Answer:
(a) 0.35
(b) 0.43
(c) 0.49
(d) 0.54
Step-by-step explanation:
The complete question is:
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 40. b) 48. c) 56. d) 64.
Solution:
(a)
There are n = 40 positive integers.
Compute the probability of selecting none of the correct six integers in a lottery as follows:
[tex]P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {34\choose 6}}{{40\choose 6}}=\frac{1344904}{3838380}=0.35038\approx 0.35[/tex]
(b)
There are n = 48 positive integers.
Compute the probability of selecting none of the correct six integers in a lottery as follows:
[tex]P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {42\choose 6}}{{48\choose 6}}=\frac{5245786}{12271512}=0.42748\approx 0.43[/tex]
(c)
There are n = 56 positive integers.
Compute the probability of selecting none of the correct six integers in a lottery as follows:
[tex]P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {50\choose 6}}{{56\choose 6}}=\frac{15890700}{32468436}=0.48942\approx 0.49[/tex]
(d)
There are n = 56 positive integers.
Compute the probability of selecting none of the correct six integers in a lottery as follows:
[tex]P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {58\choose 6}}{{64\choose 6}}=\frac{40475358}{74974368}=0.53986\approx 0.54[/tex]
Probability of selecting none of the six integers in a lottery is 0.35
Probability based problem:Assuming that number n = 40.
n = 40 as a positive integer
Probability of selecting none of the correct six integers in a lottery = C(34 , 6) / C(40 , 6)
Probability of selecting none of the correct six integers in a lottery = 1344904 / 3838380
Probability of selecting none of the correct six integers in a lottery = 0.35
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CAN SOMEONE HELP ASAP!!!
Answer:
( x-2)^2 + ( y+1) ^2 = 25
Step-by-step explanation:
The equation of a circle is
( x-h)^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
The center is ( 2,-1) and the radius is the difference from the center to a point on the circle
(2,4) and (2,-1)
since x is the same the radius is (4- -1) = 5
( x-2)^2 + ( y--1) ^2 = 5^2
( x-2)^2 + ( y+1) ^2 = 25
The perimeter of a rectangular garden is 168 feet. If the length of the garden is 6 feet more than twice the width, what is the length of the garden? Length = 52.5 feet Length = 54 feet Length = 58 feet Length = 48 feet
Answer:
Length= 58
width= 26
Step-by-step explanation:
What is the y-coordinate of point D after a translation of
(x, y) - (x + 6,7 - 4)?
Hey There!!
Your answer will be 1.
Step-by-step explanation:
If the coordinates of the point D' are (x, y), then, after translation, it will be
D(x + 6, y - 4).
that is 6 units right and 4 units down
It is given that the point before translation is D'(3, 5).
So, x + 6 = 3 + 6 = 9 and
y - 4 = 5 - 4 = 1
So, the y coordinate of point D after translation is 1.
Hope This Helps!!!
By ♡Itsbrazts♡
Anya graphed the line (y−2)=3(x−1) on the coordinate grid. A coordinate plane with a line passing through the points, (negative 2, negative 7), (0, negative 1), and (1, 2). What is the slope of Anya’s line? −3 −1 1 3
Answer:
Slope of Anya's line is m = 3
Step-by-step explanation:
Explanation:-
Given Anya graphed the line
(y−2)=3(x−1)
we know that slope intercept form is
y = mx +c
now given Anya line
y−2=3(x−1)
⇒ y - 2 = 3x - 3
⇒ y = 3x - 3 + 2
⇒ y = 3 x - 1
Comparing slope -intercept form
y = mx +c
slope of Anya's line is m = 3 and y-intercept C = -1
Answer:
M=3
Step-by-step explanation:
Hope this helps!
PLEASE HELP IMMEDIATELY
Find x when[tex] - \frac{1}{2} + x = - \frac{21}{4} [/tex]
[tex] - \frac{23}{4} [/tex]
[tex] - \frac{19}{4} [/tex]
[tex] \frac{19}{4} [/tex]
[tex] \frac{23}{4} [/tex]
Answer:
[tex]x = - \frac{19}{4} [/tex]Option B is the correct option.
