Write in index form using negative powers 7/2 x × 2 x

The expοnential decay with a cοnstant percentage rate cοuld be mοdeled by this functiοn.

Expοnential decay is a mathematical prοcess that describes the decrease οf a quantity οver time, where the rate οf decrease is prοpοrtiοnal tο the current value οf the quantity. Expοnential decay οccurs when a quantity decreases by a cοnstant percentage rate οver time.

The fοrmula fοr expοnential decay is given by:

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

where:

y is the final amοunt οr value

a is the initial amοunt οr value

r is the decay rate, which is the fractiοn by which the quantity decreases per unit time

t is the time in sοme unit οf measurement

The functiοn [tex]y = a(1 - r)^t[/tex] represents an expοnential decay curve, which is a curve that starts high and apprοaches zerο but never reaches it. The rate οf decay is highest at the beginning and decreases as the quantity gets smaller.

Expοnential decay is cοmmοnly seen in many natural and scientific phenοmena, including radiοactive decay, the decay οf a pοpulatiοn οf bacteria, and the depreciatiοn οf the value οf an asset οver time. Expοnential decay is alsο used in finance, engineering, and οther fields tο mοdel variοus prοcesses that invοlve the lοss οf value οr the dissipatiοn οf energy οver time.

The given functiοn y = 400(1 – 0.17)x represents expοnential decay where y is the final amοunt, x is the time in sοme unit, and 0.17 is the decay rate per unit time.

In particular, this functiοn mοdels a situatiοn where a quantity is decreasing οver time at a cοnstant percentage rate οf 17% per unit time. The initial quantity, οr y-intercept, is 400.

Sοme examples οf situatiοns that cοuld be mοdeled by this functiοn are:

The value οf a car that is depreciating at a cοnstant rate οf 17% per year.

The amοunt οf a radiοactive substance that is decaying at a cοnstant rate οf 17% per hοur.

The number οf bacteria in a pοpulatiοn that is dying οff at a cοnstant rate οf 17% per day due tο a lack οf resοurces.

In general, any situatiοn that invοlves expοnential decay with a cοnstant percentage rate cοuld be mοdeled by this functiοn.

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Answer:

16.48%

Step-by-step explanation:

6 democrates

3 republicans

5 independents

Total number: 6+3+5=14

Probability of selecting an independent:

#of independents/ Total number

5/14= 0.3571

Probability of selecting a democrat:

# of democrats/ Total number-1

6/13= 0.4615

Probability of independent then democrat:

0.3571x0.4615=0.1648

0.1648x100= 16.48%

Answer: 15 3/4 cups

In order to figure out how much peanut butter they have used we must multiply our amount by the number used.

4 1/2 times 3 1/2 can also be written as 4.5 and 3.5, respectively.

So our equation would be 4.5 x 3.5

4.5 x 3.5 is 15.75  

The number .75 can be written as the fraction 3/4, since 75 is 3/4th of 100.

This means the cafeteria used 15 3/4 cups of peanut butter.

I hope this helped & Good Luck <3 !!!

To calculate the amount of peanut butter used, multiply the number of jars (3 1/2) by the quantity in each jar (4 1/2 cups). This equals 15 3/4 cups of peanut butter.

To find out how many cups of peanut butter the cafeteria has used, we need to multiply the number of jars used by the number of cups in each jar. We know that there are 4 1/2 cups in one jar of peanut butter and the cafeteria has used 3 1/2 jars. So, we multiply 4 1/2 by 3 1/2 to get the total number of cups used.

This can be done by converting the mixed fractions to improper fractions: 4 1/2 becomes 9/2 and 3 1/2 becomes 7/2. Multiplying these gives 63/4, which converts back to the mixed number 15 3/4.

So, the cafeteria has used 15 3/4 cups of peanut butter.

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The coordinates of the vertices of the feasible region are plotted.

A group of two or maybe more inequalities from one or more variables is referred to as a system of inequalities.

Feasible region:

The given equation:

y ≥ -x -2

y ≥ 3x +2

y ≤ x +4

f(x, y) = -3x +5y

Thus, the coordinates of the vertices of the feasible region are plotted.

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Step-by-step explanation:

V = P(1 - r)^t

where V is the value of the car after t years, P is the initial value of the car, r is the annual depreciation rate as a decimal, and t is the number of years.

