nj bought a car for $20,000. two years later, the car has depreciated to a value that is 81% of what he paid. which equation(s) represent the exponential relationship?

Answer:

C.

Step-by-step explanation:

Hi there!

To answer this, we must set it up as

\(3x(2x^4-12x^2+7)\)

Now we just use the distributive property to solve.

this becomes \(6x^5-36x^3+21x\)

I hope this helps!

Answer:

1: No, this is not direct variation

2: Yes, this is direct variation with k= 2.34

Step-by-step explanation:

I’m Just Built Different

The ratio of the horizontal change to the vertical change of a line would not be used to describe a slope. Thus the correct option is option C.

The slope of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run) of a line.

Slope=Vertical Change/Horizontal Change

This is also represented as the "ratio of rise to run of a line".

Slope=Rise/Run

In the given question, however, option C states that the "ratio of the horizontal change to the vertical change of a line".

Horizontal Change/ Vertical Change= 1/slope

This is an incorrect statement since the ratio of the horizontal change to the vertical change of a line is the reciprocal of the correct ratio.

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Let's start solving the expression using the product to sum formulae.

Here's the given expression,

\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]

Using the product-to-sum formula,

\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]

Applying the above formula in the first term,

\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]

Using the product-to-sum formula,

\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]

Applying the above formula in the second term,

\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]

Substituting these expressions back into the original expression,

we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]

Therefore, the given expression can be written in terms of a single trigonometric function as:

\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}

Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.

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In other words, there are infinite solutions to this equation.

An equation is a mathematical statement that shows the equality of two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equal sign (=). The expressions on either side of the equal sign can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

We can simplify the left-hand side of the equation by combining like terms:

-5x - 3x + 2 = -8x + 2

-8x + 2 = -8x + 2

We end up with an identity where both sides of the equation are equal, which means that the equation is true for all values of x.

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Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

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Answer:

25 pieces

Step-by-step explanation:

Given

\(Box_1 = 3\frac{1}{3}\)

\(Box_2 = \frac{5}{6}\)

\(Pieces = \frac{1}{6}\) yard

Required

Determine the number of pieces

First, we need to determine the total yards of paper

\(Total = Box_1 + Box_2\)

\(Total = 3\frac{1}{3} + \frac{5}{6}\)

\(Total = \frac{10}{3} + \frac{5}{6}\)

\(Total = \frac{20 + 5}{6}\)

\(Total = \frac{25}{6}\)

Divide by the size of the pieces to get the number of pieces

\(Number = Total/Pieces\)

\(Number = \frac{25}{6} / \frac{1}{6}\)

\(Number = \frac{25}{6} * \frac{6}{1}\)

\(Number = \frac{25}{1} * \frac{1}{1}\)

\(Number = 25\)

Answer:

The choose a. – 2

Step-by-step explanation:

\(f( - 8) = \frac{ - 8}{4} = - 2\)

Using the given radius we know that the length of the line BR is 6.5 units.

A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary usage, it also refers to the length of such line segments.

The word "radius" is derived from Latin and means "ray" as well as "the spoke of a chariot wheel."

The radius of a circle is the separation between its center and circumference.

Always, the diameter is twice the radius. As a result, the formula is created by multiplying the diameter by two.

So, according to the given image:

SP is the perpendicular bisector of line BA.

And line BA is 13 units.

SP intersects BA st R.

Then, the length of BR will be:

= 13/2

= 6.5

Therefore, using the given radius we know that the length of the line BR is 6.5 units.

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The triangles are similar by: AA Similarity Postulate

If two triangles are seen to be similar, then we can say that the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. This proves to us that the ratio of the area of the two similar triangles is proportional to the squares of the corresponding sides of both the triangles.

The similarity theorems of triangle are:

AA Similarity

SAS Similarity

SSS Similarity

We can conclude that the triangles are similar because they have the same angle measurements. They both share the same angle that the stake makes with the ground, and the ground and the pole, and ground and Jamal make right angles. Due to this, they are similar by AA Similarity.

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Step-by-step explanation:

7(4n−6)=6+4(4+3n)

Step 1: Simplify both sides of the equation.

7(4n−6)=6+4(4+3n)

(7)(4n)+(7)(−6)=6+(4)(4)+(4)(3n) (Distribute)

28n+−42=6+16+12n

28n−42=(12n)+(6+16) (Combine Like Terms)

28n−42=12n+22

Step 2: Subtract 12n from both sides.

28n−42−12n=12n+22−12n

16n−42=22

Step 3: Add 42 to both sides.

16n−42+42=22+42

16n=64

Step 4: Divide both sides by 16.

