Answer:
The meadian decreases by 1.5 when the outlier is removed.
Step-by-step explanation:
Well first we need to find the median of the following data set,
(75, 63, 58, 59, 63, 62, 56, 59)
So we order the set from least to greatest,
56, 58, 59, 59, 62, 63, 63, 75
Then we cross all the side numbers,
Which gets us 59 and 62.
59 + 62 = 121.
121 / 2 = 60.5
So 65 is the median before the outlier is removed.
Now when we remove the outlier which is 75.
Then we order it again,
56, 58, 59, 59, 62, 63, 63
Which gets us 59 as the median.
Thus,
the median height decreases by 1.5 units when the outlier is removed.
Hope this helps :)
Triangle ABC has vertices A(-5, -2), B(7, -5), and C(3, 1). Find the coordinates of the intersection of the three altitudes
Answer:
Orthocentre (intersection of altitudes) is at (37/10, 19/5)
Step-by-step explanation:
Given three vertices of a triangle
A(-5, -2)
B(7, -5)
C(3, 1)
Solution A by geometry
Slope AB = (yb-ya) / (xb-xa) = (-5-(-2)) / (7-(-5)) = -3/12 = -1/4
Slope of line normal to AB, nab = -1/(-1/4) = 4
Altitude of AB = line through C normal to AB
(y-yc) = nab(x-xc)
y-1 = (4)(x-3)
y = 4x-11 .........................(1)
Slope BC = (yc-yb) / (xc-yb) = (1-(-5) / (3-7)= 6 / (-4) = -3/2
Slope of line normal to BC, nbc = -1 / (-3/2) = 2/3
Altitude of BC
(y-ya) = nbc(x-xa)
y-(-2) = (2/3)(x-(-5)
y = 2x/3 + 10/3 - 2
y = (2/3)(x+2) ........................(2)
Orthocentre is at the intersection of (1) & (2)
Equate right-hand sides
4x-11 = (2/3)(x+2)
Cross multiply and simplify
12x-33 = 2x+4
10x = 37
x = 37/10 ...................(3)
substitute (3) in (2)
y = (2/3)(37/10+2)
y=(2/3)(57/10)
y = 19/5 ......................(4)
Therefore the orthocentre is at (37/10, 19/5)
Alternative Solution B using vectors
Let the position vectors of the vertices represented by
a = <-5, -2>
b = <7, -5>
c = <3, 1>
and the position vector of the orthocentre, to be found
d = <x,y>
the line perpendicular to BC through A
(a-d).(b-c) = 0 "." is the dot product
expanding
<-5-x,-2-y>.<4,-6> = 0
simplifying
6y-4x-8 = 0 ...................(5)
Similarly, line perpendicular to CA through B
<b-d>.<c-a> = 0
<7-x,-5-y>.<8,3> = 0
Expand and simplify
-3y-8x+41 = 0 ..............(6)
Solve for x, (5) + 2(6)
-20x + 74 = 0
x = 37/10 .............(7)
Substitute (7) in (6)
-3y - 8(37/10) + 41 =0
3y = 114/10
y = 19/5 .............(8)
So orthocentre is at (37/10, 19/5) as in part A.
Classify the triangle with angles measuring 1130, 47°, and 20°.
A. Straight
B. Right
C. Acute
D. Obtuse
Answer:
D. Obtuse
Step-by-step explanation:
Answer:
You typed that incorrectly. That first angle should be 113 degrees.
It would be an obtuse triangle.
Step-by-step explanation:
In the diagram AB=AD and
Answer:
AC ≅ AE
Step-by-step explanation:
According to the SAS congruence theorem, if two triangles have 2 corresponding sides that are equal, and also have one included corresponding angle that are equal to each other in both triangles, both triangles are regarded as congruent.
Given ∆ABC and ∆ADC in the question above, we are told that segment AB ≅ AD, and also <BAC ≅ <DAC, the additional information that is necessary to prove that ∆ABC and ∆ADC are congruent, according to the SAS theorem, is segment AC ≅ segment AE.
This will satisfy the requirements of the SAS theorem for considering 2 triangles to be equal or congruent.
[PLEASE HELPP] write an equation that represents the area Bruce covered (y) in terms of the number of tiles he used, x?
