Answer:
E (X) = 1.8
Var (X) = 0.36
σ = 0.6
Step-by-step explanation:
Solution:-
- Denote the random variable X : is the number of red marbles that Suzan has in her hand after she selects three marbles.
- Total sample space (bag) have the following quantity of colored marbles:
Bag : { 3 Red , 2 Green }
- Suzan selects three marbles from the bag. The Event (X) defines the number of red marbles out of 3.
- The total number of outcomes / selections for randomly selecting 3 balls from the bag:
All outcomes = 5 C 3 = 10
- The probability distribution of the random variable X, we will use combinations to determine the required probabilities:
X = 1 red marble:
P ( X = 1 ) : Suzan chooses 1 Red marble from the available 3 red marble and 2 green marbles.
P ( X = 1 ) = [ 3C1*2C2 ] / all outcomes = (3*1) / 10 = 0.3
X = 2 red marble:
P ( X = 2 ) : Suzan chooses 2 Red marble from the available 3 red marble and 1 green marbles.
P ( X = 2 ) = [ 3C2*2C1 ] / all outcomes = (3*2) / 10 = 0.6
X = 3 red marble:
P ( X = 3 ) : Suzan chooses 3 Red marble from the available 3 red marble.
P ( X = 3 ) = [ 3C3] / all outcomes = (1) / 10 = 0.1
- The probability distribution is as follows:
X : 1 2 3
P (X): 0.3 0.6 0.1
- The expected value E(X) for the given random variable X is:
E ( X ) = ∑Xi*P(Xi)
= 1*0.3 + 2*0.6 + 3*0.1
=1.8
- The variance Var(X) for the given random variable X is:
Var ( X ) = ∑Xi^2*P(Xi) - [ E(X) ] ^2
= 1^2*0.3 + 2^2*0.6 + 3^2*0.1 - 1.8^2
= 0.36
- The standard deviation for the given random variable X is:
σ = √Var(X)
σ = √0.36
σ = 0.6
The expected value, the variance, and the standard deviation of the given random variable X are 1.8, 0.36, and 0.6 respectively and this can be determined by using the given data.
Given :
X is the number of red marbles that Suzan has in her hand after she selects three marbles from a bag containing three red marbles and two green ones.
The total number of outcomes are:
[tex]\rm \; ^5C_3=10[/tex]
The probability of random variable X are as follows:
X = 1 red marble
P(X = 1) = [tex]\rm \; ^3C_1 \times ^2C_2[/tex] = 0.3
X = 2 red marbles
P(X = 2) = [tex]\rm \; ^3C_2 \times ^2C_1[/tex] = 0.6
X = 3 red marbles
P(X = 3) = [tex]\rm \; ^3C_3[/tex] = 0.1
So, the expected value is given by:
[tex]\rm E(X) = \sum X_i \times P(X_i)[/tex]
[tex]= 1\times 0.3+2\times 0.6 + 3 \times 0.1[/tex]
= 1.8
Now, the variance is given by:
[tex]\rm Var(X) = \sum X^2_i \times P(X_i)-(E(X))^2[/tex]
[tex]=1^2\times 0.3+2^2\times 0.6+3^2 \times 0.1-1.8^2[/tex]
= 0.36
Now, the standard deviation is given by:
[tex]\rm \sigma=\sqrt{Var(X)}[/tex]
[tex]\rm \sigma = \sqrt{0.36}[/tex]
[tex]\sigma = 0.6[/tex]
For more information, refer to the link given below:
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A car travels 218.5 miles on 9.5 gallons of gas what is the gas mileage
Answer:
23 miles per gallon
Step-by-step explanation:
Take the miles and divide by the gallons
218.5 miles/ 9.5 gallon
23 miles per gallon
Answer:
23m/g
Step-by-step explanation:
If a car travels 218.5 miles on 9.5 gallons, you can find how many miles can be traveled on one gallon.
You can make the equation 9.5g=218.5, let g be gallons of gas.
Divide by 9.5 on both sides.
g= 23
The gas mileage is 23 miles for one gallon of gas.
What is the slope of the line that passes through the points (1, 2) and (-2, -13)?
