Draw a box plot for the data:
135, 149, 156, 112, 134, 141, 154, 116, 134, 156
Answers
We first order the data from least to greatest:
112, 116, 134, 134, 135, 141, 149, 154, 156, 156
We find the median (middle value). There are 10 data values, which puts the median between 135 and 141:
(135+141)/2 = 276/2 = 138
The Upper Quartile (UQ) is the median of the upper half of data, cut by the median. This is 154.
The Lower Quartile (LQ) is the median of the lower half of data, cut by the median. This is 134.
The middle line of the box is drawn at the median, 138. The left side of the box is at the LQ, 134. The right side of the box is at the UQ, 154. There is a whisker drawn from the right side to the highest value, 156. There is a whisker drawn from the left side to the smallest value, 112.
The solution is: The box plot is attached.
What is median?In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
We first order the data from least to greatest:
112, 116, 134, 134, 135, 141, 149, 154, 156, 156
We find the median (middle value). There are 10 data values, which puts the median between 135 and 141:
(135+141)/2 = 276/2 = 138
The Upper Quartile (UQ) is the median of the upper half of data, cut by the median. This is 154.
The Lower Quartile (LQ) is the median of the lower half of data, cut by the median. This is 134.
The middle line of the box is drawn at the median, 138. The left side of the box is at the LQ, 134. The right side of the box is at the UQ, 154. There is a whisker drawn from the right side to the highest value, 156. There is a whisker drawn from the left side to the smallest value, 112.
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Related Questions
If I get 3 problems wrong on a 12 question math paper, what grade would I get?
Answers
If you got 3 questions wrong on a 12 problem math paper, to figure out how many you got right you must subtract the number you got incorrect (3) from the total number (12).
12-3=9
To figure out your grade, you have to divide how many you got correct (9-see above) by the total number of questions (12).
9/12 = 0.75
If you multiply this decimal by 100, you get the equivalent percentage of 75%.
Therefore, you would have gotten a 75% on the paper.
Hope this helps!
Circle 1 is center at (-4,5) and has a radius of 2 centimeters. Circle 2 is centered at (2,1) and has a radius of 6 centimeters. What transformations can be applied to Circle 1 to prove the circles are similar?
Answers
1) Draw a vector from point A to B
2)Dilate circle A to circle B. It means translating mapping circle A to circle B.
3)By this way, we can claim that circles A and B are similar.
And the similarity ratio is [tex] \frac{ r_{2} }{ r_{1} } = \frac{6}{2} =3[/tex]
Phillip watched a beach volleyball game from 1:45pm to 2:00pm.how many degrees did the minutes hand turn?
Answers
We have then:
2:00 - 1:45 = 15 minutes
Then, the amount of degrees is given by:
(15/60) * (360) = 90 degrees
Answer:
the minutes hand did turn about:
90 degrees
Answer:
90 degrees
Step-by-step explanation:
What is the center of the circle with the equation (x-1)2 + (y-3)2= 9?
Answers
[tex](x-a)^2+(y-b)^2=r^2[/tex]
[tex]\text{a and b are the x and y coordinates of the center of the circle; r is a length of a radius}[/tex]
We have:
[tex](x-1)^2+(y-3)^2=9\\\\\text{therefore coordinates of the center of the circle are (1; 3) and a radius is equal 3}[/tex]
x - 1 means that x coordinate is 1 and y - 3 gives the y coordinate which is 3
Center is at ( 1, 3) answer
How do you write an equation for a circle with center (2,4) and passes through point (5, 9)?
Answers
(x - h)² + (y - k)² = radius²
where (h, k) is the center.
We can plug in the given information from the description and solve for the radius.
(x - 2)² + (y - 4)² = radius²
To find the radius, we do the distance formula from the center to the point on the circle.
Distance = [tex] \sqrt{ (Y2-Y1)^{2} + (X2 - X1)^{2} } [/tex]
D = [tex] \sqrt{ (9 - 4)^{2} + (5 - 2)^{2} } [/tex]
D = [tex] \sqrt{ 5^{2} + 3^{2} } [/tex]
D = [tex] \sqrt{25 + 9} [/tex]
D = [tex] \sqrt{34} [/tex]
That is your radius. Now we plug it in.
(x - 2)² + (y - 4)² = (√34)²
Your final answer is:
(x - 2)² + (y - 4)² = 34
At sea, the distance to the horizon is directly proportional to the square root of the elevation of the observer. if a person who is 36 feet above the water can see 7.4 miles, find how far a person 64 feet above the water can see.
Answers
The square root of 36 feet (the elevation) is 6 feet.
Equation for direct proportion: y=kx (y is directly proportionate to x, k is the amount of proportion)
7.4 miles = 6 feet * k
7.4mi = 6feet* (1.233 * whatever the conversion rate is between feet and miles)
The same applies to 64: the square root of it will be directly proportionate to the distance.
√64 = 8
8feet*k = [thenumber_we_don't_know]miles
8*1.233 = {??}
= 9.84
The answer is 9.84.
The person 64 feet above the water can see 9.84 miles.
It is given in the question that the distance to the horizon is directly proportional to the square root of the elevation of the observer.
if the elevation of the observer be h and distance to the horizon be x then:
[tex]x=k\sqrt{h}[/tex] where k is the constant of proportionality
from the given data:
[tex]7.4= k\sqrt{36}\\\\7.4=6k\\\\k=1.23[/tex]
So, if h = 64 feet then,
[tex]x=k\sqrt{h}\\\\x=1.23\sqrt{64}\\\\x=9.84 miles[/tex] is how far the person 64 feet above the water can see.
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Use the following information to answer the next two questions
Answers
y=abˣ
where:
a=initial value
b=growth factor
y=number of years
thus using point (1,63) and (2,226)
the growth factor will be:
b=(226/63)=3.587~3.6
a=63
thus the formula for the function will be:
A(y)=a(3.6)^y
substituting (1,63) in the equation and solving for a.
63=a(3.6)^1
thus
a=63/3.6=17.5
hence the formula will be:
A(y)=17.82(3.6)^y
Answer: D] 17.5(3.6)^y
2] The number of acres defoliated after 5 years will be as follows:
y=5 years
A(y)=17.82(3.6)^y
plugging in the value we get:
A(y)=17.82(3.6)^5
simplifying the above
A(y)=10775.07
A(y)=10775
Answer: D
16. Supposes that y varies inversely with x and that y-10 whenx-7. Which of the following equations models this relationship?
A. Y=70x
B. Y=-10x
C. Y=x/70
D. Y=70/x
Answers
Hope that helped!;)
The equation that models this relation is y = 70/x. So, option (D) is the correct answer.
What is constant of proportionality?The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.
For the given situation,
The values are y = 10 and x = 7
y varies inversely with x.
⇒ [tex]y[/tex] ∝ [tex]\frac{1}{x}[/tex]
To remove proportionality we introduce a constant 'k'.
⇒ [tex]y=\frac{k}{x}[/tex]
Substitute the values of x and y,
⇒ [tex]10=\frac{k}{7}[/tex]
⇒ [tex]k=70[/tex]
Now substitute the value of k = 70 in y,
⇒ [tex]y = \frac{70}{x}[/tex]
Hence we can conclude that the equation that models this relation is y = 70/x. So, option (D) is the correct answer.
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The perimeter of a rectangular garden is 100 feet (ft). the area of the rectangular garden area is 600 ft2. find the length and width of the garden. let the length of the garden be the shorter side, of necessary.
Answers
Area=x*y=600
thus
x=600/y
Perimeter=2(L+W)
100=2(x+y)
substituting the value of x we obtain:
100=2(600/y+y)
solving for y we shall have:
50=600/y+y
50y=600+y^2
thus
y^2-50y+600=0
solving the quadratic we obtain:
y=20 or y=30
thus the length=30 ft and the width=20 ft
The length of the garden is 20 feet and the width is 30 feet.
To solve this problem, we will use the formulas for the perimeter and area of a rectangle. The perimeter (P) of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. The area (A) of a rectangle is given by the formula A = lw.
Given the perimeter of the garden is 100 feet, we can set up the following equation:
[tex]\[ 2(l + w) = 100 \][/tex]
[tex]\[ l + w = 50 \][/tex]
[tex]\[ w = 50 - l \][/tex]
This equation relates the length and width of the garden.
Next, we are given that the area of the garden is 600 square feet:
[tex]\[ lw = 600 \][/tex]
Substituting the expression for w from the first equation into the area equation, we get:
[tex]\[ l(50 - l) = 600 \][/tex]
[tex]\[ 50l - l^2 = 600 \][/tex]
Rearranging the terms, we have a quadratic equation:
[tex]\[ l^2 - 50l + 600 = 0 \][/tex]
To solve this quadratic equation, we can factor it:
[tex]\[ (l - 20)(l - 30) = 0 \][/tex]
This gives us two possible solutions for the length: l = 20 feet or l = 30 feet.
Since we are asked to let the length be the shorter side, if necessary, we choose the smaller value for the length:
[tex]\[ l = 20 \text{ feet} \][/tex]
Now we can find the width by substituting the length back into the equation for the perimeter:
[tex]\[ w = 50 - l \][/tex]
[tex]\[ w = 50 - 20 \][/tex]
[tex]\[ w = 30 \text{ feet} \][/tex]
Therefore, the length of the garden is 20 feet and the width is 30 feet.
Calculate the area of the shaded sector in square inches.
Answers
Zack borrowed $1,087 for 12 months at 11 percent interest. If he must pay 11.00 per $100, what is Zack's monthly payment?
Answers
[tex] \frac{1087}{100} =10.87[/tex]
Now we know that he must pay $11.00 10.87 times each month, so the last thing we are going to do to find his monthly payment is multiply both quantities:
[tex]11.00*10.87=119.57[/tex]
We can conclude that Zack's monthly payment is $119.57
A summer camp manager wants to order 500 bag lunches for a field trip. Each lunch will have a piece of fruit. The manager is deciding on ordering apples, oranges, bananas, or plums. The camp manager surveys 50 random campers, and the results are given in this table.
Based on the results, which fruit should the manager order?
A- Apples
B- Oranges
C- Plums
D- Bananas
Answers
A bag of uninflated balloons contains 10 red, 12 blue, 15 yellow and 8 green balloons. A balloon is drawn at random, what is the probability of drawing a red balloon?
Answers
(28.57%)
We have been given that a bag of uninflated balloons contains 10 red, 12 blue, 15 yellow and 8 green balloons.
We need to find the probability of drawing a red balloon.
We know that probability is given by
[tex]\\ \text{Probability =} \frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Since we know that there are 10 red balloons. Therefore, our number of favorable outcomes is 10.
In order to find the total number of outcomes, we will add balloons of all colors.
Therefore, total outcomes are = [tex]10+12+15+8 = 45[/tex]
We can now substitute the values of favorable outcomes and total outcomes in order to find the required probability.
[tex]\\ \text{Probability =} \frac{\text{10}}{\text{45}} = \frac{2}{9}[/tex]
Please help:
In a right triangle ABC, tan(A) = 3/4. Find sin(A) and cos(A).
In a right triangle ABC with angle A equal to 90 degrees, find angle B and C so that sin(B) = cos(B).
Answers
To make sine and cos equal the opposite and adjacent sides must be equal. By corresponding angles it is isosceles so b and c must be 45
8 MIN LEFT anyone know this?
Answers
The number of tropical fish that an aquarium can hold depends on the volume of the fish tank. the interior dimensions of the fish tank are 25 cm, 30 cm, and 39 cm. each fish requires 10,000 cubic centimeters of water. how many tropical fish will this fish tank hold?
Answers
Urgent!! Need an answer ASAP!
Professor Scott has 84 students in his college mathematics lecture class. The scores on the midterm exam are normally distributed with a mean of 72.3 and a standard deviation of 8.9. How many students in the class can be expected to receive a score between 63.4 and 81.2? Express the answer to the nearest student.
Answers
=====================================================
Explanation:
Convert each raw score to a z score
If x = 63.4, then
z = (x-mu)/sigma
z = (63.4-72.3)/8.9
z = -1
if x = 81.2, then
z = (x-mu)/sigma
z = (81.2-72.3)/8.9
z = 1
So P(63.4 < x < 81.2) is the same as P(-1 < z < 1)
Through the empirical rule (aka the 68-95-99.7 rule), we know that roughly 68% of the data values are within one standard deviation of the mean. In other words
P(-1 < z < 1) = 0.68 approximately (see note below)
Multiply 0.68 by the total 84 to get
0.68*84 = 57.12
which rounds to 57 people
Note: we can use a calculator to get a more accurate result of 0.68268949; a data table works as well but it won't be as accurate. For the purposes of this problem, the value 0.68 is good enough
Answer: 57
=====================================================
Explanation:
Convert each raw score to a z score
If x = 63.4, then
z = (x-mu)/sigma
z = (63.4-72.3)/8.9
z = -1
if x = 81.2, then
z = (x-mu)/sigma
z = (81.2-72.3)/8.9
z = 1
So P(63.4 < x < 81.2) is the same as P(-1 < z < 1)
Through the empirical rule (aka the 68-95-99.7 rule), we know that roughly 68% of the data values are within one standard deviation of the mean. In other words
P(-1 < z < 1) = 0.68 approximately (see note below)
Multiply 0.68 by the total 84 to get
0.68*84 = 57.12
which rounds to 57 people
Note: we can use a calculator to get a more accurate result of 0.68268949; a data table works as well but it won't be as accurate. For the purposes of this problem, the value 0.68 is good enough
Which shapes have rotational symmetry that occurs at 180°?
Check all that apply.
regular octagon regular pentagon regular hexagon square right isosceles triangle
Answers
- Regular Hexagon
- Square
It should be regular octagon, regular hexagon, and square
Chris took a vacation trip to maine, where sales tax on taxable items is 5%. in maine, prepared food and lodging are taxed an additional 2%, for a total of 7% tax, while auto rentals are taxed an additional 5%, for a total of 10% tax.chris bought $70 worth of souvenirs, taxable at the general rate. he also spent $580 on prepared food and lodging and $620 for a rental car, all before tax. how much did he spend in total after tax was included?
a.$1333.50
b.$1316.10
c.$1270.00
d.$1376.10
Answers
$70 of souvenirs mean the tax is 5% since it is not prepared food, lodging, or auto rentals.
$580 on prepared food means that has 7% tax because it is special.
$620 on the car has a 10% tax, as stated in the problem.
So do 70(1.05)+580(1.07)+620(1.1) to get $1376.1.0
For anyone with the “TRICIA” problem: $1202.30
jane's salary is increased by 2% to £39474. how much is her salary before the rise?
Answers
x + 0.02x = 39474
1.02x = 39474
x = 39474 / 1.02 = £38,700 answer
simplify: 10(6y+x)=4
Answers
10(6y) + 10x = 4 Simplify the 10 times 6y
60y + 10x = 4
Which group of values makes the expression 3x2y−2z UNDEFINED? A) x = –1; y = 0; z = 3 B) x = –1; y = 3; z = 0 C) x = 0; y = −1; z = 3 D) x = 0; y = 3; z = −1 E) x = –1; y = 2; z = 1
Answers
Which group of values makes the expression 3x/2y−2z UNDEFINED?
we know that
So that the expression is defined, the denominator in (3x/2y) can not be zero
hence
the value of y = 0 makes the expression UNDEFINED
therefore
the answer is
the option A) x = –1; y = 0; z = 3
Answer:
The answer is A
Step-by-step explanation:
sadly i dont have the work of it just by looking it up you can get the answer tho. Answer is A
A large truck and a small car have a head-on collision. Which scenario is true?
A) The truck has the greater acceleration because it has the greater mass
B) The car has the greater acceleration because it has the smaller mass
C) Both the truck and car have the same magnitude of acceleration
(Edit: This was meant to go in the Physics section, I'm so sorry about this, if anyone here could still answer that's be amazing)
Answers
In a collision, both the car and truck experience the same force due to Newton's Third Law. However, due to Newton's Second Law, the car, with its smaller mass, experiences a greater acceleration.
Explanation:According to Newton's Third Law of Motion, 'for every action, there is an equal and opposite reaction', both the truck and the car would experience the same magnitude of force. However, let's recall Newton's Second Law, 'force equals mass times acceleration' (F=ma). Using these physics principles, we can deduce that the car with the smaller mass would experience a greater acceleration, and the large truck would experience a lesser acceleration. This is because when the same force is applied to both objects, an object with a smaller mass will have a greater acceleration compared to an object with a larger mass. Hence, option B) 'The car has the greater acceleration because it has the smaller mass' would be the correct answer based on Newton's laws of motion.
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Two mechanics worked on a car. the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. together they charged a total of $1775 . what was the rate charged per hour by each mechanic if the sum of the two rates was $100 per hour?
