A family has ninenine children. if this family has exactly threethree boysboysâ, how many different birth and gender orders areâ possible

Answers

Answer 1
This is the problem of how many permutations the set bbbgggggg has. The set has size n=9, and you choose p=3 boys.

You can calculate it as:

[tex]\binom{9}{3} = \frac{9!}{3! \cdot 6!} = \frac{362880}{6\cdot720} = 84[/tex]



Related Questions

To which part of the prism are the arrows pointing

Answers

The arrows are pointing in the vertices of the prism. Vertices are the corners of an object which faces are the 2 dimensional sides of an object and the edges are the lines link 2 vertices. Vertex classically defines a corner or a point where lines met. Vertex is likewise from time to time used to designate the 'top' or high point of to some degree. Another example such as the vertex of an isosceles triangle which is the 'top' angle conflicting its base. 

If you put down 20% on a $7000 car and pay monthly payments of $109.40 for 60 months, what is the total price of the car?

Answers

$7000 x 20% = $1400
$109.40 x 60 = $6564
$1400 + $6564 = $7964

Answer:

7964

Step-by-step explanation:

(20 points) You are writing a research paper on plant cells. You got 48,600,000 results on the online search. How do you write 48,600,000 in scientific notation?

Answers

i'm pretty sure the answer is D
[tex]48,600,000=4.86*10,000,000 = 4.86*10^7[/tex]

If a triangle has legs measuring 8 inches and 15 inches and has a hypotenuse measuring 17 inches, what is the ratio, in simplest form, of the shorter leg to the hypotenuse?

Answers

ratio of shorter leg to the hypotenuse = 8/17

hope that helps

The function f(x) is represented by this table of values .Match average rate of change of f(x) with corresponding intervals

Answers

Note:
If fx(x) changes from f(x₁) to f(x₂), the rate of change is
Rate = [f(x₂) - f(x₁)]/(x₂ - x₁)

From the table, we can compute rates of change as follows:
Change in x  Change in f(x)   Change in x    Rate
-----------------   --------------------   -----------------  ---------
    [-4,-2]          0 - (-12) = 12      0 - (-2) = 2        6
    [-2, 1]           3 - 0 = 3            1 - (-2) = 3         1
    [-3, 1]           3 - (-5) = 8         1 - (-3) = 4         2
    [-4, 0]          4 - (-12) = 16      0 - (-4) = 4        4


You give your friend a head start of 20 feet in a race. A linear equation representing your friend’s progress (in feet) after x seconds is y = 9x + 20. A linear equation representing your progress (in feet) after x seconds is y = 9x. Will you catch up to your friend? Explain.

Answers

No. You are running the same speed as your friend and your friend has a head start.
By looking at the equation : The two lines does not have an intersection point .

To catch up to your friend or not in a race explained with equations and steps.

The question is: Will you catch up to your friend? Explain.

Step-by-step explanation:

Friend's progress equation: y = 9x + 20

Your progress equation: y = 9x

To catch up, set the equations equal: 9x + 20 = 9x

Solve for x: 20 = 0 (This equation has no solution)

You will not catch up to your friend.

Alicia drove 265 miles in 5 hours What is the average rate that she traveled 49 miles per hour 51 miles per hour 53 miles per hour 55 miles per hour

Answers

265 / 5 = 53 miles per hr

The table below shows the surface area y, in square feet, of a shrinking lake in x days:


Time (x)
(days) 5 10 15 20
Surface area (y)
(square feet) 90 85 70 61


Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the lake. [Choose the value of the correlation coefficient from −1, −0.98, −0.5, −0.02.] (4 points)

Part B: What is the value of the slope of the graph of surface area versus time between 15 and 20 days, and what does the slope represent? (3 points)

Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)

