If m/n is the probability that you do not eat green candy after you eat a red candy, then m + n is 6.
A bag contains 8 green candies and 4 red candies. If you eat five candies, there are relatively prime positive integers m and n so that m/n is the probability that you do not eat green candy after you eat a red candy. Below list the ways to accomplish this ordering along with their respective probabilities:
GRRRR : [tex]\frac{8}{12}\times\frac{4}{11} \times\frac{3}{10} \times\frac{2}{9} \times\frac{1}{8}[/tex]
GGRRR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{4}{10} \times\frac{3}{9} \times\frac{2}{8}[/tex]
GGGRR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{4}{9} \times\frac{3}{8}[/tex]
GGGGR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}[/tex]
GGGGG : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}[/tex]
The sum is [tex]\frac{8\times3\times4(2+14+42+70+70)}{12.11.10.9.8}[/tex]
Probability that you do not eat green candy after you eat a red candy =[tex]\frac{1}{5}[/tex]
so m = 1 and n = 5
m + n =6
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Reflect the point in the x-axis followed by the y-axis.
Answer:
(3, - 4 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
(- 3, 4 ) → (- 3, - 4 )
under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
(- 3, - 4 ) → (3, - 4 )
A tank originally holds 10 grams of salt, mixed into 100 gallons of water. Water containing 1.5 g of salt/gallon
is entering at the rate of 5 gallons/minute. I water is exiting the tank at the same rate, find the amount of salt Q in
the tank after time t.
Let Si and S2 be subsets of a vector space V. Prove that span(Si n S2) C span(S1) nspan(S2). Give an example in which span(S1nS2) and span(Si)nspan(S2) are equal and one in which they are unequal.
Let S₁ and S₂ be subsets of a vector space V. So, proves are shown as well.
What is vector space?A vector space, also known as a linear space, is a collection of vectors that have been put together and multiplied ("scaled") by integers known as scalars. Real numbers are frequently seen as being scalars. Scalar multiplication by rational numbers, complex numbers, etc., on the other hand, seldom occurs. The term "subspace" refers to a vector space that is enclosed within another vector space. Each subspace is a vector space in and of itself, but it also has a definition in relation to another (bigger) vector space. We'll soon find out that there are a lot of different subspaces from earlier parts that we already know about.
Let, S₁ and S₂ be subsets of vector space V
Now, S₁ ⊆ V, S₂ ⊆ V
(S₁ ∩ S₂) ⊆ V
Let, x ⊆ span (S₁ ∩ S₂)
x ∈ span (S₁) and x ∈ span (S₂)
x ∈ span (S₁ ∩ S₂)
∴ span (S₁ ∩ S₂) ⊆ span (S₁) ∩ span (S₂)
span (S₁ ∩ S₂) = span (S₁) ∩ span (S₂)
where either S₁ ⊆ S₂ or, S₂ ⊆ S₁
span (S₁ ∩ S₂) ≠ span (S₁) ∩ span (S₂)
where, (S₁ ⊆ S₂) = ∅ but span (S₁) ∩ span (S₂)
(S₁ ∩ S₂) = ∅ i.e. span (S₁ ∩ S₂)
but span (S₁) = R₁²
span (S₂) = R₁²
Thus, span (S₁) ∩ span (S₂) = R₁²
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35m / 5h = help please
The solution to the given values by reducing them to their lowest term is 7m/h
Reducing values of the lowest term.The reduction of the given values to the lowest term possible can be achieved by using the long division process. So, we set up the division problem in a long division format.
5 || 35
Divide 35 by 5 . Place this digit in the quotient on top of the division symbol.
7
5 || 35
Multiply the newest quotient digit (7) by the divisor 5.
7
5 || 35
35
Subtract 35 from 35.
7
5 || 35
35
0
The result of the division to the lowest term possible is 7 m/h.
