Alicia cashed half of her paycheck and set aside the other half to take her friends out to dinner. She spent on dinner and brought home more than Write an inequality to represent the situation, using to represent the amount of Alicia’s paycheck.

In 2000, the population of the state was 23.1 million, After 13 years , the population of the state reach 28.3 million.

What is population?

The term "population" refers to all citizens who are present in a nation or who are temporarily absent from it, as well as all aliens who have made a nation their permanent home. The number of residents in a given area is depicted by this indicator. The annual changes in population brought on by births, deaths, and net migration are measured as growth rates.

Given:

[tex]A = 23.1e^0^.^0^1^5^2^t[/tex] models the population of US

where A is in million

t is years after 2000.

(a) We have to find the population in 2000.

In 2000, t = 0

Plug t = 0 in the above equation

[tex]A(0) = 23.1e^0^.^0^1^5^2^(^0^)\\A = 23.1[/tex]

Hence, in 2000 the population is 23.1 million.

(b) To find when the population of the state reach 28.3 million.

Plug A = 28.3 in above equation and solve for t.

[tex]28.3 = 23.1e^0^.^0^1^5^2^t\\e^0.0152t = \frac{28.3}{23.1} \\t*ln(0.0152) = ln( \frac{28.3}{23.1})\\t = 13.35718\\t = 13[/tex]

Hence, after 13 years the population of the state reach 28.3 million.

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Answer:

Length of each side of regular hexagon = 19 inches

Step-by-step explanation:

When the length of all sides is equal and measure of all angles is equal . it is known as Regular hexagon. In a regular hexagon, each inside angle is 120 degrees.

Perimeter of Regular hexagon = 6a

where a is each side of regular hexagon

According to the given information

Perimeter of regular hexagon = [tex]\frac{342}{3}[/tex]

                                                  = 114 inches

Perimeter of regular hexagon = 6a

                                          114   = 6a

                                           19   =  a

Length of each side of regular hexagon = 19 inches

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Answer:

<-4,4>

Step-by-step explanation:

-4 * <1,-1> = <-4 * 1, -4 * -1> = <-4, 4>

Answer:

Below

Step-by-step explanation:

2.42 x 10^4  = 24200

 24200

+ 23580

 47 780    or   4.778 x 10^4

Answer:

Albert = $2159.07; Marie = $2244.99; Hans = $2188.35; Max = $2147.40

Marie is $10 000 richer

Step-by-step explanation:

Albert

(a) $1000 at 1.2 % compounded monthly

A = P (1 + r/n )^nt

A = 1000(1 + 0.001)¹²⁰ = $1127.43

(b) $500 losing 2%

0.98 × 500 = $490

(c) $500 compounded continuously at 0.8%

A = Pe^rt

  = 500e^0.008 * 10

 =  $541.64

(d) Balance

Total = 1127.43 + 490.00+ 541.64 = $2159.07

Marie

(a) 1500 at 1.4 % compounded quarterly

A = 1500(1 + 0.0035)⁴⁰ = $1724.99

(b) $500 gaining 4 %

1.04 × 500 = $520.00

(c) Balance

Total = 1724.99 + 520.00 = $2244.99

Hans

$2000 compounded continuously at 0.9 %

A = 2000e^0.009 * 10

  = $ 2188.35

Max

(a) $1000 decreasing exponentially at 0.5 % annually

A = 1000(1 - 0.005)¹⁰= $951.11

(b) $1000 at 1.8 % compounded biannually

A = 1000(1 + 0.009)²⁰ = $1196.29

(c) Balance

Total = 951.11 + 1196.29 = $2147.40

Marie is $10,000 richer at the end of the competition.

Hope this helps!!! :)

The equation, which represents the given condition x >= 6.2.

What is the inequality equation?

Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤, or ≥.

We have,

Six more than 5 times a number x is greater than or equal to 6.

So,

5x  >= 31

5x >= 31/5

x >= 6.2

Hence, the equation, which represents the given condition x >= 6.2.

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Complete equation:

Six more than 5 times a number x is greater than or equal to 6.

Answer:

203 dollars

Step-by-step explanation:

100 percent = 145

10 percent = 14.5

30 percent = 43.5

43.5 + 14.5 + 145 = 203

Answer:

y=2x+8

Step-by-step explanation:

-6x+3y=24

-6x+6x+3y=24+6x  ==> isolate the y variable

3y=6x+24  ==> simplify

(3y=6x+24)/3

y=2x+8  <== y=mx+b  <== slope intercept form

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Answer:

ANS:- 15.9

Step-by-step explanation:

5814/365 = 15.9

Answer: x=±2/3

Step-by-step explanation:

The first thing we want to do is isolate the variable, x² in this case.

