The correct explanation of the confidence interval for the regression slope is: "The average Tip is expected to increase by between $0.080 and $0.174 for every dollar increase in Sale amount." The correct option is A).
The question refers to a scatterplot and regression analysis of data on tips and sale amounts.
In particular, the model's multiple R, R square, and adjusted R square indicate the proportion of variability in the dependent variable (tips) that can be explained by the independent variable (sale amounts). The standard error reflects the precision of the model's predictions.
The confidence interval for the slope provides a range of values within which we can be confident that the true population slope lies. In this case, we can say with 95% confidence that the average tip is expected to increase by between $0.080 and $0.174 for every dollar increase in sale amount. The correct answer is A).
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_____The given question is incomplete, the compelete question is given below:
SLRI SONNY'S SCATTERPLOT TIP ($) 0 100 200 300 400 900 1000 1100 1200 500 600 700 800 SALE AMOUNT (S) © 2020 Radha Bese Florida State University Department of States SUMMARY OUTPUT SONNY'S Regression Statistics Multiple R 0.58064672 R Square 0.337150613 Adjusted R Square 0.325722175 Standard Error 28.73607083 Observations 60 ANOVA MS df 1 F Significance F 29.50102381 1.15405E-06 Regression Residual Total SS 24360.81754 47894.18246 72255 24360.81754 825.7617666 Intercept Sale Amount Coefficients Standard Error Stat 56.95659334 12.27319518 4.640730674 0.126993685 0.023381027 5.431484494 P-value 2.02919E-05 1.15405E-06 Lower 95% 32.38912416 0.080191475 Upper 95% 81.52406252 0.173795894 Which of the following is a correct explanation of the confidence interval for the regression slope? Choose the BEST option.
A The average Tip is expected to increase by between $0.080 and $0.174 for every dollar increase in Sale amount.
B The average Sale amount is expected to increase by between $32.389 and $81.525 for every dollar increase in Tip.
C The average Tip is expected to increase by between $32.389 and $81.525 for every dollar increase in Sale amount.
D The average Sale amount is expected to decrease by between $0.080 and $0.174 for every dollar increase in Tip.
E The Tip is expected to increase by between $32.389 and $81.525 for every dollar increase in Sale amount.
F The Tip is expected to decrease by between $0.080 and $0.174 for every dollar increase in Sale amount
Mar 10, 11:04:59 PM
What is the slope of the line that passes through the points (9, 2) and
(9, 27)? Write your answer in simplest form.
Answer: There is no slope.
Step-by-step explanation:
First, we use the slope-intercept form to find out the slope. The slope-intercept form formula is : m = y2 - y1 / x2 - x1.
m = (27 - 2) / (9 - 9)
m = 25 / 0
m = undefined
This isn't a positive, nor negative slope, rather a slope called "undefined". (Think of every slope as a hill for your skateboard, if it's easier to remember.) And since the x is 0, x is stagnant, making the y and number that doesn't move from the x-coordinates. So, The entered points belong to a vertical line. There is no slope.
Hope this helps.
Question 12 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors were taking none of these courses?
Note: Consider making a Venn Diagram to solve this problem.
0
5
9
22
150 - 141 = 9 seniors are not enrolled in any classes.
What is statistics, and how can it be used?The area of mathematics known as statistics is used to gather, analyse, and interpret data. To predict the future, determine the likelihood that a specific event will occur, or learn more about a survey, statistics can be employed.
The Venn diagram reveals the amount of seniors enrolling in at least one of the courses as follows:
80 + 41 + 54 - 10 - 19 - 12 + 7
= 141
Therefore, 150 - 141 = 9 seniors are not enrolled in any classes.
= 9
So, there are 9 seniors taking none of the courses. Answer: 9.
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.2 In the diagram below, given that XY = 3cm, XZY = 30° and YZ = x, is it possible to solve for x using the theorem of Pythagoras? Motivate your answer. Show Calculations
Sin 30 =3/x
1/2=3/x
x=6
A store is selling 5 types of hard candies: cherry, strawberry, orange, lemon and pineapple. How many ways are there to choose: (a) 24 candies? (b) 24 candies with at least a piece of each flavor? (b) 24 candies with at least 2 cherry and at least 2 lemon?
