Answer: The required probability of getting two green marbles is 49.45%.
Step-by-step explanation: Given that a bag contains 10 green marbles and 4 yellow marbles. Two marbles are chosen at random, one at a time and without replacement.
We are to find the probability of getting two green marbles.
Let S denote the sample space for the experiment of choosing a marble from the bag and A denote the event of getting a green marble.
The, n(S) = 10 + 4 = 14 and n(A) = 10.
So, the probability of event A will be
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{10}{14}=\dfrac{5}{7}.[/tex]
After getting one green marble and not replacing, let S' denote the sample space for the experiment of choosing a marble from the bag
and
let B denote the event of getting another green marble.
Then, n(S') = 14 - 1 = 13 and n(B) = 10 - 1 = 9.
Then, the probability of getting two green marbles is given by
[tex]P\\\\=P(A)\times P(B)\\\\=\dfrac{5}{7}\times\dfrac{n(B)}{n(S')}\\\\\\=\dfrac{5}{7}\times\dfrac{9}{13}\\\\\\=\dfrac{45}{91}\times100\%\\\\=49.45\%.[/tex]
Thus, the required probability of getting two marbles is 49.45%.
The sides of a triangle are in the ratio 5:12:13. Describe the length of the shortest side is the perimeter is not more than 120 inches
Solve the following system of equations.
x − 2y = 5
−3x + 2y = 7
A. x = 3, y = −1
B. x = 11, y = 11/2
C. x = 3, y = 1
D. x = −6, y = -11/2
Calvin cleans 3/5 of his bathroom with 1/3 of a bottle of cleaning solution how much solution would he use if he cleaned the whole bathroom
For the following geometric sequence, find the recursive formula.
{-80, 20, -5, ...}
Answer:
[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]
Step-by-step explanation:
{-80, 20, -5, ...}
General recusive formula for geometric sequence is
[tex]a_n = r \cdot a_{n-1}[/tex]
Where 'r' is the common ratio
To find common ratio 'r' we divide second term by first term
[tex]r=\frac{20}{-80} =-\frac{1}{4}[/tex]
Replace 'r' with -1/4
First term is -80
Recursive formula becomes
[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]
a ride at an amusement park rises 8 feet every horizontal change of 2 feet. how could you determine the slope of the ride?
If you shift the linear parent function, f(x) = x, down 6 units, what is the equation of the new function?
A. g(x) = x + 6
B. g(x) = x
C. g(x) = 6x
D. g(x) = x – 6
Answer:
Option D is correct
[tex]g(x) = x-6[/tex]
Step-by-step explanation:
Vertically down :
If y =f(x) is a parent function, then the new function g(x) b units vertically down is, g(x) = f(x) -b.
As per the statement:
Given the parent function:
[tex]f(x) = x[/tex]
To shift linear parent function vertically down 6 units.
By definition we have;
g(x) = f(x) -6
⇒[tex]g(x) = x-6[/tex]
Therefore, the equation of new function g(x) is, [tex]g(x) = x-6[/tex]
Zack is purchasing a bag of apples. The cost of apples is proportional to the weight of the apples in pounds as shown on the graph. Which statements are true about the cost of the apples?
Which statements are true about the cost of the apples?
Select each correct answer
1 lb of apples will cost Zack $2.50.
10 lb of apples will cost Zack t $4.
4 lb of apples will cost Zack $10.
2.5 lb of apples will cost Zack $1.
Answer:
1 lb of apples will cost Zack $2.504 lb of apples will cost Zack $10Step-by-step explanation:
The graph axesand common sense tell you that each ordered pair represents ...
(weight, cost)
So the ordered pairs (1, 2.50) and (4, 10) mean ...
1 lb of apples will cost Zack $2.50
4 lb of apples will cost Zack $10
A and C should be the correct answers if I'm not mistaken
Graph each equation by using the x- and y-intercepts
I only just started learning Algebra, and my teacher just threw all these worksheets at us without explaining much. Can someone please explain the concept of Algebra? Staring with this question, please:
Answer:
x = -8
Step-by-step explanation:
Hello!
Algebra is based on the concept of unknown values called variables, the value of each variable must remain the same in each problem.
Here are steps to solve your problem!
