The G.C.F. of the expression 16n - 24 is evaluated to be 8(2n - 3).
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is - 16n - 24.
The greatest common factor, which is the product of two or more numbers, is the largest number (GCF). A natural number is created by dividing them by the biggest number (factor).
First of all find the G.C.F of 16n and 24 separately.
It can be written that -
16n = 2 × 2 × 2 × 2 × n
24 = 2 × 2 × 2 × 3
The common prime factor between the two is 2 × 2 × 2 = 8.
So, the GCF of 16n and 24 is 8.
Now use the GCF to factor the expression -
= 16n - 24
= 8(2n) - 8(3)
Using the distributive property -
= 8(2n) - 8(3)
= 8(2n - 3)
Therefore, the GCF value is 8(2n - 3).
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Write the expression as a single power of b.
open parentheses b to the power of begin display style 3 over 4 end style end exponent over b to the power of begin display style 1 fourth end style end exponent close parentheses to the power of 1 half end exponent
The simplified form of the given expression is x raise to the power of one-thirty.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
Simplifying indices expressions
Given the indices expression (x^1/2/(x^1/3)^1/5
Using the indices law below:
a^m/a^n = a^m-n
(a^m)^n
Applying the law above to the given equation
(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5
(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5
(x^1/2/(x^1/3)^1/5 = x^1/30
Hence the simplified form of the given expression is x raise to the power of one-thirty.
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Which of the following matrix multiplications are possible?
[a b] x [c d]
The matrix multiplication is possible for option (b) 1 × 3 by 3 × 3, and option (c) 2 × 1 by 1 × 2.
What is a matrix?
A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.
It is known that if the number of columns of a matrix A be equal to the number of rows of another matrix B then the product of matrix A and matrix B i.e. AB is defined.
a) In this option no of columns in first matrix is 1 and the no of rows in second matrix is 2.
That means no of columns in first matrix is not equal to no of rows in second matrix.
Hence, in this case matrix multiplication is not possible.
Therefore, option (a) is incorrect.
b) In this option no of columns in first matrix is 3 and the no of rows in second matrix is also 3.
That means no of columns in first matrix is equal to no of rows in second matrix.
Hence, in this case matrix multiplication is possible.
Therefore, option (b) is correct.
c) In this option no of columns in first matrix is 1 and the no of rows in second matrix is 1.
That means no of columns in first matrix is equal to no of rows in second matrix.
Hence, in this case matrix multiplication is possible.
Therefore, option (c) is correct.
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75,232 = ___ in
expanded form
Answer:
seventy-five thousand two hundred thirty-two
Step-by-step explanation:
Sample Spaces and Probabilities (18 points) For each of the following scenarios first describe the sample space and indicate how big it is (i.e., what its cardinality is) and then answer the question. (a) [3 Points] You flip a fair coin 50 times. What is the probability of exactly 20 heads? (b) [3 Points] You roll 2 fair 6-sided dice, one red and one blue. What is the probability that the sum of the two values showing is 4? (c) [3 Points] You are given a random 5 card poker hand (selected from a single deck). What is the probability you have a full-house (3 cards of one rank and 2 cards of another rank)? (d) [3 Points] 20 labeled balls are placed into 10 labeled bins (with each placement equally likely). What is the probability that bin 1 contains exactly 3 balls? (e) [3 Points] There are 30 psychiatrists and 24 psychologists attending a certain conference. Three of these 54 people are randomly chosen to take part in a panel discussion. What is the probability that at least one psychologist is chosen? What is the probability that exactly three psychologists are chosen? (f) [3 Points] You buy ten cupcakes choosing from 3 different types (chocolate, vanilla and caramel). Cupcakes of the same type are indistinguishable. What is the probability that you have at least one of each type?
(a) Sample space: 2^50 (1,024,000). Probability of exactly 20 heads: 0.000244140625.
(b) 6^2 (36). Probability of a sum of 4: 1/9.
(c) C(52,5) (2,598,960). Probability of a full house: 0.001441.
(d) 10^20 (10^19). Probability of bin 1 containing exactly 3 balls: 1/10^19.
(e) C(54,3) (19,323). Probability of at least one psychologist: C(24,1)/C(54,3) (0.841). Probability of exactly three psychologists: C(24,3)/C(54,3) (0.037).
(f) 3^10 (590,490). Probability of at least one of each type: 0.001690.
(a) The sample space consists of all the possible outcomes of flipping a fair coin 50 times, which is 2^50 (1,024,000). There are only two possible outcomes for each flip, heads or tails. The probability of getting exactly 20 heads is 0.000244140625.