The solution for question a), b) and c) are as follows. The number of ways to choose 24 candies is 20475. And the number of of ways to choose 24 candies with at least a piece of each flavor is 7700. Similarly, the total number of ways to choose 24 candies with at least 2 cherry and at least 2 lemon is 272.
(a) To choose 24 candies from 5 types of hard candies, we can use the stars and bars method. We need to distribute 24 candies among 5 types, where each type can have 0 or more candies.
We can represent this by 24 stars (*) and 4 bars (|) to separate the candies of different types. The number of ways to arrange these stars and bars is the same as the number of ways to choose 4 positions out of 28 to place the bars. Therefore, the number of ways to choose 24 candies is:
(28 choose 4) = 20475
(b) To choose 24 candies with at least a piece of each flavor, we can first choose 5 candies, one of each flavor, and then choose 19 candies from the remaining candies. The number of ways to choose 19 candies from 20 candies (excluding one candy of each flavor) is:
(19 + 4 - 1) choose (4 - 1) = 22 choose 3 = 1540
Therefore, the total number of ways to choose 24 candies with at least a piece of each flavor is:
5 * 1540 = 7700
(c) To choose 24 candies with at least 2 cherry and at least 2 lemon, we can use the inclusion-exclusion principle. Let A be the event that we choose at least 2 cherry, and let B be the event that we choose at least 2 lemon. Then the number of ways to choose 24 candies with at least 2 cherry and at least 2 lemon is:
P(A union B) = P(A) + P(B) - P(A intersect B)
To calculate P(A), we can choose 2 cherry and then choose 20 candies from the remaining 3 types, which is:
(2 choose 2) * (20 + 3 - 1) choose (3 - 1) = 22 choose 2 = 231
Similarly, P(B) is also 231.
To calculate P(A intersect B), we can choose 2 cherry, 2 lemon, and then choose 18 candies from the remaining 3 types, which is:
(2 choose 2) * (2 choose 2) * (18 + 3 - 1) choose (3 - 1) = 20 choose 2 = 190
Therefore, the total number of ways to choose 24 candies with at least 2 cherry and at least 2 lemon is:
2 * 231 - 190 = 272
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What is the value of 2 x² - 4 y when x = -4 and y = 16?
Answer:
-32
Step-by-step explanation:
2x ^ 2 - 4
2(-4) ^ 2 - 4(16)
32 - 64
-32
The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r) and radial lengths. The circuits carry the same current. Rank them according to the magnitudes of the magnetic fields they produce at C, least to greatest
solve correctly and I will pay you $100
The rank of the three circuits consisting of concentric circular arcs according to the magnitudes of the magnetic fields they produce at C, from least to greatest is (3), (2), (1).
We know that, the radial segments don't produce magnetic field at C, so consider arcs.
Assume that the current is counter clockwise and the magnetic field to be positive pointing out of the page.
Understand that, magnetic field at the center from an arc φ of radius R is [tex]\frac{{{\mu _0}i\phi }}{{4\pi R}}[/tex]
Therefore, for (1) :
[tex]\begin{gathered}\begin{array}{l}B = \frac{{{\mu _0}i\pi }}{{4\pi \left( {3r} \right)}} + \frac{{{\mu _0}i\pi }}{{4\pi r}}\\ \Rightarrow B = \frac{1}{3}\frac{{{\mu _0}i}}{r}\end{array}\end{gathered}[/tex]
For (2) :
[tex]\begin{gathered}\begin{array}{l}B = \frac{{{\mu _0}i\pi }}{{4\pi \left( {3r} \right)}} - \frac{{{\mu _0}i\pi }}{{4\pi r}}\\ \Rightarrow B = - \frac{1}{6}\frac{{{\mu _0}i}}{r}\end{array}\end{gathered} \\[/tex]
For (3) :
[tex]\begin{gathered}\begin{array}{l}B = \frac{{{\mu _0}i\pi }}{{4\pi \left( {3r} \right)}} - \frac{{{\mu _0}i\left( {\frac{\pi }{2}} \right)}}{{4\pi r}} - \frac{{{\mu _0}i\left( {\frac{\pi }{2}} \right)}}{{4\pi \left( {2r} \right)}}\\ \Rightarrow B = - \frac{5}{{48}}\frac{{{\mu _0}i}}{r}\end{array}\end{gathered}[/tex]
Therefore, the magnitude of the magnetic fields at C after arranging them in the order of least to greatest are (3), (2), (1).