Answers

The scatter graph of the data is shown in the first picture below

The 'line of best fit' shows a negative gradient

Part A: The most likely coefficient is -0.98. 
If the coefficient is -1, then each point would be exactly on the straight line (which they are not as shown on the graph). The graph however still shows a strong negative coefficient. It can be seen from the close distance of each point from the line of best fit. So -0.5 and -0.02 is unlikely as they show weak negative correlation

Part B: Refer to the second picture to see the horizontal and vertical distance between day 15 and day 20

The horizontal distance is 5 units
The vertical distance is read between 61 and 71.5, hence it's 10.5
The slope = Vertical distance ÷ Horizontal Distance = 10.5÷5 = 2.1
The 'downhill' slope shows a negative gradient, hence the value of the slope is -2.1
The value of the slope shows that the surface area of the lake shrinks by 2.1 for every one day

Part C: The data in the table represents the relation between two variables. Since one variable doesn't cause the change in the other variable, the data table represents correlation rather than a causation. 

Find the exact length of the curve. y = 3 + 2x3/2, 0 ≤ x ≤ 1

Answers

The exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex] is [tex]\(\frac{2}{27} (10\sqrt{10} - 1)\)[/tex].

To find the exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex], we can use the formula for arc length of a curve:

[tex]\[ L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx \][/tex]

where a and b are the lower and upper bounds of the interval, respectively.

First, we need to find [tex]\(\frac{dy}{dx}\)[/tex], which represents the derivative of y with respect to x:

[tex]\[ \frac{dy}{dx} = \frac{d}{dx}(3 + 2x^\frac{3}{2}) = 0 + 3x^\frac{1}{2} = 3\sqrt{x} \][/tex]

Next, we substitute this derivative into the formula for arc length:

[tex]\[ L = \int_{0}^{1} \sqrt{1 + (3\sqrt{x})^2} dx = \int_{0}^{1} \sqrt{1 + 9x} dx \][/tex]

Now, we need to integrate [tex]\(\sqrt{1 + 9x}\)[/tex]L with respect to \(x\). We can do this by making a substitution. Let u = 1 + 9x, then du = 9dx and \(dx = \frac{du}{9}\). Substituting these into the integral, we get:

[tex]\[ L = \frac{1}{9} \int_{1}^{10} \sqrt{u} du \][/tex]

Now, we can integrate [tex]\(\sqrt{u}\)[/tex]:

[tex]\[ L = \frac{1}{9} \left[\frac{2}{3}u^\frac{3}{2}\right]_{1}^{10} = \frac{2}{27} \left[10^\frac{3}{2} - 1^\frac{3}{2}\right] \][/tex]

[tex]\[ L = \frac{2}{27} (10^\frac{3}{2} - 1) \][/tex]

[tex]\[ L = \frac{2}{27} (10\sqrt{10} - 1) \][/tex]

So, the exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex] is [tex]\( \frac{2}{27} (10\sqrt{10} - 1) \)[/tex].

ms johnson and ms smith were folding report cards to send home to parents. the ratio of the number of report cards ms johnson folded to the number of report cards ms smith folded is 2:3. At the end of the day , ms Johnson and ms smith folded at total of 300 report cards. How many did each person fold?

Answers

First you would divide 300 by 5, you would add 2 and 3 together, to get 60. Then multiply 2 and 3 by 60 and you would get 120 and 180. Add those two together and you will get 300. So Ms. Johnson folded 120 report cards while Ms. Smith folded 180 report cards.

THIS IS TIMED AND I NEED HELP!!!
Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1? (1, 0) and (0, –1) (–2, –3) and (1, 0) (0, –3) and (1, 0) (–3, –2) and (0, 1)

Answers

y = x^2 + 2x - 3
y = x - 1

x^2 + 2x - 3 = x - 1
x^2 + 2x - x - 3 + 1 = 0
x^2 + x - 2 = 0
(x + 2)(x - 1) = 0

x + 2 = 0           y = x - 1
x = -2                y = -2 - 1
                         y = -3
 
x - 1 = 0            y = x - 1
x = 1                 y = 1 - 1
                         y = 0

ur solutions are : (-2,-3) and (1,0)

A. 15
B. 125
C. 135
D. 45

Answers

The angle adjacent to 9x and on same lime as the angle 3x  = 3x.
They are corresponding angles)

so 3x + 9x = 180

x = 180/12 = 15 
So angle 1 = 3x = 3*15 = 45 degrees


D
9x + 3x = 180°
12x = 180°
x = 15°

9x + 1 = 180°
9(15°) + 1 = 180°
135° + 1 = 180°
1 = 180° - 135° = 45°
Answer is D

Hope it helped!


Which statement is 1?


option 5 btw is none of these

Answers

It is the fourth one because proofs always start with the given information

Mateo is studying a human hair with a diameter of 6.5 x 10^-4 inches and a horse hair with a diameter of 1.3 x 10^-3 inches. Which statement is true?

A.The horse hair is 2 times as thick as the human hair.

B.The horse hair is 5 times as thick as the human hair

C.The human hair is 2 times as thick as the horse hair

D.The human hair is 5 times as thick as the horse hair

Answers

[tex] \cfrac{1.3*10^{-3}}{6.5*10^{-4}}= 0.2*10^1=2[/tex]

A.The horse hair is 2 times as thick as the human hair. 

Answer:

A.The horse hair is 2 times as thick as the human hair.

Step-by-step explanation:

We have been given that Mateo is studying a human hair with a diameter of [tex]6.5\times 10^{-4}[/tex] inches and a horse hair with a diameter of [tex]1.3\times 10^{-3}[/tex] inches.

Since proportions states that two fractions are equal, So we will use proportions to solve our given problem.

[tex]\frac{\text{Diameter of horse hair}}{\text{Diameter of human hair}}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}[/tex]

[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}\times \text{Diameter of human hair}[/tex]

Now we will quotient rule of exponents to simplify our given problem.

[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3--4}}{6.5}\times \text{Diameter of human hair}[/tex]

[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{-3+4}}{6.5}\times \text{Diameter of human hair}[/tex]

[tex]\text{Diameter of horse hair}=\frac{1.3\times 10^{1}}{6.5}\times \text{Diameter of human hair}[/tex]

[tex]\text{Diameter of horse hair}=\frac{13}{6.5}\times \text{Diameter of human hair}[/tex]

[tex]\text{Diameter of horse hair}=2\times \text{Diameter of human hair}[/tex]

We can see that the diameter of horse hair is 2 times the diameter of human hair. Therefore, the horse hair is 2 times as thick as the human hair and option A is the correct choice.

Express -2 in triganomic form

Answers

[tex]\bf -2\implies -2+0i\implies \stackrel{a}{-2}+\stackrel{b}{0}i\quad \begin{cases} r=\sqrt{a^2+b^2}\\ r=\sqrt{(-2)^2+0^2}\\ r=2\\ ----------\\ \theta =tan^{-1}\left( \frac{b}{a} \right)\\ \theta =tan^{-1}\left( \frac{0}{-2} \right)\\ \theta =tan^{-1}(0)\\ \measuredangle \theta =0~,~\pi \end{cases}[/tex]

now, there are two possible angles for that tangent... however, let's look at our a,b components.

"a" is negative whilst "b" is positive, so is not 0 then, thus

[tex]\bf -2+0i\implies r[cos(\theta )+i~sin(\theta )]\implies 2[cos(\pi )+i~sin(\pi )][/tex]

Final answer:

To express -2 in trigonometric form, we find the magnitude (absolute value) and the argument (angle) of the complex number.

Explanation:

The trigonometric form of a complex number is expressed in the form r(cosθ + isinθ), where r is the magnitude of the complex number and θ is the argument or angle.

In this case, to express -2 in trigonometric form, we first find the magnitude, which is the absolute value of -2, so |-2| = 2. The argument can be found using the arctan function, which is θ = arctan(b/a), where a is the real part and b is the imaginary part.

For -2, the real part is -2 and the imaginary part is 0. Thus, the argument is θ = arctan(0/(-2)) = arctan(0) = 0. Therefore, -2 in trigonometric form is 2(cos0 + isin0), which simplifies to just 2.

Are the traingles congruent? Why or why not?

Yes, A ≅ D and AB ≅ DE
Yes, they are congruent by either AAS or ASA.
No, C is not congruent to any angle in DEF.
No, the congruent sides do not correspond.

Answers

the answer is A) 
Yes, A ≅ D and AB ≅ DE

Yes , A ≅ D and AB ≅ DE

Yes, they are congruent by either AAS or ASA.

What are Congruent Triangles?

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

•  Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

•  Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

•  A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

From the given data ,

AB ≅ DE

and , ∠BAC = 33°

∠EDF = 33°

Therefore by rules of congruent triangles

The two angles are the same and the corresponding sides are same

Hence , The two triangles ΔABC and ΔDEF are congruent

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Which expression is equivalent to 34 ⋅ 3−9?

1 over 3 to the 13th power
1 over 3 to the 5th power
35
313

Answers

313 because you multiply then you subtract

Answer:

b.1 over 3 to the 5th power.

Step-by-step explanation:

We are given that an expression

[tex]3^4\cdot 3^{-9}[/tex]

We have to find that which expression is equivalent to given expression

[tex]3^4\cdot 3^{-9}[/tex]

We know that [tex]a^b+a^c=a^{b+c}[/tex]

Using this identity

Then, we get [tex]3^4\cdot 3^{-9}=3^{4-9}=3^{-5}[/tex]

[tex]3^4\cdot 3^{-9}=\frac{1}{3^5}[/tex]

Using [tex]a^{-b}=\frac{1}{a^b}[/tex]

Hence, option b is true.

Answer:b.1 over 3 to the 5th power.

A jacket that regularly cost $40 is on sale for $32 what is the percent decrease in the price of the jacket?

Answers

from 40 to 32, is just 8 bucks, so the jacket went from 40 to 8, so is discounted by 8 bucks.

now, if we take 40 to be the 100%, how much is 8 off of it in percentage?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 40&100\\ 8&x \end{array}\implies \cfrac{40}{8}=\cfrac{100}{x}[/tex]

solve for "x".
20% off the $40 dollar jacket.

Roger owns a one acre piece of land . The length of the land is 484 feet. What is the width of his property

Answers

1 acre = 43560 square feet

43560 = 484 * X

X=43560/484 = 90

the width = 90 feet

Answer:

90 feet

Step-by-step explanation:

The sum of two numbers is 49 . the smaller number is 17 less than the larger number. what are the numbers?

Answers

Let the larger number be x
So the smaller number will be x-17
Since the sum of the two numbers is 49
x-17+x=49
2x-17=49
2x=49+17
2x=66
x=33
The larger number is 33 while the smaller number is 33-17=16

Final answer:

To solve the student's algebra problem, we defined variables, set up an equation based on the given conditions, and then solved for the larger number. Ultimately, we found the two numbers to be 33 and 16.

Explanation:

The student asked a problem that involves finding two numbers given that their sum is 49 and the smaller number is 17 less than the larger number. To solve this problem, we will use algebra.

Let the larger number be x and the smaller number be x - 17. According to the problem, the sum of these two numbers is 49:

x + (x - 17) = 49

Combine like terms: 2x - 17 = 49

Add 17 to both sides: 2x = 66

Divide by 2: x = 33

Since the larger number is 33, the smaller number is 33 - 17, which is 16.

Therefore, the two numbers are 33 and 16.

Suppose that a colony of bacteria starts with 1 bacterium and doubles in number every half hour. how many bacteria will the colony contain at the end of 24

Answers

let [tex]a_n[/tex] represent the number of bacteria after [tex] \frac{n}{2} [/tex] hours.

so

[tex]a_0[/tex] is the number of bacteria after 0/2 = 0 hours

[tex]a_1[/tex] is the number of bacteria after 1/2 hours

[tex]a_2[/tex] is the number of bacteria after 2/2 = 1 hours and so on


so if we list a few terms of this sequence, we have:

[tex]a_0=1[/tex]

[tex]a_1=1*2[/tex]

[tex]a_2=1*2*2[/tex]

[tex]a_3=1*2*2*2[/tex]

[tex]a_4=1*2*2*2*2[/tex]


so clearly, [tex]a_n[/tex], the number of bacteria after [tex] \frac{n}{2} [/tex] hours, is equal to [tex] 2^{n} [/tex].
 

 [tex]a_4_8[/tex] is the number of bacteria after
 
[tex]\frac{n}{2}=\frac{48}{2}= 24[/tex] hours.

Thus, we calculate  [tex]a_4_8[/tex], which is [tex] 2^{48} [/tex].


Answer: the number of bacteria after 24 hours is [tex] 2^{48} [/tex].

Final answer:

A colony of bacteria that starts with 1 bacterium and doubles in number every half hour will contain approximately 281,474,976,710,656 bacteria at the end of 24 hours.

Explanation:

The number of bacteria in a colony that starts with 1 bacterium and doubles in number every half hour can be calculated using the formula 2ⁿ, where n is the number of generations. Since each generation is half an hour, there are 48 generations in 24 hours. Plugging in n=48 into the formula, we get 2⁴⁸, which is approximately 281,474,976,710,656 bacteria.

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What is equivalent to xy/a - 1/b

Answers

The steps in achieving the answer for the simplification are as follows:

1. The least common multiple of the denominators of the terms of the given is ab.

2. Multiply the expression with ab, such that,

                              (xy/a - 1/b) x (ab)

3. Simplifying,
                                 xyb - a

4. Writing ab as the denominator of the expression in number, we get the final answer which is equal to,
                               (xyb - a)/ab

Melanie is flying from washington,
d.c., to seattle. her flight leaves at 10
a.m. when her plane lands, the pilot announces that it is 2 p.m. in seattle. how long did her flight take

Answers

In order to answer this, you must know how to read or tell time. I'm sure you do. The typical format of time is the 12-hour format. That is 12 hours in the morning and 12 hours in the afternoon. You just simply have to count from 10 in the morning, until you reach 2 in the afternoon. That would be 11, 12, 1 and 2. You passed 4 numbers in the clock. Therefore, her flight took 4 hours.

f(x) = 16x4 – 81 = 0 Select all of the zeroes of the function.
3/2
-3/2
3/2i
-3/2i

Answers

the way to figure this one out is move the 81 over to the other side so you have the equation 16x^4 = 81.  Since 81 is not divisible by 16 you have to think of another way to simplify.  16 is a perfect square, x^4 is a perfect square, and 81 is a perfect square.  So take the square root of both sides to begin the simplification.  4x^2 = 9. Divide both sides by 4 to get x^2 = 9/4. 9 and 4 are both perfect squares, so undo the square on the x by taking the square root of both sides: x = +/- 3/2.

Here we want to find all the zeros of the function f(x) = 16*x^4 - 81.

The zeros are:

x = 3/2x = -3/2x = (3/2)*ix = (-3/2)*i

First, for a given function f(x), we define the zeros as the values of x such that:

f(x) = 0.

Then we must solve:

f(x) = 16*x^4 - 81 = 0

Solving this for x leads to:

16*x^4 = 81

x^4 =  81/16

x^2 = ±√(81/16) = 9/4

x = ±√±(9/4) = ±3/2 and ±(3/2)*i

So there are 4 zeros, and these are:

x = 3/2x = -3/2x = (3/2)*ix = (-3/2)*i

Where the two complex zeros come from evaluating the second square root on -9/4.