Answer:
5
Step-by-step explanation:
To find the slope given two points, we use the formula
m= (y2-y1)/(x2-x1)
= (-13-2)/(-2 -1)
= -15/-3
=5
Answer:
The slope is 5
Step-by-step explanation:
Δ means the change in
slope = m = Δy/Δx = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{2-(-13)}{1-(-2)}[/tex] = 15/3 = 5/1 = 5
Slope = 5
Fiona must find the length indicated by the dotted line for the tiles she is installing. She knows that each polygon is a regular hexagon with a perimeter of 7.5 in. What is the length of the dotted line? Round to the nearest hundredth.
Answer: The length of the dotted line is 3.75 inches.
Please refer to the picture attached for the missing part of the question
Step-by-step explanation: From the information given we have a regular hexagon, that is a six-sided polygon (all sides equal) with the perimeter given as 7.5 inches. The perimeter is the distance all around the figure, hence to determine the length of one side,
Length = 7.5/6
Length = 1.25
Also, the interior angles of a hexagon can be derived with the formula;
Angles = 180 (n - 2)
Where n is the number of sides of the polygon
Interior Angles = 180 (6 - 2)
Interior Angles = 180 x 4
Interior Angles = 720
If the total of the interior angles equals 720, then each angle can be calculated as;
Each Angle = 720/6
Each Angle = 120
Please refer to attached picture tagged SOLUTION Diagram)
Taking triangle GED as shown in the picture, angle E and angle D measure 60 degrees each. This is because angle E in the entire hexagon ABCDEF measures 120 degrees. The line from point G in the center of the hexagon divides the angle into two equal halves. Same applies to all other five angles in the hexagon. Having angle E and D equal to 120 (that is 60 + 60) angle G would be equal to 180 - 120 {sum of angles in a triangle equals 180) which gives us 60. In effect we have an equilateral triangle, with all angles equal. This also means all sides are equal, hence if line ED equals 1.25, it simply means line GE and line GD equals 1.25 as well.
From this result we can now conclude that the line that runs across the hexagon from point F to point C is 1.25 plus 1.25 which equals 2.50.
The dotted line as indicated in the question runs across one side of the hexagon and all through another hexagon, hence the total length of the dotted line equals;
Dotted line = 1.25 + 2.50
Dotted line = 3.75
Therefore the length of the dotted line is 3.75 inches
Mr.Estevez got a new post mounted mail box. He dug out the old one and left a square hole and only measured one side. Mr.Estevez measured a side of 9.75cm's. What is the square area of dirt Mr. Estevez needs to fill up the hole for his new mailbox. (Round to the nearest tenth)* 0 95.1cm2 0 95.06cm2 0 95.1cm O 95.06cm
Answer:
[tex]95.1\ cm^2[/tex]
Step-by-step explanation:
we know that
A square is a quadrilateral that has four equal sides and four equal interior right angles.
The area of the square is given by the formula
[tex]A=b^2[/tex]
where
b is the length side of the square
In this problem we have
[tex]b=9.75\ cm[/tex]
substitute in the formula
[tex]A=(9.75)^2=95.06\ cm^2[/tex]
Round to the nearest tenth
[tex]A=95.1\ cm^2[/tex]
Answer:
95.06cm
Step-by-step explanation:
Hope this helps
Which function shows a fabric with a price of $1.25 per square yard?
Answer:
x(1.25)
Step-by-step explanation:
x is the yards.
so for example if you need 2 yards of fabric replace x with 2.
Answer:
x=1.25
Step-by-step explanation:
edgu
-
Which of the following are alternate exterior angles?
Answer:
Are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.
In a math class with 27 students, a test was given the same day that an assignment was due. There were 17 students who passed the test and 22 students who completed the assignment. There were 3 students who failed the test and also did not complete the assignment. What is the probability that a student passed the test given that they did not complete the homework
The probability that a student passed the test given that they did not complete the homework is [tex]\( \frac{3}{5} \)[/tex] or 60%.
To find the probability that a student passed the test given that they did not complete the homework, you can use conditional probability.
Let:
- [tex]\( A \)[/tex] be the event that a student passed the test.
- [tex]\( B \)[/tex] be the event that a student did not complete the homework.