(b) The sample space consists of all the possible outcomes of rolling a red and a blue 6-sided die, which is 6^2 (36). The probability of getting a sum of 4 is 1/9.
(c) The sample space consists of all the possible 5 card poker hands (selected from a single deck), which is C(52,5) (2,598,960). The probability of getting a full house (3 cards of one rank and 2 cards of another rank) is 0.001441.
(d) The sample space consists of all the possible ways of placing 20 labeled balls into 10 labeled bins, which is 10^20 (10^19). The probability of bin 1 containing exactly 3 balls is 1/10^19.
(e) The sample space consists of all the possible ways of selecting 3 of the 54 people attending the conference, which is C(54,3) (19,323). The probability of at least one psychologist being chosen is C(24,1)/C(54,3) (0.841). The probability of exactly three psychologists being chosen is C(24,3)/C(54,3) (0.037).
(f) The sample space consists of all the possible ways of buying ten cupcakes from the 3 different types, which is 3^10 (590,490). The probability that you have at least one of each type is 0.001690.
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4
What is angle G?
70°
Step-by-step explanation:
based on you input, I would suggest you divide 70 by 4 to get 17.5.
that is the answer. trust.
#quanta #vesperdiagram
5. Jenna is making
bracelets.
She needs 7
inches of string for each
bracelet. She has a spool
with 16 feet of string. How
many bracelets can Jenna
make?
Answer:
Step-by-step explanation:
Each bracelet need 7 inches of string. Jenna has a total of 16 feet of string.
Divide the total amount of string by the number of inches needed for each bracelet.
Step 1: Convert 16 feet into inches. 12 inches = 1 foot
16 feet x (12 inches/1 foot) = 192 inches
This is the total inches of string.
Note that feet and foot units cancel and you are left with inches.
Step 2: Find the number of bracelets that can be made. Use the answer from step 1. Each bracelet needs 7 inches of string.
Total inches of string / 7 inches of string for each bracelet
192 inches / 7 inches = 27.4
Round the answer to 27.
One Step Equations Exit Ticket help i ned answers fast
The value of the equations are
n = 6
x = 20
b = -4
k = 176
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
-15 + n = -9 be equation (1)
On simplifying the equation , we get
Adding 15 on both sides of the equation , we get
n = -9 + 15
n = 6
Therefore , the value of n is 6
b)
x - 7 = 13 be equation (2)
On simplifying the equation , we get
Adding 7 on both sides of the equation , we get
x = 13 + 7
x = 20
Therefore , the value of x is 20
c)
14b = -56 be equation (3)
On simplifying the equation , we get
Dividing 14 on both sides of the equation , we get
b = - ( -56/14 )
b = -4
Therefore , the value of b is -4
d)
16 = k/11 be equation (4)
On simplifying the equation , we get
Multiply by 11 on both sides of the equation , we get
k = 16 x 11
k = 176
Therefore , the value of k is 176
Hence , the equations are solved
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what is 5 3/5 divided by 2 2/3
Answer:
Exact Form:
21/10
Decimal Form:
2.1
Mixed Number Form:
2 1/10
Step-by-step explanation:
please help with linear function equations
Answer:
f(x) = 0.5x
Step-by-step explanation:
For this problem, we simply have to find the constant of proportionality between x and f(x). In other words, what x is multiplied by to get f(x).
Since this proportion is constant (meaning it doesn't change), all we have to do is divide an f(x) value in the table by its corresponding x value.
p = f(x) / x
p = -2 / -4
p = 1/2 = 0.5
We can show the relationship of x to f(x) with the equation f(x) = px, which can be simplified using the constant of proportionality that we just solved for.
f(x) = 0.5x
The rule for the glide reflection that maps △ABC with vertices A(–4, –2), B(–2, 6), and C(4, 4) to △A′B′C′ with vertices A′(–2, –2), B′(0, –10), and C′(6, –8) is T⟨a, b⟩ ∘ Rx-axis where
The ΔABC reflects across x-axis with point a=2 and scale factor of x+2 to form the ΔA'B'C'.
What is reflection?
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
The vertices of ΔABC is given as -
A(–4, –2), B(–2, 6), and C(4, 4)
The vertices of ΔA'B'C' is given as -
A′(–2, –2), B′(0, –10), and C′(6, –8)
To find the scale factor of the reflection use the formula -
x + a = x' and y + b = y'
Substitute the values in the equation.
