Answer:
Circle
Step-by-step explanation:
r = 2 cos θ
Multiply both sides by r.
r² = 2r cos θ
Convert to rectangular.
x² + y² = 2x
x² − 2x + y² = 0
Complete the square.
x² − 2x + 1 + y² = 1
(x − 1)² + y² = 1
This is a circle with center (1, 0) and radius 1.
The given function r = 2 cos θ is a circle with a center (1, 0) and radius of 1.
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
Given function is r = 2 cos θ
Now, Multiply both sides by r.
r² = 2r cos θ
Convert to rectangular form;
x² + y² = 2x
x² − 2x + y² = 0
Using Complete the square.
x² − 2x + 1 + y² = 1
(x − 1)² + y² = 1
Hence, This is a circle with a center (1, 0) and radius of 1.
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J.D. Power and Associates conducts vehicle quality surveys to provide automobile manufacturers with consumer satisfaction information about their products (Vehicle Quality Survey, January 2010 ). Using a sample of vehicle owners from recent vehicle purchase records, the survey asks the owners a variety of questions about their new vehicles, such as those shown below. For each question, state whether the data collected are categorical or quantitative and indicate the measurement scale being used.
a. What price did you pay for the vehicle?
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
d. What is the current mileage?
e. What is your overall rating of your new vehicle? A 110 -point scale, ranging from I for
unacceptable to 10 for truly exceptional, was used.
Answer:
Categorical data includes
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
e. What is your overall rating of your new vehicle? A 1 to 10 point scale, ranging from I for unacceptable to 10 for truly exceptional, was used.
Quantitative data includes
a. What price did you pay for the vehicle?
d. What is the current mileage?
Step-by-step explanation:
Categorical data refers to the kind of data in which the variables are grouped based on a particular quality, ticking a particular box or satisfying some specific requirements.
It uses one or more qualitative property/properties to assign variables into a limited, usually fixed groups or categories. Note that the qualitative property might be a grouped data of numerical values. As long as there are easily separable and recognizable groups, it is categorical data.
This is also called qualitative data.
Quantitative data is a data that is strictly about numerical values. A dataset that consists of numerical values of the members of the dataset. Deals almost exclusively with numbers, usually ungrouped.
So, examining the given datasets one at a time
a. What price did you pay for the vehicle?
The answer to this question is a numerical value and for various customers, it builds up a dataset of strictly numerical values. Hence, this resulting data is a quantitative data.
b. How did you pay for the vehicle? (Cash, Lease, or Finance)
The answers to this question can only take 3 forms; Cash, Lease or Finance, indicating that all the variables in the dataset can only take on limited, fixed number of groups/categories. Hence, this dataset is a categorical data.
c. How likely would you be to recommend this vehicle to a friend? (Definitely Not, Probably Not, Probably Will, and Definitely Will)
The answers to this question too can take on 4 limited, fixed categories or groups, Hence, it's easy to see that this dataset is also categorical data.
d. What is the current mileage?
The answer to this question is a numerical value. Various answers from numerous persons would lead to a data of numbers. Hence, this is a quantitative data.
e. What is your overall rating of your new vehicle? A 1 to 10 point scale, ranging from I for unacceptable to 10 for truly exceptional, was used.
Limited, fixed categories or groups (10 groups) are also available for this data, hence, it is easily a categorical data.
Hope this Helps!!!
COMPUTE:
A) 40−5÷ 1/5 =
B) (4.8−1.8÷6)÷5=
Answer:
A) 15
B) 0.9
Step-by-step explanation:
Use the correct order of operations.
A) 40 − 5 ÷ 1/5 =
= 40 − 5 * 5
= 40 - 25
= 15
B) (4.8 − 1.8 ÷ 6) ÷ 5 =
= (4.8 − 0.3) ÷ 5
= 4.5 ÷ 5
= 0.9
You are given the following data, where X1 (final percentage in history class) and X2 (number of absences) are used to predict Y (standardized history test score in third grade):
Y X1 X2
465 92 2
415 95 2
345 70 3
410 72 3
370 75 4
400 82 0
390 80 1
480 98 0
420 80 2
485 99 0
485 92 6
375 92 6
310 61 5
Determine the following multiple regression values.