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Function Mathematics
The analisis and interpretation of functions, its domain and its range, indicates the following conclusions:
Case 2 - a) Domain: - 15 ≤ x < 15, b) Range: - 200 ≤ y < 400, c) f(0) = 100, d) f(x) = 0, when x = - 5.
Case 3 - g(1) = 6, g(x) = 1 when x = - 2, g(x) = 2 when x = 0 or x = 4.
How to analyze and interpret functions
In this question we must answer two exercises on functions. In the second case we have the representation of a function on Cartesian plane, whose domain is the set of all values on horizontal axis and range is for vertical axis.
By direct inspection, we find the following information:
a) Domain
- 15 ≤ x < 15
b) Range
- 200 ≤ y < 400
c) f(0) = 100
d) f(x) = 0, when x = - 5
The third case includes a table with domain and range of a functions, this must be interpreted to fill the following blanks:
g(1) = 6
g(x) = 1 when x = - 2
g(x) = 2 when x = 0 or x = 4
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Find f’(x) for f(x)=4x^3-5x^2+7x-10
Answer: The derivative of f(x) = 4x^3 - 5x^2 + 7x - 10 is given by f'(x) = 12x^2 - 10x + 7.
Step-by-step explanation:
Mensa is an organization that allows people to join only if their IQs are in the top 2% of the population. (You may need to use Table 8.1.)
(a)
What is the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa? (Remember that the mean is 100 and the standard deviation is 15. Round your answer to two decimal places.)
(b)
Mensa also allows members to qualify on the basis of certain standard tests. If you were to try to qualify on the basis of the quantitative reasoning part of the GRE exam, what score would you need on the exam? (Remember that the mean is 151.3 and the standard deviation is 8.7. Round your answer to the nearest whole number.)
(a) To be eligible for Mensa, an individual's IQ must be in the top 2% of the population. This means that the IQ score must be greater than or equal to the 97th percentile of the normal distribution. We can use the standard normal distribution table to find the 97th percentile.
Since the mean IQ score is 100 and the standard deviation is 15, we can standardize the IQ score to find the z-score:
z = (IQ - mean) / standard deviation
z = (IQ - 100) / 15
The 97th percentile corresponds to a z-score of 2.33. To find the IQ score, we can reverse the standardization formula:
IQ = z x standard deviation + mean
IQ = 2.33 x 15 + 100
IQ = 146.95
So, the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa is 147.
(b) To be eligible for Mensa on the basis of the quantitative reasoning part of the GRE exam, an individual's score must be in the top 2% of the population. This means that the score must be greater than or equal to the 97th percentile of the normal distribution. We can use the standard normal distribution table to find the 97th percentile.
Since the mean score on the quantitative reasoning part of the GRE is 151.3 and the standard deviation is 8.7, we can standardize the score to find the z-score:
z = (score - mean) / standard deviation
z = (score - 151.3) / 8.7
The 97th percentile corresponds to a z-score of 2.33. To find the score, we can reverse the standardization formula:
score = z x standard deviation + mean
score = 2.33 x 8.7 + 151.3
score = 162.291
So, the score required to be eligible for Mensa on the basis of the quantitative reasoning part of the GRE exam is approximately 162. Round to the nearest whole number, the score would be 162.
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Which of the following tables represents a relation that is a function?
x y
−5 −3
−2 3
−1 1
3 4
3 −1
x y
−5 4
−2 4
0 −4
0 4
3 4
x y
−4 0
−2 2
0 3
2 0
3 4
x y
1 −4
1 −2
1 0
1 2
1 4
For each of the following quadratic equations, find the discriminant and draw its sign diagram: Hence find values of m for which the equation has: (i) A repeated root (ii) two distinct real roots (iii) no real roots (a) x^2 − 4x + m = 0 (b) mx^2 + 3x + 2 = 0 (c) x^2 - mx + 1 = 0
a) For two distinct real roots: x > 0 or x > m
b) For two distinct real roots: x > 0 or x > 2m
c) For two distinct real roots: x > 0 or x > 4
This is based on the quadratic equation.
What is a quadratic equation?Only non-negative integer powers of x are present in the quadratic equation, making it a polynomial equation. In actuality, the Latin word quadratus, which means square, is the root of the term quadratic. The quadratic equation has the generic form ax² + bx + c = 0. where x is an unknowable variable and a, b, and c are mathematical coefficients.
a) Quadratic equation: x² - 4x + m = 0
The discriminant: Δ = b² - 4ac
Δ = (2x)² - 4.x.(m)
Δ = 4x² - 4mx
Δ = 4x (x - m)
For two distinct real roots: Δ > 0
4x (x - m) > 0
x > 0 or x > m
For two real roots: Δ ≥ 0
4x (x - m) ≥ 0
x ≥ 0 or x ≥ m
For a repeated root: Δ = 0
4x (x - m) = 0
x = 0 or x = m
(b) Quadratic equation: mx² + 3x + 2 = 0
The discriminant: Δ = b² - 4ac
Δ = (3x)² - 4.mx.(2)
Δ = 4x² - 8mx
Δ = 4x (x - 2m)
For two distinct real roots: Δ > 0
4x (x - 2m) > 0
x > 0 or x > 2m
For two real roots: Δ ≥ 0
4x (x - 2m) ≥ 0
x ≥ 0 or x ≥ 2m
For a repeated root: Δ = 0
4x (x - 2m) = 0
x = 0 or x = 2m
(c) Quadratic equation: x² - mx + 1 = 0
The discriminant: Δ = b² - 4ac
Δ = (x)² - 4.x.(1)
Δ = x² - 4x
Δ = x (x - 4)
For two distinct real roots: Δ > 0
x (x - 4) > 0
x > 0 or x > 4
For two real roots: Δ ≥ 0
x (x - 4) ≥ 0
x ≥ 0 or x ≥ 4
For a repeated root: Δ = 0
x (x - 4) = 0
x = 0 or x = 4
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How many adults binge drink four times per month?
A. 1 in 10
B. 1 in 6
C. 1 in 4
D. 1 in 8
K
Consider the numbers
Select all that apply.
Which are rational numbers?
A. 8
7
D. 0
G. √9
J.-√34
5
M. √3
8
4,√3, -2.57, 22, 19.2.-19, 125, 27.131331333-34. √2.-7.0,√/9.
B. 4
E.125
H. 7.131331333...
K. -2.57
N. 2
C.-19
OF. 22
1. 5
9
OL.
26
0. 19.2
The rational numbers in this problem are given by these following letters:
A, B, C, D, E, G, I, K, L, O.
What are rational and irrational numbers?Rational numbers are the whole numbers plus decimals that can be represented by fractions, involving both positive and negative numbers.
The set of irrational numbers is composed by numbers that cannot be represented by fractions, such as non-exact roots, which are non-terminating and non-repeating decimal numbers.
The irrational numbers are justified as follows:
7.1313313333... is a non-terminating decimal.The remaining are non-exact roots.More can be learned about rational numbers at brainly.com/question/12088221
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a factory produces 32 tables in an 8-hour day.Calculate how many tables are produced in 3 days
Answer: In an 8-hour day, the factory produces 32 tables. In 1 day, the factory produces 32 tables.
In 3 days, the factory will produce 3 days * 32 tables per day = 96 tables.
Step-by-step explanation:
Martha needs 28 strawberries for every 4 smoothies she makes.
Answer:
Step-by-step explanation:
If Martha needs 28 strawberries for every 4 smoothies she makes, then she needs 7 strawberries per smoothie.
suppose that {~v1, ~v2, ~v3} is a linearly dependent set of vectors in rn and ~v4 is vector in rn. show that {~v1, ~v2, ~v3, ~v4}is also a linearly dependent set.
True, that {~v1, ~v2, ~v3, ~v4}is also a linearly dependent set.
What is a linearly independent set?
A collection of vectors is said to be linearly independent in vector space theory if no nontrivial linear combination of the vectors equals the zero vector. The vectors are considered to be linearly dependent if such a linear combination occurs.