For vertex A and A' -
x1 + a = x1'
-4 + a = -2
a = -2 + 4
a = 2
y1 + b = y1'
-2 + b = -2
b = -2 + 2
b = 0
For vertex B and B' -
x2 + a = x2'
-2 + a = 0
a = 0 + 2
a = 2
y2 + b = y2'
6 + b = -10
b = -10 - 6
b = -16
For vertex C and C' -
x3 + a = x3'
4 + a = 6
a = 6 - 4
a = 2
y3 + b = y3'
4 + b = -8
b = -8 - 4
b = -12
It can be seen that the values of a is constant whereas the values of y varies. This happens due to reflection of coordinates across the x-axis.
Therefore, the reflection happens across the x axis.
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simplify
(-4x^2)(3x^5)/2x^-4
The expression after simplification is -6x¹¹.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is (-4x²) (3x⁵) / (2x⁻⁴).
We have the rule for exponents,
xᵃ . xᵇ = xᵃ⁺ᵇ
xᵃ / xᵇ = xᵃ⁻ᵇ
(-4x²) (3x⁵) = (-4 × 3) x²⁺⁵ = -12x⁷
-12x⁷ / 2x⁻⁴ = (-12 / 2) x⁷⁻⁻⁴
= -6x¹¹
Hence the simplification of the expression (-4x²) (3x⁵) / (2x⁻⁴) is -6x¹¹.
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The list below gives the location of 3 friends who are scuba diving together. Mallory is exploring at an elevation of -25 feet. Jacob is standing on the boat, at an elevation of 15 feet. Eva just jumped in and is 5 feet below the surface of the water.
Which inequality correctly compares the distance of the scuba divers from the surface of the water?
Which one of these?
1- Eva > Mallory
2- Mallory < Jacob
3- Jacob < Eva
4- Mallory > Eva
Mallory is further from the surface than Eva. So, Mallory > Eva. Therefore, option D is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, Mallory is exploring at an elevation of -25 feet.
So, distance between Mallory and the surface of water is 25 feet
Jacob is standing on the boat, at an elevation of 15 feet.
Distance between Jacob and the surface of water is 15 feet
Eva just jumped in and is 5 feet below the surface of the water.
Distance between Eva and the surface of water is 5 feet
In this case, the person closest to the surface is Eva, who is 5 feet from the surface.
So, the inequality is Mallory > Eva
Therefore, option D is the correct answer.
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Draw two rectangles that have the same area but are not congruent.
Violet creates a rectangle with an area of 12 square feet. Bertie makes a rectangle with an area of 12 squares meters. Do the two rectangles have the same area?
Same-sized rectangles are possible. However, because their sides might differ in length, they are not congruent.
What does it mean when two rectangles are congruent?Congruent refers to two rectangles having the same dimensions and shape. So, two rectangles are said to be congruent if their length and width are equivalent in size. The length and width of two rectangles must match for them to be congruent.
Also having the same area are congruent shapes, such as rectangles. However, congruent rectangles with the same area are not always the case. There are differences among rectangles. Figures that have the exact same shape but differ in size are referred to as similar figures.
These two polygons are incongruent because while their matching sides are equal, their corresponding angles are not. Despite the sides being the same size, they have different forms.
The complete question is:
Draw two rectangles that have the same area but are not congruent.
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You go to the grocery store and purchase the items listed in the table. What is your total if
the sales tax is 7%?
The total price is obtained following these two steps:
Adding the price of all the products in the table.Multiplying the total by 1.07, due to the sales tax of 7%.How to obtain the total price?The first step is obtain the price without taxes, which is done adding the price of all the items in the data-set.
Then the proportion is applied, relative to the sales tax of 7%.
The percentage of a sales tax of 7% is given as follows:
107%.
Hence the multiplier relative to this sales tax is given as follows:
1.07.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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6. Write a polynomial function of the least degree that has the root x = (5+ i).
Factors:
Polynomial Function:
To much to right but have it in pic: \/ \/
Write True if the statement is correct and Faise if the statement is incorrect
1. Every composite number can be expressed as a product of primes
, 2. Some quadratic equation has infinite solution
3. For any two real numbers x andythenix-yl=ly=xl
4. 2(3+√7)-2√7 = 6√7
5. 25,471,287 is not divisible by 3 and 9,
6. √6 is not rational number,
7. Between every two real numbers there is another real number,
8. For any natural numbers a and b GCF (a, b) * LCM(a,b) = a*b.
9. Integer is not closed under division,
10. The product of non zero rational number and irrational number is rational⁹
1. Every composite number can be expressed as a product of primes - True
2. Some quadratic equation has infinite solution - True
3. False (ix-yl = |x-y|, which may not equal ly = |y|)
What is Rational Number?A rational number is a number that can be expressed as the ratio of two integers.A rational number can be written in the form p/q, where p and q are integers and q ≠ 0.Examples of rational numbers include -3/4, 0, 1/2, and 5.Every integer is a rational number, since it can be expressed as the ratio of the integer and 1.Every fraction can be represented as a rational number, since it is the ratio of two integers.The decimal representation of a rational number will either terminate (e.g. 1/4 = 0.25) or repeat (e.g. 1/3 = 0.3333...).The set of rational numbers is dense, meaning that between any two rational numbers, there is another rational number.4. 2(3+√7)-2√7 = 6√7 - False
5. False (25,471,287 is divisible by 3)
6. √6 is not rational number - True
7. Between every two real numbers there is another real number -True
8. For any natural numbers a and b GCF (a, b) * LCM (a, b) = a*b. -True
9. Integer is not closed under division -True
10. False (The product of a non-zero rational number and an irrational number is not necessarily rational)
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One number is six less than three times another number. If the sum of the numbers is 38, find the numbers.
Answer: Let's call the first number "x" and the second number "y".
From the problem statement, we know that:
x = 3y - 6 (because one number is six less than three times the other number)
x + y = 38 (because the sum of the numbers is 38)
We can substitute the first equation into the second equation to solve for one of the variables:
3y - 6 + y = 38
4y - 6 = 38
4y = 44
y = 11
Now we can substitute this value of y back into the first equation to find the value of x:
x = 3(11) - 6
x = 29
So the two numbers are:
x = 29
y = 11
Step-by-step explanation:
HELP!
which is the graph of g(x) = [x+3]?
Answer:
Step-by-step explanation:
O gráfico de g(x) = [x+3] é uma Reta que passarum pelo pno (3,0) e tem inclinação 1.
Dorothy bought 4 boxes of chocolates for $12. Find the unit price.
Answer:
3
Step-by-step explanation:
12/4=3
Help please and thank you and please explain how you got it. It’s #13!
Answer:
-13a +10b
Step-by-step explanation:
[tex]-3a-4b-2(5a-7b)[/tex]
[tex]=-3a-4b-10a+14b[/tex]
[tex]=-13a+10b[/tex]
Hope this helps
Use the distributive property to solve 12x9
The value of given expression 12*9 is 108
What is Algebraic expression ?
Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The basics of algebra taught us how to express an unknown fee using letters which includes x, y, z, and so forth. these letters are known as here as variables. An algebraic expression can be a aggregate of both variables and constants. Any price that is placed before and accelerated through a variable is a coefficient.
Given expression ,
12*9 = (3*4) * (3*3)
= 9*(3*4)
= 9* 12
= 108
Hence, The value of given expression 12*9 is 108
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BENCHMARK ASSESSMENT - 2/20
Which of the ratios below has a unit rate of 8? Select all that apply.
A) 40:5
B) 24:16
C) 96:12
D) 48:6
E) 2:24
Answer: So Here you go I got the perfect answer with a explanation
Step-by-step explanation:
A unit rate is a rate in which the second term is 1. To find a unit rate, we need to divide the first term by the second term.
A) 40:5 has a unit rate of 8 (40/5 = 8)
C) 96:12 has a unit rate of 8 (96/12 = 8)
D) 48:6 has a unit rate of 8 (48/6 = 8)
So options A, C and D has a unit rate of 8.
Answer:
the ration has a unit rate of 8 A - 40:5C - 96:12 D - 48:6Dividable by 8
Step-by-step explanation:
Solve the system by substitution {2x−3y=12 −12y+8x=48
If there is one solution, type the answer as an ordered pair. If there is no solution, type ∅. If there are infinitely many solutions, type ∞.
The solution to the system is (7.5, 1)
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
2x−3y=12
−12y+8x=48
divide the first equation by 2
So, we have
x - 1.5y = 6
This gives
x = 6y + 1.5
By substitution, the second equation becomes
-12y + 8 (6y + 1.5) = 48
So, we have
-12y + 48y + 12 = 48
Evaluate
36y = 36
Divide by 36
y = 1
So, we have
x = 6 + 1.5
x = 7.5
Hence, the solution is (7.5, 1)
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The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
The likelihood of randomly selecting a chocolate chip cookie from the batch is unlikely. Therefore, option C is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Given that, the baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies.
P(chocolate chip) = 0.25
In probability, larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 0.5 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Here, 0.25<0.5
Therefore, option C is the correct answer.