Step-by-step explanation:
[tex] - \frac{1}{2} + x = - \frac{21}{4} [/tex]
Move constant to R.H.S and change its sign:
[tex]x = - \frac{21}{4} + \frac{1}{2} [/tex]
Take the L.C.M
[tex]x = \frac{ - 21 + 1 \times 2}{4} [/tex]
[tex]x = \frac{ - 21 + 2}{4} [/tex]
Calculate
[tex]x = - \frac{19}{4} [/tex]
Hope this helps...
Good luck on your assignment..
Step-by-step explanation:
-19/4 is the correct answer for your question
Work out
(8 x 1011) : (4 x 1017
Give your answer in standard form.
Trig work that i don’t understand. pls help
Answer:
B. 642.22 units squared
Step-by-step explanation:
Knowing that QP ║ MN and ∠QLP = ∠MLN, then ΔQLP ~ ΔMLN.
That means corresponding sides and heights have the same ratios.
We know that QP = 25, which corresponds to MN = 34. Also, the height of ΔQLP, LS, corresponds to the height of ΔMLN, LR = LS + SR = LS + 10. Let's say LS = x.
We can now write:
QP / MN = LS / LR
25 / 34 = x / (x + 10)
Cross-multiply:
34 * x = 25 * (x + 10)
34x = 25x + 250
34x - 25x = 250
9x = 250
x = 250/9 ≈ 27.78 units
So, LS = 27.78 units and LR = LS + SR = 27.78 + 10 = 37.78 units.
The area of a triangle is denoted by A = (1/2) * b * h, where b is the base and h is the height.
Here, the base of ΔLMN is MN = 34, and the height is LR = 37.78. Plug these in:
A = (1/2) * b * h
A = (1/2) * 34 * 37.78 ≈ 642.22 units squared
The answer is thus B.
~ an aesthetics lover
Help please and thank you: The graph of f x = x2 − 2x − 3 is shown. Which of these describes the effect changing f x to f −2x will have on the graph?
Answer:
Option (C).
Step-by-step explanation:
Graphed function is,
f(x) = x² - 2x - 3
= x² - 2x + 1 - 1 - 3
= (x² - 2x + 1) - 4
= (x - 1)² - 4
f(-2x) = (-2x)² - 2(-2x) - 3
= 4x² + 4x - 3
= 4(x² + x) - 3
= 4[x² + 2(0.5)x + (0.5)²- (0.5)²] -3
= 4(x + 0.5)² - 1 - 3
= 4(x + 0.5)² - 4
= 4[(x - 1) + 1.5]² - 4
Therefore, parent function 'f' will be a horizontal shrink by 4 units and shifted 1.5 units to the left.
Option (C) will be the answer.
The area of a rectangular garden is given by the quadratic function:A(x)=-6x^2+105x-294A . Knowing that the area, length, and width all must be a positive value puts restrictions on the value of x. What is the domain for the function? Explain how you determined the domain. For what value of x, produces the maximum area? What is the maximum area of the garden? What is the Range of the function? Explain how you determined the range? What value(s) of x produces an area of 100 square units?
Answer and Step-by-step explanation:
The domain of a function is the values the invariable can assume to result in a real value for the variable. In other words, it is all the values x can be.
Since it's related to area, the values of x has to be positive. The domain must be, then:
[tex]-6x^{2} + 105x - 294 = 0[/tex]
Solving the second degree equation:
[tex]\frac{-105+\sqrt{105^{2} - 4(-2)(-294)} }{2(-6)}[/tex]
x = 3.5 or x = 14
The domain of this function is 3.5 ≤ x ≤ 14
The maximum area is calculated by taking the first derivative of the function:
[tex]\frac{dA}{dx} = -6x^{2} + 105x - 294[/tex]
A'(x) = -12x + 105
-12x + 105 = 0
-12x = -105
x = 8.75
A(8.75) = [tex]-6.8.75^{2} + 105.8.75 - 294[/tex]
A(8.75) = 165.375
The maximum area of the garden is 165.375 square units.
The Range of a function is all the value the dependent variable can assume. So, the range of this function is: 0 ≤ y ≤ 165.375, since this value is the maximum it will reach.
