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If £2000 is placed into a bank account that pays 3% compound interest per year,
how much will be in the account after 2 years?​

We have translated the given phrase into a variable expression as (1/9) × (x - 15).

To translate the given phrase "the product of one-ninth and the difference of a number and fifteen" into a variable expression, we can use the following:

1: Identify the unknown or variable number in the expression.

Let's say the variable number is 'x'.

2: Translate the phrase "one-ninth" to a fraction as 1/9.

3: Translate the phrase "the difference of a number and fifteen" to a mathematical expression.

As we have taken 'x' as the variable number, the difference of 'x' and fifteen can be written as (x - 15).

4: Combine the above expressions using the multiplication sign to get the variable expression.

So, the variable expression is:(1/9) × (x - 15)

The variable expression obtained is (1/9) × (x - 15). Hence, we have translated the given phrase into a variable expression using the required terms.

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The sample variance is the most accurate point estimate of the population variance sigmasquared.

The best point estimate of the population variance is the sample variance. This is because the sample variance is an unbiased estimator of the population variance, meaning that it is the most accurate estimate of the population variance. The sample variance is calculated by taking each individual data point, subtracting the sample mean, squaring the result, and then summing the results. The sample variance then is the sum of these squared differences divided by the number of data points minus one. This is a consistent estimator, meaning that it will always produce the same result even if the sample size is different. This is why the sample variance is the best point estimate for the population variance.

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Yes, you can find the standard error now by taking the standard deviation divided by the square root of the sample size.

The standard deviation in a data set is the mean deviation of the data from their mean.

For sample size n for a data set with data points X1, X2, X3……..Xn for exact standard deviation:

1. Calculates the arithmetic mean M of the set data by adding them all and dividing by n.

M = ( X1+X2+ X3+…..+Xn) / n

2. Calculate the deviation (D) for each data point from the mean M

D = (Xi-M) for all

3. Squaring and sum of all deviations, sum of squares (SS)

4. Divide SS by n.This quantity is the sample variance V

5. Take the square root of V.

6. This quantity is the sample standard deviation, SD.

There are some specific terms and issues to consider. If you are estimating the standard deviation of a population from a sample and the population mean $ is not known, M serves as an unbiased estimate of $. Again, SS is divided by (n-1), not n.

The resulting standard deviation is an unbiased estimate of the population standard deviation based on the sample size, n. If the population mean is known, use that mean instead of the sample mean. , and the SD of the sample is only calculated for n through SS dives.

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The large-sample confidence interval for comparing two proportions can be used when certain conditions are met.

The large-sample confidence interval for comparing two proportions can be used when the following conditions are satisfied:

Under these conditions, the large-sample confidence interval can provide a reasonable estimate of the true difference between the two proportions. It is important to note that this method relies on asymptotic approximations and may not be accurate for small sample sizes or when the conditions are not met. In such cases, alternative methods like exact tests or simulation-based approaches may be more appropriate.

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Answer:

20.4 ft

Step-by-step explanation:

Since they're similar triangles (same shape, but not necessarily the same size), then you can set them up as fractions to find the missing measure.

6/9.7 = ?/33

A quick way to do use this setup is to multiply 33 by 6, then divide by 9.7.

This gives you 20.4 ft

The sample size required in this case is 71 pupils, which must be tested in order for the margin of error to be equal to 3 points.

When it comes to statistics, selecting a relatively small representative sample and conducting hypothesis testing on it typically makes it easier to analyze a large population. By boosting the sample size, the margin of error, which represents the sampling procedure's statistical precision, can be decreased.

From standard normal tables,

P( -2.326 < Z < 2.326) = 0.98 here

The sample size required here is computed as:

n = [(z * α) / МОЕ]² = [(2.326 * 18) / 5]² = 70.12

Therefore, the required sample size, in this case, is 71.

To ensure that the margin of error is equivalent to 3 points, 71 students must be assessed.

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COMPLETE QUESTION:

An IQ test is designed to have scores that have a standard deviation of a 10. A simple random sample of students at a torgo university will be given the test in order to construct a 95% confidence interval for the mean 10 of all students at the university. How many students must be tested so that the margin of error will be equal to 3 points? The sample size required for the desired margin of error is.(Round your answer to next whole number.)

Answer:

a is 1

b is 1,5

Step-by-step explanation:

lol

The X value corresponding to z = -2.00 is 60. The X value corresponding to z = -2.00 is 60. This means that the observation with a z-score of -2.00 is 60 units below the population mean of 80.

To find the X value corresponding to z = -2.00, we can use the formula:
z = (X - µ) / σ
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60

The z-score measures the number of standard deviations an observation is from the mean. In this case, the given z-score of -2.00 indicates that the observation is 2 standard deviations below the mean.
To find the corresponding X value, we use the formula:
z = (X - µ) / σ
Where z is the standard normal distribution value, X is the corresponding raw score, µ is the mean of the population, and σ is the standard deviation of the population.
Substituting the given values, we get:
-2.00 = (X - 80) / 10
Solving for X, we get:
X = (-2.00 x 10) + 80
X = 60

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Answer:

\(x= i\\\\ x = -i \\\\x=\sqrt 2\\\\x = -\sqrt 2\)

Step-by-step explanation:

\(~~~~~~x^4 -x^2 -2=0\\\\\implies x^2 \cdot x^2-2x^2 +x^2 -2 = 0\\\\\implies x^2(x^2 -2) +(x^2 -2) =0\\\\\implies (x^2 +1)(x^2 -2) = 0\\\\ \implies x^2 +1=0~~~~~~~~\text{or}~~~~~~~~~x^2 -2 = 0\\\\ \implies x = \pm\sqrt{-1}~~~~~~~\text{or}~~~~~~~~~~ x = \pm\sqrt 2\\\\\implies x= \pm i~~~~~~~~~~~~~\text{or}~~~~~~~~~ x= \pm\sqrt 2\)

Temperature of refrigerators - Cannot determine. Horsepower of race car engines - Ratio. Marital status of school board members - Nominal. Ratings of television programs - Ordinal. Ages of children enrolled in a daycare - Interval

The level of measurement for the temperature of refrigerators cannot be determined based on the given information. The temperature could potentially be measured on a nominal scale if the refrigerators were categorized into different temperature ranges. However, without further context, it is not possible to determine the specific level of measurement.

The horsepower of race car engines can be measured on a ratio scale. Ratio scales have a meaningful zero point and allow for meaningful comparisons of values, such as determining that one engine has twice the horsepower of another.

The marital status of school board members can be measured on a nominal scale. Nominal scales are used for categorical data without any inherent order or ranking. Marital status categories, such as "married," "single," "divorced," etc., can be assigned to school board members.

The ratings of television programs, such as "poor," "fair," "good," and "excellent," can be measured on an ordinal scale. Ordinal scales represent data with ordered categories or ranks, but the differences between categories may not be equal or measurable.

The ages of children enrolled in a daycare can be measured on an interval scale. Interval scales have equal intervals between values, allowing for meaningful differences and comparisons. Age, measured in years or months, can be represented on an interval scale.

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The decimal construction of 5 /13 repeats and can be written as 0 384615384615 .The 99th digit to the right of the decimal point in the decimal construction of 5/13 is 4.

To find the 99th digit to the right of the decimal point in the repeating decimal construction of 5/13, we need to determine the repeating pattern of the decimal representation.

The pattern in the decimal construction of 5/13 is 384615 repeating. This pattern consists of six digits: 3, 8, 4, 6, 1, and 5, which repeat indefinitely.

Since the pattern repeats every six digits, we can divide 99 by 6 to find the number of complete repetitions. The quotient is 16, and the remainder is 3.

The first three digits in the repeating pattern are 3, 8, and 4. Therefore, the 99th digit to the right of the decimal point will be the third digit of the repeating pattern, which is 4.

The 99th digit to the right of the decimal point in the decimal construction of 5/13 is 4.

