step by step answer. differentiate/simplify

The car's market value will therefore be $4,621.92 after five years.

Value is a good, service, or asset's estimated, monetary, or material worth. The term "value" can refer to a number of concepts, including shareholder value, company value, fair value, or market value.

After each year, the car's resale value will drop by 30%. Consequently, following a year, the value will be:

$27,500 × (1-0.3) = $19,250

The value after two years will be:

$19,250 × (1-0.3) = $13,475

The value after three years will be:

$13,475 × (1-0.3) = $9,432.50

The value after four years will be:

$9,432.50 × (1-0.3) = $6,602.75

The value will finally be after five years.

$6,602.75 × (1-0.3) = $4,621.92

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Answer:wth

uhhhhh 5 -7 -8 5

Step-by-step explanation:

The answer of the given question based on the mutually exclusive event is the probability of event R3 given event Q is 0.37.

Probability is  branch of mathematics that deals with  study of random events or phenomena. It is concerned with quantifying the likelihood of an event or a set of events occurring. Probability is often expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.

Using Bayes' theorem, we can find the probability of event R3 given event Q as follows:

P(R3|Q) = P(Q|R3)*P(R3)/P(Q)

so, by using the law of total probability:

P(Q) = P(Q | R1) * P(R1) + P(Q | R2) * P(R2) + P(Q | R3) * P(R3)

Substituting the given values, we get:

P(Q) = (0.5 * 0.05) + (0.6 * 0.3) + (0.2 * 0.65)

= 0.0425 + 0.18 + 0.13

= 0.3525

Now, substituting the given values for P(Q | R3) and P(R3), we get:

P(R3 | Q) = (0.2 * 0.65) / 0.3525

= 0.37

Therefore, the probability of event R3 given event Q is 0.37.

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The resultant quadrilateral is a kite, with opposing angles that are supplementary and two adjacent congruent acute angles (angles AEB and DEC) (angles BED and AEC).

In terms of geometry, a quad is a four-sided rectangle with four edges and four states. Its origins are in the Latin terms quadri and latus (meaning "side"). A rectangle is an a double shape with four sides, four edges, and four corners.

Jason can use the following procedures to draw the quadrilateral according to the requirements:

Mark A, B, C, and D as the four points on a section of a straight line.

Create two line segments, one from A to C and the other from B to D, with the intersection of the two segments at point E in the centre.

Due to the fact that angles BED and AEC are created by crossing two parallel lines with a transversal, they are opposing and supplementary (segments BD and AC).

The resultant quadrilateral is a kite, with opposing angles that are supplementary and two adjacent congruent acute angles (angles AEB and DEC) (angles BED and AEC).

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Therefore, it is not possible to divide the fields into identical rectangular flower beds of length 6m.

Area is a mathematical concept that refers to the measure of a surface enclosed by a boundary. It is typically expressed in square units such as square meters, square feet, or square centimeters. The area of a flat or 2-dimensional shape can be calculated by multiplying its length by its width, while the area of a 3-dimensional shape such as a cube or a sphere can be calculated using more complex formulas. Area is an important concept in geometry, physics, engineering, and many other fields.

Here,

Let the breadth of each flower bed be b.

For the first field with area 60m², the length of the field is 60/b, so the number of flower beds that can be made in this field is (60/b)/(6) = 10/b.

For the second field with area 84m², the length of the field is 84/b, so the number of flower beds that can be made in this field is (84/b)/(6) = 14/b

For the third field with area 108m², the length of the field is 108/b, so the number of flower beds that can be made in this field is (108/b)/(6) = 18/b.

Since all the fields are to be divided into identical rectangular flower beds, the number of flower beds in each field must be the same. So we have:

10/b = 14/b = 18/b

Multiplying both sides by b, we get:

10 = 14 = 18

This is not possible, so there is no common value of b that satisfies the given conditions.

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Answer:

the answer is d because 2.2 6+2 with a exponent of 3 = 14 and 14 is less than 20

Step-by-step explanation:

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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On simplifying the given expression, we get 16/81.

In mathematics, simplification is reducing the expression/fraction/problem in a simpler form.

Given is to simplify the expression as -

(4/9)²

We can simplify the expression as -

(4/9)²

(4 x 4)/(9 x 9)

16/81

Therefore, on simplifying the given expression, we get 16/81.

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{Complete question -

Simplify....

(4/9)²}

Answer:

Below

Step-by-step explanation:

Area of any triangle = 1/2  base * height

         base = 16  height = 9

1/2 * 16 * 9 = 72 units^2

Answer:

x^2+8x+8/2x+4

Step-by-step explanation:

Please help me with my question that I posted.  I really need help.

Answer:

Step-by-step explanation:

By solving the equation we know that the correct value of (D) x is 4.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The four mathematical operations of addition, subtraction, multiplication, and division are also used in simple equations, either singly or in combination.

