The correlation between the z-scores for X and z-scores for Y is given by: Option A: 0.92
What is the effect of change in origin and scale on the correlation coefficient?The correlation coefficient(for two variables) is independent of the change of origin and scale of any or both variables.
Thus, we get:
[tex]Corr(X, Y) = Corr\left(\dfrac{X - a}{b}, Y\right) = Corr\left(X, \dfrac{Y - c}{d}\right) = Corr\left(\dfrac{X - a}{b},\dfrac{Y - c}{d}\right)[/tex]
where a, b, c and d are constants.
How to find the z-scores for a random variable?Suppose the considered random variable be X.
Then, we get the z-scores for X as:
[tex]Z = \dfrac{X - \mu}{\sigma} = \dfrac{X - E(X)}{\sqrt{E(X^2) - [E(X)^2]}}[/tex]
where [tex]\mu = E(X)[/tex] and [tex]\sigma = \sqrt{Var(X)}[/tex] (both are constants).
For this case, we're specified that:
[tex]Corr(X,Y) = 0.92[/tex]The correlation coefficient for the z-scores of X and Y would be:
[tex]Corr\left(\dfrac{X -\mu_X}{\sigma_X}, \dfrac{Y - \mu_Y}{\sigma_Y}\right)[/tex]
Using the property that origin and scale change doesn't affect correlation coefficient, we get:
[tex]Corr\left(\dfrac{X -\mu_X}{\sigma_X}, \dfrac{Y - \mu_Y}{\sigma_Y}\right) = Corr(X,Y) = 0.92[/tex]
Thus, the correlation between the z-scores for X and z-scores for Y is given by: Option A: 0.92
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The correct answer to the question is option a) 0.92.
Formula for finding z score is:
[tex]Z = (X - \mu)/(\sigma)[/tex]= (X - E(X))/(√(E(X²) - [E(X)²]))where [tex]\mu[/tex] = E(X) and [tex]\sigma[/tex] = √(Var(X)) (both are constants).
We are provided with following information:
Corr(X,Y) = 0.92
Origin & scale change does not affect correlation coefficient between two scores, so get:
= [tex]Corr\left((X -\mu_X)/(\sigma_X)[/tex]= [tex](Y - \mu_Y)/(\sigma_Y)\right)[/tex]= Corr(X,Y) = 0.92If the correlation between two scores X and Y is 0.92, and both scores are converted to z-scores, the correlation remains unchanged.
This is a property of correlation coefficients, as they are invariant under linear transformations such as converting raw scores to z-scores.
Therefore, the correlation between the z-scores for X and z-scores for Y would be 0.92.
The correct answer is option a) 0.92.
Which shows all the exact solutions of sin^2x+3cosx-1=2? Give your answer in radians.
•0
•2pi
•2kpi
•pi+2kpi
Answer:
On edg it's 2kpi
Step-by-step explanation:
i took the test
The exact solution of the equation will be;
⇒ x = 2kπ
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ sin²x + 3cos x - 1 = 2
Now,
Since, The equation is,
⇒ sin²x + 3cos x - 1 = 2
We know that;
⇒ sin²x = 1 - cos²x
Substitute above value in equation (i), we get;
⇒ 1 - cos²x + 3cos x - 1 = 2
⇒ cos²x - 3 cos x + 2 = 0
⇒ cos²x - (2 + 1)cos x + 2 = 0
⇒ cos²x - 2cos x - cos x + 2 = 0
⇒ cos x (cos x - 2) - 1 (cos x - 2) = 0
⇒ (cos x - 2) (cos x - 1) = 0
This gives two solution,
⇒ cos x = 2
But it is not possible because the value of cos x is in between - 1 and 1.
⇒ cos x = 1
⇒ x = 2kπ + 0°
⇒ x = 2kπ
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What is an equation of the line that passes through the point (5,1)(5,1) and is parallel to the line x+y=9x+y=9?
Answer:
Step-by-step explanation:
Use the point-slope formula.
y - y_1 = m(x - x_1) you have : x_1 =5 and y_1 =1
m the slope m= -1 (same slope for the line : x+y=9 because this lines are parallel and you can write y=-x+9
an equation for this line is : y-1 = -(x-5)
Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
The arc length is a quarter of the circumference of the full circle, so 2πr/4.
The straight sides are both radii, so each length r.
Total perimeter
p = 2πr/4 + r + r = r(π/2 + 2)
We put in r=2, π=3.14 and get
p = (2(3.14/2 + 2)) = 3.14 + 4 = 7.14
Answer: 7.14 km
The perimeter is also known as the circumference. The formula for the circumference is C = pi x diameter.