Answer:
y=(x/6)
Step-by-step explanation
divide every input by 6 to get the output
−11b+7=40 b= pls help
Answer:
[tex]\boxed{b = -3}[/tex]
Step-by-step explanation:
[tex]\sf -11b+7 = 40\\Subtracting\ 7\ to\ both\ sides\\-11b = 40-7\\-11b = 33\\Dividing\ both\ sides \ by \ -11\\ b = 33/-11\\b = -3[/tex]
Which linear inequality is represented by the graph?
y > 2x + 2
y ≥ One-halfx + 1
y > 2x + 1
y ≥ One-halfx + 2
Answer: y > 2x + 1
Step-by-step explanation:
In the graph first, we can see two things:
The line is not solid (so the values in the line are not included), and the shaded part is above, so we will be using the symbol:
y > f(x)
Now, in the line we can see that when x = 0, y = 1.
So the linear equation must be something like:
f(x) = a*x + 1
The only one that has an y-intercept equal to 1 is y > 2x + 1
Answer:
C or y>2x +1
Step-by-step explanation:
edge
What is the equation perpendicular to -x+y= 7 and passes through (-1,1)
Answer:
Step-by-step explanation:
First , let us rewrite the given equation into y= mx+b format
.y= -x +7
Slope is -1
Slope of the line perpendicular to the given equation is -(-1) ie., 1
Let us find the y-intercept by plugging in the values of x,y and slope into the equation y= Mx +b
1 = -1 +b
2 = b
Equation of the line perpendicular to the given equation and passing through (-1,1) is
y=x +2
what is the surface area of a cylinder height is 4 cm and diameter is 5 cm
Answer:
20cm it's is the answers
Step-by-step explanation:
5*4=20
Need Answers ASAP!!!!
Answer:
15.9degrees
Step-by-step explanation:
in photo above
Answer:
[tex]\boxed{15.95\°}[/tex]
Step-by-step explanation:
The angle can be found by using trigonometric functions.
tan (θ) = [tex]\frac{opposite}{adjacent}[/tex]
tan (θ) = [tex]\frac{4}{14}[/tex]
θ = [tex]tan^{-1} \frac{4}{14}[/tex]
θ = 15.9453959
θ ≈ 15.95
less than 0 but greater than (−5)
Answer:
-5 < x < 0
Step-by-step explanation:
f(x) = x + 2
g(x) = x - 4
(fg)(x) =
Answer:
Step-by-step explanation:pleased to help u....
4. Simplify the following.
3
a. 2-X5-:11
3
x5
5
6
7
Answer:
[tex]1 \frac{1}{4} [/tex]Step-by-step explanation:
[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]
Convert the mixed number to an improper fraction
[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]
To divide by a fraction, multiply the reciprocal of that fraction
[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]
Reduce the number with the G.C.F 7
[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]
Reduce the numbers with the G.C.F 17
[tex] \frac{5}{6} \times \frac{3}{2} [/tex]
Reduce the numbers with the G.C.F 3
[tex] \frac{5}{2} \times \frac{1}{2} [/tex]
Multiply the fraction
[tex] \frac{5}{4} [/tex]
In mixed fraction:
[tex]1 \frac{1}{4} [/tex]
Hope this helps..
Good luck on your assignment...
Historically, the proportion of students entering a university who finished in 4 years or less was 63%. To test whether this proportion has decreased, 114 students were examined and 51% had finished in 4 years or less. To determine whether the proportion of students who finish in 4 year or less has statistically significantly decreased (at the 5% level of signficance), what is the critical value
Answer:
z(c) = - 1,64
We reject the null hypothesis
Step-by-step explanation:
We need to solve a proportion test ( one tail-test ) left test
Normal distribution
p₀ = 63 %
proportion size p = 51 %
sample size n = 114
At 5% level of significance α = 0,05, and with this value we find in z- table z score of z(c) = 1,64 ( critical value )
Test of proportion:
H₀ Null Hypothesis p = p₀
Hₐ Alternate Hypothesis p < p₀
We now compute z(s) as:
z(s) = ( p - p₀ ) / √ p₀q₀/n
z(s) =( 0,51 - 0,63) / √0,63*0,37/114
z(s) = - 0,12 / 0,045
z(s) = - 2,66
We compare z(s) and z(c)
z(s) < z(c) - 2,66 < -1,64
Therefore as z(s) < z(c) z(s) is in the rejection zone we reject the null hypothesis
According to genetic theory, there is a very close to even chance that both children in a two child family will be of the same gender. Here are two possibilities.
