Bella's actual room dimensions are 18 feet by 12 feet, resulting in an actual area of 216 square feet. This was determined by applying the scale factor from the drawing to the actual room size.
To determine the actual dimensions of Bella's room based on her drawing, we first need to use the provided scale factor. According to the scale, 1 inch on the drawing is equal to 3 feet in actual size. We can calculate the actual dimensions by multiplying the length and width of the drawing by the scale factor.
The drawing is 6 inches long by 4 inches wide.
Actual length: 6 inches × 3 feet/inch = 18 feet
Actual width: 4 inches × 3 feet/inch = 12 feet
Now, to determine the actual area of Bella's room, we multiply the actual length by the actual width:
Actual area = actual length × actual width
Actual area = 18 feet × 12 feet = 216 square feet
(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]
Write the complex number in the form a + bi. 5/2(cos 150° + i sin 150°)
Answer:
It's actually this
Step-by-step explanation
(told it to convert to rectangular form)
The complex number 5/2(cos 150° + i sin 150°), in the form a + bi, can be written as -(5√3)/4 +i(5/4).
What are complex numbers?Complex numbers are used to define imaginary numbers, that is, the square roots of negative numbers. √-1 is represented as i.
How to solve the question?In the question, we are given a complex number 5/2(cos 150° + i sin 150°), and are asked to represent it in the form a + bi.
We know that complex numbers can be written in two forms, a + bi or r(cos θ + i sin θ).
The relation between these are:
r² = a² + b²,
a = r cos θ, b = r sin θ,
tan θ = b/a.
So, comparing 5/2(cos 150° + i sin 150°), to r(cos θ + i sin θ), we can say that r = 5/2, and θ = 150°.
Therefore, a = r cos θ = (5/2) cos 150° = (5/2) (-cos 30°) = -(5√3)/4
b = r sin θ = (5/2) sin 150° = (5/2) sin 30° = 5/4.
Therefore, the complex number 5/2(cos 150° + i sin 150°), in the form a + bi, can be written as -(5√3)/4 +i(5/4).
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Quadrilateral jklm is a rhombus. the diagonals intersect at n. if the measure of angle jkl is 104°, find the measure of angle jkn.
Answer:
It is 52 degrees
Step-by-step explanation:
In a rhombus each diagonal bisects a pair of opposite angles.
Angle JKN is half of angle JKL
Angle JKN = 52°
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.
What is the equation of the blue graph?
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?
Glenn needs 20 minutes to clean his room. If his little sister Veronika pulls things out while he is cleaning, it takes 60 minutes for him to clean the room. How many minutes does it take for Veronika to pull everything out?
The rate of Glenn in finishing a job would be equivalent to:
Rate (G) = 1 job / 20 minutes
While the rate of Veronika is:
Rate (V) = 1 job / x ---> x is the unknown
Where 1 job for Glenn means completely cleaning his room while 1 job for Veronika means pulling out everything. Therefore the equation to use would be:
1 / 20 – 1 / x = 1 / 60
The rate of Veronika is subtracted from the rate of Glenn since Veronika is slowing Glenn down. Solving for x:
Multiply both sides by 60 x
(1 / 20 – 1 / x = 1 / 60) * 60 x
3 x – 60 = x
2 x = 60
x = 30
Therefore it takes 30 minutes for Veronika to pull everything out.
I will give you the simple version, if it takes 30 min for the brother to clean and the sister takes 20 minites to mess it up before he cleaned, then the sister messed the room up for 30 min because 30x2= 60.
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
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.
which repeating decimal is equal in value to the fraction below? 8/9
a) 0.7777777
b) 0.8888888
c) 0.5555555
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?
line ab contains points A(8,-4) and B(1,-5). the slope of line ab is
in circle p what is the measure of arc ab
The weights of bags of pet food are distributed normally about the mean, 50 lb. The standard deviation is 0.2 lb. In a group of 20 bags, about how many would you expect to be within one standard deviation from the mean?
Using the empirical rule for normal distributions, approximately 68% of the data falls within one standard deviation of the mean. Therefore, in a group of 20 bags of pet food with a normal distribution, about 14 bags are expected to be within one standard deviation from the mean.
Explanation:The question involves the concept of a normal distribution in statistics, and specifically, how it applies to the weights of bags of pet food. Given that the bags have a mean weight of 50 lb and a standard deviation of 0.2 lb, we can use the empirical rule (68-95-99.7 rule) for normal distributions. This rule states that approximately 68% of the data in a normal distribution falls within one standard deviation of the mean.
In this scenario, we have a group of 20 bags of pet food. To find out how many bags we would expect to fall within one standard deviation from the mean, we would calculate 68% of 20:
Expected number of bags within one standard deviation = 0.68 × 20 = 13.6
Rounding to the nearest whole number, we can expect about 14 bags to fall within one standard deviation from the mean.
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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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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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!
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 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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The sum of two numbers is twice their difference. the larger number is 2 more than twice the smaller. find the numbers. smaller number 1 larger number 3
The smaller number is 1 and the larger number is 3.
What is a linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Let the numbers be x and y.
The sum of two numbers is twice their difference.
(x + y) = 2(x -y)
The larger number is 2 more than twice the smaller.
That means,
y = x + 2.
Then,
(x + x + 2) = 2(x + 2 - x)
2x + 2 = 4
x = 1
And y = 3
Therefore, the numbers are 1 and 3.
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Please help me!!! I'm super confused
The city is planning to install streetlights and wants five lights along a walkway of 60 yards. if there is a light at the beginning and at the end of the walkway and the lights are evenly spaced, what is the distance between each light
formula one race cars reach speeds of approximately 100 meters Per second. what is the speed in meters per minute?
When n is divided by 7, the remainder is 4. What is the remainder when n+3 is divided by 7
The graph below represents the price of the banana at one store. What is the constant of proportionality?
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. :)
In the middle of the page draw an equilateral triangle with 2 inch sides and the bottom parallel to the bottom of the page. From the center of the right side draw two parallel lines an inch apart and an inch long. Draw a line from the end of one of the parallel lines to the end of the other parallel line. Which direction is the arrow pointing
Solution:
Drawn an equilateral triangle of side 2 inches.
One side is parallel to Bottom of page.
Then from the center of the right side draw two parallel lines an inch apart and an inch long.
Then drawn a line from the end of one of the parallel lines to the end of the other parallel line.
The Arrow is pointing in East of South or South of East and North of West or West of North Direction.