Solve for x in the triangle. Round your answer to the nearest tenth

Answer:

Una relación lineal es de la forma:

y = a*x + b.

donde a es la pendiente y b es la ordenada al origen.

en este caso, y es el precio de la camioneta, x es el numero de años que pasaron, a es la razon de depreciación de la camioneta y b es el precio inicial de la camioneta, b = $42,000.

Sabemos que después de 5 años, el precio de la camioneta es 21,000, entonces podemos resolver:

$21,000 = a*5 + $42,000

a*5 = $21,000 - $42,000 = -$21,000

a = -$21,000/5 = -$4,200

Esto significa que el precio decae $4,200 por año

El valor de depreciación de la camioneta es de $4200 por año.

Dado que Juana compró una camioneta 4x4 a $42 000; y además, sabe que la camioneta se depreciará (bajará su precio) en forma lineal durante 6 años, para determinar, si al quinto año la camioneta tendrá un valor de $21 000, cuál es el valor de la depreciación de la camioneta, se debe realizar el siguiente cálculo:

Por lo tanto, el valor de depreciación de la camioneta es de $4200 por año.

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Answer:

$122.28

Step-by-step explanation:

Give the following :

Insurance worth = $240,000

Price sold = $225

P(survival) = 0.999572

P(death) = 1 - 0.999572 = 0.000428

If she survives, insurance firm makes $225

If she dies, insurance firm pays $240,000, hence the company losses :

$(225 - 240,000) = $−239775

Expected value (E(x)) = sum of P(i) * X(i)

E(x) = (P(survival) * profit made) + (P(death) * loss incurred)

E(x) = (225 * 0.999572) + (0.000428 * −239775)

= 224.9037 - 102.6237

=$ 122.28

Answer:

$773.3587

Step-by-step explanation:

The probability that the female survives = 0.999572

therefore, probability that female dies = 1-0.999572 = 0.000428

if the female survives the insurance company makes = $225

x=$250

If the female dies the insurance company pays $240,000.

So, the amount with the company = 240000-225 = $ 2390775

Therefore Expected value = 250(0.999572)-2390775(0.000428)= $773.3587

Answer:

The answer to the given question can be defined as follows:

Step-by-step explanation:

\(\to GCF(42, 70) = 7\)

Therefore, the common roots of unity were  

\(\to e^{\pm i 2\pi \frac{k}{7}}\\\\\ where \\ \\ k=0,1,...... 6\)

That's why the  answer is 14 for these

False. The columns of matrix P are not necessarily eigenvectors of matrix A. While the diagonal matrix D contains the eigenvalues of A, the eigenvectors are not explicitly determined by the columns of P.

False. The columns of matrix P are not guaranteed to be eigenvectors of the transpose of matrix A (A.T).

In the given equation, \(a = PDP^(-1),\)

where D is a diagonal matrix and P is an invertible matrix.

The diagonal elements of D represent the eigenvalues of matrix A, while the columns of P correspond to the eigenvectors of A.

When considering the transpose of matrix A (A.T), we have \((A.T) = (PDP^(-1)).T = (P^{(-1)})^T D^T P^T.\)

Taking the transpose of a product involves reversing the order of the matrices and transposing each matrix individually.

Therefore, we have \((A.T) = P^T D^T (P^{(-1)})^T.\)

Since P is an invertible matrix, its transpose \(P^T\) is also invertible. Similarly, the transpose of the inverse of \(P, (P^{(-1)} )^T,\) is also invertible.

However, the key point is that the diagonal matrix\(D^T\) is not guaranteed to have the same eigenvalues as matrix A.

The eigenvalues of A are present in D, but they may not remain on the main diagonal after transposing.

Thus, the columns of matrix P, which correspond to the eigenvectors of A, may not necessarily be the eigenvectors of A.T.

In conclusion, the statement is false.

The columns of matrix P do not have to be eigenvectors of the transpose of matrix A (A.T).

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Taking the floor of this value gives us $\lfloor D\rfloor = \boxed{328}$. We can use the fact that the mode occurs more often than any other number to help us determine the value of the mode.

Since there are 121 integers in the sample, we know that the mode must occur at least 61 times (since otherwise, there would be another value with at least as many occurrences).

Let's assume that the mode occurs 61 times. In this case, there are 60 integers left in the sample that are not the mode. We can make the difference between the mode and the arithmetic mean as large as possible by making all of these integers as small as possible (i.e., equal to 1).

So, the mode is 1000 and there are 61 of them, and there are 60 integers equal to 1. The arithmetic mean is \($\frac{61\cdot 1000 + 60 \cdot 1}{121} = \frac{61060}{121}$\) Thus, the difference between the mode and the arithmetic mean is $1000 - \frac{61060}{121}$.