(i). 24 couples have two children. In 16 or more of these families, it will turn out that both children are of the same gender.
(ii). 12 couples have two children. In 8 or more of these families, it will turn out that both children are of the same gender. Which possibility is more likely and why?
Answer:
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Step-by-step explanation:
(i) probability with 16 success out of 24 = 16/24 = 2/3
(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3
Since the two experiments have the same probability, the observed probabilities are the same.
HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.
Using the binomial distribution,
(i)
p = 1/2
N = 24
x = 16 (number of successes)
P(16,24) = C(24,16) p^16* (1-p)^8
= 735471* (1/65536)*(1/256)
= 0.0438
(ii)
p = 1/2
N = 12
x = 8 (number of successes)
P(8,12) = C(12,8) p^8* (1-p)^4
= 495*1/256*1/16
= 0.1208
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Note: It would help to mention the topic you're on so answers will correspond to what is expected. Here we cover probability and binomial distribution.
a variable with an exponent is a perfect square if the exponent is divisible by____
Answer: 3
Step-by-step explanation:
√9m^2n^2 + 2√m^2n^2 - 3mn
Answer:
I think it is
Step-by-step explanation:
Answer:
5n√2m^ - 3mn
Step-by-step explanation:
another pls! lolllllll
Answer:
P = 126; A = 927
Step-by-step explanation:
Enlarging by a scale factor means multiplying each number by the given. 6 x 4.5 = 27; 8 x 4.5 = 36. 2(27) + 2(36) = 126; 27 x 36 = 927.
Answer:
Hey there!
Original Width: 6
New Width: 27
Original Length: 8
New Length: 36
Perimeter: 36+36+27+27, or 126
Area: 36(27), or 972.
Hope this helps :)
What is the equation of the line with a slope of 4 and a y-intercept of -5?
Answer:
y = 4x -5
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 4x -5
write the statement for 4p = 8
Answer:
See below
Step-by-step explanation:
The statement that can be written for 4p = 8 is:
=> Four times a certain number equals eight.
x=7 what would match this soulotion
Answer:
x = 7
Step-by-step explanation:
7 = 7
It's given
Which of the following is a point-slope equation of a line that passes through
the points (5,2) and (-1,-6)?
A. y-2-(X-5)
B. y-2-(X-5)
C. y-2 =(x-5
D. V-2--0-5)
Please, check the options of the question. The point-slope equation needs the slope, m, in the equation.
Answer:
The point-slope equation of the points (5,2) and (-1,-6) is
[tex] \\ y - 2 = \frac{4}{3}(x-5)[/tex] or,
[tex] \\ y + 6 = \frac{4}{3}(x+1)[/tex]
which are the same as
[tex] \\ 3y-4x+14 = 0[/tex] , (which is not a point-slope equation, though)
Step-by-step explanation:
The point-slope equation is given by:
[tex] \\ y - y_{1} = m(x - x_{1})[/tex]
Where m is the slope of the line:
[tex] \\ m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
Having the points (5,2) and (-1,-6), then
[tex] \\ m = \frac{-6 - 2}{-1 -5}[/tex]
[tex] \\ m = \frac{-8}{-6}[/tex]
[tex] \\ m = \frac{4}{3}[/tex]
Then, the point-slope equation of the points (5,2) and (-1,-6) is
[tex] \\ y - 2 = \frac{4}{3}(x-5)[/tex] or
[tex] \\ y + 6 = \frac{4}{3}(x+1)[/tex]
The below graph represents both lines (they are the same line).
Determine if the survey question is biased. If the question is biased, suggest a better wording. How often do you eat fruit during an average week?
1. Is the question biased?
A. Yes, because it influences the respondent into thinking that eating fruit is good for you. A better question would be "Do you think that eating fruit is good for you?"
B. No, because it influences the respondent into thinking that eating fruit is good for you.
C. Yes, because it does not lead the respondent to any particular answer. A better question would be "Why is eating fruit good for you?"
