The expression 16n-24 factored using GCF

Answer:

seventy-five thousand two hundred thirty-two

Step-by-step explanation:

The expression after simplification is -6x¹¹.

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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(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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The value of the equations are

n = 6

x = 20

b = -4

k = 176

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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The probability of x successes in the n independent trials of the experiment is 0.1640625

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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Answer:

3

Step-by-step explanation:

12/4=3

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|)

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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The solution to the system is (7.5, 1)

From 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 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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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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To much to right but have it in pic: \/ \/

The total price is obtained following these two steps:

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.

The problem is incomplete, hence the answer was given in general terms.

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Using the graph,  it's cheaper to use Company B instead of Company A; when the number of miles is less than 5 miles.

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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Answer:

greetings!!!

Look at the attachment above

and If you have any questions or unclear ideas tag on the comments.

Hope it helps!!!

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 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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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

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:

The simplified form of the given expression is x raise to the power of one-thirty.

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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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

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.

Same-sized rectangles are possible. However, because their sides might differ in length, they are not 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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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:

Answer:

Exact Form:

21/10

Decimal Form:

2.1

Mixed Number Form:

2 1/10

Step-by-step explanation:

Using what we know about lines and vertical angles we will see that:

m∠3 = 35°.

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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Mallory is further from the surface than Eva. So, Mallory > Eva. Therefore, option D is the correct answer.

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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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.

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

The likelihood of randomly selecting a chocolate chip cookie from the batch is unlikely. Therefore, option C is the correct answer.

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:

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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