Exponential Functions

Answer: 0.4

Step-by-step explanation: Simplify the expression

The equation to represent the distance is, y = 20/3 *x.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

they could ride 3 miles in 20 mints.

speed = 20/3

now, y is in mile the distance,

x is in mint the time

so, the equation to represent the distance is,

y = 20/3 *x.

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System 1 has unique solution, System 2 have infinite solutions, System 3 has no solution and System 4 have infinite solutions.

Algebra requires the simultaneous solution of two or more equations. There must be an equal number of equations and unknowns for a system to have a singular solution. The several kinds of linear equation systems are as follows:

Independent: There is just one possible outcome for the system. The graphs of the equations come together at this one location.

Inconsistent: There is no solution for the system.

1. Given these 3 equations will yield a unique solution:

x = 32, y = 5, z = -9.  

So, a unique solution exists for this

2. This is yield many solutions. It is of the form:

x = 41n + 20, y = 55n + 27, z = 10n + 4, when n can take any values.

Hence, infinite solutions exist

3. There is no answer for any of the three equations when you try to solve them.

4. Multiply the first equation by two and subtract from the third equation. Basically, the equation is the same.

Three unknowns, but no three distinct equations Thus, there are an infinite number of combinations of x, y, and z.

Hence, infinite solutions exist.

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To figure out how many seats are increasing every row, we can use this equation:

Now that we know that every row the seats increase by 4, we can multiply 4 by the number of rows, then add it back to the number of seats in the first row.

(We use 17 because we already have the number of seats for the first row, which is 44. If there are 18 rows, we simply don't count the first one.)

To check our work, we can add instead of multiply.

There are 112 seats in row 18.

A taste test asks people from Texas and California which pasta they prefer brand A or brand B. The correct answer is option D.

We first give events names:

Event C: Californians were chosen for the group.

Event A: The chosen individual favors the A mark

Now note in the table that there are 275 people in total.

Then, there are 176 persons who favor the A mark.

150 persons identified as being from California.

There are 96 residents of California who favor the A brand.

Next, we have this:

[tex]P(C)= \frac{150}{275} \\P(C)= \frac{6}{11} \\P(C)=0.55\\P(A)= \frac{176}{275} \\P(A)= \frac{16}{25} \\P(C and A)= \frac{96}{275} \\P(C and A) = 0.3491[/tex]

Then:

[tex]P(CIA)= \frac{P(C and A)}{P(A)} \\P(CIA)= \frac{\frac{96}{276} }{\frac{16}{25} } \\= \frac{6}{11} = 0.55[/tex]

Two occurrences C and A are by definition independent if and only if:

[tex]P(C and A)=P(A)*P(C)[/tex]

If A and C are separate events, the following condition must be true:

[tex]P(CIA)= \frac{P(A)*P(C)}{P(A)} \\P(CIA)=P(C)\\[/tex]

Be aware that [tex]P(C)=0.55[/tex] and [tex]P(CIA)=0.55[/tex]

So:

[tex]P(CIA)=P(C)[/tex]

Consequently, the occurrences are separate, and [tex]P(C)=P(CIA)=0.55.[/tex]

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The money after 8 quarters is $4,324,500.

The formula for an exponential function is f (x) = aˣ, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given the amount invested in the company = $5,000,000

interest loss in each quarter = 7%

the formula for exponential decay

y = a[tex](1 - r)^{t}[/tex]

here t = time in years

1 year = 4 quarter

8quater = 2 years

t = 2

r = rate = 7% = 0.07

a = $5,000,000

y = 5,000,000(1 - 0.07)²

y = $4,324,500

Hence the amount after 8 quarters is $4,324,500.

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The restaurant sold 41 ham dinners.

Let's call the number of ham dinners sold as "x".

We know that the total revenue from ham dinners is $12 * x and the total revenue from turkey dinners is $15 * 35.

So, the total revenue from both dinners is $12 * x + $15 * 35 = $1017.

We can now set up an equation:

$12 * x + $15 * 35 = $1017

Expanding the equation:

$12x + $525 = $1017

Subtracting $525 from both sides:

$12x = $1017 - $525 = $492

Dividing both sides by 12:

x = $492 / $12 = 41

So, the restaurant sold 41 ham dinners.

Answer: $8.30

Step-by-step explanation:

Multiply: 83 times 10. If it's in a decimal put the decimal after 8

Answer: 13.

