HELP MEEEEEEE PLEASE

The prime factorization of (4⁴-4²)²3³  is 2⁸ × 3⁵ × 5²  .we can solve this by  simplifying  the expression inside the parentheses.

What is prime factorization?

Prime factorization is the process of expressing a positive integer as a product of its prime factors, where a prime factor is a prime number that divides the integer exactly, without leaving any remainder.

What is parentheses?

Parentheses are punctuation marks that are used to set off a word, phrase, clause, or sentence that is not part of the main sentence but provides additional information or clarification. They are represented by the symbols "(" and ")" and are also commonly known as round brackets, curved brackets, or simply brackets.

In the given question,

First, we need to simplify the expression  which inside the parentheses:

4⁴ - 4² =>  256 - 16 =>  240

Now we can substitute this simplified value into the expression:

(4⁴-4²)²3³ = (240)²3³

Next, we can factor 240 into its prime factors:

240 = 2⁴ × 3 × 5

Substituting this factorization, we get:

(240)²3³ = (2⁴ × 3 × 5)²3³

Now by using the laws of exponents to simplify

(2⁴ × 3 × 5)²3³ = 2⁸ × 3² × 5² × 3³

Multiplying the exponents, we get:

2⁸ × 3⁵ × 5²

Therefore, the prime factorization of (4⁴-4²)²3³ is:

2⁸ × 3⁵ × 5²

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Answer:

61,63,and 65

Step-by-step explanation:

61+63+65=189

The domain of the question is expressed as; 0 ≤ x ≤ 4

The range of the question is expressed as; 100 ≤ f(x) ≤ 207.36

The domain of a graph is defined as the set of all possible input values that makes the function possible while the range is defined as the set of all possible output values that can result from the possible input values.

Now, we are told that the insect population increases by 20% each month from May 1 to September 1.

The function that represents the insect population after x months is;

f(x) = 100(1.2)ˣ

Thus, the domain is from x = 0 to 4 months inclusive. 0 ≤ x ≤ 4

f(0) = 100(1.2)⁰

f(0) = 100

f(4) = 100(1.2)⁴

f(4) = 207.36

100 ≤ f(x) ≤ 207.36

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Answer:

5x = 25|:5

x = 5

Answer:

C (20,5)

Step-by-step explanation:

The committees should contain 5 persons each

The number of people are 20

Apply combination concept

where

²⁰₅C =  20! /[ {20-5}!*5! ]

=20! / 15!*5!

=15504  ------The number of 5 person committees that could be formed from a group of 20 people.

Using the formula for the area of a rectangle, the area of the cellphone is 18x⁻¹y⁸ OR 18y⁸/x

From the question, we are to calculate the area of the cellphone shown in the diagram

From the given information,

We have a diagram that shows a cellphone which is rectangular in shape.

Thus,

We will use the formula for finding the area of a rectangle to calculate the area of the cellphone.

Area of a rectangle = Length * Width

From the given information,

Length of the cellphone = 6x²y⁶

Width of the cellphone = 3x⁻³y²

Thus,

Area of the cellphone = 6x²y⁶ × 3x⁻³y²

Area of the cellphone = 6 × 3 × x² × x⁻³ × y⁶ × y²

Area of the cellphone = 18 × x⁻¹ × y⁸

Area of the cellphone = 18x⁻¹y⁸ OR 18y⁸/x

Hence,

The area of the cellphone is 18x⁻¹y⁸ OR 18y⁸/x

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Answer:

The sum of any two consecutive numbers is always odd. Example, 4 + 5 = 9; –8 + (–7) = –15.