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Answer:unlikely
Step-by-step explanation:
-8.8/x = 1.5/10
Pls help
Answer:
x = 58.67
Step-by-step explanation:
[tex]\frac{-8.8}{x}[/tex] = [tex]\frac{1.5}{10}[/tex]
Cross multiply
1.5x = (-8.8)(10)
1.5x = -88
Divide, solve for x
x = -88/1.5 = -58.6666667 = around -58.67
The town of Simpsonville has two tow truck companies. Company A charges an initial fee of $30 plus $2 per mile. Company B charges an initial fee of $20 plus $4 per mile. Use the graph to determine when it's cheaper to use Company B instead of Company A.
Using the graph, it's cheaper to use Company B instead of Company A; when the number of miles is less than 5 miles.
How to interpret Linear equation graphs?For us to solve this question, we need to first create an equation;
If A company initially supplies $30 and then $2 per mile, then the equation here is:
y = 2x + 30
If B company initially supplies $20 and then $4 per mile, then the equation is expressed as:
y = 4x + 20
Due to the fact that the two wages are asked to be equalized, we equate these two equations with each other and find the result.
2x + 30 = 4x + 20
2x = 10
x = 10/2
x = 5
This is the number of miles that both companies will charge a customer the same amount.
Then the time for which it is cheaper to use company B is when number of miles is less than 5.
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Need help with question number 3
Using what we know about lines and vertical angles we will see that:
m∠3 = 35°.
How to find the measure of angle 3?Remember that when two lines intercept and 4 angles are formed, the vertical angles (these ones connected only by the vertex) have the same measure.
For example, 2 and 5 are vertical angles in this case.
Angles 6 and 3 also are vertical angles, and if both white lines are parallel, then the measures of angle 1 and 6 will be equal (because both are on the same quadrant) then:
m∠6 = 35°
Then the measure of angle 3 is:
m∠3 = 35°.
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given the experimental data, what is the activation energy, ea, (in kj/mol) for this reaction? hint: r
The activation energy for the given reaction is166 KJ/mol. (Option B)
Activation energy refers to the minimum amount of extra energy that is required by a reacting molecule to be converted into product. It is the minimum amount of energy required to energize or activate atoms or molecules so that they can undergo a chemical reaction or transformation. In order to calculate the activation energy (Ea), the Arrhenius equation is used which is given by:
k=Ae^((-E)/RT)
where k is the rate of chemical reaction, A is a constant depending on the chemicals involved, E is the activation energy, R is the universal gas constant, and T is the temperature.
The equation can be expressed as
ln〖k=ln〖A-(E/RT)lne〗 〗
2.303 log〖k=2.303 log〖A-E/RT〗 〗
log〖k=log〖A-E/2.303RT〗 〗
As there are two temperatures and two rate constants given, the Arrhenius equation is rearranged:
log〖k2/k1=E/2.303(1/T1〗-1/T2)
According to the data,
k1 = 2.7 x 10^-4
T1 = 600 K
k2 = 3.5 x 10^-3
T2 = 650 K
R = 8.314
log〖(3.5 x10^(-3))/(2.7 x 10^(-4) )=E/(2.303*8.314)(1/600〗-1/650)
E = 166208 J/mol or 166 KJ
Note: The question is incomplete. The complete question probably is: Calculate the activation energy (Ea) in kJ/mol for a reaction if the rate constant (k) is 2.7 × 10^-4 (M^−1sec^−1) at 600 K and 3.5 × 10^−3 (M−^1sec^−1) at 650 K. a. −166 kJ/mol b. 166 kJ/mol c. 1.64 kJ/mol d. 1.66 × 10^5 kJ/mol. (R
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Please help me out. I Need it today
Answer:
greetings!!!
Look at the attachment above
and If you have any questions or unclear ideas tag on the comments.
Hope it helps!!!
Compute the probability of x successes in the n independent trials of the experiment. n=9, p=0.5, x≤3
The probability of x successes in the n independent trials of the experiment is 0.1640625
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, n=9, p=0.5, x≤3 we need to find probability of x successes in the n independent trials of the experiment.
We know that,
P(X=x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾
q = 1-p = 1-0.5
q = 0.5
P(X=x) = ⁹C₃(0.5)³(0.5)⁹⁻³
P(X=3) = ⁹C₃ (0.5)³(0.5)⁶
⁹C₃ = 9! / 3!(9-3)! = 9!/3! × 6!
⁹C₃ = 84
P(X=3) = 84×0.125×0.015625
= 0.1640625
Hence, the probability of x successes in the n independent trials of the experiment is 0.1640625
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