A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the value of the variable x is 7.

So, solve for the given equation:

|-4+5x|=16

5x - 4 = 16

Now, by looking at the equation we can tell that the value of x needs to be 4 as follows:

5x - 4 = 16

5(4) - 4 = 16

20 - 4 = 16

16 = 16

Therefore, by solving the equation we know that the correct value of (D) x is 4.

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Complete question:

Solve : select all answers that applies

|-4+5x|=16

A. x= -11

B. x = -12/5

C. x= 4/5

D. x= 4

E. x = 3/4

Answer:

Below

Step-by-step explanation:

If you have an angle and add or subtract multiples of 360 ( a full circle around) ....you get the same angle ...

31.)   591 - 360 =   231     same angles

           231 -360 = - 129     same angle

            51 does not fit

32.)     reference is 36 so

              in Q II   this would be    180 -36 = 144 degrees

                  adding or subtracting 360° from 144 would be the same angle

                      144 - 360 =  - 216 °   ( same angle as 144)

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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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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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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Answer:

-5x^2-20x

Step-by-step explanation:

The area of the shaded region is the sum of the area of the semicircle and the area of the rectangle, giving us an answer of 32.13m².

A semicircle is considered as a two-dimensional shape that is half of a circle. It is formed by drawing a line from the center point of a circle to one of its edges. The line becomes the diameter of the semicircle, and the two sides of the semicircle form an arc.

The shaded area in the diagram is the region which is bounded by the semicircle and the rectangle.

To find the area of this shaded region, we first need to find the area of the semicircle and the area of the rectangle. The area of the semicircle is derived from the formula A = (πr²)/2, where r is the radius of the semicircle. The radius of the semicircle can be found by dividing the length of the rectangle by 2, as the semicircle is half of the rectangle, giving us a radius of 3m.

Therefore, the area of the semicircle is 14.13 m². The area of the rectangle is the length of the rectangle multiplied by its width, which is 6m×3m = 18m².

Finally, the area of the shaded region is the sum of the area of the semicircle and the area of the rectangle, giving us an answer of 32.13m².

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Question; A rectangle is placed around a semicircle as shown below. The length of the rectangle is 6m. Find the area of the shaded region.

The key features of the graph are

If the graph has a local maximum

From the given graph, we can see that:

The graph has a maximum (momentarily) at x = 1

This means that "yes", the function has a local maximum at x = 1

The local maximum

In (a), we have

x = 1

The y coordinates at this point is

y = 1

So, the local maximum is y = 1

The decreasing interval

From the graph, we can see that the y values decrease from -∝ till x = -1 and also decrease from x = 1 till ∝

The function type

Based on the appearance of the graph, the function is an odd function

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The divisions of the polynomials are listed below:

In this problem we can determine the division of a polynomial by a monomial through the use of distributive property, whose definition is shown below:

a · (b + c) = a · b + a · c

Now we proceed to show the solution to each case without prejudice to other algebra properties:

Case 1:

m³ · n² - m² · n + m · n

- m · n · (- m² · n) - m · n · m - m · n · (- 1)

- m · n · (- m² · n + m - 1)

Result: - m² · n + m - 1

Case 2:

3 · x³ · y³ + 9 · x² · y² - 27 · x · y

- 3 · x · y · (- x² · y² - 3 · x · y + 9)

Result: - x² · y² - 3 · x · y + 9

Case 3:

18 · a⁵ · b⁴ · c² - 54 · a³ · b⁶ · c⁴ - 108 · a² · b⁸ · c

18 · a² · b³ · c · (a³ · b · c - 3 · a · b³ · c³ - 6 · b⁵)

Result: a³ · b · c - 3 · a · b³ · c³ - 6 · b⁵

Case 4:

5 · p² · q · r - 7 · q² · r + 4 · p · q · r²

p · q · r · (5 · p - 7 · q / r + 4 · r)

Result: 5 · p - 7 · q / r + 4 · r

Case 5:

81 · m⁵ · n³ + 18 · m⁴ · n² - 72 · m³ · n

9 · m² · n · (9 · m³ · n² + 2 · m² · n - 8 · m)

Result: 9 · m³ · n² + 2 · m² · n - 8 · m

Case 6:

6 · x³ · y² + x² · y² + 35 · x · y

- x² · y² · [- 6 · x - 1 + 1 / (x · y)]

Result: - 6 · x - 1 + 1 / (x · y)

Case 7:

x² · y · z + x · y² · z - 3 · x · y · z

3 · x · y · z² · [(1 / 3) · (x / z) + (1 / 3) · (y / z) - 1 / z]

Result: (1 / 3) · (x / z) + (1 / 3) · (y / z) - 1 / z

Case 8:

12 · p⁵ · q² + 3 · p³ · q + 9 · p⁴ · q³

3 · p³ · q · (4 · p² · q + 1 + 3 · p · q²)

Result: 4 · p² · q + 1 + 3 · p · q²

Case 9:

5 · a² · b² · c² - 10 · a³ · b⁵ · c² + 75 · a⁴ · b³ · c²

- 5 · a² · b · c² · (- b + 2 · a · b⁴ - 15 · a² · b²)

Result: - b + 2 · a · b⁴ - 15 · a² · b²

Case 10:

y³ · z - y² · z - y · z² + y · z³

- y · z · (- y² + y + z - z²)

Result: - y² + y + z - z²

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The percent error for the 121-foot measurement is approximately 0.83%.