Taking the floor of this value gives us $\lfloor D\rfloor = \boxed{328}$.

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The surface area generated by revolving the curve y=f(x) on the interval [a,b] about the y-axis is given by the formula:

2π∫[a,b] f(x)√(1+(f'(x))^2) dx

To find the surface area generated by revolving the curve y=f(x) about the y-axis on the interval [a,b], we need to use the formula for the surface area of a surface of revolution.

This formula is derived by dividing the curve into small segments of length dx and approximating the surface area of each segment as a frustum of a cone. The formula for the surface area of a frustum of a cone is:

dA = 2πr √(dr^2 + dz^2)

where r is the radius of the circular cross-section of the frustum, and dz is the height of the frustum.

Using calculus, we can express r and dz in terms of x and dx. The radius of the circular cross-section of the frustum is equal to f(x), and the height of the frustum is equal to dx. Therefore, we have:

r = f(x)

dz = dx

Substituting these values into the formula for the surface area of a frustum of a cone, we get:

dA = 2πf(x) √(1 + (f'(x))^2) dx

To find the total surface area generated by revolving the curve y=f(x) on the interval [a,b] about the y-axis, we need to integrate dA from a to b:

A = ∫[a,b] dA

= ∫[a,b] 2πf(x) √(1 + (f'(x))^2) dx

This is the formula for the surface area generated by revolving the curve y=f(x) on the interval [a,b] about the y-axis.

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The probability that Anthony, Brian, and Chantal are in the same lab group today is approximately 0.8703, or about 87.03%.

There are 15 students in total, so there are 15 ways to choose the first student, 14 ways to choose the second student (since one has already been chosen), and 13 ways to choose the third student (since two have already been chosen). However, since the lab groups are identical, we need to divide by the number of ways to arrange the group of three students, which is 3! = 6. Therefore, the total number of ways to choose a group of three students is:

15 x 14 x 13

6

Simplifying this expression gives:

(15 x 14 x 13) / 6 = 455

There are 5 lab groups, and we want to find the probability that Anthony, Brian, and Chantal are all in the same group. There are 3 ways to choose which group they will be in, and then we need to choose 2 more students to join them, which can be done in:

12 x 11

2

ways, since there are 12 students remaining to choose from after we have chosen Anthony, Brian, and Chantal, and we need to choose 2 more students to join them. Therefore, the total number of ways that Anthony, Brian, and Chantal can be in the same group is:

3 x (12 x 11) = 396

Finally, we can calculate the probability by dividing the number of favorable outcomes (i.e., Anthony, Brian, and Chantal are in the same group) by the total number of possible outcomes:

P(Anthony, Brian, Chantal in same group) = 396 / 455

≈ 0.8703

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Answer:

357.5 miles

Don't forget units.

Step-by-step explanation:

If she moves 55 miles every hour and there are 6.5 hours, you multiply to find the total distance.

The calculated expectation of X is 0.1

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

P{X = -1}=0.2, P{X = 0} = 0.5, P{X = 1}=0.3

The expectation of X is calculated as

E(x) = ∑xp(x)

So, we have

E(x) = -1 * 0.2 + 0 * 0.5 + 1 * 0.3

Evaluate

E(x) = 0.1

Hence, the expectation of X is 0.1

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Answer:

\(\dfrac{1}{12}$ gallons\)

Step-by-step explanation:

\(M$arie bought $ \dfrac{1}{2}$ gallon of milk\)

She exhausted the half gallon in 6 days.

Since she takes equal amount of milk per day

Her Unit Rate of Milk Consumption

\(=\dfrac{1}{2}\div 6\\ =\dfrac{1}{12}$ gallons per day\)

Marie drinks \(\dfrac{1}{12}\) gallons of milk per day.

Answer: 1/12

Step-by-step explanation:

The number of cubes that have just one red face is 25.

A solid three-dimensional shape called a cube contains six square faces, eight vertices, and twelve edges.

Given:

Meg paints the whole outside of a 5 x 5 x 5 cube red and then cuts it up into 1 x 1 x 1 cube.

The surface area of the cube with dimensions 5 x 5 x 5,

= 6 x 5 x 5

= 150 square units.

The surface area of the cube with dimensions 1 x 1 x 1,

= 6 square units.

The number of cubes that have just one red face is,

= 150/6 = 25

Therefore, 25 is the required number.

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The standard deviation of the speeds of cars travelling on California freeways is approximately 13.96 miles per hour.

Given that the speeds of cars travelling on California freeways are normally distributed with a mean of 57 miles /hour and the highway patrol's policy is to issue tickets for cars with speeds exceeding 80 miles /hour.

The records show that exactly 5% of the speeds exceed this limit.

To find the standard deviation of the speeds of cars travelling on California freeways, we need to use the following formula:

z = (x - μ) / σ

Where

z is the z-score,

x is the value of the observation,

μ is the population mean, and

σ is the standard deviation.

