The probability that John chooses exactly two green marbles is calculated using the binomial probability formula and is found to be 720/3125.
To solve this problem, we can use the binomial probability formula because John is performing independent trials of the same experiment and he is interested in the probability of exactly two successes (picking a green marble) in a specific number of trials (5).
The binomial probability formula is: [tex]P(X = k) = (n choose k) \times p^k \times (1-p)^{n-k[/tex]
For John's case:
n = 5 (since he is picking 5 marbles).
k = 2 (he wants exactly two green marbles).
p = 6/10 or 3/5 (because there are 6 green marbles out of a total of 10 marbles).
Using the formula, the probability that John picks exactly two green marbles is:
[tex]P(X = 2) = (5 choose 2) \times (3/5)^2 \times (2/5)^{5-2[/tex]
Calculating further:
[tex]P(X = 2) = 10 \times (3/5)^2 \times (2/5)^3 = 10 \times 9/25 \times 8/125 \\P(X = 2) = 720/3125[/tex]
Is 9.103 greater than 9.13
Answer:
false 9.13 is greater
Step-by-step explanation:
103 thousanths are smaller then 13 hundreths
with decimals the farther you go the lower you get bc its half a number
1/2 to 1/4 to 1/8 it gets smaller
How many permutations are there of jack, queen, king, ace
Is is true that the coefficient of the expression 18z-7(-3+2z) of z is 13
What is the measure of x?
A.36
B.72
C.144
D.360
64.125 - 20.37 i need the answer
Answer:
43.755 what the other person said but I know that is the answer
Step-by-step explanation:
Which postulate or theorem proves that these two triangles are congruent?
Answer:
option B
Step-by-step explanation:
Given in the question are ∠x ≅ ∠y and ∠zwx ≅ ∠ ywz and wz is common in both.
These angles are adjacent angles of triangles.
We know theorem for congruence is Angle - Angle - Side
Therefore, for the congruence of these two triangles option B, AAS congruence theorem is the answer.
Solve for x: the quantity of x plus 4 / 3 = 2.
A.x = −2 B.x = 2 C.x = 2/ 3 D. x = negative 10/ 3
20 POINTS PLEASE HELP Write an equation for a trend line and predict the value when x is 15
X 0 3 6 9 12
Y 17.5 35.4 50.5 60.6 66.3
Solve x ym = y x3 for m.
Simplify the expression. (4 − 4i)(−2 + 5i)
Find the value of x so that the line passing through (10, 5) and (x, 9) has a slope of -2.
What’s the ratio of 42¢ to $1.25? (Change dollars to cents)
Answer:
42 125 becuase i got um right bozzzzzzzz
Step-by-step explanation:
If 6 1/2is the lesser number in an inequality, which statement is true about the other number in the inequality?
I KNOW ITS NOT A. But i think it is B. HOPE THIS HELPS!
If c(x)= [tex] \frac{5}{x-2} [/tex] and d(x) = x + 3, what is the domain of (cd)(x)?
all real values of x
all real values of x except x = 2
all real values of x except x = –3
all real values of x except x = 2 and x = –3
The domain of the composite function (cd)(x), where c(x) = 5/(x-2) and d(x) = x + 3, includes all real values except x = 2 due to a division by zero condition in the function c(x).
Explanation:In this problem, we need to figure out the domain of the combined function (cd)(x). The domain constitutes the set of all real values of x that make the function defined. The first function, c(x) = rac{5}{x-2}, isn't defined for x = 2 because it would lead to a division by zero. The second function, d(x) = x + 3, is defined for all real values since it's a linear function.
When these functions are multiplied to form (cd)(x), the domain will be the intersection of the individual function domains. This means, with c(x) having a restriction with x != 2, the composite function (cd)(x) will maintain this restriction despite d(x) being defined for all real values. So the domain for (cd)(x) is all real values except for x = 2.
Learn more about Domain of Composite Function here:https://brainly.com/question/31810210
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Find the 20th term in arithmetic sequence -4, 1, 6, 11, 16,
Which postulate or theorem proves that △JHG and △EFG are congruent?
SAS Congruence Postulate
ASA Congruence Postulate
HL Congruence Theorem
AAS Congruence Theorem
The postulate that proves that △JHG and △EFG are congruent is;
Option B; ASA Congruence Postulate
From the given image, we can see two triangles namely;
△JHG and △EFG
Now, we can see that;
FG = GH
That is given because we see that G has divided FH into 2 equal parts.
Also, we see the right angle sign at ∠F and ∠H of both triangles.
Thus, since they are both right angles, then we can say that;
∠EFG = ∠JHG
Also, at point G, we have two vertically opposite angles which are;
∠EGF and ∠JGH
Now, from vertically opposite angle theorem, vertically opposite angles are always equal;
Thus; ∠EGF = ∠JGH
So far, we have;
FG = GH
∠EFG = ∠JHG
∠EGF = ∠JGH
This is 2 corresponding equal angles and 1 corresponding equal side. The side is included between the two angles and as such the proof that △JHG and △EFG are congruent is the ASA Congruence Postulate.
Read more at; https://brainly.com/question/19413244
Emily has 32 grams of a 25% sugar syrup, but this is just too sweet for her! How much pure water should she add to have a 10% syrup?
An automobile manufacturing organization noted a drop in sales after an incident occurred due to the lack of a safety feature in their cars. Many customers began considering other brands of cars after this incident. How can the organization avoid losing customers
Answer:
introducing customer retention strategies
Step-by-step explanation:
which exponential functions have been simplified correctly check all that apply
Answer:
Option A, C, D, are the correct options.
