Identify the percentage of growth or decay for the exponential function: y = 18(0.75) x

If Lourdes buys 12 packs of paper in terms of 3 packs each she has to pay 0.5 dollars more.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given Lourdes can buy 3-packs of paper for $10.50.

∴ The cost of per pack of paper is = (10.50/3) = $3.5.

In this case, if she can buy 4-packs of paper for $13.50,

The cost per paper pack is = (13.50/4) = $3.375.

To buy 12 packs in terms of 3 packs each Lourdes has to pay,

(3.5×12) dollars.

= 42 dollars.

To buy 12 packs of paper in terms of 4 packs each she has to pay,

(3.375×12) dollars.

= 40.5 dollars.

∴ She has to pay (40.5 - 40)  = 0.5 dollars more.

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Answer:

0.000027 ÷ 0.000009

= 2.7 x 10^-5 ÷ 9.0 x 10^-6

= (2.7/9) x 10^(-5 - (-6))

= .3 x 10^1

= 3

Step-by-step explanation:

The expression  9x²y⁻³, for x = 5 and y = 3 simplifies to 25/3.

A fraction in which the numerator is greater than the denominator is called an improper fraction.A fraction is called a proper fraction when the denominator is greater than the numerator.

Given an expression with exponents 9x²y⁻³, for x = 5 and y = 3.

In this, we have to replace the variables x and y with their numerical value in the given expression.

So, 9x²y⁻³, for x = 5 and y = 3 is,

= 9(5)²(3)⁻³

= 9(5)²/(3)³.

= 9.(25)/27.

= 1.(25)/3.

= 25/3.

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Answer:

(adding/subtracting 8 from 5)

smaller number is -3

larger number is 13

or it could be -4 and 14

since the question says the distance is 8

[tex] \implies - \frac{149}{20} \\ [/tex]

[tex] \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{21}{3} \times \frac{5}{7} )( \frac{13 \times 5}{26} + \frac{1}{2} )\\[/tex]

According to the Bodmas rule,

According to the question,

[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{21}{3} \times \frac{5}{7} )( \frac{13 \times 5}{26} + \frac{1}{2} ) \\[/tex]

[tex] \implies \: \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{21 \times 5}{3 \times 7} )( \frac{65}{26} + \frac{1}{2}) \\ [/tex]

[tex] \implies \: \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{105}{21} )( \frac{65}{26} + \frac{1}{2}) \\ [/tex]

[tex] \implies \: \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{(21 \times 5 )- (2 \times 105)}{42} )( \frac{(1 \times 65 ) + (13 \times 1)}{26} ) \\ [/tex]

[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{105 - 210}{42})( \frac{65 + 13}{26} ) \\ [/tex]

[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( - \frac {105}{42})( \frac{78}{26} ) \\ [/tex]

[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( - \frac {105 \times 78}{42 \times 26})\\ [/tex]

[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( - \frac {8190}{1092})\\ [/tex]

[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} - \frac {8190}{1092}\\ [/tex]

[tex] \implies \frac{17}{60} \times \frac{3}{17} - \frac{8190}{1092} \\ [/tex]

[tex] \implies \frac{17 \times 3}{60 \times 17} - \frac{8190}{1092} \\ [/tex]

[tex] \implies \frac{51}{1020} - \frac{8190}{1092} \\ [/tex]

[tex] \implies \: \frac{(91 \times51) -(85 \times 8190) }{92820} \\ [/tex]

[tex] \implies \: \frac{4641 -696150 }{92820} \\[/tex]

[tex] \implies \: - \frac{691509 }{92820} \\[/tex]

[tex] \implies \: - \frac{691509 \div 4641 }{92820 \div 4641} \\[/tex]

[tex] \implies - \frac{149}{20} \\ [/tex]

Answer:

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Answer:

Step-by-step explanation:

You can't simplify 5/12 any more. That is the simplest form

Answer:

5/12 is the simplest form already

Value of the expression 2x at x=3 is 6.

By considering the given expression

2x=2(3)=6

A mathematical expression is created when we successfully combine numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.

An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.

Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.

Expression. Equation. A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

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[tex]log_{2} ( 0.125) = -3[/tex] is  exponential equation in logarithmic form.

How can you tell whether an exponential function is growing or deteriorating?