To find the z-score for the speed limit of 80 miles per hour, we use the formula.

z = (x - μ) / σ

  = (80 - 57) / σ

  = 23 / σ

The z-score that corresponds to 5% is -1.645.

Therefore, -1.645 = (x - 57) / σ

Now, we need to solve for σ,σ = (x - 57) / (-1.645)

Substituting 80 for x,

σ = (80 - 57) / (-1.645)

σ = 13.96 miles per hour (rounded to two decimal places)

Therefore, the standard deviation of the speeds of cars travelling on California freeways is approximately 13.96 miles per hour.

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Answer:

The one shaped like an upright U

(Top right corner)

Step-by-step explanation:

This would be a function because when you do the vertical line test, the inputs (x) are paired with one output (y)

Hope this Helps

Answer:

n=4

Step-by-step explanation:

Answer:

14400 boxes

Step-by-step explanation:

After looking at this question you would first see that it is looking for how many cuboids can fit into the container. That would mean that the final equation should be the volume of container divided by the volume of the cuboid.

First, we can find the volume of the container. Keep in mind that the volume of a rectangular prism is V=Bh (which means area of the base times the height)

For the base we would do (600)(200) which is 120000

Next, the height is 300, so we would times that by 120000 (which is 36000000)

Moving on to the cuboid!

We would do the same process, but with smaller units.

(same equation) V=Bh

B= (50)(20)

=100

(100)(25)=2500

Lastly, like mentioned in the beginning, take the volume of the container and divide by the volume of the cuboid.

36000000/2500=14400

Therefore, 14400 boxes can fit into this container!

Hope this helps! :)

Answer:

Step-by-step explanation:

so they made the boxes fit perfectly into the container.. as they are.

notice that each of the dimensions of the box fit perfectly into the dimensions of the container.

length container of 600 / length of box 50=12

width of container of  200 / width of box 20 = 10

height of container of 300 / heigth of box 25 = 12

now just multiply those 3 answers

12 * 10 * 12 = 1440 boxes  :)

BTW ( by the way )   I can see by what you have erased you did do the  

300 ÷25 =12 correctly ,  (300/25), and the  

200÷20 = 10  correctly, (200/20)  but the

600÷50 = 20 was not correct.    You can check this in your head really quickly by just multiplying  50*20 = 1000   ,  now you know that's not right, so then do 50*10=500  , that's close, hun,  now just add 2 more 50s for a total of 600  and 12 , 50s   :)  see??

The statement an assumption underlying the t-distribution is that the population from which we are sampling comes from an exponential distribution is false.

The t-distribution assumes that the population from which we are sampling follows a normal distribution, not an exponential distribution.

The t-distribution is used when the population standard deviation is unknown and is estimated from the sample standard deviation, and when the sample size is small (typically less than 30).

When the test measure is expansive (regularly more noteworthy than 30), the t-distribution gets to be exceptionally comparative to the standard typical dispersion. 

therefore, an assumption underlying the t-distribution is that the population from which we are sampling comes from an exponential distribution is false.

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the correct translation is ((∃x)E(x) → ((A(g) & ¬W(g)) ∨ (¬A(g) & W(g))))

The correct translation of the third premise "Evil can exist only if God is either able but unwilling or unable yet willing to prevent it" is:

((∃x)E(x) → ((A(g) & ¬W(g)) ∨ (¬A(g) & W(g))))

Explanation:

(∃x)E(x): There exists an x such that x is evil. This represents the existence of evil.

A(g): God is able to prevent evil.

¬W(g): God is unwilling to prevent evil.

¬A(g): God is unable to prevent evil.

W(g): God is willing to prevent evil.

The premise states that evil can exist only if one of two conditions is met:

God is able to prevent evil but unwilling to do so (A(g) & ¬W(g)).

God is unable to prevent evil yet willing to do so (¬A(g) & W(g)).

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The flow rate of 5 MGD is equivalent to 7.73615 cfs

To convert million gallons per day (MGD) to cubic feet per second (cfs), we need to use the conversion factor between the two units. The conversion factor is 1 MGD = 1.54723 cfs.

Therefore, to convert MGD to cfs, we can multiply the given value of MGD by the conversion factor. For example, if we have a flow rate of 5 MGD, we can convert it to cfs as follows:

5 MGD x 1.54723 cfs/MGD = 7.73615 cfs

So, the flow rate of 5 MGD is equivalent to 7.73615 cfs. Similarly, we can convert any given flow rate in MGD to cfs by using the same conversion factor.

It is important to note that these units are commonly used in the context of water supply and distribution systems, where flow rates are a crucial factor in the design and operation of such systems. Therefore, knowing how to convert between different flow rate units is essential for engineers and technicians working in this field.