A(x) = 100
[tex]100 = -6x^{2} + 105x-294[/tex]
[tex]-6x^{2} + 105x - 394 = 0[/tex]
Solving:
[tex]\frac{-105+\sqrt{105^{2}-4(-6)()-394} }{2(-6)}[/tex]
x = 5.45 or x = 12.05
The values of x that produces an area of 100 square units are 5.45 and 12.05
Your bank has two checking account options, one pays tax-free interest at a rate of 3% per annum and the other pays taxable interest at a rate of 4.5% per annum. You are currently in a 24% marginal tax bracket. If you converted the tax-free interest rate to the comparable taxable interest rate you would find that:
Answer:
The comparable tax rate is 3.95%, thus you should choose the 4.5% taxable account option.
Step-by-step explanation:
In order to convert the tax-free interest rate of 3% per year to the comparable taxable interest rate, one should consider that 3% is the interest rate after the marginal tax discount. If you are at the 24% marginal tax bracket, the comparable rate is:
[tex]r*(1-0.24)=0.03\\r=\frac{0.03}{0.76}\\r=0.0395\\r=3.95\%[/tex]
The comparable tax rate is 3.95%, thus you should choose the 4.5% taxable account option.
The comparable tax rate is 3.95%, so you should choose the 4.5% taxable account option.
calculation of the comparable tax rate:Since the rate is 3% per annum, the other rate should be 4.5% and there is tax rate of 24%
So,
rate (1 - 24%) = 3%
rate = 3.95%
Learn more about the rate here: https://brainly.com/question/13021566
Q2.
If ε={1, 2, 3, 4,………….., 10} and
A = Set of even numbers between 1 and 10.
B = Set of odd numbers between 1 and 10
C = Set of prime numbers between 1 and 10
(i)
List down the elements of sets A, B and C.
(ii)
List down the number of elements in sets A, B and C.
(iii)
Find AUC.
(iv)
Find BC.
(v)
Find AC
Answer:
hope its helpful to uh....
Priscilla has three cups of apples left. She wants to use them in another fruit salad.
How would she find out how much of the other fruits she needs to use up the
remaining apples?
Answer:
To use up the remaining 3cups of apples, she would need 3cups of oranges, 12cups of strawberries, 6cups of cherry and 9 cups of grape.
Step-by-step explanation:
This is a continuation of the question on the recipe for making salad. The initial recipe from her grandmother is stated below (found on brainly, ID 6786167).
The fruit salad recipe calls for one part apple, one part orange, four parts strawberry, two parts cherry, and three parts grape.
Priscilla uses the same measuring cup to measure all of the fruit, so one part is equal to one cup of diced fruit.
Number of cups required for each fruit in the original recipe:
apple = 1 cup , orange = 1 cup, strawberry = 4cups, cherry = 2cups, grape = 3cups
Original ratios of the cup of fruit respectively = 1:1:4:2:3
Total number of cups required in the original recipe: 1+1+4+2+3 = 11 cups
Now for this question, 3 cups of apples are remaining. And we want to find number of other fruits she needs in order to use up the remaining apples.
To do this we would use the ratios of the cup of fruit.
When we had 1 apple, the ratio was = 1
Now we have 3apples, the new ratio = 3×original ratio
=3×1 = 3
This means we would multiply each of the fruit ratios by 3
For orange, new ratio = 3×1 = 3
For strawberries, new ratio = 3×4 = 12
For cherry, new ratio = 3×2 = 6
For grape, new ratio = 3×3 = 9
To use up the remaining 3cups of apples, she would need 3cups of oranges, 12cups of strawberries, 6cups of cherry and 9 cups of grape.
Answer:
Priscilla uses one part orange, four parts strawberry, two parts cherry, and three parts grape for every one part apple. So, to use three times the quantity of apples, she will have to use three times the quantity of the other fruits as well. She needs three parts orange, twelve parts strawberry, six parts cherry, and nine parts grape for three parts apple.
Step-by-step explanation:
plato/edmentum answer
Q3. Ishah spins a fair 5-sided spinner. She then throws a fair coin.
(i) List all the possible outcomes she could get. The first one has been done for you.