1. Pull out like terms:
-x - 8 = -1 • (x + 8)
2. Solve -x-8 = 0
Add 8 to both sides of the equation:
-x = 8
Multiply both sides of the equation by (-1)
x = -8
Therefore, x = -8
Hope this Helps!
What is f(-4) if f(x)=|7x-3|
The number 1.258201... can be classified as which of the following? Select all that apply. Real, rational, irrational, whole, integer ,natural
Its a multiple choice question
The number can be classified as both real and irrational
The given number:
= 1.258201
A real number is any number that can represent a distance along a line
A rational number is a real number that can be expressed in form a ratio, it usually have terminating decimals.
An irrational number is any real number that cannot be expressed in form of ratio, it doesn't have terminating or repeating decimals.
A whole number does not contain fractions, it is usually positive integers.
Integers are whole numbers that includes negative and positive numbers.
The given number is a real number but it doesn't contain terminating or repeating decimals. Hence it is irrational number.
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System of Equations Applications
Bill and Cody are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of double chocolate chip cookie dough. Bill sold 9 packages of white chocolate chip cookie dough and 2 packages of double chocolate cookie dough for a total of $200. Cody sold 2 packages of white chocolate chip cookie dough and 13 packages of double chocolate chip cookie dough for a total of $283. find the cost each of one package of white chocolate chip cookie dough and one package of double chocolate chip cookie dough.
50 POINTS! + BRAINLIEST! PLEASE HELP
slope = rise over run = y/x
A (-1,3) slope = 3/-1 = -3
B (1,2) slope = 2/1 = 2
C (-3,-1) slope = -1/-3 = 1/3
2 lines need to be negative reciprocals in order to be a right triangle
negative reciprocal of -3 is 1/3
so this is a right triangle
Answer: yes it is
Step-by-step explanation: put into a graph and it will become clear
A triangle has sides of lengths 6, 2, 7. Is it right triangle?
Rational Exponent
Explain why the square root of a number is defined to be equal to that number to the 1/2 power.
Answer:
Sample Response:
Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.
Step-by-step explanation:
Randy is twice as old as his sister jane. together the sum of their ages is 15. how old is randy?
Final answer:
Randy is 10 years old.
Explanation:
The question is about solving a simple algebraic equation involving ages.
We are told Randy is twice as old as his sister Jane, and the sum of their ages is 15 years.
If we let Jane's age be represented by 'j', then Randy's age would be '2j' as he is twice as old as Jane.
The equation to represent the sum of their ages is:
j + 2j = 15
To find Jane's age, we combine the like terms:
3j = 15
Now, we divide both sides of the equation by 3 to isolate 'j':
j = 15 / 3
j = 5
Therefore, Jane is 5 years old. To find Randy's age, we multiply Jane's age by 2:
Randy's age = 2 * Jane's age
Randy's age = 2 * 5
Randy's age = 10
So, Randy is 10 years old.
The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).
A. g(x) = (x – 3)2 – 4(x – 3) + 4
B. g(x) = (x2 – 4x + 4) – 3
C. g(x) = (x2 – 4x + 4) + 3
D. g(x) = (x + 3)2 – 4(x + 3) + 4
Answer:
answer is A for APEX..
Step-by-step explanation:
The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .
What is shifting of a function?A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.
Given
f(x) = [tex]x^{2} -4x+4[/tex]
The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).
If the function is shifted to the left it is going to plus(+).
If the function is shifted to the right it is going to minus(-).
So, x = x - 3
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex]
The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create
g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .
Option A is correct.
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Un número entero de tres dígitos es igual a 25 veces la suma de sus dígitos. Si los tres dígitos se invierten, el número que resulta excede al número dado por 198.
El dígito de las decenas en uno menos que la suma de los dígitos de las centenas y de las unidades. Encuentra el número.
Let f(x)=8^x.
Which function represents a transformation of f(x) by a vertical stretch with factor 2??
A- g(x)=1/2*8^x
B- g(x)=8^2x
C- g(x)=2*8^x
D- g(x)=8 1/2^x
Please help and give reasoning with your answer. I’m very unsure.
The function that represents a vertical stretch of factor 2 of f(x) = 8^x is g(x) = 2 * 8^x.
Explanation:The function that represents a vertical stretch of factor 2 of the function f(x) = 8^x is g(x) = 2 * 8^x.
To understand why, consider that a vertical stretch by a factor of 2 means that every y-coordinate in the graph is multiplied by 2. So, if we want to stretch the function f(x) = 8^x vertically by a factor of 2, we multiply the function by 2 to get g(x) = 2 * 8^x.
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The sum of 6 consecutive odd numbers is 204. What is the fourth number in this sequence?
204 /6 = 34
29 +31 +33 + 35 +37 +39 = 207
4th number = 35
The fourth number is 35
Julie yard is rectangular.One side of the yard is 100 feet wide. The total area of the yard is 3,000 square feet. What is the length of the other side of the yard?
Jordan makes 100 3-point shots per basketball practice. She makes 44 of these shots. What decimal represents the number of the shots she made?
We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition. We know that m∠ZAB + m∠CAB = 180° by the . We also know m∠CAB + m∠ACB + m∠CBA = 180° because . Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA. Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the .
To prove that m∠ZAB = m∠ACB + m∠CBA, we start with triangle ABC and use the fact that angles in a triangle add up to 180°. Angle ZAB and CAB are a linear pair, so they add up to 180°. By substitution, we can conclude that m∠ZAB = m∠ACB + m∠CBA.
Explanation:To prove that m∠ZAB = m∠ACB + m∠CBA, we start with triangle ABC. Angle ZAB is an exterior angle created by the extension of side AC. Angle ZAB and CAB are a linear pair, which means they add up to 180°. We also know that angle CAB + angle ACB + angle CBA = 180° because the angles in a triangle add up to 180°. Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA. Therefore, we can conclude that m∠ZAB = m∠ACB + m∠CBA using the fact that the angles in a triangle add up to 180°.
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which of these ordered pairs is a solution to the inequality 4x+y>-6
The ordered pair is (1, -1) a solution to the inequality 4x+y>-6. which is the correct answer would be option (C).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We must determine if the inequality holds for a certain set of ordered pairs in order to determine which ordered pairs constitute the answer to the inequality.
We have been given inequality is:
⇒ 4x + y > -6
Option (A) (1, -12)
⇒ 4x + y > -6
Substitute x = 1 and y = -12 in the inequality, we get
⇒ 4(1) + (-12) > -6
⇒ -8 > -6
This is false.
Option (B) (0, -9)
⇒ 4x + y > -6
Substitute x = 0 and y = -9 in the inequality, we get
⇒ 4(0) + (-9) > -6
⇒ -9 > -6
This is false.
Option (C) (1, -1)
⇒ 4x + y > -6
Substitute x = 1 and y = -12 in the inequality, we get
⇒ 4(1) + (-1) > -6
⇒ 3 > -6
This is true.
Hence, the correct answer would be an option (C).
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Find the y-intercept of the line whose equation is 2x - 3y = -6.
to find y intercept, make x = 0 then solve equation:
2x-3y=-6
2(0) - 3y=-6
-3y =-6
y = -6 / -3
y=2
so y intercept is (0,2)
|3x-2|+2y if x=-4,y=7,and z=-9
Amy has 1/2 hour to do 5 chores. She plans to spend the same fraction of an hour on each chore. She wants to use the number line to help her determine what fraction of an hour she can spend on each chore.
What number is 30% of 150?.
Karl runs a car wash. On the Monday, he recorded a loss of $80 and recorded it as -$80. On Tuesday he earned a profit of $120. What is Karl's balance at the end of Tuesday?
Karl's balance at the end of Tuesday is a net profit of $40, after combining his loss of $80 from Monday with his profit of $120 from Tuesday.
To find Karl's balance at the end of Tuesday, we need to combine his loss from Monday with his profit from Tuesday. Karl recorded a loss of -$80 on Monday. On Tuesday, he made a profit of $120. Add the two amounts together to find Karl's total balance after these two days.
Monday: -$80
Tuesday: +$120
Combining them, -$80 (loss) + $120 (profit) equals to a net profit of $40.
Therefore, Karl's balance at the end of Tuesday is $40.
The following triangle FOX is transformed using a rotation: Triangle FOX is shown. F is at negative 1, 1, O is at negative 2, 3, X is at negative 3, 0. Which could be coordinates of F'O'X' after the rotation? (4 points)
The answer is F=(1,1), O=(3,2), X=(0,3)