Report intercept and slopes for regression equation accurate to 3 decimal places
Intercept: a =
Partial slope X1: b1 =
Partial slope X2: b2 =
Report sum of squares accurate to 3 decimal places:
SSreg = SS
Total =
Test the significance of the overall regression model (report F-ratio accurate to 3 decimal places and P-value accurate to 4 decimal places):
F-ratio =
P-value =
Report the variance of the residuals accurate to 3 decimal places.
Report the results for the hypothesis test for the significance of the partial slope for number of absences
Answer:
Step-by-step explanation:
Hello!
Given the variables
Y: standardized history test score in third grade.
X₁: final percentage in history class.
X₂: number of absences per student.
Determine the following multiple regression values.
I've estimated the multiple regression equation using statistics software:
^Y= a + b₁X₁ + b₂X₂
a= 118.68
b₁= 3.61
b₂= -3.61
^Y= 118.68 + 3.61X₁ - 3.61X₂
ANOVA Regression model:
Sum of Square:
SS regression: 25653.86
SS Total: 36819.23
F-ratio: 11.49
p-value: 0.0026
Se²= MMError= 1116.54
Hypothesis for the number of absences:
H₀: β₂=0
H₁: β₂≠0
Assuming α:0.05
p-value: 0.4645
The p-value is greater than the significance level, the decision is to not reject the null hypothesis. Then at 5% significance level, there is no evidence to reject the null hypothesis. You can conclude that there is no modification of the test score every time the number of absences increases one unit.
I hope this helps!
US Department of Transportation As part of a study on transportation safety, the US Department of Transportation collected data on the number of fatal accidents per 1000 licenses and the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Data collected over a one-year period are shown in the table.Use regression to investigate the relationship between the number of fatal accidents and the percentage of drivers under the age of 21.Discuss your findings.What conclusions and recommendations can you derive from your analysis?Percent Under 21 Fatal Accidents per 100013 2.96212 0.7088 0.88512 1.65211 2.09117 2.62718 3.838 0.36813 1.1428 0.6459 1.02816 2.80112 1.4059 1.43310 0.0399 0.33811 1.84912 2.24614 2.85514 2.35211 1.29417 4.18 2.1916 3.62315 2.6239 0.8358 0.8214 2.898 1.26715 3.22410 1.01410 0.49314 1.44318 3.61410 1.92614 1.64316 2.94312 1.91315 2.81413 2.6349 0.92617 3.256
Answer:
we can conclude that for every single unit of : x, y would be increased by 0.2871. and intersection of x and y will be through =1.5974it can be concluded that they are strongly positively correlated. There is strong and positive correlation between them. i.e the number of fatal accidents and the drivers under the age of 21Step-by-step explanation:
WITH THE GIVEN DATA
A ) using regression to investigate the relationship between the number of fatal accidents and the percentage of drivers under the age pf 21
to fit into a regression line we must have ∝ and β
where β = [tex]\frac{S_{xy} }{S_{xx} }[/tex] = 0.2871
and ∝ = y - βx = - 1.5974
regression line = ∝ + β * x
insert values into regression line equation
regression line = -1.5974 + 0.2871 * x
we can conclude that for every single unit of : x, y would be increased by 0.2871. and intersection of x and y will be through =1.5974
B ) conclusion and recommendations can you derive from your analysis
it can be concluded that they are strongly positively correlated. There is strong and positive correlation between them. i.e the number of fatal accidents and the drivers under the age of 21
using the correlation coefficient ( r ) = [tex]\frac{S_{xy} }{\sqrt{S_{xx}*S_{xy} } }[/tex] = 0.8394
Answer:
0.8394
Step-by-step explanation:
.
Distance between (-6,8) and (-3,9)
Answer:
[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Using the distance formula: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
substitute
[tex]d = \sqrt{((-3) - (-6))^2 + ((9)-(8))^2}[/tex]
[tex]\sqrt{10}[/tex]
Solve for x in the diagram below
Answer:
So the diagram couldn't come due to coronavirus?
Answer:
there is no diagram
Step-by-step explanation:
A type of friction that occurs when air pushes against a moving object causing it to negatively accelerate
Answer:
Air resistance
Step-by-step explanation:
Air resistance is a type of friction that occurs when air pushes against a moving object causing it to negatively accelerate
Answer:
Air resistance
Step-by-step explanation:
Air resistance is a type of friction that occurs when air pushes against a moving object causing it to negatively accelerate.
which of the following explains expressions are equivalent to - 5/6 /-1/3
Answer:
2.5
Step-by-step explanation:
(-5/6 ) / (-1/3)
multiply the numerator and denominator by the same number -3 gives:
(-5 * -3 /6 ) / (-1* -3/3)
(15/6 ) / (3/3)
(15/6 ) / 1
(15/6 )
12/6 + 3/6
2 3/6
2 1/2
2.5
A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 368 seconds.