\(\frac{16n}{16} = \frac{64}{16}\)

n=4

the standard error of the estimate provides a measure of the variability around the regression line, helping us understand how well the line predicts the dependent variable based on the independent variable(s).The correct answer is C.

The standard error of the estimate is the measure of variability around the line of regression. It quantifies how accurately the regression line predicts the dependent variable based on the independent variable(s).

To understand this concept, let's consider an example. Suppose we have a dataset of students' test scores and the amount of time they spent studying. We want to use linear regression to predict test scores based on study time. The regression line represents the best-fit line that minimizes the overall distance between the predicted and actual test scores.

The standard error of the estimate tells us how much the actual test scores vary from the predicted scores. A lower standard error indicates that the regression line is a better fit to the data, meaning the predictions are more accurate. Conversely, a higher standard error indicates more variability and less accuracy in the predictions.In summary, the standard error of the estimate provides a measure of the variability around the regression line, helping us understand how well the line predicts the dependent variable based on the independent variable(s).

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Answer:

2 x plus 3 y equals 26. X plus 4 y equals 18

Step-by-step explanation:

Number of tiles, = x

Number of pints of paint, = y

Store 1:

Cost per tile = $2 ; cost per pint = $3 ; total cost = $26

Store 2 :

Cost per tile = $1 ; cost per pint = $4 ; total cost = $18

System of equation:

2x + 3y = 26 - - - (1)

x + 4y = 18 - - - - - (2)

The radius of the circle is r = 3.78 cm for the given circle.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that the angle of the sector of the circle is 1.2 radians the area of the sector is 54 cm².

The radius of the circle will be calculated as:-

Area = Angle x πr²

54 = 1.2 x πr²

r² = ( 54 ) / ( 1.2 x π )

r² = 14.32

r = √14.32

r = 3.78 cm

Therefore, the radius of the circle is 3.78 cm.

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Answer:

E

Step-by-step explanation:

if we decidedly factor this expression-

4x^2+4xy+y^2

= (2x)^2 + 2*2xy + y^2

= (2x + y)^2

as you can see it is a perfect square so it can be grouped into (2x+y)^2

hence your solution is option e

Answer: A is cheaper

Step-by-step explanation: In the plan A, he pays $270( 45×6) as fee

Then $50/month for racket which is $300

total270+300=570

In plan b he pays 75 per month which is $450 and $37.5 on racket per month which is $225 making a total of $675

Difference in 6months is 675-570= $105 saved

Answer: 105

Step-by-step explanation:

did test

The Ball bearings produced using this manufacturing process have an average diameter of 3.5 mm which is calculated using the mean formula.

Since the ball orientation are equally dispersed between 2.5 and 4.5 mm, the normal breadth can be decided to utilize the equation:

mean = (a + b) / 2

where a is the lower dividing constraint (2.5 mm) and b is the upper dividing restrain (4.5 mm).

 Substitute the obtained value in the mean formula,

mean = (2.5 + 4.5) / 2

= 3.5

therefore, Ball bearings produced using this manufacturing process have an average diameter of 3.5 mm. 

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Answer:

y=12 .

180-106=74

74+3y+22+4y=180

96+7y=180

7y=84

y=12

4×12 = 48

Step-by-step explanation:

Good luck dear ;)

Answer:

1. lines B and C are congruent

2. lines M and N are congruent

3.  Lines A and C are congruent ?

4.  Angle 1: 76   Angle 2: 61

Step-by-step explanation:

Answer:

\( \mathsf{P = 45,230 {(1 + 0.02)}^{t} }\)

Step-by-step explanation:

Since P is growing every year at the rate of 2%.

It's an case similar finding of compounds interest.

that why we are using the formula of compounds interest in this situation.

The area under the standard normal curve within one standard deviation of the mean is approximately 0.6827. This means that about 68.27% of the data falls within one standard deviation of the mean.

For the second part, we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean. The mean of the sampling distribution of the sample mean is equal to the population mean, which is 104 minutes. The standard deviation of the sampling distribution of the sample mean, also known as the standard error, is equal to the population standard deviation divided by the square root of the sample size. In this case, the standard error is 12.78 / sqrt(39) = 2.0452.

To find the probability that a random sample of 39 movies has a mean runtime less than 105.9 minutes, we need to convert it into a z-score using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we have z = (105.9 - 104) / 2.0452 = 0.8471. Looking up this z-score in the standard normal distribution table, we find that P(Z < 0.8471) is approximately 0.7990.

For the third part, to find the probability that a random sample of 39 movies has a mean runtime between 98.3 and 102.2 minutes, we can calculate the z-scores for both values and find the probabilities associated with each z-score using the standard normal distribution table. The z-score for 98.3 is (98.3 - 104) / 2.0452 = -2.7169, and the z-score for 102.2 is (102.2 - 104) / 2.0452 = -0.8787. Finding the probabilities, we have P(-2.7169 < Z < -0.8787) is approximately 0.4115.