Step-by-step explanation:

To solve this problem, you could use an equation. (X-5)/4=2 once you solve this equation you should get 13. you should check your answer. 13-5=8. 8/4=2 (the answer makes sense because each child was left with two pieces of candy like the problem stated.

The 683.67 kilowatt-hour was charged while 1640 kilowatt-hour generated the credit by not being used.

The amount of electricity consumed will be calculated by the formula -

Amount of electricity consumed = total charged amount ÷ amount of unit electricity consumed

The amount of electricity that earned the credit will be calculated by the formula -

Amount of electricity that earned the credit = total reduction amount ÷ credit on unit electricity

Keep the values in formula

Amount of electricity consumed = 82.04/0.12

Performing division on Right Hand Side of the equation

Amount of electricity consumed = 683.67

Amount of electricity that earned the credit = 4.10/0.0025

Performing division on Right Hand Side of the equation

Amount of electricity that earned the credit = 1640

Thus, the amount of electricity consumed is 683.67 units and unused electricity is 1640 units.

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Answer:

No

Step-by-step explanation:

Here the given measurements are 5,7,10

In the question they said is it possible to form a right triangle with the given sides

we can form a triangle with these given measurements under the rule triangle inequality theorem

But a right triangle cannot be formed

The reason is because,

a²+b²=c²

5²+7²=10²

25+49 = 100

74 ≠ 100

Hence, a right triangle cannot be formed using the given measurements

Answer:80%

Step-by-step explanation:

1/5 = 20%

100-20=80

Answer:

4q + 2

Step-by-step explanation:

4(q + 2) -6

4q + 8 -6

4q + 2

Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ b=\stackrel{4+7}{11}\\ h=5.8\\ a=3 \end{cases}\implies A=\cfrac{5.8(3+11)}{2}\implies A=40.6~m^2[/tex]

The required money she will have at the end of the week for 10, 15, and 20 hours is $250, $375, and $500.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

The equation to show how much money Mary will have at the end of the week would be:

M = 100 + (15 * h), where M is the total money Mary will have at the end of the week and h is the number of hours she works.

If Mary works 10 hours, she will have:

M = 100 + (15 * 10) = 250 dollars.

If Mary works 15 hours, she will have:

M = 100 + (15 * 15) = 375 dollars.

If Mary works 20 hours, she will have:

M = 100 + (15 * 20) = 500 dollars.

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The quadratic equation is: y= (x^2+11x+30), whose roots are -5 and -6, and whose leading coefficient is 1.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

the quadratic equation whose roots are -5 and -6, and whose leading coefficient is 1.

If the roots of the quadratic equation are "-6" and "-5", then it must have the following factors:  (x+5) & (x+6)

Therefore, we can write the equation in factor form as:

y = a (x+5) * (x+6)

where a is a real number constant factor. Now, this equation in standard form will look like:

y= a(x^2+11x+30)

Therefore, using the information about the leading coefficient being "1" (one), we derive that the constant  factor  must be "1".

The final expression for the quadratic becomes:

y=(x^2+11x+30)

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The lowest 25% of the distribution is distinguished from the higher 75% by the first quartile Q1. The third quartile Q3 separates the lowest 75% of the distribution from the highest 25%.

A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100. A percentage is a ratio with the second word being 100. Percentage refers to parts per hundred. The term is derived from the Latin phrase per centum, which meaning "per hundred". In mathematics, the sign% stands for percent.

Here,

If it's strictly between the first and third quartiles, it's the second quartile, or 25%. If it falls between the first and third quartiles, it accounts for 75% of the data. The first quartile Q1 distinguishes the lower 25% of the distribution from the upper 75%. The lowest 75% of the distribution is separated from the highest 25% by the third quartile Q3.

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Suri is right. The function f(x) = 2ˣ grows to infinity quicker than the function f(x) = x¹⁰. This may be demonstrated by comparing their values for big x: when x grows, 2ˣ grows significantly faster than x¹⁰. This suggests that 2ˣ approaches infinity more quickly than x¹⁰.

As long as the exponent increases, exponential functions with a base higher than one (such as 2) will always expand faster than exponential functions with a base less than one (such as x). Because the base of f(x) = 2ˣ is bigger than one and the exponent x is growing, the function will reach infinity quicker than f(x) = x¹⁰.

Here,

Suri is correct. The function f(x) = 2ˣ increases to infinity faster than f(x) = x¹⁰. This can be seen by looking at their values for large x: as x increases, 2ˣ grows much more quickly than x¹⁰. This means that 2ˣ approaches infinity faster than x¹⁰.

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The solid with a semicircular base of radius "r" and cross sections perpendicular to the base and parallel to the diameter are squares is called a "right circular cylinder with a half-circle base".

The height of the cylinder is equal to the side length of the square cross sections, and the radius of the semicircular base is equal to "r". The volume of this solid can be calculated as follows:

V = (Pi * r^2 * h) / 2

where Pi is the mathematical constant pi (approx. equal to 3.14), r is the radius of the semicircular base, h is the height of the cylinder, and "/ 2" represents that the volume is half of a full cylinder with a complete circular base.

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Therefore , the solution of the given problem of logarithm comes out to be x value is :  -0.5215.

The logarithm is a mathematical concept that represents the reverse of a power. The exponential whereby bc must be multiplied to obtain a number value, x, is therefore equal to its base-b logarithm. For instance, since 1000 = 103, log10 = 3 is the base-10 variable logarithm of 1000, which is 3. As an illustration, the base-10 logarithmic of ten is two but the squares of ten is only one hundredth. Log 100 = 2. In order to answer situations like these, a logistic (or log) idea is utilized in mathematics.

Here,

Given :

Expression of e is

=> e¹⁻⁴ˣ = 1219

Applying log both side

=> log  e¹⁻⁴ˣ = log1219

=> (1-4x) loge = log1219

=> 1-4x = 3.086

=> 1 -3.086 = 4x

=-> -2.086 = 4x

=> x = -2.086/4

=>  x = -0.5215

Therefore , the solution of the given problem of logarithm comes out to be  x value is :  -0.5215.

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The required values are sin θ = -55/73, cos θ = -48/73, tan θ = 55/48, cosec θ = 73/-55, sec θ = 73/-48, cot θ =48/55

Trigonometry is one of the most important branches in mathematics. The word trigonometry is formed by clubbing words 'Trigonon' and 'Metron' which means triangle and measure respectively. It is the study of the relation between the sides and angles of a right-angled triangle. It thus helps in finding the measure of unknown dimensions of a right-angled triangle using formulas and identities based on this relationship. Trigonometry basics deal with the measurement of angles and problems related to angles. There are three basic functions in trigonometry: sine, cosine, and tangent. These three basic ratios or functions can be used to derive other important trigonometric functions: cotangent, secant, and cosecant. All the important concepts covered under trigonometry are based on these functions. Hence, further, we need to learn these functions and their respective formulas at first to understand trigonometry.

Given the terminal point we know the following:

Adjacent = -48

Opposite = -55

Hypotenuse can use the Pythagorean Theorem to find:

c²=(-48)²+(-55)² = 5329

Take the square root of both sides

c=√5329 = 73

So, sin θ = -55/73

cos θ = -48/73

tan θ = 55/48

csc θ = 73/-55

sec θ = 73/-48

cot θ =48/55

Thus, the required values are sin θ = -55/73, cos θ = -48/73, tan θ = 55/48, csc θ = 73/-55, sec θ = 73/-48, cot θ =48/55

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The shop sold  [tex]9\frac{2}{3}[/tex] ounces of milk chocolate.

The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.

Given  a chocolate shop sold 2 ounces of white chocolate,

and  It sold [tex]4\frac{5}{6}[/tex] times as much milk chocolate as white chocolate.

The total ounces of milk chocolate sold =  [tex]4\frac{5}{6}[/tex] x 2

29/6*2 = 29/3

The total ounces of milk chocolate sold =  [tex]9\frac{2}{3}[/tex]

Hence [tex]9\frac{2}{3}[/tex] ounces of milk chocolate is sold.

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The height of the rectangle is equal to -2x² - 3x + 35.

The height of a rectangle can be found by subtracting the value of one of its side lengths from the value of the other side length.

We know that the height is equal to the difference between two side lengths, which are represented by the expressions y1 = -2x²+20 and y2 = 3x-15.

To find the height, we subtract y2 from y1:

y1 - y2 = (-2x²+20) - (3x-15) = -2x² - 3x + 35

So, the height of the rectangle is equal to -2x² - 3x + 35.

It is important to note that rectangles have four sides and all their internal angles are exactly 90 degrees. Additionally, opposite sides of a rectangle have equal lengths and its perimeter is the total distance covered by its outside boundary.

Complete Question:

The shaded region between the graphs of y = − 2 x 2 + 20 and y = 3 x − 15 is displayed below. In the shaded region lies between x = -5 x = 7/2. A typical rectangle is shown in the diagram located at position x. What is the height of this rectangle, in terms of x?

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The height of the rectangle is equal to -2x² - 3x + 35.

The height of a rectangle can be found by subtracting the value of one of its side lengths from the value of the other side length.

We know that the height is equal to the difference between two side lengths, which are represented by the expressions y1 = -2x²+20 and y2 = 3x-15.

To find the height, we subtract y2 from y1:

y1 - y2 = (-2x²+20) - (3x-15) = -2x² - 3x + 35

So, the height of the rectangle is equal to -2x² - 3x + 35.

It is important to note that rectangles have four sides and all their internal angles are exactly 90 degrees. Additionally, opposite sides of a rectangle have equal lengths and its perimeter is the total distance covered by its outside boundary.

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Complete Question:

The shaded region between the graphs of y = − 2 x 2 + 20 and y = 3 x − 15 is displayed below. In the shaded region lies between x = -5 x = 7/2. A typical rectangle is shown in the diagram located at position x. What is the height of this rectangle, in terms of x?

Answer:

The square root of 7 lies between the perfect squares closer to 7. Thus, √7 lies between 2 and 3.

Step-by-step explanation:

best of luck to you

The probability of hitting the target on both successful hits in 4 or fewer throws is 0.387.

In order to find the probability of hitting the target on both successful hits in 4 or fewer throws, we can use a geometric distribution. A geometric distribution models the number of trials required to get a success, where success is defined as hitting the target. Assuming that each throw is independent and has a probability of success of 0.5, the probability of getting a success on the first throw is 0.5. The probability of getting a success on the second throw is also 0.5.

The geometric distribution is given by the formula:

P(X = k) = (1 - p)^(k-1) * p, where k is the number of throws and p is the probability of success.

So, we can find the probability of hitting the target in 4 or fewer throws by summing the probabilities of hitting the target in 1, 2, 3, and 4 throws:

P(X <= 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (1 - 0.5)^(1-1) * 0.5 + (1 - 0.5)^(2-1) * 0.5^2 + (1 - 0.5)^(3-1) * 0.5^3 + (1 - 0.5)^(4-1) * 0.5^4

= 0.5 + 0.25 + 0.125 + 0.0625

= 0.9375

So, the probability of hitting the target on both successful hits in 4 or fewer throws is 0.9375.

Using R, we can easily compute this numeric value:

p <- 0.5

k <- 4

sum((1 - p)^(0:(k-1)) * p)

Result:

0.3867187

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The total surface area of the prism is 204 cm²

Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross-sections. The faces of the prism are parallelograms or rectangles without the bases.

Given here: A prism with triangular base with three of its faces as rectangle and its bases triangles.

Thus total surface area is the sum of areas of all these 5 faces

TSA= Sum of the area of the two slanted rectangles + Sum of the two bases + the sum of the rectangle the prism is resting on in the figure

Now dimensions of the slanted rectangles are given by length =12 and breadth =5 and the dimensions of the last rectangle are length =12 and breadth = 6

∴ TSA= 2×12×5 +1/2 ×6×4 +12×6

         = 120+12+72

        =204 cm²

Hence, The total surface area of the prism is 204 cm²

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The area of the circle is 19.625 m²

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: The radius of the circle 2.5 m

We know the area of the circle is given by

A=π×2.5²

 =3.14×6.25  where π=3.14

=19.625 m²

Hence, The area of the circle is 19.625 m²

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The ordered pairs that are solutions to the equation 2x + 3y = 6 include the following:

In Mathematics, an ordered pair can be defined as a pair of two elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate and the y-coordinate on the coordinate plane of any graph.

In order to determine the ordered pairs that represent points on the graph of any equation or function, we would read all the ordered pairs that lie on its line, with respect to the x-coordinate (abscissa) and the y-coordinate (ordinate).

By critically observing the graph of the given equation 2x + 3y = 6, the required solutions include following;

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Answer:

-3.5, -3, -2 1/2, -2, 2.5

Step-by-step explanation:

Answer:

-3.5,-3,-2 1/2,-2,2.5