We can divide both sides by 9 which yields the equation x²=[tex]\frac{4}{9}[/tex].

Then we can take the square root of both sides, x=2/3.

Note: When the exponent is an even number both positive and negative x values will yield the same positive answer, so x=±2/3

The value of f(5) When a polynomial f(x) is divided by x -5 is 4

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.

If f(x) has a remainder of 4 when divided by x - 5

Then it means that if f(x -5) = f(0)

x -5 = 0

x = 5

so if you substitute 5 into f(x) which is f(5) it will give 4

so therefore f(5) = 4

In conclusion f(5) is same as 4

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Answer:I hope this helpful mark me brainlist if correct then no if wrong

Step-by-step explanation:

P times 3 =-0.0027

Use the commutative property to reorder the terms

3p=-0.0027

Divide both sides of the equation by 3

p=-0.009 or p=-9/1000

Answer:

f(x) = (x+2)(x+4)

Step-by-step explanation:

4 + 2 = 6

4 * 2 = 8

f(x) = (x+2)(x+4)

Hello,

I hope you and your family are doing well!

Let's call Sydney's age x and Devaughn's age y. We know that y = 3x and x + y = 116.

Substituting the first equation into the second equation gives:

3x + x = 116

4x = 116

x = 29

So Sydney's age is 29.

Please consider leaving 5 stars and brainliest if you find this helpful.

Happy Holidays!

The time needed for the account value to reach 11200 dollars is approximately 15.9 years.

Simple interest formula is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for time t.

A = P( 1 + rt )

A/P = 1 + rt

( A/P - 1 ) = rt

t = ( A/P - 1 ) / r

t = ( $11200/$5400 - 1 ) / 6.75%

t = ( $11200/$5400 - 1 ) / 6.75/100

t = ( 56/27 - 1 ) / 0.0675

t = ( 29/27 ) / 0.0675

t = 15.9 years.

Therefore, the required time to reach the accrued amount is 15.9 years.

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Answer:

Step-by-step explanation:

Answer:

A. is the answer

Step-by-step explanation:

A. Since there is one value of  y  for every value of  x

B. is not a function x  =  − 4  produces  y  =  4  and  y  =  3

C. is not a function x  =  6  produces  y  =  6  and  y  =  3

D. is not a function   x  =  6  produces  y  =  3  and  y  =  5

The complete sentence will be;

⇒ x² + x + 1/4 = ( x + 1/2)²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ x² + x + __ = (_____)²

Now,

Since, The expression is,

⇒ x² + x + __ = (_____)²

Hence, We can add the number to form the complete square as;

⇒ x² + x + 1/4 = x² + x + (1/2)²

                     = ( x + 1/2)²

Thus, The complete sentence will be;

⇒ x² + x + 1/4 = ( x + 1/2)²

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The value of x for the triangle is equal to 17.32.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Calculate the perpendicular side for both triangles by using the Pythagorean theorem.

H² = P² + B²

Here, H is the hypotenuse, P is perpendicular and B is the base.

For the first triangle, the perpendicular is calculated as,

P² = x² - 10²......................................................1

For the second triangle, the perpendicular will be,

P² = ( 30² - x² ) - 20²  .......................................2

Equate the equation 1 and 2 and solve,

x² - 10² = ( 30² - x² ) - 20²

x² - 100 = 900 - x² - 400

2x² = 900 - 400 + 100

2x² = 600

x√ = 300

x =√300

x = 17.32

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Answer:

x> -10

Step-by-step explanation:

The distance for Tucker to walk is 1 mile, only then both the donors would have the same amount. This was found using linear equations.

What are linear equations?

A linear equation is one in which the variable's maximum power is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation. A linear equation with two variables has the formula Ax + By = C as its standard form. Here, the variables are x and y, the coefficients are A and B, and the constant is C.

Since it's given that Tucker's mother will give flat $5. So let that be the RHS of the equation. Now his grandmother will give him $5 for every mile he walks.

Let that be 5x.

Now the equation would be: 5x=5

Which results in x=1.

Therefore at 1 mile, both of the donors' amounts would be the same.

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Answer:

a. [tex]1 * 10^{-10}[/tex]

Explanation:

A converted to standard notation is the same number.

