$800 is deposited in an account with a 9% interest rate, compounded continuously. what is the balance after 12 years?

Answer:

I don't see the question but okay can u mark meh.

Step-by-step explanation:

After answering the given query, we can state that  the solutions to the simultaneous equations are (x, y) ≈ (3.1, 10.2) and (x, y) ≈ (-1.9, 0.2).

In mathematics, a linear equation has become one that takes the form y=mx+b. The inclination is B, and the y-intercept is m. Since y and x are variables, the preceding clause is frequently referred by the term a "linear equation involving two variables."

Bivariate linear equations are linear equations with two variables. Linear equations can be found in many places, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When the formula has the structure y=mx+b, where m denotes the slope and b the y-intercept, it is often referred to because of being quadratic.A mathematical equation is said to be linear if its solution has the form y=mx+b, where m stands for the slope and b for the y-intercept.

To show that 3y² - 10y - 24y¯47 = O, we need to find constants C and k such that |3y² - 10y - 24y¯47| ≤ C|y| for all y > k.

3y² - 10y - 24y¯47 ≤ 3y² + 10|y| + 24

3y² + 10|y| + 24 ≥ 3y² - 10y - 24y¯47 for y ≥ 5

C = 6:

|3y² - 10y - 24y¯47| ≤ 6|y| for y ≥ 5

3y² - 10y - 24y¯47 = O.

b) Using the result from part a), we can rewrite the simultaneous equations as:

3y² - 10y - 24y¯47 = O

y - 2x = 4

y = 2x + 4

3(2x + 4)² - 10(2x + 4) - 24y¯47 = O

12x² - 8x - 79 = O

x = (8 ± √(8² + 41279))/24

x ≈ 3.1 or x ≈ -1.9

y ≈ 10.2 or y ≈ 0.2

Therefore, the solutions to the simultaneous equations are (x, y) ≈ (3.1, 10.2) and (x, y) ≈ (-1.9, 0.2).

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Answer:

69

Step-by-step explanation:

Answer:

69 m²

Step-by-step explanation:

The figure is composed of 2 right triangles

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

A of triangle on left is

A = \(\frac{1}{2}\) × 9 × 10 = 45 m²

A of triangle on right is

A = \(\frac{1}{2}\) × 8 × 6 = 24 m²

Total area = 45 + 24 = 69 m²

The individuals in this data set are B) Compression bandage styles

The style tags in the first column is what Alex is surveying.

====================================================

This data set contains A) 3 variables, 1 of which is categorical

The three variables are

The first two are quantitative data. We can do math on them such as finding the average. The last variable is categorical. We cannot apply the average as the average color doesn't really make sense. We simply have a list of labels, so this data is nominal. It is not ordinal because we cannot sort the colors.

Answer:

compression bandages styles

3 variables, 1 of which is categorical

The type of variable that represents the names of the automobile manufacturers would be the categorical variable.

A variable is defined as the quantity that may change within the context of a mathematical problem, research work or an experiment.

There are various types of variables that include the following:

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Answer:

Option (3)

Step-by-step explanation:

The ramp shown in the figure is in the shape of a triangular prism.

Therefore, total surface area of this ramp = Area of the triangular sides + Area of the base + Area of the vertical side + Area of the slanting side

Area of the triangular sides = \(2[\frac{1}{2}(Base)\times (h)]\)

                                              = bh

                                              = 4×3

                                              = 12 square feet

Area of the rectangular base = Length × Width

                                                = 4 × 8

                                                = 32 square feet

Area of the vertical side = Length × Width

                                        = 3 × 8

                                        = 24 square feet

Area of the slanting side = Length × width

                                         = 8×5

                                         = 40 square feet

Total surface area = 12 + 32 + 24 + 40

                              = 108 square feet

Option (3) will be the answer.

Answer:

C (108)  

Im on the test right now  ~edge~

Answer:

To create the histogram, we need to group the data into intervals and count the frequency of each interval. Based on the data, we can create the following intervals:

(0-5), [5-10), [10-15), [15-20), [20-25)

Then, we count the frequency of each interval:

(0-5): 2

[5-10): 3

[10-15): 3

[15-20): 5

[20-25): 3

Using this information, we can create the following histogram:

diff

Copy code

    Frequency

     |     x

     |     x

 x   |     x

 x   |  x  x

 x   |  x  x

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

(0-5) [5-10) [10-15) [15-20) [20-25)

The x-axis represents the intervals, and the y-axis represents the frequency. The title of the histogram could be "Distribution of Broken Tiles in Shipment Received by Belmont Flooring in 2022".