Convert the exponential equation to a logarithmic equation using the logarithm base (2) of the right side ( 0.125) equals the exponent

( -3 )

[tex]log_{2} ( 0.125) = -3[/tex]

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Based on the probability of getting a yellow on one spin, the number of yellows expected from 420 spins is 210 yellows

The number of yellows you can expect are:

= Number of spins x Probability of getting yellow

Solving gives:

= 420 x 1/2

= 420 / 2

= 210 yellows

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Answer:

c.) 6√3

Step-by-step explanation:

This can be solved using both sine and cosine rule.

1st method:

[tex]\sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]

[tex]\sf sin(60) = \dfrac{long \ leg}{12}[/tex]

[tex]\sf long \ leg= 12sin(60)[/tex]

[tex]\sf long \ leg= 6\sqrt{3}[/tex]

2nd method:

[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]

[tex]\sf cos(30) = \dfrac{long \ leg}{12}[/tex]

[tex]\sf long \ leg= 12cos(30)[/tex]

[tex]\sf long \ leg=6\sqrt{3}[/tex]

The value of the expression when b = -3 is 24

Functions can be defined as expression, rules or law that explains the relationship between two variables:

It is also important to note that the absolute value of a number is the distance of the number from zero irrespective of its direction in a number line.

Absolute value of a number must take a positive sign.

It is denoted with the symbol '| | '

Given the expression;

| -4b - 8 | + | -1 - b²| + 2b

Substitute the value of b as -3

We have;

|-4(-3) - 8| + |-1 - (-3)²| + 2(-3)

expand the bracket

|-12-8| + |-1 - 9| - 6

Take the absolute values

20 + 10 - 6

24

Thus, the value of the expression when b = -3 is 24

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The amount deducted from Joseph's account for each ticket is $8

The mathematical expression representing the situation is:15=55-5x

What is the total amount deducted from the subway pass?

On the premise that Joseph's subway pass was deducted each time he passes through the subway and that $40 was deducted in all for his number of passes, the total cost of $40 can be modeled into an equation as shown below:

amount left after the deductions=55-40

amount left after the deductions=15

15=total amount paid-(number of passes*cost per subway pass)

total amount paid=55

number of passes=5

cost per subway=x

15=55-5x

5x=55-15

5x=40

x=40/5

x=$8

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[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6425\\ P=\textit{initial amount}\dotfill &3500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &8\\ \end{cases}[/tex]

[tex]6425=3500(1 + \frac{r}{100})^{8} \implies \cfrac{6425}{3500}=\left( \cfrac{100+r}{100} \right)^8\implies \cfrac{257}{140}=\left( \cfrac{100+r}{100} \right)^8 \\\\\\ \sqrt[8]{\cfrac{257}{140}}=\cfrac{100+r}{100}\implies 100\sqrt[8]{\cfrac{257}{140}}=100+r \\\\\\ 100\sqrt[8]{\cfrac{257}{140}}-100=r\implies {\LARGE \begin{array}{llll} \stackrel{\%}{7.89}\approx r \end{array}}[/tex]

The percent of the population sleeps more than the recommended number of hours will be 30%.

From the information, it should be noted that the difference between the percent of adults who slept more than the recommended amount of time and the percent who slept less than the recommended amount of time is 3%.

It should be noted that this was 25% of the population.

Therefore, the percent of the population sleeps more than the recommended number of hours will be:

= 27% + 3%

= 30%

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The value of 983,512 × 1 will be 983,512 by using the multiplicative identity of multiplication.

We are given the expression:

983,512 × 1

We need to find the result after multiplication.

Multiplication is one of the basic operations of mathematics that is used to simplify the expression.

Here, we will use the property of multiplicative identity as the number is multiplied by 1.

By using this, we get that the result will be the same number as anything multiplied by 1 will always give the same number.

So, we get that:

= 983,512

Therefore, we get that, the value of 983,512 × 1 will be 983,512 by using the multiplicative identity of multiplication.

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The union of the sets is E ∪ F = (-∞, 3] or (6, ∞) and the intersection of the sets E ∩ F =  ∅ (null sets) is in interval notation.

A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.

We have:

E and F are sets of real numbers defined as follows. E={v | v ≤ 3} F={v | v > 6}

E ∪ F = (-∞, 3] or (6, ∞)

E ∩ F =  ∅ (null sets)

Thus, the union of the sets is E ∪ F = (-∞, 3] or (6, ∞) and the intersection of the sets E ∩ F =  ∅ (null sets) is in interval notation.

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Using the piecewise function graphed in this problem, we have that:

1. The x-axis represents the time in hours.

2. The y-axis represents the distance in miles.

3. The person traveled 30 miles in those 4 hours.

4. The person traveled at a rate of 7.5 miles per hour in Section A.

5. In section B, the person remained stopped 30 miles from her starting point for 2 hours.

6. The velocity for Section B was of 0 miles per hour.

7. The person traveled 30 miles in Section C.

8. 8. The speed in Section D was of 20 miles per hour.

9. The person was moving at the highest speed in Section C, at a rate of 30 miles per hour.

10. The farthest distance traveled was of 60 miles in Section D.

11. A person had an appointment 30 miles away from their home, and due to slow traffic had to leave early. Then the appointment lasted 2 hours, then the person went to another place 30 miles away to do something then came back home.

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

From the graph, the function has four different definitions, in intervals, A, B, C and D.

From the axis of the graph, we have that:

1. The x-axis represents the time in hours.

2. The y-axis represents the distance in miles.

Considering that the graph has points (0,0) and (4,30), we have that:

3. The person traveled 30 miles in those 4 hours.

The velocity is given by distance divided by time, hence:

30/4 = 7.5.

4. The person traveled at a rate of 7.5 miles per hour in Section A.

In Section B, the person remains at the same position, hence:

5. In section B, the person remained stopped 30 miles from her starting point for 2 hours.

The distance was of 0, hence:

6. The velocity for Section B was of 0 miles per hour.

In Section C, from the y-axis of the graph, the distance traveled was:

60 - 30 = 30 miles.

7. The person traveled 30 miles in Section C.

For Section D, the person traveled 60 miles in 10 - 7 = 3 hours, hence:

60/3 = 20.

8. The speed in Section D was of 20 miles per hour.

10. The farthest distance traveled was of 60 miles in Section D.

In Section C, the person traveled 30 miles in one hour = 30 miles per hour, hence:

9. The person was moving at the highest speed in Section C, at a rate of 30 miles per hour.

For item 11, a situation that can be modeled is:

A person had an appointment 30 miles away from their home, and due to slow traffic had to leave early. Then the appointment lasted 2 hours, then the person went to another place 30 miles away to do something then came back home.

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All the angles in the given diagram are;

∠5 = 81°

∠1 = 128°

∠2 = 52°

∠3 = 47°

∠4 = 133°

We are given different angles. Thus;

52 + ∠5 + 47 = 180

This is because sum of angles on a straight line is 180°. Thus;

99 + ∠5 = 180

∠5 = 180 - 99

∠5 = 81°

∠1 = ∠5 + 47° because of the definition of corresponding angles. Thus;

∠1 = 81° + 47°

∠1 = 128°

∠2 = 52° because they are corresponding angles.

∠3 = 47° because they are corresponding angles.

∠4 = 180 - 47° because sum of angles on a straight line is 180°.

∠4 = 133°

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Answer:

x = 3/16

Step-by-step explanation:

Answer: x = 3/4 or X = - 1/8

Step-by-step explanation:

Answer:

Slope: (3/2)

y-intercept: (0, -6)

Step-by-step explanation:

3x - 2y = 12

-3x              -3x

-2y = -3x + 12

÷-2    ÷-2  ÷-2

---------------------

y = (3/2)x - 6

Slope: (3/2)

y-intercept: (0, -6)

I hope this helps!

0²/₃ = 0 but 0⁻²/₃ is undefined because 1/0 is undefined.

Consider 0²/₃. So here, 0 has a positive power though a rational at that.

Any positive powers of 0 is considered as 0 itself. This expression also means that the square of the cubic root of zero. We know that cubic root of 0 is 0 and 0² = 0 itself. So we can conclude that 0²/₃ = 0.

Now consider 0⁻²/₃ .

We have [tex]a^{-b}=\frac{1}{a^b}[/tex].

So here, 0⁻²/₃ = [tex]\frac{1}{0^{\frac{2}{3}} }[/tex]

From the previous case, 0²/₃ = 0

So we get  0⁻²/₃ = 1/0, which is undefined.

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The units that need to be produced to have minimum cost is 800 units.

From the information, the manufacturer of candies has daily costs of T(x)=2x² - 3200x+6800.

Therefore, we will differentiate with respect to x. This will be:

T(x)=2x² - 3200x+6800.

4x - 3200

4x - 3200 = 0

4x = 3200

Divide

x = 3200/4

x = 800

Therefore, the units that need to be produced to have minimum cost is 800 units.