Answer:
The probability that a randomly selected boy in secondary school can run the mile in less than 368 seconds is P(X<368)=0.011.
Step-by-step explanation:
We have a normal distribution with mean 460 and standard deviation 40 to describe the time for the mile run in its secondary-school fitness test.
We have to calculate the probabiltiy that a randomly selected boy in secondary school can run the mile in less than 368 seconds.
To calculate this, we have to calculate the z-score for X=368:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{368-460}{40}=\dfrac{-92}{40}=-2.3[/tex]
Then, we can calculate the probability:
[tex]P(X<368)=P(z<-2.3)=0.011[/tex]
The cost to rent a moving truck is a flat fee of $25 plus $0.60 per mile. The equation c = 25 + 0.6m models the cost, c, in dollars for the number of miles, m, traveled in the truck. Identify the independent and dependent variables. The is the independent variable. The is the dependent variable.
Answer:
The m is the independent variableThe c is the dependent variableStep-by-step explanation:
In this scenario, cost depends on mileage. Thus cost is the dependent variable.
As a general rule, if you have the form ...
a = (some expression involving b)
you will find that "a" is the dependent variable, and "b" is the independent variable.
This problem statement gives you ...
c = (an expression involving m)
"c" is the dependent variable; "m" is the independent variable.
The independent variable is m and the dependent variable is c.
What are the dependent and independent variables?The dependent variable is the outcome or result that is affected by the independent variable. The independent variable is the factor that is changed or manipulated in order to observe the effect on the dependent variable.
Given that, the cost to rent a moving truck is a flat fee of $25 plus $0.60 per mile.
The equation c = 25 + 0.6m models the cost, c, in dollars for the number of miles, m, traveled in the truck.
In the given equation c = 25 + 0.6m, c is the dependent variable and the m is the independent variable.
Therefore, the independent variable is m and the dependent variable is c.
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The radius of a circular disk is given as 21 cm with a maximum error in measurement of 0.2 cm.
A) Use differentials to estimate the maximum error in the calculated area of the disk.
B) What is the relative error?
C) What is the percentage error?
Answer:
a) [tex]\Delta A \approx 26.389\,cm^{2}[/tex], b) [tex]r_{A} \approx 0.019[/tex], c) [tex]\delta = 1.9\,\%[/tex]
Step-by-step explanation:
a) The area of the circular disk is modelled after this expression:
[tex]A = \pi \cdot r^{2}[/tex]
The total differential is given by the following formula:
[tex]\Delta A = 2\pi r \cdot \Delta r[/tex]
The maximum absolute error in the calculated area of the disk is:
[tex]\Delta A = 2\pi \cdot (21\,cm)\cdot (0.2\,cm)[/tex]
[tex]\Delta A \approx 26.389\,cm^{2}[/tex]
b) The relative error is given by:
[tex]r_{A} = \frac{\Delta A}{A}[/tex]
[tex]r_{A} = \frac{26.389\,cm^{2}}{\pi \cdot (21\,cm)^{2}}[/tex]
[tex]r_{A} \approx 0.019[/tex]
c) The percentage error is:
[tex]\delta = r_{A}\times 100\,\%[/tex]
[tex]\delta = 0.019 \times 100\,\%[/tex]
[tex]\delta = 1.9\,\%[/tex]
please help i dont know how to answer this
Answer:
The answer is s / s + 3
Step-by-step explanation:
I applied the fraction rule a/b divided by c/d = a/b times c/d
Please mark BRAINLIEST!
1. Two people have $10 to divide between themselves. Each person names a number (nonnegative integer) no more than 10. If the sum of the two numbers is at most 10, each person gets the named amount of dollars, and the rest of the money is destroyed. If the sum exceeds 10, and the numbers are different, the person who has named the smaller number, receives the corresponding number of dollars, and the second person receives the rest. If the sum exceeds 10, and the numbers are equal, each person receives $5. Determine the be
Answer:
Step-by-step explanation:
Determine the best response of each player to each of the other player’s actions; plot them in a diagram and thus find the Nash equilibria of the game.