(1, H)
(ii) Ishah spins the spinner and tosses the coin.
Work out the probability that she will get a 2 and a head.
Answer:
see below
Step-by-step explanation:
1.
1, H - 2, H - 3, H - 4, H - 5, H
1, T - 2, T - 3, T - 4, T - 5, T
2.
2,H is one out of 10 possible outcomes, so the probability is 1/10
The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the number. Also, If the tens digit is x, then the equation is: ___?
The volume of a right circular cone with both
2507
diameter and height equal to his What is the
3
value of h?
A) 5
B) 10
C) 20
D) 40
Question:
The volume of a right circular cone with both diameter and height equal to h is 250/7 cm³.
What is the value of h?
Answer:
A. 5
Step-by-step explanation:
Given
Solid Shape: Cone
Volume = 250/7
Diameter = Height
Required
Find the height of the cone
Provided that the diameter (D) and the height (h) are equal; This implies that
D = h ------ (1)
Also, Diameter (D) = 2 * Radius (r)
D = 2r
Substitute 2r for D in (1)
2r = h
Multiply both sides by ½
½ * 2r = ½ * h
r = ½h
Volume of a cone is calculated by;
Volume = ⅓πr²h
⅓πr²h = 250/7
Substitute ½h for r
[tex]\frac{1}{3} * \pi * (\frac{1}{2}h)^2 * h = \frac{250}{7}[/tex]
Take π as 22/7, the expression becomes
[tex]\frac{1}{3} * \frac{22}{7} * (\frac{1}{2}h)^2 * h = \frac{250}{7}[/tex]
Open the bracket
[tex]\frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7}[/tex]
Multiply both sides by 7
[tex]7 * \frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7} * 7[/tex]
[tex]\frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250[/tex]
Multiply both sides by 3
[tex]3 * \frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250 * 3[/tex]
[tex]22 * \frac{1}{4}h^2 * h = 750[/tex]
Multiply both sides by 4
[tex]4 * 22 * \frac{1}{4}h^2 * h = 750 * 4[/tex]
[tex]22 * h^2 * h = 3000[/tex]
[tex]22 * h^3 = 3000[/tex]
Divide both sides by 22
[tex]h^3 = \frac{3000}{22}[/tex]
[tex]h^3 = 136.36[/tex]
Take cube root of both sides
[tex]h = \sqrt[3]{136.36}[/tex]
[tex]h = 5.15[/tex]
[tex]h = 5[/tex] (Approximated)
Maureen spent sh 207 to buy 7 exercise books and 4 pens while Sharon spent sh 165 to buy 5 exercise books and 5 pens of same type.Find the cost of each item
Answer:
book 25; pen 8
Step-by-step explanation:
If we let b and p represent the cost of a book and a pen, respectively, then the two purchases can be written as ...
7b +4p = 207
5b +5p = 165
Multiply the second equation by 4/5 and subtract the result from the first equation:
(7b +4p) -4/5(5b +5p) = (207) -4/5(165)
3b = 75 . . . . simplify
b = 25 . . . . . divide by 3
Dividing the second equation by 5 gives ...
b + p = 33
Solving for p, we have ...
p = 33 -b = 33 -25 = 8
The cost of an exercise book is 25; the cost of a pen is 8.
Please help! It is Geometry
Answer:
X=20; pqr = 130°
Step-by-step explanation:
They key here is to notice that the instructions say that qs bisects pqr, meaning that it evenly cuts it into 2 pieces. So, to find x, you just solve for x in the equation 3x+5=2x+25. Then, you plug it back into either side of the equation, at which point, you should get 65. Since it is half of pqr, just double it to get your final answer of 130°
In ΔABC, if AB = 10 and BC = 6, AC can NOT be equal to
A. 4
B. 6
C. 8
D. 10
Answer:
A
Step-by-step explanation:
The answer is A because in the triangle, the two smaller sides added up have to be more than the bigger side, or equal, if it is a right triangle. so 4 is the smallest 4+6=10, so it does not work, but lets see if it is a right triangle
4^2+6^2=16+36=52. it would have to equal 100 to be a right triangle. Use Pythagorean thereon.
