Answer:
option (c) 475
Step-by-step explanation:
let the automobile installment credit be 'C'
Given:.
Automobile installment credit accounted for 36 percent of all outstanding consumer installment credit
Now,
57 billion is [tex]\frac{1}{3}[/tex] of automobile installment credit
or
57 billion = [tex]\frac{1}{3}[/tex] × C
or
C = 57 × 3
or
C = 171 billion
now,
installment credit accounted = 36% of all outstanding consumer installment credit
or
171 billion = 0.36 × all outstanding consumer installment credit
or
All outstanding consumer installment credit = $475 billion
Hence, the correct answer is option (c) 475
Two persons are to run a race, but one can run 10 meters per second, whereas the other can run 4 meters per second. If the slower runner has a 75-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?
Answer:12.5 seconds
Step-by-step explanation:hconsidering Runner 1 with a speed of 10m/s
and Runner 2 with a speed of 4 m/s
the equation of displacement for a uniform movement is
x=V*t
so x1=V1*t
and x2=V2*t
and the problem condition is x2=x1+75m
so we proceed to solve the equations.
from equation 2 t=x2/V2
substituting in equation 1 we have
x1=V1(x2/V2) and then the 3 equation
x1=V1((x1+75m)/v2
finally x1=75*(V1/(V2-V1)) =75*(10/(10-4))=125m
then t=(x1/v1)=125/10=12.5 seconds
Answer:
12.5 seconds
Step-by-step explanation:
Speed of the first person = 10 meter per second
Speed of the second person = 4 meter per second
Relative velocity of faster person = 10 - 4 = 6 meter per second
since distance between both the person is = 75 meter.
Therefore, time to cover this distance by faster person = [tex]\frac{Distance}{Speed}[/tex]
[tex]\frac{75}{6}[/tex]
= 12.5 seconds.
Faster runner catches the slower runner after 12.5 seconds.
The city of Madison regularly checks the quality of water at swimming beaches located on area lakes. Fifteen times the concentration of fecal coliforms, in number of colony forming units (CFU) per 100ml of water, was measured during the summer at one beach. 180 1600 90 140 50 260 400 90 380 110 10 60 20 340 80. What is the sample standard deviation?
Answer:
The sample standard deviation is 393.99
Step-by-step explanation:
The standard deviation of a sample can be calculated using the following formula:
[tex]s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex]
Where:
[tex]s=[/tex] Sample standart deviation
[tex]N=[/tex] Number of observations in the sample
[tex]{\displaystyle \textstyle {\bar {x}}}=[/tex] Mean value of the sample
and [tex]\sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex] simbolizes the addition of the square of the difference between each observation and the mean value of the sample.
Let's start calculating the mean value:
[tex]\bar {x}=\frac{1}{N} \sum_{i=1}^{N}x_{i}[/tex]
[tex]\bar {x}=\frac{1}{15}*(180+1600+90+140+50+260+400+90+380+110+10+60+20+340+80)[/tex]
[tex]\bar {x}=\frac{1}{15}*(3810)[/tex]
[tex]\bar {x}=254[/tex]
Now, let's calculate the summation:
[tex]\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=(180-254)^2+(1600-254)^2+(90-254)^2+...+(80-254)^2[/tex]
[tex]\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=2173160[/tex]
So, now we can calculate the standart deviation:
[tex]s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex]
[tex]s=\sqrt[ ]{\frac{1}{15-1}*(2173160)}[/tex]
[tex]s=\sqrt[ ]{\frac{2173160}{14}}[/tex]
[tex]s=393.99[/tex]
The sample standard deviation is 393.99
To find the sample standard deviation, use the formula standard deviation = √[ Σ(x - μ)² / (n - 1) ]. Follow the steps: find the mean of the data set, subtract the mean from each value and square the result, add all the squared deviations together, divide by (n - 1), and finally, take the square root of the result.
Explanation:To find the sample standard deviation, you can use the formula:
standard deviation = √[ Σ(x - μ)² / (n - 1) ]
where Σ represents the sum of the values, x is each value in the data set, μ is the mean of the data set, and n is the number of values in the data set.
Step 1: Find the mean of the data set. Add all the values together and divide by the number of values (15 in this case). This gives you a mean of 179.3333.
Step 2: Subtract the mean from each individual value in the data set, square the result, and add all the squared values together. This gives you a sum of squared deviations of 977733.3333.
Step 3: Divide the sum of squared deviations by (n - 1), where n is the number of values in the data set. Since there are 15 values, you divide by 14 to get 69838.0952.
Step 4: Take the square root of the result from Step 3. This gives you a sample standard deviation of approximately 264.1046.
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Plzzzzz help me quickly! 20 points to whoever gets correct and I will award brainiest! A lawn service company uses the function f(x) = 2.5x + 25 to determine the cost for x hours of service. What does the constant term in the equation represent?
A. the total number of hours of lawn service provided
B. the initial fee the company charges before providing lawn service
C. the total cost for the lawn service
D. the cost per hour of lawn service
Answer:
c
Step-by-step explanation:
it is the total cost for the lawn servic3
Answer:
B
Step-by-step explanation:
f(x)= the total of the equation
The constant term is the $25 which is what they charge along with the hours determined by x
On the coordinate grid, your campsite is located at (-1,3) and the next checkpoint station is located at (3,-3). Each unit in the coordinate plane represents 1.4 miles. Find the distance you have to hike to reach the next checkpoint station
Answer:
The answer to your question is: 10. 1 miles
Step-by-step explanation:
data
P = (-1, 3)
Q = (3, -3)
Formula
d = √((x2-x1)² + (y2-y1)²)
d = √)(3- -1)² + (-3-3))
d = √ (4² + -6²)
d = √ (16 + 36)
d = √ 52
d = 7.21 units
but
1 units ----------------------- 1.4 miles
7.21 units --------------------- x
x = 7.21 x 1.4/1 = 10.1 miles
A researcher wondered whether drivers treat bicycle riders differently when they wear helmets. He rigged his bicycle with an ultrasonic sensor that could measure how close each car was that passed him. He then rode on alternating days with and without a helmet. Of the 30003000 times that a car passed him, he found that when he wore his helmet, motorists passed 3.273.27 inches closer to him, on average, than when his head was bare. What is the WhoWho in this study? That is, identify the cases under study.
A. The bike riders
B. Each instance of a car passing a rider
C. Bike helmets
D. The cars
Answer:
In this case study we have following groups:
1. Population: It had all the cars which passed the bicyclist. Out of which 3000 cars were taken.
2. Who: Each instance of a car passing a rider, means the drivers passing by.
That is the 3000 cars which passed the researcher on his bicycle.
3. What: The distance at which cars pass the bicycle rider. The distance the drivers stayed away from his bike.
The subject of this question is the cars in the study.
Explanation:The Who in this study refers to the cases under study. In this case, the cases under study are the cars. The researcher rigged his bicycle with an ultrasonic sensor to measure how close each car was that passed him, and he observed that when he wore a helmet, motorists passed closer to him compared to when his head was bare. Therefore, the cars are the subject of this study.
I need help asap! for a few questions of mine!
Find the slope of the line that passes through the following points. Simplify your answer.
(−6,9) and (−3,1)
[tex]\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-6)}}}\implies \cfrac{-8}{-3+6}\implies -\cfrac{8}{3}[/tex]
solve the system of equations y=3x.
y=x^2-4
Answer:
(x, y) = (-1, -3) or (4, 12)
Step-by-step explanation:
A graphing calculator can show the solutions to this system.
__
You can equate expressions for y and solve for x.
3x = x^2 -4
x^2 -3x = 4 . . . . add 4-3x
x^2 -3x +2.25 = 6.25 . . . . complete the square by adding (-3/2)^2 where -3 is the coefficient of x.
(x -1.5)^2 = 2.5^2 . . . . . . rewrite as squares
x -1.5 = ±2.5 . . . . . . . . . . take the square root
x = 1.5 ± 2.5 = -1, +4
y = 3x = -3, +12, respectively
Solutions are ...
(x, y) = (-1, -3) . . . . and . . . . (4, 12)
Please match this proof
Answer:
A, B, C, D, E
Step-by-step explanation:
AB ≅ AC and AD bisects ∠A
This is given information from the diagram and the statement.
∠BAD ≅ ∠CAD
This is from the definition of angle bisector.
AD ≅ AD
This is reflective property of congruence.
ΔABD ≅ ΔACD
From the previous three statements, side-angle-side congruence tells us the triangles are congruent.
∠B ≅ ∠C
Corresponding parts of congruent triangles are congruent.
Answer:
A.
B.
C.
D.
E.
refer to the attachment
A rock is thrown at a window that is located 18.0 m above the ground. The rock is thrown at an angle of 40.0° above horizontal. The rock is thrown from a height of 2.00 m above the ground with a speed of 30.0 m/s and experiences no appreciable air resistance. If the rock strikes the window on its upward trajectory, from what horizontal distance from the window was it released?
Answer:
27.32 m
Step-by-step explanation:
We are given that
Height of window from the ground=18 m
Height of rock form the ground=2 m
Speed of thrown rock=30 m/s
We have to find the horizontal distance from the window from which rock was release.
Difference between window and rock=18-2=16 m
Initial vertical velocity component=[tex]30sin40^{\circ}=19.28 [/tex]m/s
Initial horizontal velocity component=[tex]30cos 40^{\circ}=22.98 m/s[/tex]
If the rock is reached to maximum height
Then, maximum height=[tex]\frac{v^2}{2g}=\frac{(19.28)^2}{2\times 9.8}=18.9731 m[/tex]
Time taken by rock to reach maximum height=[tex]\frac{v}{g}=\frac{19.28}{9.8}=1.96775 s[/tex]
Distance between window and maximum height at which rock reached=18.9731-16=2.973 m
Time to drop 2.973 m=[tex]\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\cdot 2.973}{9.8}}=0.77893 s[/tex]
Time to be at 16 m=1.96775-0.77893=1.189 s
Horizontal distance=[tex]1.189\times 22.98=27.32 m[/tex]
Hence, horizontal distance of rock from the window from which rock was released=27.32 m
The rock was released approximately 71.1 meters horizontally from the window. This calculation is based on the rock's initial speed of 30.0 m/s, launch angle of 40.0°, and the fact that it struck the window on its upward trajectory with no air resistance.
To solve this problem, we can use the kinematic equations of motion. We need to find the horizontal distance the rock was released from the window.
1. First, we can find the time it takes for the rock to reach its maximum height. We can use the following kinematic equation:
[tex]\[v_y = u_y + at\][/tex]
Where:
- [tex]\(v_y\)[/tex] is the final vertical velocity (0 m/s at the maximum height),
- [tex]\(u_y\)[/tex] is the initial vertical velocity (30.0 m/s, since it's thrown vertically),
- \(a\) is the vertical acceleration due to gravity (-9.81 m/s²),
- \(t\) is the time.
Rearrange the equation to solve for t:
[tex]\[0 = 30 - 9.81t\]\\\\[/tex]
[tex]\[t = \frac{30}{9.81} \approx 3.06 \, \text{s}\][/tex]
2. Now, we can find the horizontal distance using the horizontal motion equation:
[tex]\[d_x = u_x \cdot t\][/tex]
Where:
- [tex]\(d_x\)[/tex] is the horizontal distance we want to find.
- [tex]\(u_x\)[/tex] is the horizontal component of the initial velocity
[tex](30.0 m/s * cos(40°)).[/tex]
- \(t\) is the time calculated in step 1.
Plug in the values:
[tex]\[d_x = (30 \cdot \cos(40°)) \cdot 3.06 \approx 71.1 \, \text{m}\][/tex]
So, the rock was released approximately 71.1 meters horizontally from the window.
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Bob and James are finishing the roof of a house. Working alone, Bob can shingle the roof in 14 hours. James can shingle the same roof in 18 hours. How long will it take them working together to shingle the roof? Round your answer to the nearest hundredth if necessary.
Please show work!
we know that Bob can do the whole job in 14 hours, how much of the work has he done in 1 hour only? well since he can do the whole lot in 14 hours in 1 hour he has only done 1/14 th of the job.
we know that James can do it in 18 hours, a bit slower, so in 1 hour he has done only 1/18 th of the job.
let's say it takes both of them working together say "t" hours, so in 1 hour Bob has done (1/14) of the work whilst James has done (1/18) of the work, the whole work being t/t or 1 whole, so for just one hour that'd 1/t done by both Bob and James.
[tex]\bf \stackrel{Bob}{\cfrac{1}{14}}~~+~~\stackrel{James}{\cfrac{1}{18}}~~=~~\stackrel{total~for~1~hour}{\cfrac{1}{t}} \\\\\\ \stackrel{\textit{using an LCD of 126}}{\cfrac{9+7}{126}=\cfrac{1}{t}}\implies \cfrac{16}{126}=\cfrac{1}{t}\implies 16t=126\implies t=\cfrac{126}{16} \\\\\\ \stackrel{\textit{7 hrs, 52 minutes and 30 seconds}}{t=\cfrac{63}{8}\implies t=7\frac{7}{8}}\implies \stackrel{\textit{rounded up}}{t=7.88}[/tex]
In the continental United States the ratio of states that border an ocean to strays that don't border an ocean is 7:9. How many of the states border an ocean
How to find the probability? Please show your work! Thanks!