The best response for player 2 can be stated as:
(where X1 equals the dollar that a person names and Y2(X1) being the amount the person receives)
X1 Y2(X1)
0 10
1 9,10
2 8,9,10
3 7,8,9,10
4 6,7,8,9,10
5 5,6,7,8,9,10
6 5,6
7 6
8 7
9 8
10 9
Th best responses for player 1 would be the same.
Nash equilibria is the set of strategies that every person forms given no person has any incentive to change. Hence, we can say that there are 4 Nash equilibria: (5,5) , (5,6) , (6,5) , (6,6)
The graph shows the amount of protein contain in a certain brand of peanut butter. Which statement describes the meaning of the point (6, 30) on the graph?
A.) There are 6 g of protein per tablespoon of peanut butter.
B.) There are 30 g of protein per tablespoon of peanut butter.
C.) There is 6 g of protein in 30 tablespoons of peanut butter.
D.) There are 30 g of protein in 6 tablespoons of peanut butter.
Answer:
D.) There are 30 g of protein in 6 tablespoons of peanut butter.
Step-by-step explanation:
Interpretation of the graph:
x-axis: tablespoons
y-axis: grams of protein.
Which statement describes the meaning of the point (6, 30) on the graph?
(6,30) means that x = 6 and y = 30.
This means that in 6 tablespoons there are 30g of protein.
So the correct answer is:
D.) There are 30 g of protein in 6 tablespoons of peanut butter.
Answer:
The answer is D
simplify 3^5•3^4
a.) 3•20
b. 3^9
c.) 6^9
d.) 3^20
Answer:
But if we are doing 3^x we need to add both of them
This is a rule you should remember if you have both same base to x power when you are multiplying
5+4 = 9
answer is 3^9 or 19683
cuanto es r2-2r-7=0
Answer:
Step-by-step explanation:
The solution is attached
Find the area of a circle with radius, r = 17cm.
Give your answer rounded to 3 SF. (SF means Significant figures)
Answer:
0.0908 [tex]m^{2}[/tex] (to 3 S.F.)
Step-by-step explanation:
Area = π[tex]r^{2}[/tex]
π * [tex]17^{2}[/tex] = 907.92
= 908 [tex]cm^{2}[/tex]
=0.0908 [tex]m^{2}[/tex]
2 Ponts
The estimate obtained from a sample of which of the following sizes would
most likely be closest to the actual parameter value of a population?
A. 15
B. 150
C. 75
D. 45
SUBM
A recent national survey found that parents read an average (mean) of 10 books per month to their children under five years old. The population standard deviation is 5. The distribution of books read per month follows the normal distribution. A random sample of 25 households revealed that the mean number of books read last month was 12. At the .01 significance level, can we conclude that parents read more than the average number of books to their children
Answer:
Step-by-step explanation:
Null hypothesis: u = 10
Alternative hypothesis: u =/ 10
Using the formula: t = (x - u) / (s /√n)
Where x = 12, u = 10, s = 5 and n = 25
t= (12-10) / (5/√25)
t = (2)/(5/5)
t = 2/1= 2
t = 2.0
At a 0.01 level of significance with a degree of freedom of 24, the p-value is 0.0569, which is greater than 0.01 we will fail to reject the null and conclude that parents do not read more than the average number of books to their children
Let two cards be dealt successively, without replacement, from a standard 52-card deck. Find the probability of the event. The first card is a queen and the second is a seven
Answer: 4 / 663
Step-by-step explanation:
There are 4 queens in a deck of 52 cards.
Probability = 4/52 = 1/13
There are 4 sevens
Probability = 4/51
Total probability = 1/13 x 4/51 = 4 / 663
The probability of drawing a queen first and a seven-second is 3/613.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
There are 4 queens in a standard deck, and once one queen is drawn, there are 51 cards left, including 3 sevens.
So, the probability of drawing a queen first is 4/52 or 1/13, and the probability of drawing a seven-second is 3/51.
By the multiplication rule of probability, multiply the probabilities of each event occurring:
P(Queen and Seven) = P(Queen) × P(Seven after Queen)
P(Queen and Seven) = (1/13) × (3/51)
P(Queen and Seven) = 3/613
Thus, the probability of drawing a queen first and a seven-second is 3/613.
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ADDITIONAL 100 POINTS PLS HELP ASAP follow up question ( first question on log )
Answer:
Hello!