D. No, because it does not lead the respondent to any particular answer.
2. Choose the best question below.
A. Do you think that eating fast food is good for you?
B. Do you think that eating fast food is bad for you?
C. Why is eating fast food bad for you?
D. The original question is not biased.
Answer:
The correct answers are:
1. No, because it does not lead the respondent to any particular answer (D)
2. The original question is not biased (D)
Step-by-step explanation:
In developing survey questions, response biases are tendencies for respondents to respond inaccurately or falsely to a particular question and this largely has to do with the way the questions are framed. Biased questions build preconceived thoughts in the mind of the respondent, increasing the tendency for them to lean towards a particular answer.
In this example, the question "How often do you eat fruit during an average week?" is not biased because it does not suggest to the respondent whether eating fruits is good or bad, it just directs the respondent to a particular number, hence the question is not biased.
in the diagram ,a and 46° are complementary angles. It is given that a and b are supplementary angles and the angle conjugate to c is 283°. Calculate the values of a,b,c and d. pleaseeeee answer soonn
Answer:
[tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
Step-by-step explanation:
It is given that a and 46° are complementary angles.
[tex]a+46^{\circ}=90^{\circ}[/tex]
[tex]a=90^{\circ}-46^{\circ}[/tex]
[tex]a=44^{\circ}[/tex]
It is given that a and b are supplementary angles.
[tex]a+b=180^{\circ}[/tex]
[tex]44^{\circ}+b=180^{\circ}[/tex]
[tex]b=180^{\circ}-44^{\circ}[/tex]
[tex]b=136^{\circ}[/tex]
Angle conjugate to c is 283°.
[tex]c+283^{\circ}=360^{\circ}[/tex]
[tex]c=360^{\circ}-283^{\circ}[/tex]
[tex]c=77^{\circ}[/tex]
Sum of all angles at a point is 360 degrees.
[tex]a+b+c+d+46^{\circ}=360^{\circ}[/tex]
[tex]44^{\circ}+136^{\circ}+77^{\circ}+d+46^{\circ}=360^{\circ}[/tex]
[tex]d+303^{\circ}=360^{\circ}[/tex]
[tex]d=360^{\circ}-303^{\circ}[/tex]
[tex]d=57^{\circ}[/tex]
Therefore, [tex]a=44^{\circ},b=136^{\circ},c=77^{\circ},d=57^{\circ}[/tex].
NEED HELP ASAP!!
What is the equation of the line that is parallel to the
given line and has an x-intercept of -3?
O y = x + 3
O y = ?X + 2
Oy=-3x + 3
y=-3x+2
Answer:
B
Step-by-step explanation:
The equation of the line that is parallel to the given line and has an x-intercept of -3 is y= 2/3x + 2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
We have a graph.
So, slope of line in graph is
= (-1-1)/ (0.-3)
= -2/ (-3)
= 2/3
and, we know that two parallel line have same slope.
so, the slope of parallel line is 2/3 and the x intercept is -3.
So, the Equation line is y= 2/3 x + b
0 = 2/3 (-3) +b
b= 2
Thus, the required equation is y= 2/3x + 2.
Learn more about Slope here:
https://brainly.com/question/2863474
#SPJ5
Determine whether the value given below is from a discrete or continuous data set. In a test of a method of gender selection, 725 couples used the XSORT method and 368 of them had baby girls. Choose the correct answer below. A. The data set is neither continuous nor discrete. B. A continuous data set because there are infinitely many possible values and those values can be counted C. A continuous data set because there are infinitely many possible values and those values cannot be counted D. A discrete data set because there are a finite number of possible values
Answer:
D. A discrete data set because there are a finite number of possible values.
Step-by-step explanation:
Assuming in a test of a method of gender selection, 725 couples used the XSORT method and 368 of them had baby girls. The value given is from a discrete data set because there are a finite number of possible values.
In Mathematics, a discrete data is a data set in which the number of possible values are either finite or countable.
On the other hand, a continuous data is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable.
Hence, if 725 couples used the XSORT method and 368 of them had baby girls; this is a discrete data because the values (725 and 368) are finite and can be counted.
A parallelogram has coordinates A(1, 1), B(5, 4), C(7, 1), and D(3, -2). What are the coordinates of parallelogram A′B′C′D′ after a 180° rotation about the origin and a translation 5 units to the right and 1 unit down? I need Help
Hey there! I'm happy to help!
First, we need to rotate our points 180° about the origin. To find the coordinates after such a rotation, we simply find the negative version of each number in the ordered pair, which can be written as (x,y)⇒(-x,-y).