For a triangle, the any two sides must be greater than the third side.The measure of AC cannot be equal to 4
What is a triangle?A triangle has three sides and angle. For a triangle, the any two sides must be greater than the third side.
Given the following parameters
AB = 10 and
BC = 6
The measure of AC must be 8 for the theorem above to be true
6 +8 > 10
6 +10 > 8
10 + 8 > 6
Hence the measure of AC cannot be equal to 4
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31.7+42.8+26.4+x/4=39.1 100.9+x/4
31.7 + 42.8 + 26.4 + x/4 = 39.1
Add up all the plain numbers on the left side:
100.9 + x/4 = 39.1
Subtract 100.9 from each side:
x/4 = 39.1
Multiply each side by 4:
x = 156.4
Answer:
Step-by-step explanation:
To solve this, we have to first find the sum of each of the terms on the numerator of the fraction on the right:
31.7 + 42.8 + 26.4 + x = 100.9 + x
The sum of terms ind the numerator of the fraction on the right.
39.1 + 100.9 + x= 140 + x
Next step is to cancel out the denominators as they are equal.
Now we are left with
100.9+x = 140+x
Rearrange and solve
To get x = 156.4
Write an equation in slope-intercept form of the line that passes through (-3,3) and (1,2)
Answer:
y = -1/4x + 9/4
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope
b = y-intercept
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
3-2/-3-1
Slope = [tex]-\frac{1}{4}[/tex]
In this problem, to find the y-intercept [tex]y-y_1 = m (x-x_1)\\[/tex].
y-3 = -1/4 (x+3)
y= -1/4x + 9/4
Answer:
yoo
Step-by-step explanation:
You are remodeling your kitchen. You've contacted two tiling companies who
gladly told you how long it took their workers to tile a floor of a similar size.
Jim completed half the floor in 12 hours. Pete completed the other half of the
floor in 10 hours. If Pete can lay 25 more tiles per hour than Jim, what
equation would you use to find the rate that Jim can lay tiles? Let x represent
Jim's rate.
Answer:
12x=10(25+x)
Step-by-step explanation:
Jim's rate=x
Pete's rate=y
Jim and Pete lays the same number of tiles.
So we have,
12x=10y
Pete's can lay 25 more tiles than Jim per hour
We have
y=25+x
Substitute y=25+x into 12x=10y
12x=10y
12x=10(25+x)
12x=250+10x
12x-10x=250
2x=250
x=250/2
=125
x=125
12x=10(25+x) is the equation used to find the rate that Jim can lay tiles
If f(x) = 3x - 5 and g(x) = 7x + 2, what is f(x) x g(x)
Answer:
21x + 1
Step-by-step explanation:
f[g(x)]
= f(7x + 2)
= 3(7x + 2) - 5
= 21x + 6 - 5
= 21x + 1
I am being timed pls asap
Answer:
Writing it in matrix form
- 2 - 4 - 5 - 155
1 1 6 101
2 2 - 3 37
I hope this helps you
What are the roots of the function y = 4x2 + 2x - 30?
To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x - 30.
Factor out the GCF of
Next, factor the trinomial completely. The equation becomes
Use the zero product property and set each factor equal to zero and solve.
The roots of the function are
Answer:
-3, 5/2
Step-by-step explanation:
What are the roots of the function y = 4x2 + 2x – 30?
To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.
Factor out the GCF of : 2, so the equation becomes 0 = 2(2x2+x-15)
Next, factor the trinomial completely. The equation becomes: 0=2(x+3)(2x-5)
Use the zero product property and set each factor equal to zero and solve.
x+3=0 2x-5 = 0
x = -3, 5/2
The roots of the function are -3, 5/2.
Hope this helped!
The roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
y = 4x² + 2x - 30
To find the roots of the quadratic equation plug y = 0
4x² + 2x - 30 = 0
4x² + 12x - 10x - 30 = 0
4x(x + 3) - 10(x + 3) = 0
(x + 3)(4x -10) = 0
x + 3 = 0 or 4x - 10 = 0
x = -3 or x = 10/4 = 5/2
Thus, the roots of the function y = 4x² + 2x - 30 are -3, 5/2 after using the zero product property.
