An account is opened with $7,595.96 with a rate of increase of 2% per year. After 1 year, the bank account contains $7,746.90. Assuming no deposits or withdrawals are made, which equation can be used to find y, the amount of money in the account after x years? (Round money values to the nearest penny.)

Answer:

468

Step-by-step explanation:

8/4*234=2*234=468

Answer:

468

Step-by-step explanation:

5+3/ 4 =2

2*234=468

The general solution for the second differential equation is y = \(e^[(1/2)x^2 + C2] - 4\)

1. \(dy/dx = 2x/y\)

Step 1: Separate variables. To do this, multiply both sides by y and divide both sides by dx:
\(y dy = 2x dx\)

Step 2: Integrate both sides:
\(∫y dy = ∫2x dx\)

Step 3: Evaluate the integrals:
\((1/2)y^2 = x^2 + C1\), where C1 is the constant of integration.

Step 4: Solve for y to obtain the general solution:
\(y^2 = 2x^2 + 2C1\\y = ±√(2x^2 + 2C1)\)

So, the general solution for the first differential equation is \(y = ±√(2x^2 + 2C1\)).

2. \(dy/dx = x(y+4)\)

Step 1: Separate variables. To do this, divide both sides by (y+4) and multiply both sides by dx:
\(dy / (y+4) = x dx\)

Step 2: Integrate both sides:
\(∫[1 / (y+4)] dy = ∫x dx\)

Step 3: Evaluate the integrals:
\(ln|y+4| = (1/2)x^2 + C2\), where C2 is the constant of integration.

Step 4: Solve for y to obtain the general solution:
\(y+4 = e^[(1/2)x^2 + C2]\\y = e^[(1/2)x^2 + C2] - 4\)

So, the general solution for the second differential equation is y = \(e^[(1/2)x^2 + C2] - 4\)

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The Taylor polynomial of degree 4 for g(x) = x^2 ln x about the center a = 1 is (x - 1) + (3/2)(x - 1)^2 + (1/3)(x - 1)^3 - (1/6)(x - 1)^4.

To find the Taylor polynomial of degree 4 for the function g(x) = x^2 ln x about the center a = 1, we first need to find the first four derivatives of g(x):

g(x) = x^2 ln x

g'(x) = 2x ln x + x

g''(x) = 2ln x + 3

g'''(x) = 2/x

g''''(x) = -4/x^3

Next, we evaluate these derivatives at x = 1 to find the coefficients of the Taylor polynomial:

g(1) = 1^2 ln 1 = 0

g'(1) = 2(1) ln 1 + 1 = 1

g''(1) = 2ln 1 + 3 = 3

g'''(1) = 2/1 = 2

g''''(1) = -4/1^3 = -4

Using these coefficients, we can write the Taylor polynomial of degree 4 for g(x) about a = 1:

P4(x) = g(1) + g'(1)(x - 1) + (g''(1)/2!)(x - 1)^2 + (g'''(1)/3!)(x - 1)^3 + (g''''(1)/4!)(x - 1)^4

P4(x) = 0 + 1(x - 1) + (3/2)(x - 1)^2 + (2/6)(x - 1)^3 - (4/24)(x - 1)^4

Simplifying and combining like terms, we get:

P4(x) = (x - 1) + (3/2)(x - 1)^2 + (1/3)(x - 1)^3 - (1/6)(x - 1)^4

Therefore, the Taylor polynomial of degree 4 for g(x) = x^2 ln x about the center a = 1 is (x - 1) + (3/2)(x - 1)^2 + (1/3)(x - 1)^3 - (1/6)(x - 1)^4.

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Answer:

x = -3.5

Step-by-step explanation:

First we create the equation.

Let x = the unknown number

7x-1 = 5x - 8

Add 8 to both sides

7x + 7 = 5x

Subtract 7x

7 = -2x

Divide by 2

-7/2 = x

-3.5 = x

Step-by-step explanation:

Everything is written in the photo and the answer and the solution (I had to write some text so that I could send it)

The general equation of a circle is given as;  (x - h)² + (y - k)² = r² Where h and k are the center points and r is the radius of the circle.

To get an equation of a circle that is parallel to the XY-plane, ignore the z-coordinate of the center point since it doesn't affect the equation.

Let us first write down the equation of the circle with the center point (5,3,7) and radius of 2.

So, (x - 5)² + (y - 3)² + (z - 7)² = 2².