To look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

For a regular polygon with n sides, the sum of its interior angles is given by ((n - 2) × 180) degrees. In the case of a round table seating 6 people, the table can be considered as a hexagon, which has 6 sides. Using the formula, we can calculate the sum of the interior angles:

((6 - 2) × 180) / 6 = (4 × 180) / 6 = 720 / 6 = 120 degrees

Since the table forms a complete circle, the sum of the interior angles is divided equally among the guests. Therefore, each guest sits at an angle of 120 degrees. To look from the guest to their left to the guest to their right, you need to rotate by the angle between adjacent guests, which is half of the angle they sit at:

120 / 2 = 60 degrees

Thus, to look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

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Answer:

32 ounce

Step-by-step explanation:

3.29/20=0.1645

4.49/32=0.1403125

So the second option is cheaper per ounce

a. Decision rule: Reject the null hypothesis if the calculated z-value is less than or equal to -1.28. b. Calculated z-value: -1.8892. c. Conclusion: Reject the null hypothesis, indicating evidence that the population mean is less than 128.

To complete parts (a) through (c), we need to perform a hypothesis test for the given hypotheses

H0: μ = 128 (null hypothesis)

HA: μ ≤ 128 (alternative hypothesis)

Given: X= 119 (sample mean)

σ = 27 (population standard deviation)

n = 46 (sample size)

α = 0.10 (significance level)

a. The decision rule is to reject the null hypothesis if the calculated value of the test statistic is less than or equal to the critical value(s) of the test statistic. Since the alternative hypothesis is one-sided (μ ≤ 128), we will use a one-sample z-test and compare the calculated z-value with the critical z-value.

To find the critical z-value, we need to determine the z-value corresponding to the significance level α = 0.10. Looking up the critical value in the standard normal distribution table, we find that the critical z-value is -1.28 (rounded to two decimal places).

b. The calculated value of the test statistic, in this case, is the z-value. We can calculate the z-value using the formula

z = (X - μ) / (σ / √n)

Substituting the given values:

z = (119 - 128) / (27 / √46) ≈ -1.8892 (rounded to two decimal places)

c. The conclusion is based on comparing the calculated value of the test statistic with the critical value. Since the calculated z-value of -1.8892 is less than the critical z-value of -1.28, we have enough evidence to reject the null hypothesis. Therefore, we conclude that the population mean is less than 128.

The conclusion statement in part (c) is inconsistent with the given alternative hypothesis and should be revised accordingly.

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Answer:

13$

Step-by-step explanation:

Dan purchased a set of knitting needles for $11 and 6 identical packs of yarn. The total cost was $89.

How muc\(rweds\)h did each pack of yarn cost?

The total cost of each pack of yarn is $13.

The total cost of an item is the sum of the cost of all items that are purchased. Total cost for more items can be found by multiplying the number of items and the cost of the individual item.

For the given situation,

There are two items purchased knitting needles and packs of yarn.

Cost of knitting needle = $11

Number of packs of yarn purchased = 6

Total cost = $89

Let the cost of yarn be x.

The cost of the yarn can be find by using the equation,

Total cost = Cost of knitting needle + (number of yarn purchased × x)

⇒ \(89=11+6x\)

⇒ \(6x=78\)

⇒ \(x=13\)

Hence we can conclude that the cost of each pack of yarn is $13.

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Answer:

10.5 children play football

Step-by-step explanation:

10.5+10.5+21=42

Answer: 35 children

Step-by-step explanation:

Let the number of children who play only football be f , the number of children who play only

tennis be t and the number of children who play both sports be b.

Since there are 42 children, f + t + b = 42.

Also, since the number of children who play tennis is equal to the number of children who play

only football, t + b = f . Therefore f + f = 42. So f = 21 and t + b = 21.

Finally, twice as many play both tennis and football as play just tennis. Therefore b = 2t.

Substituting for b, gives t + 2t = 21. Hence t = 7.

Therefore the number of children who play football is 42 − t = 42 − 7 = 35.