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There are N distinct types of coupons, and each time one is obtained it will, independently of past choices, be of type i with probability P_i, i, .., N. Hence, P_1 + P_2 +... + P_N = 1. Let T denote the number of coupons one needs to select to obtain at least one of each type. Compute P(T > n).
If T denote the number of coupons one needs to select to obtain at least one of each type., P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}
The problem of finding the probability P(T > n), where T is the number of coupons needed to obtain at least one of each type, can be solved using the principle of inclusion-exclusion.
Let S be the event that the i-th type of coupon has not yet been obtained after selecting n coupons. Then, using the complement rule, we have:
P(T > n) = P(S₁ ∩ S₂ ∩ ... ∩ Sₙ)
By the principle of inclusion-exclusion, we can write:
P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}
where the outer sum is taken over all even values of k from 0 to N, and the inner sum is taken over all sets of k distinct indices.
This formula can be computed efficiently using dynamic programming, by precomputing all values of Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ} for all x from 1 to N, and then using them to compute the final probability using the inclusion-exclusion formula.
In practice, this formula can be used to compute the expected number of trials needed to obtain all N types of coupons, which is simply the sum of the probabilities P(T > n) over all n.
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From the given graph, how many students worked at least 10 hours per week?
Answer:
39.
Step-by-step explanation:
From the group of 10-14 hours worked per week, 8 students.
From the group of 15-19 hours worked per week, 4 students.
From the group of 20-24 hours worked per week, 12 students.
From the group of 25-29 hours worked per week, 8 students.
From the group of 30-34 hours worked per week, 4 students.
And finally, from the group of 35+ hours worked per week, 3 students.
So, 8+4+12+8+4+3 = 39 students.
The surface area of a globe in Mr.Patton’s classroom is about 452.39 square inches. Find its volume in cubic inches . Use 3.14 for pi. Round to the nearest whole number
The volume of the globe is 905 cubic inches, for the given surface area.
What is surface area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a form with a curved base and surface is equal to the sum of the two areas.
The volume of the globe is given as:
V = 4/3πr³
The surface area if given as:
SA = 4πr²
Substituting the values of the given SA we have:
452.39 = 4 * 3.14(r²)
r = 6.01
Now, substitute the value of r in the equation of volume we have:
V = 4/3(3.14)(6.01)³
V = 904.78.
Hence, the volume of the globe is 905 cubic inches, for the given surface area.
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Andy has 4 red cards, 3 blue cards, and 2 green cards. He chooses a card and replaces it before choosing a card again. How many possible outcomes are in the sample space of Andy's experiment?
A) 18
B) 9
C)81
D)3
There are 81 potential outcomes in Andy's sample space.
What are the potential results?Potential Outcomes is a list of every scenario that could happen as a result of an occurrence. For instance, while rolling a dice, the possible results are 1, 2, 3, 4, 5, and 6. 6. Favorable Result - the intended outcome. For instance, if you roll a 4 on a dice, the only possible result is 4.
The total number of cards (i.e., 4 + 3 + 2 = 9) determines the number of outcomes that can occur in each draw.
We must multiply the total number of results for each draw in order to determine the total number of possible outcomes for the two draws.
For two draws with replacement, there are exactly as many outcomes available as the product of the amount of outcomes that could occur in each draw.
9 × 9 = 81.
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Interpret the slope of this function in the context of the situation. Use complete sentences.
Jennifer is painting an office complex. One wing has a large reception area with several equal-sized offices. Before painting, she must put tape on the baseboards. The amount of tape needed is given by the equation, y=12x+25 where y is total number of meters of tape, and x is the number of offices.
The slope of the function is 12. Because of the slope, Jennifer will require 12 extra meters of tape for each additional office she needs to tape the baseboards in.
What is slope?A line's slope on a graph is its steepness or inclination. It may be derived from any two locations on a line by dividing the vertical change (rise) by the horizontal change (run). Positive, negative, zero, or undefinable slopes are all possible for lines. A line on a graph with a positive slope is growing as you travel from left to right, while one with a negative slope is declining. A line has a slope of zero when it is horizontal and a slope of infinity when it is vertical.
The given function is y = 12x + 25.
The standard equation of the line is given as:
y = mx + b
where, m is the slope.
Comparing the equation with the given equation the slope of the function is 12.
Because of the slope, Jennifer will require 12 extra metres of tape for each additional office she needs to tape the baseboards in. In other words, if more offices need to be painted, the amount of sellotape required also grows linearly.
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For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete.a. X= the number of unbroken eggs in a randomly chosen standard egg cartonb. Y= the number of students on a class list for a particular course who are absent on the first day of classesc. U= the number of times a duffer has to swing at a golf ball before hitting itd. X= the length of a randomly selected rattlesnakee. Z= the amount of royalties earned from the sale of a first edition of 10,000 textbooksf. Y= the PH of a randomly chosen soil sample g. X= the tension (psi) at which a randomly selected tennis racket has been strungh. X= the total number of coin tosses required for three individuals to obtain a match (HHH or TTT)
a. X= number of unbroken eggs in a standard carton. b. Y= number of absent students on first day of a course. c. U= number of swings before hitting a golf ball. d. X= length of a rattlesnake.
e. Z= royalties earned from selling a first edition of 10,000 textbooks. f. Y= pH of a soil sample. g. X= tension (psi) of a tennis racket. h. X= total coin tosses required for three individuals to get a match.
a. X can take on values 0, 1, 2, 3, 4, 5, 6, as there can be zero to six unbroken eggs in a standard egg carton. X is a discrete random variable.
b. Y can take on values 0, 1, 2, 3, ..., n, where n is the total number of students on the class list. Y is a discrete random variable.
c. U can take on values 1, 2, 3, .... U is a discrete random variable.
d. X can take on any positive real value, as the length of a rattlesnake can vary continuously. X is a continuous random variable.
e. Z can take on any non-negative real value, as the amount of royalties earned can be any non-negative amount. Z is a continuous random variable.
f. Y can take on any value between 0 and 14, as the pH of a soil sample can range from 0 to 14. Y is a continuous random variable.
g. X can take on any positive real value, as the tension at which a tennis racket has been strung can vary continuously. X is a continuous random variable.
h. X can take on values 3, 4, 5, 6, ... as there must be at least three coin tosses and the tosses must continue until a match is obtained. X is a discrete random variable.
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ABC ~ DFE , solve for X please help
Step-by-step explanation:
x+2 is to 4 as 28 is to 7
(x+2) / 4 = 28 / 7 <====solve for 'x'
x+2 = 16
x = 14
Mr. wings class collected empty soda, cans for recycling project. each of the 20 students had to collect 40 cans. Each can has a mass of 15 grams. How many kilograms of cans did the class collect to recycle?
A 0.6 kg.
B 12 kg
C 12,000 kg
D 12,000,000 kg
Step-by-step explanation:
40 cans/student X 20 students X 15 gram/can = 12 000 gm = 12 kg
Please answer these correctly asap
Answer:
Step-by-step explanation:
13. [tex]\frac{4}{20}*100= 20[/tex]%
14. [tex]\frac{2}{25}*100=8[/tex]%
15. [tex]\frac{35}{50}*100=70[/tex]%
16. [tex]\frac{150}{200} *100=75[/tex]%
17. [tex]\frac{4}{100}*x=56\\ 56*\frac{100}{4}=1400\\[/tex]days
SUPPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: Angle 1 = 32, Angle 2 = x + 29
COMPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: 54 + x = 90
COMPLEMENTARY ANGLE Find the value of x. Answer only. Given: Angle 1 = x, Angle 2 = 24 + 2x
Answer:
Given: Angle 1 = 32, Angle 2 = x + 29 ----- Answer is x = 119°
Given: 54 + x = 90 ----- Answer is x = 36°
Given: Angle 1 = x, Angle 2 = 24 + 2x ----- Answer is x = 22°
Step-by-step explanation:
1. Supplementary angle = 180°
Angle 1 = 32° Angle 2 = x + 29
Angles 1 + 2 = 180°
32° + x + 29° = 180°
32° + x = 180° - 29°
32° + x = 151°
x = 151° - 32°
x = 119°
2. Complementary angle = 90°
Given: 54 + x = 90
90 - 54 = x
x = 36°
3. Complementary angle = 90°
Given: Angle 1 = x, Angle 2 = 24 + 2x
Angles 1 + 2 = 90°
x + 24 + 2x = 90°
3x + 24 = 90°
3x = 90° - 24
3x = 66°
x = 66°/3
x = 22°
Hope it helps!
5. Which of these statistics is used in basketball as an all-in-one rating of how well a player performs per minute they play?
O A. Wins above replacement (WAR)
O B. Field goal percentage (FG%)
O C. Double doubles (DD2)
OD. Player efficiency rating (PER)
Answer:
Player Efficiency Rating (PER)
Step-by-step explanation:
The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is Player Efficiency Rating (PER).
The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is the Player Efficiency Rating (PER). So, correct option is D.
PER is a widely used metric that quantifies a player's overall performance by taking into account various statistical categories and normalizing them based on playing time.
PER evaluates a player's contributions in areas such as points, rebounds, assists, steals, blocks, and turnovers. It considers both positive and negative statistical events and provides a single numerical value that represents a player's efficiency on the court. A higher PER indicates a more productive player.
On the other hand, Wins Above Replacement (WAR) is a metric commonly used in baseball to estimate the number of wins a player contributes to their team compared to a replacement-level player.
Field Goal Percentage (FG%) measures the accuracy of a player's shooting by calculating the percentage of successful field goal attempts. Double doubles (DD2) count the number of games in which a player achieves double-digit totals in two statistical categories.
Among the options listed, Player Efficiency Rating (PER) is specifically designed to assess a player's overall performance per minute played in basketball.
So, correct option is D.
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Trains Two trains, Train A and Train B, weigh a total of 188 tons. Train A is heavier than Train B. The difference of their
weights is 34 tons. What is the weight of each train?
Step-by-step explanation:
A + B = 188
A = 188 - B - (1)
Now,
A - B = 34
188 - B - B = 34 (Substituting eqn 1 in A)
188 - 34 = 2B
154 = 2B
• B = 77 tons
Now
A = 188 - B
A = 188 - 77
A = 111 tons
Workers are preparing an athletic field by mixing soil and sand
in the correct ratio. The table shows the volume of sand to mix
with different volumes of soil. Which statement is correct?
A For 1,425 m³ of soil, the workers should use 375 m³ of sand.
B The ratio of the volume of soil to the volume of sand is 1:4.
C A graph of the relationship includes the point (900, 225).
D The equation y = 4x models the relationship.
Option B: The ratio of the volume of soil to the volume of sand is 1:4.
Looking at the table, we can see that for every 100 m³ increase in soil, the sand volume increases by 25 m³. This gives us a ratio of 4:1, which means that the volume of sand is one-fourth of the volume of soil. Therefore, option B is correct.
Option D: The equation y = 4x models the relationship.
We can see that the volume of sand is always one-fourth of the volume of soil. Therefore, we can write y = (1/4)x or y = 0.25x. This equation is the same as y = 4x. Therefore, option D is also correct.
So, the correct statements are B and D.