Answers
x = amount of $ / hr that the mechanic obtains 1.
y = amount of $ / hr obtained by mechanic 2.
We write the system of equations:
x + y = 100
20x + 15y = 1775
Solving the system of equations we have:
x = 55 $ / hr
y = 45 $ / hr
Answer:
the rate charged per hour by each mechanic was:
x = 55 $ / hr
y = 45 $ / hr
You have a bag of chocolate candy. Ten of them are red, 7 are brown, 12 are green, and 9 are blue. What is the probability that you pick a red candy, given that you have already picked a red candy and have not replaced it?
Answers
9/37 is the correct answer.
What is the greatest common factor of 60x4y7, 45x5y5and 75x3y?
Answers
Answer:
15x^3·y
Step-by-step explanation:
The numbers 60, 45, 75 are all multiples of 15, so 15 is their greatest common factor.
The least power of the factor x is 3; the least power of the factor y is 1, so the GCF is ...
GCF = 15·x^3·y
A waitress works 1.75 hours less in the afternoon than in the evening. If she works 5 1/8
hours in the afternoon, how many hours does she work in the evening?
Answers
We know for our problem that she works [tex]5 \frac{1}{8} [/tex] in the afternoon and that she works 1.75 hours less in the afternoon than in the evening, so:
[tex]x=5 \frac{1}{8} -1.75[/tex]
Since [tex] \frac{1}{8} =0.125[/tex], we can rewrite our expression:
[tex]x=5.125-1.75[/tex]
[tex]x=3.375[/tex]
We can conclude that she works 3.375 hours in the evening, or expressed as a mixed fraction: [tex]3 \frac{3}{8} [/tex] hours.
Answer: The waitress works:[tex]\[{6 \frac{7}{8}}[/tex] hours in the evening
Let us denote the number of hours the waitress works in the evening as E and the number of hours she works in the afternoon as A.
Given that:
[tex]\[A = 5 \frac{1}{8} \text{ hours}\][/tex]
We can convert the mixed number to an improper fraction:
[tex]\[5 \frac{1}{8} = 5 + \frac{1}{8} = \frac{40}{8} + \frac{1}{8} = \frac{41}{8}\][/tex]
So, [tex]\( A = \frac{41}{8} \)[/tex] hours.
The waitress works 1.75 hours less in the afternoon than in the evening. Thus, we have:
[tex]\[A = E - 1.75\][/tex]
[tex]\[\frac{41}{8} = E - 1.75\][/tex]
Converting 1.75 to a fraction:
[tex]\[1.75 = \frac{7}{4} = \frac{14}{8}\][/tex]
Now, the equation becomes:
[tex]\[\frac{41}{8} = E - \frac{14}{8}\][/tex]
[tex]\[E = \frac{41}{8} + \frac{14}{8}\]\[E = \frac{41 + 14}{8} = \frac{55}{8}\][/tex]
Convert the improper fraction back to a mixed number:
[tex]\[\frac{55}{8} = 6 \frac{7}{8}\][/tex]
Therefore, the waitress works:
[tex]\[{6 \frac{7}{8}}[/tex] hours in the evening
Doug can paint the living room in 4 hours. it would take elaine 6 hours to paint the same room. how long would it take doug and elaine, working together, to paint the living room?
Answers
You can get this by setting up the equation:
x/4 + x/6 = 1
Where x is equal to the amount of hours spent working. In this equation x/4 would be Doug. In 4 hours he would paint on room. x/6 would be Elaine. When you add them together using common denominators, you can find x.
How is the interquartile range calculated? HELP WITH APEX PLEASE!
Answers
By definition the interquartile range or IQR is obtained when the 25th percentile or [tex] Q_{1} [/tex] is subtracted from the 75th percentile or [tex] Q_{3} [/tex].
Thus, from the above definition, the formula for IQR is:
[tex] IQR=Q_{3}-Q_{1} [/tex]
As we can see from the provided options that the definition of IQR matches the expression provided in Option A and thus, Option A is the correct answer.
Quartile 3 (Q3) minus quartile 1 (Q1) is right for apex.
The sales tax in the city of Taxemalot is 8.1%. What is the growth factor for any item purchased at your local Tarmart? a.8.1 c.1.081 b.0.81 d.81