Plugging in the values given in the problem, we get:

V = 42000(1 - 0.15)^7

V = 42000(0.85)^7

V = 42000(0.327)

V = $13734.00

Therefore, the car will be worth $13,734.00 after 7 years. Rounded to the nearest dollar, the value is $13,734.

Answer:

A) $12,800.00. B) $13,629.44. The value of a car purchased for $20,000 decreases at a rate of 12% per year. What will be the value of the car after 3 years? C) ...

The expression for the given Venn Diagrams are:

A Venn diagram employs circles or other shapes that overlap to show the logical connections between two or more groups of objects.

They frequently serve to visually group objects while highlighting how they differ and how they are similar.

The union of two sets A and B is a new set that contains all the elements that are in A or in B or in both. It is denoted by A ∪ B.

Example: Let A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}.

The intersection of two sets A and B is a new set that contains all the elements that are in both A and B. It is denoted by A ∩ B.

Example: Let A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}.

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The equation where F(x) = G has no solution (x). By graphing the functions, the answer has been discovered.

The creation of a relevant function's graph is the first step in the graphing process. If a curve reflects the function at a given point, the curve at that point satisfies the function equation.

We are given two functions as f(x) = (3x + 2) and g(x) = (3x - 5)

The graph of the given functions has been plotted and attached below.

In the graph, the red line represents the f(x) function and the blue line represents the g(x) function.

From the graph, it is clear that the two lines are parallel, therefore they will never meet.

Hence, there is no solution where F(x) = G(x).

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Question: Graph the following functions and determine where F(x) = G(x). Select all that apply.

f(x)=(3x+2) and g(x)=3x-5

The height of the trapezoid is h = 4, and the answer is B.

A trapezoid, also known as a trapezium, is a four-sided polygon with two parallel sides, also called the bases. The non-parallel sides are called legs, and they can have different lengths. The parallel sides are perpendicular to the legs.

There are two types of trapezoids:

Isosceles trapezoid: This type of trapezoid has two parallel sides of equal length and two legs of equal length.

Scalene trapezoid: This type of trapezoid has two parallel sides of different lengths and two legs of different lengths.

We can use the formula A = 1/2 * h * (b1 + b2) to solve for h. Substituting the given values, we get:

28 = 1/2 * h * (6 + 8)

28 = 1/2 * h * 14

28 = 7h

h = 4

Therefore, the height of the trapezoid is h = 4, and the answer is B.

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The answers to each part context to similar triangles is given above.

A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.

Given are two similar triangles as shown in the image.

{ 1 } -

We can write the scale factor as -

{k} = ZX/AC

{k} = 39/13

{k} = 3

{ 2 } -

m∠X = m∠A = 67°

m∠X = 67°

{ 3 } -

ZW/CD = k

CD = ZW/k

CD = 36/3

CD = 12 units

{ 4 } -

Area of triangle ABC = 1/2 x 5 x 12 = 30 square units.

A{ΔABC} = 30 square units

{5} -

Ratio of area of triangle ABC to triangle XYZ = (30)/(15 x 36) = 1/18

A{ΔABC}/A{ΔXYZ} = 1/18

Therefore, the answers to each part context to similar triangles is given above.

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If to display charts and other educational material, your teacher has requested that two rows of strips be placed around the entire room. the total length of strips is: 4L + 4W.

To find the total length of strips required, we need to know the dimensions of the room. Let's assume that the room has a length of L and a width of W.

If we place two rows of strips around the entire room, one at the top and one at the bottom, the length of each strip will be equal to the perimeter of the room.

The perimeter of the room can be calculated as:

P = 2L + 2W

So, the length of strips required for one row around the room will be:

L1 = P = 2L + 2W

Since we need two rows of strips, the total length of strips required will be:

L2 = 2L1 = 2(2L + 2W) = 4L + 4W

Therefore, the total length is 4 times the length of the room plus 4 times the width of the room.

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The exact values are;

Sin 2x = 7/8

Cos 2x = 7/4

Tan 2x = 1

Trigonometric ratios are mathematical functions that relate the angles and sides of a right-angled triangle. The three primary trigonometric ratios are:

Sine (sin) - the ratio of the length of the opposite side to the length of the hypotenuse.

Cosine (cos) - the ratio of the length of the adjacent side to the length of the hypotenuse.

Tangent (tan) - the ratio of the length of the opposite side to the length of the adjacent side.

Given that sinx = 7/16

opposite = 7

Hypotenuse = 16

Adjacent is now;

b^2 = 16^2 - 7^2

b = 14

Thus;

Sin 2x = 14/16 = 7/8

Cos 2x = 2(14/16) = 28/16 = 7/4

Tan 2x = 2(7/14) = 14/14 = 1

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Answer:

To solve this problem, we need to set up an inequality that represents the situation where Joseph will have more than 125 books.

Let w be the number of weeks.

At the end of w weeks, Joseph will have 50 + 5w books (since he adds five books to his library every week).

To find the inequality that represents having more than 125 books, we can set up the following equation:

50 + 5w > 125

Simplifying this inequality:

5w > 75

w > 15

Therefore, the inequality that represents the situation where Joseph will have more than 125 books is:

5w + 50 > 125

The answer is B.

.

just find the area of a circle which is

pi times 3.5 squared. 3.5 is the radius because 7 is the diameter

The oven will heat up by 18 degrees in 1 minute at this rate.

What is expressions ?

Expressions can be simplified, evaluated, or manipulated using mathematical rules and operations. They are used in a variety of mathematical contexts, such as algebra, geometry, calculus, and more.

We can start by finding the rate of temperature increase per minute. Since the temperature rose 3 degrees in 1/6 of a minute, we can multiply both sides by 6 to find the rate per minute:

3 degrees ÷ (1/6 minute) = 18 degrees per minute

So the oven heats up at a rate of 18 degrees per minute. To find how much the oven will heat up in 1 minute, we simply multiply the rate by the time:

18 degrees per minute × 1 minute = 18 degrees

Therefore, the oven will heat up by 18 degrees in 1 minute at this rate.

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The correct answer is c). When the value of x is -3, -x – 6 is equal to -9. Since -9 is greater than -3.5, the inequality -x - 6 > -3.5 is true.

Straight line inequalities are mathematical statements that use two or more variables and an inequality sign, such as “<” or “>”. These statements are used to describe the relationship between the variables and can be used to solve problems. An example of a straight line inequality is 2x + 3 > 7. This inequality states that for any value of x, the expression 2x + 3 must be greater than 7.

The other three options are not true when the value of x is -3. Option a) is false because -x – 6 is not less than -3.5. Option b) is false because -x – 6 is not greater than 3.5. Option d) is false because x – 6 is not greater than -3.5.

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Question: Which inequality is true when the value of x is -3?

a) -x – 6 < -3.5

b) -x – 6 > 3.5

c) -x - 6 > -3.5

d) x - 6 > -3.5

The net price using the net price factor, complement method is $2958.75.

The complementary of the product of the market discount rates is represented by the net price factor, which is a decimal number. It is used to determine an item's final price after various trade discounts have been applied. By multiplying the complementary of the discount rates collectively and deducting the result from 1, we may determine the net price factor.

We use the complement method to calculate the net price using the net price factor.

For the given trade discount rates we have:

The complement of 35% is 65%

The complement of 30% is 70%

The complement of 5% is 95%

Multiply the values:

65% × 70% × 95% = 0.65 × 0.70 × 0.95 = 0.40825

The net price is obtained by:

1 - 0.40825 = 0.59175

Multiply the net price by the list price:

0.59175 × 5000 = $2958.75

Hence, the net price using the net price factor, complement method is $2958.75.

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In this case, the boxplot is option A, which shows the box extending from 130 to 165.5 mBq, with a line segment drawn through the box at 160.75 mBq. The whiskers extend from 114 to 201 mBq, with no outliers.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The problem asks us to construct a boxplot and identify the 5-number summary of a set of data. The data represents the amounts of strontium-90 (in millibecquerels, or mBq) in a sample of baby teeth from residents born after 1979. The data is as follows:

124, 127, 131, 135, 138, 142, 142, 143, 147, 150, 154, 156, 157, 160, 163, 168, 170, 171, 174, 181

To construct the boxplot, we need to first find the 5-number summary, which consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value. We can find these values by putting the data in ascending order and then using the following formulas:

Q1 = median of the lower half of the data

Q2 = median of the entire data set

Q3 = median of the upper half of the data

Using these formulas, we find the 5-number summary to be:

Minimum value: 124 mBq

Q1: 138 mBq

Median: 150 mBq

Q3: 168 mBq

Maximum value: 181 mBq

We can now use this information to construct the boxplot. The horizontal axis represents the values in the data set, and the vertical axis represents the frequency or density of those values. The boxplot consists of a box that extends from Q1 to Q3, with a line segment drawn through the box at the median (Q2). Whiskers extend from the top and bottom of the box to the minimum and maximum values, respectively, unless there are outliers. Outliers are plotted as individual points beyond the whiskers.

Therefore, In this case, the boxplot is option A, which shows the box extending from 130 to 165.5 mBq, with a line segment drawn through the box at 160.75 mBq. The whiskers extend from 114 to 201 mBq, with no outliers.

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Each of the 40 students would occupy 8.75 m²

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

The class must seat 40 students along with the teachers Table and shelves which will occupy 350m². The space each student would occupy is:

Space for each student = Total space / Total number of students = 350 m² / 40 student = 8.75 m²

Each student would occupy 8.75 m²

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Yes, the set of coordinate points (5, 31), (6, 28), (7, 25), (8, 22), and (9, 19) forms a function.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To determine whether the set of coordinate points (5, 31), (6, 28), (7, 25), (8, 22), and (9, 19) forms a function, we need to check whether each x-value is paired with a unique y-value.

We can see that for each x-value in the set, there is only one corresponding y-value.

Therefore, the set of coordinate points does form a function.

We can also verify this by using the vertical line test.

If we draw a vertical line anywhere on the graph of this set of points, the line will intersect the graph at most once, indicating that each x-value is paired with a unique y-value.

Therefore, the coordinate points does form a function.

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Therefore, Lisa will need 52 square inches of purple paint to paint all sides of her letter L.

Surface area is the measure of the total area that the surface of a three-dimensional object occupies. It is the sum of the areas of all the faces, including the base(s) and any lateral faces, that make up the object. Surface area is usually expressed in square units, such as square centimeters, square meters, square inches, or square feet, depending on the unit of measurement used. The surface area of an object is an important factor in many physical and mathematical calculations, such as calculating the amount of material needed to cover an object, the rate of heat transfer, and the amount of friction between surfaces.

by the question.

To find the total surface area that Lisa will need to paint purple, we need to first calculate the surface area of each piece of wood and then add them together.

The longer piece of wood has a surface area of:

2 x 7 = 14 square inches on one side

2 x 2 = 4 square inches on the other side

2 x 5 = 10 square inches on the third side

So, the total surface area of the longer piece is 14 + 4 + 10 = 28 square inches.

The shorter piece of wood has a surface area of:

5 x 2 = 10 square inches on one side

2 x 2 = 4 square inches on the second side

5 x 2 = 10 square inches on the third side

So, the total surface area of the shorter piece is 10 + 4 + 10 = 24 square inches.

To get the total surface area of the letter L, we add the surface areas of the two pieces of wood together:

28 + 24 = 52 square inches.

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The surface area is obtained by adding 1,105.28 + 200.96 + 200.96.

What does surface area mean?

The area is the region that any two-dimensional object occupies in a plane. The term "surface area" refers to the size of any body's external surface.

Surface area and volume are calculated for any three-dimensional geometrical shape.

The surface area of any given object is the area or region occupied by the surface of the object.

Whereas volume is the amount of space available in an object.

The surface area will be calculated as:-

SA = 1,105.28 + 200.96 + 200.96.

SA = 1507.2

Thus, the surface area is calculated as 1,105.28 + 200.96 + 200.96.

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Answer:

the answer is multiply (200.96)(22)

Step-by-step explanation:

you have to multiply.

With speed=10 m/s, the rope will hit ground after 3.36 seconds.

Speed is a measure of how fast an object is moving, usually measured in units of distance per unit time, such as meters per second (m/s) or kilometers per hour (km/h). It is a scalar quantity, meaning it only has magnitude and no direction.

Mathematically, speed is defined as the distance an object travels per unit time. The formula for calculating speed is:

Speed = Distance / Time

where Distance is the distance traveled by the object, and Time is the time taken to cover that distance.

here, we have,

Now,

To find when the rope will hit the ground, we can use the kinematic equation:

y = vi * t + (1/2) * a * t²

where:

y = 50 m (the height of the cliff)

vi = 10 m/s (the initial velocity of the rope)

a = 9.8 m/s² (the acceleration due to gravity, acting downward)

t = time it takes for the rope to hit the ground

We can solve for t by setting y=50 and solving for t:

50 = 10t + (1/2) * 9.8 * t²

50 = t(10 + 4.9t)

t = 50/14.9=3.36 s

Therefore, the rope will hit the ground after 3.36 seconds.