Answer:

si

Step-by-step explanation:

Answer:

(i) x ≤ 1

(ii) ℝ except 0, -1

(iii) x > -1

(iv) ℝ except π/2 + nπ, n ∈ ℤ

Step-by-step explanation:

(i) The number inside a square root must be positive or zero to give the expression a real value. Therefore, to solve for the domain of the function, we can set the value inside the square root greater or equal to 0, then solve for x:

\(1-x \ge 0\)

\(1 \ge x\)

\(\boxed{x \le 1}\)

(ii) The denominator of a fraction cannot be zero, or else the fraction is undefined. Therefore, we can solve for the values of x that are NOT in the domain of the function by setting the expression in the denominator to 0, then solving for x.

\(0 = x^2+x\)

\(0 = x(x + 1)\)

\(x = 0\)     OR     \(x = -1\)

So, the domain of the function is:

\(R \text{ except } 0, -1\)

(ℝ stands for "all real numbers")

(iii) We know that the value inside a logarithmic function must be positive, or else the expression is undefined. So, we can set the value inside the log greater than 0 and solve for x:

\(x+ 1 > 0\)

\(\boxed{x > -1}\)

(iv) The domain of the trigonometric function tangent is all real numbers, except multiples of π/2, when the denominator of the value it outputs is zero.

\(\boxed{R \text{ except } \frac{\pi}2 + n\pi} \ \text{where} \ \text{n} \in Z\)

(ℤ stands for "all integers")

Answer:

(i)  x ≤ 1

(ii)  All real numbers except x = 0 and x = -1.

(iii)  x > -1

(iv)  All real numbers except x = π/2 + πn, where n is an integer.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

\(\hrulefill\)

\(\textsf{(i)} \quad f(x)=\sqrt{1-x}\)

For a square root function, the expression inside the square root must be non-negative. Therefore, for function f(x), 1 - x ≥ 0.

Solve the inequality:

\(\begin{aligned}1 - x &\geq 0\\\\1 - x -1 &\geq 0-1\\\\-x &\geq -1\\\\\dfrac{-x}{-1} &\geq \dfrac{-1}{-1}\\\\x &\leq 1\end{aligned}\)

(Note that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign).

Hence, the domain of f(x) is all real numbers less than or equal to -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x \leq 1\\\textsf{Interval notation:} \quad &(-\infty, 1]\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \leq 1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(ii)} \quad g(x) = \dfrac{1}{x^2 + x}\)

To find the domain of g(x), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.

Set the denominator to zero and solve for x:

\(\begin{aligned}x^2 + x &= 0\\x(x + 1) &= 0\\\\\implies x &= 0\\\implies x &= -1\end{aligned}\)

Therefore, the domain of g(x) is all real numbers except x = 0 and x = -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x < -1 \;\;\textsf{or}\;\; -1 < x < 0 \;\;\textsf{or}\;\; x > 0\\\textsf{Interval notation:} \quad &(-\infty, -1) \cup (-1, 0) \cup (0, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq 0,x \neq -1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iii)}\quad h(x) = \log_7(x + 1)\)

For a logarithmic function, the argument (the expression inside the logarithm), must be greater than zero.

Therefore, for function h(x), x + 1 > 0.

Solve the inequality:

\(\begin{aligned}x + 1 & > 0\\x+1-1& > 0-1\\x & > -1\end{aligned}\)

Therefore, the domain of h(x) is all real numbers greater than -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x > -1\\\textsf{Interval notation:} \quad &(-1, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x > -1\right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iv)} \quad k(x) = \tan x\)

The tangent function can also be expressed as the ratio of the sine and cosine functions:

\(\tan x = \dfrac{\sin x}{\cos x}\)

Therefore, the tangent function is defined for all real numbers except the values where the cosine of the function is zero, since division by zero is undefined.

From inspection of the unit circle, cos(x) = 0 when x = π/2 and x = 3π/2.

The tangent function is periodic with a period of π. This means that the graph of the tangent function repeats itself at intervals of π units along the x-axis.