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We will add 2 ml of klotrix to the orange juice for a 20.5kg patient.

We know that , 1 kg=2.20462 pounds

Therefore, 20.5kg=20.5x2.20462 pounds= 45.195 pounds or 45.195 lb

Additionally we have, 1 lb = 0.35 mEq

Therefore, 45.195 lb=  0.35 mEq × 45.195 = 15.818 mEq.

Also, 8mEq=1 mL

By using unitary method,

1 mEq=1/8 mL

Converting 15.818 mEq to mL, we get

15.818mEq = 15.818 ÷ 8 = 1.9 mL

Thus, 15.818mEq  = 1.9 mL

Rounding off the answer we get,

The amount of klotrix required to add to the orange juice for a 20.5 kg patient is 2mL

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Answer:

5040

Step-by-step explanation:

an illustration of permutations

The given parameter is:

number of days

dinners for 7 days

Substitute known values

The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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Answer: Choice B.

ln(3) + ln(4) + ln(5) + ln(6)

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

Explanation:

Refer to the diagram below. It shows four rectangles each of base 1. Their height varies depending on the output of the natural log function.

More specifically the heights are ln(3), ln(4), ln(5) and ln(6) from left to right. Note how this corresponds exactly to the points on the y = ln(x) curve such that they are the upper right corners of the Riemann Sum rectangles. These corner points are points A,B,C,D.

Since each base is 1 unit wide, this means each rectangle's area is equal to the height. More thoroughly, we say that

area = base*height = 1*f(x) = f(x), where x takes on the values from {3,4,5,6}

Side note: As the diagram shows, we have an overestimate of the actual area under the curve from x = 2 to x = 5.

Answer:

Step-by-step explanation:

To find when people stop watching the video, we need to find the maximum point of the quadratic function y = -0.75x² + 9.75x.

The x-coordinate of the maximum point of a quadratic function can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic function.

Using the formula with a = -0.75 and b = 9.75, we get:

x = -9.75 / 2(-0.75)

x = -9.75 / -1.5

x = 6.5

Therefore, the maximum number of views per day will occur on the 6.5th day after the video was posted.

To determine when people stop watching the video, we need to check the values of y after this point.

When x > 6.5, the quadratic function becomes negative, which means that the number of views per day will start to decrease. Therefore, people stop watching the video after 6.5 days (or sometime around the 7th day).

The eccentricity of the conic section below is: A. closer to 0 than 1.

In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.

In Mathematics, there are four (4) types of conic section and these include the following with their eccentricity:

In this context, we can reasonably infer and logically deduce that the eccentricity of the conic section is closer to zero (0) than one (1) because it represents a circle.

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Answer:

Step-by-step explanation:

Given:

Isolate the term of x from one side of the equation.

Use the distributive property.

DISTRIBUTIVE PROPERTY:

\(\Longrightarrow: \sf{A(B+C)=AB+AC}\)

Each term within the parentheses can be multiplied by a factor outside the parentheses.

3(x+1)

3*x=3x

3*1=3

Rewrite the expression down.

3x+3

3x+3+2(3x+4)

Multiply expand.

2(3x+4)

2*3x=6x

2*4=8

6x+8

3x+3+6x+8

Combine like terms.

3x+6x+3+8

Add the numbers from left to right.

3+8=11

3x+6x+11

Add.

Solutions:

3x+6x=9x

\(\Longrightarrow: \boxed{\sf{9x+11}}\)

I hope this helps. Let me know if you have any questions.

The explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have given:

\(\rm a_n=3+a_n_-_1\) and

\(\rm a_1=5\)

\(\rm a_n-a_n_-_1= 3\)

The above expression represents the common ratio:

d = 3

First term:

a = 5

The explicit rule for the arithmetic sequence:

a(n) = 5 + (n - 1)3

a(n) = 3n + 2

Thus, the explicit rule for the arithmetic sequence for the sequence is a(n) = 3n + 2.

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To convert the FSM (Finite State Machine) to a controller using a state register and logic gates, follow these steps:
1. Identify the states of the FSM: Review the FSM you created for exercise 3.30 and list down all the states it contains.