For the fourth part, to find the probability that a single randomly selected American watches television more than 2.31 hours per day, we can convert it into a z-score using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we have z = (2.31 - 2.54) / 0.87 = -0.2644. Looking up this z-score in the standard normal distribution table, we find that P(Z > -0.2644) is approximately 0.6049.

For the fifth part, to find the probability that the mean time spent watching television per day by a random sample of 81 Americans is more than 2.31 hours, we can calculate the z-score using the formula: z = (x - μ) / (σ / sqrt(n)), where x is the value, μ is the mean, σ is the standard deviation, and n is the sample size. Plugging in the values, we have z = (2.31 - 2.54) / (0.87 / sqrt(81)) = -0.5832. Looking up this z-score in the standard normal distribution table, we find that P(Z > -0.5832) is approximately 0.7190.

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A linear equation modeling Robert's weight-loss situation is x = 205 + 2y.

A linear equation is an equation modeling a straight-line relationship between two variables, for example, x and y.

The weight lost per week = 2 pounds

The number of weeks weight was lost, y = 6 weeks

Robert's weight after 6 weeks of losing 2 pounds weekly = 205

Let x = Robert's weight before the weight-loss program

x = 205 + 2y

x = 205 + 2(6)

x = 205 + 12

x = 217

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Answer: what do you mean by this she made 80.75$

Step-by-step explanation:

Step-by-step explanation:

a) The test statistic is (4.4-4)/(1.3/sqrt(70)) = 2.83. The p-value is 0.0023. Since the p-value is less than 0.05, we reject the null hypothesis.

b) The test statistic is (5.3-4.4)/sqrt((1.4^2/106)+(1.3^2/70)) = 4.09. The p-value is less than 0.0001. Since the p-value is less than 0.05, we reject the null hypothesis.

Approximately 60°C is the bare minimum temperature required to dissolve 10 g of KNO3 in 100 g of water.

Approximately 60°C is the bare minimum temperature required to dissolve 10 g of KNO3 in 100 g of water. Because potassium nitrate is a salt and salts often dissolve better in hot water than in cold, this is the case. The temperature of the water must be raised to the required level in order to accomplish the necessary level of dissolution. The solubility of the salt likewise rises with the rise in water temperature. So the minimum temperature required to dissolve 10 g of KNO3 in 100 g of H2O is roughly 60 °C. Further raising the temperature may cause more KNO3 to dissolve, but it is not required for the desired level of dissolution.

2.You start dissolving KNO₃ in the water and you find that after you’ve dissolved about 55 g of KNO₃, you can’t dissolve any more; it just sinks to the bottom.

Approximately what is the temperature of the water. Since KNO3 is most soluble at a temperature of 25 °C, the water is about that temperature.

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Answer:

B

Step-by-step explanation:

The order of every element in (Z18, +) is as follows:

Order 1: 0

Order 3: 6, 12

Order 6: 3, 9, 15

Order 9: 2, 4, 8, 10, 14, 16

Order 18: 1, 5, 7, 11, 13, 17

The set (Z18, +) represents the additive group of integers modulo 18. In this group, the order of an element refers to the smallest positive integer n such that n times the element yields the identity element (0). Let's find the order of every element in (Z18, +):

Element 0: The identity element in any group has an order of 1 since multiplying it by any integer will result in the identity itself. Thus, the order of 0 is 1.

Elements 1, 5, 7, 11, 13, 17: These elements have an order of 18 since multiplying them by any integer from 1 to 18 will eventually yield 0. For example, 1 * 18 ≡ 0 (mod 18).

Elements 2, 4, 8, 10, 14, 16: These elements have an order of 9. We can see that multiplying them by 9 will yield 0. For example, 2 * 9 ≡ 0 (mod 18).

Elements 3, 9, 15: These elements have an order of 6. Multiplying them by 6 will yield 0. For example, 3 * 6 ≡ 0 (mod 18).

Elements 6, 12: These elements have an order of 3. Multiplying them by 3 will yield 0. For example, 6 * 3 ≡ 0 (mod 18).

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Answer:

factors

Step-by-step explanation:

To find the roots of a polynomial, it is often useful to find the Factors of the polynomial.

Answer:

Solution given:

we have

f(x)=x²-9x-36

let

y=x²-9x-36

when

x=0

y=-36

when

y=0

0=x²-9x-36

x²-12x+3x-36=0

x(x-12)+3(x-12)=0

(x-12)(x+3)=0

either

x=12

x=-3

So,

x and y intercepts are (-3,0)(12,0) and 0,-36)