Answer:
median = 93.5
median = 65
MAD = 7.125
MAD = 3.75
Step-by-step explanation:
The median is the middle value when the values of the data set are placed in order from smallest to largest.
Data set: 72 82 92 93 94 97 98 102
As the number of values in the data set is even, the median is the mean of the middle two values.
[tex]\implies \sf median=\dfrac{93+94}{2}=93.5[/tex]
Data set: 53 59 64 65 65 66 67 69
As the number of values in the data set is even, the median is the mean of the middle two values.
[tex]\implies \sf median=\dfrac{65+65}{2}=65[/tex]
To find the Mean Absolute Deviation (MAD):
1. calculate the mean (by summing the data values and dividing by the number of values)
2. Subtract the mean from each value in the data set and take the absolute value of each result.
3. Sum the absolute values from step 2.
4. Divide by the number of values.
Data set: 72, 82, 93, 98, 102, 97, 92, 94
[tex]\sf Mean=\dfrac{72+82+93+98+102+97+92+94}{8}=91.25[/tex]
|72 - 91.25| = 19.25
|82 - 91.25| = 9.25
|93 - 91.25| = 1.75
|98 - 91.25| = 6.75
|102 - 91.25| = 10.75
|97 - 91.25| = 5.75
|92 - 91.25| = 0.75
|94 - 91.25| = 2.75
Sum of absolute values = 57
[tex]\sf MAD=\dfrac{57}{8}=7.125[/tex]
Data set: 53 59 64 65 65 66 67 69
[tex]\sf Mean=\dfrac{53 +59+ 64+ 65+ 65+ 66+ 67+ 69}{8}=63.5[/tex]
|53 - 63.5| = 10.5
|59 - 63.5| = 4.5
|64 - 63.5| = 0.5
|65 - 63.5| = 1.5
|65 - 63.5| = 1.5
|66 - 63.5| = 2.5
|67 - 63.5| = 3.5
|69 - 63.5| = 5.5
Sum of absolute values = 30
[tex]\sf MAD=\dfrac{30}{8}=3.75[/tex]
find the cost of 72 books at 5.75
Answer: $414
Step-by-step explanation:
Total of books= 72
Cost of each book= $5.75
72(5.75)= $414
What is the image point of (5,-4)(5,−4) after a translation left 4 units and down 3 units?
Answer:
(1,-7)
Step-by-step explanation:
1) (5,-4). 4 units to the left will be (1,-4)
2) (1,-4). 3 units down will be (1,-7)
Which of the following equations is equivalent to S= xi?n?
On-S-xr2
S
Golf
S
On-$+$12
Answer:
umm to me its 2--%456
Step-by-step explanation:
Please answer someone!!!
Answer:
TrueStep-by-step explanation:
[tex]\sqrt{(xy)^3}[/tex] = [tex]((xy)^{1/2})^3[/tex] =[tex](xy)^{{1/2}*3}[/tex] =[tex](xy)^{3/2}[/tex]The answer is TRUE
True
Write 53 minutes to 4 hours as a ratio.
Answer:
The minutes wouldn't it be hours?
Step-by-step explanation:
Answer:
53:240
Step-by-step explanation:
Turn the hours into minutes since the minutes can't change to hours.
BRAINLIEST if correct
Answer: The area of rectangle U is 12.
Step-by-step explanation:
We can solve this by finding the ratio of the two rectangle lengths which are given. We see that the ratio is 2/1. Now, from here you have two options to go. The first option is dividing 48 / 8 which is 6. Now you divide 6 / 2, because 2 is the scale factor. 6 / 2 = 3. 4 * 3 = 12, giving us the area of 12. Another way to do it is since the scale factor is 2, the ratio of the areas are the scale factor squared. 48 / 2 ^ 2 = 48 / 4 = 12.
Can you help me worth 16 points if your help me all the way
Step-by-step explanation:
120=2/5t
120×5/2=t
t=600/2
t=300
hope it helps u
please help me.......
Answer:
Step-by-step explanation:
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
Let's use CAH 1st , on the Lenovo building, b/c we have they Hypotenuse (Hyp) and an angle and we want to know the other side of the Lenovo building
Cos(30) = x/294
294*Cos(30) = x
254.611 = x
Sin(30) = y / 294
294*Sin(30) = y
147 = y
perimeter = 147+254.611+294
perimeter Lenovo = 695.611 feet
For Asus building
hyp = sqrt [ ( 144.5*[tex]\sqrt{2}[/tex])^2 + 144.5*[tex]\sqrt{2}[/tex])^2 )]
hyp = 289
perimeter = 289+144.5*[tex]\sqrt{2}[/tex]+144.5*[tex]\sqrt{2}[/tex]
perimeter Asus = 697.7077
The difference of the two buildings is
697.7077 - 695.611 =2.09671 feet
the difference is 2.10 feet ( rounded to nearest 100th)
please dont answer if you are not 100% sure.
Make sure you answer both parts and be detailed in your explanation.
a) The equation 2x + 8 = 2(x+4) works for all values of x. Explain how you know.
b) The equation 3x +7 = 3(x+7) works for no values of x. Explain how you know.
Answer:
a) 2x + 8 = 2(x + 4) has infinite solutions because it simplifies down to x = x. Here is the work where this equation is solved.
2x + 8 = 2(x + 4)
2x + 8 = 2(x) + 2(4)
2x + 8 = 2x +8
2x + 8 - 8 = 2x + 8 -8
2x = 2x
2x/2 = 2x/2
x = x
So, because the equation ends in x = x, you can substitute any value for x and the equation will remain true.
----------------------------------------------------------------------------------------------------------------
b) 3x + 7 = 3(x + 7) has no solutions because it simplifies down to an untrue statement. The equation is simplified below.
3x + 7 = 3(x + 7)
3x + 7 = 3(x) + 3(7)
3x + 7 = 3x + 21
3x + 7 - 7 = 3x + 21 - 7
3x = 3x + 14
3x/3 = 3x/3 +14
x = x + 14
However, this is false. x cannot be equal to itself plus 14.
x ≠ x + 14
The simplification of this equation is untrue, so there is no solution to it.
----------------------------------------------------------------------------------------------------------------
I hope this is helpful :) Good luck
A stock brokerage has four computers that are used for making trades on the New York Stock Exchange. The probability that a computer fails on any single day is 0.005. Failures occur independently. Any failed computers are repaired after the exchange closes, so each day can be considered an independent trial. (a) What is the probability that all four computers fail on one day
Answer:
625/100,000,000 or 6.25 out of one million
Step-by-step explanation:
(0.005)^4 = .000000000625 = 625/100,000,000
The probability that all four computers fail on one day is =6.3*[tex]10^{-10}[/tex].
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
The probability that a computer fails on any single day is 0.005.
Let X denotes no. of computers fail on day
So, n = 4 , p = 0.05, q= 1-0.05=0.995
P (X = x) = [tex]^{n} C_x \;p^{x} \;q^{n-x}[/tex]
P (X = 4)
= [tex]^{4} C_4 \;(0.005)^{4} \;(0.995)^{4-4}[/tex]
=1* 0.00000000063*1
=0.00000000063
=6.3*[tex]10^{-10}[/tex]
Hence, the probability that all four computers fail on one day is
=6.3*[tex]10^{-10}[/tex].
Learn more about probability here:
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Daniel is constructing boxes in the shape of triangular prism. How much cardboard is needed to make each box
Answer:
Area of cardboard required = 468 cm²
Step-by-step explanation:
Area of the cardboard required = Surface area of the triangular prism
Surface area of the triangular prism = Area of the lateral sides + Area of the triangular sides
Area of the one triangular side = [tex]\frac{1}{2}(\text{Base)}(\text{Height})[/tex]
= [tex]\frac{1}{2}(12)(9)[/tex]
= 54 cm²
Area of lateral sides = Perimeter of the triangular base × Height
Perimeter of the triangular base = 9 + 12 + 15
= 36 cm
Now area of the lateral sides = (36) × 10
= 360 cm²
Surface area of the prism = 360 + 2(54)
= 360 + 108
= 468 cm²
Therefore, area of cardboard required for each box = 468 cm²
The standard gasoline engine for the 2017 Toyota Corolla includes the following data: Configuration: In-line four-stroke, four-cylinder engine Bore: 3.17 in Stroke: 3.48 in Compression ratio: 10.6:1 Assuming an ideal Otto cycle to describe this engine. Consider the working fluid to be air, modeled as an ideal gas with variable specific heat. Determine: (a) The total engine volume VBDC for all cylinders (cu.in). (b) The mass of air (lbm) contained in the engine assuming ambient conditions of 540 R and 14.7 psia. (c) The efficiency of the engine (%). The maximum temperature that occurs during the cycle is 3600 R.
Answer:
a) The total engine volume is 30.3265 in³
b) the mass of air contained in the engine is 0.00129 lbm
c) The efficiency of the engine is 55.6%
Step-by-step explanation:
Given the data in the question;
The configuration is in line with four-stroke, four-cylinder engine.
Bore ( d ) = 3.17 in
Stroke ( L ) = 3.48 in
compression ratio ( r ) = 10.6 : 1
First, we calculate the swept Volume V₁ = π/4 × d²L
we substitute
V₁ = π/4 × (3.17 )² × (3.48) = 27.4655 in³
Now, Compression Ration; r = Vs + Vc / Vc
r = (V₁ + V₂) / V₂
we substitute
10.6 = (27.4655 + V₂) / V₂
10.6V₂ = 27.4655 + V₂
10.6V₂ - V₂ = 27.4655
9.6V₂ = 27.4655
V₂ = 2.861 in³
So
a) total engine volume
[tex]V_{BDC[/tex] = V₁ + V₂
we substitute
[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³
[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³
[tex]V_{BDC[/tex] = 30.3265 in³
Therefore, The total engine volume is 30.3265 in³
b) The mass of air
given that; T = 540°R, P = 14.7 psia
we know that; PV = mRT { R is constant }
we solve for m
m = PV / RT
we substitute
m = (14.7 × 30.3265) / ( 0.3704 × 1728 )540
m = 445.79955 / 345627.648
m = 0.00129 lbm
Therefore, the mass of air contained in the engine is 0.00129 lbm
c) The efficiency
from table { properties of air}
At 540°R; u₁ = 92.04 BTu/lbm, u[tex]_r[/tex]₁ = 144.32
Now process 1 - 2 ( Isentropic ) u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂ = V₁/V₁ = r
so, u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂ = r
144.32 / u[tex]_r[/tex]₂ = 10.6
u[tex]_r[/tex]₂ = 144.32/10.6
u[tex]_r[/tex]₂ = 13.61
Thus, at u[tex]_r[/tex]₂ = 13.61, u₂ = 235 BTU/lbm, T₂ = 1340°R
Now, we know that;
P₁V₁/T₁ = P₂V₂/T₂ ⇒ (P₁/V₁)r = P₂/T₂
⇒ ( 14.7 / 540 )10.6 = P₂/1340
P₂ = 386.664 psia
process 2 - 3; constant volume heat addition;
Now, At T₃ = 3600°R, u₃ = 721.44 BTU/lbm, u[tex]_r[/tex]₃ = 0.6449
so, [tex]q_{in[/tex] = u₃ - u₂
we substitute
so, [tex]q_{in[/tex] = 721.44 - 235 = 486.44 BTU/lbm
Next, process 3 - 4; Isentropic
u[tex]_r[/tex]₄/u[tex]_r[/tex]₃ = V₄/V₃ = r
u[tex]_r[/tex]₄ / 0.6449 = 10.6
u[tex]_r[/tex]₄ = 6.8359
At u[tex]_r[/tex]₄ = 6.8359; u₄ = 308 BTU/lbm
∴
Heat Rejection [tex]q_{out[/tex] = u₄ - u₁ = 308 - 92.04 = 215.96 BTU/lbm
so, [tex]W_{net[/tex] = [tex]q_{in[/tex] - [tex]q_{out[/tex]
[tex]W_{net[/tex] = 486.44 - 215.96
[tex]W_{net[/tex] = 270.48 BTU/lbm
so the efficiency; η[tex]_{thermal[/tex] = ([tex]W_{net[/tex] / [tex]q_{in[/tex] ) × 100%
η[tex]_{thermal[/tex] = ( 270.48 / 486.44 ) × 100%
η[tex]_{thermal[/tex] = ( 0.55604 ) × 100%
η[tex]_{thermal[/tex] = 55.6%
Therefore, The efficiency of the engine is 55.6%
Step by step explanation!