You're asked to find [tex]\( P(A|B) \),[/tex] the probability of passing the test given not completing the homework.
From the given information:
- Total number of students [tex](\( N \)) = 27[/tex]
- Number of students who passed the test [tex](\( A \)) = 17[/tex]
- Number of students who did not complete the homework [tex](\( B \)) = \( N - 22 = 5 \)[/tex] (since 22 students completed the assignment)
Also, given that there were 3 students who failed the test and did not complete the assignment, we can infer that out of the 5 students who did not complete the homework, 3 of them failed the test.
So, [tex]\( P(A \cap B) = 3 \)[/tex] (the probability of a student both passing the test and not completing the homework).
Using the definition of conditional probability:
[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \][/tex]
We have:
- [tex]\( P(A \cap B) = 3 \)[/tex]
- [tex]\( P(B) = 5 \)[/tex]
Now we can calculate [tex]\( P(A|B) \)[/tex]:
[tex]\[ P(A|B) = \frac{3}{5} \][/tex]
So, the probability that a student passed the test given that they did not complete the homework is [tex]\( \frac{3}{5} \)[/tex] or 60%.
The probability that a student passed the test given they didn't complete the homework is 40%.
To solve this problem, we need to determine the probability that a student passed the test given they did not complete the homework. We'll use the given data:
27 total students17 students passed the test22 students completed the assignment3 students failed the test and did not complete the assignmentFirst, calculate the number of students who did not complete the homework:
5 because 27 total - 22 completed = 5 did not complete.
Next, find the number of students who passed the test and did not complete the homework.
Let’s define variables:
Passed test: ADidn't complete homework: BFailed test and didn't complete homework: AB'We're given that AB' = 3.
Calculate AB:
The total number of students who didn’t complete the homework is 5 (B + B'). Thus, AB (students who passed the test but did not complete the assignment) can be calculated as:
2 (because 5 - 3 = 2 for AB).
Then, the probability is:
P(A|B) = AB / B = 2 / 5. Therefore, the answer is 0.4 or 40%.
The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the x-axis are semi-circles. What is the volume, in cubic units, of the solid?
Answer:
Option b) [tex]18\pi[/tex] is correct∴ the volume of the solid is [tex]A(x)=18\pi[/tex] cubic unitsStep-by-step explanation:
Given that the base of a solid is the circle [tex]x^2 + y^2 = 9[/tex] and Cross sections of the solid perpendicular to the x-axis are semi-circles.
To find the the volume of the solid in cubic units:We know that the cross sections are semicircles with the diameter in the given circle [tex]x^2 + y^2 = 9[/tex]
That is we have to find the formula for the area of any semicircle perpendicular to x-axis, and integrate it from -3 to 3.
Now the area of a semicircle is
[tex]A=\frac{\pi r^2}{2}[/tex] cubic units
Let r = y and [tex]y^2=9-x^2[/tex]
Then area of the semicircle crossing the x-axis at x is given by
[tex]A(x)=\frac{1}{2}\pi y^2[/tex] cubic units
[tex]=\frac{1}{2}\pi(9-x^2)[/tex]
Now we can find the definite integral of A(x) from x = -3 to x = 3.
Since A(x) is an EVEN function then the definite integral of A(x) from x = -3 to x = 3 is the same as twice the integral of A(x) from x = 0 to x = 3.
We have that
[tex]A(x)=2(\int_0^3 \frac{1}{2}\pi(9-x^2))dx[/tex]
[tex]=2(\frac{\pi}{2}[9x-\frac{x^3}{3}]_0^3)[/tex]
[tex]=\pi[9(3)-\frac{3^3}{3}-9(0)-(-\frac{0^3}{3})][/tex]
[tex]=\pi[27-\frac{27}{3}][/tex]
[tex]=\pi[27-9][/tex]
[tex]=\pi[18][/tex]
[tex]=18\pi[/tex]
∴ option b) [tex]18\pi[/tex] is correct∴ the volume of the solid is [tex]A(x)=18\pi[/tex] cubic unitsThe volume of the solid is 18π cubic units.
The base of the solid is defined by the circle’s equation x² + y² = 9, indicating that the radius of the circle is 3 units. The cross-sections perpendicular to the x-axis are semi-circles.