Therefore, if we combine the period and the undefined points, the domain of k(x) is all real numbers except x = π/2 + πn, where n is an integer.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &\pi n\le \:x < \dfrac{\pi }{2}+\pi n\quad \textsf{or}\quad \dfrac{\pi }{2}+\pi n < x < \pi +\pi n\\\textsf{Interval notation:} \quad &\left[\pi n ,\dfrac{\pi }{2}+\pi n\right) \cup \left(\dfrac{\pi }{2}+\pi n,\pi +\pi n\right)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq \dfrac{\pi}{2}+\pi n\;\; (n \in\mathbb{Z}) \right\}\\\textsf{(where $n$ is an integer)}\end{aligned}}\)

Answer: 28.1x−3.1

Step-by-step explanation: 1.5(x+3)+3.8(7x−2)

=(1.5)(x)+(1.5)(3)+(3.8)(7x)+(3.8)(−2)

=1.5x+4.5+26.6x+−7.6

=(1.5x+26.6x)+(4.5+−7.6)

=28.1x+−3.1

=28.1x−3.1

The corresponding answers to each expression are;

1. 5x x (3+5) / 12 - 2 x 2 = 5

2. (11 + 3²) ÷ 4 - 2 = 3

3. (48 - 12 ÷ 2 / 7 - 1) + 1 =  8

4. (25 - (4 - 1)² / 2³ - 4) + 2 = 6

5. (3² - 4) x (7 + 5) / -12 ÷ -3 = 15

1. 5 x (3+5) / 12 - 2 x 2 =

5 x 8/ 12 - 4=

40/8 = 5

2. (11 + 3²) ÷ 4 - 2 =

11 + 9  ÷  4 - 2=

20  ÷  4 - 2

5 - 2 = 3

3. (48 - 12 ÷ 2 / 7 - 1) + 1 =

(48 - 6/ 6) + 1 =

42/6) + 1 =

7 + 1 = 8

4. (25 - (4 - 1)² / 2³ - 4) + 2 =

25 - 9/ 4) + 2 =

16/4 + 2 =

4 + 2 = 6

5. (3² - 4) x (7 + 5) / -12 ÷ -3 =

9-4 x 12/ 4 =

5 x 12/ 4=

60/4 = 15

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Answer:

b. Go for a run to clear his mind.

Step-by-step explanation:

Emotion focused coping strategy is one in which a person goes for self isolation to release his stress. The person focuses on emotional distance from people because he believes the stress can increase if other people stays around him. When an employee suffers from stressful demand at work the best for him is to go for a run or walk and release stress.

Answer:

Step-by-step explanation:

Cos(90-2x) . tan(180+x) + sin^2(360-x)​

= sin(2x) * tan(x) + sin²(x)

= 2sin(x) cos(x) sin(x)/cos(x) + sin²(x)

= 2sin²(x) + sin²(x)

= 3sin²(x)

SOLUTION

Now, 9 and 51 are not compatible because 51 cannot divide 9 without a remaider.

The compatible number with 9 that is close to 51 is 54.

Hence,

9 and 54 are compatible.

This will give us

Hence,

The estimate is 600

Answer: C

Step-by-step explanation:

The rest of the quadrilaterals provided have 2 pairs of parallel lines.

The choice is:

Explanation:

The quadrilateral that has exactly one pair of parallel lines is called a trapezoid.

Here's what a trapezoid looks like :

\(\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(1,3)\qbezier(5,0)(5,0)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(3,0)(8.2,0)(0,0)\put(-0.5,-0.3){$\sf A$}\put(5.3,-0.3){$\sf B$}\put(4.2,3.1){$\sf C$}\put(0.6,3.1){$\sf D$}\end{picture}\)

Answer:

m<FLS=108 degrees

m<SLT=72 degrees

m<ALG=18 degrees

Step-by-step explanation:

(3x) + (4x +12) = 180

x = 24

4x + 12 = 108 = m<FLS

180 - 108 = 72 = m<SLT

SLG = 72 + 90 + x

x = 18 = m<ALG

Answer:-1/6

Step-by-step explanation:

Draw a line out in the 2nd quadrant.