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the function f (x) =830(1.2)x represents the number of students enrolled at a university xyears after it was founded. each year the number of students is ----- the number the year before

Answers

f(x)=830(1.2)^x

Each year the number of students is 1.2 times the number the year before.  Or you could say that each year the enrollment increases by 20%.
Answer: just did the quiz and the correct answer is indeed 1.2

Step-by-step explanation: Apex 9/25/19

The measure of ______________ in a circle is half the measure of the intercepted arc.

A. a central angle
B. an interior angle
C. an inscribed angle

Answers

YES slay5 is correct the answer is : C. an inscribed angle

Answer:  C. An inscribed angle

Step-by-step explanation:

Central angle is an angle that is subtended by an arc in a circle, it is also known as the arc's angular distance.

Interior angle is an angle between two sides inside a polygon or a shape.

Inscribed angle is an angle formed by two chords in a circle which have a common endpoint, and by the inscribed angle theorem, the measurement of inscribed angle is half the measure of the intercepted arc.  

How old am i if i was born in 05/22/1965?

Answers

Subtract the year you were born in from this year.

2017 - 1965 = 52

And since May already passed (05/22), you're birthday already passed.


So you are 52 years old if you were born in 05/22/1965.

Answer:

In 2021 you would be 56 or 55 years old

Step-by-step explanation:

2021-1965=56 or the other way you could do it 52+4 because the other person said you would be 52 in 2017 so 4 years after you would be 55 or 56

How do I find the terms?

Answers

A(n+1) = A(n)+4   <--- is a way to say, to get the next term, ADD 4 to the current one, whist A(1) = -2, is a way to say, the first term is -2.

[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ d=4\\ a_1=-2\end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=-2+(2-1)4\\ 3&a_3=-2+(3-1)4\\ 4&a_4=-2+(4-1)4\\ 5&a_5=-2+(5-1)4 \end{array}[/tex]

----------------------------------------------------------------------------------------

A(n)= 1/4 * A(n) is just a way of saying, you get the next term by multiplying the current one by 1/4, and A(1) = 8, simply means the first term's value is 8.

[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=\frac{1}{4}\\ a_1=8 \end{cases} \\\\\\ \begin{array}{llll} term&value\\ ------&------\\ 2&a_2=8\left( \frac{1}{4} \right)^{2-1}\\\\ 3&a_3=8\left( \frac{1}{4} \right)^{3-1}\\\\ 4&a_4=8\left( \frac{1}{4} \right)^{4-1}\\\\ 5&a_5=8\left( \frac{1}{4} \right)^{5-1}\\ \end{array}[/tex]

Cannon took out a mortgage for $85,290 on his new house. If the interest rate is 8.5 percent and the loan is for 25 years, how much will he pay monthly if he must pay $8.05 per $1,000?

Answers

Number of thousands on the amount of the loan is
85,290÷1,000=85.29

Monthly payment is
85.29×8.05=686.58

Answer:

The answer is $686.584

Step-by-step explanation:

Given is, Cannon pays $8.05 per month for every $1,000, so we have a ratio:   8.05 / 1000  

Now, we will find the second ratio which is an unknown payment per month over the price:   x / 85290  

Equaling them to solve for x :

[tex]\frac{8.05}{1000}=\frac{x}{85290}[/tex]

[tex]1000x=8.05*85290[/tex]

[tex]1000x = 686584.50[/tex]

So, x = 686.584

Hence, the answer is $686.584

Which of the following is a description of the data with a correlation coefficient of -0.3?
A.)low positive correlation
B.)low negative correlation
C.)high positive correlation
D.)high negative correlation

Answers

The magnitude of this number is far from 1, so it's low correlation

Since it's negative, so it's low negative correlation
Other Questions
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