Step 1) Find the diameter
d = r x 2
d = 2 x 2 = 4 km
Step 2) Find the whole circumference
C = pi x 4
C = 4pi km
Step 3) Find 1/4 of the circumference
4pi x 1/4 = 1pi
1pi = 3.14
Step 4) Add the sides not part of the arc
3.14 + 2 + 2 = 7.14
C = 7.14 km
Hope this helps! :)
Which of these four sets of side lengths will form a right triangle?
Set 1
6 cm, 7 cm, StartRoot 12 EndRoot cm
Set 2
8 in., StartRoot 29 EndRoot in., StartRoot 35 EndRoot in.
Set 3
StartRoot 3 EndRoot mm, 4 mm, StartRoot 5 EndRoot mm
Set 4
9 ft, StartRoot 26 EndRoot ft, 6 ft
Only Set 3 forms a right triangle as it satisfies the Pythagorean theorem, with side lengths matching the equation (√3)^2 + 4^2 = (√5)^2.
The question is about determining which set of side lengths will form a right triangle. To form a right triangle, the side lengths must satisfy the Pythagorean theorem, where the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides (a^2 + b^2 = c^2).
Let's check each set of side lengths:
Set 1: 62 + 72
eq (√12)2 (Not a right triangle)
Set 2: 82 + (√29)2
eq (√35)2 (Not a right triangle)
Set 3: (√3)2 + 42 = (√5)2 (Right triangle)
Set 4: 92 + (√26)2
eq 62 (Not a right triangle)
Therefore, only Set 3 forms a right triangle because it is the only set that satisfies the Pythagorean theorem.
Suppose you are researching the eating habits of people your age. What sampling method could you use to find the percent of students in your grade who eat five servings of fruit and vegetables each day? What is an example of a survey question that does not have bias?
Answer:
You can wait at the front of the luchline and survey every tenth student.
Step-by-step explanation:
This way it is equal for everyone.
Answer:
What do you eat every week?
If you include a type of food, then the survey question would be bias though.
Solve for n 12/6 = 4/n
Answer:
The answer to your question will be n = 2
Step-by-step explanation:
as much as I would like to, I'm really not that great at explaining things
can two distinct quadratic equations have two real solutions
Answer:
A quadratic equation has two solutions. Either two distinct real solutions, one double real solution or two imaginary solutions. All methods start with setting the equation equal to zero.
Step-by-step explanation:
Does that make sense?
h(x) = -(x + 1)(x - 7)
What is the maximum height that the ball will reach?
Answer:
16
Step-by-step explanation:
All we have to do is write this in vertex form of a quadratic. It is now in factored form. To get it into vertex form we must complete various steps. Here you can skip it using desmos graphing calculator:
Answer: 16 units.
Step-by-step explanation:
To find the vertex, first simplify the quadratic equation into its standard form:
[tex]h(x)=-(x+1)(x-7)\\h(x)=(-x-1)(x-7)\\h(x)=-x^2+6x+7\\[/tex]
Using this formula, we can then find the axis of symmetry by using the formula S = -b/2a:
[tex]S=\frac{-6}{-2}[/tex]
The axis of symmetry lies on x = 3.
You can then substitute x for 3 in the equation to find the vertex of the parabola:
[tex]h(3)=-9+18+7\\h(3)=16[/tex]
The ball will be 16 units high after travelling 3 units horizontally. This is the maximum height the ball will reach before falling.
the surface areas of two cubes are in ratio 1:9. what is it the ratio of their volumes?
a) 1:3
b) 1:9
c) 1:27
d) 1:81
Answer:
c
Step-by-step explanation:
Use the interactive graph to plot each set of points. Which sets represent proportional relationships? Check all that apply. A.(1, 4), (3, 8), (5, 9) B.(3, 2), (6, 4), (9, 6) C.(2, 2), (4, 4), (6, 6) D.(1, 3), (2, 7), (3, 8) E.(0, 0), (1, 2), (2, 4), (4, 8)
The sets that represent proportional relationships are: B, C, and E.
Here's how we can determine which sets of points represent proportional relationships:
Set A:
Plot the points (1, 4), (3, 8), and (5, 9) on the graph.
Calculate the ratio of y to x for each point:
(4/1) = 4
(8/3) = (8/3)
(9/5) = (9/5)
As you can see, the ratios are not the same. Therefore, set A does not represent a proportional relationship.
Set B: (attachment 1)
Plot the points (3, 2), (6, 4), and (9, 6) on the graph.