To find the volume, we need to integrate the area of these semi-circular cross-sections. For a slice at a given x-coordinate, the diameter of the semi-circle is the length of the chord of the circle at that x-coordinate, which is given by 2√(9 - x²). The radius of the semi-circle is then √(9 - x²), and the area of the semi-circle is (1/2)πr².
The area of each semi-circular slice is: A(x) = (1/2)π(√(9 - x²))² = (1/2)π(9 - x²).
The volume V of the solid is obtained by integrating this area from x = -3 to x = 3:
V = ∫[from x = -3 to x = 3] (1/2)π(9 - x²) dx
This simplifies to:
V = (π/2) ∫[from x = -3 to x = 3] (9 - x²) dx
We solve the integral:
V = (π/2) [9x - (x³ / 3)] (from x = -3 to x = 3)
Evaluating this, we get:
V = (π/2) [(9×3 - (3³ / 3)) - (9×(-3) - ((-3)³ / 3))]
V = (π/2) [(27 - 9) - (-27 + 9)]
V = (π/2) [18 + 18]
V = (π/2) 36
V = 18π
Thus, the volume of the solid is 18π cubic units.
Bella manages a volunteer group. The time (T) that it takes a group of volunteers to construct a house varies inversely as the number of volunteers (V). It takes 20 volunteers to build a house in 63 hours. Write an equation to model this situation. Next, find how many volunteers it would take to build a house in 30 hours.
Answer:
42 Volunteers
Step-by-step explanation:
The time (T) that it takes a group of volunteers to construct a house varies inversely as the number of volunteers (V).
This is written as:
[tex]V \propto \frac{1}{T} \\$Introducing the variation constant k\\V = \frac{k}{T}\\$It takes 20 volunteers to build a house in 63 hours.$\\When V=20, T=63\\V = \frac{k}{T}\\20 = \frac{k}{63}\\k=20*63=1260\\$Therefore, the equation connecting V and T is:$\\V = \frac{1260}{T}\\$When T=30 hours, we want to determine the number of volunteers needed V$\\V = \frac{1260}{30}=42\\$42 Volunteers will be needed.$[/tex]
rate of change in the equation y = 5 - 0.5x
In your own words, what is relative frequency?
Answer:
A frequency is the number of times a given datum occurs in a data set.
Step-by-step explanation:
If you were to flip a coin 140 times, how many times would you expect the coin to land on tails?
Answer: 70 times
Step-by-step explanation:
If you were to flip a coin 140 times you would expect it to land on tails 70 since 140 divided by 2 is 70 although coins are normally not evenly weighed meaning that it most likely not going to land evenly on both sides.
what is the percent change of 10 feet to 6 feet
Answer:It would be a decrease of 40 percent
Step-by-step explanation:You go from 10/10 to 6/10 meaning you decrease by 4/10 and 4/10 is the same as 40/100 and anything over 100 is its percent value so you would be going down by 40%
Answer:
40 % decrease or -40%.
Step-by-step explanation:
The decrease is 10 - 6 = 4 feet.
% decrease = (4/10) * 100
= 0.4 * 100
= 40 % decrease.
NEED HELP
8x + √1 - √9y - √9x^2
5x + 3√y + 1
5x - 3√y - 1
5x - 3√y + 1
Answer:
Last one: 5x - 3√y + 1
Step-by-step explanation:
8x + √1 - √9y - √9x^2
8x + 1 - 3√y - 3x
5x + 1 - 3√y
5x - 3√y + 1
Answer:Answer:
Last One: 5x - 3√y + 1
Step-by-step explanation:
8x + √1 - √9y - √9x^2
8x + 1 - 3√y - 3x
5x + 1 - 3√y
5x - 3√y + 1
Step-by-step explanation:
12.6 is what percent of 42?
What is the result of adding 17 to its opposite
The answer is zero (0), when you add any number to it's opposite you always get zero
The Wilson family is planning an extended vacation in summer the map they are using has the scale 1 in. = 80 mi. How many inches represent 2,160 miles?
Answer:
27 inches
Step-by-step explanation:
you divide 2160 by 80 to get the number of inches
2160/80=27
A rectangle has a length of 6 feet and a width of 4 feet. The perimeter of the rectangle can be found using the equation =2×6+2×4. Which equation can also be used to find the perimeter of the rectangle?
Answer:
The correct answer is perimeter is given by 2 × ( l + w), where l is the length and w is the width of the rectangle.
Step-by-step explanation:
A rectangle has a length of 6 feet and a width of 4 feet. The perimeter of the rectangle can be found using the equation =2×6+2×4.
Let l be the length and w be the width of a rectangle.
Since there four sides of a rectangle, the perimeter is given by adding all the sides.
Therefore perimeter of the rectangle is given by l + l + b + b = 2×l +2×w = 2 × ( l + w).
The equation given by 2 × ( l + w) can also be used to find the perimeter of any given rectangle.
Coll
4/15 version of 4/7 version of M4T2 Test Review
Created by Meena Frazier
Q1: What is the distance between (2, 3) and (-2, 7)? Round to the nearest tenth, if necessary.
Answer:
The answer to your question is 5.7
Step-by-step explanation:
Data
Point A = (2, 3)
Point B = (-2, 7)
Process
To find the distance between points A and B use the formula of the distance between two points, substitute and simplify.
Formula
dAB = [tex]\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2}}[/tex]
-Identify wich is the value of x1, y1, x2, y2
x1 = 2 y1 = 3 x2 = -2 y2 = 7
-Substittion
dAB = [tex]\sqrt{(-2 - 2)^{2} + (7 - 3)^{2}}[/tex]
-Simplification
dAB = [tex]\sqrt{(-4)^{2} + (4)^{2}}[/tex]
dAB = [tex]\sqrt{16 + 16}[/tex]
dAB = [tex]\sqrt{32}[/tex]
-Result
dAB = 5.65 ≈ 5.7
Point O is the center of the circle. Circle O is shown. Tangents D C and B C intersect at point C outside of the circle. Lines are drawn from points D and point B to center point O to form a quadrilateral. A line is drawn from point C to point A on the opposite side of the circle. The length of O D is 6, and the length of B C is 8. Angles D and B are right angles. What is the perimeter of quadrilateral DOBC?
Answer:
The perimeter is 28 (6 plus 8=14 14x2= 28)
Step-by-step explanation:
Plz mark brainliest!
The perimeter of quadrilateral DOBC that forms two right triangles is: 28 units.
What are Congruent Right Triangles?Based on the tangent theorem, triangles ODC and OBC are right triangles that are congruent. Therefore, their corresponding side lengths are equal.
Perimeter of quadrilateral DOBC = OB + DO + BC + CD = 6 + 6 + 8 + 8
Perimeter of quadrilateral DOBC = 28 units.
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Write 0.06 as a fraction in
simplest form.
Answer:
[tex]\frac{3}{50}[/tex]
Step-by-step explanation:
Answer: 6/10
Step-by-step explanation:
the 6 is in the tenth place which means it is by ten
Solve 2x^2+5x +5=0 round solutions to the nearest hundredth
Answer: i3
Step-by-step explanation:
Answer:13
Step-by-step explanation:
Martin has a shoe box with the dimensions 4 inches, by 6 inches, by 10 inches. He wants to determine if a relay baton inches will fit in the box. What is the longest length that the relay baton can be and still fit in the box? (Round to the nearest tenth if needed.) Your answer: 10 inches 12.3 inches 10.8 inches 7.2 inches
Answer:
10 inches.
Step-by-step explanation:
First we need to find what is the bigger dimension of the box, because the relay baton will occupy the box, and the larger dimension of the relay baton (that is, it's length) need to be less or equal than the larger dimension of the box.
The dimensions of the box are: 4 inches, 6 inches and 10 inches.
The larger dimension of the box is 10 inches. So, If we want the relay baton to fit in the box, the maximum length it can have is 10 inches.
The perimeter of a rectangle is found by using the formula P = 2l + 2w, where P is the perimeter, l is the length and w is the width. Use the formula and operations of equations to fill in the missing information on the table below. Complete your work in the space provided. Include the entire process for completing the table.
Answer:
#1: 11 cm
#2: 16.5 in
#3: 2.5 feet
Step-by-step explanation:
#1
[tex]P=2l+2w[/tex] Solve for width by substracting 2l on both sides to isolate 2w
[tex]P-2l=2w[/tex]
or
[tex]2w=P-2l[/tex]
Replace.
[tex]2w=26-2(2)\\2w=26-4\\2w=22\\w=\frac{22}{2}\\ w=11cm[/tex]
----------------------------------------------------------------------------
#2
[tex]P=2l+2w[/tex]
[tex]P=2(3.5)+2(4.75)\\P =7+9.5\\P=16.5in[/tex]
----------------------------------------------------------------------------
#3
[tex]P=2l+2w[/tex]
Solve for l
[tex]2l=P-2w\\2l=7-2(1)\\2l=7-2\\2l=5\\l=\frac{5}{2}\\ l=2.5feet[/tex]
Tom and Martha are making punch for a party. The proportions given in the recipe are 2 parts of lemonade to 1 part each of pineapple juice and ginger ale. If they need 6 liters of punch, how many liters of each of the ingredients should they buy?
Answer:
They need to buy 3 litters of lemonade, 1.5 litters of pineaple juice and 1.5 litters of ginger ale.
Step-by-step explanation:
In order to calculate the amount of each ingredient they need for 6 liters of punch we can first create fractions for each ingredient based on the proportions we were given. This is shown bellow:
2 litters lemonade + 1 litter pineapple juice + 1 litter ginger ale = 4 litters punch
Then we have:
lemonade = 2/4
pineaple juice = 1/4
ginger ale = 1/4
If we want to make 6 liters of punch we can just apply this fractions to know how much of each we need:
lemonade = 6*(2/4) = 12/4 = 3 litters
pineaple juice = 6*(1/4) = 1.5 litters
ginger ale = 6*(1/4) = 1.5 litters
They need to buy 3 litters of lemonade, 1.5 litters of pineaple juice and 1.5 litters of ginger ale.
x² - 12x + 27? what is the factored form of this polynomial
Answer:
( x - 9 )( x - 3 )
Step-by-step explanation:
plz give brainliest
Sam and Janet each have a whole number of dollars, and $\frac13$ of Sam's money equals $\frac12$ of Janet's money. Together, they have more than $\$10$. What is the least number of dollars they could have combined?
Answer:
$15
Step-by-step explanation:
Let Sam's Money =s
Let Janet's Money =j
[tex]$\frac13$[/tex] of Sam's money equals [tex]$\frac12$[/tex] of Janet's money.
Let n be the number of dollars held by Sam and Jane respectively
Therefore: [tex]$n=\frac13s=\frac12j$[/tex]
s=3n
j=2n
s+j=3n+2n=5n
Together, they have more than $10
Therefore:
5n>10
n>2
The least sum they could have is at n=3
At n=3
s+j=5n=5X3=$15
The least number of dollars they could have combined is $15.
The diameter of a circle is 7 inches. Find its area to the nearest tenth
Step-by-step explanation:
diameter=7 inches
Area of the circle= π(7/2)² inches²
=38.465
38.5 inches²
Answer:
38.5 inches
Step-by-step explanation:
r = 1/2d
r = 1/2 × 7
r = 3.5
[tex] \boxed{ \bold{formula = \pi \: {r}^{2} }}[/tex]
= 3.14 × 3.5 × 3.5
= 38.465 inches
Find its area to the nearest tenth
38.465 inches
= 38.5 inches
3x ^ 3 - x ^ 2 Determine if the expression is polynomial or not . If it is a polynomial , state the type and degree of the polynomimal . The given expression a polynomial
The expression
[tex]3x^{3} -x^{2}[/tex]is a polynomial. Its type is cubic and the degree is 3.
Explanation:The given mathematical expression
[tex]3x^{3} -x^{2}[/tex]is a polynomial. A polynomial is an expression that is made up of variables and coefficients, using only the operations of addition, subtraction, and multiplication and non-negative integer exponents. The type of this polynomial is cubic, because the highest power of the variable (the degree) is 3. In this case, the highest degree is the highest exponent of the variable 'x', which is 3. Hence the given polynomial is cubic, with degree of 3.
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Express in the form 1 : n 6 : 24
Answer: n=4
Step-by-step explanation: 1:4 = 6:24