Learn more about the function here:
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Orion is working with a data set that compares the outside temperature, in degrees Celsius, to the number of gallons of ice cream sold per day at a local grocery store.
The data has a line of best fit modeled by the function f(x) = 3x + 4 . Orion determines that when the temperature is 25∘C, the store should sell about 79 gallons of ice cream. The correlation coefficient of the data is 0.39.
Explain how accurate Orion expects the prediction to be.
Answer: kindly check Explanation.
Step-by-step explanation:
The function f(x) = 3x + 4 is a linear regression model. Orion's prediction was obtained by Substituting 25 for x to obtain the predicted variable
f(25) = 3(25) + 4 = 75 + 4 = 79.
However, with a correlation Coefficient of 0.39, which is a numerical value of range - 1 to +1 and is used to measure the statistical relationship between the dependent variable (number of gallons of ice-cream sold per day) and the independent variable (temperature).
The closer the correlation Coefficient (r) value is to +1 or - 1, the stronger the degree of correlation. Positive r values depicts positive relationship while negative r values depicts negative relationship. The closer the r value is to 0. The weaker the relationship and a r value of means there is no Relationship exists between the two variables.
With a correlation Coefficient of 0.39, we can Infer that that only a moderate positive relationship exists between temperature and gallons of ice cream sold per day.
help i need to submits this quickly
============================================================
Explanation:
Pick two points on this diagonal line where (x,y) has whole number coordinates. Two such points that fit the description are (-3,2) and (1,-1)
Use the slope formula to find the slope through these points
m = (y2-y1)/(x2-x1)
m = (-1-2)/(1-(-3))
m = (-1-2)/(1+3)
m = -3/4 is the slope
-------------------------
Extra info:
It doesn't matter which two points you pick as you'll always get the same slope value. Of course, the points must be on the diagonal line.
The negative slope indicates the line goes downhill as you move from left to right.
slope = rise/run = -3/4
rise = -3, a negative rise means we go down 3 units
run = 4, we go to the right 4 units
so we go down 3 and over to the right 4. This will move us from (-3,2) to (1,-1)
? of 72 = 45 (answer in fraction)
Answer:
5/8
Step-by-step explanation:
72 = 16/10 of 45
45 = 10/16 = 5/8 of 72
How many ways are possible to choose 3 days out of February? NOTE: Use 28 days for the number of days in February. A) 3276 B) 378 C) 20475 D) 2925
Answer:
A) 3,276 ways.
Step-by-step explanation:
In this case, choosing February 1, February 12, and February 20 would be the same thing as choosing February 12, February 1, and February 20. So, since order does not matter, we will use a combination to solve the question.
The formula for combinations is...
n! / [r!(n - r)!], where n = the number of days in February (28) and r = the number of days you are choosing (3).
28! / [3! * (28 - 3)!]
= 28! / (6 * 25!)
= (28 * 27 * 26) / 6
= (14 * 9 * 26) / 1
= 14 * 9 * 26
= 126 * 26
= A) 3,276.
Hope this helps!
THIS IS A WHOLE PAGE ITS FOR 40 points MIDDLE SCHOOL PLEASE HELP
Answer:
the leanth of the track is 1/2 miles long.
Step-by-step explanation:
Im sorry that i couldn't complete all the questions, I had a family thing to go to so sorry.
In a collection of red, blue, and green marbles, there are 25% more red marbles than blue marbles, and there are 60% more green marbles than red marbles. Suppose that there are $r$ red marbles. What is the total number of marbles in the collection?
Answer:
The total number of marbles is 3.4*r
Step-by-step explanation:
We have 25% more red than blue, so we can write the equation:
[tex]red = 1.25*blue[/tex]
We have 60% more green than red, so:
[tex]green = 1.6*red[/tex]
In total we have 'r' red marbles, so:
[tex]red = r[/tex]
The total number of marbles in the collection is the sum of all three amount of marbles:
[tex]total = red + blue + green[/tex]
[tex]total = red + (red/1.25) + 1.6*red[/tex]
[tex]total = r + 0.8*r + 1.6*r[/tex]
[tex]total = 3.4*r[/tex]
The total number of marbles is 3.4*r