Simplify the expression
(Please show the work)

The percent decrease of the exponential function is 22%

Suppose we have an initial value A and we increase/decrease it by a percentage X, the new value will be:

A' = A*(1 ± X/100%)

Where the sign depends if it is an increase or decrease.

And if we apply that t times, then we have the exponential function:

A'(t) =  A*(1 ± X/100%)^t

If we want to solvethe percentage, then we need to solve:

0.78 = 1 ± X/100%

Obviously we need to take the negative sign:

0.78 = 1 - X/100%

X = 100%*(1 - 0.78) = 22%

Thet is the percent decrease.

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The factored form of the equation is g(x) = -(x + 2)(x − 4)..

A quadratic expression that is written as the product of a constant times two linear factors is said to be in factored form.

Given:

As, the equation of the function in factored form,

g(x) = a(x − [tex]r_1[/tex])(x − [tex]r_2[/tex]),

The function has x-intercepts of -2 and 4.

So (x + 2 )and (x − 4) are factors of the equation.

Now, the value of y changes for 1 unit to the right of the vertex.

The y-value goes down 1 unit for a point 1 unit to the right of the vertex, so a = -1.

So, the equation of this quadratic function is

g(x) = -(x + 2)(x − 4).

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The height of the cylinder jar is 6/4 centimeters

The formula for determining the volume of a cylinder is expressed with the equation;

V = πr²h

Such that the parameters are;

From the information give, we have that;

Volume = 24π cubic centimeters

Radius = 4cm

Now, substitute the values into the formula

24π = π(4)²h

find the square

24π = 16πh

Make 'h' the subject of formula, we get;

h = 24π/16π

h = 24/16

h = 6/4

Hence, the value is 6/4

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The relative frequency of responders who chose the vegetarian meal is 0.5, or 50%.

The concept used in this problem is relative frequency, which is a measure of the number of times an event occurs in a data set, expressed as a fraction of the total number of events.

The relative frequency is a useful tool for summarizing and understanding the distribution of data, and provides a way to compare the relative frequencies of different events in a data set.

To create a relative frequency distribution in Excel, you would first create a table with the four meal options (chicken, fish, steak, and vegetarian) and count the number of times each option was selected. The relative frequency is calculated as the count of each meal option divided by the total number of responses (20 in this case).

Here is the frequency distribution as :

Meal Option → Frequency → Relative Frequency

Chicken → 6 → 0.3 (6/20)

Fish → 2 → 0.1 (2/20)

Steak → 2→ 0.1 (2/20)

Vegetarian →  10 → 0.5 (10/20)

Thus, the relative frequency of responders who chose the vegetarian meal is 0.5, or 50%.

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The relative frequency of responders who chose the vegetarian meal is 0.5, or 50%.

The concept used in this problem is relative frequency, which is a measure of the number of times an event occurs in a data set, expressed as a fraction of the total number of events.

The relative frequency is a useful tool for summarizing and understanding the distribution of data and provides a way to compare the relative frequencies of different events in a data set.

To create a relative frequency distribution in Excel, you would first create a table with the four meal options (chicken, fish, steak, and vegetarian) and count the number of times each option was selected. The relative frequency is calculated as the count of each meal option divided by the total number of responses (20 in this case).

Here is the frequency distribution as :

Meal Option → Frequency → Relative Frequency

Chicken → 6 → 0.3 (6/20)

Fish → 2 → 0.1 (2/20)

Steak → 2→ 0.1 (2/20)

Vegetarian →  10 → 0.5 (10/20)

Thus, the relative frequency of responders who chose the vegetarian meal is 0.5, or 50%.

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y = -2x + 12 is the linear equation's slope intercept form.

In the form of a slope-intercept equation, the line's equation is stated as follows: y = mx + b, where m denotes the slope and b denotes the y-intercept.

Values for the slope and y-intercept describe the properties of the relationship between the two variables x and y.Slope is a measure of how quickly y changes for every unit change in x.

In the event that the x-value is 0, the y-intercept shows the y-value. An equation's slope intercept form is shown as follows:

y = mx + c

where

slope = m

y-intercept = c

Therefore,

4x + 2y = 24

2y = -4x + 24

multiply both sides by two.

2y / 2 = -4x /2 + 24 / 2

y = -2x + 12

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Answer:

computer sold for $410

Monitor sold for $100

Step-by-step explanation:

The computer cost = x

the monitor = x-310

2x-310=510

x=410

So computer sold for $410

Monitor sold for $100

Answer: The monitor sold for 200.

Step-by-step explanation:

If you have a total of $510, and one item costs $310, subtract $310 from $510 and you get $200.

Example:    $510 - $310 = $200

The expression for m in terms of p will be m = 5p - 4

A function shows the relationship between the variables that are provided or the data given regarding an information.

Function A    x   + 4   then × 2  = y

x = m

y = (m + 4) × 2   = 2m +  8

Function B     x ÷ 5   Then + 1  =  y

x =  2m +  8

y = 2p+1

(2m + 8)  ÷ 5   + 1  =  2p+1

= (2m + 8)  ÷ 5  = 2p

= 2m +  8 = 10p

= m + 4 = 5p

m = 5p - 4

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Here is a composite function find an expression for m in terms of p give your answer in its simplest form

Function A    x   + 4   then ×2  = y

Function B     x ÷ 5   Then + 1  =  y

m  Function A   then Function B   = 2p+1

Answer:A function f(x) is even if f(-x) = f(x). The function is odd if f(-x) = -f(x). An even function has reflection symmetry about the y-axis. An odd function has rotational symmetry about the origin.

Step-by-step explanation:

The function is even when f(-x) = f(x) and is odd when f(-x) = -f(x).This has been obtained using even-odd functions.

What are even-odd functions?

When the output value of a real-valued function, f(x), is equal to f(x), for all values of x inside the domain of f, the function is said to be an even function.

It is claimed that a real-valued function f(x) is an odd function when, for all values of x in the domain of f, the output value of f(-x) is equal to the negative of f(x).

We have an even function if we have an expression that is equivalent to f(x) and we have an odd function if we obtain an expression that is equivalent to -f(x).

If we take a function and substitute x for -x, simplify the result, and then compare it to what you started with, you can "determine algebraically" if the function is even, odd, or neither.

The function is even if you come out with exactly what you started with (i.e., if f (-x) = f (x), in which case all of the signs are the same. If you come out with exactly the opposite of what you started with (i.e., if f(-x) = -f (x), in which case all of the signs are switched), it is an odd function.

Hence, the function is even when f(-x) = f(x) and is odd when f(-x) = -f(x).

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Answer: Polynomials are an important part of the "language" of mathematics and algebra. They are used in nearly every field of mathematics to express numbers as a result of mathematical operations. Polynomials are also "building blocks" in other types of mathematical expressions, such as rational expressions.

Step-by-step explanation:

Answer:

3: Multiplying the first equation by −2 so the x-variables are eliminated.

Step-by-step explanation:

The elimination method is a strategy to solve a system of linear equations by eliminating one of the variables (usually the y variable) by adding or subtracting the equations. This can be done by multiplying one or both of the equations so that when added or subtracted, the y variable will cancel out.

In this case, the best option for multiplying to solve the system using the elimination method is to multiply the first equation by -2 so that the x-variables are eliminated. This is because when the first equation is multiplied by -2, it becomes -6x + 12y = 8, which has the same coefficient for x as the second equation. When the two equations are added, the x variable will cancel out, leaving us with an equation in terms of y, which can then be solved for x.

The equation after the elimination will look like this:

-6x + 12y + 6x + 11y = -2 + 8

6y = 6

y = 1

Finally, we can use this value of y to solve for x in one of the original equations:

3x - 6(1) = 4

3x = 10

x = 10/3 = 3.33

So the solution to the system is (3.33, 1).

The constant of proportionality is 5/3.

and, the equation is y= 5/3x.

The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional. When y and x are two values that are directly proportional to one another, the proportionality constant k is defined as k=y/x.

Given:

y=20 and x= 12

As, from equation of proportionality we have

y=kx

20=k(12)

k= 20/12

k = 5/3

So, Based on the above calculations, the equation that relates x and y is:

y= (5/3)x

y =1.667 x

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The total area of the ribbon is equals to 46 sq. inches with a 4 square inches of school logo in between.

The four-sided polygonal shape known as a quadrilateral has four edges and four corners. The Latin words quadri, a variation of four, and latus, meaning "side," were used to create the term.

In American and Canadian English, a quadrilateral having at least one set of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides.

The total area of the ribbon = area of the top square + area of the bottom trapizium

Area of the square = 4*4 = 16 sq. inches

Area of the trapizium = (1/2)*(sum of parallel sides)*height = (1/2)*(4+8)*5 = 30 sq. inches.

The total area of the ribbon is equal to 30 + 16 = 46 sq. inches with a 4 square inches of school logo in between.

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The percentage 31.25% has no equivalent fraction or decimal

From the question, we have the following parametes that can be used in our computation:

Percentage = 31.25%

Convert the percentage to decimal

So, we have

Decimal = 0.3125

When the fractions are evaluated, we have

15/16 = 0.9375

23/12 = 1.9167

312/40 = 7.8

41/8 = 5.125

See that none of these values can be evaluated to 0.3125

Hnce, the percentage has no equivalent expression in the options

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42 red blood cells are needed to make a line 1 inch long

The diameter of a red blood cell is 6 x [tex]10^{-6}[/tex] m,

so we need to determine how many cells can fit in a

line 1 inch long (2.54 x[tex]10^{-5}[/tex] m).

Dividing the length by the diameter gives the number of cells:

2.54 x [tex]10^{-5}[/tex] m / 6 x [tex]10^{-6}[/tex] m = 42.33.

So, approximately 42 red blood cells are needed to make a line 1 inch long.

This highlights the small size of red blood cells and the remarkable ability of the human body to produce and maintain billions of these cells for proper blood circulation and oxygen delivery.

Red blood cells, also known as erythrocytes, are one of the main types of blood cells. They are biconcave discs with a diameter of about 7.5 micrometers, and their primary function is to transport oxygen from the lungs to the tissues and carbon dioxide from the tissues to the lungs.

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The simplification of csc²x-cscx+2/CSCX-1 = 1/sin²(x) - sin(x) / (sin²(x)-1)

First, let's recall the definition of cosecant (csc): it's the reciprocal of sine, so csc(x) = 1/sin(x).

Next, we can simplify the equation by substituting the definition of cosecant into the equation:

csc²x-cscx / CSCX-1 = (1/sin(x))² - (1/sin(x)) / (1/(sin(x))-1)

Next, we can simplify the numerator and denominator using algebraic identities:

(1/sin(x))² = 1/sin²(x)

(1/sin(x)) / (1/(sin(x))-1) = sin(x) / (sin²(x)-1)

So, the equation becomes:

1/sin²(x) - sin(x) / (sin²(x)-1)

And this is the simplified form of the equation.

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so hmmm let's notice the denominators in each, so hmmm the 1st equation has an LCD of 6, so let's multiply both sides by that, and the 2nd equation has an LCD of 12, so let's multiply it by that to do away with the denominators, oddly enough, it gives us an elimination of a variable, so let's do so

[tex]\begin{array}{llll} \cfrac{1}{2}x-\cfrac{2}{3}y=6 \\\\\\ \cfrac{1}{4}x+\cfrac{1}{3}y=-1 \end{array}\hspace{5em} \begin{array}{llll} 6\left( \cfrac{1}{2}x-\cfrac{2}{3}y=6 \right) \\\\\\ 12\left( \cfrac{1}{4}x+\cfrac{1}{3}y=-1 \right) \end{array}\hspace{5em} \begin{array}{llll} ~~ 3x-4y&=36 \\\\\\\\\\ -3x-4y&=12\\\cline{1-2} ~\hfill -8y&=48 \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]-8y=48\implies y=\cfrac{48}{-8}\implies y=-6 \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{3x-4y=36}\implies 3x-4(-6)=36\implies 3x+24=36 \\\\\\ 3x=12\implies x=\cfrac{12}{3}\implies x=4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (4~~,~-6) \end{array}}~\hfill[/tex]

The total amount Robin will get after 20year is $900

Simple interest is the cost of borrowing money without accounting for the effects of compounding. In other words, simple interest only applies to the principal amount.

The total amount is expressed as :

A = P+I

and I = P×r×t/100

where r is the rate

t is the time and

p is the principal

I = 500×4×20/100

I = $400

after 20 years the interest will be $400

The total amount Robin will receive after 20 years is

A = 500+400

A = $900

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Answer: -2/3

Step-by-step explanation: rise / run, also keep in mind that this is a negative slope.

Answer:

[tex] \sf \: x = 20[/tex]

Step-by-step explanation:

Given equation,

→ x - 18 = 2

Now the value of x will be,

→ x - 18 = 2

→ x = 2 + 18

→ [ x = 20 ]

Hence, the value of x is 20.

The radical expression is written as 38 in its simplest form.

A mathematical expression shows the value of something by combining numbers, variables, and operators. A mathematical statement known as an equation involves setting two expressions equal to one another.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

1 + 7n - 5 will therefore equal:

= 1 + 7n - 5

= 1 + 7(6) - 5

= 1 + 42 - 5

= 38

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12 mygs will cost 27, and 5 flasks will cost 30

Option B is the correct answer. Ceteris paribus is a phrase do we use to indicate that we are trying to study the relationship between two variables while the values of all other variables are held unchanged.

This is the most commonly-used phrase that defines 'all other things being unchanged or constant'. It is used in economics to rule out the possibility of 'other' factors changing, which is the specific causal relation between two variables is focused.

This is the Latin phrase that is generally used for saying 'with other things being the same'. It is particularly crucial in the study of cause and effect relationships between two specific variables such that other relevant factors influence.

The opposite word for this phrase is 'mutat's mutants, which defines changing some factors that are used to be changed. Ceteris paribus is often a fundamental assumption to the predictive purpose of scrutiny.

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Assuming the solid Fe is pure iron, the atomic mass of iron is 55.845 g/mol. This means that in one cubic centimeter of iron there are 6.02 x 10²² atoms of Fe.

Solid iron has a density of 7.87 g/cm³. This means that in one cubic centimeter of iron, there are 6.02 x 10²² atoms of iron. This is calculated by taking the atomic mass of iron (55.845 g/mol) and dividing it by the density of iron (7.87 g/cm³). This gives us the number of atoms of iron in one cubic centimeter of iron, which is 6.02 x 10²² atoms.

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Answer:

2399.03

Step-by-step explanation:

2000*(1+2.3%)^8 =2399.03

Answer: 2399.0

Step-by-step explanation: because you would multiply 2000 by 1+2.3% ^8 and get your answer 2399.0 and if you round it to be the nearest hundredth you will get 2399.03

The independent variable is the number of 5-minute breaks, and the dependent variable is fatigue.

The cause is the independent variable. Its value is unaffected by the other study variables.

Effect is the dependent variable. Changes in the independent variable affect its value.

The independent variable is a variable in an experimental design that is manipulated or changed by the researcher to observe its effect on the dependent variable. It is also referred to as the "predictor variable" or the "explanatory variable". In the research scenario described, the independent variable is the number of 5-minute breaks (ten or zero) that are assigned to the participants.

The dependent variable is a variable in an experimental design that is being studied and measured to determine its relationship with the independent variable. It is also referred to as the "outcome variable" or the "response variable". In the research scenario described, the dependent variable is fatigue, as Ivan wants to study the impact of the number of 5-minute breaks on fatigue and will measure fatigue levels by using a questionnaire.

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The independent variable is the number of 5-minute breaks, and the dependent variable is fatigue.

The cause is the independent variable. Its value is unaffected by the other study variables.

Effect is the dependent variable. Changes in the independent variable affect its value.

The independent variable is a variable in an experimental design that is manipulated or changed by the researcher to observe its effect on the dependent variable. It is also referred to as the "predictor variable" or the "explanatory variable". In the research scenario described, the independent variable is the number of 5-minute breaks (ten or zero) that are assigned to the participants.

The dependent variable is a variable in an experimental design that is being studied and measured to determine its relationship with the independent variable. It is also referred to as the "outcome variable" or the "response variable". In the research scenario described, the dependent variable is fatigue, as Ivan wants to study the impact of the number of 5-minute breaks on fatigue and will measure fatigue levels by using a questionnaire.

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The sample size should be e) 2,500.

To calculate the sample size needed for the manager's confidence interval, we need to use the formula for the margin of error:

Margin of error = z * (standard deviation of the sample proportion) / sqrt(sample size)

Given the sample data, the sample proportion of time spent mowing is 200 / 400 = 0.5.

Plugging in the values, we get:

Margin of error = 1.96 * sqrt(0.5 * 0.5 / 400) = 0.02

Rearranging the formula and solving for the sample size, we get:

Sample size = (z / margin of error)^2 * (sample proportion * (1 - sample proportion))

= (1.96 / 0.02)^2 * (0.5 * 0.5)

= 2500

So, the sample size needed for a 95.44 percent confidence interval with a margin of error of 0.02 is 2,500. The answer is option (e).

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Answer:

Yes because the distance of (7,-7) from origin is equal to the radius of the circle.

Step-by-step explanation: