Answer:
we choose C
Step-by-step explanation:
We need to understand an infinite number of solutions happens when all numbers are solutions. This situation means that there is no one solution.
So let analyse 3 options:
A.
2x – 6y = 18 (1) x – y = 9 <=> y = x -9 (2)Substitute (2) in (1) we have:
2x – 6(x - 9) = 18
<=> -4x + 54 = 18
<=> x = 9
=> y = 0
There is only 1 solution => A is wrong
B.
2x – 6y = 18 <=> x = 9 + 3y (1) x + 3y = 9 (2)Substitute (1) in (2) we have:
(9+ 3y) + 3y = 9
<=> 3y = 0
<=> y = 0
=> x = 9
There is only 1 solution => B is wrong
C.
2x – 6y = 18 (1)
x – 3y = 9 <=> x = 9+ 3y (2)
Substitute (2) in (1) we have:
2(9+3y) - 6y = 18
<=> 18 + 6y - 6y = 18
<=> 18=18
Yes, this system of equations has an infinite number of solutions
So we choose C
Final answer:
The system of equations with an infinite number of solutions is when one equation is a multiple of the other, which results in the same line and infinite solutions.
Explanation:
The system of equations that has an infinite number of solutions is:
A. 2x – 6y = 18
x – y = 9
To determine this, we notice that the second equation x - y = 9 is a multiple of the first equation 2x - 6y = 18. Since one equation is a multiple of the other, these equations represent the same line, leading to an infinite number of solutions.
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
y = 50 + 2x
y = 40 + 2x
Which statement about the pair of equations is true?
Answer:
what are the statements
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.
The correlation between two scores X and Y equals 0.92. If both scores were converted to z-scores, then the correlation between the z-scores for X and z-scores for Y would be:
a) 0.92
b) −0.92
c) 0.08
d) −0.08
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
Learn more about correlation coefficient here:
https://brainly.com/question/10725272
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.
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)
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
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
Math question please answer my question First one answered will be marked brainliest.
Answer:
7^12
Step-by-step explanation:
We know that a^b ÷ a^c = a^(b-c)
7 ^ 14÷ 7^2
7^ (14-2)
7^12
Answer:
7¹²
Step-by-step explanation:
7¹⁴ ÷ 7²
7^(14-2)
7¹²
What is the standard number for 4 1/2 million.
Answer:
4,500,000
Step-by-step explanation:
4 million is 4,000,000
half of a million is 500,000
added together is 4,500,000
145 = 3500(0.06)(t)
Answer:
t = 29/42
Step-by-step explanation:
in this equation you have to first multiply everything out on the right side. 3500 * 0.06 = 210.
Now you have 145 = 210t
divide by 210 on both sides
145/210 can be simplified to 29/42
so t = 29/42
Identify the outlier or outliers in the data set: 3, 2, 2, 1, 2, 3, 6, 2, 1, 1, 3, 2, 2, 2, 1, 3
Answer:
the outlier would be 6
Step-by-step explanation:
6 is the number that stands out the most therefore it is an outlier!
:)
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
Find the period of the graph shown below
A. 4π
B. π
C. 2π
D. 2/3π
6-2x+1x=-4x+18+1 x combine like terms
Answer:
x = 6
Step-by-step explanation:
first of all, you should know how to do this, this is the basic level of math that students learn in 4th grade.
first you combine like terms (terms that have the same variable)
6 - 2x + 1x = -4x + 18 + 1x
= 6 - 1x = -3x + 18
= 6 = -2x + 18
= -12 = -2x
= 6 = x
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]
Learn more information about 'Fractions' here:
brainly.com/question/870112
A sector with an area of 48\pi cm^(2) has a radius of 16 cm. what is the central angle measure of the sector in radians
Answer:
The central angle is = 3/8 π
Step-by-step explanation:
To calculate the area of the sector, we will follow the steps below;
First write down the formula for calculating the area of a sector.
If angle Ф is measured in degree, then
area of sector = Ф/360 × πr²
but if angle Ф is measured in radians, then
area of sector = 1/2 × r² × Ф
In this case, since we are asked to find the central angle measure of the sector in radians, then we will use the second formula
area = 48π cm² and radius = 16 cm
area of sector = 1/2 × r² × Ф
48π = 1/2 × 16² × Ф
48π = 1/2 ×256 × Ф
48π = 128×Ф
Divide both-side of the equation by 128
[tex]\frac{48}{128}[/tex] π = Ф
Ф = [tex]\frac{48}{128}[/tex] π
The right-hand side can be reduced to its lowest term
Ф = 48 ÷ 16 / 128 ÷16 π
Ф = 3/8 π
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:
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
1. $1,200,000 is equal to
million___dollars.
O 0.0012
0 0.12
O 1.2
O 12
O 1200
Answer:
1.2^6
Step-by-step explanation:
cuz count the zeroes, and that is the scientific notation
Fill in the blank: 2 yards = __________ feet
Answer:
6 feet
Step-by-step explanation:
1 yard = 3 feet
2 yard =6 feet
Sorry I can't have a better explanation it is really simple.
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:
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]
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:
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
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
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
cx=d+r solve for x, pls help
Answer:
x = d/ C + r/ C
Step-by-step explanation:
The "/" means fraction
Mark me as brainliest please
Marjorie has 36 boxes of video games to unpack and put on shelves.Each box contains 28 video games.How many video games in all need to be unpacked.
36 boxes
28 video games per box
That means, we have to multiply 36 by 28 to get the total number of video games.
36 x 28 = 1008
Therefore, 1,008 video games need to be unpacked.
Marjorie must unpack a total of 1008 video games, calculated by multiplying 36 boxes by 28 video games per box.
Marjorie has 36 boxes of video games to unpack, with each box containing 28 video games.
To find out the total number of video games that need to be unpacked, we simply multiply the number of boxes by the number of video games in each box.
The calculation is as follows:
36 boxes × 28 video games per box = 1008 video games
Therefore, Marjorie needs to unpack a total of 1008 video games.
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.
To learn more about the median visit:
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