(i.e., all coefficients = 0). A single element set {v} is linearly independent if and only if v ≠ 0.
Now,
As given that
x1v1 + x2v2 + x3v3 = 0 with x1, x2, x3 not all zero, then x1v1 + x2v2 + x3v3 + 0 v4 = 0 and still the coefficients are not ALL zero.
Hence,
It is True that {~v1, ~v2, ~v3, ~v4}is also a linearly dependent set.
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Can you help me with this
Answer:
two plus two equals five
Step-by-step explanation:
A mechanic charger a flat rate of $30 per hour. You have already bought all the parts needed and only have $120 to fix your car. How many hours can the machine work on your car? Find the y-intercept and slope
Answer: 4 hours
Step-by-step explanation: y int = 120, slope = 30
find the difference of the polynomials 2a^2+3a and 3a^2-4a by subtracting the second from the first
Answer:
-a^2+7a
Step-by-step explanation:
Which pair of transformations could map ABC to A’B’C’, such that the triangles are similar but not congruent?
The pair of transformations that could map ABC to A’B’C’, such that the triangles are similar but not congruent are dilation and rotation
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the triangle be represented as ΔABC
Let the dilated triangle be represented as ΔA'B'C'
Let the dilation scale factor be represented as k
Now , when a triangle is dilated by a scale factor of k , there is a change in the shape of the triangle
After a dilation , the triangle will enlarge or compress by a factor k , but it will be similar to the parent triangle
Now , when the triangle is rotated , it only changes the initial coordinates of A , B and C
Hence , the transformations are dilation and rotation
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What is the solution to x=√-x+6
a. 2 and -3
b.-2 and 3
c. -3
d.2
The equation x = √-x + 6 cannot have any real solutions, because taking the square root of a negative number is not a real number. So the answer is none of the options listed.
What is equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept. Identity equations and conditional equations are the two types of equations. An identity holds true for all possible values of the variables. A conditional equation is valid only for certain values of the variables. An equation consists of two expressions joined by an equals sign ("=").
Here,
The equation x = √-x + 6 cannot have any real solutions, because taking the square root of a negative number is not a real number.
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The half-life of Carbon is 5730 years. If 10 grams of Carbon are present at time t = 0, how many will be present in 2,000 years?
The amount of Carbon that will be presented in 2,000 years is given as follows:
7.85 grams.
What is an exponential function?An exponential function is defined as follows:
y = a(b)^(x/n).
In which:
a is the initial amount.b is the rate of change.n is the time needed for the rate of change.Considering the initial amount of 10 grams and the half life of 5730 years, the parameters for this problem are given as follows:
a = 10, b = 0.5, n = 5730.
Hence the function is defined as follows:
y = 10(0.5)^(x/5730)
Then the amount after 2,000 years is given as follows:
y = 10(0.5)^(2000/5730)
y = 7.85 grams.
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There are five boxes. The weight of the first box is 200 kg and the weight of the second box is 20% higher than the weight of the third box, whose weight is 25% higher than the first box's weight. The fourth box at 350 kg is 30% lighter than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.
The difference in the average weight of the four heaviest boxes and the four lightest boxes is 75 Kg.
Given:
The weight of boxes is :
1st box = 200 kg
2nd box = 300 kg
3rd box = 250 kg
4th box = 350 kg
5th box = 500 kg
Since , heavier weight = 500 Kg
lighter weight = 200 Kg
Average weight of four heaviest boxes =1400/4=350kg
Average weight of four lightest boxes =1100/4=275kg
∴ Difference =(350−200)/2=150/2=75kg
Hence , the difference in the average weight of the four heaviest boxes and the four lightest boxes is 75 Kg.
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what is 0.6 as a whole number
The number which correctly represents the decimal 0.6 as a whole number is; 1.
Which number represents 0.6 as a whole number?It follows from the task content that the number which correctly represents the number 0.6 as a whole number is to be determined.
Since the given number is 0.6. It follows that the closest whole number can be determined by rounding off to th nearest whole number.
Hence, by rounding off; we have; 1.
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the number of marbles peter had to be the number of marbles ravi had was in the ratio 8:5. after giving 18 marbles to his friends, peter had the same number of marbles as ravi. how many marbles did ravi have?
Answer:
30
Step-by-step explanation:
before
p:r
=8:5
after
p:r
=5:5
3 units=18
1 unit=6
no. of marbles Ravi has=5 units=6×5=30
Find the distance between the points on a number line. -5,-20 distance is
Answer:
15
Step-by-step explanation:
The distance can't be negative.
20-5=15
If the hot-tub heater provides 5900 kJ/min, how long, in hours, will it take to heat the water in the hot tub from 65 °F to 104 °F?
Express your answer to two significant figures and include the appropriate units.
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Value
20
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So, using a heater with a heating output of 5900 kJ/min, it will take roughly 9.05 hours to heat the water in the hot tub from 65°F to 104°F.
What kind of energy does heating use?When the temperature rises, atoms and molecules move faster and collide, creating thermal energy (also known as heat energy). Thermal energy is the energy that results from the heated substance's temperature.
How do you calculate kW for heating?Calculate the square footage or square metres of your room. The room's dimensions are then multiplied by its width, height, and length. Then double this amount by 6. For BTUs or 0.0606 for kW, respectively.
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help is you can god bless!!!
Answer: sorry downbad for points god bless
Step-by-step explanation:
pls help it’d overdue!!
Which is different?
O Solve
3
==
X
O Solve
O Find x so that 3:x and 12:8 are equivalent.
O
Find x so that 3:12 and x:8 are equivalent.
12
8
12 3
X
8
=
Find "both" answers
The answer to the "different" question is x =
The answer to the "same" questions is x =
D
The answer to the "different" question is: 32
The answer to the "same" question is: 2
A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate to the nearest degree the angle of the sector.
Answer:
177°
Step-by-step explanation:
A sector is the area between two radi.
We are given the perimeter of the sector as 21.4cm and the radius 4.2cm. Subtracting two radi from the perimeter will give us the arc of the sector as 13.
As we know, the formula for the length of an arc is: length of arc = ∅/360 × πd. Diameter is double the radius so in this case it's 8.4; so filling in the blanks our new formula is: 13 = ∅/360 × 8.4π.
We are trying to find ∅ which is the degree of the sector. So from this formula we can rearrange it by dividing 8.4π on both sides of the equation giving ¹³/8.4π = ∅/360; from here we multiply 360 on both sides and therefore getting ∅ on its own therefore allowing us to equate it.
Plug that all into a calculator and you get 177.3440794 so you can round it down to 177°
I saw this question a few minutes ago but spent a bit of time calculating it...sorry :)
How long would it take a falling rock with an acceleration of 9.81m/s² to reach the ground from a height of 100 meters?
The time it would take for the rock to reach the ground is given as follows:
3.19 seconds.
How to model the projectile's height?The quadratic equation that models a projectile's height is given as follows:
y = -9.81t² + v(0)t + h(0).
In which:
v(0) is the initial velocity.h(0) is the initial height.The parameters for this problem are given as follows:
v(0) = 0, h(0) = 100.
The rock reaches the ground when y = 0, hence:
9.81t² = 100
t = sqrt(100/9.81)
t = 3.19 seconds.
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What is an equation for the linear function whose graph contains the point (2, 5) with a slope of -5?
Answer:
y=-5x+15.
Step-by-step explanation:
1. if the given slope is (-5), then it is possible to make up the required equation in slope-interception form: y=-5x+interception, where 'interception' is unknown number;
2. in order to calculate the 'interception' it is enought to substitute the given coordinates of the point into the last equation (y=5; x=2):
5=-5*2+interception; ⇒ interception=15. Then
3. finally, the required equqaiton is y=-5x+15.