Answer:
yhe picture is blur.
Step-by-step explanation:
Define the following terms using your own words. (2-3 sentences only)
1. Frequency
2 Class size
3. Ogive
4. Variance
5. Range
Answer:
Frequency: the rate at which something occurs over a particular period of time or in a given sample.Class size :Class size is the average number of students per class, calculated by dividing the number of students enrolled by the number of classes..O give :Ogive is the curve which is constructed by plotting cumulative frequency data on the graph paper, in the form of a smooth curve.Variance: The term variance refers to a statistical measurement of the spread between numbers in a data set. Range: The range, the difference between the largest value and the smallest value.consider this data set.
18, 11, 4, 9, 2, 3, 5
which box plot displays the data shown?
Answer:
d
Step-by-step explanation:
Answer:
its d
Step-by-step explanation:
need help.
The scatter plot and line of best fit below show the length of 9 people's femur (the long leg bone in the thigh) and their height in centimeters. What is the meaning of the xx-value on the line when y=160y=160?
Answer:
c
Step-by-step explanation:
The true statement is (d) The expected height of 160 cm when the femur length has a length of 42.5 cm
How to interpret the scatter plot?From the given figure, we have:
x values represents the femur length in centimetersy values represents the height in centimetersSo, when the y value is 160, the x value is:
The expected height of 160 cm when the femur length has a length of 42.5 cm
Hence, the true statement is (d)
Read more about scatter plots at:
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4^?=1024? i know the answer is 5 but is there an easier way to find that out instead of guessing?
Answer:
here you go............
Step-by-step explanation:
I hope it helped
Please look at the images below. (I will mark you as Brainliest if you are correct!)
Answer:
ima say its a that is my lucky guess im sorry if you get it wrong
i need help with these problems, thanks
1. C
2. A
3. B
Hope This Helped!
(Brainliest will be appreciated)
Answer:
1- distributive property
2- Subtraction.
3- -3/2
Step-by-step explanation:
1- When the given equation is given, the 4 outside the parenthesis multiplied with the variable x and number 1. This process of multiplication between a number and all the variables in parenthesis is called known as the distributive property.
2- As it was adding with 2x on the left side when it passed with Inverse Operation to the right side, its sign change to subtraction.
3- The 2 passes to the other side of the equation with Inverse Operation, therefore dividing. The -3, otherwise, as it didn't move to the other side, has no effect and remains the negative.
How many faces does a triangular pyramid have?
A. 3
B. 6
C. 4
D. 5
[tex]\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}[/tex]
C. 4.
thanks hope it helpsPls help i'll give brainlest
Answer: B. 183 cm^3
V = pi r^2 h/3
V = pi (5^2) (7/3)
V = pi (25) (2.33)
V = 183
Answer:
B.183 [tex]cm^{3}[/tex]
Step-by-step explanation:
Volume of cone is [tex]V=\pi r^{2} \frac{h}{3}[/tex]
where h=7 and r=5 (because r=d/2, where d=10)
V=[tex]5^{2}\frac{7}{3}\pi[/tex]
V=25·[tex]\frac{7}{3} \pi[/tex]
V=175/3[tex]\pi[/tex]
V=183.2595715 or 183 [tex]cm^{3}[/tex]
Please Help! (picture)
Step-by-step explanation:
f(g(x))
f(x-1)
(x-1)^2
x^2 -2x + 1
Pre-Test
Active
1
2
3
4
10
The quotient of (x4 + 5x - 3x – 15) and a polynomial is (x3 - 3). What is the polynomial?
x? + 5x6 - 6x4 - 30x3 + 9x + 45
x-5
x + 5
x7 + 5x + 6x4 + 30x3 + 9x + 45
Answer:
x5
Step-by-step explanation:
Answer: C.