Step-by-step explanation:
To check the exponential functions which have been simplified correctly we will take option one by one.
A). [tex]f(x)=5(\sqrt[3]{16})^{x}=5(\sqrt[3]{2^{4}})^{x}=5(2\sqrt[3]{2})^{x}[/tex]
B). [tex]f(x)=2.3(8^{\frac{1}{2}})^{x}=2.3(2.\sqrt{2})^{x}\neq 2.3(4^{x})[/tex]
C). [tex]f(x)=81^{\frac{x}{4}}=(3^{4})^{\frac{x}{4}}=(3^{\frac{4}{4}})^{x}=3^{x}[/tex]
D). [tex]f(x)=\frac{3}{4}(\sqrt{27})^{x}=\frac{3}{4}(\sqrt{3^{3}})^{x}=\frac{3}{4}.(3\sqrt{3})^{x}[/tex]
[tex]f(x)=(24)^{\frac{1}{3}x}=(2^{3}.3)^{\frac{1}{3}x}=(2.3^{\frac{1}{3}})^{x}\neq 2(\sqrt[3]{3})^{x}[/tex]
Exponential functions and their inverses like the natural logarithm are inverse functions, meaning they can undo each other. Simplifications like ln(e^x) result in x, and e^(ln x) simplifies to x. This property is integral to correctly simplifying exponential functions.
Explanation:The exponential functions and their inverses, like the natural logarithm (ln), have specific properties where they can "undo" each other. This relationship allows us to simplify expressions involving exponentials and logarithms. For example, when you have ln(ex), this simplifies to x because the natural logarithm and the exponential function are inverse functions.
Similarly, when applying the exponential function to a natural logarithm, like eln(x), the result is just x. Furthermore, when taking square roots of exponentials, you can adjust the exponent to be evenly divisible by 2 and then take the square root of the base number, followed by dividing the exponent by 2. Also, while dividing exponentials, you subtract the exponents when the bases are the same.
Here is an example of this simplification: to compute the square root of e4, we can write it as e4/2, which simplifies to e2.
does anyone know how to do this?
apply the distributive property and the greatest common factor to write an equivalent expression.
32k + 24 = _ (_)
what numbers should be in place of the underscores?
The inequality x2 + 12x + 35 ≥ 0 has two critical points and three possible intervals for solutions. Choose each set of possible test points for the three intervals.
–8, –6, –4
–10, –6, 0
–6, 0, 6
–6, 0, 10
-8,-6,-4
-10,-6,0
these are the possible test points for your three intervals
The given inequality is, x² + 12 x+35≥0
→ x²+7 x +5 x+5×7≥0
→ x (x+7) +5(x+7)≥0
→ (x+5)(x+7)≥0
→ x+5=0 ∧ x+7=0 gives x= -7 ∧ x= -5
Now drawing the number line and marking point ,-5 and -7 on it.
Now the three intervals are (-∞ , -7], [-7,-5] and [-5,∞).
The solution set of inequality (x+5)(x+7)≥0 is (-∞ , -7] and [-5,∞).
The set of possible test points for
⇒ (-∞ , -7] → -8, -10
⇒ [-7,-5] → -6
⇒ [-5,∞) → -4, 0
Option (1) -8,-6,-4 and Option (2) -10,-6,0 satisfies the given condition.
Write the polynomial in factored form. 4x3 + 8x2 – 96x
The lenght of a rectangleis 6 inches more thans its width the area of a rectangle is 91 inches find the dimernins
Mrs. simms told her class to find two consecutive even integers such that twice the lesser of two integers is 4 less than two times the greater integer.
a. write and solve an equation to find the integers.
b. does the equation have one solution, no solutions, or is it an identity? explain.
Final answer:
To find two consecutive even integers, we can set up and solve an equation. The equation in this case is an identity, meaning it is true for all values of x. Therefore, there are infinitely many solutions.
Explanation:
To find two consecutive even integers, let's represent the first integer as x and the second integer as x + 2. Now, according to the given information, twice the lesser of the two integers is 4 less than two times the greater integer. We can write this as:
2x = 2(x + 2) - 4
Simplifying the equation:
2x = 2x + 4 - 4
2x = 2x
This equation is an identity, meaning it is true for all values of x. Therefore, there are infinitely many solutions. In this case, there are infinitely many pairs of consecutive even integers that satisfy the given conditions.
Which expression is a perfect cube?
A. -8x21y8
B. -64x64y64
C. -125x9y20
D. -216x9y18
Can somebody plz help me
Please help! I need to show my work
MATH PLEASE HELP 50 POINTS 1 QUESTION
Complete the reasons in the proof below.
Given: ∠1 and ∠5 are supplementary.
Prove: a ∥ b
Statements
1. ∠1 and ∠5 are supplementary
2. ∠1 ≅ ∠2
3. ∠2 and ∠5 are supplementary
4. a ∥ b
What does it mean when u cant find the mean of a set of numbers?
Answer:
Another word for mean is the "average", your goal is to find the average of the following data set, it's pretty easy, you just have to add up all the numbers in the data set and divide it with the total numbers in the data set.
For example:
Find the mean of the following data set:
4, 1, 8, 5, 7, 3
Mean: 4 + 1 + 8 + 5 + 7 + 3 = 28
then we divide 28 with 6 since there are 6 numbers in the following data set.
Mean: 4 + 1 + 8 + 5 + 7 3 = 28/6 = 4.6
We get the final answer of 4.6!