On a scatter plot, a positive correlation indicates an increasing relationship between two variables, represented by an upward slope. Negative correlation shows a decreasing relationship, represented by a downward slope. The strength of these relationships is determined by the correlation coefficient.
Explanation:In a scatter plot, a positive correlation and a negative correlation represent different types of relationships between two variables. A positive correlation suggests that as one variable increases, the other also increases. For example, height and weight are usually positively correlated, as the taller a person is, the more they tend to weigh.
On the other hand, a negative correlation means that as one variable increases, the other decreases. Graphically, this is represented by a downward slope from left to right. An example of this is the relationship between hours of sleep and tiredness, more hours of sleep typically correspond to less tiredness.
The strength of these correlations are determined by the correlation coefficient. A correlation coefficient closer to 1 or -1 indicates a stronger relationship, and a coefficient closer to 0 indicates a weaker relationship.
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{3, 4, 7} list all the subsets.
The subsets of {3, 4, 7} are {}, {3}, {4}, {7}, {3, 4}, {3, 7}, {4, 7}, {3, 4, 7}
Explanation:
When listing all the subsets of {3, 4, 7}, we include the empty set {}, as well as all the subsets that can be formed by selecting one or more elements from the original set. In this case, the subsets are:
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Daniel ate 0.55 of a candy bar. Which fraction represents the part of the candy bar that Daniel ate?
A. 10/22
B. 11/20
C. 2/5
D. 3/4
E. 11/40
Answer:
The answer is B 11/20
Step-by-step explanation:
To transform a decimal to a fraction you must do the following:
1. Multiply by an specific power of 10 until your decimal becomes a whole number. In this case 0.55 we multiply by 10 ^2 or 100 and we obtain 55.
2 Divide the decimal by this same power of 10 so that you do not change the original value. For example
0.55 *(100/100) = 55/100 As you see Im multiplying and dividing by 100 ( thats equivalent to 1 so it doesnt change the original number)
3 Simplify the fraction
To simplify your fraction you must find the Greatest Common Factor of 55 and 100. For doing this, you only perform a prime factorization. Divide 55 and 100 by the smallest common prime factor, besides 1. (For this case is 5) until you arrive to two number without common prime factors.
55/5 = 11
100/5 = 20
As 11 and 20 have no common prime factors it is the most simplified fraction
A function has a domain of {1, 3, 5, 7} and a range of {2, 4, 6}. Which set of ordered pairs represents this function?
A.{(1, 2), (3, 4), (5, 6), (7, 2)}
B.{(1, 2), (3, 6), (5, 4), (5, 2)}
C.{(1, 2), (3, 2), (5, 2), (7, 2)}
D.{(1, 4), (3, 4), (5, 6), (7, 6)}
WHO LIKES PARABOLAS 3 MULTIPLE CHOICE
1. What is the vertex of the parabola? y−3=12(x+5)^2
2. The equation of a parabola is y=12x2+6x+23 .
What is the equation of the directrix?
y = 5.5
y = 4.5
y = 2
y = 0.5
3.The equation of a parabola is 132(y−2)2=x−1 .
What are the coordinates of the focus?
(−7, 2)
(1, 10)
(1, −6)
(9, 2)
The equation of a circle is x2 − 4x + y2 + 8y − 29 = 0. what are the center and radius of the circle? enter your answers in the boxes.
Final answer:
The center of the circle described by the equation x2 − 4x + y2 + 8y − 29 = 0 is (2, -4), and the radius is 7 units.
Explanation:
The equation of a circle given in the question is x2 − 4x + y2 + 8y − 29 = 0. To find the center and radius of the circle, we will complete the square for both x and y terms.
This involves adding and subtracting the squared half of the coefficients of x and y to complete the square:
(x2 - 4x + 4) - 4 + (y2 + 8y + 16) - 16 = 29 + 4 + 16
(x - 2)2 + (y + 4)2 = 49
This equation is now in standard circle form, which is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius.
The center of the circle is therefore at (2, -4) and the radius is √(49) = 7 units.
Rectangle ABCD is shown below with line EF passing through the center:
If rectangle ABCD is dilated by a scale factor of five about the center of the rectangle to create rectangle A'B'C'D', dilated line E'F' will
A: be parallel to the original line
B: shift five units to the right
C: be perpendicular to the original line
D: lie on the same line as the original
Answer:
D lie on thesame line as the original
Step-by-step explanation:
I took the test and hurray! It was correct
Complete the solution of the equation. Find the value of Y when X equals 2. 2x - 2y = 22
In the data set below, what is the mean absolute deviation?4461526If the answer is a decimal, round it to the nearest tenth.mean absolute deviation (MAD):
how do I solve this?
two negative integers have a sum of -18 and a product of 80. what are the integers?
An item is priced at $13.04. If the sales tax is 5%, what does the item cost including sales tax? If necessary, round to the nearest cent.
A.
$13.56
B.
$13.24
C.
$12.39
D.
$13.69
Before a renovation, a movie theater had 111 seats. After the renovation, the theater has 154 seats. What is the approximate percentage increase of the number of seats in the theater? If necessary, round to the nearest tenth of a percent.
A. 28.1% B. 38.7% C. 43.3% D. 24.8%
What is the inverse of the function f(x)= 19/x^3 ?
A barn is an atomic unit of area equal to 10–28 m2. what is the surface area of the earth expressed in units of barn? assume the earth is a sphere with a radius of km. (the surface area of a sphere is 4πr2.)
the number of mosquito at the beginning of the summer was 4,000. the population of mosquito is expected to grow at a rate of 25% a month . how many mosquitoes will there be after 4 months
Using the formula for exponential growth and given an initial population of 4,000 mosquitoes with a 25% monthly growth rate, the mosquito population is expected to grow to approximately 9,766 after 4 months.
Explanation:The question involves calculating the growth of a mosquito population over a period, specifically after 4 months, given an initial population of 4,000 mosquitoes and a monthly growth rate of 25%. To find the population after 4 months, we use the formula for exponential growth:
P = P0 × (1 + r)n
where P is the population at the end, P0 is the initial population, r is the growth rate (expressed as a decimal), and n is the number of time periods.
Substituting the values, we get:
P = 4000 × (1 + 0.25)4
P = 4000 × (1.25)4
After calculating, we find that P = 9765.63. Thus, the population of mosquitoes after 4 months is expected to be approximately 9,766.
The mosquito population grows from 4,000 to approximately 9,766 over 4 months with a 25% monthly increase.
The initial number of mosquitoes is 4,000, and the population increases at a rate of 25% per month. To find the population after 4 months, we use the formula for compound interest:
P = P0 [tex](1 + r)^{t[/tex]
where:
P0 is the initial populationr is the growth ratet is the time in monthsGiven:
P0 = 4,000r = 25% or 0.25t = 4Substitute these values into the formula:
P = 4000 × (1 + 0.25)⁴
First, calculate (1 + 0.25):
1 + 0.25 = 1.25
Then, raise this to the power of 4:
(1.25)⁴ = 2.4414
Finally, multiply by the initial population:
P = 4000 × 2.4414 = 9765.6
Thus, the mosquito population after 4 months is approximately 9,766.
Which of the following have been used to measure wealth in early societies?
Cows
Dogs
Grain
Land
Metals
The answer is cows, metals, land, and grains.
Which of the following is equivalent to the midpoint between the points (8, -9) and (0, 5)?
(4, -2)
(4, 2)
(-2, 4)
(2, 4)
The perimeter of a rectangle is 30 centimeters. The width of the rectangle is 6 centimeters. How long is the rectangle?
If prices increase at a monthly rate of 1.1%, by what percentage do they increase in a year, What is the annual inflation rate
Final answer:
To find the annual inflation rate when prices increase at a monthly rate of 1.1%, you use the formula for compounding interest, resulting in an approximate annual rate of 13.97%.
Explanation:
If prices increase at a monthly rate of 1.1%, to calculate the annual inflation rate, you should consider the compounding effect over the year. The general formula for finding the total percentage increase over multiple periods when compounded at each period is:
(1 + rate)^number of periods - 1.
In this case, the monthly rate is 1.1%, or 0.011 when expressed as a decimal. The number of periods (months) in a year is 12. Plugging these values into the formula gives:
(1 + 0.011)^12 - 1,
which calculates to:
1.011^12 - 1 = 0.1397 or 13.97%.
So, the annual inflation rate when prices increase at a monthly rate of 1.1% is approximately 13.97%.
Select the statement that is true. Answer Choices The sum of 0.12x2+0.3⎯⎯⎯ and 1.5x2−0.75 is 1.62x2+0.416 . -0.45x2+0.9 subtracted from 2.5x2−7.32 is -2.95x2+8.22 . The difference of 18.94x−0.4⎯⎯⎯ and -10.2x+4.5 is 8.74x−4.94⎯⎯⎯ . The product of 0.6⎯⎯⎯x+3.4 and -6x+5.7 is -4x2−16.6x+19.38 .
Due tomorrow. Please help!!!!
Anyone know this geometry question? Will give brainiest
If f(x) =3x-2, find f-1(x)
To find the inverse of a function, follow these steps: replace f(x) with y, interchange x and y, solve for y, and replace y with f-1(x). Applying these steps to the given function f(x) = 3x - 2 results in the inverse function f-1(x) = (x + 2)/3.
Explanation:To find the inverse of a function, we can follow these steps:
Replace the function notation f(x) with yInterchange x and y in the equationSolve the resulting equation for yReplace y with f-1(x)Let's apply these steps to the given function f(x) = 3x - 2:
Replace f(x) with y: y = 3x - 2Interchange x and y: x = 3y - 2Solve for y: x + 2 = 3yTherefore, the inverse of the function f(x) = 3x - 2 is f-1(x) = (x + 2)/3.
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The inverse function of [tex]\( f(x) = 3x - 2 \)[/tex] is [tex]\( f^{-1}(x) = \frac{x + 2}{3} \).[/tex]
To find the inverse function [tex]\( f^{-1}(x) \)[/tex] for the given function [tex]\( f(x) = 3x - 2 \)[/tex], follow these steps:
Start with the original function:
[tex]\[ y = 3x - 2 \][/tex]
Swap y and x to find the inverse:
[tex]\[ x = 3y - 2 \][/tex]
Solve for y:
[tex]\[ x + 2 = 3y \][/tex]
[tex]\[ y = \frac{x + 2}{3} \][/tex]
Rewrite y as [tex]\( f^{-1}(x) \):[/tex]
[tex]\[ f^{-1}(x) = \frac{x + 2}{3} \][/tex]
So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[f^{-1}(x) = \frac{x + 2}{3}\][/tex]
Complete Question:
If [tex]f(x) =3x-2[/tex], find [tex]f^{-1}(x)[/tex]
Chauncey has 42 coins, all dimes and quarters. the total value of all these coins is $5.70. how many dimes does he have?
To determine the number of dimes Chauncey has, you can use the system of equations stemming from the total number of coins and their total value. Following through with the calculations, it turns out that Chauncey has 32 dimes.
Explanation:The subject at hand revolves around the concept of linear equations. Given that Chauncey has 42 coins (all dimes and quarters) worth $5.70, you can use a system of equations to figure out the number of each type of coin.
First, let d be the number of dimes and q be the number of quarters. The total number of coins is 42, so the first equation is d + q = 42.Second, a dime is worth $0.10 and a quarter is worth $0.25. Since the total value of coins is $5.70, another equation you can form is 0.10d + 0.25q = 5.70.Having formed this system of two equations, you can solve it by multiplying the first equation by 0.10, which gives 0.10d + 0.10q = 4.2.Subtract this new equation from the second equation: 0.10d + 0.25q - 0.10d - 0.10q = 5.70 - 4.2. Simplify this to 0.15q = 1.5.Divide each side by 0.15, then q = 10. Substitute q = 10 into the first equation to solve for d. This gives d = 42 - 10 = 32.So, Chauncey has 32 dimes.
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What is the equation for a line that passes through the points (-3,-3) and (6,21)?
You are painting a ceiling in a room. The room measures 30 feet by 40 feet. One gallon of paint costs $25 and covers 200 square feet. How much will it cost to paint the ceiling?
A. $6
B. $17.50
C. $150
D. $1,200
Answer:
C. $150
Step-by-step explanation:
we know that
the area of the room=30*40------> 1200 ft²
1 gallon of paint cover----------------> 200 ft²
x---------------------------> 1200 ft²
x=1200/200------> x=6 gallons
1 gallon cost------------> $25
6 gallons-----------> x
x=6*25-----> x=$150
the answer is
the option C. $150
A professor wants to arrange his books on a shelf. he has 30 books and only space on the shelf for 20 of them. how many different 20-book arrangements can he make using the 30 books? this is an example of a problem that can be solved using which method?
Answer: Total arrangement are 30045015
Given problem will be solved with help of combination.
Step-by-step explanation:
When we find the arrangement in which the order does not matter then we use combination,
Here, we have to find the possible arrangement in which order does not matter,
Thus, we will use combination to find the answer.
Here the total number of books = 30
A self contains, the number of book = 20,
Hence, the total arrangement of 20 books out of 30 books
[tex]=^{30}C_{20}[/tex]
[tex]=\frac{30!}{20!(30-20)!}[/tex]
[tex]=\frac{30\times 29\times 28\times 27\times 26\times 25\times 24\times 23\times 22\times 21}{10!}[/tex]
[tex]=\frac{4.9557887\times 10^{12} }{3628800 }=30045015 [/tex]
Urgent!!! What is the slope-intercept form of the equation of the line that passes through the points (2, 7) and (4, −1) ?
Best rentals charges a daily fee plus a mileage fee for renting its cars. barney was charged $81 for 3 days and 300 miles, while mary was charged $145 for 5 days and 600 miles. what does best rental charge per day and per mile?
The population of a town increased from 5,400 to 6,000 people. What was the percent of the increase?