Tony puts $9,308.00 into an account to use for school expenses. The account earns 9.45% interest, compounded quarterly. How much will be in the account after 10 years?

a. The distribution of X, the average milk production per cow per day, can be considered approximately normal

b. 80 percent confidence interval for the mean milk production is approximately

c. Margin of error no greater than 0.15 gallons with 95 percent confidence, a sample size of at least 19 cows is required.

a. The distribution of X, the average milk production per cow per day, can be considered approximately normal. This is due to the Central Limit Theorem, which states that for a large enough sample size, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution.

b. To find an 80 percent confidence interval for the mean milk production of all cows on the farm, we can use the formula:

CI = x(bar) ± Z × (σ/√n)

Where:

x(bar) is the sample mean

Z is the Z-score corresponding to the desired confidence level (80 percent in this case)

σ is the population standard deviation

n is the sample size

Using the given values:

x(bar) = 6.28 gallons

σ = 0.42 gallons

n = 12

The Z-score corresponding to an 80 percent confidence level can be found using a standard normal distribution table or calculator. For an 80 percent confidence level, the Z-score is approximately 1.282.

Plugging in the values:

CI = 6.28 ± 1.282 × (0.42/√12) ≈ 6.28 ± 0.316

The 80 percent confidence interval for the mean milk production is approximately (5.964, 6.596) gallons.

c. To find a 99 percent lower confidence bound on the mean milk production of all cows, we can use the formula:

Lower bound = x(bar) - Z × (σ/√n)

Using the given values:

x(bar) = 6.28 gallons

σ = 0.42 gallons

n = 12

The Z-score corresponding to a 99 percent confidence level can be found using a standard normal distribution table or calculator. For a 99 percent confidence level, the Z-score is approximately 2.617.

Plugging in the values:

Lower bound = 6.28 - 2.617 × (0.42/√12) ≈ 6.28 - 0.455

The 99 percent lower confidence bound on the mean milk production is approximately 5.825 gallons.

d. To determine the sample size required to be 95 percent confident with a margin of error no greater than 0.15 gallons, we can use the formula:

n = (Z² × σ²) / E²

Where:

Z is the Z-score corresponding to the desired confidence level (95 percent in this case)

σ is the estimated or known population standard deviation

E is the desired margin of error

Using the given values:

Z = 1.96 (corresponding to a 95 percent confidence level)

σ = 0.42 gallons

E = 0.15 gallons

Plugging in the values:

n = (1.96² × 0.42²) / 0.15² ≈ 18.487

To have a margin of error no greater than 0.15 gallons with 95 percent confidence, a sample size of at least 19 cows is required.

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Answer:

The answer is 25√3cm²

Answer:

triangles have 3 sides. quadrilaterals have 4 sides. also, you have to know a side lenght and height of a triangle to get its area.

if ur talking about equilateral, then it would be 25√3 cm²

The general solution for d^2y/dt^2 - 2dy/dt - 15y = e^4t is a sum of a homogeneous solution (c1e^(r1t) + c2e^(r2t)) and a particular solution (Ate^4t).

What is differentiation ?

Differentiation is a method of finding the derivative of a function. Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.

The general solution for the second-order homogeneous linear ordinary differential equation d^2y/dt^2 - 2dy/dt - 15y = 0 can be found using the characteristic equation:

r^2 - 2r - 15 = 0

The characteristic equation has two roots, which are the eigenvalues of the corresponding homogeneous linear system. Let r1 and r2 be the roots of the characteristic equation, then the general solution for the homogeneous equation is:

y(t) = c1e^(r1t) + c2e^(r2t)

where c1 and c2 are arbitrary constants.

y(t) = c1e^(r1t) + c2e^(r2t) + Ate^4t

The general solution for d^2y/dt^2 - 2dy/dt - 15y = e^4t is a sum of a homogeneous solution (c1e^(r1t) + c2e^(r2t)) and a particular solution (Ate^4t).

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To check whether the given lines are parallel, perpendicular, skew or neither, we will find their direction vectors. If the direction vectors are parallel, then the lines are parallel. If the direction vectors are perpendicular, then the lines are perpendicular. If the direction vectors are neither parallel nor perpendicular, then the lines are skew. If the direction vectors of one line is parallel to the vector joining two points of the other line, then the lines are neither parallel nor perpendicular.