Step-by-step explanation:

8x³ + 216

(2 * 2 * 2 * x * x * x) + (2 * 3 * 2 * 3 * 2 * 3)

The confidence interval of this confidence level as calculate from the given data is 3.68 and 99% respectively.

Number of random sample (n)=28

Sample Standard deviation (S)=19.52

Confidence interval = 439.23 -  460.77 =  21.54

t = s/root of n

=19.52 /5.29

=3.68

v = n -1 = 27

now, confidence level

= 1 - alpha

= 99%

Confidence Interval, put simply, is a range within which we are confident that the genuine value exists. The probability that a confidence interval will contain the real parameter value depends on the confidence level that is chosen for the interval.

The phrase "Confidence Interval" refers to the range of values that is typically used to handle population-based data, extracting precise, important information with a given level of confidence.

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Answer: There is no y-intercept on this equations

Step-by-step explanation:

so yes you were wrong

The appropriate estimate for the diameter of the speck of dust is 2 × 10⁻⁵ inches. So the answer is option A, 2 × 10⁻⁵ in.

In scientific notation, numbers are written with the base 10 much like in decimal notation. Scientific notation is the term used when a number is expressed as the product of two numbers.

Where the first number is more than or equal to one but less than ten and the second number is the power of ten expressed in exponential form.

Step - 1 Move the decimal point up to the first number that is equal to 1 but less than 10.

Step - 2 Count the number of places that the point moved.

Step - 3 Now Write the resultant number as a product with a power of 10.            

Here we have

Diameter of a speck of duct = 0.00002 inches

Convert the given decimal into a scientific notation

As we learn above

Move the decimal point up to a whole number toward the right

=> 0.00002 = 2. = 2

Count the number of zeros or places moved

=> n = 5

Now write the number as a power of 10, Now write the above whole number part as the product of 10

=> 2 × 10⁻⁵     [ ∵ The power is moved right we need to use negative ]    

Therefore,

The appropriate estimate for the diameter of the speck of dust is 2 × 10⁻⁵ inches. So the answer is option A, 2 × 10⁻⁵ in.

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Answer:

Step-by-step explanation:

Let x be the number.

The square of the number is x2

Increased by twice the number means add 2x.

So your equation is :

X2 +2x = 48.

Can you take it from here?

The asked number is 12.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, When the square of a certain number is added to the number, the result is the same as when 48 is added to three times the number.

Let the number be x,

x²+x = 48X3 + x

x² = 144

x = 12

Hence, The asked number is 12.

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Answer:

a)  A' = (2, 4)

b)  A'' = (1, -2)

Step-by-step explanation:

When reflecting a shape in a vertical line, each vertex of the shape will be the same distance from the vertical line but in the opposite direction.  

Therefore, the x-values change but the y-values remain the same.

To reflect point A in x = -1, determine the number of horizontal units the point is from x = -1.  Count the same number of units on the other side of the vertical line (remembering that the y-value remains unchanged).

The x-value of point A is x = -4.  This is 3 units to the left of x = -1.

Therefore, the x-value of point A' is 3 units to the right of x = -1.

The y-value of point A is y = 4, so the y-value of point A' is also y = 4.

Therefore, the coordinates of the point A' are:

To translate point A' by the given vector, translate the point:

Therefore, the coordinates of the point A'' are:

Answer:

-5

-9+5

Step-by-step explanation:

The value of P({2}) for the given Finite set is found as P({2}) = 1/6.

For the stated question;

P({2}) will contain only element with is not present in set P({1}) counting from P({1, 2}).

Thus,

P({2}) = P({1, 2}) - P({1})

P({2}) = 2/3 - 1/2

P({2}) = 1/6

Thus, the value of P({2}) for the given Finite set is found as P({2}) = 1/6.

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Answer:

2.51 x 10^5

Step-by-step explanation:

Scientific notation gives you a number between 1 and 10 multiplied by a power of ten. In this case, you'll want to use the significant digits, 251, and divide or multiply by a power of ten to get a number between 1 and 10.

251,000 can become 2.51 (which is between 1 and 10) multiplied by 10 to a certain exponent. All you need to do is calculate the exponent.

2.51 x 10^(?) = 251,000

For each power of 10, the decimal moves a space. Since you want the decimal to move 5 spaces, you'll want to multiply 2.51 by 10^5.

2.51 x 10 = 25.1

2.51 x 10^2 = 251

2.51 x 10^3 = 2510

2.51 x 10^4 = 25,100

2.51 x 10^5 = 251,000