Manuel borrowed $1,500 from his bank and signed a
contract to make monthly payments for two years at 4%
interest compounded annually. How much total interest
will Manuel pay on this loan?

Answer:

  x = 13

Step-by-step explanation:

The relevant fact about vertical angles is that they are congruent, their measures are equal. This lets you write an equation relating the expressions for the measures of angles A and B.

__

  ∠A = ∠B

  (8x -12)° = (6x +14)° . . . . . substitute given expressions

  2x = 26 . . . . . . . . . . . divide by °, add 12-6x

  x = 13 . . . . . . . . . . divide by 2

SOLUTION

Write out the equation

The first step in solving this equation is to multiply both sides by 2 this is called

MULTIPLICATION PROPERTY OF EQUALITY

Step1; MUltiply both sides by 2

The next step in solving this equation is to add 7 to both sides of

the equation this is called ADDITION PROPERTY OF EQUALITY

step2: Add 7 to both sides of the equation

Hence the solution to the equation is y=-15

The steps are

Step1; MULTIPLICATION PROPERTY OF EQUALITY

Step2: SIMPLIFYING

Step3: ADDITION PROPERTY OF EQUALITY

Step4: SIMPLIFYING

To radix sort the given list of integers in base 10, we can perform multiple passes of counting sort based on the digits from right to left. Here's the step-by-step process:

First sort:

Original list: 483 525 582 143 645 522

Counting sort based on the least significant digit (unit place):

143 522 483 582 645 525

Second sort:

Original list: 143 522 483 582 645 525

Counting sort based on the tens place:

143 522 525 582 645 483

Third sort:

Original list: 143 522 525 582 645 483

Counting sort based on the hundreds place:

143 483 522 525 582 645

The final sorted list is: 143 483 522 525 582 645

The time complexity of Quick sort depends on the partitioning scheme and the initial ordering of the elements. In the worst case scenario, when the array is already sorted or contains equal elements, Quick sort has a time complexity of O(n^2). This is because in each recursive call, the pivot chosen will always be the smallest or largest element, resulting in uneven partitioning.

In the given array A = {12, 8, 7, 4, 2, 6, 11}, making a call to Partition(A, 1, 7) means partitioning the array from the first element to the seventh element. The resulting sequence of numbers in A after the partition operation will depend on the chosen pivot. Since the pivot index is not specified, it is not possible to determine the exact resulting sequence without knowing the pivot selection mechanism.

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The area of Carlton Garden is 96 square feet.

The width of the garden is 8 feet

We are asked to find the length of fencing Carlton would need to fence around the garden.

Recall that the area of a rectangular shape is given by

Where L is the length and W is the width.

Let us substitute the values of area and width into the above formula

Therefore, the length of fencing Carlton would need to fence around the garden is 12 feet.

Answer:

665.5

Step-by-step explanation:

840.50 - 175 =

The additional information needed to evaluate the adequacy of the sample size, the type of confirmation used, and the percent of accounts confirmed will depend on the specific context of the study or investigation.

In general, some important pieces of information to consider may include the size and diversity of the population being studied, the level of accuracy or precision desired, the expected effect size or variability of the variables being examined, and any potential biases or confounding factors that could impact the results. Additionally, information about the study design, sampling method, and data analysis techniques may also be important to consider.

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Answer:

Father=36 years old

Step-by-step explanation:

5 people 4 children and a father

average age=12

add the ages

3+5+6+10=24

24+12=36

check the work

36 +24=60

60/5=12

answer=36

Answer:

36 years old

Step-by-step explanation:

The average age of father and four children can be expressed in mathematics as:

\(\displaystyle \large{\dfrac{f+c_1+c_2+c_3+c_4}{5}}\)

The above expression is what you call average value or mostly known as mean - the mean value is sum of all data values divided by number of data values. The formula reference for mean/average value is:

\(\displaystyle \large{\dfrac{x_1+x_2+x_3+...+x_n}{n} = \dfrac{1}{n} \sum_{i=1}^n x_i}\)

Determine or let the following be:

It is also given in the question that children’s ages are 3, 5, 6 and 10. Hence:

\(\displaystyle \large{\dfrac{f+3+5+6+10}{5} = 12}\)

From above, it is also given that average of father’s age and children’s age is 12 years old - that now gives us an equation. What we have to do now is to solve for f.

First, multiply 5 both sides to get rid of denominator.

\(\displaystyle \large{\dfrac{f+3+5+6+10}{5} \cdot 5 = 12 \cdot 5}\\\\\displaystyle \large{f+3+5+6+10=60}\)

Evaluate 3+5+6+10 which equals 24.

\(\displaystyle \large{f+24=60}\)

Next, subtract both sides by 24 to isolate f-term.

\(\displaystyle \large{f+24-24=60-24}\\\\\displaystyle \large{f=36}\)

Finally, we have received the value of term which is f = 36. We know that the term represents father’s age and therefore, father’s age is 36 years old!

If you have any doubts, please let me know in the comment!

Answer:

-12n-28

Step-by-step explanation:

4(-3n-7)

first- use the distribution property (4*-3n and 4*-7)

so, -12n-28

Answer:

-12n -28

Step-by-step explanation:

4(- 3n - 7)

-12n -28

To prove that two triangles are similar, we must show that they have the same shape, but not necessarily the same size. This can be done by showing that the corresponding angles of the two triangles are equal and that the corresponding sides are in proportion.

To do this, we can use the Side-Side-Side (SSS) Similarity Theorem. This theorem states that if all three pairs of corresponding sides of two triangles are in proportion, then the two triangles are similar. To prove this, we must show that the ratio of each pair of corresponding sides is equal.

For example, let's say we have two triangles ABC and DEF. To prove that these two triangles are similar, we must show that the ratio of AB to DE is equal to the ratio of BC to EF. We can do this by solving the following equation:

AB/DE = BC/EF

If the equation is true, then the two triangles are similar.

We can also use the Angle-Angle-Angle (AAA) Similarity Theorem to prove that two triangles are similar. This theorem states that if all three pairs of corresponding angles of two triangles are equal, then the two triangles are similar. To prove this, we must show that the measure of each pair of corresponding angles is equal.

For example, let's say we have two triangles ABC and DEF. To prove that these two triangles are similar, we must show that the measure of angle A is equal to the measure of angle D, the measure of angle B is equal to the measure of angle E, and the measure of angle C is equal to the measure of angle F.

If the measures of the corresponding angles are equal, then the two triangles are similar.

Therefore, to prove that two triangles are similar, we must show that either the corresponding sides are in proportion (using the SSS Similarity Theorem) or the corresponding angles are equal (using the AAA Similarity Theorem).

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Answer:

The formula for circumference of s circle is pi x diameter.

If the circumference is 28 we can divide it by pi to get the Diameter.

28/ pi = 8.9126768131461388030574907488608042739297 rounded to 8.91 (2dp)

The radius is half of the diameter, so this means 8.91 / 2 = 4.46 ft (rounded to 2dp)

Locally weighted linear regression has the advantage of adaptively fitting the data based on the query sample, but it can be computationally intensive and may suffer from overfitting.

In locally weighted linear regression, the contribution to the loss function from a training sample decreases exponentially as the distance between that sample (Xi) and the query sample (Xq) increases. This is due to the weighting factor e^(-d(Xi,Xq)), where d(Xi,Xq) represents the squared Euclidean distance. Samples closer to the query have higher weights, indicating their stronger influence on the prediction.

The objective function to be minimized in locally weighted regression is given by:

J(θ) = ∑[wi * (yi - θ^T * Xi)^2]

Here, wi represents the weight assigned to each sample, yi is the corresponding output, θ represents the model parameters, and Xi is the input feature vector. The goal is to find the optimal θ that minimizes the weighted sum of squared errors.

To derive the gradient-based learning rule, we differentiate the objective function with respect to θ and set it to zero. The resulting equation can be solved iteratively using methods like gradient descent or normal equations to update θ and minimize the objective function.

The strengths of locally weighted linear regression include its adaptability to fit the data around the query sample, allowing for more flexible and accurate predictions in localized regions. However, it can be computationally intensive, especially with large datasets, due to the need to calculate distances and assign weights for each query.

Additionally, the weighting scheme can lead to overfitting if the weights are not carefully tuned, as samples with high weights can dominate the model and potentially introduce bias. In contrast, standard linear regression treats all samples equally, which may be more suitable when the data exhibits global trend, when computational efficiency is a priority.

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Answer:

19 R (remainder) 11

Step-by-step explanation:

Hope this helps! :D

Answer:

19 Remainder 11

Step-by-step explanation:

Answer: X = 83°

Step-by-step explanation:

- Every triangle has three sides that add up to 180 degrees

- On the bottom right we see a right angle with part of it taking 30°

 > Meaning that the rest of the angle is 60°

The top triangle has an angle of 37°

We add the 37° with the 60°. Which will add up to 97°

Since we know that all triangles have interior angles that add up to 180°

we subtract 97° ,from the two angles that we combined to find the missing angle which is X

180 - 97 =  83°

X = 83°

Answer:

17.5%

Convert fraction (ratio) 7 / 40 Answer: 17.5%

Step-by-step explanation:

Brainliest?

Answer:

x:b116.67

Step-by-step explanation:

120/100

140×100/120

Although the sample size is sufficiently big to adopt a normal approximation, the population is increases. He can calculate the confidence interval as a result. Option d is appropriate.

Based on the information given, we can assume that the sample size is large enough (n=50) to use a normal distribution approximation to calculate the confidence interval. The fact that the population is right skewed is not a problem because we are using a normal distribution approximation.

The manager can use the following formula to calculate the confidence interval for the population mean:

CI = X ± z* (σ/√n)

Here X = sample mean = 100,000 hours

z* = z-score for the desired confidence level (e.g., 1.96 for a 95% confidence level)

σ = population standard deviation = 3,000 hours

n = sample size = 50

Since the confidence level is not specified in the problem, let's assume a 95% confidence level. Thus, the z-score for a 95% confidence level is 1.96. Substituting the values into the formula, we get:

CI = 100,000 ± 1.96 * (3,000/√50)

Simplifying the expression, we get:

CI = 100,000 ± 837.83

Therefore, the confidence interval for the average length of life of the electronic components is (99162.17, 100837.83) hours.

The manager can be confident that the true population mean lies within this interval with a 95% confidence level.

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This assumption does not affect the calculation of the confidence interval for the sample mean. Option d. The population is right-skewed, but the sample size is large enough to use a normal approximation. Thus, he can compute the confidence interval.

The manager has a sample size of 50, which is considered a large sample size. Therefore, he can use a normal distribution to compute the confidence interval. Additionally, the sample standard deviation is known, and the sample mean is normally distributed due to the Central Limit Theorem. Hence, he can calculate the confidence interval using the formula:

Confidence interval = sample mean ± (z-score) x (standard error)

where the standard error = standard deviation / square root of sample size.

Since the population is assumed to be right-skewed, it is not appropriate to assume a normal distribution for the individual data points. However, this assumption does not affect the calculation of the confidence interval for the sample mean.

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I would assume that the angle of f equals 50°... sincesince the triangles are similar that means that the angles are most likely equal to each other. since the big triangle you can do it 90 + 40 which equals 130 then 180, since that is the total degrees in a triangle, minus 130 equals 50 this means 50 ° is the angle of c. keep in mind angle c equals angle f.

The fraction that should go in Box A is 9/13,the fraction that should go in Box B is 4/13.

To determine the fractions that should go in the boxes marked A and B, we need to consider the given information.

We know that there are 13 marbles in total, with 9 of them being yellow and the rest being purple. This means that there are 4 purple marbles in the bag.

For Box A, we need to find the probability of picking a yellow marble on the first draw. Since there are 9 yellow marbles and a total of 13 marbles, the probability is:

Probability of picking a yellow marble on the first draw = Number of favorable outcomes / Total number of possible outcomes

Probability of picking a yellow marble on the first draw = 9 / 13

The fraction that should go in Box A is 9/13.

For Box B, we need to find the probability of picking a purple marble on the second draw, given that a yellow marble was picked and replaced on the first draw. Since the marbles are replaced after each draw, the probability remains the same.

The probability of picking a purple marble on the second draw is the same as the probability of picking a purple marble from the original set of marbles, which is:

Probability of picking a purple marble on the second draw = Number of purple marbles / Total number of marbles

Probability of picking a purple marble on the second draw = 4 / 13

The fraction that should go in Box B is 4/13.

Box A: 9/13

Box B: 4/13

Answer:

2.6

Step-by-step explanation:

 A= -1.3

B=1.3

1.3--1.3=2.6

Answer:

2.6 units

Step-by-step explanation:

If you round down the distance is 2. then you all the 2 decimals 0.3 and 0.3 to get 2.6 units.

A rectangle with sodes of lengrh 84 and 45 has the same perimeter asa hexagon. If the sides of the hexagon all have the same length then what is the length of a side of the hexagon

(A) 41

(B) 46

(C) 43

(D) 45

(E)Other

A square has an area of 25. Two opposite side of the square each have their length tripled what is the perimeter of the new figure

(A) 40

(B) 25

(C) 60

(D) 35

(E)Other

A rectangle measures 6 centimeters by 25 centimeters the probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 is p/q are relatively prime positive whole numbers what is the sum of p and q

(A) 5

(B) 19

(C) 37

(D) 47

(E)Other

The three values of x that are solutions to X^3 + mx = 37x^2 +n are positive whole numbers that form a geometric sequence what is the sum of the possible values of the common ration of the geometric sequence

(A) 25/12

(B) 9/4

(C) 7/4

(D) 2

(E)Other

In metric system speed measured by using kilometres per hour and miles per hour units. Thus, the conversion of 180 miles per hour is equals to the 289.68192 kmh.

To convert from one unit of measure to another, multiply by the conversion factor. Speed is defined as the distance an object travels per unit time. This is a scalar value. Some speed units are miles per hour, cm/h, km/h, etc. Miles per hour is a commonly used unit of speed in the United States. That's exactly 1.609344 kilometers per hour. Kilometers per hour, kmh is a unit of speed. Moving at 1 kilometer per hour is moving at about 0.278 meters per second or about 0.621 miles per hour. A value of 180 miles per hour must be defined in kilometers per hour. So 1 mph = 1.609344 kmh

180 mph = 180×1.609344 kmh

= 289.68192 kmh.

Hence, required value is 289.68192 kmh.

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Answer:

  B’

Step-by-step explanation:

You want to know the vertex that has coordinates (24, 12) after dilation by a factor of 6 about the origin.

When the center of dilation is the origin, the scale factor multiplies each coordinate value. Then the coordinates of the original point whose dilated location is (24, 12) is ...

  6(x, y) = (24, 12)

  (x, y) = (24, 12)/6 = (24/6, 12/6) = (4, 2) . . . . . . matches point B

The image point is B'.

On solving the provided question we can say that - and a lines need only two points to drawn; so, yes we can draw a line

A line is an endlessly long object without breadth, depth, or curvature in geometry. Consequently, a line is a one-dimensional entity, while it may also exist in two-, three-, and more-dimensional regions. In common use, a line segment with two points serving as its ends is referred to as a line. A line is a single-dimensional, straight form with no thickness that can go on forever in both directions. To indicate that a line has no "wobble" anywhere along its length, it is frequently referred to as a straight line or an ancient accurate line (Casey 1893)

here we have,

2 points

(1,5) and (4,5)

and a lines need only two points to drawn,

so, yes we can draw a line

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The radius of the container is then r = 1 in. and the height is h = 12.15 in.

The volume of a right circular cylinder is given by the formula V = πr^2h, where r is the radius, h is the height, and π is a constant approximately equal to 3.14. We are given that V = 38 in.3, so we can write the equation 38 = πr²h. To minimize the amount of metal used, we want to minimize either the radius or the height (since the volume is fixed). Since h is squared in the formula, it is more effective to minimize the radius.

If we let r = 1, then the equation becomes 38 = π(1)²h, or 38 = πh. Solving for h, we get h = 38/π ≈ 12.15.

Thus, the radius of the container is then r = 1 in. and the height is h = 12.15 in.

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Step-by-step explanation:

0.01408450704

or the other way around 71

Answer:

Step-by-step explanation:

34/2414= 0.014 (rounded to the thousandth)

or

2414/34= 71

/ means divide btw :)

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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The type of influence on wellness that this represents is given as follows:

A. Social.

An influence on wellness is an activity that improves the morale of certain aspect of our lives.

The aspect improved in this problem is the social aspect, along with the physical aspect, as follows:

Since this is an example of social bonding, option A gives the correct option regarding which type of influence on wellness this is an example of.

For example, reading a book would be intellectual influence, while recycling would be environmental influence.

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The number is 19.

To find the number when the product of 12 and that number is 228, we can use a basic algebraic equation.

Let x be the number we are looking for. Then we can write the equation as:

12x = 228

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 12:

12x/12 = 228/12

x = 19

Therefore, the number we are looking for is 19. We can check our answer by substituting 19 for x in the original equation:

12 x 19 = 228

228 = 228

The equation is true, so our answer of x = 19 is correct. Hence, the number we are looking for is 19.

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Step-by-step explanation:

\(\displaystyle \boxed {y = sin\:(x + \frac{\pi}{2})} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{2}} \hookrightarrow \frac{-\frac{\pi}{2}}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1\)

OR

\(\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1\)

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = sin\:x,\)in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted \(\displaystyle \frac{\pi}{2}\:unit\)to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD \(\displaystyle \frac{\pi}{2}\:unit,\)which means the C-term will be negative, and by perfourming your calculations, you will arrive at \(\displaystyle \boxed{-\frac{\pi}{2}} = \frac{-\frac{\pi}{2}}{1}.\)So, the sine graph of the cosine graph, accourding to the horisontal shift, is \(\displaystyle y = sin\:(x + \frac{\pi}{2}).\)Now, with all that being said, in this case, sinse you ONLY have a wourd problem to wourk with, you MUST use the above formula for calculating the period. Onse you do that, the rest should be easy. Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 0,\)in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

Properties of y = cos(x)

The cosine wave is a sinusoidal function (sine and cosine waves are the same except for a horizontal shift).

It is a continuous function and so its domain is (-∞, ∞)

The center line is y = 0

The Amplitude (the height from the center line to the peak) is 1, and so its range is -1 ≤ x ≤ 1

The y-intercept is at (0, 1)

Its period (length of one wave) is 2π (360°)