I believe this is what you are looking for:
x=3
33=27
32=9
S=Surface area
V=Volume
L=Length
R=Radius
I hope this helped. If not, please let me know. I will try my best again. :)
Step-by-step explanation:
To convert a measurement, Pete must move the decimal point to the left 4 places. This is a shortcut for an operation. Which operation is he using? Which power of 10 is involved? iLL GIVE 50 POINTS PLEASE IM TIMED IM PANICKING
Answer: The moving of decimal to the left is a shortcut to the operation of multiplying number by decimal numbers
Step-by-step explanation:
the power of 10 that is involved in converting the measurements of pete is -4, so he needs to multiply the measurement by 10^-4 to convert it.
Answer:
Sample Response: Because he moved the decimal 4 places to the left, Pete is dividing by 10 to the 4th power, or 10,000. Pete moved the decimal place 4 places to the left. Pete is dividing by 10 to the 4th power, or 10,000.
Step-by-step explanation:
it was on edg
hope it helps :b
What is X:Compute
|x|=−4
Answer:
The answer is No Solution
Answer:
No solution
Step-by-step explanation:
There is no solution to this question.
Since the x is an absolute number, the answer cannot be -4. It would have to equal 4
So if that x was a -4 it would equal 4 since it is in absolute value brackets
Suppose 44% of a large sample of a population favor a tax increase. If there
are 95,000 people in the population about how many people in the population
favor a tax increase?
A. 13,300
B. 22,800
C. 41,800
D. 32,300
Answer:
C. 41,800
Step-by-step explanation:
Multiply 0.44 by 95,000.
0.44 x 95,000 = 41,800
The function h(t) = -4.92f^2 + 17.69f + 575 is used to model the height of an object being tossed from a tall building, where h(t) is the height in meters and t is the time in seconds. What are the domain and range?
Answer:
rounded to 3 decimal places ...
domain: [0, 12.757]range: [0, 590.901]Step-by-step explanation:
The function can be put into vertex form:
h(t) = -4.92(t -(1769/984))^2 +575 +4.92(1769/984)^2
h(t) ≈ -4.92(t -1.79776)^2 +590.90122
The value of h(t) is zero for ...
t = √(590.90122/4.92) +1.79776 ≈ 12.75686
For practical purposes, the domain of the function is those values of t between the time the object is tossed and the time it hits the ground. That is, the domain is ...
0 ≤ t ≤ 12.75686
The range is the set of useful vertical heights, so extends from 0 to the maximum height, given by the vertex.
The range is 0 ≤ h(t) ≤ 590.90122.
_____
Alternate interpretation of the question
The function h(t) is defined for all values of t, so that could be considered the domain.
The function h(t) only gives values less than its vertex value, so the range could be considered to extend from negative infinity to that maximum.
Which of the following is(are) the solution(s) to | x-1|-8?
A. X= 7.-9
B. X = 9
C. X = -79
D. X = 7
Answer:
Step-by-step explanation:
|x-1|=8
if (x-1) >= 0 meaning x >= 1
then |x-1| = x-1
and then the solution of the equation is
x-1=8
<=> x = 9
if (x-1) <= 0 meaning x <= 1
then |x-1| = -(x-1) = -x+1
so the solution of the equation is
-x+1=8
<=> -x = 7
<=> x = -7
so the solutions are -7 and 9
answer C
do no hesitate if you need further explanation
thank you
What should be done to both sides of the equation in order to solve w - 9 1/2 = 15?
Answer:
Solve for
w
by simplifying both sides of the equation, then isolating the variable.
Exact Form:
w
=
49
2
Decimal Form:
w
=
24.5
Mixed Number Form:
w
=
24
Answer:
24
Step-by-step explanation:
subtract 2 16/21 - (-8 5/21). reduce if possible
Answer:
11
Step-by-step explanation:
When a feasible region is bounded on all sides, where will the maximum and minimum values of the objective function occur?
at the center of the feasible region
at the top of the feasible region
anywhere within the feasible region
at the vertices of the feasible region
Answer:
Option 4: at the vertices of the feasible region.
I completed the quiz
Answer:
at the vertices of the feasible region
Step-by-step explanation:
this is the correct answer
hope i helped
calculate the middle between -4 and 5
Answer:
eight (8)
Step-by-step explanation:
-3,-2,-1,0,1,2,3,4
