could be used to determine Kamdyns current age,k
Answers
Answer:
k+10=3k
Step-by-step explanation:
sam borrows 5500 at a rate of 12% interest per year what is the amount due at the end of five years if the interest is compounded continuously
Answers
Answer:
$ 10 021 . 65
Step-by-step explanation:
The equation for continuous compounding is e^(i * t)
where i = decimal yearly interest t = years
FV = 5500 e^(.12 * 5) = 10 021 .65
The circle below has center , and its radius is . Given that , 130 degress find the length of the arc 7
and the area of the shaded region.
Give exact answers in terms of , and be sure to include the correct units in your answer.
Answers
For the given circle, the length of the arc and area of the sector are given as 3.66 ft and 12.82 ft² respectively.
How to find the area of a sector of circle?The area of the sector of circle can be found by substituting the values of angle and radius in the expression θ/360 × πr². In the same way the length of the circle can be found as θ/360 × 2πr.
The radius of circle is 7 ft.
And, the angle is given as ∠AOB = 30°.
The length of the arc subtending angle 30° is given as,
30/360 × 2πr
⇒ 1/12 × 2πr
Substitute π = 3.14 and r = 7 to get,
1/12 × 2πr
⇒ 1/12 × 2 × 3.14 × 7 = 3.66 ft
And, the area of the shaded region is given as,
30/360 × πr²
Substitute π = 3.14 and r = 7 to get,
1/12 × 3.14 × 7²
⇒ 12.82 ft²
Hence, the length of the arc and area of the sector are given as 3.66 ft and 12.82 ft² respectively.
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The missing diagram and question are attached here.
The circumference of a circle is 2\piπ m. Find its radius, in meters.
Answers
Answer:
r≈0.32Step-by-step explanation: please give brainlest
What is the percent
increase from 70 to 77?
Answers
Percentage change = 10%
We can use the formula:
Percent change = \(\frac{New-Old}{Old}\) x 100
Percent change = \(\frac{77-70}{70}\)x100
Percent change = \(\frac{7}{70}\) x 100
Percent change = 0.1 x 100
Percent change = 10%
Answer: 53.9
Step-by-step explanation:
1 ) 62) If the following equation true, enter 1. Otherwise enter 0. 1 1 1 + --- y x+y X ans:1
Answers
Therefore, the answer is 1, indicating that the equation is true.
Is the equation 1 + (1/y) = (1/x) + (1/(x+y)) true? (Enter 1 for yes or 0 for no.)The given equation is 1 + (1/y) = (1/x) + (1/(x+y)).
To determine if the equation is true, we can simplify it further:
Multiply both sides of the equation by xy(x+y) to eliminate the denominators:
xy(x+y) + xy = y(x+y) + x(x+y)Expand and simplify:
x²y + xy² + xy = xy + y² + x² + xyRearrange the terms:
x²y + xy² = y²+ x²This equation is true, as both sides are equal.
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George bought a model of a Viking ship for $68. If he paid
$5.10 in sales tax, what was the sales tax rate?
Answers
Answer:
We can convert 6.75% to a decimal by dividing by 100.
If x is the price of the house, then the sales tax is 0.0675x. The price of the house and the sales tax add up to $319,000.
x+0.0675x=319,000
Combe terms on the left.
1.0675x=319,000
Finally, divide both sides by 1.0675.
x=319,0001.0675=298,829.04
Jenny has saved $600 for her summer job. During the school year she withdraws $20 from her account every week for her daily expenses. She wants to keep more than $300 in her account for college. The number of weeks, w, that Jenny can withdraw money from her account is represented by the inequality 600-20w>300 how many weeks can Jenny continue to withdraw $20 from her account
Answers
The number of weeks that Jenny can withdraw from her account is 14 weeks.
How many weeks can Jenny withdraw from her account?Given the inequality, 600-20w>300 , in order to determine the value of w, take the following steps:
Combine similar terms together:
600 - 300 > 20w
Add similar terms together
300 > 20w
Divide both sides of the equation by 20
300 / 20 > 20w / 20
15 > w
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Find the area of sector TOP
Answers
The area of sector TOP is 70.83 square meters.
Given that r = 3m and arc TP = 297
we can find the central angle θ using the formula:
θ = (arc length / circumference) × 360
The circumference of a circle can be calculated using the formula:
circumference = 2πr
Let's calculate the central angle first:
circumference = 2 × π × 3m
circumference = 6π m
θ = (297 / (6π)) × 360
θ = (49.5 / π) × 360
θ= 49.5×57.3
θ = 2833.35
Now, we can calculate the area of sector TOP:
Area = (θ/360) × π × r²
Area = (2833.35/360) × π × (3m)²
Area = 7.87 × 9
Area = 70.83 m²
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as part of video game, the point (5,2) is rotated counterclockwise about the origin through an angle of 5 degrees. find the new coordinates of this point
Answers
The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).
To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.
Converting the angle of rotation from degrees to radians:
theta = 5 degrees * (pi/180) ≈ 0.08727 radians
Plugging in the values into the rotation formula:
x' = 5 * cos(0.08727) - 2 * sin(0.08727)
y' = 5 * sin(0.08727) + 2 * cos(0.08727)
Evaluating the trigonometric functions and simplifying:
x' ≈ 4.993
y' ≈ 2.048
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