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Answer: The quotient of 3 1/3 and 1 5/6 is 60/33, which can be simplified to 20/11.

Step-by-step explanation:

To divide 3 1/3 by 1 5/6, we first need to convert the mixed numbers to improper fractions:

3 1/3 = (3 x 3 + 1) / 3 = 10/3

1 5/6 = (1 x 6 + 5) / 6 = 11/6

Now, we can divide the fractions by multiplying the first fraction by the reciprocal of the second fraction:

(10/3) ÷ (11/6) = (10/3) x (6/11)

Multiplying the numerators and denominators, we get:

(10 x 6) / (3 x 11) = 60/33

The quotient of 3 1/3 and 1 5/6 is therefore 60/33, which can be simplified to 20/11.

Answer:

y= -x to the power of 2

so the answer is the first one!

Hope this helps!!

Based solely on the mileage of the Eurovan, it is likely to be in above-average condition.

The condition of a vehicle is influenced by several factors, including mileage, maintenance history, usage, and overall care. While high mileage can generally indicate wear and tear on a vehicle, it does not necessarily imply poor condition. Eurovans are known for their durability and reliability, so even with 81,718 thousand miles, it is possible for the van to be in above-average condition.

To determine the true condition of the Eurovan, additional information beyond mileage is required. Factors such as regular maintenance, service records, and the overall care provided by the previous owner(s) play a crucial role in assessing the van's condition. If the van has been well-maintained, with routine servicing and repairs, it is more likely to be in above-average condition despite the higher mileage. Additionally, the overall usage of the van should be considered. If the majority of the mileage consists of long highway trips rather than stop-and-go city driving, it can contribute to less wear and tear on the engine and components. Furthermore, factors such as storage conditions, accident history, and the quality of the driving surface can also impact the condition of the Eurovan.

In summary, while the mileage of the Eurovan may initially suggest a below-average condition, it is essential to consider additional factors such as maintenance history, usage patterns, and overall care to make a more accurate assessment. Without this additional information, it is reasonable to assume that the Eurovan is likely to be in above-average condition based on its reputation and durability.

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Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

Answer:

x-intercept: (4,0)

y-intercept (0,12)

Answer:

The answer to your question is given below.

Step-by-step explanation:

To divide 2635 by 17 using long division method, we simply do the following:

2635 ÷ 17

17 can not go into 2. Therefore, we try 17 into 26, keeping 35 constant.

26 ÷ 17 = 1

Put the 1 on top.

Multiply 17 by 1

17 x 1 = 17

Subtract 17 from 26

26 – 17 = 9

Put the 9 in from of 35 to become 935

Next:

935 ÷ 17

17 can not go into 9. Therefore, we try 17 inot 93 keeping 5 constant.

93 ÷ 17 = 5

Put the 5 on top together with the 1 to become 15.

Multiply 17 by 5

17 x 5 = 85

Subtract 85 from 93

93 – 85 = 8

Put the 8 in front of 5 to become 85

Next:

85 ÷ 17

17 can not go into 8. Therefore, we try 85

85 ÷ 17 = 5

Put the 5 on top together with 15 to become 155

Multiply 17 by 5

17 x 5 = 85

Subtract 85 from 85

85 – 85 = 0

Since no number is remaining, we shall stop here.

Therefore,

2635 ÷ 17 = 155

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We introduced three conditions that should be met before we construct a confidence interval for an unknown population proportion: Random, Normal, and Independent.

There are three crucial requirements that must be met in order to establish a confidence interval. These are Independent, Random, and Normal.

Any survey is carried out objectively.

It is required to assure randomness. An independent choice is equally likely to be made in a random sample. Similar to how the confidence interval is built, normal is used to confirm which phenomena are being employed or to correct the approach if necessary. In a similar vein, independent is crucial because it contains the facts to be analyzed. For the purpose of calculating the standard deviation, independent is used.

Therefore, it's crucial to consider the Random, Normal, and Independent criteria while building a confidence interval.

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There are 324 miles can Mario drive with 9 gallons of gas.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

He can drive 18 miles on ½ a gallon of gas.

Now,

Since, He can drive 18 miles on ½ a gallon of gas.

Let the number of miles cover with 9 gallons of gas = x

So, By definition of proportion, we get;

⇒ 18 / (1/2) = x / 9

⇒ 18 × 2 = x / 9

⇒ 36 × 9 = x

⇒ x = 324 miles

Thus, The number of miles cover with 9 gallons of gas = 324 miles

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Answer:

x = 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

(h, k ) are the coordinates of the vertex and a is a multiplier

h(x) = 19(x - 5)² + 6 ← is in vertex form

with vertex (h, k ) = (5, 6 )

The axis of symmetry is a vertical line passing through the vertex

with equation x = 5