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There are two possibilities: (i) Perpendicular line: y = 2 · x + 6, Parallel lines: y = - (1 / 2) · x + 7 / 2, y = - (1 / 2) · x + 6, (ii) Perpendicular line: y = - 2 · x + 6, Parallel lines: y = (1 / 2) · x + 7 / 2, y = (1 / 2) · x + 6.

The missing coordinate of one of the points of intersection can be found by using the least distance between the two parallel lines and the Pythagorean theorem:

(a - 0)² + (4 - 6)² = 5

a² + (- 2)² = 5

a² + 4 = 5

a² = 1

a = ± 1

There are two possibilities: (x₁, y₁) = (- 1, 4), (x₂, y₂) = (1, 4). Now we proceed to find the equations associated to each case:

(x₁, y₁) = (- 1, 4), (x₃, y₃) = (0, 6)

The equation of the perpendicular line is:

Slope

m = (6 - 4) / [0 - (- 1)]

m = 2

Equation of the line

y - 4 = 2 · (x + 1)

y - 4 = 2 · x + 2

y = 2 · x + 6

The slope of the two parallel lines is:

m' = - 1 / m

m' = - 1 / 2

First parallel line

y - 4 = (- 1 / 2) · (x + 1)

y - 4 = - (1 / 2) · x - 1 / 2

y = - (1 / 2) · x + 7 / 2

Second parallel line

y - 6 = - (1 / 2) · x

y = - (1 / 2) · x + 6

(x₂, y₂) = (1, 4), (x₃, y₃) = (0, 6)

The equation of the perpendicular line is:

Slope

m = (6 - 4) / (0 - 1)

m = - 2

Equation of the line

y - 4 = - 2 · (x - 1)

y - 4 = - 2 · x + 2

y = - 2 · x + 6

The slope of the two parallel lines:

m' = - 1 / m

m' = 1 / 2

First parallel line

y - 4 = (1 / 2) · (x - 1)

y - 4 = (1 / 2) · x - 1 / 2

y = (1 / 2) · x + 7 / 2

Second parallel line

y - 6 = (1 / 2) · x

y = (1 / 2) · x + 6

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If a random sample of 49 people is selected from a population and it is found that 12 people in the sample are over six feet tall, then the best point estimate of the proportion of people in the population who are over six feet tall is 0.24

The point estimate is a term used in mathematics to calculate a single value as an approximate of a parameter of a population.

Point estimate can be given the formula:

point estimate = Number of successes / Total number of samples

In this case, the total number of samples = 49

number of people over six feet tall (successes) = 12

Therefore,

proportion of people over six feet tall = 12 / 49

proportion of people over six feet tall = 0.2448

Decimal can be rounded to two decimal places, if the third digit is less than 5, round the second digit down. On the other hand, if the third digit is more than 5, round the second digit up.

Therefore,

proportion of people over six feet tall = 0.2448 = 0.24

Thus the point estimate of the proportion of people in the population who are over 6 feet tall is calculated to be 0.24

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Answer: 6 CHOOSE 4 can also be denoted as 6C4.

Draw 4 out of 6 elements at a time and replace the drawn elements again after the event occurred in the statistical experiments.

In 15 possible combinations, AB and BA are not considered as different events.

AB and BA considered as a single combination in 15 events.

Step-by-step explanation:

The interval of I₁ or I₂ or I₄ is  (2.5 ,10].

The interval of I₁ and I₂ is  [3 , 5.5] .

The interval of I₁ and I₃ is  [5.5]

The interval of I₁ and I₄ is (5.6 , 7]

(a) because the all 3 intervals square measure connected by or which suggests they're going to all embrace the quantity lying from interval one to three and is given by (2.5 ,10].

(b) because the interval square measure connected by and which suggests the common numbers lying in interval one and a couple of and is given by [3 , 5.5] .

(c) because the interval square measure connected by and which suggests the common numbers lying in interval one and three and is given by [5.5]

(d)As the interval square measure connected by and which suggests the common numbers lying in interval one and four and is given by (5.6 , 7] .

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The complete question is given below :

Given the intervals I₁ = (2.5, 5.5], I₂ =[3, 6], I₃=[5.5, 7] and I₄ = (5.5, 10]. Find

(a) I₁ or I₂ or I₄

(b) I₁ and I₂

(c) I₁ and I₃

(d) I₁ and I₄