Total shoppers 255.
Number of shoppers who did not shop at the store = 20+70 = 90
Probability = 90/255 = 0.353
Penny had a bag of marbles she gave 1/3 of them to Rebecca and 1/4 of the remaining marbles to John Penny then had 24 marbles left in the bag how many marbles the penny start with
Answer:
38
Step-by-step explanation:
1/3+1/4=7/12
7/12*24=12
24+12=26
The sun is an excellent source of electrical energy. A field of solar panels yields 16.22 watts per square feet. DETERMINE tha amount of electricity produced by a field of solar panels that is 305 feet by 620 feet
Answer: 11,658.45
Step-by-step explanation:
First multiply 305 x 620 to determine the square footage
divide that answer by 16.22 to get your answer
The required amount of electricity produced by a field of solar panels which is 305 feet by 620 feet, is 3,067,202 watt.
Given that,
A field of solar panels yields 16.22 watts per square foot.
T0 determines the amount of electricity produced by a field of solar panels that is 305 feet by 620 feet.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
A field of solar panels yields 16.22 watts per square foot.
The amount of electricity produced by a field of solar panels is 305 feet by 620 feet,
= 16.22 * 305 * 620
= 3,067,202 watt,
Thus the required amount of electricity produced by a field of solar panels that is 305 feet by 620 feet, is 3,067,202 watt.
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Can I get some help? How to find the indicated probability? Please explain or show your work. Thanks!
Answer:
the easyiest way for me to explain why the answer is A 0.077
Step-by-step explanation:
first add all your numbers it comes up to 1112 then youre going to take that number and put it aside then you dived 86 (the total for anyone at least 31+) and it gices you 0.077
The volume of an open-top rectangular box is 4500 cc (cubic centimeters). The length of the rectangular base of the box is twice the width. What height will make the surface area as small as possible?
Answer:
The height that make the surface area as small as possible is 10 cm
Step-by-step explanation:
Let
L -----> the length of the base of the box
W -----> the width of the base of the box
H ----> the height of the box
we know that
The volume of the box is equal to
[tex]V=LWH[/tex]
we have
[tex]V=4,500\ cm^3[/tex]
so
[tex]4,500=LWH[/tex] ----> equation A
[tex]L=2W[/tex] ------> equation B
substitute equation B in equation A
[tex]4,500=(2W)WH[/tex]
[tex]4,500=2W^2H[/tex]
Solve for H
[tex]H=\frac{2,250}{W^{2}}[/tex] -----> equation C
The surface area of a open box is equal to
[tex]SA=2(L+W)H+LW[/tex] ----> equation D
Substitute equation B and equation C in equation D
[tex]SA=2(2W+W)(\frac{2,250}{W^{2}})+(2W)W[/tex]
[tex]SA=6W(\frac{2,250}{W^{2}})+2W^2[/tex]
[tex]SA=6(\frac{2,250}{W})+2W^2[/tex]
[tex]SA=\frac{13,500}{W}+2W^2[/tex]
Convert to function notation
[tex]f(W)=\frac{13,500}{W}+2W^2[/tex]
Find the derivative
[tex]f'(W)=-\frac{13,500}{W^2}+4W[/tex]
set equal to zero
[tex]f'(W)=0[/tex]
[tex]0=-\frac{13,500}{W^2}+4W[/tex]
Solve for W
[tex]\frac{13,500}{W^2}=4W[/tex]
[tex]W^3=\frac{13,500}{4}[/tex]
[tex]W=15\ cm[/tex]
Find the value of L (equation B)
[tex]L=2(15)=30\ cm[/tex]
Find the value of H (equation C)
[tex]H=\frac{2,250}{15^{2}}=10\ cm[/tex]
therefore
The height that make the surface area as small as possible is 10 cm
Please please help me out...................
Answer:
y = [tex]\frac{1}{2}[/tex] x + 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (4, 3)
m= [tex]\frac{3-1}{4-0}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
Note the line crosses the y- axis at (0, 1) ⇒ c = 1
y = [tex]\frac{1}{2}[/tex] x + 1 ← equation of line
Robert has 96 balloons and 72 pieces of candy to make gift bags for his party. How many gift bags can he make if he wants to use all of the balloons and all of the candy?