2. Design the state register: Create a state register that can store the different states of the FSM. You can use flip-flops or any other suitable storage device.

3. Implement the logic gates: Use logic gates (such as AND, OR, and NOT gates) to implement the transitions between different states. Connect the outputs of the logic gates to the inputs of the state register.

4. Connect the state register to the FSM: Connect the outputs of the state register to the inputs of the FSM to control its behavior based on the current state.

5. Test and verify: Test the controller by simulating different inputs and checking if it transitions between the states correctly according to the desired behavior of the original FSM.

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For this problem, let's pick (2x - 4) and (3x + 7) as the two binomial factors.

To multiply two binomials, we use the FOIL method, which stands for First, Outer, Inner, Last.

First: Multiply the first term of each binomial together, which gives 2x × 3x = 6x²

Outer: Multiply the outer terms of each binomial together, which gives 2x × 7 = 14x

Inner: Multiply the inner terms of each binomial together, which gives -4 × 3x = -12x

Last: Multiply the last term of each binomial together, which gives -4 × 7 = -28

Then, we combine the like terms to get the final result:

(2x - 4)(3x + 7) = 6x² + 14x - 12x - 28 = 6x² + 2x - 28

To factor by grouping, we first group the terms in pairs:

(2x - 4)(3x + 7) = (2x + ?)(3x + ?)

We want to fill in the question marks with two numbers that multiply to give 6x² and add up to 2x. The numbers are 6x and 1x:

(2x - 4)(3x + 7) = (2x + 6x)(3x + 1) - 4(3x + 1) = (2x + 6x - 4)(3x + 1) = 2( x + 3 )( 3x + 1 )

The expressions in 2) and 3) are the same because they are both equivalent forms of the same polynomial. The FOIL method in step 2) expands the polynomial, while the factor by grouping method in step 3) breaks it down into its factors. Since multiplication is distributive over addition, the product of the factors in step 3) can be expanded using the distributive property to give the polynomial obtained in step 2).

Answer:

The y-intercept is 6

Step-by-step explanation:

The y-intercept of a function is where the graph of an equation touches or crosses the vertical axis. This is usually the value of y when x = 0.

For this particular function, when x = 0 ⇒

f(0) = 0^2 + 4(0) + 6

= 0 + 0 + 6

= 6

Therefore, the y-intercept of this function is 6

Answer:

6

Step-by-step explanation:

the y-intercept is the last number of the equation

so because 6 is the last number, the y-intercept is 6

Answer:

NO

Step-by-step explanation:

Because the sum of the interior angles of a triangle have to be equal to 180

ANSWER: No

i just needed to answer a question to continue...

Answer: y=4 or y= 4 over 3

Step-by-step explanation:

Answer:

y=4

Step-by-step explanation:

Answer: 38

Step-by-step explanation:

Subtract 1/8 from 1/2

12 - 18 is 38.

Steps for subtracting fractions

Find the least common denominator or LCM of the two denominators:

LCM of 2 and 8 is 8

Next, find the equivalent fraction of both fractional numbers with denominator 8

For the 1st fraction, since 2 × 4 = 8,

12 = 1 × 42 × 4 = 48

Likewise, for the 2nd fraction, since 8 × 1 = 8,

18 = 1 × 18 × 1 = 18

Subtract the two like fractions:

48 - 18 = 4 - 18 = 38

Using the inscribed angle theorems, the measure of the indicated angles are:

1. m∠BOA = 26°

2. m∠BDA = 13°

3. m∠BCA = 13°

Based on the inscribed angle theorem, the following relationships are established:

Given:

Intercepted arc BA = 26°

1. ∠BOA is central angle

Thus:

m∠BOA = 26° (inscribed angle theorems)

2. ∠BDA is inscribed angle.

m∠BDA = 1/2(30) = 13° (inscribed angle theorems)

3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)

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Answer: I believe the answer is x = 38°

114° / 3

x = 38°

Hope this helps :)