Let's convert this below
A: (1,1)⇒(-1,-1)
B: (5,4)⇒(-5,-4)
C: (7,1)⇒(-7,-1)
D: (3,-2)⇒(-3,2)
Now, we need to translate these new points five units to the right and one unit down. This means we will add 5 to our x-value and subtract 1 from our y-value. This will look like (x,y)⇒(x+5,y-1). Let's do this below.
A: (-1,-1)⇒(4,-2)
B: (-5,-4)⇒(0,-5)
C: (-7,-1)⇒(-2,-2)
D: (-3,2)⇒(2,1)
Therefore, this new parallelogram has coordinates of A'(4,-2), B'(0,-5), C'(-2,-2), and D'(2,1)
Now you know how to find the coordinates of translated figures! Have a wonderful day! :D
A keypad at the entrance of a building has 10 buttons labeled 0 through 9. What is the probability of a person correctly guessing a 9-digit e
A keypad at the entrance of a building has 10 buttons labeled 0 through 9. What is the probability of a person correctly guessing a 9-digit entry code if they know that no digits repeat?
Answer:
the probability of a person correctly guessing a 9-digit entry code if they know that no digits repeat is 0.1
Step-by-step explanation:
We know that probability= number of required outcomes /number of all possible outcome.
From the given information;
the number of required outcome is guessing a 9-digit = 1 outcome
the number of all possible outcome = ¹⁰C₉ since there are 10 numbers and 9 number are to be selected.
Since there are only 9-digit that opens the lock;
the probability of a person correctly guessing a 9-digit entry code is
[tex]P =\dfrac{1}{^{10}C_9}[/tex]
[tex]P =\dfrac{1}{\dfrac{10!}{9!1!}}[/tex]
[tex]P =\dfrac{1}{10}[/tex]
P = 0.1
A cylinder has a volume of 200 mm3 and a height of 17 mm.
a) The volume formula for a cylinder is v = pie r squareℎ. Isolate for the variable r in this formula.
b) Using the equation where you isolated for r in part a, find the radius of the cylinder. Round your answer to the nearest hundredth. (1 mark)
Answer:
The radius of the cylinder is 1.93mm.
Step-by-step explanation:
1) Formula to find the missing radius : V= pi r^2 (h)
( V= volume, pi=3.14 r=radius, h= height)
2) Plug all the give variables into the formula: 200=pi r^2 (17)
3) Multiply pi with 17 and then round it to the nearest hundredth which you get 53.401707511 -> 53.41, now your equation is: 200= 53.41 r^2
4) Next you want to isolate the r^2 by dividing both sides by 53.41
200/53.41= 53.41r^2/53.41 ( 3.74461711 round to the nearest hundredth --> 3.74) ---> 3.74=r^2
5) Now you have to square both sides to get rid of that exponent : squared 3.74 = squared r^2
6) Your equation would be 1.933907961 = r, round that whole decimal to the nearest hundredth and you will get 1.93 ( 19.3 = r)
7) So the radius of the cylinder given the volume is 200 mm^3 and a height of 17 mm is 1.93 mm.
The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle. Find the measure of both angles.
Answer:
We have the measure of both angles as 55 degrees and 35 degrees
Step-by-step explanation:
We know that there are three angles in a right-angled triangle. One of which is 90. FOr now, the other two are unknown, so we would designate them to be x and y.
We now set up an equation using the information we are given about the problem.
From this statement "The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle." we can set up the following equation:
x =2y -15 -------- equation 1
similarly, we know that the sum of angles in a triangle = 180 degrees. Hence, we can use this to set up another equation as follows:
x + y + 90 = 180
x+ y = 90 ------------- equation 2
we can now solve the two equations simultaneously as
x -2y =-15
x+ y = 90
from this, we have that
x = 55 and y = 35
We have the measure of both angles as 55 degrees and 35 degrees
plzzz helppppp. 4>n/-4
Answer:
-16 < n
Step-by-step explanation:
4>n/-4
Multiply each side by -4, remembering to flip the inequality
-4 *4 < n/-4 * -4
-16 < n
Answer:
[tex]n > -16[/tex]
Step-by-step explanation:
[tex]4 > n/-4[/tex]
Multiply each part by -4 (flip sign).
[tex]-4 *4 < n/-4 * -4[/tex]
[tex]-16 < n[/tex]
Switch sides.
[tex]n>-16[/tex]