The specific details of the car-following model, such as acceleration and deceleration behavior, can vary depending on the chosen model. Additionally, you may need to consider factors like traffic conditions, driver behavior, and road characteristics to create a more accurate simulation.

To simulate their behavior, we can follow these steps:

1. Initialize the positions and velocities of both vehicles.
  - Vehicle 1: Position = 0, Velocity = 17 m/s
  - Vehicle 2: Position = 0, Velocity = 17 m/s

2. Calculate the distance between the two vehicles using the equation:
  Distance = Position of Vehicle 2 - Position of Vehicle 1

3. Determine the desired following distance between the vehicles. Let's say it is 10 meters.

4. Calculate the relative velocity between the vehicles using the equation:
  Relative Velocity = Velocity of Vehicle 2 - Velocity of Vehicle 1

5. Apply the car-following model to update the velocities of both vehicles. This model can be based on the relative velocity and distance between the vehicles. One commonly used model is the "Intelligent Driver Model (IDM)".

6. Update the positions of both vehicles based on their velocities and the system update time (0.5 seconds).

7. Repeat steps 2 to 6 until the desired simulation time is reached.

By following these steps, you can simulate the car following behavior for the given situation using a system update time of 0.5 seconds and initial speeds of 17 m/s for both vehicles.

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The quota sampling produces the same advantages for convenience sampling that stratified random sampling produces for probability sampling.

Sampling:

Sampling is defined as the process in statistical analysis where researchers take a predetermined number of observations from a larger population.

Given,

Here we need to find the type of sampling that produces the same advantages for convenience sampling quota sampling.

Before, move on to the result, first we have to know the details about quota sampling and the probability sampling.

Probability sampling defined as the selection of a sample from a determined number of population, when this selection is based on the principle of randomization, that is, random selection or chance.

In contrast to probability sampling, Quota sampling means a non-probability sampling method in which researchers create a sample involving individuals that represent a population.

Based on these definition we have identified that the method that is best suitable answer for this one is stratified random sampling.

Because the stratified random sampling means, is a probability sampling technique in which the total population is divided into homogenous groups to complete the sampling process.

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To determine Bob's expected utility for each option, we calculate the utility for each outcome and weigh them by their respective probabilities.

Option A:

Expected utility = 0.5v(316 - 30) + 0.5v(4 - 0)

= 0.5v(48) + 0.5v(4) = 0.548 + 0.54 = 26.

Option B: Expected utility = v(8) = 8.  

Bob would choose Option A as it has a higher expected utility.

ii. Option A: Expected utility = 0.5v(-16) + 0.5v(-4) = 0.5*(-32) + 0.5*(-8)

= -20.

Option B: Expected utility = v(-12) = -24. Bob would choose Option B as it has a higher expected utility.

iii. Option A: Expected utility = 0.5v(8) + 0.5v(-4) = 0.58 + 0.5(-8) = 0. Option B: Expected utility = v(1) = 1.  Bob would choose Option B as it has a higher expected utility.

 (b) If Bob buys the hammer for $2, his utility would be v(-2) = -4. If he does not buy the hammer, his utility would be v(0) = 0. Bob would prefer not to buy the hammer since the utility is higher at 0.

(c) If Bob sells the hammer for $2, his utility would be v(2) = 2. If he does not sell the hammer, his utility would be v(0) = 0. Bob would prefer to sell the hammer since the utility is higher at 2. (d) Bob's buying price is not the same as his selling price.

This concept is known as loss aversion, where individuals tend to value losses more than equivalent gains. One study that demonstrates a similar concept is the "Prospect Theory" by Daniel Kahneman and Amos Tversky, which shows how people's decision-making is influenced by the potential for gains and losses and how they weigh them differently.

The study revealed that individuals are generally more averse to losses and are willing to take greater risks to avoid losses compared to the risks they are willing to take for potential gains of equal value.

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If line J is perpendicular of line K, they should cross to make an X. If the slope of line K is -5, Line J would be 5.

The parametric equations for the line are:x = 2t + 6 y = t - 3

We can use the point-slope form of the equation of a line to get the parametric equations of the curve:

Let the parameter t represent the distance along the line from the point (6,-3). Let (x,y) be any point on the line. Then the slope of the line is 1/2, so we have:

(y - (-3)) / (x - 6) = 1/2

Multiplying both sides by (x - 6) and simplifying, we get:

y + 3 = (1/2)x - 9/2

y = (1/2)x - 15/2

Now, to get the parametric equations, we can substitute x = 2t + 6 (since the slope of the line is 1/2) and simplify:

y = (1/2)(2t + 6) - 15/2

y = t - 3

So the parametric equations for the line are:

x = 2t + 6

y = t - 3

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Answer:

It's either b or d more likely d though.

Step-by-step explanation:

The correct new balance on Lisa Valente's credit card statement is $265.17.

1. Start with the given information: Unauthorized sales slip = $82.59, Incorrectly listed sales slip = $24.68 listed as $42.68, Current balance = $329.76.

2. Deduct the amount of the unauthorized sales slip from the current balance: $329.76 - $82.59 = $247.17.

3. Deduct the difference between the incorrectly listed sales slip and the actual amount from the previous result: $247.17 - ($42.68 - $24.68) = $247.17 - $18 = $229.17.

4. Finally, add the correct amount of the incorrectly listed sales slip to the previous result to obtain the correct new balance: $229.17 + $24.68 = $265.17.

Therefore, the correct new balance on Lisa Valente's credit card statement is $265.17.

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Marginal means refers to the average of all participants on one level of the independent variable, ignoring the other independent variable.

A marginal value can be defined as a value that is valid under specific conditions, the change in a value brought on by a particular change in an independent variable, whether that independent variable or a dependent variable, or any combination of these.

In statistical modeling, experimental sciences, and mathematical modeling, there are dependent and independent variables. Dependent variables are so named because they are studied in an experiment under the assumption or demand that they are dependent on the values of other variables according to some rule or law.

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Using the cosine rule, the equation to use to solve for x is: x = √(4.0² + 4.7² − 2(4.0)(4.7) × cos(41)) ≈ 3.1 cm.

The cosine rule is given as, c = √(a² + b² − 2ab × cos(C))

Given the following:

Plug in the values:

x = √(4.0² + 4.7² − 2(4.0)(4.7) × cos(41))

x ≈ 3.1 cm

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Answer:

OG, OC, TG, TC, VG, VC

Step-by-step explanation:

Soups: O, T, V

Salads: G, C

For each soup, he can choose 2 salads.

OG, OC, TG, TC, VG, VC

The sample space represents all the possible ways to choose one soup and one salad is {OG, OC, TG, TC, VG, VC}.

Sample space is the set of all the possible values or the outcomes of a event.

Let suppose the coin are tossed two times. Then the set of possible outcome or sample space of it can be given as,

\(S=\{HH,HT,TH,TT\}\)

Here, H denotes the head and T denotes the tail part of the coin.

A customer at a restaurant can choose a soup and a salad from the menu choices shown.

For this menu the customer choose one onion as soup and one garden as salad which can be represented as (OG). Similarly, the sample space of his choice can be,

\(\{OG, OC, TG, TC, VG, VC\}\)

Thus, the sample space represents all the possible ways to choose one soup and one salad is {OG, OC, TG, TC, VG, VC}.

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Answer:

You will wait for 11 minutes

Step-by-step explanation:

Find the number of minutes between 5:00am and 8:37am

60 mins in an hour.

8-5=3 hours

60x3=180+37=217 minutes

Divide 217 by 12 to see how many bus stops have already been made

217/12=18

18*12=216

217-216=1 minute

12-1=11 minutes

Therefore you will have to wait 11 minutes.

Hope this helps!

Answer:

11 minutes

Step-by-step explanation:

you will have to wait 11 minutes. the last bus arrived at 8:36 am

Answer:

354

Step-by-step explanation:

276+78

354

The skier's displacement from his starting point is 127.179 m and makes an angle of 33.78°.

The law of cosines, commonly referred to as the cosine rule or the cosine formula, in trigonometry essentially connects the length of the triangle to the cosines of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.

Given A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º

base distance = 100 m

We will utilize the cosine rule to determine the magnitude of displacement because the triangle formed by the starting point, where he begins to ascend, and the ending point does not have a 90-degree angle. Cosine law requires a triangle with two sides and an angle between them, both of which are present.

a² = b² + c² - 2.b.ccos(α)

here a is the length of the third side,

b = base = 100m

c = 35 m

and α = 180 - 35 = 135°

so a² = b² + c² - 2.b.ccos(α)

a² = 100² + 35² - 2(100)(35)cos(135)

a² = 10000 + 1225 + 4949.74

a² = 16174.74

a = 127.179 m

and the angle between sides 100m and 127.179 m is given by

cosβ = (a² + c² - b²)/2a.c

cosβ = (127.179² + 35² - 100²)/2(127.179)(35)

cosβ = 0.831

β = cos⁻¹(0.831)

β = 33.78°

Hence displacement from the starting point is 127.179 m and forms an angle of 33.78°.