In the event of contrasting a measured or trial value with a known or accepted value, percent error is employed, whereas percent difference is used to compare two values. The percentage difference is determined by dividing the absolute variance of two numbers by their average, then multiplying the result by 100%.

For the 121-foot measurement:

Absolute error = |121 - 120| = 1

Percent error = (absolute error / actual value) x 100%

Percent error = (1 / 120) x 100%

Percent error ≈ 0.83%

Therefore, the percent error for the 121-foot measurement is approximately 0.83%.

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Where the above probability condition exists,

a. The probability value of 0.049 indicates that the sample results could not have easily occurred by chance. Therefore, we can conclude that there is sufficient evidence to suggest that 200 mg of caffeine has an enhancing effect on long-term memory.

b. The probability value of 0.75 indicates that the difference in performance between the two groups could easily be due to chance. Therefore, we cannot conclude that there is a significant difference in performance between the 200 mg and 300 mg groups based on this probability value. However, further research may be needed to investigate this question more thoroughly.

The study found that participants who were given 200mg of caffeine performed better on a memory test 24 hours later compared to the placebo group. With a probability of 0.049, it can be concluded that the difference between the two groups was not due to chance.

Therefore, there is sufficient evidence to suggest that caffeine has an enhancing effect on long-term memory. On the other hand, the group given 300mg of caffeine did not show a significant difference compared to the 200mg group, with a probability of 0.75 that the difference was due to chance.

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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

Substituting the values shows that the point that lies on the exponential function are

We can use substitution to determine which ordered pairs lie on the graph of the exponential function f(x) = 3(4)^2x.

For the first ordered pair (0, 3),

f(0) = 3(4)^2(0) = 3(1) = 3

(0, 3) lies on the graph of the exponential function.

For the second ordered pair (1, 48)

f(1) = 3(4)^2(1) = 3(16) = 48

(1, 48) lies on the graph of the exponential function.

For the third ordered pair (1/2, 12),

f(1/2) = 3(4)^2(1/2) = 3(4) = 12

(1/2, 12) lies on the graph of the exponential function.

For the fourth ordered pair (.25, 8), :

f(0.25) = 3(4)^2(0.25) = 6

say that (0.25, 8) does not lie on the graph of the exponential function.

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Juli earned $13.25 per candle sold.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

For a charity fundraiser, Juli sold 16 candles.

Juli earned a total of $212 ($12 in donations + $100 to Charity A + $100 to Charity B).

To find out how much she earned per candle, we need to divide the total amount earned by the number of candles sold:

$212 ÷ 16 candles = $13.25 per candle

Therefore, per candle, the earning amount is $13.25.

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Answer:

Step-by-step explanation:

the volume of a cylinder is found with the formula V=[tex]\pi r^{2} h[/tex] where r is the radius and h is the height of the cylinder

plugging the numbers given into the formula results in 32791.5 [tex]cm^{3}[/tex]

Answer:

The unit rate in the equation y = 2x is 2.

This means that the cost per day for Austin's high-speed internet is $2.

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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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:

The given expression simplifies to zero.

Step-by-step explanation:

Tangent Trigonometric Identity:

[tex]\boxed{\tan \theta=\dfrac{\sin \theta}{\cos \theta}}[/tex]

Given expression:

[tex]\tan^2 \theta \cos^2 \theta - \sin^2 \theta[/tex]

To simplify the given expression, rewrite tan²θ using the tan trigonometric identity:

[tex]\implies \dfrac{\sin^2 \theta}{\cos^2 \theta} \cdot \cos^2 \theta - \sin^2 \theta[/tex]

[tex]\implies \dfrac{\sin^2 \theta \cos^2 \theta}{\cos^2 \theta} - \sin^2 \theta[/tex]

Cancel the common factor cos²θ:

[tex]\implies \sin^2 \theta - \sin^2 \theta[/tex]

Add similar elements:

[tex]\implies \sin^2 \theta - \sin^2 \theta=0[/tex]

Therefore, the given expression simplifies to zero.

The value of length of AG is,

⇒ AG = 8

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔABC,

G is centroid and GE = 4

Hence, We get;

⇒ AG : GE = 2 : 1

Hence, The length of AG is,

AG = 2 × 4

AG = 8

Thus, The value of length of AG is,

⇒ AG = 8

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