Mark opens a bank account with $20. He plans to put in $5 each week.

Complete the table below to show the total amount of money Mark has in his bank account from 0 to 10 weeks.

Time
(weeks)
0
1
2
3
4
5
6
7
8
9
10
Money ($)
$20
Make sure to align the money next to the weeks

The technique often used to prove the correctness of a recursive function is **mathematical induction**.

Mathematical induction is a method of proof used to establish that a property holds for all natural numbers (or a well-ordered set). It consists of two steps:

1. **Base Case**: The base case establishes that the property holds for a specific initial value or base case. It typically involves showing that the property is true for the smallest possible input or base case of the recursive function.

2. **Inductive Step**: The inductive step demonstrates that if the property holds for a specific value, it also holds for the next value. This step involves assuming that the property is true for a certain input, and then proving that it holds for the subsequent input using the recursive definition of the function.

By proving that the base case is true and showing that the inductive step holds, mathematical induction establishes the correctness of a recursive function for all valid inputs.

The other options you mentioned, such as commutativity, diagonalization, and matrix multiplication, are not directly related to proving the correctness of recursive functions. Commutativity refers to the order of operations or elements, diagonalization is a technique used in mathematics and logic, and matrix multiplication is a mathematical operation for matrices. While these concepts may have applications in other areas of mathematics and computer science, they are not specifically used for proving the correctness of recursive functions.

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The length of the two diagonals of a rhombus if one is twice as long as the other are 10 and 20.

Given that the length of two diagonals of the rhombus are 10 and 20.

Let d1 and d2 be the lengths of the diagonals of the rhombus. Since the area of the rhombus is 100, we have:

d1 * d2 / 2 = 100

We are also given that one diagonal is twice as long as the other, so:

d1 = 2d2

Substituting d1 = 2d2 into the first equation, we get:

2d2 * d2 / 2 = 100

d2^2 = 100

d2 = 10 or -10 (we ignore the negative solution)

Since d1 = 2d2, we have d1 = 20.

Therefore, the length of the two diagonals of the rhombus are 10 and 20.

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6 x 10 - 59.94 = 0.06

Based on the provided information, the Type 1 error is that you conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds. (Option C)

In statistical hypothesis testing, a Type I error refers to the rejection of null hypothesis when it's actually true while a type II error is the failure to reject a null hypothesis that is actually false. Type I error means to conclude that results are statistically significant when, in actuality they are caused purely by chance or because of unrelated factors. The risk of committing this error is the significance level (alpha or α) chosen. As the null hypothesis states that weightlifting bar can withstand weights of 800 pounds or less while alternative hypothesis states that weightlifting bar can withstand weights of over 800 pounds, the type I error would be to conclude that weightlifting bar can withstand weights of greater than 800 pounds when, in fact, it cannot.

Note: The question is incomplete. The complete question probably is: Suppose the null hypothesis, H0, is a weightlifting bar that can withstand weights of 800 pounds and less. The alternative hypothesis, Ha, is a weightlifting bar can withstand weights greater than 800 pounds. What is the Type 1 error in this scenario? Select the correct answer below: A) You cannot conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of greater than 200 pounds B) You cannot conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds. C) You conclude the weightlifting bar can withstand weights of greater than 800 pounds when, in fact, the weightlifting bar can withstand weights of less than or equal to 800 pounds. D) You conclude the weightlifting bar can withstand weights of greater than 100 pounds when, in fact, the weightlifting bar can withstand weights of greater than 800 pounds.

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The sequence c0, c1, c2, ... defined as c0 = 2, c1 = 2, c2 = 6, and ck = 3ck - 3 for every integer k ≥ 3 can be proven to have cn as even for each integer n ≥ 0.

We can prove by induction that cn is even for each integer n ≥ 0.

Base case: For n = 0, c0 = 2, which is an even number.

Inductive step: Assume that cn is even for some integer n ≥ 0. We need to prove that cn+1 is also even.

Using the recursive formula, cn+1 = 3cn - 3. Since cn is even (as per our assumption), it can be written as cn = 2m for some integer m. Substituting this into the recursive formula, we have cn+1 = 3(2m) - 3 = 6m - 3 = 2(3m - 1).

Since 3m - 1 is an integer, we can let it be represented by another integer k. Therefore, cn+1 = 2k, which implies that cn+1 is also an even number.

By induction, we have proven that cn is even for each integer n ≥ 0.

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Slope of lines 3x - 5y = 2 and 3x + 5y = -2 are m₁ = 3/5 and m₂ = -3/5 respectively.

The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line. The net change in the y coordinate is Δy and the net change in the x coordinate is Δx. Therefore, the change in y-coordinate for a change in x-coordinate can be written as

Line slope is a measure of the steepness or direction of a line in the coordinate plane.  

m = Δy/Δx

where,m is the slope

Given,

equations of the line

3x - 5y = 2

Moving 3x to RHS
-5y = -3x + 2

y = (3/5)x - 2/5

comparing with slope intercept equation of the line y = mx + c

slope m₁ = 3/5

Now, equation

3x + 5y = -2

moving 3x to RHS

5y = -3x - 2

y = (-3/5)x - 2

comparing with slope intercept equation of the line y = mx + c

slope m₂ = -3/5

Hence, m₁ = 3/5 and m₂ = -3/5 are slope of lines 3x - 5y = 2 and 3x + 5y = -2 respectively.

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Answer:

The point after the reflection: \((-4,-8)\)

Step-by-step explanation:

-Statement: If you reflect the point \((x,y)\) across x-axis or the y-axis, then the \(x\) and the \(y\) of the point can change either positive, negative or the same, depending on where the point is located on a graph.

-So, if you reflect the point \((-4,8)\) across x-axis, then the point after the reflection, would be \((-4, -8)\) :

The following point: \((-4, 8)\)

The point after the reflection: \((-4,-8)\)

The ratio of similarity  DEFG to TSRQ is '3: 1'.

Two quadrilaterals are considered similar if they have the same shape but may have different sizes. Similar quadrilaterals have corresponding angles that are congruent, and their corresponding sides are in proportion to each other.

The ratio of similarity is a measure of how much two geometric figures are enlarged or reduced to become similar.

Here we have

Quadrilateral DEFG and Quadrilateral TSRQ.

Where DEFG similar to TSRQ

Hence, the ratio of corresponding sides will be equal

=> DE/TS  = EF/SR  = FG/RQ = DG/TQ

=> 24/8  = 24/8  = 24/8 = 24/8 = 3/1

Therefore,

The ratio of similarity  DEFG to TSRQ is '3: 1'.

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Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

The research hypothesis. "Does the new steering system lower the miss distance" is H_a: mu < 0.88 (i.e., true mean missed distance for all missiles is less than 0.88).

The long-range missile missed its target by an average of 0.88 miles. A new steering device is supposed to increase accuracy, and a random sample of 8 missiles was equipped with this new mechanism and tested. These 8 missiles missed by distances with a mean of 0.76 miles and a standard deviation of 0.04 miles.The hypothesis test is used to determine whether the mean distance missed by all missiles using the new steering system is less than 0.88 miles.

The research hypothesis. "Does the new steering system lower the miss distance" is as follows:H_a: mu < 0.88 (i.e., true mean missed distance for all missiles is less than 0.88).This is because the null hypothesis is H_0: mu >= 0.88, and we are looking for evidence to support the alternative hypothesis that the mean missed distance using the new steering system is less than the old one.

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The price that Maura sell each scarf would be =$33. Maura sells each scarf for $33. That is option A.

To calculate the amount of money that Maura spends on each scarf the following is carried out.

The amount of money that she spends on the scarf material = $5.50

The percentage selling price of each scarf = 600% of $5.50

That is ;

= 600/100 × 5.50/1

= 3300/100

= $33.

Therefore, each price that is sold by Maura would probably cost a total of $33.

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Answer:

x=2

Step-by-step explanation:

The standard error of the sample mean of a given sample of 43 observations with standard deviation 8.85 is equal to 1.35 ( round to 2 decimal places).

As given in the question,

Population mean of the random variable 'μ' = 141

Standard deviation 'σ' = 8.85

Sample size 'N' = 43 observations

Standard error of the sample mean

= σ / √N

= 8.85 / √43

= 8.85 / 6.56

= 1.349

= 1.35 (round to 2 decimal places )

Therefore, for the given standard deviation and sample size the standard error of the sample mean is equal to 1.35.

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Answer:

The equation that relates distance, rate, and time is

       d  =  rt

Step-by-step explanation:

Using the formula of Simple Interest, the value for the principal amount is obtained to be P = $1333.33.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

The value for Simple Interest is given as = $180

The value for rate is given as = 4.5%

The value for time is given as = 3 years

To find the value for Principal amount, follow the formula for Simple Interest -

SI = P R T/100

Where P is the principal amount, R is the rate and T is the time.

Substitute the values in the equation -

180 = (P × 4.5 × 3)/100

180 = 13.5P / 100

P = (180 × 100) / 13.5

P = 18000 / 13.5

P = 1333.33

Therefore, the value for principal amount is $1333.33.

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Answer:

7x

Step-by-step explanation:

x +2x + x + x + x + x

= x + x + x + x + x + 2x

= 5x + 2x

= 7x

Answer:

The missing angle is 71.1

m=71.1

Step-by-step explanation:

First, add the given values of the triangles.

30.3+40.8=71.1

Then subtract 71.1 from 180 degrees.

You get 108.9

SOLUTION

The given equation is:

To graph the equation, calculate a few values of y

When x=3, it follows:

It follows that the point (0,4) is on the graph.

Following the same procdure few other possible points are:

The graph of the function is shown below:

Answer:

the answer is 7/13

Step-by-step explanation:

because the total number of translators is 13, therefore, the probability of picking yellow is 7/13

g(3) is equal to 25.

g(9/8) is equal to 10.

To find g(3), we substitute x = 3 into the function g(x):

g(3) = 3^2 + 1

= 9 + 1

= 10

Therefore, g(3) is equal to 10.

To find g(9/8), we substitute x = 9/8 into the function g(x):

g(9/8) = 3(9/8)^2 + 1

= 3(81/64) + 1

= (3/1)(81/64) + 1

= 243/64 + 1

= 243/64 + 64/64

= (243 + 64)/64

= 307/64

To find g(3), we substitute x = 3 into the function g(x) = 3x^2 + 1. Simplifying, we get g(3) = 3(3)^2 + 1 = 9(3) + 1 = 27 + 1 = 28.

To find g(9/8), we substitute x = 9/8 into the same function. We have g(9/8) = 3(9/8)^2 + 1 = 3(81/64) + 1 = 243/64 + 1 = (243 + 64)/64 = 307/64.

Therefore, g(3) is equal to 28 and g(9/8) is equal to 307/64.

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The unit price of the pair of gloves is $5.19.

Here, a package of 5 pairs of insulated gloves costs $25.95.

We have to find the unit price of the pairs of gloves.

5 pairs of insulted gloves = $25.95

So we have to find the value of 1 pair of gloves, so by dividing the value by 5 we will get the value of 1 pair of gloves.

Unitary method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit.

So by using the unitary method we have:

1 pair of insulated gloves = 25.95/ 5

                                          = 5.19

Therefore the unit price of the pair of gloves = is $5.19.

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\(\frac{12+12.3935}{2}\)The value of   x in \(x^2/(.200-x)=12\)

=0.1967 or x=0.197

x= \(\frac{-12+\sqrt{12^2-4.1(-2.4)} }{2.1}\)

x=\(\frac{12+12.3935}{2}\)

x=0.1967

or x=0.197

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Numbers and arithmetic operators make into a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.

Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

The quantity of terms in an algebraic expression determines how it is categorized. The several kinds of algebraic expressions include:

From the question :

Given:

\(\frac{x^2}{0.200-x}\)=12

\(x^2=12\)×\(0.2\)-\(12x\)

\(x^2+12x-2.4=0\) --------(0)

This is the quadratic equation.

x=\(\frac{-12+\sqrt{12^2-4.1(-2.4)} }{2.1}\)

x=\(\frac{12+12.3935}{2}\)

x=0.1967

or x=0.197

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question:

Answer:

\(18 \sqrt{2} + 18\)

Step-by-step explanation:

\(3 \sqrt{6} (2 \sqrt{3} + \sqrt{6} ) \\ =( 3 \sqrt{6} \times 2 \sqrt{3} ) + (3 \sqrt{6} \times \sqrt{6} ) \\ = 6 \sqrt{18} + 18 \\ \)

To further simplify:

\(6 \sqrt{18} = 6 \times \sqrt{9 \times 2} \\ = 6 \times 3 \times \sqrt{2 \\ } \\ = 18 \sqrt{2} \)

Thus, the answer is:

\(18 \sqrt{2} + 18\)

Answer:

2 + V3i is a known root

Step-by-step explanation:

We want the positive and negative values from the square root

Answer:

Step-by-step explanation:

I am taking the assignment and got it correct. Good luck

Answer:

The answer to ur question is probably 100%

{(5, 2), (4, 2), (3, 2), (2, 2), (1, 2)}, {(−8, −3), (−6, −5), (−4, −2), (−2, −7), (−1, −4)} and {(−6, 4), (−3, −1), (0, 5), (1, −1), (2, 3)} are the sets of ordered pairs considered as a function.

{(−4, −2), (−1, −1), (3, 2), (3, 5), (7, 10)} is not a function.

In mathematics, ordered pair is a pair of numbers that are written in a specific order. They are generally written in (x, y) form. For example (3, 5) is an ordered pair.

The function can also be represented by a set of ordered pairs. A function Is a set of ordered pairs in which no two different ordered pairs have the same value of x coordinate.

Option (a) : {(5, 2),(4, 2),(3, 2),(2, 2),(1, 2)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (b) : {(-4, -2),(-1, -1),(3, 2),(3, 5),(7, 10)}

Two ordered pairs have the same value of x coordinate (3, 2) and (3, 5).

So, it can not be considered a function.

Option (c) : {(-8, -3),(-6, -5),(-4, -2),(-2, -7),(-1, -4)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (d) : {(-6, 4),(-3, -1),(0, 5),(1, -1),(2, 3)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Therefore, Options (a), (c), and (d) are the functions.

Option (b) is not a function.

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The statement "A histogram with the hills to the far left means the image is overexposed" is not accurate. In fact, a histogram with the hills to the far left indicates that the image is underexposed, not overexposed.

A histogram is a graphical representation of the distribution of pixel values in an image. It displays the frequency of occurrence of different tonal values. The horizontal axis represents the tonal values, while the vertical axis represents the frequency or number of pixels.

When the hills of the histogram are concentrated towards the left side, it means that a significant portion of the image has darker or lower tonal values. This indicates an underexposed image, where the exposure settings were insufficient to capture enough light, resulting in a darker overall appearance.

Conversely, an overexposed image would have the hills of the histogram concentrated towards the right side, indicating that a significant portion of the image has brighter or higher tonal values.

Therefore, the correct interpretation is that a histogram with the hills to the far left means the image is underexposed, not overexposed.

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Plugging in the values, we see that object 1 has more potential energy (the ball to the left)

Hi! So we have to use the Order of Operations, aka PEMDAS so it's:

Parentheses

Exponents

Multiplication/Division

Addtion/Subtraction

Exponent comes first so we'll deal with that. 10^-5=0.00001

And then 7*0.00001=0.00007