Step-by-step explanation:
EDGE 2023
Suppose that there is a black urn containing nine black balls and three yellow balls and there is a yellow urn containing six black balls and six yellow balls. An experiment consists of selecting at random a ball from the black urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball.
1. Construct a tree diagram showing the probabilities associated with this problem. Write a probability on each branch (6 branches). Multiply the the probabilities along each path and write that number at the end of the path (4 answers).
2. Find the probability that the second ball is yellow.
Answer:
See Annex ( Tree diagram )
Step-by-step explanation:
1) Attached
2) Probability of the second ball is yellow is
P(2nd ball is yellow ) = Probability 2nd ball s yellow (if the first one was black) + Probability 2nd ball s yellow (if the first one was Yellow)
P(2nd ball is yellow ) = 0,204 + 0,045
P(2nd ball is yellow ) = 0,249
What is the equation of this line?
Y=3x
Y=3
Y=-3
X=3
An agricultural scientist collected data to study the relationship between the amount of nitrogen added to a cornfield and the number of
bushels of corn produced. This is the regression line of the data, where y is measured in bushels of corn and x is measured in pounds of
nitrogen.
y = 0.43x + 28.5
What is the meaning of the slope of the regression line?
O A. For every 0.43 pounds of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.
OB. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.
-
OC. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.
OD. For every 28.5 pounds of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.
Answer:
D.
Step-by-step explanation:
just done the assignment
Linear regression line is a algebraic model to show the relationship between the two models by putting the value of the one variable to get the value of other.. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels. Therefore the option B is the correct option.
Given information-The equation of the experiment to know the relationship between the amount of nitrogen added to a cornfield and the number of bushels of corn produced is,
[tex]y=0.43x+28.5[/tex]
Linear regression lineLinear regression line is a algebraic model to show the relationship between the two models by putting the value of the one variable to get the value of other.
Linear regression line can be represent as,
[tex]y=Ax+B[/tex]
Here x is the explanatory variable and y is the dependent variable. A is the slope of the line and B is the intercept.
In the given equation there are two variable given.
Variable x represent the amount of nitrogen added, and the variable y, represents the number of bushels of corn produced.
As putting the value of x the y increases with value of number 0.43. Thus as we are increasing the value of the nitrogen with unit 1 the number of bushels of corn produced is increased by unit 0.43.
Hence for every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels. Therefore the option B is the correct option.
Learn more about the linear regression here;
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Can someone please help me I will mark u brilliant
Answer:
The answer is 7/20 miles.
Step-by-step explanation:
Just multiply 7/6 x 2/5, then you have the answer
Use the picture below and determine which of the lines or line segments 20 points
is/are a diameter
mA
VE
Line m
Line Segment BC
Ο Ο Ο Ο Ο
Line Sesnent AB or AC
Line Segment DE
Line 1
Part B.
What is the volume of each cubic block?
Answer:
1 / 36 ft³
Step-by-step explanation:
Length = 1/2 ft
Width = 1/6 ft
Height = 1/3 ft
The volume of the tank can be obtained using the relation :
Volume = Length * width * height
Volume = (1/2 * 1/6 * 1/3) ft³
Volume = 1 / 36 ft³
Which of the following represents a geometric sequence?
I 1/4,1/4,1/4,1/4
II 1/4,1/5,1/6,1/7
III 1/4,1,-4,16
IV 1/4,-4,1/4,-4
OOOO
A. I
B. II
C. III
D. IV
Next
Save and Exit
Answer:
A. I
Step-by-step explanation:
The other person is wrong and I took the test