Line 1:x=t−3, y=3t+8, z=5−2tThis line can be written as(r_1): r= a_1+ t u_1where r_1 is the position vector of any point on the line. a_1 = i(-3) + j(8) + k(5) = -3i + 8j + 5k is the point of intersection of the line with the coordinate axis. And u_1 is the direction vector of the line.u_1 = i + 3j - 2k

Line 2: x=2s−1, y=s−1, z=s−4This line can be written as(r_2): r= a_2+ s u_2where r_2 is the position vector of any point on the line. a_2 = i(-1) + j(-1) + k(-4) = -i - j - 4k is the point of intersection of the line with the coordinate axis. And u_2 is the direction vector of the line.u_2 = 2i + j + k Now we will find the direction vectors of the two lines and then check their properties. The direction vectors of the lines areu_1 = i + 3j - 2ku_2 = 2i + j + kSince the direction vectors are not parallel, we need to check whether they are perpendicular or not.u_1.u_2 = (i + 3j - 2k).(2i + j + k) = 2 + 3 - 2 = 3Since u_1.u_2 is not equal to zero, the two lines are neither parallel nor perpendicular to each other. Therefore, the lines are skew lines.

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The last year's salary was Rs 8250 and he is drawing this year Rs 9075.

What is the percentage of a number?

The percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'  known as percentage symbol.

The monthly salary of Mr. Maharjan was Rs 7500 before last year and it was increased by 10% last year.

So, The last year's Salary was 7500 +750 = 8250

Again, it increased by 20% this year.

Then, Drawings of current year = 7500 + 20% of 7500

7500 + 1500 = 9000

8250 + 10% of 8250 = 9075

Drawings of current year = 9075.

Hence, the last year's salary was Rs 8250 and he is drawing this year Rs 9075.

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Answer:

475

Step-by-step explanation:

7.125 x 10^10    = 712.5 x 10 ^8

              divided by 1.5 x 10^8 =    475 time bigger

(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.

This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.

M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.

(B)  1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.

Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.

(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.

The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.

(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).

The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).

Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).

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Values of x and y will be 12 and 5 respectively.

It's given in the question,

Since, expression for the coordinates of a point (h, k) which divides the segment joining points \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio of m : n is given by,

h = \(\frac{mx_2+nx_1}{m+n}\)

k = \(\frac{my_2+my_1}{m+n}\)

Since, R is a point on segment QS dividing in the ratio of 3 : 2, coordinates of R will be,

\(8=\frac{3x+2\times 2}{3+2}\)

\(8=\frac{3x+4}{5}\)

\(3x+4=40\)

\(3x=36\)

\(x=12\)

Similarly, \(3=\frac{3y+2\times 0}{3+2}\)

\(3=\frac{3y}{5}\)

\(3y=15\)

\(y=5\)

       Therefore, values of x and y will be 12 and 5 respectively.

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39 subjects were tested in this simple one-way ANOVA.

The df for F distribution is (treatment df, error df)

Using given information

Treatment df = 7

Error df = 31

Total df= 7+31 = 38

Again, total df = N-1, N= number of subjects tested

Then, N-1 = 38

=> N= 39

One-way ANOVA is typically used when there is a single independent variable or factor and the goal is to see whether variation or different levels of that factor have a measurable effect on the dependent variable.

The t-test is a method of determining whether two populations are statistically different from each other, and ANOVA determines whether three or more populations are statistically different from each other.

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According to the given inequality,

W – 4 > –10 uses Addition Property

12 ≥ 20x not uses Addition Property

7y10 ≤ 5. 5 –3. 25 < x – 9. 75 uses Addition Property

Let's analyze each given inequality to see whether we can use the Addition Property of Inequality to solve them.

W – 4 > –10: We can use the Addition Property of Inequality to solve this inequality. To do this, we need to add 4 to both sides of the inequality, which gives us: W – 4 + 4 > –10 + 4, or W > –6.

12 ≥ 20x: We cannot use the Addition Property of Inequality to solve this inequality since we need to isolate "x" on one side of the inequality. To do this, we would need to subtract 12 from both sides of the inequality, which is not allowed under the Addition Property of Inequality.

7y + 10 ≤ 5.5 – 3.25x: We cannot use the Addition Property of Inequality to solve this inequality either since we need to isolate "y" on one side of the inequality.

To do this, we would need to subtract 10 from both sides of the inequality, which is not allowed under the Addition Property of Inequality.

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Based on the given data set, we can only determine a single mode, which is 4.