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The surface area of the shape is 110 square units.

The area of a two-dimensional figure is the area enclosed by its perimeter. The area of a closed figure is the number of unit squares that cover its surface. Area is measured in square units such as cm2 and m2. The area of a shape is measured in two dimensions.

The rectangle's surface area is:

Area = 10 × 9 = 90 unit square

The area of the triangle is:

Area = 0.5 × 10 × 4 = 20 unit square

The figure's area is as follows:

Total = 90 + 20

Total = 110 unit square

Hence, the shape's area is 110 unit square.

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The amount of ice cream in a properly filled cone is approximately 167.46 cubic cm.

The volumes of a cone and a cylinder with the same base and height are proportionate to one another. A cone's volume is specifically one-third that of a cylinder with the same base and height.

The volume of a cone, which is given by:

V = (1/3)πr²h

Substituting the values of radius and height we have:

V = 1/3π(4)²(10)

V = 167.46 cubic cm.

Hence, the amount of ice cream in a properly filled cone is approximately 167.46 cubic cm.

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Answer:

24% of 10,000 is 2,400.

Step-by-step explanation:

To find out what number is 24% of 10,000, we can multiply 10,000 by 24% (or 0.24):

Number = 10,000 x 0.24

Number = 2,400

Therefore, 24% of 10,000 is 2,400.

Answer:

 2,400  

Step-by-step explanation

:24% of 10,000 = 24% × 10,000 = 24/100 × 10,000 = (24 ÷ 100) × 10,000 = 24 × 10,000 ÷ 100 = 240,000 ÷ 100 =

Answer:

Step-by-step explanation:

Let the sweater price be x

Let the shirt price be y

x + 4y=38

4x+5y=86
4x+16y= 152

11y=66

y=6

Substitute into x+4y=38,

x+4x6=38

x=14

As a result, for purchases of $9500, the salesperson gets a royalty of $285.

Commission, also known as a sales bonus, is paid to employees in accordance with the amount of sales they make. Statement generation is offered without charge by SumUp Bills. Frequently, a fee is calculated as a percentage of the sale's value.

To find the commission that the salesperson receives for $9500 in sales, we can use the formula:

commission = rate x sales

where rate is the commission rate as a decimal, and sales is the amount of sales.

In this case, the rate is 3% or 0.03, and the sales is $9500.When these numbers are added to the algorithm, we obtain:

commission = 0.03 x $9500

Simplifying this expression, we get:

commission = $285

Therefore, the salesperson receives a commission of $285 for $9500 in sales.

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The area of the triangle is given as follows:

9.3 units².

The area of a triangle is obtained multiplying the triangle's base by the triangle's height and dividing by 2, that is:

A = bh/2.

Considering segment (-5,3) to (-5,6) as the base, the base length is given as follows:

b = 6 - 3 = 3.

The midpoint of the base segment is given as follows:

(-5,4.5).

The height is given by the distance between the third vertex and the midpoint, hence:

h = sqrt[(-5 - 1)² + (4.5-3)²]

h = 6.2.

Hence the area is of:

A = 0.5 x 6.2 x 3

A = 9.3 units².

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The value of m if the ratio of their heights is equal to 1:m is 4/3.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

Area of A=144cm²

Area of B=256cm²

Ratio of heights= 1:m

Now,

The ratio of the areas of two similar solids is equal to the square of the ratio of their corresponding heights. So, we have:

(area of A) / (area of B) = (height of A)^2 / (height of B)^2

Substituting the given values, we get:

144 / 256 = 1^2 / m^2

9 / 16 = 1 / m^2

Multiplying both sides by m^2, we get:

9m^2 / 16 = 1

Multiplying both sides by 16/9, we get:

m^2 = 16/9

Taking the square root of both sides (and noting that m must be positive since it is a length), we get:

m = 4/3

Therefore, by the given ratio answer will be 4/3.

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Answer:

7m + 20 ≥ 150

Closest option is 7m + 20 > 150 which is the second choice

Step-by-step explanation:

The words "at least" indicate a ≥ inequality.

There is a fixed earning of $20 for entering the race. So this amount will be earned on regardless of how much Carol runs

For each mile she runs she earns $7. For running m miles, she earns 7m dollars

Total amount earned for running m miles = 7m + 20
This must be at least $150
So the correct inequality is
7m + 20 ≥ 150

I don't see this exact inequality in any of the answer choices but that is the correct answer.