What is a graph?In mathematics, a graph is a visual representation of data or a mathematical function. It consists of a set of points or vertices connected by lines or curves called edges or arcs, which represent the relationships between the points. Graphs can be used to show trends, patterns, and relationships in data, and they are commonly used in fields such as statistics, economics, and computer science. Some common types of graphs include line graphs, bar graphs, pie charts, scatterplots, and network graphs.
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The table mentioned in the question has been attached below.
a water park sold 1679 tickets for total of 44,620 on a wa summer day..each adult tocket is $35 and each child ticket is $20. how many of each type of tixkwt were sold?
Therefore , the solution of the given problem of unitary method comes out to be the attraction sold 943 child tickets and 736 adult tickets on that particular day.
What is an unitary method?It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.
Here,
Assume the attraction sold x tickets for adults and y tickets for kids.
Based on the supplied data, we can construct the following two equations:
=> x + y = 1679 (equation 1, representing the total number of tickets sold)
=> 35x + 20y = 44620 (equation 2, representing the total revenue generated)
Using the elimination technique, we can find the values of x and y.
When we divide equation 1 by 20, we obtain:
=> 20x + 20y = 33580 (equation 3)
Equation 3 is obtained by subtracting equation 2 to yield:
=> 15x = 11040
=> x = 736
When we enter x = 736 into equation 1, we obtain:
=> 736 + y = 1679
=> y = 943
As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.
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PLEASE HELPPPPP 30 POINTSSSS!
Answer:
the answer will be 117
Step-by-step explanation:
you need to multiply
I need help with this
By answering the presented question, we may conclude that As a result, the slope equation for the line perpendicular to y = 1/4 and passing through (-6,9) is x = -6.
what is slope?Slope is the slope of the regression of a curve or a line in mathematics. It serves as a measure of the way the como of a formula varies once the x-value alters. The slope of a line is commonly symbolised by the letter m and may be computed as follows: m = (y2 - y1) / (x2 - x1) (x1, y1) and (x2, y2) have been any 2 things on the line. A line's slopes might be favorable, zero, zero, or unknown. A positive slope signifies that the line ascends to left to right, even though a negative slope indicates that now the line drops from left to right.
We must first determine the slope of a line perpendicular to the line y = 1/4 in order to derive its equation.
Because y = 1/4 is a horizontal line, its slope is zero. The slope of a line perpendicular to this line is the inverse of the slope of y = 1/4.
The negative reciprocal of 0 is undefined, although the perpendicular line can be considered a vertical line. The equation of a vertical line going through the point (-6,9) is x = -6.
As a result, the equation for the line perpendicular to y = 1/4 and passing through (-6,9) is x = -6.
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The equation of a perpendicular line passing through a point (x1, y1) may be expressed in the form: if the slope-intercept form of the equation of the original line is [tex]y = mx + b[/tex] , where m is the slope and b is the y-intercept, then Thus, option A is correct.
What is the equation for perpendicular line?The given equation is [tex]y = 7 - 11x[/tex] .
In order to determine the equation of the line perpendicular to this one, we must first determine its slope. Given that x has a -11 coefficients, the slope of the given line is -11.
The slope of the line we are looking for will be 1/11, which is the negative reciprocal of -11 because it is perpendicular to the line we are looking for.
Using the point-slope form of a line's equation, we can determine the equation of the line passing through (-6,-9) and having a slope of 1/11:
[tex]y - (-9) = (1/11)(x - (-6))[/tex]
Simplifying this equation gives:
[tex]y + 9 = (1/11)(x + 6)[/tex]
Multiplying both sides by 11 gives:
[tex]11y + 99 = x + 6[/tex]
Subtracting 6 from both sides gives:
[tex]x = 11y + 93[/tex]
Therefore, the answer is A. [tex]x = -9[/tex] .
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write and equation to state the following: a varies jointly with b and the square root of c and inversely with the cube of d.
The equation that expresses the joint variation of a with b and the square root of c, and the inverse variation of a with the cube of d is:
[tex]a = k * \frac{(b * \sqrt{c})}{d^3}[/tex]
In mathematics, A variation equation is an equation that describes how one variable (the dependent variable) changes with respect to changes in one or more other variables (the independent variables). There are several types of variation equations, including direct variation, inverse variation, joint variation, and combined variation.