The equation is not parallel to the xy-plane because it contains the z coordinate. The circle should only involve the x and y-coordinates of the center point.

This can be achieved by setting z = 7 and  the equation;(x - 5)² + (y - 3)² + (7 - 7)² = 2²

(x - 5)² + (y - 3)² = 4.

This is the equation of the circle that is parallel to the XY-plane, has a radius of 2, and is centered at (5,3).

The equation of the circle is (x - 5)² + (y - 3)² = 4.

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Answer:

whats the question?

Step-by-step explanation:

Answer:

Never

Step-by-step explanation:

This is because when,

Δ JKL ≅ Δ MNP

Then, ∠J ≅ ∠M

∠K ≅ ∠N

∠L ≅ ∠P

Therefore, ∠L ≠ ∠N

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Let x be the number of child tickets sold

Let y be the number of adult tickets sold

Amount received for the child tickets: 5.90x

Amount received for the adult tickets: 9.40y

Total sales of 1001.30:

127 tickets were sold:

Use the two equations above as a system of equations, to solve it:

1. Solve y in the second equation.

2. Use the value you get in step 1 to substitute y in the first equation:

3. Solve x:

The value of x is 55

Answer:

Sure, Help you with what?

Step-by-step explanation:

Let me know :)

Have an AWESOME Friday <3

Answer:

what is the question

Step-by-step explanation:

Answer:

When  x =  -16, y = -1.

Step-by-step explanation:

Let's plug in y = -1 into this equation

-1 = 1/4x + 3

Now, we need to solve the equation for x. To do so, we want x to be by itself on one side of the equation. We will use inverse operations to get the x by itself. First, subtract 3 from either side to under the +3 on the right side of the equation.

-1 - 3 = 1/4x + 3 - 3

-4 = 1/4x

Next, we will divide by 1/4 to undo the *1/4. Dividing by 1/4 is the same as multiplying by 4, so we will multiply each side by 4.

-4 * 4 = 1/4x * 4

-16 = x

bye now

im tyler

Answer:

10

20

Step-by-step explanation:

Answer:

No, it would freeze at -16.61°C.

Step-by-step explanation:

The required two way frequency table is shown below.

We know that a two-way frequency table is nohting but the way to display frequencies for two different categories collected from a single group of people.

While making the two-way frequency tables first we need to identify the two variables of interest. Then we need to determine the possible values of each variable. Select a variable to be represented by the rows and the other to be represented by the columns. And then complete the table with frequencies.

Here we have two variables as:

Time ( practiced for atleast 10,000 hours and did not practiced for atleast 10,000 hours) and the second (won a prize and do not won a major)

Based on the information provided, we can obtain a two way frequency table as shown below:

                                   practiced for atleast          did not practiced for

                                       10,000 hours               atleast 10,000 hours

have won a major                  9                                      1

haven't won a major              1                                       2

Thus the required two-way frequency table is shown in attached figure.

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Find the complete question below.

By using what we know about right triangles, we will see that the hobbits are at 744.39 meters from the Dark Tower.

This position can be visualized as a right triangle, with the catheti being the tower's height and the distance between the hobbits and the Dark Tower.

Then we can use the relation:

Tan(θ) = (opposite cathetus)/(adjacent cathetus)

Where θ = 28°

The adjacent cathetus to this angle exists the height of the tower, then:

Adjacent cathetus = 1,400 m

The opposite cathetus exists the distance,

Tan(28°) = D/1,400m

Solving for D we get:

Tan(28°)*1,400m = D = 744.39m

The hobbits are at 744.39 meters from the Dark Tower.

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Answer:

34

Step-by-step explanation:

Substitute the values.

s = 3 and t = -2

8s-5t

8 (3) - 5(-2)

( 8 x 3 ) - ( 5 x -2 )

24 + 10 [ - x - = + ]

= 34

Josh will need approximately 43.96 feet of rope to mark the plot for the circular flower bed.

To calculate the approximate length of rope that Josh will need to mark the circular plot for the flower bed, we can use the formula for the circumference of a circle.

The formula for the circumference of a circle is:

C = 2 * π * r

where C is the circumference, π (pi) is approximately 3.14, and r is the radius of the circle.

In this case, the radius is given as 7 feet. Plugging this value into the formula, we have:

C = 2 * 3.14 * 7

C ≈ 43.96 feet

Therefore, Josh will need approximately 43.96 feet of rope to mark the plot for the circular flower bed.