Calculate the ratio of y to x for each point:
(2/3) = (2/3)
(4/6) = (2/3)
(6/9) = (2/3)
In this case, the ratios are all the same, which is 2/3. Therefore, set B represents a proportional relationship.
Set C: (attachment 2)
Plot the points (2, 2), (4, 4), and (6, 6) on the graph.
Calculate the ratio of y to x for each point:
(2/2) = 1
(4/4) = 1
(6/6) = 1
All the ratios are equal to 1. Therefore, set C represents a proportional relationship.
Set D:
Plot the points (1, 3), (2, 7), and (3, 8) on the graph.
Calculate the ratio of y to x for each point:
(3/1) = 3
(7/2) = (7/2)
(8/3) = (8/3)
The ratios are not the same. Therefore, set D does not represent a proportional relationship.
Set E: (attachment 3)
Plot the points (0, 0), (1, 2), (2, 4), and (4, 8) on the graph.
Calculate the ratio of y to x for each point:
(0/0) = undefined (division by zero)
(2/1) = 2
(4/2) = 2
(8/4) = 2
Ignoring the undefined ratio at (0, 0), we see that the ratios are all equal to 2. Therefore, set E represents a proportional relationship.
Complete and correct question:
Use the interactive graph to plot each set of points. Which sets represent proportional relationships? Check all that apply.
A.(1, 4), (3, 8), (5, 9)
B.(3, 2), (6, 4), (9, 6)
C.(2, 2), (4, 4), (6, 6)
D.(1, 3), (2, 7), (3, 8)
E.(0, 0), (1, 2), (2, 4), (4, 8)
Maria’s hair was 10 inches long, and then she cut ℎ inches
Answer:
please finish the question?
Step-by-step explanation:
Answer:
10-h
Step-by-step explanation:
i think ur teacher told u to write a equation out of it and if that is it then the equation is 10-h
Help please!!
What is the median of the data set?
24, 2, 13, 12, 2, 5, 10, 18
Enter your answer in the box.
Answer:
The median of the data set is 11.
Step-by-step explanation:
2, 2, 5, 10, 12, 13, 18, 24
10 + 12 = 22
22 / 2 = 11
The median of the data set is 11.
We have given the data set,
24, 2, 13, 12, 2, 5, 10, 18
We have to find the median
So first arrange the given data set in asending order.
2, 2, 5, 10, 12, 13, 18, 24
What is the median?The median is the central number of a data set.
There are two number at center that are 10 and 12
So we have to find the mean of this two number.
10 + 12 = 22
22 / 2 = 11
So the median is 11.
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Is 12, 13, or 14 a solution of the inequality 4x > 52?
Answer:
[tex]4x > 52 \\ x > \frac{52}{4} \\ x > \frac{26}{2} \\ x > 13[/tex]
Answer:
14
Step-by-step explanation:
Plug in the numbers:
12 * 4 = 48 WRONG
13 * 4 = 52 WRONG
14 * 4 = 56 RIGHT
14
A bakery sold 31 bagels in the first hour of business and 42 bagels in the second hour .If the bakery had 246 bagels to start with, how many bagels were left after the second hour
Answer:
173 bagels are left
Step-by-step explanation:
31+42=73
246-73=173
Gavin is building a dresser. He built drawers that all have a volume of of a cubic foot. The expression below represents the total volume of all the drawers in the dresser if there are b drawers across, and c drawers high. If the dresser is 6 drawers high and 3 drawers wide, what is the total volume of all the drawers in the dresser?
The total volume of all the drawers in the dresser, which has 6 drawers high and 3 drawers wide, is found by multiplying these two values. Therefore, the total volume of all the drawers in the dresser is 18 cubic feet.
Explanation:This problem involves the calculation of volume in a real-world context. We know that each drawer has a volume of 1 cubic foot, and the total volume of all the drawers can be obtained by multiplying the number of drawers across (width) by the number of drawers high (height). From the question, we know the dresser is 6 drawers high and 3 drawers wide. Therefore, the total volume is obtained by multiplying 6 (height) by 3 (width), which yields 18 cubic feet. Hence, the total volume of all the drawers in the dresser is 18 cubic feet.
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Which fractions are equivalent to 4/9?
Answer:
[tex] \frac{8}{18} [/tex]
Step-by-step explanation:
[tex] \frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18} \\ [/tex]
Answer:
8/18, 12/27, 16/36, 20/45
i don’t understand how to solve this (geometry)
Answer:
29.9
Step-by-step explanation:
Geometry Question!!
Answer:
14
Step-by-step explanation:
Since angle ADC and ABC are both inscribed angles to opposite angles that must add up to 360 degrees, together they must add up to 180 degrees. You can therefore set up the following formula:
7x+2+6x-4=180
13x=182
x=14 degrees
Hope this helps!
Multiply and simplify.
(x - 3)(x2 + 3x + 9)
A) x3 - 27
B) x3 - 27x2
C) x3 - 6x2 + 3x - 27
D) x3 - 9x2 + 6x - 27
Answer:
Answer A is correct[tex] {x}^{3} - 27[/tex]
Step-by-step explanation:
[tex](x - 3)( {x}^{2} + 3x + 9) \\ x( {x}^{2} + 3x + 9) - 3( {x}^{2} + 3x + 9) \\ {x}^{3} + 3 {x}^{2} + 9x - 3 {x}^{2} - 9x - 27 \\ {x}^{3} - 27[/tex]
someone solve this please
Answer:
∠NKL = 50°
Step-by-step explanation:
A parallelogram consists of two pairs of congruent angles.
So..
130 + 130 = 260
360 - 260 = 100
100 / 2 = 50
5/10 plus 8/100 equals?
Answer:
29/50
Step-by-step explanation:
To solve this expression, we first have to make sure that the denominators are equal. If the denominators aren't equal, we can't add the fractions together. To make equivalent denominators, the easiest way is to find the LCM. Looking at these two fractions, we see that the LCM is 100. To get to 100 from 10 in the first fractions denominator we multiply by 10. Since we multiplied by 10 in the denominator, we must multiply by 10 in the numerator, leaving us with the fraction:
5/10 = 50/100
Since the denominators are now equal, we can add these two fractions:
50/100 + 8/100 = 58/100 = 29/50
Adding two fractions equal
[tex]\frac{5}{10}+ \frac{8}{100}=\frac{29}{50}[/tex]
Adding Fractions:To add any two fractions , the denominators should be same.
Least common denominator:LCD is the smallest number of all the common multiples of the given denominators
We need to add [tex]\frac{5}{10}+ \frac{8}{100}[/tex]
To add two fractions, we need to make the denominators same
multiples of 10 are 10,20,30,40,50,60,70,80,90,100......
multiples of 100 are 100,200, 300, 400 .......
Common multiple is 100. so LCD is 100
[tex]\frac{5}{10}+ \frac{8}{100}\\\\\frac{5 \cdot 10}{10 \cdot 10}+ \frac{8}{100}\\\\\frac{50}{100}+ \frac{8}{100}\\ \frac{50+8}{100}\\\\\frac{58}{100}\\\\\frac{29}{50}[/tex]
Adding two fractions,
[tex]\frac{5}{10}+ \frac{8}{100}=\frac{29}{50}[/tex]
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What is the value of the power
The value of the power in the expression 5^4 is 625. This is found by multiplying the base (5) by itself 4 times, which is the exponent.
The value of the power is 54. This is because 54 is the base of the expression raised to the exponent 4. In other words, 54 is multiplied by itself 4 times.
Identify the base: The base is the number that is being raised to the power. In this case, the base is 5.
Determine the exponent: The exponent is the small number written above and to the right of the base. In this case, the exponent is 4.
Write the expression in expanded form: The expanded form of the expression is 5 x 5 x 5 x 5.
Evaluate the expression: 5 x 5 x 5 x 5 = 625.
Therefore, the value of the power is 625.
How far away can a person live from a radio station and hear its broadcast if the signal covers a circular area of 40,000 square miles? Write your answer as a whole number.
Answer:
The person can live at a distance of 113 miles
Step-by-step explanation:
In this question, we are concerned with calculating how far a person live from a radio station and hear its broadcast given that the broadcast covers an area of 40,000 square miles.
Now this question is asking us to calculate the farthest distance from the radio station to the house of the person.
With the radio station being the center, what we are asked to calculate is the radius which is the distance from the center to the edge ( circumference)
Mathematically, the area can be calculated as
A = π * r^2
Here, we have the Area as 40,000 square miles
Thus,
40,000 = π * r^2
r^2 = 40,000/π
r = √(40,000/π)
r = 112.8379
As a whole number r = 113 miles
What is x? Please help fast
Answer:
x = 47°
Step-by-step explanation:
m∠DPB + ∠BPC = 180° (Definition of a straight line)
Plug in the corresponding numbers and variables to the corresponding places:
x + 133 = 180
Isolate the variable, x. Subtract 133 from both sides:
x + 133 (-133) = 180 (-133)
x = 180 - 133
x = 47
47° is your answer.
