What conclusion can be determined from the dot plot below?
A dot plot showing two dots above 2, three dots above 3 five dots above 4, three dots above 5, and two dots above 6.
A) The median of the data set is 3.
B) The mean of the data set is 3.
C) The range of the data set is 5.
D) The number of observations is 15.
Please give the correct answer, there will be consequences if you don't which include being reported
Answers
Answer:
The correct option is D.
Step-by-step explanation:
From the given figure it is clear that two dots above 2, three dots above 3 five dots above 4, three dots above 5, and two dots above 6. It means the data set is
2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6
Total number of observations = 15
Therefore option D is correct.
15 is an odd number, so the median of the data is
[tex]Median=\frac{(\frac{n+1}{2})th}{2}[/tex]
[tex]Median=\frac{(\frac{15+1}{2})th}{2}=8th[/tex]
The 8th term of the data is 4, therefore the median of the data is 4. Option A is incorrect.
The mean of the data is
[tex]Mean=\frac{\sum x}{n}=\frac{2+2+3+3+3+4+4+4+4+4+5+5+5+6+6}{15}=\frac{60}{15}=4[/tex]
The mean of the data is 4. Option B is incorrect.
Range of the data is
[tex]Range=Maximum-Minimum[/tex]
[tex]Range=6-2=4[/tex]
Range of the data is 4. Option C is incorrect.
Related Questions
Can anyone help me with this problem?
Answers
Use Pythagorean theorem:
[tex]|AB|^2=|BC|^2+|CA|^2\\\\9^2=6^2+|CA|^2\\\\81=36+|CA|^2\ \ \ \ |-36\\\\|CA|^2=45\to|CA|=\sqrt{45}\\\\|CA|=\sqrt{9\cdot5}\\\\|CA|=\sqrt9\cdot\sqrt5\\\\|CA|=3\sqrt5[/tex]
[tex]\tan\Theta=\dfrac{6}{3\sqrt5}=\dfrac{2}{\sqrt5}\cdot\dfrac{\sqrt5}{\sqrt5}=\dfrac{2\sqrt5}{5}[/tex]
Four girls and eight boys are running for president or vice president of the student council. find each probability: find the prbability that two girls are elected
Answers
The probability that a girl is elected for one office is 4/12, since there are 4 girls out of 12 students.
The probability that a girl is elected for the second office is 3/11. This is because after one girl is elected, there are 3 girls left out of 11 students left.
Together, this gives us
4/12(3/11) = 12/132 = 1/11
The probability that two girls are elected president and vice president from a group of 4 girls and 8 boys is calculated using a hypergeometric distribution, resulting in a probability of 1/11.
The question is asking for the probability that two girls are elected president and vice president of the student council when there are four girls and eight boys running for these positions. This is an example of a hypergeometric distribution problem, as we are selecting without replacement from a finite population divided into two groups.
To find the probability, we need to determine the number of successful outcomes divided by the total number of possible outcomes. The successful outcome is that the two elected individuals are both girls. Since there are 4 girls, there are 4 choose 2 ways to select 2 girls, which equates to 6 possible successful outcomes. The total number of ways to choose 2 individuals from 12 candidates (4 girls + 8 boys) is 12 choose 2, resulting in 66 possible outcomes.
The probability can be calculated by dividing the number of successful outcomes by the total number of possible outcomes.
Probability = Successful outcomes / Total outcomes = 6 / 66 = 1 / 11
12q^2-17q-7
A. (3q+1)(4q-7)
B. (3q-1)(4q+7)
C. (3q+7)(4q-1)
D. (3q-7)(4q+1)
Answers
find the greatest common factor 6x^2a + 6xa^2
Answers
If you multiply 6xa with a and x ----> 6xa(x+a), you'll get 6x^2a + 6xa^2
Simplify the trigonometric expression.
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[tex](1+sin \alpha )(1-sin \alpha )=1-sin^2 \alpha [/tex]
Now we can rewrite our expression using the common denominator:
[tex]\frac{1-sin \alpha }{1-sin^2 \alpha } + \frac{1+sin \alpha }{1-sin^2 \alpha} = \frac{2}{1-sin^2 \alpha} [/tex]
Finally, we can use the trig identities: [tex]1-sin^2 \alpha =cos^2 \alpha [/tex] and [tex]sec \alpha = \frac{1}{cos \alpha } [/tex] to simplify our trig expression:
[tex]\frac{2}{cos^2\alpha}=2sec^2 \alpha [/tex]
We can conclude that the correct answer is the fourth one.
THe answer is letter D. 2 sec^2 theta
Hope it help! Goodluck!
PLEASE ANSWER ASAP Becky purchased a home entertainment center for $2,254 using an 18-month deferred payment plan with an interest rate of 22.48%. She did not make any payments during the deferment period. What will Becky's monthly payment be if she must pay off the home entertainment center within three years after the deferment period?
$121.01
$87.45
$62.61
$113.72
Answers
Answer:
$62.61
Step-by-step explanation:
Data:
The price of home entertainment = $ 2 254
Time to pay = 18 months
interest rate = 22.48 %
monthly payment = $ 2254/ 18
= $ 125. 22
= - 22.48 (2254)/18
= $ 62.61
Line RS is tangent to circle Q at point R.
What is the measure of ∠SQR ?
Enter your answer in the box.
Answers
Now that we know 2 angles, we can find the 3rd:
180 - 90 - 32 = 58
Using the tangent and radius theorem, the measure of ∠SQR is 58°.
What is Circle Geometry??From the question, we are to determine the measure of ∠SQR
In the given diagram, QR is a radius
By the tangent and radius theorem,
If a tangent and a radius meet at the point of tangency, then they are perpendicular to one another
∴ ∠QRS = 90°
∠SQR + ∠RSQ + ∠QRS = 180° (Sum of angles in a triangle)
∠SQR + 32° + 90° = 180°
∠SQR + 122° = 180°
∠SQR = 180° - 122°
∠SQR = 58°
Hence, the measure of ∠SQR is 58°.
Learn more on Circle geometry here: https://brainly.com/question/21872415
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The square root of 136 is between which two whole numbers?
Answers
Hope this helps!
What is cos 45? Please HELP !!!
Answers
Answer:
A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Step-by-step explanation:
Given : Triangle 90 -45 -45 .
To find : What is cos 45.
Solution : We have given
Triangle 90 -45 -45
Hypotenuse = √2 ,
Adjacent side to 45 degree = 1 .
By the trigonometric ratio : cosine is the ratio of the adjacent side to angle to the hypotenuse .
Cos ( theta) = [tex]\frac{Adjacent}{hypotenuse}[/tex].
Plug the values Hypotenuse = √2 , Adjacent side to 45 degree = 1 .
Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
Therefore, A) Cos ( 45) = [tex]\frac{1}{\sqrt{2}}[/tex].
The cosine of 45° is √2 / 2.
In a triangle with angles of 90°, 45°, and 45°, we can use the trigonometric functions to find the ratios of the sides.
In this case, we want to find the cosine of 45°.
The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse.
In the given triangle, the adjacent side to the 45° angle is 1, and the hypotenuse is √2.
Using the formula for cosine, we have:
cos 45° = adjacent side / hypotenuse
Substituting the values, we get:
cos 45° = 1 / √2
To rationalize the denominator, we multiply both the numerator and denominator by √2:
cos 45° = (1 / √2) * (√2 / √2) = √2 / 2
Therefore, the cosine of 45° is √2 / 2.
To learn more about cosine function;
https://brainly.com/question/29277391
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A ball is rolling in a circular path that has a radius of 10 inches as shown in
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we know that
[circumference]=2*pi*r
for r=10 in
[circumference]=2*pi*10-----> 62.8 in
if 360° (full circle) has a length of --------> 62.8 in
54°------------------------------> X
x=54*62.8/360-----> x=9.42 in
the answer is 9.42 in
The area of the rectangle shown is given by the function A(x) = 2x2 - 5x. If the width of the rectangle is 13, what is the area?
Answers
area of rectangle=length*width
let
x-----> the length side
y-----> the width side
y=13 units
A=2x²-5x
A=x*y------> 2x²-5x=x*13------> 2x²-18x=0-----> x²-9x=0
x*(x-9)=0
the solutions are
x=0
x=9
hence
the dimensions of the rectangle are
length is 9 units
width is 13 units
the area of rectangle is -----> 9*13-----> 117 units²
the answer is
117 units²
Solve the system of equations and choose the correct answer from the list of options. (4 points) x − y = 7 y = 3x + 12
Answers
y = -33/2
Start by plugging in the second equation for y in the first equation. Then solve for x. After you can use that value to solve for y.
Need this geometry answer quick!
Answers
90 + 6x + 4x = 180
Combine like terms:
90 + 10x = 180
Subtract 90 from both sides:
10x = 90
Divide both sides by 10:
x = 9
Answer: 9
x2+y2-4+2y-11=0 what are the center and radius of the circle?
Answers
You need to complete the square for both x and y.
[tex] x^2 - 4x + y^2 + 2y = 11 [/tex]
[tex] x^2 - 4x + 4 + y^2 + 2y + 1 = 11 + 4 + 1 [/tex]
[tex] (x - 2)^2 + (y + 1)^2 = 16 [/tex]
[tex] (x - 2)^2 + (y + 1)^2 = 4^2 [/tex]
The center is (2, -1).
The radius is 4.
This is probably easy but I'm not smart and don't know what else to do I know this is the correct formula it's just confusing to me because there're three numbers and I'm just really dumb.
Answers
Right side rectangle = 4 × 1 = 4
Left side rectangle = 4 × 1 = 4
Both triangles = 4 × 3 = 12
Both triangles = 6
3 + 4 + 4 + 12 = 23
I think the answer is 23 cm
Hope this helped☺☺
Area of a right triangular prism = 1/2(2B) + Ph
The 1/2 and 2 cancel each other out: B + Ph.
Base of the triangular prism: 3 × 4 = 12 cm²
Perimeter of the base (use the Pythagorean Theorem →a² + b² = c²← to figure out the missing side; hypotenuse): 3² + 4² = c²
9 + 16 = c²
√25 = 5
3 + 4 + 5 = 12 cm
Height of triangular prism: 1 cm
Plug these numbers into the formula (B + Ph):
(12 + 12×1) = 24 cm²
The area of the right triangular prism is 24 cm².
Need help to write equations for 5, 6 & 7
Answers
The x-values go up by 1: -2, -1, 0, 1, 2
The y values are always 3 times the previous value.
This is an exponential function.
[tex] y = a(b)^x [/tex]
We need to find a and b.
Look at x = 0.
For x = 0, y = 4.
[tex] y = a(b)^x [/tex]
[tex] 4 = a(b)^0 [/tex]
Since b^0 = 1, this simplifies to
[tex] 4 = a [/tex]
Now we know a = 4. We have
[tex] y = 4(b)^x [/tex]
Look at x = 1. For x = 1, y = 12.
[tex] 12 = 4(b)^1 [/tex]
[tex] 12 = 4b [/tex]
[tex] b = 3 [/tex]
Now that we know a and b, we can write the function.
[tex] y = 4(3)^x [/tex]
Now that you have the function written out, notice the following.
In the exponential equation we found, the number raised to x
is the number you multiply each y value to get the next y value.
In this case, each y value is 3 times the previous one, so you have 3^x.
The way you find "a" in the exponential equation is to look at the y-coordinate
when x = 0. When x = 0, b^x is 1, so b^x drops out, and you get "a" equal to
the y-value. In this case, when x = 0, y = 4, so "a" is 4.
With b = 3, and a = 4, you can quickly write:
y = 4(3)^x.
A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square feet of sheet metal, then what is the largest volume of such a bin? what are its dimensions?