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Answer:

The left

Step-by-step explanation:

4×3=12-5=7

7=7

Answer:

The answer is 4x-5\(\leq\)7

Step-by-step explanation:

4x-

Answer:

Here are the steps in the correct order to prove that if 7n + 4 is even, then n is even using contraposition:

Assume that n is odd. (This is the contrapositive of the original statement.)

n can be written as 2k + 1 for some integer k.

Substitute 2k + 1 for n in the expression 7n + 4 to get 14k + 11.

Rearrange the expression 14k + 11 to get 2(7k + 5) + 1.

The obtained integer is 1 more than 2 times an integer, so it is odd.

Therefore, if 7n + 4 is odd (by contrapositive), then n is odd as well (by step 5).

Therefore, if n is even, then 7n + 4 is odd (by contrapositive).

Therefore, if 7n + 4 is even, then n is even (by contrapositive).

So, the correct order is:

Assume that n is odd.

n can be written as 2k + 1 for some integer k.

Substitute 2k + 1 for n in the expression 7n + 4 to get 14k + 11.

Rearrange the expression 14k + 11 to get 2(7k + 5) + 1.

The obtained integer is 1 more than 2 times an integer, so it is odd.

Therefore, if 7n + 4 is odd (by contrapositive), then n is odd as well (by step 5).

Therefore, if n is even, then 7n + 4 is odd (by contrapositive).

Therefore, if 7n + 4 is even, then n is even (by contrapositive).

The correct order to prove that if 7n + 4 is even, then n is even using contraposition is as follows:
1. Assume that n is odd.
2. n can be written as 2k +1 for some integer k.
3. Then 7n + 4 = 7(2k + 1) + 4 = 14k + 11 = 2(7k + 5) + 1.
4. The obtained integer is 1 more than 2 times an integer, so it is odd.
5. Therefore, if n is odd, then 7n + 4 is odd.
6. By contraposition, if 7n + 4 is even, then n is even.

So the correct order of the options is: 1, 2, 3, 4.

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we need a sample size of at least 248 to have a probability of 0.8664 that the sample mean is within 0.8 of the population mean.

Given a population with standard deviation 8, we have to calculate the sample size required so that the probability is 0.8664 that the sample mean is within 0.8 of the population mean.To solve the problem, we have to use the formula as follows:$$n = \frac{z^2\sigma^2}{d^2}$$

Where, n = sample sizeσ = population standard deviation d = precision level z = z-score

So, z can be found using the standard normal table. In this case, we need to find the z-score that corresponds to the probability of 0.8664 plus half of the remaining probability of 1 - 0.8664, which is equal to 0.0668.Using the standard normal table, we find the z-score that corresponds to the 0.9334 probability, which is 1.48 (approximately).Now, we can substitute all the values into the formula and solve for n.$$n = \frac{z^2\sigma^2}{d^2}$$$$n = \frac{(1.48)^2 \cdot 8^2}{(0.8)^2}$$$$n = 247.15$$

Therefore, we need a sample size of at least 248 to have a probability of 0.8664 that the sample mean is within 0.8 of the population mean.

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The needed sample size is given as follows:

n = 250.

We first must use the z-score formula, as follows:

\(Z = \frac{X - \mu}{\sigma}\)

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: \(s = \frac{\sigma}{\sqrt{n}}\).

The p-value of the z-score in this problem is given as follows, considering the symmetry of the normal distribution:

0.5 + 0.8864/2 = 0.9432.

Hence the z-score is given as follows:

z = 1.58.

Then the sample size is obtained as follows:

\(1.58 = \frac{0.8}{\frac{8}{\sqrt{n}}}\)

\(\sqrt{n} = 15.8\)

n = 15.8²

n = 250.

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Answer:

375

Step-by-step explanation: sorry if I got it wrong I just learned this

Answer:

In the diagram below O is circumscribed about quadrilateral DEFG.