(6.04)The line of best fit for a scatter plot is shown:
What is the equation of this line of best fit in slope-intercept form?
y = 1x + one half
y = one halfx + 1
y = 1x − one half
y = negative one halfx + 1
Answer: The correct option is (B) [tex]y=\dfrac{1}{2}x+1.[/tex]
Step-by-step explanation: We are given a line of best fit for a scatter plot in the figure.
We are to find the equation of the line of best fit in slope-intercept form.
We know that the slope-intercept form of a line is given by
[tex]y=mx+c,[/tex]
where m is the slope and c is the y-intercept of the line.
From the figure, we note that
the line passes through the points (0, 1) and (2, 2). So, the slope of the line will be
[tex]m=\dfrac{2-1}{2-0}\\\\\\\Rightarrow m=\dfrac{1}{2}.[/tex]
At x = 0, y = 1, so the y-intercept of the line, c = 1.
Therefore, the equation of the line will be
[tex]y=mx+c\\\\\Rightarrow y=\dfrac{1}{2}x+1.[/tex]
Thus, the equation of the line of best fit in slope-intercept form is
[tex]y=\dfrac{1}{2}x+1.[/tex]
Option (B) is CORRECT.
Identify the 25th term of the arithmetic sequence 2,1 (3 / 5), 1 ( 1 / 5) ... (2 points)
The 25th term of the arithmetic sequence is -31.6.
Looking at the sequence:
- First term [tex]\( a_1 = 2 \)[/tex]
- Second term [tex]\( a_2 = 1 \left( \frac{3}{5} \right) = \frac{3}{5} \)[/tex]
- Third term [tex]\( a_3 = 1 \left( \frac{1}{5} \right) = \frac{1}{5} \)[/tex]
Calculate the common difference d:
[tex]\[ d = a_2 - a_1 = \frac{3}{5} - 2 = \frac{3}{5} - \frac{10}{5} = -\frac{7}{5} \][/tex]
Now that we have [tex]\( d = -\frac{7}{5} \)[/tex], we can find the general term [tex]\( a_n \)[/tex] of the arithmetic sequence:
[tex]\[ a_n = a_1 + (n-1)d \][/tex]
Substitute [tex]\( a_1 = 2 \)[/tex] and [tex]\( d = -\frac{7}{5} \)[/tex]:
[tex]\[ a_n = 2 + (n-1) \left( -\frac{7}{5} \right) \]\[ a_n = 2 - \frac{7(n-1)}{5} \]\[ a_n = 2 - \frac{7n - 7}{5} \]\[ a_n = \frac{10 - 7n + 7}{5} \]\[ a_n = \frac{17 - 7n}{5} \][/tex]
Now, find [tex]\( a_{25} \)[/tex]:
[tex]\[ a_{25} = \frac{17 - 7 \cdot 25}{5} \]\[ a_{25} = \frac{17 - 175}{5} \]\[ a_{25} = \frac{-158}{5} \]\[ a_{25} = -31.6 \][/tex]
Which iniquality is represented by the graph? If you can do the top ones thanks too:) please show work if there is any:)
Find all real numbers X such that 6x-21<=-3 AND 14x+11>=-17
What are the key aspects of any parabola? What do the key aspects tell you about the graph?
A parabola is an open curve that is formed when a cone is sliced parallel to the side of it. The key aspects of a parabola when it is graphed looks like a curve that opens upward, downward, leftward or rightward. It has a latus rectum which is the length of the ends of a curved line. The directrix is the distance between the vertex of a parabola and the line. The vertex is the point where the curve ends.
One of the key aspects of any parabola is that It looks like a curve that opens upward, downward, leftward or rightwards.
What is a Parabola?This refers to the open curve that is so shaped when there is a sliced parallel to a cone on either side of it.
From the complete question, there is an image shown and some key concepts that can be gotten from it are:
It has a latus rectum which is the length of the ends of a curved line. The directrix is the distance between the vertex of a parabola and the line. The vertex is the point where the curve ends.Read more about parabolas here:
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line ab contains points A(8,-4) and B(1,-5). the slope of line ab is
A card is drawn at random from a deck. what is the probability it is a red card, an ace, or both?
52 cards total
26 are red
so you would have a 26/52 reduced to 1/2 probability of picking a red one.
There are 4 aces so you would have a 4/52 reduced to 1/13 probability of picking an ace.
There are 2 red aces so you would have a 2/52 reduced to 1/26 probability of picking a red Ace
What is 8.61×10^−8 in decimal form?
Answer:
0,00000000861
hope this helps all u k12 cheaters. :)
Is the following relation a function?
X Y
6 ----> -1
-1 ----> 2
4 ----> 3
0 ----> 3
Yes or No (both 4 and 0 are pointing to 3)
Answer: Yes, it is definitely a function. Although one might say that it is not a one to one or injective function because of the presence of (-1,-2) and (6,-2).. The correct option among the two options that are given in the question is the second option. I hope that this is the answer that has actually come to your desired help
Step-by-step explanation: I took the test on FLVS
If you start with a number, add 5, then multiply by 7, the result is 133. what was the original number
David is making his own strawberry yogurt. In his mixture, the number of strawberries is proportional to the amount of milk in cups david uses 2 1/2cups of milk for every 14 strawberries. If david uses 203 strawberries, how much milk will he need?
In the diagram, diameter AC¯¯¯¯¯ intersects chord BD¯¯¯¯¯ at point E such that AE = 2.5 units and BE = 3.4 units. Point O is the center of the circle, and the radius of the circle is 5 units. What is the approximate length of DE¯¯¯¯¯?
A. 5.5
B. 4.5 units
C. 6.0 units
D. 5.0 units
Answer:
(A) 5.5 units
Step-by-step explanation:
Given: Diameter AC intersects chord BD at point E such that AE = 2.5 units and DE = 3.4 units. Point O is the center of the circle, and the radius of the circle is 5 units. we have to find the approximate length of BE.
Now, CE=CO+OE=5+(OA-AE)=5+2.5=7.5 units.
Now, by Intersecting Chord Theorem which states that when two chords intersect each other inside a circle then the products of their segments are equal.
Thus, [tex]CE{\times}AE=BE{\times}DE[/tex]
Substituting the given values, we get
[tex]7.5{\times}2.5=3.4{\times}DE[/tex]
[tex]\frac{7.5{\times}2.5}{3.4}=DE[/tex]
[tex]5.541=DE[/tex]
[tex]DE[/tex]≈[tex]5.5{\text{units}[/tex]
therefore, the measure of DE is 5.5 units.
Hence, option A is correct.
Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.
Independence Day in the United States is July 4.
Select one:
a. July 4 is not Independence Day in the United States. False; it is Independence Day.
b. Non-Independence Day in the United States is not July 4. True
c. Non-Independence Day in the United States is July 4. False; July 4 is Independence Day in the United States.
d. Non-July 4 is not Independence Day in the United States. True
Answer:
The correct answer is option B. Non-Independence Day in the United States is not July 4. True
Step-by-step explanation:
The inverse of the conditional statement is found by negating both the hypothesis and conclusion of that conditional statement.
Here the given statement is :
Independence Day in the United States is July 4.
Its inverse will be :
B. Non-Independence Day in the United States is not July 4. True
And yes this is true.
A rectangle is placed around a semicircle as shown below. The length of the rectangle is 6cm . Find the area of the shaded region. Use the value 3.14 for π , and do not round your answer. Be sure to include the correct unit in your answer.
The tens digit is two less than the units digit. If the digits are reversed, the sum of the reversed number and the original number is 154. Find the original number.
The value of the original number obtained using a system of linear equations is 68
Let the two digit number = ab
Tens digit = a Unit digit = bWe can create the system of equations as follows :
b - a = 2 - - - - - - - - - - - - (1)
(10b + a) + (10a + b) = 154
10b + a + 10a + b = 154
11b + 11a = 154 - - - - - - - - - (2)
From (1) :
b = 2 + a ----- (3)
Substitute b = 2 + a into (2)
11(2 + a) + 11a = 154
22 + 11a + 11a = 154
22 + 22a = 154
22a = 154 - 22
22a = 132
a = 132 / 22
a = 6
From (3) :
b = 2 + 6
b = 8
Therefore, the original number, ab = 68
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Lines are cut by transversal such that the alternate interior angles have measures of 3X +17 X +53°
Three-Fourths of the student body attended the pep-rally. If there were 1230 students at the pep rally, how many students are there in all?
To find the total number of students, set up a proportion and solve for x. The total number of students is 1640.
Explanation:To find the total number of students, we can set up a proportion using the information given. If three-fourths of the student body attended the pep-rally, that means three-fourths of the total number of students is equal to 1230. Let's let x represent the total number of students. Then, we can write the proportion as:
3/4 = 1230/x
Now, to solve for x, we can cross multiply:
3x = 4 x 1230
Dividing both sides by 3:
x = 4 x 1230 / 3
Calculating the expression on the right side of the equation:
x = 4920 / 3
Finally, divide 4920 by 3 to get:
x = 1640
So, there are 1640 students in total.
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Geneva wants to put fencing around her rectangular flower bed. The width of her flower bed is 2/3 the length. The perimeter of the flower bed is 20 feet. What are the dimensions of her flower bed?
The dimensions of her rectangular flower bed will be 4 feet by 6 feet.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
Geneva needs to put fencing around her rectangular bloom bed. The width of her bloom bed is 2/3 the length.
W = (2/3)L
3W = 2L
The perimeter of the bloom bed is 20 feet. Then we have
2(L + W) = 20
2L + 2W = 20
3W + 2W = 20
5W = 20
W = 4 feet
Then the length of the rectangle is given as,
2L = 3 x 4
L = 6 feet
The dimensions of her rectangular flower bed will be 4 feet by 6 feet.