Answers
In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:
V = length x width x height
That is:
[tex]V = xxy = x^{2}y[/tex]
We also know that the bin is constructed from 48 square feet of sheet metal, so:
Surface area of the square base = [tex]x^{2}[/tex]
Surface area of the rectangular sides = [tex]4xy[/tex]
Therefore, the total area of the cube is:
[tex]A = 48 ft^{2} = x^{2} + 4xy[/tex]
Isolating the variable y in terms of x:
[tex]y = \frac{48- x^{2} }{4x}[/tex]
Substituting this value in V:
[tex]V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3} [/tex]
Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:
[tex]\frac{dv}{dx} = 48-3x^{2} =0[/tex]
Solving for x:
[tex]x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4[/tex]
Solving for y:
[tex]y = \frac{48- 4^{2} }{(4)(4)} = 2[/tex]
Then, the dimensions of the largest volume of such a bin is:
Length = 4 ft
Width = 4 ft
Height = 2 ft
And its volume is:
[tex]V = (4^{2} )(2) = 32 ft^{3}[/tex]
Sarah is hiking on a trail near her home. She traveled 5 miles before stopping for a break. After the break, Sarah plans on increasing her speed to 3 miles per hour. Which equation models the total distance, D, Sarah travels after hiking for an additional h hours?
A. D = 3h + 5
B. D = 3(h - 5)
C. D = 3h - 5
D. D = 5h + 3
Answers
Answer: A. [tex]D=3h+5[/tex]
Step-by-step explanation:
Given: The rate of increasing speed = 3 miles per hour
The distance she traveled before stopping = 5 miles
Let h represents the number of additional hours for hiking.
Then the equation that models the total distance 'D' Sarah travels after hiking for an additional h hours is given by :-
[tex]D=3h+5[/tex]
PLS HELP ME ASAP WITH 3, 4, AND 5! PLS! (Read directions carefully :)
(BRAINLIEST WILL BE GIVEN HOPEFULLY!)
(Random answers gets moderated!)
Answers
a. d(0) = 20
b. d(2) = 18
c. d(4) = 12
d. d(6) = 10
e. d(9) = 15
f. d(3) = 15, or d(9) = 15
4) The domain is the horizontal extent: 0 to 12.
The range is the vertical extent: 10 to 20.
5)
a. f(7) = -2*7 +5 = -9
b. f(-3) = -2(-3) +5 = 11
c. -2x +5 = 17; -2x = 12; x = -6, so f(-6) = 17
If x varies directly as y, and x = 48 when y = 16, find x when y = 5.
A) 5/3
B) 153.6
C) 15
Answers
48 = k* 16
k = 3
x=3*5
x=15
Answer:
15
Step-by-step explanation:
x =ky
48 = k16
divide by 16
k = 3
plug k into x=ky
x=3*5
x=15
Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the length of the chord whose endpoints are the points of tangency.
2r
r²
r√2
Answers
.......................
Jason was hired to mow a lawn that covers an area of acres 2 3/4. It took him 4 1/8 hours to complete the job. What was his unit rate in hours per acre?
I understand the steps where I am stuck is how did you get 2/3/
Answers
Divide 2 3/4 acres by 4 1/8 hours:
Divide 2.75 acres by 4.125 hours:
2.75 acres
--------------- = 2.667 acres/hour, or 2 2/3 acres / hour.
4.125 hrs
If this is not entirely clear to you, please share the work you've done yourself and I will respond.
The expression 8x + 2y
Answers
_________________ lines are lines that never intersect and are not coplanar. A) Parallel B) Perpendicular C) Skew D) Transversal
Answers
Skew lines are lines that never intersect and are not coplanar.
So the answer would be C. ^-^
Use substitution to determine which of the following points is a solution to the standard form equation below. 2y = 5
Answers
This is the complete question as I found in internet:
Use substitution to determine which of the following points is a solution to the standard form equation below 5x-2y = 10
these are the points:
-1,5
1,5
0,-5
0,5
Answer: (0, -5)
Explanation:
point x y 5x - 2y = 10 ?
-1,5 -1 5 5(-1) - 2(5) = - 5 - 10 = - 15 ≠ 10 ⇒ not a solution
1,5 1 5 5(1) - 2(5) = 5 - 10 = 5 ≠ 10 ⇒ not a solution
0,-5 0 -5 0 -2(-5) = 10 ⇒ a solution
0,5 0 5 0 - 2(5) = - 10 ≠ 10 ⇒ not a solution
Answer:
(10,5/2) answer is A
Step-by-step explanation:
just took test.
Find the sum of the summation of 2 i minus 12, from i equals 7 to 16.
22
110
220
440
Answers
S=[2(7)-12]+[2(8)-12]+[2(9)-12]+[2(10)-12]+[2(11)-12]+[2(12)-12]+[2(13)-12]+[2(14)-12]+[2(15)-12]+[2(16)-12]
S=2(7+8+9+10+11+12+13+14+15+16)-10(12)
S=2(115)-120
S=230-120
S=110
Answer: Second option 110
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
[tex]\sum_{7}^{16}(2i-12)\\\\=\sum_{7}^{16}2(i-6)\\\\=2\sum_{7}^{16}(i-6)\\\\=2[(16-6)+(15-6)+(14-6)+(13-6)+(12-6)+(11-6)+(10-6)+(9-6)+(8-6)+(7-6)]\\\\=2[10+9+8+7+6+5+4+3+2+1]\\\\\text{Sum of n natural numbers }\\\\=2(\frac{10\times (10+1)}{2})\\\\\=\frac{n(n+1)}{2}\\\\=2\times \frac{10\times 11}{2}\\\\=10\times 11\\\\=110[/tex]
Hence, the value of summation is 110.
Therefore, Second option is correct.
Identify a counterexample to disprove 6n>n^2/6,where n is a real number.
Answers
A counterexample to disprove the inequality [tex]6n > n^2/6[/tex] is n = 12, because when plugged into the inequality, it results in 72 > 24, which is false.
The question is asking for a counterexample to disprove the inequality [tex]6n > n^2/6[/tex], where n is a real number. To find a counterexample, let's test an arbitrary positive number, such as n = 7, to see if the inequality holds.
Substituting 7 for n, we get:
6 x 7 > 72/6
42 > 49/6
42 > 8.167
This is indeed true, so 7 is not a counterexample. However, we can think of a larger value of n. Let's try n = 12:
6 x 12 > 122/6
72 > 144/6
72 > 24
This is false. Hence, n = 12 serves as a counterexample to disprove the given inequality. So, the inequality does not hold for all real numbers.
Sophia and Tyler are running around a 400-meter track. They start running from the same place, at the same time. Sophia runs at a speed of 5 m/s and Tyler runs at a speed of 4 m/s. How long will it take Sophia to lap Tyler?
Answers
S: Runner Sophia.
T: Runner Tyler.
At the beginning the distance between both runners is 400m
At t = 1s Sophia runs 5m and Tyler 4m
At t = 2s Sophia runs 10m and Tyler 8m
and so on.
So, for example at t = 1s, the distance between both runner is:
D = 400m - 5m(the advantage of Sophia) + 4m(what Tyler recovers)
So, we can find a general equation for this matter. Knowing that the distance, velocity and time are related by this equation:
[tex]d=vt[/tex]
Then, the distance between both runners, at any time, is given by:
[tex]D = 400-5t+4t[/tex]
So we need to find the how long it will take Sophia to lap Tyler. This happens when D = 0:
[tex]0 = 400 - 5t+4t[/tex]
∴ [tex]400-t = 0[/tex]
∴ [tex]t = 400s[/tex]
Answer: 400 seconds
Step-by-step explanation:
5x = 400 + y
4x = y
take 4x and add it to the top so it looks like this:
5x = 400 + 4x
cancel 4x if you don't know how to do it you do it like this you take +4x and instead you do -4x to cancel.
and you do it to 5x so you cancel 4x and 5x - 4x = x so x = 400
x = 400
Find the slope of the line on the graph
Answers
1st point ( -4,0)
2nd point (0,3)
slope = change in y over change in x
change in y = 3-0 = 3
change in x = 0 - -4 = 0+4 = 4
slope = 3/4
triangle XYZ is obtuse which list could represent the angle measures of triangle XYZ?
A. 20 60 100
B. 30 60 90
C. 50 50 80
D. 60 60 60