To determine the mode(s) of the given data set representing the number of new seeds planted in the garden for 15 varieties of sunflower, we need to find the value(s) that appear most frequently.

Here are the steps to find the mode(s):

1. Organize the data set in ascending or descending order to make it easier to identify repeated values. For example, let's say the data set is: 4, 5, 6, 2, 7, 4, 3, 5, 2, 4, 6, 4, 7, 3, 4.

2. Count the frequency of each value in the data set. In our example, we have:

  - Value 2 appears 2 times.
  - Value 3 appears 2 times.
  - Value 4 appears 5 times.
  - Value 5 appears 2 times.
  - Value 6 appears 2 times.
  - Value 7 appears 2 times.

3. Identify the value(s) with the highest frequency. In our example, the value 4 appears most frequently with a count of 5 times.

Therefore, the mode of the data set is 4, indicating that the number 4 is the most common value among the number of new seeds planted in the garden for the 15 varieties of sunflower.

It's important to note that in some cases, there may be multiple modes if two or more values have the same highest frequency.

However, based on the given data set, we can only determine a single mode, which is 4.

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The expressions that can be used to describe how many milligrams of vitamin C are in the salad are:

(Choice A) 200b + (300s + 42d)

(Choice E) 300s + 200b + 42d

So, the correct answers are A and E.

The milligrams of vitamin C in the salad can be determined by considering the quantities of spinach, berries, and dressing used in the salad, along with their respective vitamin C content.

In the given scenario, the salad includes 300 milliliters (mL) of spinach, 200 mL of berries, and 42 mL of dressing. The vitamin C content is measured in milligrams per milliliter (mg/mL), with values denoted as s for spinach, b for berries, and d for dressing.

To calculate the milligrams of vitamin C in the salad, we can use the expressions provided:

(Choice A) 200b + (300s + 42d)

(Choice E) 300s + 200b + 42d

In Choice A, the expression 200b represents the milligrams of vitamin C in the berries, while (300s + 42d) represents the combined vitamin C content of spinach and dressing.

In Choice E, the expression 300s represents the milligrams of vitamin C in the spinach, 200b represents the milligrams of vitamin C in the berries, and 42d represents the milligrams of vitamin C in the dressing.

By substituting the respective values of s, b, and d into either expression, we can calculate the total milligrams of vitamin C in the salad.

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Answer:

24.

Step-by-step explanation:

The pattern is clearly going up by twos.

So continuing the pattern,

1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

1 2  3   4 5   6   7   8   9   10  11    12   13

The overall probability of selecting three Americans is:5/13 * 4/12 * 3/11 = 5/143 Answer: 5/143

Probability of selecting first American = number of Americans / total number of people= 5 / (5 + 8)= 5 / 13

Probability of selecting the second American = number of Americans / total number of remaining people after selecting the first American

= 4 / 12 (as there will be 12 people remaining after selecting the first American, which includes 4 Americans and 8 Italians)

Probability of selecting the third American = number of Americans / total number of remaining people after selecting the first and second American

= 3 / 11 (as there will be 11 people remaining after selecting the first and second American, which includes 3 Americans and 8 Italians)

Therefore, the overall probability of selecting three Americans is:5/13 * 4/12 * 3/11 = 5/143 Answer: 5/143

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False. Since the domains of X, Y, and Z are the set of real negative numbers, the equation 22 - y2 = x must hold true for all real negative values of x and y.

VzVx3y (22 - y² = x), with the assumption that the domains of X, Y, and Z are the set of real negative numbers. Given this information, the statement is False.

Since the domains of X, Y, and Z are the set of real negative numbers, it means y² will always be positive (as squaring any negative number results in a positive number). Thus, the equation 22 - y² = x cannot hold true because 22 - y² will always be less than 22 (given y² is positive), making x a positive number, which contradicts the given domain of x being negative numbers.

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Answer:

GCF, Greatest Common Factor

Step-by-step explanation:

Hope this helped

Answer:

The answer would be the third option

Step-by-step explanation:

The value of the angle cos(L)° will be 0.42.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is a fundamental area of study in mathematics, with applications in a wide range of fields such as physics, engineering, navigation, architecture, and more.

Given that in a triangle JKL the side KL is 15 and the side JK is 36. The value of cos(L)° is the ratio of the side JK and KL.

cos(L)° = JK / KL

cos(L)° = 15/36

cos(L)° = 0.42

Therefore, the value of the angle cos(L)° will be 0.42.

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Answer:

The unit cubes that are required to create a larger cube with an edge length of 3 units is:

Step-by-step explanation:

To identify the number of cubes you need to create a larger cube, you must think in the number of cubes of the length (3 cubes in this case), and use the exponent 3, because you need to form a cube. Below I'll show you:

To understand it in a better form, suppose that you need a cube with an edge of 5 units, in that case, remember you use the number 5 how base and the exponent is 3, because is a cube, in that case, it would be:

If it wasn't a cube but a square, you must elevate to the number 2, in the case of the cube is elevated to 3, so, the unit cubes that are required to create a larger cube with an edge length of 3 units is 27 cubes.

Answer:

I would say that a is NOT an inverse, however b is.

Step-by-step explanation:

If you look at the two tables for a, you can tell that every pair has swapped places (as they should) except 0 and 9. In which in the second table, what should be the 9 in the x row, is just another 0 in its place.

While if you look at the two tables for b, every single pair has been swapped like it should, meaning the second table is the inverse of the first table.

Hope this helps you btw. I'm sorry if it doesn't though.

Answer:

2 units

Step-by-step explanation:

Congruent triangles are those triangles, which have same shape & size (same side & angle size).

If  ΔEFG ≅ ΔXYZ. And, E (0, 0), F (0, 2), and G (3, 0)

So, length EF = length XY.

Length of E (0,0) & F (0,2) is 2 units

As triangles are congruent, EF = XY

Hence, measure of XY = 2 units

Answer:

2 units

Step-by-step explanation:

The study of statistics rests on two major​ concepts probability which  is the branch of mathematics that deals with the likelihood of events occurring and Data Analysis is the process of examining and interpreting data in order to gain insights and make better decisions

Probability theory is based on the idea that, given enough data, the frequency of an event can be predicted and allows for the formulation of mathematical models that can quantify the likelihood of particular outcomes. Probability is the foundation of statistics and helps to explain the behavior of chance events.It involves the collection, organization, and analysis of data from a variety of sources, such as survey responses, observations, experiments, or existing databases.

Data analysis is used to identify patterns and relationships in data, draw conclusions, and make decisions. It is an important part of statistics, as it helps to uncover insights that would otherwise remain hidden. Data analysis tools, such as statistical models, can be used to gain greater insight into the data.

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Answer:

\(9x + 4 - 3y^2\)

Step-by-step explanation:

Given

\(5x+4x - 1+3 - 7y^2 +2+4y^2\)

Required

Simplify

\(5x+4x - 1+3 - 7y^2 +2+4y^2\)

Collect Like Terms

\(5x+4x - 1+3 +2+4y^2- 7y^2\)

Simplify like terms

\(9x + 4 - 3y^2\)

Hence,

\(5x+4x - 1+3 - 7y^2 +2+4y^2\) \(= 9x + 4 - 3y^2\)

The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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Answer:

(5,0)

Step-by-step explanation:

(x, y)

Answer:

2n+17

Step-by-step explanation:

To determine the exact concentration of the solution made, one can divide the mass of the solute with the volume of the solution.

A solution is the substance formed by the mixture of solute in solvent. The solute may or may not be dissolved in the solution. One can determine the exact concentration of the solution if the mass of solute added in the specific volume of solution is known. If the solution is made by someone else, then its concentration can be determined by process of titration.

The concentration of a solution is expressed in the form of moles or grams per unit liter. If the solution is unknown and only its dissolved chemical is known, then titration will help in determining the closest value of concentration if performed without human error. In titration, the use of glassware that that is more precise than the flasks, beakers, and graduated cylinders are used.

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Refer to complete question below:

How do we determine concentration a solution? If it is a solution that we have made up, we can readily do the calculations required. But what if it is a solution that someone else has made? What technique can be used to gather information about a solution that we are given with no other information than the name of the chemical dissolved.

15 Weeks should be the answer

Answer:

Step-by-step explanation:

\(\frac{x}{(x-2)^{2} } -\frac{x}{(x-2)(x-1)} = \frac{x^{2}-x-x^{2} +2x }{(x-2)^{2}(x-1) }\)

? = 2x -x = x

Answer:

y = 2x - 5

Step-by-step explanation:

Slope intercept form: y = mx + c

3y - 6x = -15

3y = 6x - 15

\(\frac{3y}{3}=\frac{6x}{3} -\frac{15}{3}\\\\y =2x - 5\)