Answer:
24
Step-by-step explanation:
The greatest common divisor of 72 and 96 is 24. Robert can make any number of bags that is a divisor of 24. If he wants to make the largest number possible, then he can make 24 bags with 4 balloons and 3 pieces of candy in each one.
__
72 = 2³·3²
96 = 2⁵·3
The greatest common divisor is the product of the common factors: 2³·3 = 24.
A ladder is leaning against a building. The ladder is 10m long and it is sitting on
the ground 4m out from the building. What is the angle that the ladder makes with
the ground?
Check the picture below.
make sure your calculator is in Degree mode.
The angle that the ladder makes with the ground would be 66.42 degrees.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We are given that ladder is leaning against a building. The ladder is 10m long and it is sitting on the ground 4m out from the building.
The side adjacent to the angle is given, and the hypotenuse of the triangle is the unknown.
The cosine relation applies
Cos = Adjacent/Hypotenuse
We are given the hypotenuse = ladder length
Cos (∅)= (4 )/10
Cos (∅)≈ 2/5
(∅)≈ [tex]Cos^{-1}[/tex]2/5
(∅) = 66.42
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Your friend said that there are exactly 12 different pairs of numbers with a difference of 12 and that he had found them all. How would you respond to him?
Answer:
See explanation
Step-by-step explanation:
I wouls say to my friend that he is incorrect, because there are infinitely many pairs of numbers with a difference of 12.
For example,
[tex]13-1=12\\ 14-2=12\\15-3=12\\16-4=12\\...[/tex]
Here we can increase the first and the second number by 1 and get their difference equal to 12 after this operation.
The same is possible with negative numbers:
[tex]-1-(-13)=12\\ -2-(-14)=12\\-3-(-15)=12\\ ...[/tex]
Actuall, we can do this with decimals too
[tex]12.5-0.5=12\\ \\13.4-1.4=12\\ \\12\dfrac{1}{8}-\dfrac{1}{8}=12\\...[/tex]
Such pairs of numbers are infinitely many (because there are infinitely many real numbers) and we cannot find all possible numbers with difference of 12.
Robert stands atop a 1,380-foot hill. He climbs down, reaching the bottom of the hill in 30 minutes. What is Robert’s average rate of elevation change in feet per minute?
A.
+460
B.
+46
C.
-46
or
D.
-460
Answer:
-46 feet/min
Step-by-step explanation:
Initial elevation = 1,380 ft
Final Elevation = 0 feet
Change in elevation
= Final elevation - Initial Elevation
= 0 - 1,380
= - 1,380 feet
Given that the journey took 30 min,
rate of descent = Change in elevation / time
= -1,380 / 30
= - 46 feet/min
A plumber earns $50 for a repair job, plus an additional $75 per hour he works. On Tuesday, he completed 3 repair jobs and earned a total of more than $600.
Part A Write an inequality that can be used to determine h, the number of hours the plumber worked Tuesday
Part B: Solve your inequality to determine the number of hours the plumber worked Tuesday. Provide mathematical justification for your answer.
Answer:
A. [tex]150+75h>600[/tex]
B. More than 6 hours
Step-by-step explanation:
A plumber earns $50 for a repair job, so he will earn $150 for three repair jobs.
Let h be the number of hours the plumber worked on Tuesday. He earns $75 per hour worked, so he will earn $75h in h hours.
In total, the plumber earned $(150 + 75h)
A. On Tuesday, he completed 3 repair jobs and earned a total of more than $600. Thus
[tex]150+75h>600[/tex]
B. Solve this inequality. Subtract 150:
[tex]150+75h-150>600-150\\ \\75h>450[/tex]
Divide by 75:
[tex]h>\dfrac{450}{75}\\ \\h>6[/tex]
This means, the plumber worked more than 6 hours.
A lion is running 75 feet per second and is 108 feet behind a wildebeest that is running at 66 feet per second. A lion can only maintain this speed for a very short period. How many seconds will it take lion to catch up to the wildebeest?
Answer:
12 seconds
Step-by-step explanation:
75 t=66t+108
75t-66t=108
9t=108
t=108/9=12
Answer:
The answer to your question is: 12 seconds
Step-by-step explanation:
Lion v = 75 ft/s
wildebeest = 66 ft/s and is 108 feet behind the lion
t = time = ?
Formula
v = d/ t solve for d d = vt
Process
lion d = 75t
wildebeest = d = 108 + 66t
Now
75t = 108 + 66t
solve for t 75t - 66t = 108
9t = 108
t = 12 s
A football team gains 2 yards on the first play,loses 5 yards on the second play, loses 3 yards on the third play , and gains 4 yards on the fourth play. What is the teams overall gain or loss for all four plays show work
Answer:
2 yard loss
Step-by-step explanation:
When the team gains yards we use a positive value, and when the team loses yards we use a negative value. So the operation would be 2 -5 -3 +4 = -2, this means that the team had a 2 yard loss.
What is the value of 5 in 5,476,807,139
The value of 5 in 5,476,807,139 is five billion, as it is positioned in the billions place. This is explained by the concept of place value.
Explanation:The value of 5 in the number 5,476,807,139 refers to its place value in the numerical system. In this case, the 5 is in the billions place. This means that, in terms of place value, that 5 actually represents [5 × 1,000,000,000], which is 5,000,000,000 or five billion. The concept of place value is important in mathematics, it tells you how much each digit in a number is worth according to its position.
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Paula knits hats. The number of hats h she can knit varies directly with the amount of yarn (y) in yards she has. The constant of proportionality is 42. H = 42y. What does the constant of proportionality, 42, represent in this problem?
- answer correctly
Answer:
42 = the number of hats Paula can knit from one yard of yarn
Step-by-step explanation:
The way this problem is written, the constant 42 is the multiplier of yards to get hats. That is, it has units of hats per yard, so represents the number of hats that can be knit from 1 yard of yarn.
_____
Comment on the problem
It seems more likely that the proportion should be written as ...
y = 42h
or
h = y/42
Then the constant would be the number of yards of yarn required for each hat.
My statistics book says there are 8 degrees of freedom for this data set. I don't understand how they got that number. # of Books Education Level 68 11 345 15 276 16 756 12 43 6 546 14 58 6 187 14 286 9 93 8 376 11 623 18 876 12 28 4 289 15
Answer:
It's a bit unclear with the table this way, but I count fifteen points, fifteen lines of the table, each a pair of numbers.
That's 15 degrees of freedom in the data. When modeling, each parameter in the model uses up one degree of freedom, so you'd use a smaller number of degrees of freedom when calculating t statistics, etc.
Describe the line segments. the cut sides of a wedge of apple pie: a) parallel b) intersecting c) skew
Answer:
They are intersecting line segments ⇒ answer b
Step-by-step explanation:
* Lets explain the types of the lines
- Parallel lines lie in the same plane and never intersect each other
- Intersecting lines are lines that meet each other in exactly one point
- Skew lines are lines that are in different planes and never intersect
* Now lets solve the problem
- The line segments that cut sides of a wedge of apple pie
∵ The wage of apple pie could represent a plane
∵ The line segments cut the sides of the wedge
∴ The lines are in the same plane
∵ Skew lines are in different planes and never intersect
∴ The lines can not be skew
∵ The line segments that cut sides of the wage must be intersected
at exactly one point
∵ Parallel lines never intersected
∴ The lines can not be parallel lines
∴ They are intersecting line segments
Connie and ron walked to a dock at 2 miles per hour, jumped in a boat and motired to dillons at 7 miles per hour. If the total distance was 14 miles and the trip took 3.25 hours in all, how far did they travel by boat?
Answer:
10.5 miles
Step-by-step explanation:
Let b represent the distance traveled by boat. The relation between speed, distance, and time is ...
time = distance / speed
We are told the total time and the total distance so we have ...
b/7 + (14-b)/2 = 3.25
2b +7·14 -7·b = 14·3.25 . . . multiply by 14
3.75·14 = 5b . . . . . . . . . . . .add 5b-14·3.25
b = 10.5 . . . . . . . . . . . . . . . divide by 5
They traveled 10.5 miles by boat.
_____
Check
10.5/7 +3.5/2 = 1.5 +1.75 = 3.25 . . . . the answer checks OK
They spent 1.75 hours walking 3.5 miles to the dock and 1.5 hours traveling 10.5 miles by boat.
What is the equation of a line that contains the point (4, 0) and is parallel to x + y = 2?
Answer:
x + y = 4 or y = -x + 4
Step-by-step explanation:
0 = -1[4] + b
4 = b
y = -x + 4
If you want it in Standard Form:
y = -x + 4
+x +x
_________
x + y = 4 >> Line in Standard Form
* Since the rate of change [slope] is -1 and that parallel lines have SIMILAR SLOPES, -1 remains the same.
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