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Answer:

2x-32

Step-by-step explanation:

You would distribute the 4.

Answer:

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

m = y2 - y1/x2 - x1

m = (-2 - 6)/(8 - 6)

m = -8/2

m = -4

Let's denote the width of the rectangle as "w" (in inches).

According to the given information, the length of the rectangle is 6 inches more than the width. Therefore, the length can be represented as "w + 6" (in inches).

The perimeter of a rectangle is given by the formula: 2(length + width).

So, for the given rectangle, the perimeter can be expressed as:

2(w + (w + 6)) = 72

Simplifying the equation:

2(2w + 6) = 72

4w + 12 = 72

4w = 72 - 12

4w = 60

Dividing both sides of the equation by 4:

w = 60 / 4

w = 15

Therefore, the width of the rectangle is 15 inches.

Substituting the value of the width into the equation for the length:

Length = w + 6 = 15 + 6 = 21

So, the dimensions of the rectangle are:

Width = 15 inches

Length = 21 inches

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To know the number of boxes that can fit divide the volume of the shipping container by the volume of one cereal box.

To do this use the formula;

Since both the container and the boxes likely have a defined rectangular shape you can use this formula:

For example:

Dimensions of the container:

120 cm x 100 cm x 100 cm = 1200000 cubic centimeters

Dimensions of the boxes:

30 cm x 30 cm x 10 cm = 9000 cubic centimeters.

1200000 cc / 9000 cc = 133 boxes.

Note: This question is incomplete because the diagram is not provided; due to this, I answered it based on general knowledge.

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Answer:

C

Step-by-step explanation:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

C is the correct answer since it can be expressed as a fraction which equals to 7/9.

Hope it helps:)

Answer:

A

Step-by-step explanation:

Pi is an irrational number so it can't be B.

√(5) is an irrational number so it can't be D.

It could be either A or C... Hm, go with A. Let me know if it works.

Answer:

x = -60

Step-by-step explanation:

Given the equation:

\( \displaystyle{0.1x - 5 = - 11}\)

Add both sides by 5

\( \displaystyle{0.1x - 5 + 5= - 11 + 5} \\ \\ \displaystyle{0.1x = - 6}\)

Multiply both sides by 10 to get rid of the decimal

\( \displaystyle{0.1x \times 10 = - 6 \times 10} \\ \\ \displaystyle{x= - 60}\)

Therefore, x = -60

Answer:

Step-by-step explanation:

0.1x − 5 = −11

0.1x = -11 + 5

0.1x = -6          multiply by 10 both sides

x = -60

--------------------------

0.1 x (- 60) - 5 = -11

-6 - 5 = -11

-11 = -11

Solving problems involving normal proportions requires careful attention to detail, as well as a good understanding of statistical concepts such as standardization and probability.

When solving a problem where you want to find normal proportions, you can follow the following steps:

Define the problem: Clearly define the problem you are trying to solve, including any relevant details such as the population, sample size, and the variable of interest.

Check assumptions: Check if the conditions for using normal distributions are met. The data should be continuous, the sample size should be large enough, and the distribution should be approximately normal.

Calculate the sample mean and standard deviation: If you are working with a sample, calculate the sample mean and standard deviation.

Standardize the data: Convert the data into standard normal distribution, by subtracting the mean from each observation and dividing by the standard deviation.

Determine the probability: Once the data has been standardized, you can use a standard normal distribution table or a calculator to determine the probability of the variable falling within a certain range or above/below a certain value.

Interpret the results: After determining the probability, interpret the results in the context of the problem. For example, you might conclude that there is a 95% chance that a randomly selected observation falls within a certain range, or that the variable of interest is higher than a certain value in 5% of cases.

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Answer:

Samantha has 8 quarts of milk.  The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have?   x  a. 1 over 32   x  b. begin mathsize 16px style 1 half end style   x  c. 2   x  d. 32

Step-by-step explanation:Samantha has 8 quarts of milk.  The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have?   x  a. 1 over 32   x  b. begin mathsize 16px style 1 half end style   x  c. 2   x  d. 32Samantha has 8 quarts of milk.  The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have?   x  a. 1 over 32   x  b. begin mathsize 16px style 1 half end style   x  c. 2   x  d. 32Samantha has 8 quarts of milk.  The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have?   x  a. 1 over 32   x  b. begin mathsize 16px style 1 half end style   x  c. 2   x  d. 32

Answer:

A

Step-by-step explanation:

Got it right on Edge.

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a. the costs of non-compliance, enforcement, prevention and evaluation are -75 d/p, -$7500, $17500 and $5000 respectively

b. The percentage of effort devoted to each component is:

a) To calculate the costs of non-compliance, enforcement, prevention, and evaluation, we need to determine the deviations in effort for each component and multiply them by the corresponding cost per person-day.

Non-compliance cost:

Non-compliance cost = Actual effort - Predicted effort

To calculate the actual effort, we need to sum up the effort for each component mentioned:

Actual effort = Plan development + Software development + Reviews + Tests + Training + Methodology

Actual effort = 25 + 75 + 20 + 30 + 20 + 5 = 175 d/p

Non-compliance cost = Actual effort - Predicted effort = 175 - 250 = -75 d/p

Enforcement cost:

Enforcement cost = Non-compliance cost * Cost per person-day

Assuming a cost of $100 per person-day, we can calculate the enforcement cost:

Enforcement cost = -75 * $100 = -$7500 (negative value indicates a cost reduction due to underestimation)

Prevention cost:

Prevention cost = Predicted effort * Cost per person-day

Assuming a cost of $100 per person-day, we can calculate the prevention cost for each component:

Plan development prevention cost = 25 * $100 = $2500

Software development prevention cost = 75 * $100 = $7500

Reviews prevention cost = 20 * $100 = $2000

Tests prevention cost = 30 * $100 = $3000

Training prevention cost = 20 * $100 = $2000

Methodology prevention cost = 5 * $100 = $500

Total prevention cost = Sum of prevention costs = $2500 + $7500 + $2000 + $3000 + $2000 + $500 = $17500

Evaluation cost:

Evaluation cost = Total project cost - Prevention cost - Enforcement cost

Evaluation cost = $25000 - $17500 - (-$7500) = $5000

b) To calculate the percentage of effort devoted to each component out of the total cost, we can use the following formula:

Percentage of effort = (Effort for a component / Total project cost) * 100

Percentage of effort for each component:

Plan development = (25 / 250) * 100 = 10%

Software development = (75 / 250) * 100 = 30%

Reviews = (20 / 250) * 100 = 8%

Tests = (30 / 250) * 100 = 12%

Training = (20 / 250) * 100 = 8%

Methodology = (5 / 250) * 100 = 2%

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Answer:

7

9+12/3-6

12/3=4

9+4-6

9+4=13

13-6=(7)

Step-by-step explanation:

In linear equation, 50x is the total cost of dance classes each month.

What is a linear equation example?

C = 50x + 75, where 75 is the application fee. When they take out the application fee, it will become:

C = 50x +75 (-75)

C = 50x

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The probability that a homebuilder takes 200 days or less to complete a house is approximately 0.8238, or 82.38%.

Explanation :

To answer this question, we can use the concept of the z-score. The z-score tells us how many standard deviations a data point is from the mean.

Let's calculate the z-score for a completion time of 200 days:
z = (x - μ) / σ
where x is the completion time, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get:
z = (200 - 176.7) / 24.8 = 0.93

To find the probability associated with this z-score, we can use a z-table or a calculator. In this case, the probability is 0.8238.

This means that there is an 82.38% chance that the completion time of a house will be 200 days or less, given that the completion time follows a normal distribution with a mean of 176.7 days and a standard deviation of 24.8 days.

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A sampling distribution is normal only if the population is normal. This  statement is false because A sampling distribution is normal only if n≥30.

If the underlying population is normally distributed, the sampling distribution (such as the sample mean distribution, also known as the xbar distribution) is also normally distributed. Even though the population is not normally distributed, the x(bar) distribution is approximately normal if n > 30, due to the central limit theorem. Some textbooks may use values ​​above 30, but after a certain threshold the x(bar) distribution is effectively "normal".

Option B is close, but misses the normal population part. n > 30 is not necessary if we know the population is normal.

A sampling distribution is the probability distribution of a statistic obtained from a large number of samples drawn from a particular population. The sampling distribution for a given population is the frequency distribution of a range of different outcomes that can occur in the population.

In statistics, a population is the entire basin from which a statistical sample is drawn. A population can refer to an entire population of people, objects, events, hospital visits, or measurements. Thus, a population can be said to be a global observation of subjects grouped by common characteristics.

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