Your y=\(\sqrt{35}\)    hypotenuse=6  use pythagorean theorem to solve for x

6² = 35 + x²

x=1

so

cosΘ = -1/6

Answer:

8 Hours.

Step-by-step explanation:

Answer:

The answer is: 803,800,000

Step-by-step explanation:

None

It was guessed, and I got it right.

The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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Total revenue when the market price is =0.59~0.6

total revenue at the current market rate,

(42-48)/[(42+48)/2]=13.33 % CHANGE IN DEMAND

(125-100)/[(125+100)/2]=(125-100) = 22.22

Ep=13.33/22.22

=0.59~0.6

inelastic

decrease

inelastic.

Your company's sales for the entire year are what make up your annual income. Costs and expenses are not included in this. The quantity of each product you sell is multiplied by the retail price to determine annual sales, which are then added to determine annual sales as a whole.

Sales are the total annual revenue derived from the sale of products or services associated with a business's core operations. The whole profit or profit of the company is known as income or net income. The financial health of a corporation is influenced by both sales and net income, yet they are mutually exclusive.

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Our starting value: $89.50.

Deposits means putting money in the account, so money will increase.

Withdrawal means that you are depleting the account, so money will decrease.

1. 11/4 - Deposited $17.25

So you will add $89.50 + $17.25 = $106.75

2. 11/4 = Withdrawal $35.90

So you will subtract $106.75 - $35.90 = $70.85

3.  11/7 - Deposit $10.77

So you will add $10.77 + $70.85 = $81.62

4. 11/11 - Withdrawal of $3.02

So you will now subtract $81.62- $3.02 = $78.60

$78.60 is our final balance! I hope this helps!

The standard deviation of the data sample is 2.55.

The standard deviation of the data sample is calculated by applying the following formula;

S.D = √ (x -  μ)²/(n - 1)

where;

The given parameters;

mean,  μ = 64

x, = 12

number of samples = 9

The standard deviation of the data sample is calculated as;

S.D = √ (12 -  64)²/(9 - 1)

S.D = 2.55

Thus, the standard deviation of the data sample is calculated by applying the formula for standard deviation.

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The volume of air passing through the filter is 800 cubic feet per minute. It is calculated by multiplying the air flow speed (100ft/min) by the area of the filter (8ft²).

The volume of air passing through the HEPA filter can be calculated using the formula for the speed of air flow multiplied by area. The speed of the air flow is given as 100ft/min and the area of the filter is given as 4ft x 2ft, which equals 8 square feet. Therefore, the volume of the air passing through the filter can be calculated as 8ft2 x 100ft/min = 800 cubic feet per minute.

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Answer:

h=8

Step-by-step explanation:

h = -16t^2 + 20t + 32

h = -16(2)^2 + 20(2) + 32

h = -16(4) + 40 + 32

h = -64 + 72

h = 8

Answer:

2 seconds

Step-by-step explanation:

i got it right, no explanation <3

Answer:

Ryan: (100/13)(1/1,609.34)(3,600) =

17.21 miles per hour

Ryan is faster than Juan, by about 2.21 miles per hour

The following equations represent two families babysitting payment plans.

Where y represents the wages earned and x represents the hours worked.

Let us solve this system of equations to find out when do the two plans pay the same and how much do they pay?

Substitute eq.2 into eq.1 and solve for x

This means that the two plans pay the same when they work for 3 hours.

Substitute x = 3 into eq.2 to find the value of y

This means that the plan pays $21 when they work for 3 hours.

Therefore, the solution is

x = 3 hours

y = $21

Answer:

Step-by-step explanation: 5.) Circular shape.

     6.) Feet.

     7.) Circle.

     8.) The circumference is 9 and the radius is 18.

     9.)  By the way we would need to use The Circumference as 2 and the radius to be 9 to equal 18 for the radius circle.