~
Answer:
47 degrees
Step-by-step explanation:
DPC = DPB +BPC = 180
-> x + 133 = 180
-> x = 47
Which statements are true about surface area and volume? Check all that apply.
******************************************************************************************************
Volume is labeled with cubic units.
Surface area is labeled with cubic units.
Volume of a prism is the product of the area of the base and height.
Surface area is the sum of the areas of each side.
The volume of a prism is One-third the volume of a pyramid.
Answer:
1. True
2. False
3. True
4. True
5. False
Step-by-step explanation:
1. Volume is labeled in cubic units, as it is the multiplication of 3 dimensions
2. Surface area is only labeled in square units, not cubic units, it is area after all, and that is the multiplication of 2 dimensions
3. The volume of many figures in general is through multiplication of base and height. Though there are exeptions, the Volume of a Prism is computed through base and height multiplication
4. Yes, surface area is the sum of the areas of the sides of a 3-dimensional figure
5. Actually it is the volume of a pyramid that is One-third the volume of a prism, not the other way around
The statements 1,3 and 4 are true.
What is surface area?
Surface area is explained as the sum of the areas of all the closed surfaces of a solid. The surface of any area is the region occupied by the surface of an object.
What is volume?Volume is the amount of space available in an object. It is the space enclosed by a boundary or occupied by an object or the capacity to hold something.
For the given situation,
There are several statements, we need to check which statements are true.
Statement 1: Volume is labeled with cubic units.
Volume is the measure of three dimensional space. So volume should be labeled in cubic units.
Thus, statement 1 is true.
Statement 2: Surface area is labeled with cubic units.
Surface area is the total area of the faces of a three-dimensional shape. Surface area is labelled in square units.
Thus, statement 2 if false.
Statement 3: Volume of a prism is the product of the area of the base and height.
The volume of the prism is defined as the product of the area of the base and the length (height).
Thus, statement 3 is true.
Statement 4: Surface area is the sum of the areas of each side.
The surface area of a three-dimensional object is the total area of all its faces.
Thus, statement 4 is true.
Statement 5: The volume of a prism is One-third the volume of a pyramid.
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The volume of a pyramid is found using the formula V = (1/3) Bh, where B is the base area and 'h' is the height of the pyramid.
Thus, statement is false.
Hence we can conclude that the statements 1,3 and 4 are true.
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Is flipping 2 coins dependent?
Answer:
No
Step-by-step explanation:
Flipping two coins is independent because the outcome of the first coin doesn't affect the outcome of the second coin. There is still a 1/2 chance of of getting heads or tails.
If this answer is correct, please make me Brainliest!
jim says that the output of the floor function is the number before the decimal point in the input true or false?
Answer:
its correct for positive numbers
Answer:
Jim’s statement is correct for all numbers greater than or equal to 0, and negative integers. It does not work for negative non-integer numbers. For example, the floor of –3.5 is –4, where –4 is not equal to –3, the number before the decimal point.
Step-by-step explanation: Math
Write an expression for the area of a triangle with a height of 2x^2 units and a base of 5x^2+4x units
Answer:
The area of the triangle is [tex]5x^4 + 4x^3[/tex] square units
Step-by-step explanation:
Given
Shape: Triangle
[tex]Height = 2x^2[/tex]
[tex]Base = 5x^2+4x[/tex]
Required
The area of the triangle
The area of a triangle is calculated as thus;
[tex]Area = \frac{1}{2}(base)(height)[/tex]
By substituting [tex]Height = 2x^2[/tex] and [tex]Base = 5x^2+4x[/tex]; This gives
[tex]Area = \frac{1}{2}(5x^2 + 4x)(2x^2)[/tex]
[tex]Area = \frac{(5x^2 + 4x)(2x^2)}{2}[/tex]
[tex]Area = (5x^2 + 4x)(x^2)[/tex]
Open Bracket
[tex]Area = 5x^2 * x^2 + 4x * x^2[/tex]
[tex]Area = 5x^4 + 4x^3[/tex]
Hence, the area of the triangle is [tex]5x^4 + 4x^3[/tex] square units
2: Determine the number of solutions of the quadratic equation below.
9x2 – 12x + 4 = 0
Answer:
1 real number solution
Step-by-step explanation:
b^2-4ac=0 1 real number solution
Answer:
1 real
Step-by-step explanation:
use the properties of rational numbers to multiply the following 7/12 * 253 / 5
Answer:
the answer is 29.516 i had this question and got it right have a great day
Step-by-step explanation:
Answer:
1771/60
Step-by-step explanation: