Question: 18 The auditorium at McCaskey East High School in Lancaster, PA has 800 seats. Suppose that the drama club has a goal of making $3400 each night of their spring play to cover expenses and raise money for the club. Adult tickets are $7 and students/senior tickets are $4.

Answer:57

Step-by-step explanation:

Answer:

Inverse property

Step-by-step explanation:

3/4 is the reciprocal of 4/3 which means they would cancel each other out. So you would only be left with x=x

The exponential model for the given data set is [tex]y(x) = 70 + (110)e^{-0.135x}[/tex].

Given that cake recipe says to bake the cake until the center is 180⁰F , then let the cake cool to 120⁰F and the table shows temperature readings for the cake and the room temperature is 70°F.

Temperature at time = 0 min, y₀= 180° F

Ambient (room) tempertaure = y₁ = 70° F

Using Newton's cooling method,

y(x) = y₁ + (y₀ - y₁)e⁻ⁿˣ

y(x) = 70 + (180-70)e⁻ⁿˣ

y(x) = 70 + (110)e⁻ⁿˣ

Given, at x=5 min, y(5) = 126,

y(5) = 70 + (110)e⁻⁵ⁿ  = 126

Solving,  e⁻⁵ⁿ  = (126-70)/110 = 0.5091

Taking and log and solving for n,

- 5n = log(0.5091)

-5n= -0.67511

n = 0.135

Thus, the exponential model is [tex]y(x)=70+(110)e^{-0.135x}[/tex]

Hence, an exponential model for given data set when a room temperature  of 70°F is [tex]y(x)=70+(110)^{-0.135x}[/tex].

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We have expression ln a-2 ln b+1/3 ln c as a single natural logarithm

㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

We have been asked to express ln a-2 ln b+1/3 ln c as a single natural logarithm.

⇒ ln a-2 ln b+1/3

⇒ ㏑ (a) - ㏑ (b²) + ㏑ [tex]c^{\frac{1}{3} }[/tex]

Use the quotient property of logarithms for ln a-2 ln b

⇒ ㏑ [tex](\frac{a}{b^2} )[/tex] + ㏑ [tex]c^{\frac{1}{3} }[/tex]

Use the quotient property of logarithms for ㏑ [tex](\frac{a}{b^2} )[/tex] + ㏑ [tex]c^{\frac{1}{3} }[/tex]

⇒ ㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]

Finally, we have expressed ln a-2 ln b+1/3 ln c as a single natural logarithm ㏑ [tex](\frac{ac^{\frac{1}{3} }}{b^2} )[/tex]

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The function [y = log(x)] is translated 1 unit to the right and 2 units down, yielding [g(x) = log(x - 1) - 2] as the translated function. and this may be established by using the transformation's rules.

Given:

One unit to the right and two units down translate the function y=log(x).

The translated function's graph can be drawn using the procedures listed below:

First, write the function that is supplied.

y = log(x) (x)

Step 2: Multiply the given function in the right direction—that is, in the positive x-axis direction—by factor 1 in accordance with the data provided. The aforementioned function is now:

f(x) = lox (x - 1)

Step 3: Next, move the graph of the function f(x) in a downward direction, or in the opposite direction of the y-axis.

g(x) = log(x - 1) - 2

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Answer:

25

Step-by-step explanation:

if the formula for distance is distance = rate times time then you have to divide the rate 60 by the distance 150 to get 25 .

Decimal value                                     Scientific Notation

987,650,000                                       9.8765 × 108

6.5 can be translated to 6 1/2 times 5 3/4 or 5 3/4 can be translated to 5.75 times 6.5 which equals 37.375

Answer:

-15,-9,-3,3,9

Step-by-step explanation:

Answer:

X intercept (18,0)

Y intercept(0,16)

Step-by-step explanation:

hope this was helpful!

Solution of this polynomial equation is x = 4

In mathematics, polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non  negative number as their powers are part of polynomial equation.

Types of polynomial equations :

Some examples of polynomial equation are :

According to question,

2x = 8

=> 2x / 2 = 8 /2

=> x = 4

Thus solution for given equation is x = 4.

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La cantidad 855672019 descrita en palabras es Ochocientos cincuenta y cinco millones seiscientos setenta y dos mil diecinueve.

En este ejercicio debemos representar en palabras la cantidad asociada al conjunto de dígitos descritos en el enunciado. Para leer y describir un número se lee de izquierda a derecha, en donde un dígito a la derecha tiene más magnitud que un dígito a la izquierda, de modo que se comienza con el dígito de mayor magnitud hasta alcanzar el de menor magnitud.

8 - Ochocientos millones

5 - Cincuenta millones

5 - Cinco millones

6 - Seiscientos mil

7 - Setenta mil

2 - Dos mil

01 - Diez

9 - Nueve

En consecuencia, la cantidad 855672019 es Ochocientos cincuenta y cinco millones seiscientos setenta y dos mil diecinueve.

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Answer:

Step-by-step explanation:

30 and 20

Answer:

f(x) = x - 8

Step-by-step explanation:

Answer:

2/3 and 3/2

Step-by-step explanation:

→ Divide the smaller triangle by the larger one for the first one

8 ÷ 12 = 8/12 = 2/3

→ Divide the larger triangle by the smaller one for the second one

12 ÷ 8 = 12/8 = 3/2

Answer:

see explanation

Step-by-step explanation:

a rational number has the form

[tex]\frac{a}{b}[/tex] , where a and b are integers

given

0.3596 ← with 6 in the [tex]\frac{1}{10000}[/tex] place

= [tex]\frac{3596}{10000}[/tex] = [tex]\frac{899}{2500}[/tex] ← a rational number

Answer:

12

Step-by-step explanation:

[tex]\sqrt{8} * \sqrt{18} =12[/tex]

The state and local tax that will be paid by Mei will be $17 and $12.50 respectively.

From the information, Mei has a weekly taxable income of $265.85. her state tax rate is 6.4% and her local county tax rate is 4.7%.

The state tax that will be paid will be:

= Rate × Income

= 6.4% × $265.85

= 0.064 × $265.85.

= $17

The local tax that will be paid will be:

= Rate × Income

= 4.7% × $265.85

= 0.047 × $265.85.

= $12.50

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The domain of the function is (3,∞) , {x|x>3}

and the range of the function is (−∞,∞),  {y|y ∈ R}

given the function is y = log₂(x ₋ 3)

Set the argument in  log₂(x ₋ 3)  greater than 0 to find where the expression is defined.

x ₋ 3 > 0

Add 3 to both sides of the inequality.

x > 3

The domain is all values of x that make the expression defined.

Interval Notation:

(3,∞)

Set-Builder Notation:

{x|x>3}

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation:

(−∞,∞)

Set-Builder Notation:

{y|y∈R}

Determine the domain and range.

Domain: (3,∞) , {x|x>3}

Range :  (−∞,∞),  {y|y ∈ R}

Hence we get the required domain and range of the given function.

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The actual area of the care park in hectares is 18.75

As per the known fact, ratio of measurement on scale is equal to the ratio of measurement in real. So, writing the equation first -

Area of car park = 3 cm²

Keep the value of 1 cm in the above mentioned equation.

Area of car park = 3 × (250)²

Taking square

Area of car park = 3 × 62,500

Performing multiplication

Area of car park = 1,87,500 m²

Converting the area in hectares

10,000 m² = 1 hectare

1,87,500 m² = (1 ÷ 10,000) × 1,87,500

1,87,500 m² = 18.75 hectares.

Therefore, the actual area of the care park is 18.75 hectares.

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Answer:

12

Step-by-step explanation:

2 x 6 = 12

to find area you multiply length x width or in this case base x height

The expression that is equivalent to (2x + 3)/4 is: A. x/2 + 3/4.

Express the given expressions in their simplest form to determine the expression that is equivalent to (2x + 3)/4.

A. x/2 + 3/4

Find the common denominator. The common denominator is 4. Therefore:

=  2(x) + 1(3)/4

= (2x + 3)/4

x/2 + 3/4 ≠ (2x + 3)/4

Thus, the expression, x/2 + 3/4 is equivalent to (2x + 3)/4.

B. x/2 - 3/4 = (2x - 3)/4

Therefore, x/2 - 3/4 ≠ (2x + 3)/4

C. 3x/4 + 3/4 = (3x + 3)/4

Therefore, 3x/4 + 3/4 ≠ (2x + 3)/4

D. 8x + 24 ≠ (2x + 3)/4

Therefore, 8x + 24 ≠ (2x + 3)/4

In summary, we can conclude that, the expressions, x/2 - 3/4, 3x/4 + 3/4, and 8x +24x/2 + 3/4 is not equivalent to (2x + 3)/4. Thus, the expression that is equivalent to (2x + 3)/4 is: A. x/2 + 3/4.

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The slope of the line that passes through the coordinates is -6/5.

The slope of the line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

Where, the coordinates are given.

(x₁ ,y₁) = (2, 8)

(x₂, y₂) = (-3, 14)

Put the value in the slope;

m = (14 - 8)/(-3 - 2)

m = 6/-5

m = -6/5

Therefore, the slope of line passing from the points is -6/5

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Answer:

[tex]3\sqrt{21}[/tex]

Step-by-step explanation:

By the Pythagorean theorem,

[tex]\sqrt{17^2-10^2}=\sqrt{189}=3\sqrt{21}[/tex]

Answer: 96%

How to Solve

Formula:

y ÷ x *100
Substitute
=> 24 ÷ 25 * 100

Lets Multiply 24 * 100 (or you can divde 24 and 25 then multiply with 100. do as you're convenience, answer will remain)
Answer 2400

Now As our formula says divide 2400 by 25
Answer  96

Hence 96%

So, 24/25

as a percentage is 96%

All done!

Answer:

96%

Step-by-step explanation:

First, divide 100 but 25 (the denominator) and you get 4. This means that to get a number over 100, which is a percentage you need to multiply the initial fraction by 4. You get 96/100, and you can remove the 100 to get 96%

Two random numbers 180000000 and 0.00000534 can be written as 1.8 x 10⁸ and 5.34 x 10⁻⁶.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It may be called scientific form.

When a number is written using only the digits of the number, that is considered standard notation. Since words are not used in conventional number notation, this is the way that numbers are typically written.

Let the bigger number by 180000000  and the smaller number be 0.00000534. The two numbers in scientific notations can be written as below:-

180000000   = 1.8 x 10⁸

0.00000534 = 5.34 x 10⁻⁶.

Therefore, two random numbers 180000000 and 0.00000534 can be written as 1.8 x 10⁸ and 5.34 x 10⁻⁶.

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Answer:

Step-by-step explanation:

1/2÷4 = 1/8 = 0.125.

[tex]\cfrac{1}{2}\div -4\implies \cfrac{1}{2}\div \cfrac{-4}{1}\implies \cfrac{1}{2}\cdot \cfrac{1}{-4}\implies {\LARGE \begin{array}{llll} -\cfrac{1}{8} \end{array}}[/tex]

Based on table shown above, we have that: B. No, because one x-value corresponds to two different y-values.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

Based on table shown above, we can reasonably infer and logically deduce that this table does not represent a function because one x-value corresponds to two different y-values.

In conclusion, this table is not a function because no function can have the same x-values (3) for different y-values (5 and 6).

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Step-by-step explanation:

if that is a geometric sequence to find the common ratio

[tex] \frac{t2}{t1} [/tex]

you divide the exceeded term with the previous term

simply you can say

[tex] \frac{tn}{t(n - 1)} [/tex]

therefore now we have

[tex] \frac{2x - 1}{x + 1} or \\ \frac{3x + 1}{2x - 1} [/tex]

therefore you will substitute x=0 in any of the given equations they should give youbthe same answer

[tex] \frac{2(0) -1 }{0 + 1} = - 1[/tex]

or

[tex] \frac{3(0) + 1}{2(0) - 1} = - 1[/tex]