Now let's consider the given question:
It is given that,
a varies jointly with b and the square root of c, means
[tex]a \propto b[/tex] and [tex]a\propto \sqrt{c}[/tex].
It is also given,
a varies inversely with the cube of d, means
[tex]a \propto \frac{1}{d^3}[/tex]
Then by combining those, we can write
[tex]a \propto \frac{(b * \sqrt{c})}{d^3}[/tex]
The equation that expresses the joint variation of a with b and the square root of c, and the inverse variation of a with the cube of d is:
[tex]a = k * \frac{(b * \sqrt{c})}{d^3}[/tex]
Where k is the constant of proportionality. This equation states that as b and the square root of c increase, and as d decreases, the value of a increases proportionally. The constant of proportionality k depends on the specific values of a, b, c, d, and the units of measurement being used.
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Imagine that there is an urn containing 5 blue chips and 5 red chips where chips are of equal dimensions and all chips in the urn at a time are equally likely to be selected. Let
X
denote the total number of blue chips obtained when 3 consecutive chips are drawn from the urn without replacement. (a) (10 points) Compute the probability that
X=3
The probability that X = 3 is 1/12.
To compute the probability that X = 3, we need to consider all possible ways of drawing three chips and count the number of ways in which we obtain three blue chips.
The total number of ways of drawing three chips from the urn without replacement is:
10C3 = (10!)/(3!7!) = 120
This is because we need to choose 3 chips out of the 10 in the urn, and the order in which we draw them does not matter.
Now, we need to count the number of ways in which we can obtain three blue chips. Since there are 5 blue chips in the urn, the number of ways of choosing 3 blue chips out of 5 is:
5C3 = (5!)/(3!2!) = 10
Therefore, the probability of obtaining three blue chips is:
P(X = 3) = 10/120 = 1/12
Hence, the probability that X = 3 is 1/12.
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The probability that X which denotes the total number of blue chips obtained when 3 consecutive chips are drawn from the urn without replacement is 1/12.
To calculate the probability that X = 3, the first step is to consider all the possible ways in which three chips can be drawn and count the number of ways in which we obtain three blue chips.
The total number of ways of drawing three chips from the urn without replacement is:
¹⁰C₃ = (10!)/(3!)(7!) = 120
This is because we need to choose 3 chips out of the 10 in the urn, and the order in which we draw them does not matter. Now, we need to count the number of ways in which we can obtain three blue chips. Since there are 5 blue chips in the urn, the number of ways of choosing 3 blue chips out of 5 is:
⁵C₃ = (5!)/(3!)(2!) = 10
Therefore, the probability of obtaining three blue chips is:
P(X = 3) = 10/120 = 1/12
Hence, the probability that X = 3 is 1/12.
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Danielle is saving money to buy a new computer game. She needs to save at least 45 dollars to buy the
game. She has saved 11 dollars so far. Let n represent the number of dollars she still needs to save in order to buy the game. Which number sentence best describes this situation?
Answer choices:
A. 11 + n ≥ 45
B. 11 + n ≤ 45
C. 11n ≥ 45
D. 11n ≤ 45
Answer:
Step-by-step explanation:
A
Find the standard normal area for each of the following (round your answer to 4 decimal places)
What are the values of the interior angles?
Round each angle to the nearest degree.
A) m∠X = 131º, m∠Y = 16º, m∠Z = 33º
B) m∠X = 120º, m∠Y = 15º, m∠Z = 30º
C) m∠X = 145º, m∠Y = 18º, m∠Z = 36º
We can see here the values of the interior angles will be: A) m∠X = 131º, m∠Y = 16º, m∠Z = 33º.
What is interior angle?An interior angle is an angle created between two adjacent sides of a polygon. To put it another way, it is the angle created by two polygonal sides that have a shared vertex.
Sum of interior angles of a triangle = 180°
[tex]2p + \frac{1}{4} p + \frac{1}{2} p = 180[/tex]
11p/4 = 180°
p = 720°/11
m∠X = 2p = 2 × 720°/11 = 130.9 ≈ 131°
m∠Y = [tex]\frac{1}{4} p[/tex] = 1/4 × 720°/11 = 16.3 ≈ 16°
m∠Z = [tex]\frac{1}{2} p[/tex] = 1/2 × 720°/11 = 32.7 ≈ 33°
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What gravitational force does the moon produce on the Earth if their centers are 3.88x108 m apart and the moon has a mass of 7.34x1022 kg?
The gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]
What is gravitational force?
Gravitational force is the force of attraction that exists between any two objects in the universe with mass. This force is directly proportional to the masses of the objects and inversely proportional to the square of the distance between their centers.
The gravitational force that the moon produces on the Earth can be calculated using the formula:
[tex]F = G \cdot \frac{m_1 \cdot m_2}{r^2}[/tex]
where:
[tex]G$ = gravitational constant = $6.67430 \times 10^{-11}\ \mathrm{N(m/kg)^2}$[/tex]
[tex]m_1$ = mass of the moon = $7.34 \times 10^{22}\ \mathrm{kg}$[/tex]
[tex]m_2$ = mass of the Earth = $5.97 \times 10^{24}\ \mathrm{kg}$ (approximate)[/tex]
[tex]r$ = distance between the centers of the Earth and the moon = $3.88 \times 10^8\ \mathrm{m}$[/tex]
Substituting these values into the formula, we get:
[tex]F &= 6.67430 \times 10^{-11} \cdot \frac{7.34 \times 10^{22} \cdot 5.97 \times 10^{24}}{(3.88 \times 10^8)^2} \&= 1.98 \times 10^{20}\ \mathrm{N}[/tex]
Therefore, the gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]
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Divide 240g in the ratio 5 4 3
Step-by-step explanation:
240g divided in ratios.
divide 240g in the ratio 5:4:3
To divide 240g in the ratio 5:4:3, we need to determine the amount of each part of the ratio.
First, we need to find the total number of parts in the ratio, which is 5 + 4 + 3 = 12.
Next, we divide the total amount (240g) by the total number of parts (12) to find the value of one part:
240g ÷ 12 = 20g
Therefore, one part of the ratio is equal to 20g.
To find the amount of each part of the ratio, we can multiply the value of one part by the corresponding number in the ratio.
The amounts are:
5 parts: 5 × 20g = 100g
4 parts: 4 × 20g = 80g
3 parts: 3 × 20g = 60g
Therefore, to divide 240g in the ratio 5:4:3, we need 100g, 80g, and 60g for each part of the ratio, respectively.
Answer
100g , 80g , 60g
Step-by-step explanation:
Ratio:Ratio = 5 : 4 : 3
Let the unit share be 'x'.
So, three shares are 5x, 4x and 3x.
Total weight = 240 g
Total shares = 5x + 4x + 3x = 12x
Sum of all the shares equal to the total weight.
12x = 240g
x = 240 ÷ 12 = 20
The value of unit share is 20 g. From this we can find the weight of each share.
5x = 5 * 20 = 100g
4x = 4 * 20 = 80 g
3x = 3 * 20 = 60 g
If cos is the third quadrant find sin
The value of sinθ = -[tex]\frac{7}{8}[/tex] using trigonometry.
Trigonometry: What Is It?One of the most significant areas of mathematics, trigonometry has a wide range of applications. Trigonometry is a field of mathematics that primarily focuses on the analysis of how a right-angle triangle's sides and angles relate to one another. Therefore, using trigonometric formulas, functions, or trigonometric identities can be helpful in determining the absent or unknown angles or sides of a right triangle. Angles in geometry can be expressed as either degrees or radians. 0°, 30°, 45°, 60°, and 90° are some of the trigonometric angles that are most frequently used in computations.
In this question,
sin²θ + cos²θ= 1
sin²θ + (-1/4)² = 1
sin²θ = 1- (1/8)
sinθ = ± √(7/8)
since, it is in the third quadrant,
sinθ= -[tex]\frac{7}{8}[/tex]
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