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The figure shows two parallel lines AB and DE cut by the transversals AE and BD:
Which statement best explains the relationship between Triangle ABC and Triangle EDC ?
A. Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5
B. Triangle ABC is similar to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
C. Triangle ABC is congruent to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5
D. Triangle ABC is congruent to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
The sum of two numbers is 46 . the larger number is 12 more than the smaller number. what are the numbers?
The required number for the given arithmetic problem is 29 and 12.
Given that,
The sum of the two numbers is 46 . the larger number is 12 more than the smaller number. what the numbers are to be determined.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the number be x and y
According to the question,
x = y + 12 - - - - - (1)
x + y = 46 - - - - - - (2)
Substitute x in equation 2
y + 12 + y = 46
2y = 46 - 12
2y = 34
y = 17
mow put this y in equation 1
x = 17 + 12
x = 29
Thus, the required number for the given arithmetic problem is 29 and 17.
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Carlos Martin received a statement from his bank showing a balance of $56.75 as of March 15. His checkbook shows a balance of $87.37 as of March 20. The bank returned all the cancelled checks but two. One check was for $5.00 and the other was for $13.25. How much did Carlos deposit in his account between March 15 and March 20?
A fair coin is tossed 16 times. what is the probability that exactly 7 tails occur?
To calculate the probability of getting exactly 7 tails in 16 tosses of a fair coin, use the binomial probability formula with p = 0.5, q = 0.5, n = 16, and k = 7. Calculate C(16, 7) and then multiply it by (0.5^7) × (0.5^9) to find the probability.
Explanation:Calculating Probability of Exactly 7 Tails in 16 Coin Tosses
To find out the probability of getting exactly 7 tails when a fair coin is tossed 16 times, you can use the binomial probability formula. The formula for the binomial probability of getting exactly k successes (in our case, tails) in n trials (coin tosses) is given by:
P(X = k) = C(n, k) × (p^k) × (q^(n-k))
Where:
Here, the probability of getting a tail p is 0.5, the probability of not getting a tail q is also 0.5, n is 16, and k is 7. Substituting these values into the formula, we can calculate the probability of getting exactly 7 tails in 16 tosses of a fair coin.
The combination C(16, 7) can be calculated using the binomial coefficient formula or by using a calculator with binomial functions. Once we have the value of C(16, 7), we multiply it by (0.5^7) × (0.5^9) to get the probability. The final answer represents the probability of getting exactly 7 tails when a fair coin is tossed 16 times.
Ayesha has a theory about 2 digit numbers that have a larger tens digit than ones digit she says that reversing the digits and subtracting the reversed number from the original number will always generate a number that is a multiple of 9 is ayesha right? If so why do you think this works? If not,why not?
What is the equation of the blue graph?
given the following right triangle, what is the measure of angle B
need the arctan of the 2 lengths given
9/12 reduces to 3/4
arctan on the calculator is tan^-1
arctan(3/4) = 36.86989 degrees
round off the answer as needed
in circle p what is the measure of arc ab
Part A: Factor 3x2c2 + 2xc2 − 1c2. Show your work. (4 points)
Part B: Factor x2 − 2x + 1. Show your work. (3 points)
Part C: Factor x2 − 64. Show your work. (3 points)
plz help!!!!!!!!!!!!!!! thanks!!!!!!!!!!
Which of the following is equal to the rational expression when x does not equal 3 or -10? (x+5)(x-3)/(x-3)(x+10)
A x+5/x-3
Bx-3/x+10
Cx+5/x+10
Dx-3/x+5
Answer:
C. x+5/x+10
Step-by-step explanation:
Just had this question on A.P.E.X and C was correct!:) good luck on yall's studies you got this!
Abel and Zöe’s grandparents opened a savings account for an equal amount upon the birth of each child. Now, the values of their accounts could be found by the following expressions, where t represents the years since 2011.
Abel: y = 1266.77(1.03)t
Zöe: y = 1159.27(1.03)t
Based upon this information, find the difference in the children’s ages.
Abel is ___ years older than Zöe.
Suggestions: Find the ratio 1266.77/1159.26. What does that ratio represent in terms of powers of 1.03? You also can graph both equations and figure out the shift.
Answer:
Abel is 3 years older than Zöe.
Step-by-step explanation:
Abel and Zöe’s grandparents opened a savings account for an equal amount upon the birth of each child. Now, the values of their accounts could be found by the following expressions, where t represents the years since 2011.
Abel: y = 1266.77(1.03)^t
Zöe: y = 1159.27(1.03)^t
To find the difference in children's ages first we take ratio of 1266.77/1159.26
Ratio of 1266.77/1159.26= 1.09
now we write ratio in terms of powers of 1.03
1.03^t = 1.09
Take ln on both sides
t ln(1.03) = ln(1.09)
Divide both sides by ln(1.03)
t= 3
Abel is 3 years older than Zöe.
Candle stubs can be remoulded to form new candles. 6 stubs are required for each new candle. If there are 301 candle stubs, how many new candles can possibly be made IN TOTAL?